=== family a=1 b=0.5 N=3 tau=1
  J=0.99131843766616152435070 lambda=0.24567806121421984291538 caustic axes=(0.8685170918213,0.0657414540893) closure_err=7.9738e-58 worst tangency/closure=4.6176e-57
  checks: {'chk_polar_two_defs': '5.2742e-57', 'chk_polar_tangent_circle': '4.6673e-61', 'chk_polar_circumcircle': '3.9827e-59', 'chk_dualR_on_circle': '7.9732e-61', 'chk_ant_is_polar_reciprocal_of_inv': '5.4659e-58', 'chk_invped_eq_polar': '5.2742e-57'}
  O_p(f1)=['-4.33012701892219', '6.1741716440317e-60'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 6.18e-60 Rstar-a/b^2=0.0  O_p spread over members: 2.39e-59
  k813 Apol/Adag               spread=  2.4077e-55   value(member0)=698.1329224445429721394452
  k814R Apol/AdualR            spread=  2.2494e-55   value(member0)=25722.29577126293762653929
  k814P Apol/AdualP            spread=  2.2494e-55   value(member0)=102889.1830850517505061572
  k815(i) ApedX*AdualR         spread=     0.71388   value(member0)=0.0008342546074791232672492406
  k815(ii) Apol*AdualR         spread=     0.91808   value(member0)=12.23813380964121162006052
  k815(iii) Aped*AdualR        spread=   1.458e-56   value(member0)=0.0005335446638475541214354741
  k815(i)P ApedX*AdualP        spread=     0.71388   value(member0)=0.0002085636518697808168123102
  k816(i) ApedX/AdualR         spread=     0.71368   value(member0)=1.753449022203981887035431
  k816(ii) Apol/AdualR         spread=  2.2499e-55   value(member0)=25722.29577126293762653929
  k816(iii) Aped/AdualR        spread=     0.91808   value(member0)=1.12141228917223259487587
  k816(i)P ApedX/AdualP        spread=     0.71368   value(member0)=7.013796088815927548141723
  k817 Adag*Aant               spread=     0.30558   value(member0)=20.25805189564301859927276
  k818 Adag/Aant               spread=     0.91814   value(member0)=0.03188240013306566470136976
  Aant/A                       spread=     0.71388   value(member0)=49.04297703951504360529991
  k804 A*Adag                  spread=     0.71368   value(member0)=0.4130673364163974953815247
  k805 A/Adag                  spread=     0.71388   value(member0)=0.639546559364858843811662
  k802 Ldag                    spread=  2.0815e-57   value(member0)=16.22043838971177773755499
  k803 sumcos_dag              spread=  5.6531e-58   value(member0)=1.019904910687327087652879
  k801 sum 1/d                 spread=  1.8398e-57   value(member0)=8.605551275463989293119221
  A                            spread=     0.16668   value(member0)=0.5139803437789364334911736
  Adag                         spread=     0.71378   value(member0)=0.8036636836720321265197749
  Apol                         spread=     0.71378   value(member0)=561.0640761445025207052243
  AdualR                       spread=     0.71378   value(member0)=0.02181236391703907639153267
  Aped                         spread=     0.71378   value(member0)=0.02446065295246459679648296
  ApedX                        spread=     0.16668   value(member0)=0.03824686818228958478701742
  Aant                         spread=     0.71398   value(member0)=25.20712619871242828886137
  k908(i) ApedX1/ApedX2        5.3163e-56 value0=1.0
  k908(ii) Apol1/Apol2         0.91808 value0=0.42845147223
  k908(iii) Aped1/Aped2        0.91808 value0=2.33398661182
  k907R AdualR1/AdualR2        0.91808 value0=0.42845147223
  k907R AdualR1*AdualR2        2.0796e-59 value0=0.00111046232884
  k903a Adag1*Adag2            1.5772e-56 value0=1.50746434151
=== family a=1 b=0.5 N=4 tau=1
  J=0.89442719099991587856366 lambda=0.2 caustic axes=(0.8944271909999,0.2236067977499) closure_err=1.4536e-58 worst tangency/closure=6.7861e-58
  checks: {'chk_polar_two_defs': '5.7265e-59', 'chk_polar_tangent_circle': '3.7338e-60', 'chk_polar_circumcircle': '8.4245e-56', 'chk_dualR_on_circle': '4.6673e-61', 'chk_ant_is_polar_reciprocal_of_inv': '3.7824e-60', 'chk_invped_eq_polar': '5.7265e-59'}
  O_p(f1)=['-4.33012701892219', '-1.01620618441349e-60'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 5.17e-60 Rstar-a/b^2=4.98e-60  O_p spread over members: 1.01e-59
  k813 Apol/Adag               spread=  3.9457e-57   value(member0)=32.0
  k814R Apol/AdualR            spread=  2.4852e-57   value(member0)=2048.0
  k814P Apol/AdualP            spread=  2.4857e-57   value(member0)=4096.0
  k815(i) ApedX*AdualR         spread=     0.58606   value(member0)=0.009576260360856083628475679
  k815(ii) Apol*AdualR         spread=     0.35662   value(member0)=11.07141059752359967745917
  k815(iii) Aped*AdualR        spread=     0.35662   value(member0)=0.02767852649380899919364793
  k815(i)P ApedX*AdualP        spread=     0.58606   value(member0)=0.00478813018042804181423784
  k816(i) ApedX/AdualR         spread=     0.35662   value(member0)=1.771425695603775948393468
  k816(ii) Apol/AdualR         spread=  2.4845e-57   value(member0)=2048.0
  k816(iii) Aped/AdualR        spread=  1.0138e-57   value(member0)=5.12
  k816(i)P ApedX/AdualP        spread=     0.35662   value(member0)=3.542851391207551896786935
  k817 Adag*Aant               spread=   1.692e-57   value(member0)=8.0
  k818 Adag/Aant               spread=     0.35662   value(member0)=2.767852649380899919364793
  Aant/A                       spread=  1.1354e-57   value(member0)=2.0
  k804 A*Adag                  spread=   1.794e-57   value(member0)=4.0
  k805 A/Adag                  spread=     0.35662   value(member0)=0.1806454545590920873204423
  k802 Ldag                    spread=  2.7051e-58   value(member0)=17.88854381999831757127339
  k803 sumcos_dag              spread=      0.9963   value(member0)=0.5714357609905601290163308
  k801 sum 1/d                 spread=   2.478e-58   value(member0)=10.0
  A                            spread=     0.19789   value(member0)=0.8500481270118582816909309
  Adag                         spread=     0.19789   value(member0)=4.705615920902087324851683
  Apol                         spread=     0.19789   value(member0)=150.5797094688667943952539
  AdualR                       spread=     0.19789   value(member0)=0.07352524876409511445080755
  Aped                         spread=     0.19789   value(member0)=0.3764492736721669859881347
  ApedX                        spread=     0.48394   value(member0)=0.1302445149363778559655335
  Aant                         spread=     0.19789   value(member0)=1.700096254023716563381862
  k908(i) ApedX1/ApedX2        5.3729e-57 value0=1.0
  k908(ii) Apol1/Apol2         3.9353e-57 value0=1.0
  k908(iii) Aped1/Aped2        1.2766e-57 value0=1.0
  k907R AdualR1/AdualR2        6.6018e-58 value0=1.0
  k907R AdualR1*AdualR2        0.35662 value0=0.00540596220582
  k903a Adag1*Adag2            0.35662 value0=22.142821195
=== family a=1 b=0.5 N=5 tau=1
  J=0.77103682775135063277371 lambda=0.14862444743721648632027 caustic axes=(0.9227001422795,0.3183952772306) closure_err=7.8283e-59 worst tangency/closure=3.1678e-58
  checks: {'chk_polar_two_defs': '1.0706e-59', 'chk_polar_tangent_circle': '1.2446e-59', 'chk_polar_circumcircle': '7.8136e-57', 'chk_dualR_on_circle': '1.0112e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.2076e-60', 'chk_invped_eq_polar': '1.0706e-59'}
  O_p(f1)=['-4.33012701892219', '6.03793059305759e-61'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 2.63e-60 Rstar-a/b^2=1.87e-60  O_p spread over members: 4.52e-60
  k813 Apol/Adag               spread=  8.8637e-58   value(member0)=8.722622532927449375172054
  k814R Apol/AdualR            spread=   4.556e-58   value(member0)=912.8028560005785889737824
  k814P Apol/AdualP            spread=  4.7555e-58   value(member0)=1603.995858019214956469636
  k815(i) ApedX*AdualR         spread=     0.25001   value(member0)=0.04654910050907882152735282
  k815(ii) Apol*AdualR         spread=    0.090698   value(member0)=8.302563765719027052641633
  k815(iii) Aped*AdualR        spread=  1.5959e-58   value(member0)=0.08779832961540179690854596
  k815(i)P ApedX*AdualP        spread=     0.25001   value(member0)=0.02649018803665522134133789
  k816(i) ApedX/AdualR         spread=      0.1752   value(member0)=5.117714610562266457086629
  k816(ii) Apol/AdualR         spread=   4.543e-58   value(member0)=912.8028560005785889737824
  k816(iii) Aped/AdualR        spread=    0.090698   value(member0)=9.652749233426496077008482
  k816(i)P ApedX/AdualP        spread=      0.1752   value(member0)=8.992952841792041772894338
  k817 Adag*Aant               spread=     0.86724   value(member0)=2.520483013052770888721182
  k818 Adag/Aant               spread=       0.854   value(member0)=39.51948506764714769201849
  Aant/A                       spread=     0.86078   value(member0)=0.2256367303219492277091353
  k804 A*Adag                  spread=    0.046415   value(member0)=11.17053508733452104298815
  k805 A/Adag                  spread=    0.046439   value(member0)=0.1121447443015296146329235
  k802 Ldag                    spread=  1.0136e-58   value(member0)=20.08769350144636452053464
  k803 sumcos_dag              spread=  8.4827e-58   value(member0)=0.2799658337134454628096737
  k801 sum 1/d                 spread=  1.0454e-58   value(member0)=11.9172740837077929701025
  A                            spread=  0.00026854   value(member0)=1.119248319668336444206611
  Adag                         spread=    0.046427   value(member0)=9.980390312888432821026362
  Apol                         spread=    0.046427   value(member0)=87.05517743061148088651447
  AdualR                       spread=    0.046427   value(member0)=0.09537128072981872891408732
  Aped                         spread=    0.046427   value(member0)=0.9205950569556608928450336
  ApedX                        spread=     0.21349   value(member0)=0.4880829968190288437390236
  Aant                         spread=     0.86077   value(member0)=0.2525435312682992519425755
  k908(i) ApedX1/ApedX2        0.38179 value0=0.865815224999
  k908(ii) Apol1/Apol2         0.090698 value0=0.971834774732
  k908(iii) Aped1/Aped2        0.090698 value0=1.02898149562
  k907R AdualR1/AdualR2        0.090698 value0=0.971834774732
  k907R AdualR1*AdualR2        1.274e-58 value0=0.00935928763257
  k903a Adag1*Adag2            5.8938e-58 value0=102.494985143
=== family a=1 b=0.5 N=6 tau=1
  J=0.66666666666666666666666 lambda=0.11111111111111111111111 caustic axes=(0.9428090415820,0.3726779962499) closure_err=6.6469e-60 worst tangency/closure=2.7099e-59
  checks: {'chk_polar_two_defs': '7.0953e-60', 'chk_polar_tangent_circle': '6.223e-60', 'chk_polar_circumcircle': '2.9684e-58', 'chk_dualR_on_circle': '6.223e-61', 'chk_ant_is_polar_reciprocal_of_inv': '1.5965e-60', 'chk_invped_eq_polar': '7.0953e-60'}
  O_p(f1)=['-4.33012701892219', '1.17462323517411e-61'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 2.74e-60 Rstar-a/b^2=2.49e-60  O_p spread over members: 6.05e-60
  k813 Apol/Adag               spread=  5.0319e-59   value(member0)=4.266666666666666666666667
  k814R Apol/AdualR            spread=  2.6189e-59   value(member0)=614.4
  k814P Apol/AdualP            spread=  3.0953e-59   value(member0)=983.04
  k815(i) ApedX*AdualR         spread=    0.022388   value(member0)=0.1847018463808498538546649
  k815(ii) Apol*AdualR         spread=    0.022388   value(member0)=8.51106108122956126562296
  k815(iii) Aped*AdualR        spread=    0.022388   value(member0)=0.1641794190051998700930355
  k815(i)P ApedX*AdualP        spread=    0.022388   value(member0)=0.1154386539880311586591656
  k816(i) ApedX/AdualR         spread=  5.9648e-59   value(member0)=13.33333333333333333333333
  k816(ii) Apol/AdualR         spread=  2.6577e-59   value(member0)=614.4
  k816(iii) Aped/AdualR        spread=  2.5308e-59   value(member0)=11.85185185185185185185185
  k816(i)P ApedX/AdualP        spread=  5.5424e-59   value(member0)=21.33333333333333333333333
  k817 Adag*Aant               spread=      1.8819   value(member0)=1.186539312583049036876894e-58
  k818 Adag/Aant               spread=        1.05   value(member0)=2.420891650578095959364957e+60
  Aant/A                       spread=        1.87   value(member0)=5.576457747200818470654726e-60
  k804 A*Adag                  spread=    0.022388   value(member0)=21.2776527030739031640574
  k805 A/Adag                  spread=  3.8199e-59   value(member0)=0.07407407407407407407407407
  k802 Ldag                    spread=  7.1282e-60   value(member0)=22.0
  k803 sumcos_dag              spread=  1.8436e-59   value(member0)=-0.6666666666666666666666667
  k801 sum 1/d                 spread=  8.0899e-60   value(member0)=14.0
  A                            spread=    0.011257   value(member0)=1.255437143966163983790811
  Adag                         spread=    0.011257   value(member0)=16.94840144354321378117595
  Apol                         spread=    0.011257   value(member0)=72.31317949245104546635071
  AdualR                       spread=    0.011257   value(member0)=0.1176972322468278734803885
  Aped                         spread=    0.011257   value(member0)=1.394930159962404426434234
  ApedX                        spread=    0.011257   value(member0)=1.569296429957704979738514
  Aant                         spread=      1.8759   value(member0)=7.000892187593784420537072e-60
  k908(i) ApedX1/ApedX2        1.4484e-58 value0=1.0
  k908(ii) Apol1/Apol2         3.0493e-59 value0=1.0
  k908(iii) Aped1/Aped2        2.9637e-59 value0=1.0
  k907R AdualR1/AdualR2        2.4814e-59 value0=1.0
  k907R AdualR1*AdualR2        0.022388 value0=0.0138526384786
  k903a Adag1*Adag2            0.022388 value0=287.248311491
=== family a=1 b=0.5 N=7 tau=1
  J=0.58359414474661612997789 lambda=0.08514553144563358477488 caustic axes=(0.9564802499552,0.4060227438880) closure_err=1.5679e-61 worst tangency/closure=5.2057e-60
  checks: {'chk_polar_two_defs': '5.2804e-60', 'chk_polar_tangent_circle': '4.2317e-59', 'chk_polar_circumcircle': '6.8453e-60', 'chk_dualR_on_circle': '2.8198e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.4412e-60', 'chk_invped_eq_polar': '5.2804e-60'}
  O_p(f1)=['-4.33012701892219', '4.35003492269361e-61'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.83e-60 Rstar-a/b^2=-1.87e-60  O_p spread over members: 1.82e-59
  k813 Apol/Adag               spread=  2.1575e-60   value(member0)=2.740133089305912912127782
  k814R Apol/AdualR            spread=  6.7007e-60   value(member0)=487.3871041661461460252249
  k814P Apol/AdualP            spread=  1.0576e-59   value(member0)=723.0423837129041357340181
  k815(i) ApedX*AdualR         spread=   0.0062112   value(member0)=0.4626193872675738649928434
  k815(ii) Apol*AdualR         spread=   0.0057575   value(member0)=8.542313421449882712768031
  k815(iii) Aped*AdualR        spread=  5.0117e-60   value(member0)=0.2328171034677706706773759
  k815(i)P ApedX*AdualP        spread=   0.0062112   value(member0)=0.3118416410579164234577595
  k816(i) ApedX/AdualR         spread=  0.00045642   value(member0)=26.39504222887551367853915
  k816(ii) Apol/AdualR         spread=  6.7007e-60   value(member0)=487.3871041661461460252249
  k816(iii) Aped/AdualR        spread=   0.0057575   value(member0)=13.2835273375215507295512
  k816(i)P ApedX/AdualP        spread=  0.00045642   value(member0)=39.1572409040660479254855
  k817 Adag*Aant               spread=     0.39625   value(member0)=-4.20382527553401926755472
  k818 Adag/Aant               spread=     0.39275   value(member0)=-131.9050929770127392197433
  Aant/A                       spread=      0.3945   value(member0)=-0.1340716673298746777618576
  k804 A*Adag                  spread=   0.0028828   value(member0)=31.35506076157596147906765
  k805 A/Adag                  spread=   0.0028829   value(member0)=0.05654593964164737339049673
  k802 Ldag                    spread=  1.3759e-60   value(member0)=23.51883657007761685754583
  k803 sumcos_dag              spread=  8.9304e-61   value(member0)=-1.742079079385644393250874
  k801 sum 1/d                 spread=  7.7072e-61   value(member0)=16.14851967420103352175103
  A                            spread=   1.0656e-6   value(member0)=1.331540976945231018160154
  Adag                         spread=   0.0028829   value(member0)=23.54795031055635229015719
  Apol                         spread=   0.0028829   value(member0)=64.52451783128690896354327
  AdualR                       spread=   0.0028829   value(member0)=0.1323886440156837756274158
  Aped                         spread=   0.0028829   value(member0)=1.758588171959744284164826
  ApedX                        spread=    0.003338   value(member0)=3.494403849417540820699098
  Aant                         spread=      0.3945   value(member0)=-0.1785219188970973410013563
  k908(i) ApedX1/ApedX2        0.0066649 value0=0.996704247077
  k908(ii) Apol1/Apol2         0.0057575 value0=0.997153613455
  k908(iii) Aped1/Aped2        0.0057575 value0=1.00285451159
  k907R AdualR1/AdualR2        0.0057575 value0=0.997153613455
  k907R AdualR1*AdualR2        7.6065e-60 value0=0.017576783384
  k903a Adag1*Adag2            5.1567e-60 value0=556.088807528
=== family a=1 b=0.5 N=8 tau=1
  J=0.51744792677702726866667 lambda=0.06693808923146094345944 caustic axes=(0.9659512983419,0.4278573486204) closure_err=1.4684e-58 worst tangency/closure=5.1176e-58
  checks: {'chk_polar_two_defs': '4.2321e-60', 'chk_polar_tangent_circle': '1.8047e-59', 'chk_polar_circumcircle': '2.2845e-57', 'chk_dualR_on_circle': '1.2446e-60', 'chk_ant_is_polar_reciprocal_of_inv': '2.7237e-60', 'chk_invped_eq_polar': '4.2321e-60'}
  O_p(f1)=['-4.33012701892219', '1.87594528337851e-61'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 8.17e-61 Rstar-a/b^2=1.24e-60  O_p spread over members: 1.13e-59
  k813 Apol/Adag               spread=  4.3222e-58   value(member0)=2.040151245050941330088163
  k814R Apol/AdualR            spread=  1.9638e-58   value(member0)=419.814874704390298436266
  k814P Apol/AdualP            spread=   2.566e-58   value(member0)=585.7690441452613918714545
  k815(i) ApedX*AdualR         spread=   0.0016144   value(member0)=0.9222978491714442891086592
  k815(ii) Apol*AdualR         spread=   0.0016144   value(member0)=8.745533490166293574306693
  k815(iii) Aped*AdualR        spread=   0.0016144   value(member0)=0.2930773726013883138301331
  k815(i)P ApedX*AdualP        spread=   0.0016144   value(member0)=0.6610017375619810210173345
  k816(i) ApedX/AdualR         spread=  7.7375e-58   value(member0)=44.27338325619700607959687
  k816(ii) Apol/AdualR         spread=  1.9657e-58   value(member0)=419.814874704390298436266
  k816(iii) Aped/AdualR        spread=  2.6389e-58   value(member0)=14.06869467662449162077052
  k816(i)P ApedX/AdualP        spread=  7.1539e-58   value(member0)=61.77479397155846136146254
  k817 Adag*Aant               spread=  5.3339e-58   value(member0)=-11.16987326637235845531265
  k818 Adag/Aant               spread=   0.0016144   value(member0)=-78.97163951781248790962406
  Aant/A                       spread=  4.9473e-58   value(member0)=-0.2714636234592769274047629
  k804 A*Adag                  spread=  3.4833e-58   value(member0)=41.14685099990196165508363
  k805 A/Adag                  spread=   0.0016144   value(member0)=0.04664630030166890906106299
  k802 Ldag                    spread=  7.4982e-59   value(member0)=24.69894466845803015181203
  k803 sumcos_dag              spread=  7.5114e-59   value(member0)=-2.887242173889492086847737
  k801 sum 1/d                 spread=  1.3838e-58   value(member0)=18.32938640783208718217272
  A                            spread=  0.00080753   value(member0)=1.385405488732252903365815
  Adag                         spread=  0.00080753   value(member0)=29.70022230643414893170041
  Apol                         spread=  0.00080753   value(member0)=60.59294551676136928172789
  AdualR                       spread=  0.00080753   value(member0)=0.1443325360003679411662904
  Aped                         spread=  0.00080753   value(member0)=2.030570380892089247264061
  ApedX                        spread=  0.00080753   value(member0)=6.390089682683141603346542
  Aant                         spread=  0.00080753   value(member0)=-0.3760871939316278261745959
  k908(i) ApedX1/ApedX2        2.0735e-57 value0=1.0
  k908(ii) Apol1/Apol2         2.2457e-58 value0=1.0
  k908(iii) Aped1/Aped2        3.0648e-58 value0=1.0
  k907R AdualR1/AdualR2        2.5118e-58 value0=1.0
  k907R AdualR1*AdualR2        0.0016144 value0=0.0208318809483
  k903a Adag1*Adag2            0.0016144 value0=882.103205052
=== family a=1 b=0.5 N=9 tau=1
  J=0.46405820651522461292350 lambda=0.05383750475853171384652 caustic axes=(0.9727088440234,0.4429023540708) closure_err=9.146e-59 worst tangency/closure=3.1103e-58
  checks: {'chk_polar_two_defs': '4.045e-60', 'chk_polar_tangent_circle': '7.4054e-59', 'chk_polar_circumcircle': '1.0592e-57', 'chk_dualR_on_circle': '4.6089e-60', 'chk_ant_is_polar_reciprocal_of_inv': '2.8687e-60', 'chk_invped_eq_polar': '4.045e-60'}
  O_p(f1)=['-4.33012701892219', '1.64832704466725e-61'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 5.07e-61 Rstar-a/b^2=0.0  O_p spread over members: 3.86e-59
  k813 Apol/Adag               spread=   1.927e-58   value(member0)=1.65911160590089142130023
  k814R Apol/AdualR            spread=  8.9648e-59   value(member0)=378.9552168070273694633731
  k814P Apol/AdualP            spread=  1.2895e-58   value(member0)=503.1156301494551778387245
  k815(i) ApedX*AdualR         spread=    0.000404   value(member0)=1.541192290703796507812578
  k815(ii) Apol*AdualR         spread=   0.0003953   value(member0)=8.896241656513476644878267
  k815(iii) Aped*AdualR        spread=  7.2927e-59   value(member0)=0.3423973984879861604169775
  k815(i)P ApedX*AdualP        spread=    0.000404   value(member0)=1.160852145443147918104643
  k816(i) ApedX/AdualR         spread=   8.7002e-6   value(member0)=65.65051638827315944400648
  k816(ii) Apol/AdualR         spread=  8.9123e-59   value(member0)=378.9552168070273694633731
  k816(iii) Aped/AdualR        spread=   0.0003953   value(member0)=14.58517938113525899763566
  k816(i)P ApedX/AdualP        spread=   8.7002e-6   value(member0)=87.16016948024418413111905
  k817 Adag*Aant               spread=    0.035731   value(member0)=-16.6886769123264102792528
  k818 Adag/Aant               spread=    0.036112   value(member0)=-73.38737471869664959671793
  Aant/A                       spread=    0.035922   value(member0)=-0.3349122948398209905388592
  k804 A*Adag                  spread=  0.00019767   value(member0)=49.82999182012153065463487
  k805 A/Adag                  spread=  0.00019767   value(member0)=0.04068624003454558797353613
  k802 Ldag                    spread=  3.5469e-59   value(member0)=25.6155258149819516224585
  k803 sumcos_dag              spread=  3.9143e-59   value(member0)=-4.069879484394511895863298
  k801 sum 1/d                 spread=  8.0271e-59   value(member0)=20.52856784781101861163554
  A                            spread=   5.4511e-9   value(member0)=1.423866218474512369988422
  Adag                         spread=  0.00019767   value(member0)=34.99625960190831114317741
  Apol                         spread=  0.00019767   value(member0)=58.06270046864658921655146
  AdualR                       spread=  0.00019767   value(member0)=0.1532178418280317254459425
  Aped                         spread=  0.00019767   value(member0)=2.234709707452251761493572
  ApedX                        spread=  0.00020637   value(member0)=10.05883043590704156965838
  Aant                         spread=    0.035922   value(member0)=-0.476870302774196856358284
  k908(i) ApedX1/ApedX2        0.0004127 value0=0.999779031535
  k908(ii) Apol1/Apol2         0.0003953 value0=0.999788345034
  k908(iii) Aped1/Aped2        0.0003953 value0=1.00021169977
  k907R AdualR1/AdualR2        0.0003953 value0=0.999788345034
  k907R AdualR1*AdualR2        7.1433e-59 value0=0.0234806768563
  k903a Adag1*Adag2            2.7635e-58 value0=1224.99746292
=== family a=1 b=0.5 N=10 tau=1
  J=0.42027662546120616973153 lambda=0.04415811047726474252515 caustic axes=(0.9776716675462,0.4536980157800) closure_err=2.3558e-58 worst tangency/closure=7.8807e-58
  checks: {'chk_polar_two_defs': '3.7411e-60', 'chk_polar_tangent_circle': '6.5964e-59', 'chk_polar_circumcircle': '2.2695e-57', 'chk_dualR_on_circle': '4.2005e-60', 'chk_ant_is_polar_reciprocal_of_inv': '3.0765e-60', 'chk_invped_eq_polar': '3.7411e-60'}
  O_p(f1)=['-4.33012701892219', '-3.69596409768485e-61'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 2.08e-60 Rstar-a/b^2=2.49e-60  O_p spread over members: 3.5e-59
  k813 Apol/Adag               spread=  3.9896e-58   value(member0)=1.427224646673674481469936
  k814R Apol/AdualR            spread=  1.8912e-58   value(member0)=352.1069369295193371952385
  k814P Apol/AdualP            spread=  2.8042e-58   value(member0)=448.9502054379588440146141
  k815(i) ApedX*AdualR         spread=  0.00012034   value(member0)=2.283855123787525822739881
  k815(ii) Apol*AdualR         spread=  0.00012034   value(member0)=9.035501346957140426306536
  k815(iii) Aped*AdualR        spread=  0.00012034   value(member0)=0.3828421747759948684374343
  k815(i)P ApedX*AdualP        spread=  0.00012034   value(member0)=1.791203617432673781033556
  k816(i) ApedX/AdualR         spread=  8.5919e-58   value(member0)=89.00017842379371437491028
  k816(ii) Apol/AdualR         spread=  1.8833e-58   value(member0)=352.1069369295193371952385
  k816(iii) Aped/AdualR        spread=  2.8681e-58   value(member0)=14.91908199794667902003737
  k816(i)P ApedX/AdualP        spread=  7.8397e-58   value(member0)=113.4787310236243268978674
  k817 Adag*Aant               spread=  0.00012034   value(member0)=-20.98780789500886018545542
  k818 Adag/Aant               spread=  5.8041e-58   value(member0)=-74.4175010170851782356491
  Aant/A                       spread=  3.1143e-58   value(member0)=-0.365922242006808960386107
  k804 A*Adag                  spread=  0.00012034   value(member0)=57.35592288653042844717928
  k805 A/Adag                  spread=  3.5057e-58   value(member0)=0.03672282725559092062378524
  k802 Ldag                    spread=  7.4677e-59   value(member0)=26.33298910575707218190006
  k803 sumcos_dag              spread=  8.9504e-59   value(member0)=-5.270197298726545279719027
  k801 sum 1/d                 spread=  2.0339e-58   value(member0)=22.73917012361638149080541
  A                            spread=   6.0172e-5   value(member0)=1.451299985615327802996622
  Adag                         spread=   6.0172e-5   value(member0)=39.52037721699035334907059
  Apol                         spread=   6.0172e-5   value(member0)=56.40445640992939187319445
  AdualR                       spread=   6.0172e-5   value(member0)=0.1601912671809126514302097
  Aped                         spread=   6.0172e-5   value(member0)=2.38990665042702059181535
  ApedX                        spread=   6.0172e-5   value(member0)=14.25705136103483630876325
  Aant                         spread=   6.0172e-5   value(member0)=-0.5310629445608103433478707
  k908(i) ApedX1/ApedX2        2.4613e-57 value0=1.0
  k908(ii) Apol1/Apol2         1.9439e-58 value0=1.0
  k908(iii) Aped1/Aped2        3.2352e-58 value0=1.0
  k907R AdualR1/AdualR2        2.6868e-58 value0=1.0
  k907R AdualR1*AdualR2        0.00012034 value0=0.025661242081
  k903a Adag1*Adag2            0.00012034 value0=1561.86021537
=== family a=1 b=0.5 N=11 tau=1
  J=0.38382615303997266954284 lambda=0.03683062893936613023828 caustic axes=(0.9814119273070,0.4617026868674) closure_err=4.5136e-59 worst tangency/closure=1.441e-58
  checks: {'chk_polar_two_defs': '3.3512e-60', 'chk_polar_tangent_circle': '9.5212e-59', 'chk_polar_circumcircle': '3.9827e-58', 'chk_dualR_on_circle': '6.1063e-60', 'chk_ant_is_polar_reciprocal_of_inv': '4.212e-60', 'chk_invped_eq_polar': '3.3512e-60'}
  O_p(f1)=['-4.33012701892219', '1.87771646163832e-60'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.88e-60 Rstar-a/b^2=-3.11e-61  O_p spread over members: 4.99e-59
  k813 Apol/Adag               spread=  6.9933e-59   value(member0)=1.274720522448638015245921
  k814R Apol/AdualR            spread=  3.3806e-59   value(member0)=333.403811263967813347403
  k814P Apol/AdualP            spread=  5.5197e-59   value(member0)=411.2852492816177018334006
  k815(i) ApedX*AdualR         spread=   2.5753e-5   value(member0)=3.100490949853144383610724
  k815(ii) Apol*AdualR         spread=   2.5471e-5   value(member0)=9.14934112904243553827343
  k815(iii) Aped*AdualR        spread=  3.0871e-59   value(member0)=0.4157607262597704817461995
  k815(i)P ApedX*AdualP        spread=   2.5753e-5   value(member0)=2.513378491633348536441009
  k816(i) ApedX/AdualR         spread=   2.8236e-7   value(member0)=112.9825071435134125119898
  k816(ii) Apol/AdualR         spread=  3.4165e-59   value(member0)=333.403811263967813347403
  k816(iii) Aped/AdualR        spread=   2.5471e-5   value(member0)=15.1504035923284229371429
  k816(i)P ApedX/AdualP        spread=   2.8236e-7   value(member0)=139.3746473347650057783596
  k817 Adag*Aant               spread=    0.003533   value(member0)=-24.96464963414544808135734
  k818 Adag/Aant               spread=   0.0035076   value(member0)=-75.19776788371871648099914
  Aant/A                       spread=   0.0035203   value(member0)=-0.3915103419156970971366882
  k804 A*Adag                  spread=   1.2735e-5   value(member0)=63.76498130800596094252617
  k805 A/Adag                  spread=   1.2735e-5   value(member0)=0.03396657927298431051437167
  k802 Ldag                    spread=   1.462e-59   value(member0)=26.90073049973878487269882
  k803 sumcos_dag              spread=  1.6048e-59   value(member0)=-6.475819945273002785625062
  k801 sum 1/d                 spread=  4.2389e-59   value(member0)=24.957404565087721133059
  A                            spread=  3.2547e-11   value(member0)=1.471692322613238090188587
  Adag                         spread=   1.2735e-5   value(member0)=43.32765777753088721671571
  Apol                         spread=   1.2735e-5   value(member0)=55.23065455864996681458094
  AdualR                       spread=   1.2735e-5   value(member0)=0.1656569382013508749956805
  Aped                         spread=   1.2735e-5   value(member0)=2.509769471619873853989087
  ApedX                        spread=   1.3018e-5   value(member0)=18.71633620370668515121927
  Aant                         spread=   0.0035203   value(member0)=-0.5761827644210152434992149
  k908(i) ApedX1/ApedX2        2.6035e-5 value0=0.999990504578
  k908(ii) Apol1/Apol2         2.5471e-5 value0=0.999990710535
  k908(iii) Aped1/Aped2        2.5471e-5 value0=1.00000928955
  k907R AdualR1/AdualR2        2.5471e-5 value0=0.999990710535
  k907R AdualR1*AdualR2        2.9852e-59 value0=0.0274424761002
  k903a Adag1*Adag2            9.6656e-59 value0=1877.30336763
=== family a=1 b=0.5 N=12 tau=1
  J=0.35306083872173792869384 lambda=0.03116298895972426009074 caustic axes=(0.9842951849116,0.4678001828134) closure_err=3.0626e-58 worst tangency/closure=1.008e-57
  checks: {'chk_polar_two_defs': '2.717e-60', 'chk_polar_tangent_circle': '3.236e-59', 'chk_polar_circumcircle': '2.3946e-57', 'chk_dualR_on_circle': '1.828e-60', 'chk_ant_is_polar_reciprocal_of_inv': '3.1678e-60', 'chk_invped_eq_polar': '2.717e-60'}
  O_p(f1)=['-4.33012701892219', '2.02967208103623e-60'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 5.51e-60 Rstar-a/b^2=-5.29e-60  O_p spread over members: 2.41e-59
  k813 Apol/Adag               spread=  4.0819e-58   value(member0)=1.168563367515658228391388
  k814R Apol/AdualR            spread=  1.8295e-58   value(member0)=319.7964254199533929994076
  k814P Apol/AdualP            spread=  2.8985e-58   value(member0)=383.9173074642980228814941
  k815(i) ApedX*AdualR         spread=    8.467e-6   value(member0)=3.948811189348254576039319
  k815(ii) Apol*AdualR         spread=    8.467e-6   value(member0)=9.244281831058860105948921
  k815(iii) Aped*AdualR        spread=    8.467e-6   value(member0)=0.4427053049224472477465704
  k815(i)P ApedX*AdualP        spread=    8.467e-6   value(member0)=3.289290892751222836905326
  k816(i) ApedX/AdualR         spread=  9.3981e-58   value(member0)=136.6050631179470324610237
  k816(ii) Apol/AdualR         spread=   1.832e-58   value(member0)=319.7964254199533929994076
  k816(iii) Aped/AdualR        spread=  2.7485e-58   value(member0)=15.31493485551086378310412
  k816(i)P ApedX/AdualP        spread=  8.4053e-58   value(member0)=163.9951039145056373539988
  k817 Adag*Aant               spread=  3.6521e-58   value(member0)=-28.44230966728695592219402
  k818 Adag/Aant               spread=    8.467e-6   value(member0)=-76.11625042847559004133389
  Aant/A                       spread=  2.0725e-58   value(member0)=-0.4109982904297525209271658
  k804 A*Adag                  spread=  3.3955e-58   value(member0)=69.20298777288537495157146
  k805 A/Adag                  spread=    8.467e-6   value(member0)=0.03196558069016414025080037
  k802 Ldag                    spread=  7.9621e-59   value(member0)=27.3553197167409477200956
  k803 sumcos_dag              spread=  9.6921e-59   value(member0)=-7.679148805250136620043542
  k801 sum 1/d                 spread=   2.806e-58   value(member0)=27.18100976874697430358445
  A                            spread=   4.2335e-6   value(member0)=1.487317615593458182619704
  Adag                         spread=   4.2335e-6   value(member0)=46.5287219403183927121394
  Apol                         spread=   4.2335e-6   value(member0)=54.37175999677815236478597
  AdualR                       spread=   4.2335e-6   value(member0)=0.1700199116527888439926675
  Aped                         spread=   4.2335e-6   value(member0)=2.603843871102173540088433
  ApedX                        spread=   4.2335e-6   value(member0)=23.22558076263699819804739
  Aant                         spread=   4.2335e-6   value(member0)=-0.6112849973349671429638761
  k908(i) ApedX1/ApedX2        2.5717e-57 value0=1.0
  k908(ii) Apol1/Apol2         1.6779e-58 value0=1.0
  k908(iii) Aped1/Aped2        3.0298e-58 value0=1.0
  k907R AdualR1/AdualR2        2.5903e-58 value0=1.0
  k907R AdualR1*AdualR2        8.467e-6 value0=0.0289067703584
  k903a Adag1*Adag2            8.467e-6 value0=2164.9219654
=== family a=1 b=0.5 N=13 tau=1
  J=0.32677645685055017297926 lambda=0.02669571318794986976903 caustic axes=(0.9865618514883,0.4725508298712) closure_err=1.4298e-59 worst tangency/closure=4.7877e-59
  checks: {'chk_polar_two_defs': '3.3076e-60', 'chk_polar_tangent_circle': '2.8626e-59', 'chk_polar_circumcircle': '9.7701e-59', 'chk_dualR_on_circle': '2.003e-60', 'chk_ant_is_polar_reciprocal_of_inv': '6.3049e-60', 'chk_invped_eq_polar': '3.3076e-60'}
  O_p(f1)=['-4.33012701892219', '6.03392138855821e-60'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.28e-59 Rstar-a/b^2=-1.24e-59  O_p spread over members: 1.81e-59
  k813 Apol/Adag               spread=   1.682e-59   value(member0)=1.091405701279404044559244
  k814R Apol/AdualR            spread=  1.0035e-59   value(member0)=309.5577694407081286712082
  k814P Apol/AdualP            spread=  1.4798e-59   value(member0)=363.3442087369220010842701
  k815(i) ApedX*AdualR         spread=   2.3286e-6   value(member0)=4.795137780700955722812209
  k815(ii) Apol*AdualR         spread=   2.3117e-6   value(member0)=9.323006039491609024663073
  k815(iii) Aped*AdualR        spread=  4.8524e-60   value(member0)=0.4648897873996717396678575
  k815(i)P ApedX*AdualP        spread=   2.3286e-6   value(member0)=4.08530566845888370273189
  k816(i) ApedX/AdualR         spread=   1.6929e-8   value(member0)=159.216045690301763285422
  k816(ii) Apol/AdualR         spread=  9.9067e-60   value(member0)=309.5577694407081286712082
  k816(iii) Aped/AdualR        spread=   2.3117e-6   value(member0)=15.43603479538826342883696
  k816(i)P ApedX/AdualP        spread=   1.6929e-8   value(member0)=186.8802331922888247749139
  k817 Adag*Aant               spread=  0.00047985   value(member0)=-31.38910002062856774681385
  k818 Adag/Aant               spread=  0.00048216   value(member0)=-77.18739320257818310386358
  Aant/A                       spread=  0.00048101   value(member0)=-0.4252657184118231229323257
  k804 A*Adag                  spread=   1.1558e-6   value(member0)=73.81055810906364477035359
  k805 A/Adag                  spread=   1.1558e-6   value(member0)=0.03046444364424244754188861
  k802 Ldag                    spread=    4.22e-60   value(member0)=27.7235935733440692784874
  k803 sumcos_dag              spread=  4.0665e-60   value(member0)=-8.875702994528515711342134
  k801 sum 1/d                 spread=  1.3204e-59   value(member0)=29.40854822411413357426973
  A                            spread=  2.3414e-13   value(member0)=1.499532456422218225037329
  Adag                         spread=   1.1558e-6   value(member0)=49.22238114483402576734283
  Apol                         spread=   1.1558e-6   value(member0)=53.72158741201969479596216
  AdualR                       spread=   1.1558e-6   value(member0)=0.1735430110802287089064394
  Aped                         spread=   1.1558e-6   value(member0)=2.678815957530861291770426
  ApedX                        spread=   1.1728e-6   value(member0)=27.63083198138223928208297
  Aant                         spread=  0.00048101   value(member0)=-0.6376997473622404837653647
  k908(i) ApedX1/ApedX2        2.3455e-6 value0=1.00000018812
  k908(ii) Apol1/Apol2         2.3117e-6 value0=1.0000001854
  k908(iii) Aped1/Aped2        2.3117e-6 value0=0.999999814596
  k907R AdualR1/AdualR2        2.3117e-6 value0=1.0000001854
  k907R AdualR1*AdualR2        7.1835e-60 value0=0.0301171711109
  k903a Adag1*Adag2            2.2619e-59 value0=2422.84235636
=== family a=1 b=0.5 N=14 tau=1
  J=0.30407796570507254179991 lambda=0.02311585230683381821823 caustic axes=(0.9883744976946,0.4763235745721) closure_err=2.1382e-58 worst tangency/closure=6.8981e-58
  checks: {'chk_polar_two_defs': '2.5658e-60', 'chk_polar_tangent_circle': '2.6012e-58', 'chk_polar_circumcircle': '1.3983e-57', 'chk_dualR_on_circle': '1.6024e-59', 'chk_ant_is_polar_reciprocal_of_inv': '5.9359e-60', 'chk_invped_eq_polar': '2.5658e-60'}
  O_p(f1)=['-4.33012701892219', '-4.32885103365583e-60'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.22e-59 Rstar-a/b^2=1.24e-59  O_p spread over members: 1.32e-58
  k813 Apol/Adag               spread=  2.2627e-58   value(member0)=1.033392225541296231049056
  k814R Apol/AdualR            spread=  1.0787e-58   value(member0)=301.6440079166159981772084
  k814P Apol/AdualP            spread=  1.8226e-58   value(member0)=347.454101249262935760859
  k815(i) ApedX*AdualR         spread=   7.3347e-7   value(member0)=5.616128630001664113439616
  k815(ii) Apol*AdualR         spread=   7.3347e-7   value(member0)=9.38865493882520147050055
  k815(iii) Aped*AdualR        spread=   7.3347e-7   value(member0)=0.4832943117659096927865436
  k815(i)P ApedX*AdualP        spread=   7.3347e-7   value(member0)=4.875670031920653323843827
  k816(i) ApedX/AdualR         spread=  5.4652e-58   value(member0)=180.4381522132002228864817
  k816(ii) Apol/AdualR         spread=  1.0721e-58   value(member0)=301.6440079166159981772084
  k816(iii) Aped/AdualR        spread=  1.4556e-58   value(member0)=15.52755257853935887230953
  k816(i)P ApedX/AdualP        spread=  4.8883e-58   value(member0)=207.8409461581142933004924
  k817 Adag*Aant               spread=   7.3347e-7   value(member0)=-33.91210113857996767227689
  k818 Adag/Aant               spread=  2.7031e-58   value(member0)=-78.20112514917566222759672
  Aant/A                       spread=  9.1547e-59   value(member0)=-0.4363225335984709846858141
  k804 A*Adag                  spread=   7.3347e-7   value(member0)=77.72255276136581052734022
  k805 A/Adag                  spread=   2.018e-58   value(member0)=0.02930753929058514398966325
  k802 Ldag                    spread=  4.4676e-59   value(member0)=28.02529507254274866033232
  k803 sumcos_dag              spread=  5.7141e-59   value(member0)=-10.06302000021362911597022
  k801 sum 1/d                 spread=  1.9952e-58   value(member0)=31.63905987754691265212331
  A                            spread=   3.6673e-7   value(member0)=1.509257025432813869299362
  Adag                         spread=   3.6673e-7   value(member0)=51.49722774295325617564851
  Apol                         spread=   3.6673e-7   value(member0)=53.21683478649744875708391
  AdualR                       spread=   3.6673e-7   value(member0)=0.1764226485188735298954235
  Aped                         spread=   3.6673e-7   value(member0)=2.739411950921977681538644
  ApedX                        spread=   3.6673e-7   value(member0)=31.83337670730442484249423
  Aant                         spread=   3.6673e-7   value(member0)=-0.6585228491881373069249877
  k908(i) ApedX1/ApedX2        1.4283e-57 value0=1.0
  k908(ii) Apol1/Apol2         8.2222e-59 value0=1.0
  k908(iii) Aped1/Aped2        1.5659e-58 value0=1.0
  k907R AdualR1/AdualR2        1.3893e-58 value0=1.0
  k907R AdualR1*AdualR2        7.3347e-7 value0=0.0311249509104
  k903a Adag1*Adag2            7.3347e-7 value0=2651.96446521
=== family a=1 b=0.5 N=15 tau=1
  J=0.28428919797452628144837 lambda=0.02020508702124984949160 caustic axes=(0.9898459036530,0.4793692866452) closure_err=3.1925e-58 worst tangency/closure=1.0195e-57
  checks: {'chk_polar_two_defs': '3.7411e-60', 'chk_polar_tangent_circle': '6.223e-59', 'chk_polar_circumcircle': '1.9596e-57', 'chk_dualR_on_circle': '3.8116e-60', 'chk_ant_is_polar_reciprocal_of_inv': '6.3786e-60', 'chk_invped_eq_polar': '3.7411e-60'}
  O_p(f1)=['-4.33012701892219', '4.08370381406503e-60'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.02e-59 Rstar-a/b^2=-9.96e-60  O_p spread over members: 2.56e-59
  k813 Apol/Adag               spread=  3.0838e-58   value(member0)=0.9885672120438160714475893
  k814R Apol/AdualR            spread=  1.3483e-58   value(member0)=295.3911199694702899837245
  k814P Apol/AdualP            spread=  2.2619e-58   value(member0)=334.9059373506473083682222
  k815(i) ApedX*AdualR         spread=    2.143e-7   value(member0)=6.396996967684497103026349
  k815(ii) Apol*AdualR         spread=   2.1311e-7   value(member0)=9.443737710946667137034104
  k815(iii) Aped*AdualR        spread=  1.0225e-58   value(member0)=0.4986831577794009850828148
  k815(i)P ApedX*AdualP        spread=    2.143e-7   value(member0)=5.642229318697316553405337
  k816(i) ApedX/AdualR         spread=   1.1913e-9   value(member0)=200.0919716920228240345857
  k816(ii) Apol/AdualR         spread=  1.3456e-58   value(member0)=295.3911199694702899837245
  k816(iii) Aped/AdualR        spread=   2.1311e-7   value(member0)=15.59833415487805700385241
  k816(i)P ApedX/AdualP        spread=   1.1913e-9   value(member0)=226.8585099741048922960891
  k817 Adag*Aant               spread=    6.473e-5   value(member0)=-36.07458813099946176128483
  k818 Adag/Aant               spread=   6.4517e-5   value(member0)=-79.12752220766133589036627
  Aant/A                       spread=   6.4624e-5   value(member0)=-0.4450571948548140478327575
  k804 A*Adag                  spread=   1.0655e-7   value(member0)=81.05607222632961767172706
  k805 A/Adag                  spread=   1.0655e-7   value(member0)=0.02839596336684901505629217
  k802 Ldag                    spread=  6.2065e-59   value(member0)=28.27505959370365220804507
  k803 sumcos_dag              spread=  7.9615e-59   value(member0)=-11.23992410529511012535346
  k801 sum 1/d                 spread=  3.0807e-58   value(member0)=33.87187758647818415769481
  A                            spread=  1.4512e-15   value(member0)=1.5171240086425116322325
  Adag                         spread=   1.0655e-7   value(member0)=53.42745336873072369292971
  Apol                         spread=   1.0655e-7   value(member0)=52.81662862332712061392892
  AdualR                       spread=   1.0655e-7   value(member0)=0.1788023574601223785515722
  Aped                         spread=   1.0655e-7   value(member0)=2.789018919342942252653888
  ApedX                        spread=   1.0775e-7   value(member0)=35.77691624737775297918757
  Aant                         spread=   6.4624e-5   value(member0)=-0.6752069555333268910457213
  k908(i) ApedX1/ApedX2        2.1549e-7 value0=1.00000008484
  k908(ii) Apol1/Apol2         2.1311e-7 value0=1.00000008391
  k908(iii) Aped1/Aped2        2.1311e-7 value0=0.999999916093
  k907R AdualR1/AdualR2        2.1311e-7 value0=1.00000008391
  k907R AdualR1*AdualR2        9.5652e-59 value0=0.0319702803508
  k903a Adag1*Adag2            3.5272e-58 value0=2854.49253396
=== family a=1 b=0.5 N=16 tau=1
  J=0.26689128233781273700064 lambda=0.01780773914698051825554 caustic axes=(0.9910561340575,0.4818633217552) closure_err=3.8102e-58 worst tangency/closure=1.2274e-57
  checks: {'chk_polar_two_defs': '2.8687e-60', 'chk_polar_tangent_circle': '2.7755e-58', 'chk_polar_circumcircle': '2.1656e-57', 'chk_dualR_on_circle': '1.7619e-59', 'chk_ant_is_polar_reciprocal_of_inv': '5.2326e-60', 'chk_invped_eq_polar': '2.8687e-60'}
  O_p(f1)=['-4.33012701892219', '-5.18501215654946e-60'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.55e-59 Rstar-a/b^2=1.56e-59  O_p spread over members: 1.62e-58
  k813 Apol/Adag               spread=  3.3126e-58   value(member0)=0.9531480797616059989494161
  k814R Apol/AdualR            spread=  1.4375e-58   value(member0)=290.3588847816825336412831
  k814P Apol/AdualP            spread=  2.5149e-58   value(member0)=324.8118809284352949298432
  k815(i) ApedX*AdualR         spread=   6.3983e-8   value(member0)=7.129497746567928147683367
  k815(ii) Apol*AdualR         spread=   6.3983e-8   value(member0)=9.490257771660620434111515
  k815(iii) Aped*AdualR        spread=   6.3983e-8   value(member0)=0.5116506018472986124172109
  k815(i)P ApedX*AdualP        spread=   6.3983e-8   value(member0)=6.373267532055218511373679
  k816(i) ApedX/AdualR         spread=  8.3085e-58   value(member0)=218.1303252824870987479065
  k816(ii) Apol/AdualR         spread=  1.4389e-58   value(member0)=290.3588847816825336412831
  k816(iii) Aped/AdualR        spread=  2.0457e-58   value(member0)=15.65418998353114644020655
  k816(i)P ApedX/AdualP        spread=  7.4036e-58   value(member0)=244.0129266091111432767706
  k817 Adag*Aant               spread=  2.9425e-58   value(member0)=-37.93260240936756066465
  k818 Adag/Aant               spread=   6.3983e-8   value(member0)=-79.96127951187156787947009
  Aant/A                       spread=  1.1899e-58   value(member0)=-0.4520662879719830724870492
  k804 A*Adag                  spread=  2.8265e-58   value(member0)=83.90938103245257631485405
  k805 A/Adag                  spread=   6.3983e-8   value(member0)=0.02766420177462326512038705
  k802 Ldag                    spread=  6.7028e-59   value(member0)=28.48384461441933201410107
  k803 sumcos_dag              spread=  8.7882e-59   value(member0)=-12.40604359002440131387979
  k801 sum 1/d                 spread=  3.6925e-58   value(member0)=36.1065224161485377662342
  A                            spread=   3.1992e-8   value(member0)=1.523576728512717308802373
  Adag                         spread=   3.1992e-8   value(member0)=55.07394505451858767258061
  Apol                         spread=   3.1992e-8   value(member0)=52.49362497361058904924518
  AdualR                       spread=   3.1992e-8   value(member0)=0.1807887677109654652449081
  Aped                         spread=   3.1992e-8   value(member0)=2.830101716635934735694782
  ApedX                        spread=   3.1992e-8   value(member0)=39.43551270821289747452783
  Aant                         spread=   3.1992e-8   value(member0)=-0.6887576760992419358204791
  k908(i) ApedX1/ApedX2        2.1201e-57 value0=1.0
  k908(ii) Apol1/Apol2         1.11e-58 value0=1.0
  k908(iii) Aped1/Aped2        2.2099e-58 value0=1.0
  k907R AdualR1/AdualR2        1.9175e-58 value0=1.0
  k907R AdualR1*AdualR2        6.3983e-8 value0=0.0326845785304
  k903a Adag1*Adag2            6.3983e-8 value0=3033.13942387
=== family a=1 b=0.5 N=5 tau=2
  J=0.99995422403016947985507 lambda=0.24997711253894459340870 caustic axes=(0.8660386177654,0.0047840841396) closure_err=9.7954e-58 worst tangency/closure=7.5135e-57
  checks: {'chk_polar_two_defs': '1.6397e-52', 'chk_polar_tangent_circle': '2.8498e-57', 'chk_polar_circumcircle': '4.2175e-48', 'chk_dualR_on_circle': '1.7825e-58', 'chk_ant_is_polar_reciprocal_of_inv': '2.5768e-53', 'chk_invped_eq_polar': '1.6397e-52'}
  O_p(f1)=['-4.33012701892219', '2.48188830698837e-59'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 2.88e-59 Rstar-a/b^2=1.49e-59  O_p spread over members: 5.33e-57
  k813 Apol/Adag               spread=  5.5951e-53   value(member0)=141327.6069455794725283211
  k814R Apol/AdualR            spread=  5.5928e-53   value(member0)=4893317.145853589385961972
  k814P Apol/AdualP            spread=   5.652e-53   value(member0)=1918431736.794739795337492
  k815(i) ApedX*AdualR         spread=     0.90357   value(member0)=0.00002349638321195698289744381
  k815(ii) Apol*AdualR         spread=     0.91638   value(member0)=2443.591943625969907658109
  k815(iii) Aped*AdualR        spread=    4.08e-54   value(member0)=0.000002875264061953505288202918
  k815(i)P ApedX*AdualP        spread=     0.90357   value(member0)=5.993189782645738744178538e-8
  k816(i) ApedX/AdualR         spread=     0.13288   value(member0)=0.04705174083444036092382354
  k816(ii) Apol/AdualR         spread=  5.5926e-53   value(member0)=4893317.145853589385961972
  k816(iii) Aped/AdualR        spread=     0.91638   value(member0)=0.005757744851759625191871898
  k816(i)P ApedX/AdualP        spread=     0.13288   value(member0)=18.44669989655565107232948
  k817 Adag*Aant               spread=     0.32719   value(member0)=3722.958598803813627551769
  k818 Adag/Aant               spread=     0.90396   value(member0)=0.0001608014022438295835601382
  Aant/A                       spread=     0.66714   value(member0)=9201.512994422832748097011
  k804 A*Adag                  spread=     0.71021   value(member0)=0.4046028735774596551777758
  k805 A/Adag                  spread=     0.71146   value(member0)=0.6758509437958791068196218
  k802 Ldag                    spread=  1.3999e-57   value(member0)=32.08351343087091849590795
  k803 sumcos_dag              spread=  1.4667e-57   value(member0)=3.249059874175660937856015
  k801 sum 1/d                 spread=  1.2661e-57   value(member0)=16.53662893368549018076607
  A                            spread=     0.16509   value(member0)=0.5229256486058518674616425
  Adag                         spread=     0.71083   value(member0)=0.7737292570294703538747864
  Apol                         spread=     0.71083   value(member0)=109349.3043197562193027528
  AdualR                       spread=     0.71083   value(member0)=0.02234666200052343956697012
  Aped                         spread=     0.71083   value(member0)=0.0001286663780875262808813759
  ApedX                        spread=     0.66652   value(member0)=0.001051449348963465447570262
  Aant                         spread=     0.66796   value(member0)=4811.707150763734031937894
  k908(i) ApedX1/ApedX2        0.88868 value0=0.483819789707
  k908(ii) Apol1/Apol2         0.91638 value0=0.445190804336
  k908(iii) Aped1/Aped2        0.91638 value0=2.24622788759
  k907R AdualR1/AdualR2        0.91638 value0=0.445190804336
  k907R AdualR1*AdualR2        2.0569e-57 value0=0.00112170623854
  k903a Adag1*Adag2            2.1544e-56 value0=1.3447199658
=== family a=1 b=0.5 N=7 tau=2
  J=0.95292094642652302110608 lambda=0.22701458253460508942707 caustic axes=(0.8791958925435,0.1516094240652) closure_err=3.1968e-58 worst tangency/closure=1.652e-57
  checks: {'chk_polar_two_defs': '2.1158e-58', 'chk_polar_tangent_circle': '9.9568e-60', 'chk_polar_circumcircle': '1.0618e-54', 'chk_dualR_on_circle': '7.7788e-61', 'chk_ant_is_polar_reciprocal_of_inv': '2.9099e-59', 'chk_invped_eq_polar': '2.1158e-58'}
  O_p(f1)=['-4.33012701892219', '4.78520344186746e-61'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 3.21e-60 Rstar-a/b^2=3.11e-60  O_p spread over members: 7.67e-60
  k813 Apol/Adag               spread=  1.1761e-56   value(member0)=99.35773044791956789689587
  k814R Apol/AdualR            spread=  8.8916e-57   value(member0)=4680.654593662205524912503
  k814P Apol/AdualP            spread=  8.8711e-57   value(member0)=10666.02094379890539645022
  k815(i) ApedX*AdualR         spread=     0.73903   value(member0)=0.00614900100911166293333782
  k815(ii) Apol*AdualR         spread=    0.060295   value(member0)=55.88837807180551461285165
  k815(iii) Aped*AdualR        spread=  6.0513e-58   value(member0)=0.02904372743276690946365828
  k815(i)P ApedX*AdualP        spread=     0.73903   value(member0)=0.002698414898244238725535458
  k816(i) ApedX/AdualR         spread=     0.75476   value(member0)=0.5149791568965143168741654
  k816(ii) Apol/AdualR         spread=  8.8958e-57   value(member0)=4680.654593662205524912503
  k816(iii) Aped/AdualR        spread=    0.060295   value(member0)=2.432413695215716103144123
  k816(i)P ApedX/AdualP        spread=     0.75476   value(member0)=1.173506475037822074920313
  k817 Adag*Aant               spread=     0.14701   value(member0)=44.01239599265526281951927
  k818 Adag/Aant               spread=    0.092275   value(member0)=0.6020738472448423338672323
  Aant/A                       spread=     0.12009   value(member0)=5.86584663127846238005933
  k804 A*Adag                  spread=    0.030596   value(member0)=7.503161735932184235889118
  k805 A/Adag                  spread=    0.030637   value(member0)=0.283151934750840274301589
  k802 Ldag                    spread=  3.5788e-58   value(member0)=33.76117904251005144294058
  k803 sumcos_dag              spread=  7.4344e-58   value(member0)=2.106045829711322845808974
  k801 sum 1/d                 spread=  3.1756e-58   value(member0)=18.38948772560133424595367
  A                            spread=  0.00013031   value(member0)=1.457578389753934049170513
  Adag                         spread=    0.030616   value(member0)=5.147690023861327606665477
  Apol                         spread=    0.030616   value(member0)=511.4627978202584369397421
  AdualR                       spread=    0.030616   value(member0)=0.1092716387389062258990311
  Aped                         spread=    0.030616   value(member0)=0.2657938305671796852904961
  ApedX                        spread=     0.74702   value(member0)=0.05627261639046242113435946
  Aant                         spread=     0.12007   value(member0)=8.549931287362399708856971
  k908(i) ApedX1/ApedX2        0.92996 value0=0.528343727449
  k908(ii) Apol1/Apol2         0.060295 value0=1.01665580699
  k908(iii) Aped1/Aped2        0.060295 value0=0.98361706403
  k907R AdualR1/AdualR2        0.060295 value0=1.01665580699
  k907R AdualR1*AdualR2        5.7508e-58 value0=0.0117446740092
  k903a Adag1*Adag2            3.3282e-57 value0=26.0645858703
=== family a=1 b=0.5 N=7 tau=3
  J=0.99999976398215907244766 lambda=0.24999988199109346232914 caustic axes=(0.8660254719169,0.0003435242444) closure_err=7.0805e-54 worst tangency/closure=4.2793e-53
  checks: {'chk_polar_two_defs': '9.9172e-48', 'chk_polar_tangent_circle': '5.9185e-55', 'chk_polar_circumcircle': '1.1005e-39', 'chk_dualR_on_circle': '3.2568e-56', 'chk_ant_is_polar_reciprocal_of_inv': '1.4975e-48', 'chk_invped_eq_polar': '9.9172e-48'}
  O_p(f1)=['-4.33012701892219', '6.94463511117898e-56'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 6.94e-56 Rstar-a/b^2=-4.76e-59  O_p spread over members: 1.04e-54
  k813 Apol/Adag               spread=  7.5239e-47   value(member0)=27420326.69204914833509746
  k814R Apol/AdualR            spread=  7.5239e-47   value(member0)=949080714.5690928131864982
  k814P Apol/AdualP            spread=  7.6034e-47   value(member0)=71809432985608.68505193432
  k815(i) ApedX*AdualR         spread=     0.90379   value(member0)=0.0000001229935260965458526948437
  k815(ii) Apol*AdualR         spread=     0.91637   value(member0)=474069.3505896481376915879
  k815(iii) Aped*AdualR        spread=  5.4929e-48   value(member0)=1.482636509122298020186673e-8
  k815(i)P ApedX*AdualP        spread=     0.90379   value(member0)=1.625563366563221533243698e-12
  k816(i) ApedX/AdualR         spread=     0.13082   value(member0)=0.0002462314500819177333389501
  k816(ii) Apol/AdualR         spread=  7.5239e-47   value(member0)=949080714.5690928131864982
  k816(iii) Aped/AdualR        spread=     0.91637   value(member0)=0.0000296821913455027416406664
  k816(i)P ApedX/AdualP        spread=     0.13082   value(member0)=18.63038679659051885722242
  k817 Adag*Aant               spread=      0.3273   value(member0)=721951.7483232495078508171
  k818 Adag/Aant               spread=     0.90388   value(member0)=0.0000008288798935453932957332255
  Aant/A                       spread=     0.66689   value(member0)=1784550.041907156516205494
  k804 A*Adag                  spread=     0.71019   value(member0)=0.4045567405617252872963243
  k805 A/Adag                  spread=     0.71145   value(member0)=0.6760513186747109982475391
  k802 Ldag                    spread=  6.4747e-54   value(member0)=48.08206475484235843275671
  k803 sumcos_dag              spread=  6.6493e-54   value(member0)=5.267759839288790652026753
  k801 sum 1/d                 spread=  5.9129e-54   value(member0)=24.53590403950827083392723
  A                            spread=     0.16508   value(member0)=0.5229733434272700319261028
  Adag                         spread=     0.71082   value(member0)=0.7735704804961766538789574
  Apol                         spread=     0.71082   value(member0)=21211555.29453059780750135
  AdualR                       spread=     0.71082   value(member0)=0.02234957993447500661050674
  Aped                         spread=     0.71082   value(member0)=0.0000006633845081066957728176638
  ApedX                        spread=     0.66729   value(member0)=0.000005503169475987512795774533
  Aant                         spread=     0.66773   value(member0)=933272.1019294604922836199
  k908(i) ApedX1/ApedX2        0.88919 value0=0.483228794068
  k908(ii) Apol1/Apol2         0.91637 value0=0.445283661997
  k908(iii) Aped1/Aped2        0.91637 value0=2.24575946828
  k907R AdualR1/AdualR2        0.91637 value0=0.445283661997
  k907R AdualR1*AdualR2        7.5289e-55 value0=0.00112176521593
  k903a Adag1*Adag2            1.495e-52 value0=1.34388781662
=== family a=1 b=0.5 N=8 tau=3
  J=0.99936381282854245658975 lambda=0.24968200759780051008231 caustic axes=(0.8662089773271,0.0178323414671) closure_err=9.4259e-57 worst tangency/closure=5.5433e-56
  checks: {'chk_polar_two_defs': '1.0475e-54', 'chk_polar_tangent_circle': '3.5409e-58', 'chk_polar_circumcircle': '1.9808e-49', 'chk_dualR_on_circle': '1.2679e-59', 'chk_ant_is_polar_reciprocal_of_inv': '1.0178e-55', 'chk_invped_eq_polar': '1.0475e-54'}
  O_p(f1)=['-4.33012701892219', '-2.04782269956285e-61'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 6.48e-61 Rstar-a/b^2=-6.22e-61  O_p spread over members: 1.08e-58
  k813 Apol/Adag               spread=  2.8528e-53   value(member0)=10122.80377184769147199179
  k814R Apol/AdualR            spread=  2.8376e-53   value(member0)=352017.6730151990276840343
  k814P Apol/AdualP            spread=  2.8666e-53   value(member0)=10567959.400435037708784
  k815(i) ApedX*AdualR         spread=      0.3031   value(member0)=0.002666341108834432378798058
  k815(ii) Apol*AdualR         spread=      0.3031   value(member0)=1853.113198528438892628928
  k815(iii) Aped*AdualR        spread=      0.3031   value(member0)=0.0001873852645792821356627217
  k815(i)P ApedX*AdualP        spread=      0.3031   value(member0)=0.00008881555625185542485074429
  k816(i) ApedX/AdualR         spread=  1.8261e-55   value(member0)=0.5064985740439418504441995
  k816(ii) Apol/AdualR         spread=  2.8376e-53   value(member0)=352017.6730151990276840343
  k816(iii) Aped/AdualR        spread=  5.8252e-55   value(member0)=0.03559573416611440316628028
  k816(i)P ApedX/AdualP        spread=   1.453e-55   value(member0)=15.20564669673134912607739
  k817 Adag*Aant               spread=   6.861e-54   value(member0)=1292.101722696310949806791
  k818 Adag/Aant               spread=      0.3031   value(member0)=0.004926835647341235906178672
  Aant/A                       spread=  7.0282e-54   value(member0)=490.2389411484361435324139
  k804 A*Adag                  spread=  1.7883e-55   value(member0)=2.635657052598529053294967
  k805 A/Adag                  spread=      0.3031   value(member0)=0.4140226677164297087626368
  k802 Ldag                    spread=  8.4494e-57   value(member0)=48.19451492985803468008573
  k803 sumcos_dag              spread=  1.0403e-56   value(member0)=4.26920818513959723864315
  k801 sum 1/d                 spread=  7.5679e-57   value(member0)=25.08702145716665099628232
  A                            spread=      0.1652   value(member0)=1.044615605906050636536582
  Adag                         spread=      0.1652   value(member0)=2.523087954743394443032403
  Apol                         spread=      0.1652   value(member0)=25540.72426497991074759005
  AdualR                       spread=      0.1652   value(member0)=0.07255523294103799655961494
  Aped                         spread=      0.1652   value(member0)=0.002582656784129695426019934
  ApedX                        spread=      0.1652   value(member0)=0.03674912202406178253210102
  Aant                         spread=      0.1652   value(member0)=512.1112485465143215625399
  k908(i) ApedX1/ApedX2        3.6513e-55 value0=1.0
  k908(ii) Apol1/Apol2         4.573e-53 value0=1.0
  k908(iii) Aped1/Aped2        1.1166e-54 value0=1.0
  k907R AdualR1/AdualR2        5.3964e-56 value0=1.0
  k907R AdualR1*AdualR2        0.3031 value0=0.00526426182713
  k903a Adag1*Adag2            0.3031 value0=6.36597282737
=== family a=1 b=0.5 N=9 tau=2
  J=0.83134169224465035142161 lambda=0.17278225231604973456458 caustic axes=(0.9095151167979,0.2778808156097) closure_err=1.6839e-58 worst tangency/closure=7.1161e-58
  checks: {'chk_polar_two_defs': '2.0069e-59', 'chk_polar_tangent_circle': '1.9914e-59', 'chk_polar_circumcircle': '3.3569e-56', 'chk_dualR_on_circle': '1.478e-60', 'chk_ant_is_polar_reciprocal_of_inv': '2.196e-60', 'chk_invped_eq_polar': '2.0069e-59'}
  O_p(f1)=['-4.33012701892219', '2.66473554270916e-61'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 3.65e-60 Rstar-a/b^2=2.49e-60  O_p spread over members: 1.05e-59
  k813 Apol/Adag               spread=  1.4095e-57   value(member0)=14.99246920687300069199458
  k814R Apol/AdualR            spread=  7.8399e-58   value(member0)=1258.443756251637436566897
  k814P Apol/AdualP            spread=  7.9743e-58   value(member0)=2340.997005842552000859238
  k815(i) ApedX*AdualR         spread=    0.045579   value(member0)=0.09021944393775598036198955
  k815(ii) Apol*AdualR         spread=   0.0026093   value(member0)=35.77494673679715309578369
  k815(iii) Aped*AdualR        spread=  2.0471e-58   value(member0)=0.2131722270965112163567163
  k815(i)P ApedX*AdualP        spread=    0.045579   value(member0)=0.04849903508317418658556605
  k816(i) ApedX/AdualR         spread=    0.043083   value(member0)=3.173620264238813387473615
  k816(ii) Apol/AdualR         spread=  7.8399e-58   value(member0)=1258.443756251637436566897
  k816(iii) Aped/AdualR        spread=   0.0026093   value(member0)=7.498690638718133853461925
  k816(i)P ApedX/AdualP        spread=    0.043083   value(member0)=5.903669114616137589299071
  k817 Adag*Aant               spread=    0.030535   value(member0)=25.82456236706799918649747
  k818 Adag/Aant               spread=    0.033065   value(member0)=7.755923282845057039784778
  Aant/A                       spread=    0.031801   value(member0)=0.8912661924902980934077988
  k804 A*Adag                  spread=   0.0013055   value(member0)=28.97513962120706523331795
  k805 A/Adag                  spread=   0.0013055   value(member0)=0.1446635312929459767767876
  k802 Ldag                    spread=  1.3048e-58   value(member0)=38.00223923835809824711654
  k803 sumcos_dag              spread=  7.1935e-58   value(member0)=1.334188408548841486688785
  k801 sum 1/d                 spread=  1.2565e-58   value(member0)=21.85164290525813661893555
  A                            spread=   2.1468e-7   value(member0)=2.047350975604809952531862
  Adag                         spread=   0.0013055   value(member0)=14.15250241236605312437345
  Apol                         spread=   0.0013055   value(member0)=212.1809566175939094663795
  AdualR                       spread=   0.0013055   value(member0)=0.1686058320552916074047868
  Aped                         spread=   0.0013055   value(member0)=1.264322974466297030696267
  ApedX                        spread=    0.044332   value(member0)=0.5350908852795195435898953
  Aant                         spread=    0.031801   value(member0)=1.824734708718596143152409
  k908(i) ApedX1/ApedX2        0.086692 value0=1.0228412541
  k908(ii) Apol1/Apol2         0.0026093 value0=1.0006509983
  k908(iii) Aped1/Aped2        0.0026093 value0=0.999349425222
  k907R AdualR1/AdualR2        0.0026093 value0=1.0006509983
  k907R AdualR1*AdualR2        1.6583e-58 value0=0.028409432111
  k903a Adag1*Adag2            7.8764e-58 value0=200.163018747
=== family a=1 b=0.5 N=9 tau=4
  J=0.99999999878337879677230 lambda=0.24999999939168939875619 caustic axes=(0.8660254041356,0.0000246639534) closure_err=4.9313e-51 worst tangency/closure=2.947e-50
  checks: {'chk_polar_two_defs': '1.4323e-43', 'chk_polar_tangent_circle': '6.0085e-53', 'chk_polar_circumcircle': '2.859e-32', 'chk_dualR_on_circle': '6.2955e-54', 'chk_ant_is_polar_reciprocal_of_inv': '3.7435e-44', 'chk_invped_eq_polar': '1.4323e-43'}
  O_p(f1)=['-4.33012701892219', '6.59147319281215e-54'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 6.59e-54 Rstar-a/b^2=-9.33e-61  O_p spread over members: 4.53e-53
  k813 Apol/Adag               spread=  1.0075e-41   value(member0)=5319402649.864172273640269
  k814R Apol/AdualR            spread=  1.0075e-41   value(member0)=184116468879.8762731434362
  k814P Apol/AdualP            spread=  1.0182e-41   value(member0)=2702397850577230883.022881
  k815(i) ApedX*AdualR         spread=     0.90379   value(member0)=6.340548030820126304972474e-10
  k815(ii) Apol*AdualR         spread=     0.91637   value(member0)=91966985.55598580780026046
  k815(iii) Aped*AdualR        spread=  7.3558e-43   value(member0)=7.642676800800812572801031e-11
  k815(i)P ApedX*AdualP        spread=     0.90379   value(member0)=4.319864722910798040991151e-17
  k816(i) ApedX/AdualR         spread=     0.13081   value(member0)=0.000001269367814047997414223292
  k816(ii) Apol/AdualR         spread=  1.0075e-41   value(member0)=184116468879.8762731434362
  k816(iii) Aped/AdualR        spread=     0.91637   value(member0)=0.0000001530051960327636500610744
  k816(i)P ApedX/AdualP        spread=     0.13081   value(member0)=18.63134174332494134314944
  k817 Adag*Aant               spread=      0.3273   value(member0)=140054558.6876322530100379
  k818 Adag/Aant               spread=     0.90388   value(member0)=4.272692208737089854259144e-9
  Aant/A                       spread=     0.66689   value(member0)=346192825.3931795122342804
  k804 A*Adag                  spread=     0.71019   value(member0)=0.4045565026616855061115436
  k805 A/Adag                  spread=     0.71145   value(member0)=0.6760523520487375391119259
  k802 Ldag                    spread=  3.3535e-51   value(member0)=64.08205352884792829200635
  k803 sumcos_dag              spread=  3.3338e-51   value(member0)=7.26794774428662125353155
  k801 sum 1/d                 spread=   3.078e-51   value(member0)=32.53589842374369271831386
  A                            spread=     0.16508   value(member0)=0.5229735893532711036557496
  Adag                         spread=     0.71082   value(member0)=0.7735696618293389533338136
  Apol                         spread=     0.71082   value(member0)=4114928508.989517267764969
  AdualR                       spread=     0.71082   value(member0)=0.0223495949820449462928977
  Aped                         spread=     0.71082   value(member0)=3.41960416148065779735275e-9
  ApedX                        spread=      0.6673   value(member0)=2.836985652721648549363897e-8
  Aant                         spread=     0.66772   value(member0)=181049704.5042213471387818
  k908(i) ApedX1/ApedX2        0.8892 value0=0.483225771582
  k908(ii) Apol1/Apol2         0.91637 value0=0.445284140897
  k908(iii) Aped1/Aped2        0.91637 value0=2.24575705298
  k907R AdualR1/AdualR2        0.91637 value0=0.445284140897
  k907R AdualR1*AdualR2        1.839e-52 value0=0.00112176552
  k903a Adag1*Adag2            1.032e-49 value0=1.34388352681
=== family a=1 b=0.5 N=10 tau=3
  J=0.96890879587423662108220 lambda=0.23469606368061578197988 caustic axes=(0.8748165158016,0.1237090793732) closure_err=9.8807e-58 worst tangency/closure=5.3813e-57
  checks: {'chk_polar_two_defs': '4.5413e-58', 'chk_polar_tangent_circle': '1.7424e-59', 'chk_polar_circumcircle': '7.9561e-54', 'chk_dualR_on_circle': '1.4002e-60', 'chk_ant_is_polar_reciprocal_of_inv': '7.9907e-59', 'chk_invped_eq_polar': '4.5413e-58'}
  O_p(f1)=['-4.33012701892219', '-4.69523381860594e-60'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 5.17e-60 Rstar-a/b^2=2.49e-60  O_p spread over members: 9.41e-60
  k813 Apol/Adag               spread=  3.9609e-56   value(member0)=166.6721531585629649728188
  k814R Apol/AdualR            spread=  3.2291e-56   value(member0)=7126.378596370592168122187
  k814P Apol/AdualP            spread=  3.2275e-56   value(member0)=17759.67986951630775904102
  k815(i) ApedX*AdualR         spread=   0.0095558   value(member0)=0.0132797347764584005210954
  k815(ii) Apol*AdualR         spread=   0.0095558   value(member0)=150.308716262272500908272
  k815(iii) Aped*AdualR        spread=   0.0095558   value(member0)=0.0352038746100816194523616
  k815(i)P ApedX*AdualP        spread=   0.0095558   value(member0)=0.005328723173601260297611101
  k816(i) ApedX/AdualR         spread=  1.8635e-56   value(member0)=0.6296136380494462636727001
  k816(ii) Apol/AdualR         spread=  3.2292e-56   value(member0)=7126.378596370592168122187
  k816(iii) Aped/AdualR        spread=  3.2927e-57   value(member0)=1.66907245813242108398339
  k816(i)P ApedX/AdualP        spread=   1.865e-56   value(member0)=1.569062954209933081128634
  k817 Adag*Aant               spread=   0.0095558   value(member0)=111.6909902550130853239755
  k818 Adag/Aant               spread=  1.6066e-56   value(member0)=0.3452302346192237750714344
  Aant/A                       spread=  7.3217e-57   value(member0)=9.084791568597366305974033
  k804 A*Adag                  spread=   0.0095558   value(member0)=12.2942820879992362471408
  k805 A/Adag                  spread=  9.5115e-57   value(member0)=0.3188425022691625962738087
  k802 Ldag                    spread=  7.9049e-58   value(member0)=49.82282019758834649701765
  k803 sumcos_dag              spread=   1.226e-57   value(member0)=3.104764456975801470260161
  k801 sum 1/d                 spread=  6.9819e-58   value(member0)=26.90672638762270986324661
  A                            spread=   0.0047894   value(member0)=1.979883750259247303077443
  Adag                         spread=   0.0047894   value(member0)=6.209597955632200488512492
  Apol                         spread=   0.0047894   value(member0)=1034.967061514229594682225
  AdualR                       spread=   0.0047894   value(member0)=0.1452304347177583396809533
  Aped                         spread=   0.0047894   value(member0)=0.2424001186700090198539921
  ApedX                        spread=   0.0047894   value(member0)=0.09143906235815043381971988
  Aant                         spread=   0.0047894   value(member0)=17.98683120115814355517508
  k908(i) ApedX1/ApedX2        3.2608e-56 value0=1.0
  k908(ii) Apol1/Apol2         5.0944e-56 value0=1.0
  k908(iii) Aped1/Aped2        3.333e-57 value0=1.0
  k907R AdualR1/AdualR2        2.98e-57 value0=1.0
  k907R AdualR1*AdualR2        0.0095558 value0=0.0210918791683
  k903a Adag1*Adag2            0.0095558 value0=38.5591067706
=== family a=1 b=0.5 N=11 tau=3
  J=0.93471969250927012449259 lambda=0.21842522589115612302009 caustic axes=(0.8840671773733,0.1776929208180) closure_err=4.507e-59 worst tangency/closure=2.3824e-58
  checks: {'chk_polar_two_defs': '1.5465e-58', 'chk_polar_tangent_circle': '2.3025e-59', 'chk_polar_circumcircle': '6.5362e-56', 'chk_dualR_on_circle': '1.2057e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.208e-59', 'chk_invped_eq_polar': '1.5465e-58'}
  O_p(f1)=['-4.33012701892219', '-2.23730841858003e-61'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 4.69e-60 Rstar-a/b^2=4.98e-60  O_p spread over members: 9.29e-60
  k813 Apol/Adag               spread=  6.9402e-58   value(member0)=64.27300335863434006564179
  k814R Apol/AdualR            spread=  4.9666e-58   value(member0)=3355.135432035587250900783
  k814P Apol/AdualP            spread=  4.9567e-58   value(member0)=7219.946918447641820391286
  k815(i) ApedX*AdualR         spread=     0.10566   value(member0)=0.0296059996076189600353857
  k815(ii) Apol*AdualR         spread=   0.0017372   value(member0)=107.6368823643423496351424
  k815(iii) Aped*AdualR        spread=  6.6748e-59   value(member0)=0.1072156633262817044593935
  k815(i)P ApedX*AdualP        spread=     0.10566   value(member0)=0.01375801503894040169575072
  k816(i) ApedX/AdualR         spread=     0.10722   value(member0)=0.92284481027723024883716
  k816(ii) Apol/AdualR         spread=  4.9923e-58   value(member0)=3355.135432035587250900783
  k816(iii) Aped/AdualR        spread=   0.0017372   value(member0)=3.3420056675143380385193
  k816(i)P ApedX/AdualP        spread=     0.10722   value(member0)=1.98587826904026306478487
  k817 Adag*Aant               spread=   0.0063174   value(member0)=84.44586812150958146956919
  k818 Adag/Aant               spread=   0.0080436   value(member0)=1.035226957537662915860686
  Aant/A                       spread=   0.0071808   value(member0)=3.809581389336438853184539
  k804 A*Adag                  spread=  0.00086896   value(member0)=22.16670533877701084771639
  k805 A/Adag                  spread=  0.00086898   value(member0)=0.253563752894692539941331
  k802 Ldag                    spread=  2.8571e-59   value(member0)=51.57637460707330017122688
  k803 sumcos_dag              spread=  1.1794e-58   value(member0)=3.134202338654722921328309
  k801 sum 1/d                 spread=  2.5741e-59   value(member0)=28.33388247670229518711757
  A                            spread=   8.9881e-8   value(member0)=2.370795856882476472237087
  Adag                         spread=  0.00086897   value(member0)=9.349900487815743697445088
  Apol                         spread=  0.00086897   value(member0)=600.9461854562781492403408
  AdualR                       spread=  0.00086897   value(member0)=0.1791123481092026550327195
  Aped                         spread=  0.00086897   value(member0)=0.5985944825027563017718678
  ApedX                        spread=     0.10644   value(member0)=0.1652929009091463442712878
  Aant                         spread=   0.0071809   value(member0)=9.031739774295417768088977
  k908(i) ApedX1/ApedX2        0.20134 value0=0.892125041968
  k908(ii) Apol1/Apol2         0.0017372 value0=1.00088314977
  k908(iii) Aped1/Aped2        0.0017372 value0=0.999117629491
  k907R AdualR1/AdualR2        0.0017372 value0=1.00088314977
  k907R AdualR1*AdualR2        5.7941e-59 value0=0.0320529257111
  k903a Adag1*Adag2            2.4578e-58 value0=87.3435017382
=== family a=1 b=0.5 N=12 tau=5
  J=0.99999671275578259915592 lambda=0.24999835638059279321417 caustic axes=(0.8660263527280,0.0012820372097) closure_err=1.2609e-54 worst tangency/closure=7.8189e-54
  checks: {'chk_polar_two_defs': '3.4372e-50', 'chk_polar_tangent_circle': '6.5394e-56', 'chk_polar_circumcircle': '1.009e-42', 'chk_dualR_on_circle': '2.1035e-57', 'chk_ant_is_polar_reciprocal_of_inv': '4.1974e-51', 'chk_invped_eq_polar': '3.4372e-50'}
  O_p(f1)=['-4.33012701892219', '7.90969787632857e-58'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 7.91e-58 Rstar-a/b^2=3.11e-60  O_p spread over members: 2.18e-56
  k813 Apol/Adag               spread=  7.4594e-49   value(member0)=1968680.512290654712731135
  k814R Apol/AdualR            spread=  7.4592e-49   value(member0)=68142103.90433957375073453
  k814P Apol/AdualP            spread=   7.538e-49   value(member0)=370298228771.4951873558562
  k815(i) ApedX*AdualR         spread=      0.3029   value(member0)=0.00001704824849985450422958102
  k815(ii) Apol*AdualR         spread=      0.3029   value(member0)=358581.3791655422674623874
  k815(iii) Aped*AdualR        spread=      0.3029   value(member0)=0.0000009687021295103706279971608
  k815(i)P ApedX*AdualP        spread=      0.3029   value(member0)=3.137210578938401051187885e-9
  k816(i) ApedX/AdualR         spread=  4.0233e-51   value(member0)=0.003239720711007071511474383
  k816(ii) Apol/AdualR         spread=  7.4592e-49   value(member0)=68142103.90433957375073453
  k816(iii) Aped/AdualR        spread=  1.5685e-50   value(member0)=0.0001840848549220869093280712
  k816(i)P ApedX/AdualP        spread=   3.857e-51   value(member0)=17.60530967292085728156001
  k817 Adag*Aant               spread=  1.8445e-49   value(member0)=249658.8203710688535342375
  k818 Adag/Aant               spread=      0.3029   value(member0)=0.00002525258681984265929647437
  Aant/A                       spread=  1.8447e-49   value(member0)=95063.4619201165928442167
  k804 A*Adag                  spread=  2.4389e-53   value(member0)=2.626233205990975902123708
  k805 A/Adag                  spread=      0.3029   value(member0)=0.4165628165962163341979341
  k802 Ldag                    spread=   6.907e-55   value(member0)=80.16436918207418904555615
  k803 sumcos_dag              spread=  7.3031e-55   value(member0)=8.531900300187686749409613
  k801 sum 1/d                 spread=  6.2825e-55   value(member0)=41.07192798736521166251459
  A                            spread=     0.16508   value(member0)=1.045940295297065284263368
  Adag                         spread=     0.16508   value(member0)=2.510882521497156653787043
  Apol                         spread=     0.16508   value(member0)=4943125.488722673205709066
  AdualR                       spread=     0.16508   value(member0)=0.07254142748016728510748727
  Aped                         spread=     0.16508   value(member0)=0.00001335377815352768323802203
  ApedX                        spread=     0.16508   value(member0)=0.0002350139650135154728441625
  Aant                         spread=     0.16508   value(member0)=99430.70543268806989223419
  k908(i) ApedX1/ApedX2        7.1021e-51 value0=1.0
  k908(ii) Apol1/Apol2         1.2065e-48 value0=1.0
  k908(iii) Aped1/Aped2        3.1355e-50 value0=1.0
  k907R AdualR1/AdualR2        7.3646e-54 value0=1.0
  k907R AdualR1*AdualR2        0.3029 value0=0.00526225870086
  k903a Adag1*Adag2            0.3029 value0=6.30453103676
=== family a=1 b=0.5 N=13 tau=5
  J=0.99973523964148447930095 lambda=0.24986763734525409996724 caustic axes=(0.8661018200273,0.0115048969897) closure_err=4.4778e-56 worst tangency/closure=2.6387e-55
  checks: {'chk_polar_two_defs': '5.6402e-54', 'chk_polar_tangent_circle': '7.7477e-58', 'chk_polar_circumcircle': '5.4307e-48', 'chk_dualR_on_circle': '4.3094e-59', 'chk_ant_is_polar_reciprocal_of_inv': '8.4488e-55', 'chk_invped_eq_polar': '5.6402e-54'}
  O_p(f1)=['-4.33012701892219', '-4.40576435759359e-60'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 6.79e-60 Rstar-a/b^2=5.6e-60  O_p spread over members: 6.5e-58
  k813 Apol/Adag               spread=  2.3264e-52   value(member0)=24393.65632209182770367737
  k814R Apol/AdualR            spread=  2.3212e-52   value(member0)=845968.1213348981184486409
  k814P Apol/AdualP            spread=  2.3455e-52   value(member0)=58709297.60338196438552415
  k815(i) ApedX*AdualR         spread=    0.048833   value(member0)=0.002989537645126644539847704
  k815(ii) Apol*AdualR         spread=    0.051379   value(member0)=10617.20410764704727838054
  k815(iii) Aped*AdualR        spread=  5.0766e-54   value(member0)=0.0001814795088662078553919437
  k815(i)P ApedX*AdualP        spread=    0.048833   value(member0)=0.00004307756434752603874374589
  k816(i) ApedX/AdualR         spread=   0.0026768   value(member0)=0.23820334616023728608913
  k816(ii) Apol/AdualR         spread=  2.3212e-52   value(member0)=845968.1213348981184486409
  k816(iii) Aped/AdualR        spread=    0.051379   value(member0)=0.01446010433817964791251055
  k816(i)P ApedX/AdualP        spread=   0.0026768   value(member0)=16.53106161704474194642004
  k817 Adag*Aant               spread=    0.087645   value(member0)=7314.398197858592920653622
  k818 Adag/Aant               spread=     0.03823   value(member0)=0.002063629667443056977782242
  Aant/A                       spread=    0.063296   value(member0)=1215.514099568764483464664
  k804 A*Adag                  spread=    0.025995   value(member0)=6.01753463859741946127853
  k805 A/Adag                  spread=    0.026062   value(member0)=0.3986651165702812076618333
  k802 Ldag                    spread=  2.4087e-56   value(member0)=80.26725849452007005726439
  k803 sumcos_dag              spread=  2.7346e-56   value(member0)=7.582429352978511116240667
  k801 sum 1/d                 spread=  2.1654e-56   value(member0)=41.61825522262808066412007
  A                            spread=    0.000105   value(member0)=1.548864470559688843325414
  Adag                         spread=    0.026028   value(member0)=3.885126654382456986642916
  Apol                         spread=    0.026028   value(member0)=94772.44437480409313728272
  AdualR                       spread=    0.026028   value(member0)=0.1120283873407163495278344
  Aped                         spread=    0.026028   value(member0)=0.001619942169784762435762645
  ApedX                        spread=    0.023414   value(member0)=0.0266855367294938012468539
  Aant                         spread=    0.063264   value(member0)=1882.666602286411310669695
  k908(i) ApedX1/ApedX2        0.046267 value0=1.02240262515
  k908(ii) Apol1/Apol2         0.051379 value0=1.02497555823
  k908(iii) Aped1/Aped2        0.051379 value0=0.975633020684
  k907R AdualR1/AdualR2        0.051379 value0=1.02497555823
  k907R AdualR1*AdualR2        8.627e-56 value0=0.0122445452181
  k903a Adag1*Adag2            6.0249e-55 value0=14.7264088392
=== family a=1 b=0.5 N=14 tau=3
  J=0.81074386690810170660004 lambda=0.16432640443227543337122 caustic axes=(0.9141518449184,0.2927005219806) closure_err=3.3459e-58 worst tangency/closure=1.4197e-57
  checks: {'chk_polar_two_defs': '2.2848e-59', 'chk_polar_tangent_circle': '2.2403e-59', 'chk_polar_circumcircle': '5.2443e-56', 'chk_dualR_on_circle': '1.2835e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.8447e-60', 'chk_invped_eq_polar': '2.2848e-59'}
  O_p(f1)=['-4.33012701892219', '-1.83012314673795e-61'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 7.43e-61 Rstar-a/b^2=-3.11e-61  O_p spread over members: 6.75e-60
  k813 Apol/Adag               spread=  1.6537e-57   value(member0)=12.27837535684166018175757
  k814R Apol/AdualR            spread=  8.9562e-58   value(member0)=1115.287259952391479360779
  k814P Apol/AdualP            spread=   9.175e-58   value(member0)=2033.437290561390803866393
  k815(i) ApedX*AdualR         spread=   1.5229e-5   value(member0)=0.268849408393639178432162
  k815(ii) Apol*AdualR         spread=   1.5229e-5   value(member0)=78.83005521387953667510069
  k815(iii) Aped*AdualR        spread=   1.5229e-5   value(member0)=0.5786098444444274514866001
  k815(i)P ApedX*AdualP        spread=   1.5229e-5   value(member0)=0.147456880730451432473242
  k816(i) ApedX/AdualR         spread=  1.5296e-57   value(member0)=3.80368019803657322981176
  k816(ii) Apol/AdualR         spread=  8.9547e-58   value(member0)=1115.287259952391479360779
  k816(iii) Aped/AdualR        spread=  5.8017e-58   value(member0)=8.186169427904760836864061
  k816(i)P ApedX/AdualP        spread=  1.5225e-57   value(member0)=6.935025113070573548531829
  k817 Adag*Aant               spread=   1.5229e-5   value(member0)=53.58418898212752910750717
  k818 Adag/Aant               spread=  1.5563e-57   value(member0)=10.88328741051663626401348
  Aant/A                       spread=  1.2311e-57   value(member0)=0.6987824497103675772332299
  k804 A*Adag                  spread=   1.5229e-5   value(member0)=76.68221920046387260823458
  k805 A/Adag                  spread=  1.0789e-57   value(member0)=0.13149157056884602523849
  k802 Ldag                    spread=  1.6423e-58   value(member0)=58.10997980619327582619678
  k803 sumcos_dag              spread=  9.1281e-58   value(member0)=1.641287443515741568903263
  k801 sum 1/d                 spread=  1.6166e-58   value(member0)=33.7522812927978817988067
  A                            spread=   7.6147e-6   value(member0)=3.17538429758879971321477
  Adag                         spread=   7.6147e-6   value(member0)=24.14895710692146613876243
  Apol                         spread=   7.6147e-6   value(member0)=296.5099598350508024934363
  AdualR                       spread=   7.6147e-6   value(member0)=0.2658597210620947920724555
  Aped                         spread=   7.6147e-6   value(member0)=2.176372720669807819156044
  ApedX                        spread=   7.6147e-6   value(member0)=1.011245356459416837681021
  Aant                         spread=   7.6147e-6   value(member0)=2.218902818240936308833312
  k908(i) ApedX1/ApedX2        3.541e-57 value0=1.0
  k908(ii) Apol1/Apol2         1.2835e-57 value0=1.0
  k908(iii) Aped1/Aped2        6.447e-58 value0=1.0
  k907R AdualR1/AdualR2        4.8944e-58 value0=1.0
  k907R AdualR1*AdualR2        1.5229e-5 value0=0.0706813912832
  k903a Adag1*Adag2            1.5229e-5 value0=583.172129352
=== family a=1 b=0.5 N=14 tau=5
  J=0.99763796282984623190059 lambda=0.24882037621982141295550 caustic axes=(0.8667061923052,0.0343456515468) closure_err=7.3739e-57 worst tangency/closure=4.4081e-56
  checks: {'chk_polar_two_defs': '9.5344e-56', 'chk_polar_tangent_circle': '1.0859e-58', 'chk_polar_circumcircle': '1.136e-50', 'chk_dualR_on_circle': '8.1288e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.527e-56', 'chk_invped_eq_polar': '9.5344e-56'}
  O_p(f1)=['-4.33012701892219', '-4.08042070251669e-60'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 7.24e-60 Rstar-a/b^2=6.85e-60  O_p spread over members: 1.11e-58
  k813 Apol/Adag               spread=   3.363e-54   value(member0)=2690.611146777603775940257
  k814R Apol/AdualR            spread=  3.2979e-54   value(member0)=94753.52575317187923082529
  k814P Apol/AdualP            spread=  3.3293e-54   value(member0)=901127.8351057843309338816
  k815(i) ApedX*AdualR         spread=   0.0085791   value(member0)=0.02423944231153995939588955
  k815(ii) Apol*AdualR         spread=   0.0085791   value(member0)=2050.349250366351527151976
  k815(iii) Aped*AdualR        spread=   0.0085791   value(member0)=0.002853086124831332427652445
  k815(i)P ApedX*AdualP        spread=   0.0085791   value(member0)=0.002548775580813575832878536
  k816(i) ApedX/AdualR         spread=  3.5749e-56   value(member0)=1.120186046791122916971766
  k816(ii) Apol/AdualR         spread=   3.298e-54   value(member0)=94753.52575317187923082529
  k816(iii) Aped/AdualR        spread=  5.0787e-56   value(member0)=0.1318506930255512876489345
  k816(i)P ApedX/AdualP        spread=  1.4152e-56   value(member0)=10.65322708824690539949059
  k817 Adag*Aant               spread=   0.0085791   value(member0)=1398.292350310759668387169
  k818 Adag/Aant               spread=  7.7741e-55   value(member0)=0.01919213840047589599326473
  Aant/A                       spread=  6.9209e-55   value(member0)=131.3324857047598761590755
  k804 A*Adag                  spread=   0.0085791   value(member0)=10.64696478412942605672981
  k805 A/Adag                  spread=   8.532e-56   value(member0)=0.3967386114940550097622598
  k802 Ldag                    spread=  4.0001e-57   value(member0)=80.5163205379229235883006
  k803 sumcos_dag              spread=  4.3914e-57   value(member0)=6.062602049624867836602901
  k801 sum 1/d                 spread=  3.5599e-57   value(member0)=42.23788921466481635531282
  A                            spread=   0.0042988   value(member0)=2.055252302049947742214765
  Adag                         spread=   0.0042988   value(member0)=5.18036874281076870638458
  Apol                         spread=   0.0042988   value(member0)=13938.35788382493594539889
  AdualR                       spread=   0.0042988   value(member0)=0.1471012057127420262371533
  Aped                         spread=   0.0042988   value(member0)=0.01939539591811922031026421
  ApedX                        spread=   0.0042988   value(member0)=0.1647807181055642371421534
  Aant                         spread=   0.0042988   value(member0)=269.9213935786495889735804
  k908(i) ApedX1/ApedX2        8.9652e-56 value0=1.0
  k908(ii) Apol1/Apol2         5.1161e-54 value0=1.0
  k908(iii) Aped1/Aped2        9.9632e-56 value0=1.0
  k907R AdualR1/AdualR2        3.549e-56 value0=1.0
  k907R AdualR1*AdualR2        0.0085791 value0=0.0216387647221
  k903a Adag1*Adag2            0.0085791 value0=26.8362203115
=== family a=1 b=0.5 N=15 tau=4
  J=0.92501765736168957636051 lambda=0.21391441660772703452586 caustic axes=(0.8866146758272,0.1899620577701) closure_err=6.4931e-58 worst tangency/closure=3.2025e-57
  checks: {'chk_polar_two_defs': '1.0047e-58', 'chk_polar_tangent_circle': '4.4806e-59', 'chk_polar_circumcircle': '7.9838e-55', 'chk_dualR_on_circle': '3.1115e-60', 'chk_ant_is_polar_reciprocal_of_inv': '9.672e-60', 'chk_invped_eq_polar': '1.0047e-58'}
  O_p(f1)=['-4.33012701892219', '-5.25918202905748e-61'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.53e-60 Rstar-a/b^2=1.87e-60  O_p spread over members: 5.05e-60
  k813 Apol/Adag               spread=  7.1603e-57   value(member0)=52.96382344820756095946846
  k814R Apol/AdualR            spread=  4.8925e-57   value(member0)=2911.732556641515975164423
  k814P Apol/AdualP            spread=  4.8935e-57   value(member0)=6129.719211848536004640711
  k815(i) ApedX*AdualR         spread=   0.0049154   value(member0)=0.06962708378231316212795086
  k815(ii) Apol*AdualR         spread=   3.2585e-5   value(member0)=181.1300581117336221187236
  k815(iii) Aped*AdualR        spread=  7.5756e-58   value(member0)=0.2358600338466767402560566
  k815(i)P ApedX*AdualP        spread=   0.0049154   value(member0)=0.03307418164947704384368382
  k816(i) ApedX/AdualR         spread=   0.0049478   value(member0)=1.119281077842455108745341
  k816(ii) Apol/AdualR         spread=   4.893e-57   value(member0)=2911.732556641515975164423
  k816(iii) Aped/AdualR        spread=   3.2585e-5   value(member0)=3.791537122669592368338467
  k816(i)P ApedX/AdualP        spread=   0.0049478   value(member0)=2.356287396883382512883684
  k817 Adag*Aant               spread=  0.00022516   value(member0)=143.9639511189856918520625
  k818 Adag/Aant               spread=  0.00019258   value(member0)=1.305959151437039900578396
  Aant/A                       spread=  0.00020887   value(member0)=3.205155834165767893319564
  k804 A*Adag                  spread=   1.6293e-5   value(member0)=44.91636555838676284401755
  k805 A/Adag                  spread=   1.6293e-5   value(member0)=0.2389028096007741056862712
  k802 Ldag                    spread=  3.3497e-58   value(member0)=69.43547805325313450235764
  k803 sumcos_dag              spread=  1.7304e-57   value(member0)=4.120891195961435346078763
  k801 sum 1/d                 spread=  3.0097e-58   value(member0)=38.30893280386346454704871
  A                            spread=  6.7788e-11   value(member0)=3.275766464349075129421101
  Adag                         spread=   1.6293e-5   value(member0)=13.71171176187984360723784
  Apol                         spread=   1.6293e-5   value(member0)=726.2246809289150694528471
  AdualR                       spread=   1.6293e-5   value(member0)=0.2494132502905986276899483
  Aped                         spread=   1.6293e-5   value(member0)=0.9456595973624871934457727
  ApedX                        spread=   0.0049316   value(member0)=0.2791635316134512618716225
  Aant                         spread=  0.00020887   value(member0)=10.49934199457300806937037
  k908(i) ApedX1/ApedX2        0.0098506 value0=0.997462786286
  k908(ii) Apol1/Apol2         3.2585e-5 value0=1.00000836235
  k908(iii) Aped1/Aped2        3.2585e-5 value0=0.999991637725
  k907R AdualR1/AdualR2        3.2585e-5 value0=1.00000836235
  k907R AdualR1*AdualR2        7.4263e-58 value0=0.0622064492287
  k903a Adag1*Adag2            2.8632e-57 value0=188.009467241
=== family a=1 b=0.5 N=16 tau=5
  J=0.97958883490309034318569 lambda=0.23989857136669849734286 caustic axes=(0.8718379600781,0.1005058636762) closure_err=3.44e-58 worst tangency/closure=2.0575e-57
  checks: {'chk_polar_two_defs': '1.7795e-57', 'chk_polar_tangent_circle': '4.5428e-59', 'chk_polar_circumcircle': '6.6894e-54', 'chk_dualR_on_circle': '2.6253e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.184e-58', 'chk_invped_eq_polar': '1.7795e-57'}
  O_p(f1)=['-4.33012701892219', '6.9322898015902e-60'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 7.3e-60 Rstar-a/b^2=-2.8e-60  O_p spread over members: 1.13e-59
  k813 Apol/Adag               spread=  1.3514e-56   value(member0)=272.9898634513523337755314
  k814R Apol/AdualR            spread=  1.1695e-56   value(member0)=10895.5405911168087198858
  k814P Apol/AdualP            spread=  1.1725e-56   value(member0)=30559.301844703500372985
  k815(i) ApedX*AdualR         spread=  0.00023133   value(member0)=0.03214585986248125043307343
  k815(ii) Apol*AdualR         spread=  0.00023133   value(member0)=524.5857091184145573038419
  k815(iii) Aped*AdualR        spread=  0.00023133   value(member0)=0.05352812795823877384433965
  k815(i)P ApedX*AdualP        spread=  0.00023133   value(member0)=0.01146120820259253873564278
  k816(i) ApedX/AdualR         spread=  4.1183e-57   value(member0)=0.6676631003856722073796955
  k816(ii) Apol/AdualR         spread=  1.1697e-56   value(member0)=10895.5405911168087198858
  k816(iii) Aped/AdualR        spread=  8.9558e-58   value(member0)=1.111768545726501072542975
  k816(i)P ApedX/AdualP        spread=   4.088e-57   value(member0)=1.872630187059397785812683
  k817 Adag*Aant               spread=   1.681e-57   value(member0)=379.1876520581953532109578
  k818 Adag/Aant               spread=  0.00023133   value(member0)=0.2022637287453562144888227
  Aant/A                       spread=  2.4343e-57   value(member0)=14.34310908358929787930496
  k804 A*Adag                  spread=  2.0507e-57   value(member0)=26.43692171957639229970431
  k805 A/Adag                  spread=  0.00023133   value(member0)=0.3446979411453597938161419
  k802 Ldag                    spread=  1.7447e-58   value(member0)=82.1233196790093969742154
  k803 sumcos_dag              spread=  1.8614e-58   value(member0)=5.054923847042451676274093
  k801 sum 1/d                 spread=  1.5396e-58   value(member0)=44.04244858855397609917372
  A                            spread=  0.00011567   value(member0)=3.018733589927906723329342
  Adag                         spread=  0.00011567   value(member0)=8.757620019131187334328509
  Apol                         spread=  0.00011567   value(member0)=2390.741493181452443379851
  AdualR                       spread=  0.00011567   value(member0)=0.2194238526476269105792065
  Aped                         spread=  0.00011567   value(member0)=0.2439485375557582323675022
  ApedX                        spread=  0.00011567   value(member0)=0.1465012097572834723631031
  Aant                         spread=  0.00011567   value(member0)=43.29802517463108954129302
  k908(i) ApedX1/ApedX2        7.1766e-57 value0=1.0
  k908(ii) Apol1/Apol2         1.8859e-56 value0=1.0
  k908(iii) Aped1/Aped2        7.9655e-58 value0=1.0
  k907R AdualR1/AdualR2        9.3057e-58 value0=1.0
  k907R AdualR1*AdualR2        0.00023133 value0=0.0481468271107
  k903a Adag1*Adag2            0.00023133 value0=76.6959083995
=== family a=1 b=0.5 N=16 tau=7
  J=0.99999998305465484335609 lambda=0.24999999152732749346422 caustic axes=(0.8660254086761,0.0000920471211) closure_err=5.6928e-52 worst tangency/closure=3.421e-51
  checks: {'chk_polar_two_defs': '1.6431e-45', 'chk_polar_tangent_circle': '8.9793e-54', 'chk_polar_circumcircle': '1.6961e-35', 'chk_dualR_on_circle': '4.4172e-55', 'chk_ant_is_polar_reciprocal_of_inv': '1.4302e-46', 'chk_invped_eq_polar': '1.6431e-45'}
  O_p(f1)=['-4.33012701892219', '1.26891782451904e-55'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.27e-55 Rstar-a/b^2=-8.71e-60  O_p spread over members: 1.07e-53
  k813 Apol/Adag               spread=  6.4635e-44   value(member0)=381915930.6271497737682559
  k814R Apol/AdualR            spread=  6.4635e-44   value(member0)=13218969373.22323362926118
  k814P Apol/AdualP            spread=  6.5318e-44   value(member0)=13930283494866232.52165926
  k815(i) ApedX*AdualR         spread=      0.3029   value(member0)=8.798175906760450759710689e-8
  k815(ii) Apol*AdualR         spread=      0.3029   value(member0)=69561499.29902973142208729
  k815(iii) Aped*AdualR        spread=      0.3029   value(member0)=4.993554268222303501274262e-9
  k815(i)P ApedX*AdualP        spread=      0.3029   value(member0)=8.348919668042532174590034e-14
  k816(i) ApedX/AdualR         spread=  3.4832e-46   value(member0)=0.00001671942367885667238953186
  k816(ii) Apol/AdualR         spread=  6.4635e-44   value(member0)=13218969373.22323362926118
  k816(iii) Aped/AdualR        spread=  1.3592e-45   value(member0)=0.00000094893930694905985692206
  k816(i)P ApedX/AdualP        spread=   3.345e-46   value(member0)=17.61909761202981747837706
  k817 Adag*Aant               spread=  1.5985e-44   value(member0)=48431153.13924833296546955
  k818 Adag/Aant               spread=      0.3029   value(member0)=0.0000001301685815383461468677575
  Aant/A                       spread=  1.5985e-44   value(member0)=18441641.68362616298725052
  k804 A*Adag                  spread=  1.0883e-50   value(member0)=2.626184478047258101453512
  k805 A/Adag                  spread=      0.3029   value(member0)=0.4165760025107302538266439
  k802 Ldag                    spread=   2.205e-52   value(member0)=112.1641087964977650792995
  k803 sumcos_dag              spread=  2.2247e-52   value(member0)=12.53586461960741411446793
  k801 sum 1/d                 spread=  2.0195e-52   value(member0)=57.07179771725900138302745
  A                            spread=     0.16508   value(member0)=1.045947145758644638041792
  Adag                         spread=     0.16508   value(member0)=2.510819489011979050837929
  Apol                         spread=     0.16508   value(member0)=958921961.7827946348480757
  AdualR                       spread=     0.16508   value(member0)=0.07254135588854737599228634
  Aped                         spread=     0.16508   value(member0)=6.883734398202324916275827e-8
  ApedX                        spread=     0.16508   value(member0)=0.000001212849663339347903879124
  Aant                         spread=     0.16508   value(member0)=19288982.48209243100379035
  k908(i) ApedX1/ApedX2        6.1173e-46 value0=1.0
  k908(ii) Apol1/Apol2         1.0415e-43 value0=1.0
  k908(iii) Aped1/Aped2        2.7114e-45 value0=1.0
  k907R AdualR1/AdualR2        3.27e-51 value0=1.0
  k907R AdualR1*AdualR2        0.3029 value0=0.00526224831415
  k903a Adag1*Adag2            0.3029 value0=6.3042145064
=== family a=1 b=0.8 N=3 tau=1
  J=0.94009199689734490425010 lambda=0.56561469608348002629059 caustic axes=(0.6590791332734,0.2727366933812) closure_err=2.1584e-58 worst tangency/closure=5.3018e-58
  checks: {'chk_polar_two_defs': '1.8376e-59', 'chk_polar_tangent_circle': '1.1668e-61', 'chk_polar_circumcircle': '2.4892e-60', 'chk_dualR_on_circle': '3.8894e-61', 'chk_ant_is_polar_reciprocal_of_inv': '1.0579e-59', 'chk_invped_eq_polar': '1.8376e-59'}
  O_p(f1)=['-1.5375', '4.29201873224491e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 6.53e-61 Rstar-a/b^2=6.22e-61  O_p spread over members: 1.09e-60
  k813 Apol/Adag               spread=  2.8324e-57   value(member0)=23.3586625876538954760221
  k814R Apol/AdualR            spread=  2.3506e-57   value(member0)=67.59903462518400045869101
  k814P Apol/AdualP            spread=  2.3502e-57   value(member0)=270.396138500736001834764
  k815(i) ApedX*AdualR         spread=     0.24456   value(member0)=0.06593806357331579359355767
  k815(ii) Apol*AdualR         spread=     0.42885   value(member0)=11.25913989299433075869511
  k815(iii) Aped*AdualR        spread=  5.0772e-58   value(member0)=0.05622823423824635535003344
  k815(i)P ApedX*AdualP        spread=     0.24456   value(member0)=0.01648451589332894839838942
  k816(i) ApedX/AdualR         spread=     0.24395   value(member0)=0.3958872067469037327145956
  k816(ii) Apol/AdualR         spread=  2.3496e-57   value(member0)=67.59903462518400045869101
  k816(iii) Aped/AdualR        spread=     0.42885   value(member0)=0.337590116945719503310669
  k816(i)P ApedX/AdualP        spread=     0.24395   value(member0)=1.583548826987614930858383
  k817 Adag*Aant               spread=    0.019178   value(member0)=7.848090786347353633970987
  k818 Adag/Aant               spread=     0.42931   value(member0)=0.1777402325230333703619184
  Aant/A                       spread=     0.24456   value(member0)=6.597752190621740627389275
  k804 A*Adag                  spread=     0.24395   value(member0)=1.18950978448431041698158
  k805 A/Adag                  spread=     0.24456   value(member0)=0.852743183392500025847978
  k802 Ldag                    spread=  1.6433e-58   value(member0)=6.941387842618461513276623
  k803 sumcos_dag              spread=   1.218e-58   value(member0)=1.176347621251931110056153
  k801 sum 1/d                 spread=  1.2246e-58   value(member0)=3.933232012466331801034254
  A                            spread=   0.0096356   value(member0)=1.007147635800073503649406
  Adag                         spread=     0.24426   value(member0)=1.181067940986992687907296
  Apol                         spread=     0.24426   value(member0)=27.58816752661028493614886
  AdualR                       spread=     0.24426   value(member0)=0.4081148152422330783092258
  Aped                         spread=     0.24426   value(member0)=0.1377755282049061733700588
  ApedX                        spread=   0.0096356   value(member0)=0.16156743423827634545317
  Aant                         spread=     0.24487   value(member0)=6.644910520379441963819805
  k908(i) ApedX1/ApedX2        2.014e-57 value0=1.0
  k908(ii) Apol1/Apol2         0.42885 value0=1.10796247905
  k908(iii) Aped1/Aped2        0.42885 value0=0.902557639731
  k907R AdualR1/AdualR2        0.42885 value0=1.10796247905
  k907R AdualR1*AdualR2        2.5873e-60 value0=0.150327926775
  k903a Adag1*Adag2            4.7525e-58 value0=1.25899703971
=== family a=1 b=0.8 N=4 tau=1
  J=0.78086880944303032762051 lambda=0.39024390243902439024390 caustic axes=(0.7808688094430,0.4997560380435) closure_err=2.0802e-58 worst tangency/closure=3.757e-58
  checks: {'chk_polar_two_defs': '1.6756e-60', 'chk_polar_tangent_circle': '1.2446e-60', 'chk_polar_circumcircle': '2.8433e-57', 'chk_dualR_on_circle': '4.6673e-61', 'chk_ant_is_polar_reciprocal_of_inv': '1.0436e-60', 'chk_invped_eq_polar': '1.6756e-60'}
  O_p(f1)=['-1.5375', '-1.44488973966274e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.49e-61 Rstar-a/b^2=0.0  O_p spread over members: 7.46e-61
  k813 Apol/Adag               spread=   7.239e-58   value(member0)=4.8828125
  k814R Apol/AdualR            spread=  4.4715e-58   value(member0)=18.6264514923095703125
  k814P Apol/AdualP            spread=  4.4715e-58   value(member0)=37.252902984619140625
  k815(i) ApedX*AdualR         spread=    0.090697   value(member0)=0.330948775288073260325632
  k815(ii) Apol*AdualR         spread=    0.046426   value(member0)=8.143653666901052794931757
  k815(iii) Aped*AdualR        spread=    0.046426   value(member0)=0.5079857101382771169243523
  k815(i)P ApedX*AdualP        spread=    0.090697   value(member0)=0.165474387644036630162816
  k816(i) ApedX/AdualR         spread=    0.046426   value(member0)=0.7569576950941638900702481
  k816(ii) Apol/AdualR         spread=  4.4729e-58   value(member0)=18.6264514923095703125
  k816(iii) Aped/AdualR        spread=  3.2082e-58   value(member0)=1.161882807852468768590125
  k816(i)P ApedX/AdualP        spread=    0.046426   value(member0)=1.513915390188327780140496
  k817 Adag*Aant               spread=  2.7389e-58   value(member0)=8.0
  k818 Adag/Aant               spread=    0.046426   value(member0)=0.7952786784083059370050544
  Aant/A                       spread=  1.7347e-58   value(member0)=2.0
  k804 A*Adag                  spread=  4.1881e-58   value(member0)=4.0
  k805 A/Adag                  spread=    0.046426   value(member0)=0.628710430161053304019601
  k802 Ldag                    spread=   9.812e-59   value(member0)=8.003905296791060858110272
  k803 sumcos_dag              spread=     0.98011   value(member0)=0.2039776258333246478581411
  k801 sum 1/d                 spread=  8.7304e-59   value(member0)=5.125
  A                            spread=    0.023489   value(member0)=1.585825249087746495159601
  Adag                         spread=    0.023489   value(member0)=2.522346016562051205849415
  Apol                         spread=    0.023489   value(member0)=12.31614265899439065356159
  AdualR                       spread=    0.023489   value(member0)=0.6612178741656423513061889
  Aped                         spread=    0.023489   value(member0)=0.7682576802378169050534802
  ApedX                        spread=    0.068825   value(member0)=0.5005139579834875296545297
  Aant                         spread=    0.023489   value(member0)=3.171650498175492990319203
  k908(i) ApedX1/ApedX2        1.1531e-57 value0=1.0
  k908(ii) Apol1/Apol2         5.7757e-58 value0=1.0
  k908(iii) Aped1/Aped2        3.2507e-58 value0=1.0
  k907R AdualR1/AdualR2        2.8509e-58 value0=1.0
  k907R AdualR1*AdualR2        0.046426 value0=0.437209077116
  k903a Adag1*Adag2            0.046426 value0=6.36222942727
=== family a=1 b=0.8 N=5 tau=1
  J=0.65191867063894238765918 lambda=0.27199869000169333987011 caustic axes=(0.8532299279785,0.6066311152572) closure_err=9.4329e-60 worst tangency/closure=1.7774e-59
  checks: {'chk_polar_two_defs': '9.3345e-61', 'chk_polar_tangent_circle': '1.5558e-60', 'chk_polar_circumcircle': '6.2852e-59', 'chk_dualR_on_circle': '6.223e-61', 'chk_ant_is_polar_reciprocal_of_inv': '6.4145e-61', 'chk_invped_eq_polar': '9.3345e-61'}
  O_p(f1)=['-1.5375', '-2.39021151867119e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 4.65e-61 Rstar-a/b^2=0.0  O_p spread over members: 7.88e-61
  k813 Apol/Adag               spread=  2.4831e-59   value(member0)=2.606348180147010402837832
  k814R Apol/AdualR            spread=  1.4787e-59   value(member0)=11.95197684577386331768661
  k814P Apol/AdualP            spread=   1.627e-59   value(member0)=19.27724079579724638902807
  k815(i) ApedX*AdualR         spread=    0.017316   value(member0)=0.8951615590291589365876142
  k815(ii) Apol*AdualR         spread=    0.005544   value(member0)=8.417309328603414598469154
  k815(iii) Aped*AdualR        spread=  2.8665e-60   value(member0)=1.139764040320820100590786
  k815(i)P ApedX*AdualP        spread=    0.017316   value(member0)=0.5550042321967512604202885
  k816(i) ApedX/AdualR         spread=    0.011837   value(member0)=1.271065349872141659296598
  k816(ii) Apol/AdualR         spread=  1.4683e-59   value(member0)=11.95197684577386331768661
  k816(iii) Aped/AdualR        spread=    0.005544   value(member0)=1.61838336786184384896906
  k816(i)P ApedX/AdualP        spread=    0.011837   value(member0)=2.050090385285804136102386
  k817 Adag*Aant               spread=     0.02309   value(member0)=9.639264590649175302442779
  k818 Adag/Aant               spread=    0.017643   value(member0)=1.536399879265902832762136
  Aant/A                       spread=     0.02037   value(member0)=1.325476486127819272361028
  k804 A*Adag                  spread=   0.0027757   value(member0)=7.272301464063569227976584
  k805 A/Adag                  spread=   0.0027759   value(member0)=0.491047730129588529703135
  k802 Ldag                    spread=  3.8399e-60   value(member0)=8.751242488231635668731844
  k803 sumcos_dag              spread=  7.6342e-60   value(member0)=-0.9170441077245686822614631
  k801 sum 1/d                 spread=  4.3966e-60   value(member0)=6.369415233374996519419872
  A                            spread=   1.0171e-6   value(member0)=1.889721441574524522752565
  Adag                         spread=   0.0027758   value(member0)=3.848345742430828579946057
  Apol                         spread=   0.0027758   value(member0)=10.0301289223610857030884
  AdualR                       spread=   0.0027758   value(member0)=0.8392025061450541713689268
  Aped                         spread=   0.0027758   value(member0)=1.358151378213132478217973
  ApedX                        spread=     0.01458   value(member0)=1.066681227086841391150162
  Aant                         spread=     0.02037   value(member0)=2.504781336138597891165986
  k908(i) ApedX1/ApedX2        0.028954 value0=1.00069466374
  k908(ii) Apol1/Apol2         0.005544 value0=1.00013140775
  k908(iii) Aped1/Aped2        0.005544 value0=0.999868609512
  k907R AdualR1/AdualR2        0.005544 value0=1.00013140775
  k907R AdualR1*AdualR2        4.5292e-60 value0=0.704168313144
  k903a Adag1*Adag2            1.3028e-59 value0=14.807819091
=== family a=1 b=0.8 N=6 tau=1
  J=0.55555555555555555555555 lambda=0.19753086419753086419753 caustic axes=(0.8958064164776,0.6651835354264) closure_err=2.4728e-58 worst tangency/closure=3.9458e-58
  checks: {'chk_polar_two_defs': '8.8007e-61', 'chk_polar_tangent_circle': '1.5558e-60', 'chk_polar_circumcircle': '7.7757e-58', 'chk_dualR_on_circle': '5.4451e-61', 'chk_ant_is_polar_reciprocal_of_inv': '5.9241e-61', 'chk_invped_eq_polar': '8.8007e-61'}
  O_p(f1)=['-1.5375', '-2.09421469554804e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 4.33e-61 Rstar-a/b^2=0.0  O_p spread over members: 1.39e-60
  k813 Apol/Adag               spread=  3.3087e-58   value(member0)=1.860119047619047619047619
  k814R Apol/AdualR            spread=  1.6631e-58   value(member0)=9.579317910330636160714286
  k814P Apol/AdualP            spread=  2.0673e-58   value(member0)=13.68473987190090880102041
  k815(i) ApedX*AdualR         spread=  0.00081143   value(member0)=1.727633881964988263599954
  k815(ii) Apol*AdualR         spread=  0.00081143   value(member0)=8.715468079806833032201416
  k815(iii) Aped*AdualR        spread=  0.00081143   value(member0)=1.706305068607395815901189
  k815(i)P ApedX*AdualP        spread=  0.00081143   value(member0)=1.209343717375491784519967
  k816(i) ApedX/AdualR         spread=  4.1375e-58   value(member0)=1.898871527777777777777778
  k816(ii) Apol/AdualR         spread=  1.6631e-58   value(member0)=9.579317910330636160714286
  k816(iii) Aped/AdualR        spread=  1.9386e-58   value(member0)=1.875428669410150891632373
  k816(i)P ApedX/AdualP        spread=  3.7898e-58   value(member0)=2.712673611111111111111111
  k817 Adag*Aant               spread=  0.00081143   value(member0)=11.03051428850552305637992
  k818 Adag/Aant               spread=  2.9643e-58   value(member0)=2.1875
  Aant/A                       spread=  5.8225e-59   value(member0)=1.084821428571428571428571
  k804 A*Adag                  spread=  0.00081143   value(member0)=10.16804609310797187090165
  k805 A/Adag                  spread=  2.6157e-58   value(member0)=0.4213991769547325102880658
  k802 Ldag                    spread=  5.8799e-59   value(member0)=9.25
  k803 sumcos_dag              spread=   8.133e-59   value(member0)=-2.088888888888888888888889
  k801 sum 1/d                 spread=  8.4959e-59   value(member0)=7.625
  A                            spread=   0.0004058   value(member0)=2.069977356125782066915288
  Adag                         spread=   0.0004058   value(member0)=4.912153296275049240824366
  Apol                         spread=   0.0004058   value(member0)=9.137189911225910046176276
  AdualR                       spread=   0.0004058   value(member0)=0.9538455657027603764345649
  Aped                         spread=   0.0004058   value(member0)=1.788869320108700551655188
  ApedX                        spread=   0.0004058   value(member0)=1.811230186610059308550877
  Aant                         spread=   0.0004058   value(member0)=2.245555792582879652948282
  k908(i) ApedX1/ApedX2        9.8635e-58 value0=1.0
  k908(ii) Apol1/Apol2         1.5519e-58 value0=1.0
  k908(iii) Aped1/Aped2        2.1407e-58 value0=1.0
  k907R AdualR1/AdualR2        1.7277e-58 value0=1.0
  k907R AdualR1*AdualR2        0.00081143 value0=0.909821363211
  k903a Adag1*Adag2            0.00081143 value0=24.1292500061
=== family a=1 b=0.8 N=7 tau=1
  J=0.48254765063088498714874 lambda=0.14902543048280744725493 caustic axes=(0.9224828288467,0.7006957752956) closure_err=3.7502e-58 worst tangency/closure=5.8855e-58
  checks: {'chk_polar_two_defs': '7.7788e-61', 'chk_polar_tangent_circle': '2.1781e-60', 'chk_polar_circumcircle': '8.3404e-58', 'chk_dualR_on_circle': '9.3345e-61', 'chk_ant_is_polar_reciprocal_of_inv': '1.0698e-60', 'chk_invped_eq_polar': '7.7788e-61'}
  O_p(f1)=['-1.5375', '-5.11725653814744e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 5.68e-61 Rstar-a/b^2=6.22e-61  O_p spread over members: 1.44e-60
  k813 Apol/Adag               spread=  3.6222e-58   value(member0)=1.515733578837912142289981
  k814R Apol/AdualR            spread=  1.7765e-58   value(member0)=8.420947651447778478954299
  k814P Apol/AdualP            spread=  2.4228e-58   value(member0)=11.10635846510177190437107
  k815(i) ApedX*AdualR         spread=  0.00013734   value(member0)=2.724013911921025366096668
  k815(ii) Apol*AdualR         spread=   0.0001173   value(member0)=8.953857864344279319514594
  k815(iii) Aped*AdualR        spread=  7.7555e-59   value(member0)=2.158443100144793092582844
  k815(i)P ApedX*AdualP        spread=  0.00013734   value(member0)=2.06537350889405470535889
  k816(i) ApedX/AdualR         spread=   2.0042e-5   value(member0)=2.56188772500492635669518
  k816(ii) Apol/AdualR         spread=  1.7765e-58   value(member0)=8.420947651447778478954299
  k816(iii) Aped/AdualR        spread=   0.0001173   value(member0)=2.029978209429512338368623
  k816(i)P ApedX/AdualP        spread=   2.0042e-5   value(member0)=3.378864778521326693118902
  k817 Adag*Aant               spread=   0.0013139   value(member0)=12.10443616515762235100096
  k818 Adag/Aant               spread=    0.001431   value(member0)=2.711320485472731915574067
  Aant/A                       spread=   0.0013724   value(member0)=0.9679682387821322973954171
  k804 A*Adag                  spread=   5.8653e-5   value(member0)=12.50499311876911332508432
  k805 A/Adag                  spread=   5.8653e-5   value(member0)=0.3810290055084303550473875
  k802 Ldag                    spread=  6.6581e-59   value(member0)=9.58961469509624446553889
  k803 sumcos_dag              spread=  9.5527e-59   value(member0)=-3.306062077335601928357752
  k801 sum 1/d                 spread=  1.2313e-58   value(member0)=8.884691770434255358553628
  A                            spread=   4.469e-10   value(member0)=2.182834187915875612587519
  Adag                         spread=   5.8653e-5   value(member0)=5.728787458065524883839864
  Apol                         spread=   5.8653e-5   value(member0)=8.683315516215403562342291
  AdualR                       spread=   5.8653e-5   value(member0)=1.031156572351155427080705
  Aped                         spread=   5.8653e-5   value(member0)=2.093225372382871883560637
  ApedX                        spread=   7.8694e-5   value(member0)=2.641707365264579323289171
  Aant                         spread=   0.0013724   value(member0)=2.112914164430356127171415
  k908(i) ApedX1/ApedX2        0.00015738 value0=0.999961653932
  k908(ii) Apol1/Apol2         0.0001173 value0=0.999971419737
  k908(iii) Aped1/Aped2        0.0001173 value0=1.00002858108
  k907R AdualR1/AdualR2        0.0001173 value0=0.999971419737
  k907R AdualR1*AdualR2        6.8328e-59 value0=1.0633142665
  k903a Adag1*Adag2            2.738e-58 value0=32.8199437423
=== family a=1 b=0.8 N=8 tau=1
  J=0.42584383871862952815949 lambda=0.11605950398375562064612 caustic axes=(0.9401810974574,0.7238373408551) closure_err=4.2819e-58 worst tangency/closure=6.5417e-58
  checks: {'chk_polar_two_defs': '9.8395e-61', 'chk_polar_tangent_circle': '3.7338e-60', 'chk_polar_circumcircle': '7.1394e-58', 'chk_dualR_on_circle': '1.8669e-60', 'chk_ant_is_polar_reciprocal_of_inv': '8.9883e-61', 'chk_invped_eq_polar': '9.8395e-61'}
  O_p(f1)=['-1.5375', '-5.25109211746115e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 5.52e-61 Rstar-a/b^2=7.78e-61  O_p spread over members: 1.71e-60
  k813 Apol/Adag               spread=  3.0149e-58   value(member0)=1.325647679817518018115578
  k814R Apol/AdualR            spread=  1.4482e-58   value(member0)=7.756098211157091636855639
  k814P Apol/AdualP            spread=  2.1221e-58   value(member0)=9.671526626632992219869884
  k815(i) ApedX*AdualR         spread=   1.6827e-5   value(member0)=3.767384447533816362391693
  k815(ii) Apol*AdualR         spread=   1.6827e-5   value(member0)=9.134286436527396897102732
  k815(iii) Aped*AdualR        spread=   1.6827e-5   value(member0)=2.507486249237472744116116
  k815(i)P ApedX*AdualP        spread=   1.6827e-5   value(member0)=3.021260748410997187687821
  k816(i) ApedX/AdualR         spread=  5.2767e-58   value(member0)=3.198958558755991284312312
  k816(ii) Apol/AdualR         spread=  1.4506e-58   value(member0)=7.756098211157091636855639
  k816(iii) Aped/AdualR        spread=  2.0109e-58   value(member0)=2.129154778247295370953584
  k816(i)P ApedX/AdualP        spread=  4.6771e-58   value(member0)=3.988966105921507110695391
  k817 Adag*Aant               spread=  2.2572e-58   value(member0)=12.9083240034712026693638
  k818 Adag/Aant               spread=   1.6827e-5   value(member0)=3.123142757045908949543348
  Aant/A                       spread=  5.5551e-59   value(member0)=0.9003904610643590572435508
  k804 A*Adag                  spread=  2.4395e-58   value(member0)=14.33636245791871832954738
  k805 A/Adag                  spread=   1.6827e-5   value(member0)=0.3556127131728609995192985
  k802 Ldag                    spread=  5.7368e-59   value(member0)=9.827947547379199872562352
  k803 sumcos_dag              spread=  9.1661e-59   value(member0)=-4.535157985235255740905272
  k801 sum 1/d                 spread=  1.3297e-58   value(member0)=10.14635526223138571901495
  A                            spread=   8.4137e-6   value(member0)=2.257917790950330791648712
  Adag                         spread=   8.4137e-6   value(member0)=6.349373088505898868831067
  Apol                         spread=   8.4137e-6   value(member0)=8.417031703073633316866359
  AdualR                       spread=   8.4137e-6   value(member0)=1.085214688355260070485568
  Aped                         spread=   8.4137e-6   value(member0)=2.310590039135751509428057
  ApedX                        spread=   8.4137e-6   value(member0)=3.47155681540177499279977
  Aant                         spread=   8.4137e-6   value(member0)=2.033007640839187429954083
  k908(i) ApedX1/ApedX2        1.2772e-57 value0=1.0
  k908(ii) Apol1/Apol2         1.2298e-58 value0=1.0
  k908(iii) Aped1/Aped2        2.2628e-58 value0=1.0
  k907R AdualR1/AdualR2        1.7883e-58 value0=1.0
  k907R AdualR1*AdualR2        1.6827e-5 value0=1.17769091982
  k903a Adag1*Adag2            1.6827e-5 value0=40.314538617
=== family a=1 b=0.8 N=9 tau=1
  J=0.38073300665454513196994 lambda=0.09277287830797434095590 caustic axes=(0.9524847094268,0.7397480122933) closure_err=4.1825e-58 worst tangency/closure=6.3681e-58
  checks: {'chk_polar_two_defs': '9.4633e-61', 'chk_polar_tangent_circle': '4.9784e-60', 'chk_polar_circumcircle': '5.7812e-58', 'chk_dualR_on_circle': '2.0225e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.0766e-60', 'chk_invped_eq_polar': '9.4633e-61'}
  O_p(f1)=['-1.5375', '-9.65326010431936e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.07e-60 Rstar-a/b^2=1.09e-60  O_p spread over members: 2.34e-60
  k813 Apol/Adag               spread=  2.2928e-58   value(member0)=1.208479245287754166571056
  k814R Apol/AdualR            spread=  1.0936e-58   value(member0)=7.334735627946553206172254
  k814P Apol/AdualP            spread=  1.6927e-58   value(member0)=8.779176036713734590471005
  k815(i) ApedX*AdualR         spread=   1.1708e-6   value(member0)=4.775043406004011800388906
  k815(ii) Apol*AdualR         spread=   1.0928e-6   value(member0)=9.269372790727619876180727
  k815(iii) Aped*AdualR        spread=  6.0419e-59   value(member0)=2.775786822096085186704104
  k815(i)P ApedX*AdualP        spread=   1.1708e-6   value(member0)=3.989404113614188837476449
  k816(i) ApedX/AdualR         spread=   7.7971e-8   value(member0)=3.778430513663656692816674
  k816(ii) Apol/AdualR         spread=  1.0962e-58   value(member0)=7.334735627946553206172254
  k816(iii) Aped/AdualR        spread=   1.0928e-6   value(member0)=2.196444458462061714894873
  k816(i)P ApedX/AdualP        spread=   7.7971e-8   value(member0)=4.522522460871667600143747
  k817 Adag*Aant               spread=   2.9411e-5   value(member0)=13.52037072685812232796915
  k818 Adag/Aant               spread=   2.8319e-5   value(member0)=3.443244173190056504480097
  Aant/A                       spread=   2.8865e-5   value(member0)=0.8577389684448941673677958
  k804 A*Adag                  spread=    5.464e-7   value(member0)=15.7628033985338801053471
  k805 A/Adag                  spread=    5.464e-7   value(member0)=0.338592268859708217749217
  k802 Ldag                    spread=  4.4431e-59   value(member0)=10.00026640365788227339702
  k803 sumcos_dag              spread=  7.8239e-59   value(member0)=-5.75855786307837258289769
  k801 sum 1/d                 spread=   1.272e-58   value(member0)=11.40912500521270901326159
  A                            spread=  2.2172e-13   value(member0)=2.310230154400012578148178
  Adag                         spread=    5.464e-7   value(member0)=6.823044608136725255827607
  Apol                         spread=    5.464e-7   value(member0)=8.245507798605750108626497
  AdualR                       spread=    5.464e-7   value(member0)=1.124172460584537583875162
  Aped                         spread=    5.464e-7   value(member0)=2.46918237140656807157059
  ApedX                        spread=   6.2437e-7   value(member0)=4.247607527692971200256326
  Aant                         spread=   2.8865e-5   value(member0)=1.981574429505355368937606
  k908(i) ApedX1/ApedX2        1.2487e-6 value0=0.999998596602
  k908(ii) Apol1/Apol2         1.0928e-6 value0=0.999998771858
  k908(iii) Aped1/Aped2        1.0928e-6 value0=1.00000122814
  k907R AdualR1/AdualR2        1.0928e-6 value0=0.999998771858
  k907R AdualR1*AdualR2        5.3181e-59 value0=1.26376527322
  k903a Adag1*Adag2            2.0147e-58 value0=46.5539948995
=== family a=1 b=0.8 N=10 tau=1
  J=0.34408049975023009848797 lambda=0.07577048979735558071549 caustic axes=(0.9613685610641,0.7511521218785) closure_err=4.163e-58 worst tangency/closure=6.29e-58
  checks: {'chk_polar_two_defs': '9.0715e-61', 'chk_polar_tangent_circle': '7.4676e-60', 'chk_polar_circumcircle': '4.7902e-58', 'chk_dualR_on_circle': '2.8781e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.235e-60', 'chk_invped_eq_polar': '9.0715e-61'}
  O_p(f1)=['-1.5375', '9.13395429436663e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.33e-60 Rstar-a/b^2=-1.09e-60  O_p spread over members: 4.86e-60
  k813 Apol/Adag               spread=  1.7805e-58   value(member0)=1.130636714514071367562811
  k814R Apol/AdualR            spread=  8.6869e-59   value(member0)=7.049051895272871451040728
  k814P Apol/AdualP            spread=  1.3934e-58   value(member0)=8.181667281572421889166685
  k815(i) ApedX*AdualR         spread=   4.2187e-7   value(member0)=5.70292092866709581313156
  k815(ii) Apol*AdualR         spread=   4.2187e-7   value(member0)=9.372076618653365447249834
  k815(iii) Aped*AdualR        spread=   4.2187e-7   value(member0)=2.983646891326721264520466
  k815(i)P ApedX*AdualP        spread=   4.2187e-7   value(member0)=4.913446635914300444776026
  k816(i) ApedX/AdualR         spread=   3.701e-58   value(member0)=4.289357334190073306292518
  k816(ii) Apol/AdualR         spread=  8.6693e-59   value(member0)=7.049051895272871451040728
  k816(iii) Aped/AdualR        spread=  1.2881e-58   value(member0)=2.244100494470095243004045
  k816(i)P ApedX/AdualP        spread=  3.2599e-58   value(member0)=4.978555283959520605744175
  k817 Adag*Aant               spread=   4.2187e-7   value(member0)=13.99118706981491286020507
  k818 Adag/Aant               spread=  1.6805e-58   value(member0)=3.693735615629631211073437
  Aant/A                       spread=  3.3598e-59   value(member0)=0.8288679582250435403306018
  k804 A*Adag                  spread=   4.2187e-7   value(member0)=16.87987444921378678003853
  k805 A/Adag                  spread=  1.5051e-58   value(member0)=0.3266245630194696172848304
  k802 Ldag                    spread=  3.4776e-59   value(member0)=10.12826736525608722922984
  k803 sumcos_dag              spread=  6.6712e-59   value(member0)=-6.96811395329074463737763
  k801 sum 1/d                 spread=  1.2178e-58   value(member0)=12.67258188755619822784021
  A                            spread=   2.1093e-7   value(member0)=2.348059116759619298990942
  Adag                         spread=   2.1093e-7   value(member0)=7.188862634986992373793173
  Apol                         spread=   2.1093e-7   value(member0)=8.127992030714662936237528
  AdualR                       spread=   2.1093e-7   value(member0)=1.153061738155926188795263
  Aped                         spread=   2.1093e-7   value(member0)=2.587586416750261447300064
  ApedX                        spread=   2.1093e-7   value(member0)=4.945893823333075890402325
  Aant                         spread=   2.1093e-7   value(member0)=1.946230965900244761753144
  k908(i) ApedX1/ApedX2        9.1828e-58 value0=1.0
  k908(ii) Apol1/Apol2         6.9387e-59 value0=1.0
  k908(iii) Aped1/Aped2        1.45e-58 value0=1.0
  k907R AdualR1/AdualR2        1.1318e-58 value0=1.0
  k907R AdualR1*AdualR2        4.2187e-7 value0=1.329551372
  k903a Adag1*Adag2            4.2187e-7 value0=51.6797459847
=== family a=1 b=0.8 N=11 tau=1
  J=0.31375674959138168745781 lambda=0.06300371066505535532769 caustic axes=(0.9679856865341,0.7596027180934) closure_err=4.1783e-58 worst tangency/closure=6.343e-58
  checks: {'chk_polar_two_defs': '8.0182e-61', 'chk_polar_tangent_circle': '7.1565e-60', 'chk_polar_circumcircle': '4.2099e-58', 'chk_dualR_on_circle': '2.8781e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.1242e-60', 'chk_invped_eq_polar': '8.0182e-61'}
  O_p(f1)=['-1.5375', '1.21447476859339e-60'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.36e-60 Rstar-a/b^2=-9.33e-61  O_p spread over members: 4.47e-60
  k813 Apol/Adag               spread=  1.4545e-58   value(member0)=1.07603975882227201762623
  k814R Apol/AdualR            spread=  7.0361e-59   value(member0)=6.845604790200128046614387
  k814P Apol/AdualP            spread=  1.1692e-58   value(member0)=7.759854034649615320915291
  k815(i) ApedX*AdualR         spread=   7.3767e-8   value(member0)=6.53361933833102592273097
  k815(ii) Apol*AdualR         spread=   7.0506e-8   value(member0)=9.451366862751911818039982
  k815(iii) Aped*AdualR        spread=  4.4993e-59   value(member0)=3.146593757650155730167918
  k815(i)P ApedX*AdualP        spread=   7.3767e-8   value(member0)=5.763842417667669983894587
  k816(i) ApedX/AdualR         spread=   3.2609e-9   value(member0)=4.732286503033935451714472
  k816(ii) Apol/AdualR         spread=  7.0361e-59   value(member0)=6.845604790200128046614387
  k816(iii) Aped/AdualR        spread=   7.0506e-8   value(member0)=2.279071124101083101150891
  k816(i)P ApedX/AdualP        spread=   3.2609e-9   value(member0)=5.364296309692785657772987
  k817 Adag*Aant               spread=   3.4705e-6   value(member0)=14.35780200309512439787353
  k818 Adag/Aant               spread=    3.541e-6   value(member0)=3.891901560226417157054066
  Aant/A                       spread=   3.5058e-6   value(member0)=0.8082893298706194737289341
  k804 A*Adag                  spread=   3.5253e-8   value(member0)=17.76319626215198965762295
  k805 A/Adag                  spread=   3.5253e-8   value(member0)=0.3178859309937768861372581
  k802 Ldag                    spread=  2.8846e-59   value(member0)=10.22563925075685374257571
  k803 sumcos_dag              spread=  5.8259e-59   value(member0)=-8.160798951593174485718312
  k801 sum 1/d                 spread=  1.2172e-58   value(member0)=13.93649714225354247852324
  A                            spread=  1.5298e-16   value(member0)=2.376272328925993049322917
  Adag                         spread=   3.5253e-8   value(member0)=7.475235917164614289225309
  Apol                         spread=   3.5253e-8   value(member0)=8.043651053445396925780354
  AdualR                       spread=   3.5253e-8   value(member0)=1.175009557221348817938467
  Aped                         spread=   3.5253e-8   value(member0)=2.677930352405975377220963
  ApedX                        spread=   3.8514e-8   value(member0)=5.560481868574469674678341
  Aant                         spread=   3.5058e-6   value(member0)=1.920715568337687176942061
  k908(i) ApedX1/ApedX2        7.7028e-8 value0=0.999999961447
  k908(ii) Apol1/Apol2         7.0506e-8 value0=0.999999964711
  k908(iii) Aped1/Aped2        7.0506e-8 value0=1.00000003529
  k907R AdualR1/AdualR2        7.0506e-8 value0=0.999999964711
  k907R AdualR1*AdualR2        3.9664e-59 value0=1.38064750828
  k903a Adag1*Adag2            1.4299e-58 value0=55.8791539892
=== family a=1 b=0.8 N=12 tau=1
  J=0.28827743308173563806607 lambda=0.05318648219148452406994 caustic axes=(0.9730434305869,0.7660375433413) closure_err=3.8409e-58 worst tangency/closure=5.7212e-58
  checks: {'chk_polar_two_defs': '7.0446e-61', 'chk_polar_tangent_circle': '1.0579e-59', 'chk_polar_circumcircle': '3.4071e-58', 'chk_dualR_on_circle': '4.3561e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.4475e-60', 'chk_invped_eq_polar': '7.0446e-61'}
  O_p(f1)=['-1.5375', '-1.31988901384465e-60'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.54e-60 Rstar-a/b^2=1.4e-60  O_p spread over members: 6.01e-60
  k813 Apol/Adag               spread=  1.1201e-58   value(member0)=1.03614098751663222206861
  k814R Apol/AdualR            spread=   5.298e-59   value(member0)=6.695181613915312613748954
  k814P Apol/AdualP            spread=  9.0882e-59   value(member0)=7.449954660004454923861876
  k815(i) ApedX*AdualR         spread=    1.061e-8   value(member0)=7.265508543084474303792965
  k815(ii) Apol*AdualR         spread=    1.061e-8   value(member0)=9.513601787118115649013928
  k815(iii) Aped*AdualR        spread=    1.061e-8   value(member0)=3.276009771304642992365301
  k815(i)P ApedX*AdualP        spread=    1.061e-8   value(member0)=6.529422182198181888079825
  k816(i) ApedX/AdualR         spread=   2.551e-58   value(member0)=5.11308969009718615123904
  k816(ii) Apol/AdualR         spread=  5.2887e-59   value(member0)=6.695181613915312613748954
  k816(iii) Aped/AdualR        spread=  8.2731e-59   value(member0)=2.30548648962212862246626
  k816(i)P ApedX/AdualP        spread=  2.2247e-58   value(member0)=5.689507553400641144927747
  k817 Adag*Aant               spread=  8.5394e-59   value(member0)=14.6477507059427412765906
  k818 Adag/Aant               spread=    1.061e-8   value(member0)=4.050407175275429206902173
  Aant/A                       spread=  2.1382e-59   value(member0)=0.7930715929310761797888267
  k804 A*Adag                  spread=  9.3398e-59   value(member0)=18.46964490533169274846275
  k805 A/Adag                  spread=    1.061e-8   value(member0)=0.3113070257041671197206617
  k802 Ldag                    spread=  2.2473e-59   value(member0)=10.30126955571254404156447
  k803 sumcos_dag              spread=  4.6125e-59   value(member0)=-9.336193222428169124609132
  k801 sum 1/d                 spread=   1.098e-58   value(member0)=15.20073469270020652326125
  A                            spread=   5.3048e-9   value(member0)=2.397859508247080885050705
  Adag                         spread=   5.3048e-9   value(member0)=7.702555067053802814098525
  Apol                         spread=   5.3048e-9   value(member0)=7.980933013578366569801261
  AdualR                       spread=   5.3048e-9   value(member0)=1.19204130280659440107598
  Aped                         spread=   5.3048e-9   value(member0)=2.748235118692164185421672
  ApedX                        spread=   5.3048e-9   value(member0)=6.095014095550415802491062
  Aant                         spread=   5.3048e-9   value(member0)=1.901674259830439437468938
  k908(i) ApedX1/ApedX2        6.4284e-58 value0=1.0
  k908(ii) Apol1/Apol2         4.1772e-59 value0=1.0
  k908(iii) Aped1/Aped2        9.389e-59 value0=1.0
  k907R AdualR1/AdualR2        7.2343e-59 value0=1.0
  k907R AdualR1*AdualR2        1.061e-8 value0=1.4209624676
  k903a Adag1*Adag2            1.061e-8 value0=59.329354561
=== family a=1 b=0.8 N=13 tau=1
  J=0.26658165707364525875310 lambda=0.04548209912840358350247 caustic axes=(0.9769943197744,0.7710498692507) closure_err=4.444e-58 worst tangency/closure=6.7172e-58
  checks: {'chk_polar_two_defs': '9.1048e-61', 'chk_polar_tangent_circle': '4.9784e-60', 'chk_polar_circumcircle': '3.6047e-58', 'chk_dualR_on_circle': '2.1781e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.577e-60', 'chk_invped_eq_polar': '9.1048e-61'}
  O_p(f1)=['-1.5375', '1.8215116873381e-60'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 2.72e-60 Rstar-a/b^2=-2.49e-60  O_p spread over members: 3.96e-60
  k813 Apol/Adag               spread=  1.1335e-58   value(member0)=1.006028328738814154334641
  k814R Apol/AdualR            spread=  5.3713e-59   value(member0)=6.580611377602114712455644
  k814P Apol/AdualP            spread=  9.4013e-59   value(member0)=7.215046927108633792262038
  k815(i) ApedX*AdualR         spread=   1.8365e-9   value(member0)=7.904866561618121035365495
  k815(ii) Apol*AdualR         spread=   1.7726e-9   value(member0)=9.563205393995598899961609
  k815(iii) Aped*AdualR        spread=  3.3783e-59   value(member0)=3.380129623343099166928533
  k815(i)P ApedX*AdualP        spread=   1.8365e-9   value(member0)=7.209773596671090677755898
  k816(i) ApedX/AdualR         spread=  6.3875e-11   value(member0)=5.439478991685311800659341
  k816(ii) Apol/AdualR         spread=  5.3808e-59   value(member0)=6.580611377602114712455644
  k816(iii) Aped/AdualR        spread=   1.7726e-9   value(member0)=2.325927190804387482007469
  k816(i)P ApedX/AdualP        spread=  6.3875e-11   value(member0)=5.963898174812417258862019
  k817 Adag*Aant               spread=   1.4897e-7   value(member0)=14.88035832132831425398545
  k818 Adag/Aant               spread=   1.4719e-7   value(member0)=4.178649242987873070715127
  Aant/A                       spread=   1.4808e-7   value(member0)=0.7814819924398038798783893
  k804 A*Adag                  spread=  8.8629e-10   value(member0)=19.04120435951634660202492
  k805 A/Adag                  spread=  8.8629e-10   value(member0)=0.3062281474259132675369278
  k802 Ldag                    spread=  2.2823e-59   value(member0)=10.36109198556266310881974
  k803 sumcos_dag              spread=  4.7436e-59   value(member0)=-10.49511894459375841144167
  k801 sum 1/d                 spread=   1.282e-58   value(member0)=16.46520819538973667196526
  A                            spread=  1.0466e-19   value(member0)=2.414736576890513372907725
  Adag                         spread=  8.8629e-10   value(member0)=7.885416795249751290015592
  Apol                         spread=  8.8629e-10   value(member0)=7.932952679934083173868852
  AdualR                       spread=  8.8629e-10   value(member0)=1.20550389997726065989049
  Aped                         spread=  8.8629e-10   value(member0)=2.803914299577843197209525
  ApedX                        spread=  9.5017e-10   value(member0)=6.557313138321020785600391
  Aant                         spread=   1.4808e-7   value(member0)=1.887073151325670071963276
  k908(i) ApedX1/ApedX2        1.9003e-9 value0=0.999999999204
  k908(ii) Apol1/Apol2         1.7726e-9 value0=0.999999999257
  k908(iii) Aped1/Aped2        1.7726e-9 value0=1.00000000074
  k907R AdualR1/AdualR2        1.7726e-9 value0=0.999999999257
  k907R AdualR1*AdualR2        2.9226e-59 value0=1.45323965394
  k903a Adag1*Adag2            1.0993e-58 value0=62.179798081
=== family a=1 b=0.8 N=14 tau=1
  J=0.24789345638928496979884 lambda=0.03932874606120085069832 caustic axes=(0.9801383850961,0.7750298406763) closure_err=6.8142e-58 worst tangency/closure=1.0301e-57
  checks: {'chk_polar_two_defs': '1.134e-60', 'chk_polar_tangent_circle': '1.089e-59', 'chk_polar_circumcircle': '5.1993e-58', 'chk_dualR_on_circle': '4.5895e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.7926e-60', 'chk_invped_eq_polar': '1.134e-60'}
  O_p(f1)=['-1.5375', '-8.92776911831774e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.61e-60 Rstar-a/b^2=1.56e-60  O_p spread over members: 4.3e-60
  k813 Apol/Adag               spread=  1.5602e-58   value(member0)=0.982702964965844358543375
  k814R Apol/AdualR            spread=  7.3147e-59   value(member0)=6.491217240447612853208618
  k814P Apol/AdualP            spread=  1.2999e-58   value(member0)=7.032436143709074025416501
  k815(i) ApedX*AdualR         spread=  2.9383e-10   value(member0)=8.461258328114096610819815
  k815(ii) Apol*AdualR         spread=  2.9383e-10   value(member0)=9.603303131903133884495907
  k815(iii) Aped*AdualR        spread=  2.9383e-10   value(member0)=3.464928960622549497721188
  k815(i)P ApedX*AdualP        spread=  2.9383e-10   value(member0)=7.810076737698895880034663
  k816(i) ApedX/AdualR         spread=  3.7713e-58   value(member0)=5.719268170643556009367666
  k816(ii) Apol/AdualR         spread=  7.3052e-59   value(member0)=6.491217240447612853208618
  k816(iii) Aped/AdualR        spread=  1.1346e-58   value(member0)=2.342069837554117559432437
  k816(i)P ApedX/AdualP        spread=  3.2782e-58   value(member0)=6.196124195040059162268906
  k817 Adag*Aant               spread=  2.9383e-10   value(member0)=15.06938893639117196687807
  k818 Adag/Aant               spread=  1.4746e-58   value(member0)=4.283577283574317191773739
  Aant/A                       spread=  2.7694e-59   value(member0)=0.7724392211150669174160218
  k804 A*Adag                  spread=  2.9383e-10   value(member0)=19.50883451339707479333468
  k805 A/Adag                  spread=  1.3513e-58   value(member0)=0.3022240881742896847746058
  k802 Ldag                    spread=  3.0968e-59   value(member0)=10.40917228971872992839358
  k803 sumcos_dag              spread=  6.6192e-59   value(member0)=-11.63892138069255449092603
  k801 sum 1/d                 spread=  2.0133e-58   value(member0)=17.72986003986250600730295
  A                            spread=  1.4692e-10   value(member0)=2.428176213159692273519069
  Adag                         spread=  1.4692e-10   value(member0)=8.034356982688245311669803
  Apol                         spread=  1.4692e-10   value(member0)=7.895386428481773721990034
  AdualR                       spread=  1.4692e-10   value(member0)=1.216318316892030871201607
  Aped                         spread=  1.4692e-10   value(member0)=2.848702442857416426363296
  ApedX                        spread=  1.4692e-10   value(member0)=6.956450635171334450460549
  Aant                         spread=  1.4692e-10   value(member0)=1.875618542823205400147984
  k908(i) ApedX1/ApedX2        9.3003e-58 value0=1.0
  k908(ii) Apol1/Apol2         5.4918e-59 value0=1.0
  k908(iii) Aped1/Aped2        1.2788e-58 value0=1.0
  k907R AdualR1/AdualR2        9.9179e-59 value0=1.0
  k907R AdualR1*AdualR2        2.9383e-10 value0=1.47943024801
  k903a Adag1*Adag2            2.9383e-10 value0=64.5508921253
=== family a=1 b=0.8 N=15 tau=1
  J=0.23163335704022743079877 lambda=0.03433856773998430635547 caustic axes=(0.9826807377068,0.7782425279178) closure_err=6.6244e-58 worst tangency/closure=9.9801e-58
  checks: {'chk_polar_two_defs': '1.1711e-60', 'chk_polar_tangent_circle': '1.3068e-59', 'chk_polar_circumcircle': '4.7046e-58', 'chk_dualR_on_circle': '5.3674e-60', 'chk_ant_is_polar_reciprocal_of_inv': '2.952e-60', 'chk_invped_eq_polar': '1.1711e-60'}
  O_p(f1)=['-1.5375', '8.89908702329417e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.93e-60 Rstar-a/b^2=-1.87e-60  O_p spread over members: 6.66e-60
  k813 Apol/Adag               spread=  1.3537e-58   value(member0)=0.9642436581028586158911611
  k814R Apol/AdualR            spread=   6.252e-59   value(member0)=6.420055217774264986747983
  k814P Apol/AdualP            spread=  1.1177e-58   value(member0)=6.887493697304380945076426
  k815(i) ApedX*AdualR         spread=  4.7307e-11   value(member0)=8.945031019280727884447554
  k815(ii) Apol*AdualR         spread=  4.5894e-11   value(member0)=9.636133487424601934455712
  k815(iii) Aped*AdualR        spread=  4.0052e-59   value(member0)=3.534782091459141238554873
  k815(i)P ApedX*AdualP        spread=  4.7307e-11   value(member0)=8.337952177141277346424595
  k816(i) ApedX/AdualR         spread=  1.4132e-12   value(member0)=5.959609540842325529945849
  k816(ii) Apol/AdualR         spread=  6.2811e-59   value(member0)=6.420055217774264986747983
  k816(iii) Aped/AdualR        spread=  4.5894e-11   value(member0)=2.35504170210830679391206
  k816(i)P ApedX/AdualP        spread=  1.4132e-12   value(member0)=6.393523382370044722580869
  k817 Adag*Aant               spread=   5.9326e-9   value(member0)=15.22483947467124924509604
  k818 Adag/Aant               spread=   5.9785e-9   value(member0)=4.370340414331543494124941
  Aant/A                       spread=   5.9555e-9   value(member0)=0.7652407035133057050154391
  k804 A*Adag                  spread=  2.2947e-11   value(member0)=19.89549092824297957860457
  k805 A/Adag                  spread=  2.2947e-11   value(member0)=0.2990106598485947894384622
  k802 Ldag                    spread=  2.6921e-59   value(member0)=10.4483628941059696717337
  k803 sumcos_dag              spread=   5.741e-59   value(member0)=-12.76910148391411084193842
  k801 sum 1/d                 spread=  1.9801e-58   value(member0)=18.99465021171925446627203
  A                            spread=  7.2094e-23   value(member0)=2.439049788435173573988541
  Adag                         spread=  2.2947e-11   value(member0)=8.15706633893987565727645
  Apol                         spread=  2.2947e-11   value(member0)=7.865399486047078099193135
  AdualR                       spread=  2.2947e-11   value(member0)=1.225129569644712787707416
  Aped                         spread=  2.2947e-11   value(member0)=2.885231226999301794678719
  ApedX                        spread=   2.436e-11   value(member0)=7.301293872022682654184423
  Aant                         spread=   5.9555e-9   value(member0)=1.866460176006111666906488
  k908(i) ApedX1/ApedX2        4.872e-11 value0=0.999999999991
  k908(ii) Apol1/Apol2         4.5894e-11 value0=0.999999999991
  k908(iii) Aped1/Aped2        4.5894e-11 value0=1.00000000001
  k907R AdualR1/AdualR2        4.5894e-11 value0=0.999999999991
  k907R AdualR1*AdualR2        3.3894e-59 value0=1.50094246243
  k903a Adag1*Adag2            1.254e-58 value0=66.5377312585
=== family a=1 b=0.8 N=16 tau=1
  J=0.21736051450585177291477 lambda=0.03023717969039910335553 caustic axes=(0.9847653630736,0.7808731140906) closure_err=5.9394e-58 worst tangency/closure=8.7969e-58
  checks: {'chk_polar_two_defs': '1.0436e-60', 'chk_polar_tangent_circle': '1.7113e-59', 'chk_polar_circumcircle': '3.9158e-58', 'chk_dualR_on_circle': '7.0009e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.7988e-60', 'chk_invped_eq_polar': '1.0436e-60'}
  O_p(f1)=['-1.5375', '-1.01008171844333e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 4.33e-61 Rstar-a/b^2=-1.56e-61  O_p spread over members: 8.11e-60
  k813 Apol/Adag               spread=  1.0758e-58   value(member0)=0.9493700871112814392567663
  k814R Apol/AdualR            spread=  4.9687e-59   value(member0)=6.362439763735668802905825
  k814P Apol/AdualP            spread=  9.0076e-59   value(member0)=6.770418497656879363562741
  k815(i) ApedX*AdualR         spread=  7.5507e-12   value(member0)=9.366084718485049572168233
  k815(ii) Apol*AdualR         spread=  7.5507e-12   value(member0)=9.663325585860621284638122
  k815(iii) Aped*AdualR        spread=  7.5507e-12   value(member0)=3.592927821725211075267322
  k815(i)P ApedX*AdualP        spread=  7.5507e-12   value(member0)=8.8016937009181495941459
  k816(i) ApedX/AdualR         spread=  2.7115e-58   value(member0)=6.166733110038230703014257
  k816(ii) Apol/AdualR         spread=  4.9589e-59   value(member0)=6.362439763735668802905825
  k816(iii) Aped/AdualR        spread=  7.6682e-59   value(member0)=2.365623163378154713033837
  k816(i)P ApedX/AdualP        spread=  2.3442e-58   value(member0)=6.562162545929064693729998
  k817 Adag*Aant               spread=  8.4627e-59   value(member0)=15.35406592991072493910063
  k818 Adag/Aant               spread=  7.5507e-12   value(member0)=4.442790222721234445151186
  Aant/A                       spread=  1.8438e-59   value(member0)=0.7594125109309519968887222
  k804 A*Adag                  spread=  9.0121e-59   value(member0)=20.21834735259814734604461
  k805 A/Adag                  spread=  7.5507e-12   value(member0)=0.2963919778991878063375536
  k802 Ldag                    spread=  2.1375e-59   value(member0)=10.48070815589357718163952
  k803 sumcos_dag              spread=  4.6693e-59   value(member0)=-13.88713579902841350157013
  k801 sum 1/d                 spread=  1.7668e-58   value(member0)=20.25954999118507517788408
  A                            spread=  3.7753e-12   value(member0)=2.447969763230210403365158
  Adag                         spread=  3.7753e-12   value(member0)=8.259230835400145620156989
  Apol                         spread=  3.7753e-12   value(member0)=7.841066697676018021738302
  AdualR                       spread=  3.7753e-12   value(member0)=1.232399360755940921795266
  Aped                         spread=  3.7753e-12   value(member0)=2.9153924743366846610682
  ApedX                        spread=  3.7753e-12   value(member0)=7.599877942763611005594808
  Aant                         spread=  3.7753e-12   value(member0)=1.859018864577702129650024
  k908(i) ApedX1/ApedX2        6.5264e-58 value0=1.0
  k908(ii) Apol1/Apol2         3.656e-59 value0=1.0
  k908(iii) Aped1/Aped2        8.6344e-59 value0=1.0
  k907R AdualR1/AdualR2        6.6742e-59 value0=1.0
  k907R AdualR1*AdualR2        7.5507e-12 value0=1.51880818439
  k903a Adag1*Adag2            7.5507e-12 value0=68.2148939924
=== family a=1 b=0.8 N=5 tau=2
  J=0.99571766401994416783675 lambda=0.63453034652245402650756 caustic axes=(0.6045408617103,0.0739571056596) closure_err=1.8596e-57 worst tangency/closure=7.1115e-57
  checks: {'chk_polar_two_defs': '3.0891e-57', 'chk_polar_tangent_circle': '4.7256e-60', 'chk_polar_circumcircle': '7.6768e-53', 'chk_dualR_on_circle': '6.223e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.7087e-57', 'chk_invped_eq_polar': '3.0891e-57'}
  O_p(f1)=['-1.5375', '-2.15973209561117e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 2.18e-61 Rstar-a/b^2=0.0  O_p spread over members: 5.41e-60
  k813 Apol/Adag               spread=  3.2646e-55   value(member0)=365.3566331242026326237112
  k814R Apol/AdualR            spread=  3.2131e-55   value(member0)=946.3582472650055967789568
  k814P Apol/AdualP            spread=  3.6506e-55   value(member0)=34743.55269771500333685381
  k815(i) ApedX*AdualR         spread=     0.34157   value(member0)=0.01472292022298446007357731
  k815(ii) Apol*AdualR         spread=      0.3668   value(member0)=196.2982948759986987732949
  k815(iii) Aped*AdualR        spread=  9.9221e-56   value(member0)=0.004684502786386034421861893
  k815(i)P ApedX*AdualP        spread=     0.34157   value(member0)=0.0004010285619916591871582072
  k816(i) ApedX/AdualR         spread=    0.038322   value(member0)=0.07097951098173130197418662
  k816(ii) Apol/AdualR         spread=   3.213e-55   value(member0)=946.3582472650055967789568
  k816(iii) Aped/AdualR        spread=      0.3668   value(member0)=0.02258408739124697278092021
  k816(i)P ApedX/AdualP        spread=    0.038322   value(member0)=2.605863463840299665371104
  k817 Adag*Aant               spread=    0.036118   value(member0)=110.366686239824093725496
  k818 Adag/Aant               spread=     0.34318   value(member0)=0.01260956493414736349340365
  Aant/A                       spread=     0.17481   value(member0)=86.75448645372635504975383
  k804 A*Adag                  spread=     0.20448   value(member0)=1.272172665083922316167451
  k805 A/Adag                  spread=     0.20404   value(member0)=0.9141299839233292973047464
  k802 Ldag                    spread=  1.1142e-57   value(member0)=12.91774818884818130165419
  k803 sumcos_dag              spread=  7.6731e-58   value(member0)=3.630902168249821196095862
  k801 sum 1/d                 spread=  8.0834e-58   value(member0)=6.900944763679738669238987
  A                            spread=   0.0066242   value(member0)=1.078392868059161866299647
  Adag                         spread=     0.20426   value(member0)=1.17969313667060478792144
  Apol                         spread=     0.20426   value(member0)=431.0087125337019886512691
  AdualR                       spread=     0.20426   value(member0)=0.455439273424547049148104
  Aped                         spread=     0.20426   value(member0)=0.01028568035242599550644989
  ApedX                        spread=     0.17256   value(member0)=0.03232685690954936238973649
  Aant                         spread=     0.17458   value(member0)=93.55541946383367063776018
  k908(i) ApedX1/ApedX2        0.31545 value0=1.20621045866
  k908(ii) Apol1/Apol2         0.3668 value0=1.25363945426
  k908(iii) Aped1/Aped2        0.3668 value0=0.797677511348
  k907R AdualR1/AdualR2        0.3668 value0=1.25363945426
  k907R AdualR1*AdualR2        3.2768e-58 value0=0.165458203372
  k903a Adag1*Adag2            5.1144e-57 value0=1.11010856589
=== family a=1 b=0.8 N=7 tau=2
  J=0.85896176867627840780083 lambda=0.47220180483038746758848 caustic axes=(0.7264972093336,0.4096317799800) closure_err=3.513e-59 worst tangency/closure=7.5157e-59
  checks: {'chk_polar_two_defs': '6.129e-60', 'chk_polar_tangent_circle': '1.5558e-60', 'chk_polar_circumcircle': '1.2869e-57', 'chk_dualR_on_circle': '6.223e-61', 'chk_ant_is_polar_reciprocal_of_inv': '2.0537e-60', 'chk_invped_eq_polar': '6.129e-60'}
  O_p(f1)=['-1.5375', '-1.30804470470976e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 2.99e-61 Rstar-a/b^2=-3.11e-61  O_p spread over members: 1.28e-60
  k813 Apol/Adag               spread=  1.1176e-58   value(member0)=8.575116034584215172523489
  k814R Apol/AdualR            spread=  8.0804e-59   value(member0)=28.77225473704621088126014
  k814P Apol/AdualP            spread=  7.7922e-59   value(member0)=70.91800282111336960919525
  k815(i) ApedX*AdualR         spread=   0.0094026   value(member0)=0.6745476527581253500214513
  k815(ii) Apol*AdualR         spread=   0.0015116   value(member0)=33.78955182292163067308332
  k815(iii) Aped*AdualR        spread=  8.9172e-60   value(member0)=0.9508462608691676746434222
  k815(i)P ApedX*AdualP        spread=   0.0094026   value(member0)=0.273671791722471363345178
  k816(i) ApedX/AdualR         spread=      0.0109   value(member0)=0.5743863369110300889087424
  k816(ii) Apol/AdualR         spread=  8.0458e-59   value(member0)=28.77225473704621088126014
  k816(iii) Aped/AdualR        spread=   0.0015116   value(member0)=0.8096582925061734158734351
  k816(i)P ApedX/AdualP        spread=      0.0109   value(member0)=1.415750424627556819167276
  k817 Adag*Aant               spread=   0.0036386   value(member0)=29.50091129808531041953557
  k818 Adag/Aant               spread=   0.0021302   value(member0)=0.4481680429341882711818403
  Aant/A                       spread=   0.0028847   value(member0)=3.029599341950518583298793
  k804 A*Adag                  spread=  0.00075608   value(member0)=9.737561957315456394893594
  k805 A/Adag                  spread=  0.00075608   value(member0)=0.7365019765797510040635293
  k802 Ldag                    spread=   1.144e-59   value(member0)=15.01389839299509129144433
  k803 sumcos_dag              spread=  1.5197e-59   value(member0)=1.310407726933194468626399
  k801 sum 1/d                 spread=  9.0963e-60   value(member0)=9.030453570580301726396945
  A                            spread=   6.5924e-8   value(member0)=2.6780092659717633269878
  Adag                         spread=  0.00075608   value(member0)=3.636119591162806796211628
  Apol                         spread=  0.00075608   value(member0)=31.18014740984598549690572
  AdualR                       spread=  0.00075608   value(member0)=1.083688007589459127033725
  Aped                         spread=  0.00075608   value(member0)=0.87741698183429857454057
  ApedX                        spread=    0.010152   value(member0)=0.6224555850337220021022224
  Aant                         spread=   0.0028847   value(member0)=8.113295109925445473602727
  k908(i) ApedX1/ApedX2        0.020201 value0=0.992366063286
  k908(ii) Apol1/Apol2         0.0015116 value0=1.00056820671
  k908(iii) Aped1/Aped2        0.0015116 value0=0.999432115969
  k907R AdualR1/AdualR2        0.0015116 value0=1.00056820671
  k907R AdualR1*AdualR2        8.3506e-60 value0=1.17371278632
  k903a Adag1*Adag2            3.8712e-59 value0=13.2138574788
=== family a=1 b=0.8 N=7 tau=3
  J=0.99972604720292604427581 lambda=0.63964938845183175244517 caustic axes=(0.6002921051856,0.0187246241128) closure_err=2.0675e-56 worst tangency/closure=8.4563e-56
  checks: {'chk_polar_two_defs': '9.701e-55', 'chk_polar_tangent_circle': '2.0318e-58', 'chk_polar_circumcircle': '2.2236e-49', 'chk_dualR_on_circle': '8.3622e-59', 'chk_ant_is_polar_reciprocal_of_inv': '4.3251e-55', 'chk_invped_eq_polar': '9.701e-55'}
  O_p(f1)=['-1.5375', '6.33472418447393e-60'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 6.35e-60 Rstar-a/b^2=7.78e-61  O_p spread over members: 1.18e-58
  k813 Apol/Adag               spread=  5.8949e-53   value(member0)=5759.443937711516255718328
  k814R Apol/AdualR            spread=  5.8891e-53   value(member0)=14794.8234380364142452671
  k814P Apol/AdualP            spread=  6.7587e-53   value(member0)=8155486.001036268180578365
  k815(i) ApedX*AdualR         spread=      0.3436   value(member0)=0.001047559962349414882355654
  k815(ii) Apol*AdualR         spread=     0.36513   value(member0)=3091.95973894818790554518
  k815(iii) Aped*AdualR        spread=  1.8517e-53   value(member0)=0.0003028925355189546881522624
  k815(i)P ApedX*AdualP        spread=      0.3436   value(member0)=0.00000190037291238638273330656
  k816(i) ApedX/AdualR         spread=      0.0328   value(member0)=0.005012505333910939178719465
  k816(ii) Apol/AdualR         spread=  5.8891e-53   value(member0)=14794.8234380364142452671
  k816(iii) Aped/AdualR        spread=     0.36513   value(member0)=0.001449320806882990355507534
  k816(i)P ApedX/AdualP        spread=      0.0328   value(member0)=2.763089215092103331191919
  k817 Adag*Aant               spread=     0.03772   value(member0)=1725.867333036174654161814
  k818 Adag/Aant               spread=     0.34032   value(member0)=0.0007990521012219871120327092
  Aant/A                       spread=     0.17209   value(member0)=1355.878933879390128806607
  k804 A*Adag                  spread=     0.20323   value(member0)=1.272877164702446955372187
  k805 A/Adag                  spread=      0.2032   value(member0)=0.923004862423955717198644
  k802 Ldag                    spread=  8.9955e-57   value(member0)=19.12256797135752262625676
  k803 sumcos_dag              spread=  6.0164e-57   value(member0)=5.780294927826006903220547
  k801 sum 1/d                 spread=  6.6257e-57   value(member0)=10.00251165810498106045227
  A                            spread=   0.0061943   value(member0)=1.083915039239135603189856
  Adag                         spread=     0.20321   value(member0)=1.174332967642883800608631
  Apol                         spread=     0.20321   value(member0)=6763.504891345581282714755
  AdualR                       spread=     0.20321   value(member0)=0.4571534712578659422381992
  Aped                         spread=     0.20321   value(member0)=0.0006625620378328102073521027
  ApedX                        spread=     0.17619   value(member0)=0.002291484213095954261324436
  Aant                         spread=     0.17208   value(member0)=1469.657567819396499467296
  k908(i) ApedX1/ApedX2        0.32135 value0=1.21373785232
  k908(ii) Apol1/Apol2         0.36513 value0=1.2548669823
  k908(iii) Aped1/Aped2        0.36513 value0=0.7968972123
  k907R AdualR1/AdualR2        0.36513 value0=1.2548669823
  k907R AdualR1*AdualR2        3.5479e-57 value0=0.166542987609
  k903a Adag1*Adag2            6.024e-56 value0=1.09896741117
=== family a=1 b=0.8 N=8 tau=3
  J=0.98363035699037172963119 lambda=0.61921835468352392381425 caustic axes=(0.6170750726746,0.1441584035582) closure_err=3.0899e-58 worst tangency/closure=1.0208e-57
  checks: {'chk_polar_two_defs': '2.3095e-58', 'chk_polar_tangent_circle': '3.7338e-60', 'chk_polar_circumcircle': '7.8638e-55', 'chk_dualR_on_circle': '1.478e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.3584e-58', 'chk_invped_eq_polar': '2.3095e-58'}
  O_p(f1)=['-1.5375', '-1.6262190704778e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.02e-60 Rstar-a/b^2=-4.67e-61  O_p spread over members: 2.57e-60
  k813 Apol/Adag               spread=  7.2763e-57   value(member0)=93.21030611439593578180265
  k814R Apol/AdualR            spread=  6.8694e-57   value(member0)=247.4970402869159788551222
  k814P Apol/AdualP            spread=  7.6156e-57   value(member0)=2656.577193216208055450699
  k815(i) ApedX*AdualR         spread=    0.014415   value(member0)=0.1400044985914172184210937
  k815(ii) Apol*AdualR         spread=    0.014415   value(member0)=162.3261621696707690973618
  k815(iii) Aped*AdualR        spread=    0.014415   value(member0)=0.07010490056195660748141336
  k815(i)P ApedX*AdualP        spread=    0.014415   value(member0)=0.01304336238250968779753052
  k816(i) ApedX/AdualR         spread=  6.8654e-58   value(member0)=0.2134634279840297999623842
  k816(ii) Apol/AdualR         spread=  6.8707e-57   value(member0)=247.4970402869159788551222
  k816(iii) Aped/AdualR        spread=  1.3162e-57   value(member0)=0.1068882253284409307258664
  k816(i)P ApedX/AdualP        spread=  9.7096e-59   value(member0)=2.291268104502270477513186
  k817 Adag*Aant               spread=  4.1558e-57   value(member0)=114.9412241742746774412131
  k818 Adag/Aant               spread=    0.014415   value(member0)=0.04023044568775133467014423
  Aant/A                       spread=  4.7209e-57   value(member0)=25.15180345212146255812596
  k804 A*Adag                  spread=  7.7497e-58   value(member0)=4.56989990372160791917624
  k805 A/Adag                  spread=    0.014415   value(member0)=0.9882709408262753990391722
  k802 Ldag                    spread=  1.0491e-58   value(member0)=19.76531694625121256171219
  k803 sumcos_dag              spread=  7.4504e-59   value(member0)=4.827803950585956741152098
  k801 sum 1/d                 spread=  7.6016e-59   value(member0)=10.7733220910783668002261
  A                            spread=   0.0072338   value(member0)=2.125158647567954824736861
  Adag                         spread=   0.0072338   value(member0)=2.150380588739306900686769
  Apol                         spread=   0.0072338   value(member0)=200.4376329388457501767821
  AdualR                       spread=   0.0072338   value(member0)=0.8098587066192159172198041
  Aped                         spread=   0.0072338   value(member0)=0.08656435991731448764183345
  ApedX                        spread=   0.0072338   value(member0)=0.1728752156976505148149899
  Aant                         spread=   0.0072338   value(member0)=53.45157260820546477115375
  k908(i) ApedX1/ApedX2        2.174e-57 value0=1.0
  k908(ii) Apol1/Apol2         1.4862e-56 value0=1.0
  k908(iii) Aped1/Aped2        2.6885e-57 value0=1.0
  k907R AdualR1/AdualR2        7.2405e-58 value0=1.0
  k907R AdualR1*AdualR2        0.014415 value0=0.655871124687
  k903a Adag1*Adag2            0.014415 value0=4.62413667643
=== family a=1 b=0.8 N=9 tau=2
  J=0.71176479619356018115121 lambda=0.32422984006429456751302 caustic axes=(0.8220524070493,0.5619343021525) closure_err=3.4403e-58 worst tangency/closure=5.8339e-58
  checks: {'chk_polar_two_defs': '1.8143e-60', 'chk_polar_tangent_circle': '1.2446e-60', 'chk_polar_circumcircle': '2.6955e-57', 'chk_dualR_on_circle': '6.223e-61', 'chk_ant_is_polar_reciprocal_of_inv': '6.9575e-61', 'chk_invped_eq_polar': '1.8143e-60'}
  O_p(f1)=['-1.5375', '-1.82462060349239e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 6.47e-61 Rstar-a/b^2=4.67e-61  O_p spread over members: 1.38e-60
  k813 Apol/Adag               spread=  4.3773e-58   value(member0)=3.378532695335826940653896
  k814R Apol/AdualR            spread=  2.5007e-58   value(member0)=14.28386718516239411628404
  k814P Apol/AdualP            spread=  2.6403e-58   value(member0)=25.18124203342947537565176
  k815(i) ApedX*AdualR         spread=  0.00014041   value(member0)=2.307432031922703332208745
  k815(ii) Apol*AdualR         spread=   9.5781e-6   value(member0)=33.08458625568544233816679
  k815(iii) Aped*AdualR        spread=  4.5274e-59   value(member0)=3.298862978966830998984445
  k815(i)P ApedX*AdualP        spread=  0.00014041   value(member0)=1.308873193745500868025903
  k816(i) ApedX/AdualR         spread=  0.00013083   value(member0)=0.996205678017491242763038
  k816(ii) Apol/AdualR         spread=  2.5033e-58   value(member0)=14.28386718516239411628404
  k816(iii) Aped/AdualR        spread=   9.5781e-6   value(member0)=1.424243914959460065608624
  k816(i)P ApedX/AdualP        spread=  0.00013083   value(member0)=1.756225815323552356314654
  k817 Adag*Aant               spread=   4.3612e-5   value(member0)=35.29302958000538869817455
  k818 Adag/Aant               spread=   5.3189e-5   value(member0)=1.17307645718524639795214
  Aant/A                       spread=     4.84e-5   value(member0)=1.560652848549838985238672
  k804 A*Adag                  spread=    4.789e-6   value(member0)=22.6142730029934112408696
  k805 A/Adag                  spread=    4.789e-6   value(member0)=0.5462197155138102079924294
  k802 Ldag                    spread=  6.6406e-59   value(member0)=16.83068872012946656389937
  k803 sumcos_dag              spread=  3.6505e-58   value(member0)=-0.7277031641788107164698973
  k801 sum 1/d                 spread=   6.651e-59   value(member0)=11.48975904751026110575002
  A                            spread=   9.665e-12   value(member0)=3.514592688526893801733989
  Adag                         spread=    4.789e-6   value(member0)=6.434393685736584304285868
  Apol                         spread=    4.789e-6   value(member0)=21.7388094419234479760973
  AdualR                       spread=    4.789e-6   value(member0)=1.521913439835466951520413
  Aped                         spread=    4.789e-6   value(member0)=2.167575955780684135886266
  ApedX                        spread=  0.00013562   value(member0)=1.516138810215223720326479
  Aant                         spread=     4.84e-5   value(member0)=5.48505909084193381365658
  k908(i) ApedX1/ApedX2        0.00027124 value0=1.00023511804
  k908(ii) Apol1/Apol2         9.5781e-6 value0=1.00000830063
  k908(iii) Aped1/Aped2        9.5781e-6 value0=0.999991699441
  k907R AdualR1/AdualR2        9.5781e-6 value0=1.00000830063
  k907R AdualR1*AdualR2        5.6287e-59 value0=2.31620129243
  k903a Adag1*Adag2            2.4735e-58 value0=41.4010784481
=== family a=1 b=0.8 N=9 tau=4
  J=0.99998283760996578107842 lambda=0.63997803232926668405984 caustic axes=(0.6000183061130,0.0046869681813) closure_err=4.4307e-55 worst tangency/closure=1.8186e-54
  checks: {'chk_polar_two_defs': '3.3597e-52', 'chk_polar_tangent_circle': '4.7165e-57', 'chk_polar_circumcircle': '1.2357e-45', 'chk_dualR_on_circle': '1.9319e-57', 'chk_ant_is_polar_reciprocal_of_inv': '9.9933e-53', 'chk_invped_eq_polar': '3.3597e-52'}
  O_p(f1)=['-1.5375', '-3.7075317106027e-58'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 3.71e-58 Rstar-a/b^2=1.71e-60  O_p spread over members: 6.26e-57
  k813 Apol/Adag               spread=  2.0489e-50   value(member0)=91984.29583339344569697117
  k814R Apol/AdualR            spread=  2.0487e-50   value(member0)=236162.5502641224922660323
  k814P Apol/AdualP            spread=  2.3517e-50   value(member0)=2072531545.095515897187015
  k815(i) ApedX*AdualR         spread=     0.34364   value(member0)=0.00006608105950272801107643895
  k815(ii) Apol*AdualR         spread=     0.36495   value(member0)=49373.0482589383398474211
  k815(iii) Aped*AdualR        spread=  6.4467e-51   value(member0)=0.00001898831799415133672289783
  k815(i)P ApedX*AdualP        spread=     0.34364   value(member0)=7.529859592848924229511475e-9
  k816(i) ApedX/AdualR         spread=    0.032461   value(member0)=0.0003160807786157751716529938
  k816(ii) Apol/AdualR         spread=  2.0487e-50   value(member0)=236162.5502641224922660323
  k816(iii) Aped/AdualR        spread=     0.36495   value(member0)=0.00009082545560498338989935046
  k816(i)P ApedX/AdualP        spread=    0.032461   value(member0)=2.773883427947831748880798
  k817 Adag*Aant               spread=    0.037818   value(member0)=27549.59372881626065042262
  k818 Adag/Aant               spread=     0.34006   value(member0)=0.0000500216941280840630597374
  Aant/A                       spread=     0.17187   value(member0)=21644.03743502222688648948
  k804 A*Adag                  spread=      0.2031   value(member0)=1.272849107359158897970882
  k805 A/Adag                  spread=     0.20309   value(member0)=0.9236412648162885136217599
  k802 Ldag                    spread=   1.478e-55   value(member0)=25.36806263067910909962292
  k803 sumcos_dag              spread=  9.6155e-56   value(member0)=7.798213216064183826261781
  k801 sum 1/d                 spread=  1.1014e-55   value(member0)=13.12521095655259967966682
  A                            spread=   0.0061814   value(member0)=1.084276698745065411271313
  Adag                         spread=      0.2031   value(member0)=1.173915393397594847686543
  Apol                         spread=      0.2031   value(member0)=107981.7808296588114204161
  AdualR                       spread=      0.2031   value(member0)=0.457234987972871934376521
  Aped                         spread=      0.2031   value(member0)=0.00004152857610117519410089446
  ApedX                        spread=     0.17636   value(member0)=0.0001445231910088399571168455
  Aant                         spread=     0.17187   value(member0)=23468.12545756051337818615
  k908(i) ApedX1/ApedX2        0.32162 value0=1.21407052066
  k908(ii) Apol1/Apol2         0.36495 value0=1.25479120441
  k908(iii) Aped1/Aped2        0.36495 value0=0.796945337588
  k907R AdualR1/AdualR2        0.36495 value0=1.25479120441
  k907R AdualR1*AdualR2        8.0568e-56 value0=0.166612447945
  k903a Adag1*Adag2            1.2846e-54 value0=1.0982523196
=== family a=1 b=0.8 N=10 tau=3
  J=0.88632502674577575143934 lambda=0.50276611394297606472030 caustic axes=(0.7051481305775,0.3704509226024) closure_err=6.3738e-58 worst tangency/closure=1.3281e-57
  checks: {'chk_polar_two_defs': '8.3491e-60', 'chk_polar_tangent_circle': '3.1115e-60', 'chk_polar_circumcircle': '3.1455e-56', 'chk_dualR_on_circle': '1.2446e-60', 'chk_ant_is_polar_reciprocal_of_inv': '3.7596e-60', 'chk_invped_eq_polar': '8.3491e-60'}
  O_p(f1)=['-1.5375', '-1.29008284117192e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.99e-61 Rstar-a/b^2=-3.11e-61  O_p spread over members: 9.03e-61
  k813 Apol/Adag               spread=  1.4972e-57   value(member0)=11.15167884274285592457093
  k814R Apol/AdualR            spread=  1.1014e-57   value(member0)=35.65822151354014342116304
  k814P Apol/AdualP            spread=  1.0777e-57   value(member0)=98.12393267055387479727241
  k815(i) ApedX*AdualR         spread=   5.1413e-5   value(member0)=1.154943026887449263275408
  k815(ii) Apol*AdualR         spread=   5.1413e-5   value(member0)=78.52729433729589725488447
  k815(iii) Aped*AdualR        spread=   5.1413e-5   value(member0)=1.47891548742288084468287
  k815(i)P ApedX*AdualP        spread=   5.1413e-5   value(member0)=0.4197061121321112148352235
  k816(i) ApedX/AdualR         spread=  6.0353e-58   value(member0)=0.5244445849793093440371559
  k816(ii) Apol/AdualR         spread=  1.1017e-57   value(member0)=35.65822151354014342116304
  k816(iii) Aped/AdualR        spread=  3.8572e-58   value(member0)=0.6715562594556881846081899
  k816(i)P ApedX/AdualP        spread=  6.2719e-58   value(member0)=1.443161295254327508677761
  k817 Adag*Aant               spread=   5.1413e-5   value(member0)=65.68258424698492206230302
  k818 Adag/Aant               spread=  1.1612e-57   value(member0)=0.3428069149248801095658114
  Aant/A                       spread=  5.1476e-58   value(member0)=3.72287839188954505070016
  k804 A*Adag                  spread=   5.1413e-5   value(member0)=17.64295723171547366751361
  k805 A/Adag                  spread=  6.4717e-58   value(member0)=0.7835587705085427864860131
  k802 Ldag                    spread=  1.3222e-58   value(member0)=21.9698785435774542294445
  k803 sumcos_dag              spread=   1.034e-58   value(member0)=2.461416011232874049164427
  k801 sum 1/d                 spread=  1.0371e-58   value(member0)=12.94942313101779954407385
  A                            spread=   2.5707e-5   value(member0)=3.718103532261814272858439
  Adag                         spread=   2.5707e-5   value(member0)=4.745149530836982027721804
  Apol                         spread=   2.5707e-5   value(member0)=52.91638362868596147163672
  AdualR                       spread=   2.5707e-5   value(member0)=1.483988302910523650622897
  Aped                         spread=   2.5707e-5   value(member0)=0.9965816337785860102764211
  ApedX                        spread=   2.5707e-5   value(member0)=0.7782696296340591766552039
  Aant                         spread=   2.5707e-5   value(member0)=13.84204729906570030599434
  k908(i) ApedX1/ApedX2        1.5385e-57 value0=1.0
  k908(ii) Apol1/Apol2         1.9031e-57 value0=1.0
  k908(iii) Aped1/Aped2        3.8108e-58 value0=1.0
  k907R AdualR1/AdualR2        4.1305e-58 value0=1.0
  k907R AdualR1*AdualR2        5.1413e-5 value0=2.20222128318
  k903a Adag1*Adag2            5.1413e-5 value0=22.51644407
=== family a=1 b=0.8 N=11 tau=3
  J=0.83208758607417315970737 lambda=0.44311664057519649716435 caustic axes=(0.7462461788343,0.4437154036370) closure_err=7.9403e-58 worst tangency/closure=1.5171e-57
  checks: {'chk_polar_two_defs': '5.3583e-60', 'chk_polar_tangent_circle': '2.4892e-60', 'chk_polar_circumcircle': '1.8228e-56', 'chk_dualR_on_circle': '1.0112e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.899e-60', 'chk_invped_eq_polar': '5.3583e-60'}
  O_p(f1)=['-1.5375', '-2.23618615275299e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 2.41e-61 Rstar-a/b^2=1.56e-61  O_p spread over members: 8.1e-61
  k813 Apol/Adag               spread=  1.2326e-57   value(member0)=6.891921401166805100909728
  k814R Apol/AdualR            spread=  8.2169e-58   value(member0)=24.2048004358889524897312
  k814P Apol/AdualP            spread=  8.0231e-58   value(member0)=54.81595950776986162642603
  k815(i) ApedX*AdualR         spread=  0.00011409   value(member0)=1.953154432052333635272193
  k815(ii) Apol*AdualR         spread=   4.2099e-6   value(member0)=74.64487137193814369851841
  k815(iii) Aped*AdualR        spread=  8.4308e-59   value(member0)=2.893469127889338601447395
  k815(i)P ApedX*AdualP        spread=  0.00011409   value(member0)=0.8624443259375527585168496
  k816(i) ApedX/AdualR         spread=   0.0001183   value(member0)=0.6333417471206402227177346
  k816(ii) Apol/AdualR         spread=  8.2179e-58   value(member0)=24.2048004358889524897312
  k816(iii) Aped/AdualR        spread=   4.2099e-6   value(member0)=0.9382539151148733406168059
  k816(i)P ApedX/AdualP        spread=   0.0001183   value(member0)=1.434311993470075415735856
  k817 Adag*Aant               spread=   1.2445e-5   value(member0)=67.7657517293859025888225
  k818 Adag/Aant               spread=   1.6655e-5   value(member0)=0.5613200925859379508831175
  Aant/A                       spread=    1.455e-5   value(member0)=2.564305096197981830613825
  k804 A*Adag                  spread=    2.105e-6   value(member0)=26.42655580642886367896034
  k805 A/Adag                  spread=    2.105e-6   value(member0)=0.6947358600772187392835869
  k802 Ldag                    spread=   1.416e-58   value(member0)=23.04643925935050313654884
  k803 sumcos_dag              spread=  4.1873e-58   value(member0)=1.474282863745848440925787
  k801 sum 1/d                 spread=  1.1795e-58   value(member0)=14.15018190646936815980156
  A                            spread=  5.9315e-13   value(member0)=4.284795908448613081947031
  Adag                         spread=    2.105e-6   value(member0)=6.167517980103064089731337
  Apol                         spread=    2.105e-6   value(member0)=42.50604915915337304472764
  AdualR                       spread=    2.105e-6   value(member0)=1.756099963382833137994496
  Aped                         spread=    2.105e-6   value(member0)=1.647667665977028904765908
  ApedX                        spread=   0.0001162   value(member0)=1.112211418927375860124037
  Aant                         spread=    1.455e-5   value(member0)=10.98752398420303971793032
  k908(i) ApedX1/ApedX2        0.00023238 value0=1.00010890481
  k908(ii) Apol1/Apol2         4.2099e-6 value0=0.999998027337
  k908(iii) Aped1/Aped2        4.2099e-6 value0=1.00000197267
  k907R AdualR1/AdualR2        4.2099e-6 value0=0.999998027337
  k907R AdualR1*AdualR2        9.7364e-59 value0=3.08389316487
  k903a Adag1*Adag2            4.8857e-58 value0=38.0383530717
=== family a=1 b=0.8 N=12 tau=5
  J=0.99891056426030313115102 lambda=0.63860628185013580234613 caustic axes=(0.6011603098590,0.0373325347366) closure_err=1.2122e-56 worst tangency/closure=4.9043e-56
  checks: {'chk_polar_two_defs': '5.6291e-56', 'chk_polar_tangent_circle': '5.1884e-59', 'chk_polar_circumcircle': '8.2625e-51', 'chk_dualR_on_circle': '2.4348e-59', 'chk_ant_is_polar_reciprocal_of_inv': '3.8724e-56', 'chk_invped_eq_polar': '5.6291e-56'}
  O_p(f1)=['-1.5375', '-7.46248173524804e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.1e-60 Rstar-a/b^2=1.09e-60  O_p spread over members: 2.32e-59
  k813 Apol/Adag               spread=  4.6632e-54   value(member0)=1445.800945831781679969148
  k814R Apol/AdualR            spread=   4.645e-54   value(member0)=3720.262728189765112685619
  k814P Apol/AdualP            spread=  5.3239e-54   value(member0)=520008.4942693278560992618
  k815(i) ApedX*AdualR         spread=    0.012431   value(member0)=0.01336342264841700812898422
  k815(ii) Apol*AdualR         spread=    0.012431   value(member0)=2507.104858965322252833528
  k815(iii) Aped*AdualR        spread=    0.012431   value(member0)=0.004869926538447714386845623
  k815(i)P ApedX*AdualP        spread=    0.012431   value(member0)=0.00009560505981697223806411247
  k816(i) ApedX/AdualR         spread=  4.2766e-55   value(member0)=0.01982982204440791939906951
  k816(ii) Apol/AdualR         spread=   4.645e-54   value(member0)=3720.262728189765112685619
  k816(iii) Aped/AdualR        spread=  1.2589e-54   value(member0)=0.007226425382736585857676036
  k816(i)P ApedX/AdualP        spread=  2.5465e-55   value(member0)=2.771760129951581036035909
  k817 Adag*Aant               spread=  3.2341e-54   value(member0)=1722.004396709704617177161
  k818 Adag/Aant               spread=    0.012431   value(member0)=0.002591163663168189199649391
  Aant/A                       spread=  3.2592e-54   value(member0)=376.4454714810511925994749
  k804 A*Adag                  spread=  3.6257e-56   value(member0)=4.574379364785063301624573
  k805 A/Adag                  spread=    0.012431   value(member0)=1.02518697099829247849023
  k802 Ldag                    spread=  3.1477e-57   value(member0)=32.01761582605968774886763
  k803 sumcos_dag              spread=  2.1058e-57   value(member0)=9.478519978329296572203062
  k801 sum 1/d                 spread=  2.3037e-57   value(member0)=16.89157987300712608405743
  A                            spread=   0.0062351   value(member0)=2.165547072954336003499669
  Adag                         spread=   0.0062351   value(member0)=2.112343537535986570322922
  Apol                         spread=   0.0062351   value(member0)=3054.028284491181011203845
  AdualR                       spread=   0.0062351   value(member0)=0.8209173673003557652212436
  Aped                         spread=   0.0062351   value(member0)=0.005932298100188583842498914
  ApedX                        spread=   0.0062351   value(member0)=0.01627864530672990764138159
  Aant                         spread=   0.0062351   value(member0)=815.2103888927053804046762
  k908(i) ApedX1/ApedX2        9.2193e-55 value0=1.0
  k908(ii) Apol1/Apol2         1.0571e-53 value0=1.0
  k908(iii) Aped1/Aped2        2.5522e-54 value0=1.0
  k907R AdualR1/AdualR2        3.4229e-56 value0=1.0
  k907R AdualR1*AdualR2        0.012431 value0=0.673905323935
  k903a Adag1*Adag2            0.012431 value0=4.46199522057
=== family a=1 b=0.8 N=13 tau=5
  J=0.98948426075714437292758 lambda=0.62661062546311198700293 caustic axes=(0.6110559504144,0.1157124649157) closure_err=1.2339e-57 worst tangency/closure=4.394e-57
  checks: {'chk_polar_two_defs': '4.529e-58', 'chk_polar_tangent_circle': '5.6007e-60', 'chk_polar_circumcircle': '7.9232e-54', 'chk_dualR_on_circle': '1.7113e-60', 'chk_ant_is_polar_reciprocal_of_inv': '4.5123e-58', 'chk_invped_eq_polar': '4.529e-58'}
  O_p(f1)=['-1.5375', '-1.20220019514756e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 2.67e-61 Rstar-a/b^2=1.56e-61  O_p spread over members: 1.52e-60
  k813 Apol/Adag               spread=  3.0536e-56   value(member0)=146.863501236161261578591
  k814R Apol/AdualR            spread=  2.9407e-56   value(member0)=385.3247801954335631310351
  k814P Apol/AdualP            spread=  3.3035e-56   value(member0)=6111.74816409152414917668
  k815(i) ApedX*AdualR         spread=  0.00037112   value(member0)=0.2292063715280376644424172
  k815(ii) Apol*AdualR         spread=  0.00041519   value(member0)=572.0166363761866354407862
  k815(iii) Aped*AdualR        spread=  7.5609e-57   value(member0)=0.102540612814115794261743
  k815(i)P ApedX*AdualP        spread=  0.00037112   value(member0)=0.01445067636250717232660217
  k816(i) ApedX/AdualR         spread=   4.4083e-5   value(member0)=0.1543991714785565955632193
  k816(ii) Apol/AdualR         spread=   2.941e-56   value(member0)=385.3247801954335631310351
  k816(iii) Aped/AdualR        spread=  0.00041519   value(member0)=0.06907393348559802378147287
  k816(i)P ApedX/AdualP        spread=   4.4083e-5   value(member0)=2.448970067128072440310395
  k817 Adag*Aant               spread=  0.00074067   value(member0)=402.2428367061548554656448
  k818 Adag/Aant               spread=  0.00032562   value(member0)=0.02540501907040089604541086
  Aant/A                       spread=  0.00053316   value(member0)=39.09786203078261781526873
  k804 A*Adag                  spread=  0.00020761   value(member0)=10.28810312925704502189032
  k805 A/Adag                  spread=  0.00020762   value(member0)=1.006763507207521753311631
  k802 Ldag                    spread=   2.709e-58   value(member0)=32.65590029636898380839352
  k803 sumcos_dag              spread=  1.8934e-58   value(member0)=8.492770412435127644413649
  k801 sum 1/d                 spread=  1.9706e-58   value(member0)=17.65886262286740410742418
  A                            spread=   5.3426e-9   value(member0)=3.218336027969034520954712
  Adag                         spread=  0.00020761   value(member0)=3.196715022871450399692325
  Apol                         spread=  0.00020761   value(member0)=469.4807607131365313552202
  AdualR                       spread=  0.00020761   value(member0)=1.218402721140902867015469
  Aped                         spread=  0.00020761   value(member0)=0.08415986851875836175172579
  ApedX                        spread=  0.00016354   value(member0)=0.1881203706713742351128645
  Aant                         spread=  0.00053316   value(member0)=125.8300579902302599236042
  k908(i) ApedX1/ApedX2        0.00032705 value0=1.00006045575
  k908(ii) Apol1/Apol2         0.00041519 value0=1.00007675162
  k908(iii) Aped1/Aped2        0.00041519 value0=0.999923254274
  k907R AdualR1/AdualR2        0.00041519 value0=1.00007675162
  k907R AdualR1*AdualR2        1.5763e-58 value0=1.48439126145
  k903a Adag1*Adag2            1.378e-57 value0=10.2182026739
=== family a=1 b=0.8 N=14 tau=3
  J=0.69082930821505564343076 lambda=0.30543688517689110189554 caustic axes=(0.8334045325189,0.5784143107004) closure_err=4.2197e-58 worst tangency/closure=7.2387e-58
  checks: {'chk_polar_two_defs': '1.9679e-60', 'chk_polar_tangent_circle': '1.8669e-60', 'chk_polar_circumcircle': '2.8725e-57', 'chk_dualR_on_circle': '6.223e-61', 'chk_ant_is_polar_reciprocal_of_inv': '8.5179e-61', 'chk_invped_eq_polar': '1.9679e-60'}
  O_p(f1)=['-1.5375', '5.10482491220082e-62'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 3.46e-61 Rstar-a/b^2=-1.56e-61  O_p spread over members: 9.57e-61
  k813 Apol/Adag               spread=  3.2918e-58   value(member0)=3.069186267480591930591918
  k814R Apol/AdualR            spread=  1.8267e-58   value(member0)=13.36098787073456418257383
  k814P Apol/AdualP            spread=  1.9688e-58   value(member0)=22.79633548593748907075205
  k815(i) ApedX*AdualR         spread=   6.3228e-9   value(member0)=6.069841878057354507511732
  k815(ii) Apol*AdualR         spread=   6.3228e-9   value(member0)=74.84353533889423139387652
  k815(iii) Aped*AdualR        spread=   6.3228e-9   value(member0)=8.377422357804828177267829
  k815(i)P ApedX*AdualP        spread=   6.3228e-9   value(member0)=3.557549140300602035071626
  k816(i) ApedX/AdualR         spread=  2.8098e-58   value(member0)=1.083581679336517720674559
  k816(ii) Apol/AdualR         spread=  1.8258e-58   value(member0)=13.36098787073456418257383
  k816(iii) Aped/AdualR        spread=  1.6769e-58   value(member0)=1.495528478228946419396061
  k816(i)P ApedX/AdualP        spread=  2.6802e-58   value(member0)=1.84879229945837377289599
  k817 Adag*Aant               spread=   6.3228e-9   value(member0)=81.89457919533399537179437
  k818 Adag/Aant               spread=  2.7388e-58   value(member0)=1.29625729991714272805529
  Aant/A                       spread=  7.3262e-59   value(member0)=1.467362846868889461798984
  k804 A*Adag                  spread=   6.3228e-9   value(member0)=55.81072150632921749713363
  k805 A/Adag                  spread=  2.3259e-58   value(member0)=0.5257402970217565683534781
  k802 Ldag                    spread=  5.2302e-59   value(member0)=25.60507309138986289354277
  k803 sumcos_dag              spread=  1.6363e-58   value(member0)=-1.635353283046146276339414
  k801 sum 1/d                 spread=  5.3804e-59   value(member0)=17.8580496947952102191869
  A                            spread=   3.1614e-9   value(member0)=5.416820589768139991505262
  Adag                         spread=   3.1614e-9   value(member0)=10.3032250342110967609302
  Apol                         spread=   3.1614e-9   value(member0)=31.62251678576295016816964
  AdualR                       spread=   3.1614e-9   value(member0)=2.366779843803899693748738
  Aped                         spread=   3.1614e-9   value(member0)=3.539586658106989610194387
  ApedX                        spread=   3.1614e-9   value(member0)=2.564599277768850735275219
  Aant                         spread=   3.1614e-9   value(member0)=7.948441281580194704966871
  k908(i) ApedX1/ApedX2        6.7776e-58 value0=1.0
  k908(ii) Apol1/Apol2         1.9346e-58 value0=1.0
  k908(iii) Aped1/Aped2        1.7673e-58 value0=1.0
  k907R AdualR1/AdualR2        1.4966e-58 value0=1.0
  k907R AdualR1*AdualR2        6.3228e-9 value0=5.60164682904
  k903a Adag1*Adag2            6.3228e-9 value0=106.156446106
=== family a=1 b=0.8 N=14 tau=5
  J=0.96851829661428455210619 lambda=0.60033772216104657389271 caustic axes=(0.6321884828426,0.1991539049051) closure_err=9.4265e-58 worst tangency/closure=2.6992e-57
  checks: {'chk_polar_two_defs': '9.3875e-59', 'chk_polar_tangent_circle': '5.2896e-60', 'chk_polar_circumcircle': '6.1783e-55', 'chk_dualR_on_circle': '2.0225e-60', 'chk_ant_is_polar_reciprocal_of_inv': '3.3885e-59', 'chk_invped_eq_polar': '9.3875e-59'}
  O_p(f1)=['-1.5375', '-4.00620671525996e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 4.19e-61 Rstar-a/b^2=6.22e-61  O_p spread over members: 1.63e-60
  k813 Apol/Adag               spread=  5.8849e-57   value(member0)=47.00143818108128744728409
  k814R Apol/AdualR            spread=  5.2993e-57   value(member0)=128.6583258438491752488417
  k814P Apol/AdualP            spread=  5.6967e-57   value(member0)=810.696361203801114901699
  k815(i) ApedX*AdualR         spread=   1.6497e-5   value(member0)=0.8048492693096474645593701
  k815(ii) Apol*AdualR         spread=   1.6497e-5   value(member0)=328.1264965046004819108868
  k815(iii) Aped*AdualR        spread=   1.6497e-5   value(member0)=0.5161745721280290892533679
  k815(i)P ApedX*AdualP        spread=   1.6497e-5   value(member0)=0.1277303864942264691662234
  k816(i) ApedX/AdualR         spread=  5.6705e-58   value(member0)=0.3155812183688515857199688
  k816(ii) Apol/AdualR         spread=  5.2992e-57   value(member0)=128.6583258438491752488417
  k816(iii) Aped/AdualR        spread=  9.1877e-58   value(member0)=0.2023919342101234263385122
  k816(i)P ApedX/AdualP        spread=  3.2601e-58   value(member0)=1.988526927564720997667767
  k817 Adag*Aant               spread=   1.6497e-5   value(member0)=239.4946445581291228860046
  k818 Adag/Aant               spread=  4.7787e-57   value(member0)=0.07979232081109526658888987
  Aant/A                       spread=   3.579e-57   value(member0)=13.13046609383915224521154
  k804 A*Adag                  spread=   1.6497e-5   value(member0)=18.23961486565207408587448
  k805 A/Adag                  spread=  1.1997e-57   value(member0)=0.9544622591838411654341984
  k802 Ldag                    spread=  1.6714e-58   value(member0)=33.59912536222614634489519
  k803 sumcos_dag              spread=  1.3041e-58   value(member0)=7.13377479512970297758147
  k801 sum 1/d                 spread=  1.2191e-58   value(member0)=18.60153946285410456195613
  A                            spread=   8.2483e-6   value(member0)=4.172412253279085100382773
  Adag                         spread=   8.2483e-6   value(member0)=4.371479556296868941028902
  Apol                         spread=   8.2483e-6   value(member0)=205.4658261251479412296148
  AdualR                       spread=   8.2483e-6   value(member0)=1.596988183839100807622391
  Aped                         spread=   8.2483e-6   value(member0)=0.3232175274379077862860474
  ApedX                        spread=   8.2483e-6   value(member0)=0.5039794767766029728793632
  Aant                         spread=   8.2483e-6   value(member0)=54.7857176212000440869248
  k908(i) ApedX1/ApedX2        2.45e-57 value0=1.0
  k908(ii) Apol1/Apol2         1.0438e-56 value0=1.0
  k908(iii) Aped1/Aped2        1.5213e-57 value0=1.0
  k907R AdualR1/AdualR2        1.2913e-57 value0=1.0
  k907R AdualR1*AdualR2        1.6497e-5 value0=2.55037125932
  k903a Adag1*Adag2            1.6497e-5 value0=19.1098335111
=== family a=1 b=0.8 N=15 tau=4
  J=0.81893331651911464570435 lambda=0.42921713721919770409673 caustic axes=(0.7555017291712,0.4591109482258) closure_err=2.9618e-58 worst tangency/closure=5.5089e-58
  checks: {'chk_polar_two_defs': '4.1745e-60', 'chk_polar_tangent_circle': '5.2896e-60', 'chk_polar_circumcircle': '5.8272e-57', 'chk_dualR_on_circle': '2.3336e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.3915e-60', 'chk_invped_eq_polar': '4.1745e-60'}
  O_p(f1)=['-1.5375', '3.51727396296928e-61'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 5.94e-61 Rstar-a/b^2=0.0  O_p spread over members: 1.27e-60
  k813 Apol/Adag               spread=  3.1744e-58   value(member0)=6.259420066967398312512301
  k814R Apol/AdualR            spread=  2.0752e-58   value(member0)=22.46718382597511522955101
  k814P Apol/AdualP            spread=   2.032e-58   value(member0)=49.09723708315762066830478
  k815(i) ApedX*AdualR         spread=   8.9047e-7   value(member0)=3.89892213802524407011473
  k815(ii) Apol*AdualR         spread=   1.2742e-8   value(member0)=132.0188466778142037242456
  k815(iii) Aped*AdualR        spread=  2.4932e-59   value(member0)=5.865520168741133711627141
  k815(i)P ApedX*AdualP        spread=   8.9047e-7   value(member0)=1.784169651946193555554621
  k816(i) ApedX/AdualR         spread=   9.0321e-7   value(member0)=0.6635249633103930836661569
  k816(ii) Apol/AdualR         spread=  2.0752e-58   value(member0)=22.46718382597511522955101
  k816(iii) Aped/AdualR        spread=   1.2742e-8   value(member0)=0.9982038412112380242948876
  k816(i)P ApedX/AdualP        spread=   9.0321e-7   value(member0)=1.449992250322896063668712
  k817 Adag*Aant               spread=   7.0576e-8   value(member0)=122.1473029321530960536046
  k818 Adag/Aant               spread=   5.7834e-8   value(member0)=0.6197727757681175618006605
  Aant/A                       spread=   6.4205e-8   value(member0)=2.388515955300802885409052
  k804 A*Adag                  spread=    6.371e-9   value(member0)=51.13941259679390049808774
  k805 A/Adag                  spread=    6.371e-9   value(member0)=0.6755217828750983990052933
  k802 Ldag                    spread=  3.8542e-59   value(member0)=31.06493730459623581709534
  k803 sumcos_dag              spread=   1.917e-58   value(member0)=1.636886797436902580287203
  k801 sum 1/d                 spread=  3.2676e-59   value(member0)=19.27296382735858897229575
  A                            spread=  5.6584e-18   value(member0)=5.877566432850545096484667
  Adag                         spread=    6.371e-9   value(member0)=8.700780021977894458412255
  Apol                         spread=    6.371e-9   value(member0)=54.46183706783747349221802
  AdualR                       spread=    6.371e-9   value(member0)=2.424061577529454078368436
  Aped                         spread=    6.371e-9   value(member0)=2.419707578022474330066959
  ApedX                        spread=   8.9684e-7   value(member0)=1.608425369292364596805632
  Aant                         spread=   6.4205e-8   value(member0)=14.03866120320395203558547
  k908(i) ApedX1/ApedX2        1.7937e-6 value0=1.00000023791
  k908(ii) Apol1/Apol2         1.2742e-8 value0=0.99999999831
  k908(iii) Aped1/Aped2        1.2742e-8 value0=1.00000000169
  k907R AdualR1/AdualR2        1.2742e-8 value0=0.99999999831
  k907R AdualR1*AdualR2        2.8276e-59 value0=5.87607454159
  k903a Adag1*Adag2            1.3218e-58 value0=75.7035731188
=== family a=1 b=0.8 N=16 tau=5
  J=0.90823072569566083538170 lambda=0.52792515270250669774694 caustic axes=(0.6870770315601,0.3347758164764) closure_err=1.4576e-57 worst tangency/closure=3.2146e-57
  checks: {'chk_polar_two_defs': '1.4231e-59', 'chk_polar_tangent_circle': '3.1115e-60', 'chk_polar_circumcircle': '1.1022e-55', 'chk_dualR_on_circle': '1.2446e-60', 'chk_ant_is_polar_reciprocal_of_inv': '5.6804e-60', 'chk_invped_eq_polar': '1.4231e-59'}
  O_p(f1)=['-1.5375', '5.04726993550777e-63'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.54e-61 Rstar-a/b^2=3.11e-61  O_p spread over members: 6.82e-61
  k813 Apol/Adag               spread=  2.6063e-57   value(member0)=14.36632601597510785880686
  k814R Apol/AdualR            spread=  2.0121e-57   value(member0)=44.1446218124753199504241
  k814P Apol/AdualP            spread=  1.9963e-57   value(member0)=136.4999782318804880037329
  k815(i) ApedX*AdualR         spread=   6.2518e-8   value(member0)=2.498096656664985285440391
  k815(ii) Apol*AdualR         spread=   6.2518e-8   value(member0)=227.9469030584732801952013
  k815(iii) Aped*AdualR        spread=   6.2518e-8   value(member0)=2.863188939916084648833468
  k815(i)P ApedX*AdualP        spread=   6.2518e-8   value(member0)=0.8078941373320213499771232
  k816(i) ApedX/AdualR         spread=  9.7406e-58   value(member0)=0.4837860513998570204275933
  k816(ii) Apol/AdualR         spread=  2.0122e-57   value(member0)=44.1446218124753199504241
  k816(iii) Aped/AdualR        spread=  6.8516e-58   value(member0)=0.5544905029827705100122303
  k816(i)P ApedX/AdualP        spread=  9.8987e-58   value(member0)=1.495919157841914687452663
  k817 Adag*Aant               spread=   2.535e-58   value(member0)=184.1348359596717047557811
  k818 Adag/Aant               spread=   6.2518e-8   value(member0)=0.2647793441520359848352187
  Aant/A                       spread=  9.8466e-58   value(member0)=4.581335010416854034790052
  k804 A*Adag                  spread=  8.3955e-58   value(member0)=40.19239709407702578363314
  k805 A/Adag                  spread=   6.2518e-8   value(member0)=0.824373166837681284183936
  k802 Ldag                    spread=  1.9465e-58   value(member0)=35.85838973963174247039433
  k803 sumcos_dag              spread=  1.3958e-58   value(member0)=4.783712161830055714275823
  k801 sum 1/d                 spread=  1.4934e-58   value(member0)=20.801488784946516865478
  A                            spread=   3.1259e-8   value(member0)=5.756173527200330711492316
  Adag                         spread=   3.1259e-8   value(member0)=6.982485309755016274293996
  Apol                         spread=   3.1259e-8   value(member0)=100.3126603616974998776838
  AdualR                       spread=   3.1259e-8   value(member0)=2.272364248306891799810376
  Aped                         spread=   3.1259e-8   value(member0)=1.260004395003753655378661
  ApedX                        spread=   3.1259e-8   value(member0)=1.099338127030595417568726
  Aant                         spread=   3.1259e-8   value(member0)=26.3709593061975465319031
  k908(i) ApedX1/ApedX2        2.2925e-57 value0=1.0
  k908(ii) Apol1/Apol2         3.8086e-57 value0=1.0
  k908(iii) Aped1/Aped2        5.7407e-58 value0=1.0
  k907R AdualR1/AdualR2        7.6318e-58 value0=1.0
  k907R AdualR1*AdualR2        6.2518e-8 value0=5.16363927698
  k903a Adag1*Adag2            6.2518e-8 value0=48.7551011009
=== family a=1 b=0.8 N=16 tau=7
  J=0.99993138751227512920021 lambda=0.63991217902862318732542 caustic axes=(0.6000731796800,0.0093712844037) closure_err=9.6399e-56 worst tangency/closure=3.9292e-55
  checks: {'chk_polar_two_defs': '1.7449e-53', 'chk_polar_tangent_circle': '7.0499e-58', 'chk_polar_circumcircle': '1.6473e-47', 'chk_dualR_on_circle': '2.8416e-58', 'chk_ant_is_polar_reciprocal_of_inv': '6.3005e-54', 'chk_invped_eq_polar': '1.7449e-53'}
  O_p(f1)=['-1.5375', '6.25841560040552e-59'] R*=1.5625  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 6.26e-59 Rstar-a/b^2=-9.33e-61  O_p spread over members: 5.84e-58
  k813 Apol/Adag               spread=  5.8162e-52   value(member0)=23006.0026466786381064605
  k814R Apol/AdualR            spread=  5.8148e-52   value(member0)=59072.44883035799905160282
  k814P Apol/AdualP            spread=  6.6746e-52   value(member0)=129741814.1645182560396643
  k815(i) ApedX*AdualR         spread=     0.01233   value(member0)=0.0008645539697669650388680796
  k815(ii) Apol*AdualR         spread=     0.01233   value(member0)=39874.75270408929220935669
  k815(iii) Aped*AdualR        spread=     0.01233   value(member0)=0.0003075349478905796792872253
  k815(i)P ApedX*AdualP        spread=     0.01233   value(member0)=0.0000003936380916901721940508787
  k816(i) ApedX/AdualR         spread=  5.3481e-53   value(member0)=0.001280793401256740090242992
  k816(ii) Apol/AdualR         spread=  5.8148e-52   value(member0)=59072.44883035799905160282
  k816(iii) Aped/AdualR        spread=  1.6095e-52   value(member0)=0.0004555976210718921890883914
  k816(i)P ApedX/AdualP        spread=  3.2498e-53   value(member0)=2.813028116139233606219341
  k817 Adag*Aant               spread=  4.0791e-52   value(member0)=27335.66323430417550488238
  k818 Adag/Aant               spread=     0.01233   value(member0)=0.0001628062342715879353627765
  Aant/A                       spread=  4.0811e-52   value(member0)=5975.692364810353500599701
  k804 A*Adag                  spread=  2.8899e-55   value(member0)=4.574476322656497549813835
  k805 A/Adag                  spread=     0.01233   value(member0)=1.027876027594270532538715
  k802 Ldag                    spread=  1.7972e-56   value(member0)=44.48818802173613138191862
  k803 sumcos_dag              spread=  1.1923e-56   value(member0)=13.58791956263423719305453
  k801 sum 1/d                 spread=  1.3316e-56   value(member0)=23.12647237099356993310456
  A                            spread=    0.006184   value(member0)=2.168408298927166361251644
  Adag                         spread=    0.006184   value(member0)=2.109601003150443793417921
  Apol                         spread=    0.006184   value(member0)=48533.48626191501987761217
  AdualR                       spread=    0.006184   value(member0)=0.8215925905034279329606055
  Aped                         spread=    0.006184   value(member0)=0.0003743156297236550484718931
  ApedX                        spread=    0.006184   value(member0)=0.001052290368438221520243837
  Aant                         spread=    0.006184   value(member0)=12957.74091569047467285419
  k908(i) ApedX1/ApedX2        1.1237e-52 value0=1.0
  k908(ii) Apol1/Apol2         1.3438e-51 value0=1.0
  k908(iii) Aped1/Aped2        3.2988e-52 value0=1.0
  k907R AdualR1/AdualR2        2.7375e-55 value0=1.0
  k907R AdualR1*AdualR2        0.01233 value0=0.67501438477
  k903a Adag1*Adag2            0.01233 value0=4.45041639249
=== family a=1.7 b=0.3 N=3 tau=1
  J=0.58816288315314136477085 lambda=0.08997784360865601536561 caustic axes=(1.6733266735432,0.0047070576100) closure_err=8.7617e-56 worst tangency/closure=8.6522e-55
  checks: {'chk_polar_two_defs': '7.243e-52', 'chk_polar_tangent_circle': '1.8669e-60', 'chk_polar_circumcircle': '2.0392e-56', 'chk_dualR_on_circle': '8.4059e-60', 'chk_ant_is_polar_reciprocal_of_inv': '3.5803e-54', 'chk_invped_eq_polar': '7.243e-52'}
  O_p(f1)=['-20.2657650871587', '-8.29949759277239e-59'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.48e-58 Rstar-a/b^2=-1.19e-58  O_p spread over members: 5.2e-57
  k813 Apol/Adag               spread=  5.7081e-52   value(member0)=505501.4804387877975495182
  k814R Apol/AdualR            spread=  5.6633e-52   value(member0)=1017960527.341640453806534
  k814P Apol/AdualP            spread=  5.6633e-52   value(member0)=4071842109.366561815226136
  k815(i) ApedX*AdualR         spread=     0.95237   value(member0)=0.0000001247125120025061661313578
  k815(ii) Apol*AdualR         spread=     0.99825   value(member0)=9.202594130935064489634081
  k815(iii) Aped*AdualR        spread=  4.7772e-54   value(member0)=0.0000001241756450222489295727813
  k815(i)P ApedX*AdualP        spread=     0.95237   value(member0)=3.117812800062654153283945e-8
  k816(i) ApedX/AdualR         spread=     0.96321   value(member0)=13.79528562032457685752467
  k816(ii) Apol/AdualR         spread=  5.6636e-52   value(member0)=1017960527.341640453806534
  k816(iii) Aped/AdualR        spread=     0.99825   value(member0)=13.73589917053018171547435
  k816(i)P ApedX/AdualP        spread=     0.96321   value(member0)=55.18114248129830743009867
  k817 Adag*Aant               spread=     0.86362   value(member0)=146.4632447584951801132015
  k818 Adag/Aant               spread=     0.99773   value(member0)=0.0002503039432669004635456872
  Aant/A                       spread=     0.95237   value(member0)=4012.415606333857447808385
  k804 A*Adag                  spread=     0.96321   value(member0)=0.03650251098796781645160441
  k805 A/Adag                  spread=     0.95237   value(member0)=0.9956951634472213347526281
  k802 Ldag                    spread=  7.0263e-56   value(member0)=75.56958229925179949345172
  k803 sumcos_dag              spread=  2.2593e-57   value(member0)=1.000250106342588249132934
  k801 sum 1/d                 spread=  6.9177e-56   value(member0)=38.07887230265713740650804
  A                            spread=      0.6307   value(member0)=0.1906446265814974595409169
  Adag                         spread=     0.95814   value(member0)=0.191468868766482595122936
  Apol                         spread=     0.95814   value(member0)=96787.79661939692945422758
  AdualR                       spread=     0.95814   value(member0)=0.00009508010774460385171338474
  Aped                         spread=     0.95814   value(member0)=0.001306010773103024353360204
  ApedX                        spread=      0.6307   value(member0)=0.001311657243148044950723119
  Aant                         spread=     0.97023   value(member0)=764.9454749592909659802099
  k908(i) ApedX1/ApedX2        3.712e-53 value0=1.0
  k908(ii) Apol1/Apol2         0.99825 value0=0.0363807710019
  k908(iii) Aped1/Aped2        0.99825 value0=27.4870480328
  k907R AdualR1/AdualR2        0.99825 value0=0.0363807710019
  k907R AdualR1*AdualR2        1.3788e-57 value0=2.48489150718e-7
  k903a Adag1*Adag2            1.4081e-53 value0=1.00768418857
=== family a=1.7 b=0.3 N=4 tau=1
  J=0.57928444636349224020825 lambda=0.08728187919463087248322 caustic axes=(1.6741320499904,0.0521356001727) closure_err=1.2282e-57 worst tangency/closure=1.2049e-56
  checks: {'chk_polar_two_defs': '4.957e-56', 'chk_polar_tangent_circle': '3.1364e-58', 'chk_polar_circumcircle': '2.2717e-53', 'chk_dualR_on_circle': '1.1814e-60', 'chk_ant_is_polar_reciprocal_of_inv': '3.3537e-58', 'chk_invped_eq_polar': '4.957e-56'}
  O_p(f1)=['-20.2657650871587', '1.63552002560966e-59'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 4.7e-59 Rstar-a/b^2=4.48e-59  O_p spread over members: 3.97e-58
  k813 Apol/Adag               spread=  9.4978e-56   value(member0)=2062.246913580246913580247
  k814R Apol/AdualR            spread=  6.2801e-56   value(member0)=8175437.009940896543548578
  k814P Apol/AdualP            spread=  6.2672e-56   value(member0)=16350874.01988179308709716
  k815(i) ApedX*AdualR         spread=     0.98165   value(member0)=0.00001216636489071777370807177
  k815(ii) Apol*AdualR         spread=     0.86452   value(member0)=59.44046071152597718295544
  k815(iii) Aped*AdualR        spread=     0.86452   value(member0)=0.0004391568653757960635752563
  k815(i)P ApedX*AdualP        spread=     0.98165   value(member0)=0.000006083182445358886854035883
  k816(i) ApedX/AdualR         spread=     0.86452   value(member0)=1.673361017283173539000367
  k816(ii) Apol/AdualR         spread=  6.2827e-56   value(member0)=8175437.009940896543548578
  k816(iii) Aped/AdualR        spread=  1.3785e-56   value(member0)=60.40160603376224294200962
  k816(i)P ApedX/AdualP        spread=     0.86452   value(member0)=3.346722034566347078000734
  k817 Adag*Aant               spread=  9.8574e-56   value(member0)=8.0
  k818 Adag/Aant               spread=     0.86452   value(member0)=14.28307879458044434423189
  Aant/A                       spread=  1.0808e-55   value(member0)=2.0
  k804 A*Adag                  spread=  3.5811e-56   value(member0)=4.0
  k805 A/Adag                  spread=     0.86452   value(member0)=0.03500645814470472908309825
  k802 Ldag                    spread=  9.6865e-58   value(member0)=76.723006673920305592027
  k803 sumcos_dag              spread=     0.85317   value(member0)=0.5342040753656657612952068
  k801 sum 1/d                 spread=  9.5532e-58   value(member0)=38.95424836601307189542484
  A                            spread=     0.63193   value(member0)=0.3742002573206209278867428
  Adag                         spread=     0.63193   value(member0)=10.68946352052541291396722
  Apol                         spread=     0.63193   value(member0)=22044.31315303217313549275
  AdualR                       spread=     0.63193   value(member0)=0.002696407926111773707364051
  Aped                         spread=     0.63193   value(member0)=0.1628673692593172469055087
  ApedX                        spread=     0.95013   value(member0)=0.004512063910248809881654279
  Aant                         spread=     0.63193   value(member0)=0.7484005146412418557734856
  k908(i) ApedX1/ApedX2        3.1245e-55 value0=1.0
  k908(ii) Apol1/Apol2         2.5334e-55 value0=1.0
  k908(iii) Aped1/Aped2        2.0152e-56 value0=1.0
  k907R AdualR1/AdualR2        7.1854e-57 value0=1.0
  k907R AdualR1*AdualR2        0.86452 value0=7.270615704e-6
  k903a Adag1*Adag2            0.86452 value0=114.264630357
=== family a=1.7 b=0.3 N=5 tau=1
  J=0.54600817697152982268375 lambda=0.07754229411607306908322 caustic axes=(1.6770383734082,0.1116140935721) closure_err=3.2462e-59 worst tangency/closure=3.2797e-58
  checks: {'chk_polar_two_defs': '4.3737e-57', 'chk_polar_tangent_circle': '7.1191e-58', 'chk_polar_circumcircle': '3.2479e-56', 'chk_dualR_on_circle': '1.6335e-60', 'chk_ant_is_polar_reciprocal_of_inv': '3.1436e-59', 'chk_invped_eq_polar': '4.3737e-57'}
  O_p(f1)=['-20.2657650871587', '-3.16777168903259e-59'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.96e-58 Rstar-a/b^2=1.82e-58  O_p spread over members: 2.98e-58
  k813 Apol/Adag               spread=  7.2546e-58   value(member0)=142.9570613958355714692479
  k814R Apol/AdualR            spread=  4.0219e-58   value(member0)=1687356.82860665607709016
  k814P Apol/AdualP            spread=  4.2486e-58   value(member0)=3252197.638422086135308929
  k815(i) ApedX*AdualR         spread=     0.91489   value(member0)=0.00005194546376785096855908932
  k815(ii) Apol*AdualR         spread=     0.53585   value(member0)=9.10694548518150078232845
  k815(iii) Aped*AdualR        spread=   2.555e-58   value(member0)=0.001844579038035758534326817
  k815(i)P ApedX*AdualP        spread=     0.91489   value(member0)=0.00002695117048493694729280383
  k816(i) ApedX/AdualR         spread=     0.81664   value(member0)=9.624580837388871336266347
  k816(ii) Apol/AdualR         spread=  4.1727e-58   value(member0)=1687356.82860665607709016
  k816(iii) Aped/AdualR        spread=     0.53585   value(member0)=341.7680539318944638427943
  k816(i)P ApedX/AdualP        spread=     0.81664   value(member0)=18.55033774688045796718294
  k817 Adag*Aant               spread=     0.73915   value(member0)=-416.564765640616653615569
  k818 Adag/Aant               spread=     0.87893   value(member0)=-1.805036185005896842849131
  Aant/A                       spread=     0.82257   value(member0)=-16.96580088516577899976223
  k804 A*Adag                  spread=     0.31981   value(member0)=24.55320373380335402065641
  k805 A/Adag                  spread=     0.31762   value(member0)=0.0326542506332263473354558
  k802 Ldag                    spread=  2.1955e-59   value(member0)=81.17996666016879596138166
  k803 sumcos_dag              spread=  7.5339e-59   value(member0)=1.881223211580991219735288
  k801 sum 1/d                 spread=  2.2147e-59   value(member0)=41.58659156900895706274848
  A                            spread=    0.018442   value(member0)=0.8954141324394448537559382
  Adag                         spread=     0.31872   value(member0)=27.42105897626519788834268
  Apol                         spread=     0.31872   value(member0)=3920.03401160877199686276
  AdualR                       spread=     0.31872   value(member0)=0.002323180221960378730890955
  Aped                         spread=     0.31872   value(member0)=0.7939887833924652693531637
  ApedX                        spread=     0.87508   value(member0)=0.02235963584608068590389675
  Aant                         spread=     0.82229   value(member0)=-15.19141788073108156800997
  k908(i) ApedX1/ApedX2        0.98243 value0=0.303402225774
  k908(ii) Apol1/Apol2         0.53585 value0=0.766216702084
  k908(iii) Aped1/Aped2        0.53585 value0=1.30511381086
  k907R AdualR1/AdualR2        0.53585 value0=0.766216702084
  k907R AdualR1*AdualR2        1.2478e-58 value0=7.04391633467e-6
  k903a Adag1*Adag2            1.143e-57 value0=981.333966402
=== family a=1.7 b=0.3 N=6 tau=1
  J=0.5 lambda=0.065025 caustic axes=(1.6807661943292,0.1580348062927) closure_err=7.2281e-59 worst tangency/closure=6.7063e-58
  checks: {'chk_polar_two_defs': '1.0034e-57', 'chk_polar_tangent_circle': '7.9655e-58', 'chk_polar_circumcircle': '1.7076e-56', 'chk_dualR_on_circle': '2.6983e-60', 'chk_ant_is_polar_reciprocal_of_inv': '7.3043e-59', 'chk_invped_eq_polar': '1.0034e-57'}
  O_p(f1)=['-20.2657650871587', '1.92424913958027e-59'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 8.91e-59 Rstar-a/b^2=7.97e-59  O_p spread over members: 3.65e-58
  k813 Apol/Adag               spread=   5.844e-58   value(member0)=32.36307275016952436307275
  k814R Apol/AdualR            spread=    2.71e-58   value(member0)=779850.9071485751869839661
  k814P Apol/AdualP            spread=  3.0219e-58   value(member0)=1433239.505029813857159722
  k815(i) ApedX*AdualR         spread=     0.25961   value(member0)=0.001448570606655343228930037
  k815(ii) Apol*AdualR         spread=     0.25961   value(member0)=9.892237538938749781608226
  k815(iii) Aped*AdualR        spread=     0.25961   value(member0)=0.006170289347561507012996745
  k815(i)P ApedX*AdualP        spread=     0.25961   value(member0)=0.0007881928300918779333884022
  k816(i) ApedX/AdualR         spread=  9.2665e-58   value(member0)=114.1975308641975308641975
  k816(ii) Apol/AdualR         spread=  2.6681e-58   value(member0)=779850.9071485751869839661
  k816(iii) Aped/AdualR        spread=  4.6186e-58   value(member0)=486.4324907407407407407407
  k816(i)P ApedX/AdualP        spread=  9.1068e-58   value(member0)=209.8765432098765432098765
  k817 Adag*Aant               spread=     0.25961   value(member0)=-1249.352963251153213158669
  k818 Adag/Aant               spread=  6.6764e-58   value(member0)=-5.895511187593418409620323
  Aant/A                       spread=  1.7774e-58   value(member0)=-13.21321321321321321321321
  k804 A*Adag                  spread=     0.25961   value(member0)=94.55330380968954999587196
  k805 A/Adag                  spread=   5.269e-58   value(member0)=0.01283719354838709677419355
  k802 Ldag                    spread=  6.8337e-59   value(member0)=87.71241830065359477124183
  k803 sumcos_dag              spread=   1.392e-58   value(member0)=0.9941176470588235294117647
  k801 sum 1/d                 spread=  7.1696e-59   value(member0)=45.6209150326797385620915
  A                            spread=     0.13954   value(member0)=1.101725492872172668771932
  Adag                         spread=     0.13954   value(member0)=85.82292451379271605423225
  Apol                         spread=     0.13954   value(member0)=2777.493549672181124698453
  AdualR                       spread=     0.13954   value(member0)=0.003561569941397811575153813
  Aped                         spread=     0.13954   value(member0)=1.732463337541491521643863
  ApedX                        spread=     0.13954   value(member0)=0.4067224933077747786441082
  Aant                         spread=     0.13954   value(member0)=-14.55733383975243165944895
  k908(i) ApedX1/ApedX2        3.4059e-57 value0=1.0
  k908(ii) Apol1/Apol2         8.7861e-58 value0=1.0
  k908(iii) Aped1/Aped2        7.5423e-58 value0=1.0
  k907R AdualR1/AdualR2        3.6568e-58 value0=1.0
  k907R AdualR1*AdualR2        0.25961 value0=1.26847804475e-5
  k903a Adag1*Adag2            0.25961 value0=7365.5743721
=== family a=1.7 b=0.3 N=7 tau=1
  J=0.45362959147730595950883 lambda=0.05352332760923193560959 caustic axes=(1.6841842750693,0.1909886708440) closure_err=2.3006e-58 worst tangency/closure=2.1542e-57
  checks: {'chk_polar_two_defs': '5.571e-58', 'chk_polar_tangent_circle': '4.6996e-57', 'chk_polar_circumcircle': '2.6087e-56', 'chk_dualR_on_circle': '1.3136e-59', 'chk_ant_is_polar_reciprocal_of_inv': '3.1147e-59', 'chk_invped_eq_polar': '5.571e-58'}
  O_p(f1)=['-20.2657650871587', '-5.4689551373668e-59'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.51e-58 Rstar-a/b^2=1.49e-58  O_p spread over members: 2.45e-57
  k813 Apol/Adag               spread=  9.6639e-58   value(member0)=12.92653532908945900632837
  k814R Apol/AdualR            spread=    6.48e-58   value(member0)=495062.1341594685347749318
  k814P Apol/AdualP            spread=  7.5689e-58   value(member0)=863090.8857876999782668959
  k815(i) ApedX*AdualR         spread=      0.1178   value(member0)=0.008572846675966594632044467
  k815(ii) Apol*AdualR         spread=       0.116   value(member0)=8.719968682975951537503659
  k815(iii) Aped*AdualR        spread=  8.9559e-58   value(member0)=0.01151798045333465458941958
  k815(i)P ApedX*AdualP        spread=      0.1178   value(member0)=0.004917317331363727001325912
  k816(i) ApedX/AdualR         spread=   0.0020322   value(member0)=486.7095198990444315974524
  k816(ii) Apol/AdualR         spread=  6.5303e-58   value(member0)=495062.1341594685347749318
  k816(iii) Aped/AdualR        spread=       0.116   value(member0)=653.914732006684045972852
  k816(i)P ApedX/AdualP        spread=   0.0020322   value(member0)=848.5289454912315707767929
  k817 Adag*Aant               spread=     0.36286   value(member0)=-2721.920120667383182466618
  k818 Adag/Aant               spread=     0.27926   value(member0)=-9.491502883087161636221781
  Aant/A                       spread=     0.32236   value(member0)=-14.11328331151885749318078
  k804 A*Adag                  spread=    0.059778   value(member0)=192.8622887096604914755272
  k805 A/Adag                  spread=    0.059796   value(member0)=0.007465122802129592330525157
  k802 Ldag                    spread=  9.2736e-59   value(member0)=94.69835377941713086439004
  k803 sumcos_dag              spread=  8.7887e-57   value(member0)=-0.03954868188749099290311674
  k801 sum 1/d                 spread=  1.3323e-58   value(member0)=50.44696088912579591963494
  A                            spread=   0.0004731   value(member0)=1.199891940600230536466687
  Adag                         spread=    0.059787   value(member0)=160.7330478552790411555122
  Apol                         spread=    0.059787   value(member0)=2077.721421653491223395236
  AdualR                       spread=    0.059787   value(member0)=0.00419689020486511152116137
  Aped                         spread=    0.059787   value(member0)=2.74440833357584670358268
  ApedX                        spread=    0.061698   value(member0)=2.042666416678900657055678
  Aant                         spread=     0.32235   value(member0)=-16.93441490089920987745553
  k908(i) ApedX1/ApedX2        0.11959 value0=1.00756610311
  k908(ii) Apol1/Apol2         0.116 value0=1.00732361029
  k908(iii) Aped1/Aped2        0.116 value0=0.99272963503
  k907R AdualR1/AdualR2        0.116 value0=1.00732361029
  k907R AdualR1*AdualR2        7.16e-58 value0=1.74858280018e-5
  k903a Adag1*Adag2            2.798e-57 value0=25647.2819747
=== family a=1.7 b=0.3 N=8 tau=1
  J=0.41164971252303927599797 lambda=0.04407537186186025861023 caustic axes=(1.6869868488337,0.2143003223005) closure_err=2.2593e-58 worst tangency/closure=2.0523e-57
  checks: {'chk_polar_two_defs': '3.67e-58', 'chk_polar_tangent_circle': '3.0617e-57', 'chk_polar_circumcircle': '1.4875e-56', 'chk_dualR_on_circle': '8.7803e-60', 'chk_ant_is_polar_reciprocal_of_inv': '7.8031e-59', 'chk_invped_eq_polar': '3.67e-58'}
  O_p(f1)=['-20.2657650871587', '-5.29461015442061e-59'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.3e-58 Rstar-a/b^2=1.24e-58  O_p spread over members: 2.09e-57
  k813 Apol/Adag               spread=  4.9636e-58   value(member0)=6.973244645946887217649481
  k814R Apol/AdualR            spread=  2.9858e-58   value(member0)=367840.9099864752831491818
  k814P Apol/AdualP            spread=  3.6407e-58   value(member0)=608496.3422264698158056835
  k815(i) ApedX*AdualR         spread=     0.04953   value(member0)=0.03316169864317979174220636
  k815(ii) Apol*AdualR         spread=     0.04953   value(member0)=8.330813801001217475094085
  k815(iii) Aped*AdualR        spread=     0.04953   value(member0)=0.01757028170646167054909439
  k815(i)P ApedX*AdualP        spread=     0.04953   value(member0)=0.02004651229450544068634596
  k816(i) ApedX/AdualR         spread=  1.6335e-57   value(member0)=1464.230229721195354295953
  k816(ii) Apol/AdualR         spread=  3.0246e-58   value(member0)=367840.9099864752831491818
  k816(iii) Aped/AdualR        spread=  8.9511e-58   value(member0)=775.8027686138938071893374
  k816(i)P ApedX/AdualP        spread=  1.7036e-57   value(member0)=2422.185011981213209335242
  k817 Adag*Aant               spread=   4.892e-58   value(member0)=-4574.757250100780887112971
  k818 Adag/Aant               spread=     0.04953   value(member0)=-13.77557063386313411375299
  Aant/A                       spread=   3.199e-58   value(member0)=-14.06074522023505222765415
  k804 A*Adag                  spread=  4.3138e-58   value(member0)=325.3566705352979204982359
  k805 A/Adag                  spread=     0.04953   value(member0)=0.005162761504535186833970544
  k802 Ldag                    spread=  7.3216e-59   value(member0)=101.3140395322226053806344
  k803 sumcos_dag              spread=  3.0291e-58   value(member0)=-1.13404952540084729866402
  k801 sum 1/d                 spread=  1.2187e-58   value(member0)=55.71965021182966123529312
  A                            spread=    0.025079   value(member0)=1.296047411896406582818668
  Adag                         spread=    0.025079   value(member0)=251.0376299114154370317604
  Apol                         spread=    0.025079   value(member0)=1750.546808710973843564198
  AdualR                       spread=    0.025079   value(member0)=0.00475897802877699947486176
  Aped                         spread=    0.025079   value(member0)=3.69202833049788698774862
  ApedX                        spread=    0.025079   value(member0)=6.968239492314267376560201
  Aant                         spread=    0.025079   value(member0)=-18.22339245202040882585577
  k908(i) ApedX1/ApedX2        6.1409e-57 value0=1.0
  k908(ii) Apol1/Apol2         7.3447e-58 value0=1.0
  k908(iii) Aped1/Aped2        1.2643e-57 value0=1.0
  k907R AdualR1/AdualR2        7.0351e-58 value0=1.0
  k907R AdualR1*AdualR2        0.04953 value0=2.26478718784e-5
  k903a Adag1*Adag2            0.04953 value0=63019.8916315
=== family a=1.7 b=0.3 N=9 tau=1
  J=0.37504153484105840628659 lambda=0.03658466535782916856277 caustic axes=(1.6892055335696,0.2311175775274) closure_err=2.9743e-58 worst tangency/closure=2.6953e-57
  checks: {'chk_polar_two_defs': '2.84e-58', 'chk_polar_tangent_circle': '6.7756e-57', 'chk_polar_circumcircle': '1.6737e-56', 'chk_dualR_on_circle': '1.8708e-59', 'chk_ant_is_polar_reciprocal_of_inv': '8.2534e-59', 'chk_invped_eq_polar': '2.84e-58'}
  O_p(f1)=['-20.2657650871587', '-2.04817965360153e-59'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 5.29e-59 Rstar-a/b^2=5.48e-59  O_p spread over members: 4.23e-57
  k813 Apol/Adag               spread=  5.6328e-58   value(member0)=4.493170028378245720951169
  k814R Apol/AdualR            spread=  3.6737e-58   value(member0)=298960.8114021443347766967
  k814P Apol/AdualP            spread=  5.0966e-58   value(member0)=470680.344299396777283172
  k815(i) ApedX*AdualR         spread=    0.020695   value(member0)=0.09663109946459249701252752
  k815(ii) Apol*AdualR         spread=    0.020649   value(member0)=8.538921654391970404302943
  k815(iii) Aped*AdualR        spread=  7.8413e-58   value(member0)=0.02412172635310534044057339
  k815(i)P ApedX*AdualP        spread=    0.020695   value(member0)=0.06137692438722241297423364
  k816(i) ApedX/AdualR         spread=   4.7147e-5   value(member0)=3383.203766456500639083212
  k816(ii) Apol/AdualR         spread=  3.6942e-58   value(member0)=298960.8114021443347766967
  k816(iii) Aped/AdualR        spread=    0.020649   value(member0)=844.5388275972377622633658
  k816(i)P ApedX/AdualP        spread=   4.7147e-5   value(member0)=5326.475755007065582277109
  k817 Adag*Aant               spread=     0.10686   value(member0)=-6411.812491409253998066188
  k818 Adag/Aant               spread=     0.12531   value(member0)=-19.7210835323968536087296
  Aant/A                       spread=     0.11613   value(member0)=-13.36896102296218970659862
  k804 A*Adag                  spread=    0.010376   value(member0)=479.6043971103279340481268
  k805 A/Adag                  spread=    0.010381   value(member0)=0.003792901551044478950724304
  k802 Ldag                    spread=  7.8358e-59   value(member0)=107.2450867783535343830721
  k803 sumcos_dag              spread=  2.0511e-58   value(member0)=-2.261784025429469472817629
  k801 sum 1/d                 spread=   1.744e-58   value(member0)=61.26103518450678296987654
  A                            spread=   1.4855e-5   value(member0)=1.348737284161565335465988
  Adag                         spread=    0.010378   value(member0)=355.5951205193168583833372
  Apol                         spread=    0.010378   value(member0)=1597.749337754944635850678
  AdualR                       spread=    0.010378   value(member0)=0.005344343729405213186858153
  Aped                         spread=    0.010378   value(member0)=4.513505787508528042230337
  ApedX                        spread=    0.010425   value(member0)=18.0810038345618985217652
  Aant                         spread=     0.11613   value(member0)=-18.03121618217184605207719
  k908(i) ApedX1/ApedX2        0.020742 value0=1.01005753431
  k908(ii) Apol1/Apol2         0.020649 value0=1.01001203711
  k908(iii) Aped1/Aped2        0.020649 value0=0.990087210113
  k907R AdualR1/AdualR2        0.020649 value0=1.01001203711
  k907R AdualR1*AdualR2        5.6286e-58 value0=2.82788806952e-5
  k903a Adag1*Adag2            1.9515e-57 value0=125194.438375
=== family a=1.7 b=0.3 N=10 tau=1
  J=0.34347319509491582012519 lambda=0.03068499467823949830995 caustic axes=(1.6909509174786,0.2435467210244) closure_err=1.6865e-59 worst tangency/closure=1.5993e-58
  checks: {'chk_polar_two_defs': '2.1178e-58', 'chk_polar_tangent_circle': '1.6523e-56', 'chk_polar_circumcircle': '8.9362e-58', 'chk_dualR_on_circle': '4.642e-59', 'chk_ant_is_polar_reciprocal_of_inv': '6.0584e-59', 'chk_invped_eq_polar': '2.1178e-58'}
  O_p(f1)=['-20.2657650871587', '-1.85746714954375e-59'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 8.41e-59 Rstar-a/b^2=8.46e-59  O_p spread over members: 1.0e-56
  k813 Apol/Adag               spread=   3.549e-59   value(member0)=3.243915603192241753255173
  k814R Apol/AdualR            spread=  4.2702e-58   value(member0)=256957.8584836864694906857
  k814P Apol/AdualP            spread=   1.156e-57   value(member0)=386649.564611273816429683
  k815(i) ApedX*AdualR         spread=   0.0091295   value(member0)=0.2136537295341793108939225
  k815(ii) Apol*AdualR         spread=   0.0091295   value(member0)=8.488970453430242379414785
  k815(iii) Aped*AdualR        spread=   0.0091295   value(member0)=0.02986648885749879026159222
  k815(i)P ApedX*AdualP        spread=   0.0091295   value(member0)=0.1419890511278613066610526
  k816(i) ApedX/AdualR         spread=  4.4705e-58   value(member0)=6467.215912616512117419447
  k816(ii) Apol/AdualR         spread=  4.2306e-58   value(member0)=256957.8584836864694906857
  k816(iii) Aped/AdualR        spread=  4.4151e-58   value(member0)=904.0470878478169636053317
  k816(i)P ApedX/AdualP        spread=  1.1761e-57   value(member0)=9731.347512063068102334754
  k817 Adag*Aant               spread=   0.0091295   value(member0)=-9051.566367721285155902714
  k818 Adag/Aant               spread=   3.413e-59   value(member0)=-22.90098133142907654018603
  Aant/A                       spread=  1.4895e-59   value(member0)=-14.28883904279317466854769
  k804 A*Adag                  spread=   0.0091295   value(member0)=633.471084712554069671022
  k805 A/Adag                  spread=  3.3906e-59   value(member0)=0.003055969131882719518781586
  k802 Ldag                    spread=  1.4879e-59   value(member0)=112.4223506916402574705715
  k803 sumcos_dag              spread=  9.6694e-60   value(member0)=-3.410954709119807692256773
  k801 sum 1/d                 spread=   1.784e-59   value(member0)=66.97496830363307170077411
  A                            spread=   0.0045752   value(member0)=1.391354764544912368534375
  Adag                         spread=   0.0045752   value(member0)=455.290843755259860977002
  Apol                         spread=   0.0045752   value(member0)=1476.925072048248486387446
  AdualR                       spread=   0.0045752   value(member0)=0.005747732646760107935285226
  Aped                         spread=   0.0045752   value(member0)=5.196220961031300806891585
  ApedX                        spread=   0.0045752   value(member0)=37.17182803459239211032904
  Aant                         spread=   0.0045752   value(member0)=-19.88084428200564856818283
  k908(i) ApedX1/ApedX2        3.7486e-58 value0=1.0
  k908(ii) Apol1/Apol2         4.1694e-59 value0=1.0
  k908(iii) Aped1/Aped2        6.7364e-59 value0=1.0
  k907R AdualR1/AdualR2        4.6043e-58 value0=1.0
  k907R AdualR1*AdualR2        0.0091295 value0=3.30364305786e-5
  k903a Adag1*Adag2            0.0091295 value0=207289.752407
=== family a=1.7 b=0.3 N=11 tau=1
  J=0.31626464602561946975184 lambda=0.02601606717731727011480 caustic axes=(1.6923309170557,0.2529504552727) closure_err=2.644e-58 worst tangency/closure=2.3488e-57
  checks: {'chk_polar_two_defs': '1.5363e-58', 'chk_polar_tangent_circle': '2.3209e-56', 'chk_polar_circumcircle': '1.4037e-56', 'chk_dualR_on_circle': '6.4199e-59', 'chk_ant_is_polar_reciprocal_of_inv': '8.7872e-59', 'chk_invped_eq_polar': '1.5363e-58'}
  O_p(f1)=['-20.2657650871587', '-7.79201033230384e-60'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 3.09e-59 Rstar-a/b^2=2.99e-59  O_p spread over members: 1.15e-56
  k813 Apol/Adag               spread=   4.464e-58   value(member0)=2.529489148884093157004879
  k814R Apol/AdualR            spread=  4.9474e-58   value(member0)=229207.7805862197729478787
  k814P Apol/AdualP            spread=   1.347e-57   value(member0)=331136.7796061356979341544
  k815(i) ApedX*AdualR         spread=   0.0040577   value(member0)=0.4066983880156045047284063
  k815(ii) Apol*AdualR         spread=   0.0040548   value(member0)=8.644703225151104827201444
  k815(iii) Aped*AdualR        spread=  6.8826e-58   value(member0)=0.03533295121472997138062368
  k815(i)P ApedX*AdualP        spread=   0.0040577   value(member0)=0.28151036256355102880136
  k816(i) ApedX/AdualR         spread=   2.9102e-6   value(member0)=10783.30076315841852038769
  k816(ii) Apol/AdualR         spread=  4.9429e-58   value(member0)=229207.7805862197729478787
  k816(iii) Aped/AdualR        spread=   0.0040548   value(member0)=936.8265304848421406955964
  k816(i)P ApedX/AdualP        spread=   2.9102e-6   value(member0)=15578.64867895911830860134
  k817 Adag*Aant               spread=    0.042621   value(member0)=-11601.6707377220982276451
  k818 Adag/Aant               spread=    0.038723   value(member0)=-26.6927468185015129512174
  Aant/A                       spread=    0.040674   value(member0)=-14.58626419258877720961788
  k804 A*Adag                  spread=   0.0020294   value(member0)=795.3832855719740055692341
  k805 A/Adag                  spread=   0.0020294   value(member0)=0.002568399977222370962224855
  k802 Ldag                    spread=  7.5049e-59   value(member0)=116.8836252644250803392962
  k803 sumcos_dag              spread=  1.1196e-58   value(member0)=-4.574633832330925363404844
  k801 sum 1/d                 spread=  2.1129e-58   value(member0)=72.80597335086633283567597
  A                            spread=   4.8596e-7   value(member0)=1.429287379271961742840263
  Adag                         spread=   0.0020294   value(member0)=556.4894066140285820535041
  Apol                         spread=   0.0020294   value(member0)=1407.633915499133199199335
  AdualR                       spread=   0.0020294   value(member0)=0.006141300752963015767583102
  Aped                         spread=   0.0020294   value(member0)=5.753333477062290683602231
  ApedX                        spread=   0.0020324   value(member0)=66.22349309621145821590011
  Aant                         spread=    0.040674   value(member0)=-20.84796332119367043409463
  k908(i) ApedX1/ApedX2        0.0040606 value0=1.00164322143
  k908(ii) Apol1/Apol2         0.0040548 value0=1.00164086893
  k908(iii) Aped1/Aped2        0.0040548 value0=0.998361819112
  k907R AdualR1/AdualR2        0.0040548 value0=1.00164086893
  k907R AdualR1*AdualR2        5.6325e-58 value0=3.76537900043e-5
  k903a Adag1*Adag2            1.0156e-57 value0=309173.147063
=== family a=1.7 b=0.3 N=12 tau=1
  J=0.29272008675930220179722 lambda=0.02228668129493632347195 caustic axes=(1.6934324074804,0.2602178293373) closure_err=2.7525e-58 worst tangency/closure=2.3873e-57
  checks: {'chk_polar_two_defs': '1.2528e-58', 'chk_polar_tangent_circle': '9.8622e-57', 'chk_polar_circumcircle': '1.4159e-56', 'chk_dualR_on_circle': '2.7702e-59', 'chk_ant_is_polar_reciprocal_of_inv': '9.1323e-59', 'chk_invped_eq_polar': '1.2528e-58'}
  O_p(f1)=['-20.2657650871587', '-2.72775116924819e-60'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 3.98e-59 Rstar-a/b^2=3.98e-59  O_p spread over members: 5.59e-57
  k813 Apol/Adag               spread=  4.3882e-58   value(member0)=2.08252418444021975831536
  k814R Apol/AdualR            spread=  4.0289e-58   value(member0)=209791.1050705788640965406
  k814P Apol/AdualP            spread=  7.7688e-58   value(member0)=292296.3918299297166875833
  k815(i) ApedX*AdualR         spread=    0.001724   value(member0)=0.6769056731349958856047174
  k815(ii) Apol*AdualR         spread=    0.001724   value(member0)=8.734533110267027759456246
  k815(iii) Aped*AdualR        spread=    0.001724   value(member0)=0.04004865125192365344779358
  k815(i)P ApedX*AdualP        spread=    0.001724   value(member0)=0.4858383242656019372750935
  k816(i) ApedX/AdualR         spread=  1.3819e-57   value(member0)=16258.31482951392843714117
  k816(ii) Apol/AdualR         spread=  4.0571e-58   value(member0)=209791.1050705788640965406
  k816(iii) Aped/AdualR        spread=  5.6782e-58   value(member0)=961.9118385218907005063726
  k816(i)P ApedX/AdualP        spread=  1.4302e-57   value(member0)=22652.27956305958742114751
  k817 Adag*Aant               spread=  3.4553e-58   value(member0)=-13617.69555518421305592986
  k818 Adag/Aant               spread=    0.001724   value(member0)=-31.02723237254640162312473
  Aant/A                       spread=  1.8419e-58   value(member0)=-14.3858641962124192415787
  k804 A*Adag                  spread=  3.3827e-58   value(member0)=946.6025377029171882219077
  k805 A/Adag                  spread=    0.001724   value(member0)=0.002240376484284641639229428
  k802 Ldag                    spread=  8.1745e-59   value(member0)=120.7069107722042473554857
  k803 sumcos_dag              spread=   1.048e-58   value(member0)=-5.747751195549061794373097
  k801 sum 1/d                 spread=  2.4171e-58   value(member0)=78.72003945606968675562509
  A                            spread=  0.00086237   value(member0)=1.456278155241567010137532
  Adag                         spread=  0.00086237   value(member0)=650.0149262665380199560375
  Apol                         spread=  0.00086237   value(member0)=1353.671804197191670256355
  AdualR                       spread=  0.00086237   value(member0)=0.006452474730717412128367827
  Aped                         spread=  0.00086237   value(member0)=6.206711831240427516215567
  ApedX                        spread=  0.00086237   value(member0)=104.9063656014867936691976
  Aant                         spread=  0.00086237   value(member0)=-20.94981977321593008333633
  k908(i) ApedX1/ApedX2        4.07e-57 value0=1.0
  k908(ii) Apol1/Apol2         2.7055e-58 value0=1.0
  k908(iii) Aped1/Aped2        7.0413e-58 value0=1.0
  k907R AdualR1/AdualR2        4.8508e-58 value0=1.0
  k907R AdualR1*AdualR2        0.001724 value0=4.16344301505e-5
  k903a Adag1*Adag2            0.001724 value0=422519.404369
=== family a=1.7 b=0.3 N=13 tau=1
  J=0.27222756030863379348664 lambda=0.01927545037827277986757 caustic axes=(1.6943212651742,0.2659408761768) closure_err=4.464e-58 worst tangency/closure=3.9217e-57
  checks: {'chk_polar_two_defs': '1.4204e-58', 'chk_polar_tangent_circle': '1.3551e-56', 'chk_polar_circumcircle': '2.2114e-56', 'chk_dualR_on_circle': '3.7766e-59', 'chk_ant_is_polar_reciprocal_of_inv': '8.969e-59', 'chk_invped_eq_polar': '1.4204e-58'}
  O_p(f1)=['-20.2657650871587', '-4.4569025827275e-59'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.47e-58 Rstar-a/b^2=1.44e-58  O_p spread over members: 7.24e-57
  k813 Apol/Adag               spread=  6.6654e-58   value(member0)=1.78370223946544246278111
  k814R Apol/AdualR            spread=  5.1509e-58   value(member0)=195607.639739591841657146
  k814P Apol/AdualP            spread=  1.0148e-57   value(member0)=263925.2575855142114444913
  k815(i) ApedX*AdualR         spread=  0.00076089   value(member0)=1.02692328615676686069275
  k815(ii) Apol*AdualR         spread=  0.00076063   value(member0)=8.839511873642854830063298
  k815(iii) Aped*AdualR        spread=  6.4265e-58   value(member0)=0.04421809538411721035300364
  k815(i)P ApedX*AdualP        spread=  0.00076089   value(member0)=0.7611019954528815680812977
  k816(i) ApedX/AdualR         spread=   2.6025e-7   value(member0)=22724.5625177228651217457
  k816(ii) Apol/AdualR         spread=  5.1717e-58   value(member0)=195607.639739591841657146
  k816(iii) Aped/AdualR        spread=  0.00076063   value(member0)=978.4926357367741836465135
  k816(i)P ApedX/AdualP        spread=   2.6025e-7   value(member0)=30661.30762577874354105681
  k817 Adag*Aant               spread=    0.012033   value(member0)=-15715.30492407541042063343
  k818 Adag/Aant               spread=    0.012784   value(member0)=-34.58171832747065128822673
  Aant/A                       spread=    0.012409   value(member0)=-14.43212720797350027595949
  k804 A*Adag                  spread=  0.00038039   value(member0)=1088.911197747271565407225
  k805 A/Adag                  spread=  0.00038039   value(member0)=0.00200365563776335093928052
  k802 Ldag                    spread=  1.2906e-58   value(member0)=123.9794281920613738321141
  k803 sumcos_dag              spread=  1.6002e-58   value(member0)=-6.926264050738707683249859
  k801 sum 1/d                 spread=  4.3286e-58   value(member0)=84.69521057934442607271273
  A                            spread=   1.8498e-8   value(member0)=1.477092773115474882896242
  Adag                         spread=  0.00038039   value(member0)=737.1989204513856262682187
  Apol                         spread=  0.00038039   value(member0)=1314.943365340643113321507
  AdualR                       spread=  0.00038039   value(member0)=0.006722351780795465659169855
  Aped                         spread=  0.00038039   value(member0)=6.577771712340352834373389
  ApedX                        spread=  0.00038065   value(member0)=152.7625033088121930003741
  Aant                         spread=    0.012409   value(member0)=-21.31759079958087343241768
  k908(i) ApedX1/ApedX2        0.00076115 value0=0.999927726595
  k908(ii) Apol1/Apol2         0.00076063 value0=0.999927775997
  k908(iii) Aped1/Aped2        0.00076063 value0=1.00007222922
  k907R AdualR1/AdualR2        0.00076063 value0=0.999927775997
  k907R AdualR1*AdualR2        4.9649e-58 value0=4.51932775042e-5
  k903a Adag1*Adag2            1.0849e-57 value0=543501.502169
=== family a=1.7 b=0.3 N=14 tau=1
  J=0.25427698886913096088738 lambda=0.01681723031647839436569 caustic axes=(1.6950465390907,0.2705231407542) closure_err=4.4498e-58 worst tangency/closure=3.8689e-57
  checks: {'chk_polar_two_defs': '1.2646e-58', 'chk_polar_tangent_circle': '1.7683e-56', 'chk_polar_circumcircle': '2.0862e-56', 'chk_dualR_on_circle': '5.0596e-59', 'chk_ant_is_polar_reciprocal_of_inv': '1.097e-58', 'chk_invped_eq_polar': '1.2646e-58'}
  O_p(f1)=['-20.2657650871587', '-1.00008267518683e-59'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 2.9e-59 Rstar-a/b^2=2.74e-59  O_p spread over members: 8.85e-57
  k813 Apol/Adag               spread=  6.2476e-58   value(member0)=1.573529248020313769889499
  k814R Apol/AdualR            spread=  4.8968e-58   value(member0)=184894.3140668664504584227
  k814P Apol/AdualP            spread=  1.0098e-57   value(member0)=242495.9553166056041870575
  k815(i) ApedX*AdualR         spread=  0.00033355   value(member0)=1.448326021380045112223709
  k815(ii) Apol*AdualR         spread=  0.00033355   value(member0)=8.936078581840988942251321
  k815(iii) Aped*AdualR        spread=  0.00033355   value(member0)=0.04785911493129788925245475
  k815(i)P ApedX*AdualP        spread=  0.00033355   value(member0)=1.104295722865278226727386
  k816(i) ApedX/AdualR         spread=  1.7834e-57   value(member0)=29966.97531425337178309035
  k816(ii) Apol/AdualR         spread=  4.8527e-58   value(member0)=184894.3140668664504584227
  k816(iii) Aped/AdualR        spread=  7.0312e-58   value(member0)=990.2417650009771244643586
  k816(i)P ApedX/AdualP        spread=  1.6212e-57   value(member0)=39302.83277478704892421627
  k817 Adag*Aant               spread=  0.00033355   value(member0)=-17619.70850655113984415807
  k818 Adag/Aant               spread=  6.6804e-58   value(member0)=-37.87234319155797716054921
  Aant/A                       spread=  2.0664e-58   value(member0)=-14.4370785536142320071801
  k804 A*Adag                  spread=  0.00033355   value(member0)=1220.448336629723220755158
  k805 A/Adag                  spread=  5.7476e-58   value(member0)=0.001828935982823647257244527
  k802 Ldag                    spread=   1.222e-58   value(member0)=126.7841060713645941621497
  k803 sumcos_dag              spread=  1.5107e-58   value(member0)=-8.106917121564152548911686
  k801 sum 1/d                 spread=  4.5944e-58   value(member0)=90.71668766378872581801323
  A                            spread=  0.00016679   value(member0)=1.494028740700582484685984
  Adag                         spread=  0.00016679   value(member0)=816.8841089746563523197002
  Apol                         spread=  0.00016679   value(member0)=1285.391037714635056940141
  AdualR                       spread=  0.00016679   value(member0)=0.00695203118712334987208394
  Aped                         spread=  0.00016679   value(member0)=6.884191633078864249794847
  ApedX                        spread=  0.00016679   value(member0)=208.3313469684449888277057
  Aant                         spread=  0.00016679   value(member0)=-21.56941029085165785645275
  k908(i) ApedX1/ApedX2        4.9532e-57 value0=1.0
  k908(ii) Apol1/Apol2         3.0819e-58 value0=1.0
  k908(iii) Aped1/Aped2        8.0705e-58 value0=1.0
  k907R AdualR1/AdualR2        5.7337e-58 value0=1.0
  k907R AdualR1*AdualR2        0.00033355 value0=4.83307376267e-5
  k903a Adag1*Adag2            0.00033355 value0=667299.647495
=== family a=1.7 b=0.3 N=15 tau=1
  J=0.23845178331616943173663 lambda=0.01478909169662863496624 caustic axes=(1.6956446881063,0.2742460725395) closure_err=3.3768e-58 worst tangency/closure=2.9336e-57
  checks: {'chk_polar_two_defs': '1.4468e-58', 'chk_polar_tangent_circle': '1.962e-56', 'chk_polar_circumcircle': '1.509e-56', 'chk_dualR_on_circle': '5.5837e-59', 'chk_ant_is_polar_reciprocal_of_inv': '8.0981e-59', 'chk_invped_eq_polar': '1.4468e-58'}
  O_p(f1)=['-20.2657650871587', '-3.94155891506569e-59'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.69e-58 Rstar-a/b^2=1.67e-58  O_p spread over members: 1.11e-56
  k813 Apol/Adag               spread=  4.4272e-58   value(member0)=1.419701508725236413328442
  k814R Apol/AdualR            spread=   3.678e-58   value(member0)=176582.6010360950485675867
  k814P Apol/AdualP            spread=  9.0939e-58   value(member0)=225870.783369178995981097
  k815(i) ApedX*AdualR         spread=  0.00014993   value(member0)=1.928880063908543288696873
  k815(ii) Apol*AdualR         spread=   0.0001499   value(member0)=9.020178588567962271927108
  k815(iii) Aped*AdualR        spread=  4.2255e-58   value(member0)=0.05102804088486827701059591
  k815(i)P ApedX*AdualP        spread=  0.00014993   value(member0)=1.507971299744989546606615
  k816(i) ApedX/AdualR         spread=   3.0928e-8   value(member0)=37760.52274655842627078658
  k816(ii) Apol/AdualR         spread=  3.6676e-58   value(member0)=176582.6010360950485675867
  k816(iii) Aped/AdualR        spread=   0.0001499   value(member0)=998.9452089835805278118997
  k816(i)P ApedX/AdualP        spread=   3.0928e-8   value(member0)=48300.33538497629911326714
  k817 Adag*Aant               spread=   0.0037853   value(member0)=-19336.35073360139472194818
  k818 Adag/Aant               spread=   0.0036359   value(member0)=-40.86904062885968956070853
  Aant/A                       spread=   0.0037106   value(member0)=-14.42768962175024771772975
  k804 A*Adag                  spread=   7.4953e-5   value(member0)=1340.225028437759594989174
  k805 A/Adag                  spread=   7.4953e-5   value(member0)=0.001695933293294620499406922
  k802 Ldag                    spread=  9.3715e-59   value(member0)=129.1944756099237836698774
  k803 sumcos_dag              spread=  1.0801e-58   value(member0)=-9.28713939237621893759955
  k801 sum 1/d                 spread=  3.6679e-58   value(member0)=96.77412912484888323028226
  A                            spread=  7.1511e-10   value(member0)=1.507624703377576671190218
  Adag                         spread=   7.4953e-5   value(member0)=888.9646245748118994812961
  Apol                         spread=   7.4953e-5   value(member0)=1262.064418712223828412442
  AdualR                       spread=   7.4953e-5   value(member0)=0.007147161788913997684976855
  Aped                         spread=   7.4953e-5   value(member0)=7.139623026866154676227794
  ApedX                        spread=   7.4984e-5   value(member0)=269.8805653036202231258514
  Aant                         spread=   0.0037106   value(member0)=-21.75154128641495857596485
  k908(i) ApedX1/ApedX2        0.00014996 value0=0.999926078739
  k908(ii) Apol1/Apol2         0.0001499 value0=0.999926109226
  k908(iii) Aped1/Aped2        0.0001499 value0=1.00007389623
  k907R AdualR1/AdualR2        0.0001499 value0=0.999926109226
  k907R AdualR1*AdualR2        4.0697e-58 value0=5.10856963986e-5
  k903a Adag1*Adag2            5.3544e-58 value0=790316.500843
=== family a=1.7 b=0.3 N=16 tau=1
  J=0.22441379814336287565249 lambda=0.01309903988253351790426 caustic axes=(1.6961429657070,0.2773102236079) closure_err=3.4943e-58 worst tangency/closure=3.0363e-57
  checks: {'chk_polar_two_defs': '1.2976e-58', 'chk_polar_tangent_circle': '4.8619e-56', 'chk_polar_circumcircle': '1.5137e-56', 'chk_dualR_on_circle': '1.3615e-58', 'chk_ant_is_polar_reciprocal_of_inv': '1.5838e-58', 'chk_invped_eq_polar': '1.2976e-58'}
  O_p(f1)=['-20.2657650871587', '6.09328632604698e-60'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 6.83e-59 Rstar-a/b^2=-6.72e-59  O_p spread over members: 2.47e-56
  k813 Apol/Adag               spread=  4.3529e-58   value(member0)=1.303455609576602753019481
  k814R Apol/AdualR            spread=    5.53e-58   value(member0)=169991.3173370533445151789
  k814P Apol/AdualP            spread=  1.4276e-57   value(member0)=212687.0245174211580215158
  k815(i) ApedX*AdualR         spread=   6.0977e-5   value(member0)=2.456282831940165118790444
  k815(ii) Apol*AdualR         spread=   6.0977e-5   value(member0)=9.097948816856198196369499
  k815(iii) Aped*AdualR        spread=   6.0977e-5   value(member0)=0.05380306456954929669621951
  k815(i)P ApedX*AdualP        spread=   6.0977e-5   value(member0)=1.963198062041135441503836
  k816(i) ApedX/AdualR         spread=  1.2102e-57   value(member0)=45894.60358144553893385743
  k816(ii) Apol/AdualR         spread=  5.5624e-58   value(member0)=169991.3173370533445151789
  k816(iii) Aped/AdualR        spread=  4.9411e-58   value(member0)=1005.287456223418326306777
  k816(i)P ApedX/AdualP        spread=  1.1957e-57   value(member0)=57421.67794246845930245808
  k817 Adag*Aant               spread=  3.5014e-58   value(member0)=-20965.59519515236806105926
  k818 Adag/Aant               spread=   6.0977e-5   value(member0)=-43.41807271509888954735868
  Aant/A                       spread=  1.0779e-58   value(member0)=-14.46773501053532219241887
  k804 A*Adag                  spread=  3.4431e-58   value(member0)=1449.127674780146381537928
  k805 A/Adag                  spread=   6.0977e-5   value(member0)=0.001591948128327306649621775
  k802 Ldag                    spread=  9.0411e-59   value(member0)=131.2734881713461203019955
  k803 sumcos_dag              spread=  1.0739e-58   value(member0)=-10.46495907530076428421208
  k801 sum 1/d                 spread=  4.0172e-58   value(member0)=102.8600853224824033691669
  A                            spread=   3.0489e-5   value(member0)=1.518860128377052357391132
  Adag                         spread=   3.0489e-5   value(member0)=954.0889563863808869249599
  Apol                         spread=   3.0489e-5   value(member0)=1243.612602236914857150605
  AdualR                       spread=   3.0489e-5   value(member0)=0.007315741896223555838552849
  Aped                         spread=   3.0489e-5   value(member0)=7.354423561241665266359377
  ApedX                        spread=   3.0489e-5   value(member0)=335.7530742313527840094206
  Aant                         spread=   3.0489e-5   value(member0)=-21.97446585542685440553111
  k908(i) ApedX1/ApedX2        2.9522e-57 value0=1.0
  k908(ii) Apol1/Apol2         1.8436e-58 value0=1.0
  k908(iii) Aped1/Aped2        4.6641e-58 value0=1.0
  k907R AdualR1/AdualR2        4.3616e-58 value0=1.0
  k907R AdualR1*AdualR2        6.0977e-5 value0=5.35200794922e-5
  k903a Adag1*Adag2            6.0977e-5 value0=910285.736698
=== family a=1.7 b=0.3 N=5 tau=2
  J=0.58823528958665147217583 lambda=0.08999999861351535582563 caustic axes=(1.6733200534824,0.0000372355293) closure_err=1.3571e-51 worst tangency/closure=1.3397e-50
  checks: {'chk_polar_two_defs': '1.4755e-43', 'chk_polar_tangent_circle': '5.5641e-53', 'chk_polar_circumcircle': '9.3217e-35', 'chk_dualR_on_circle': '1.8217e-55', 'chk_ant_is_polar_reciprocal_of_inv': '6.2829e-46', 'chk_invped_eq_polar': '1.4755e-43'}
  O_p(f1)=['-20.2657650871587', '-2.05363833274352e-54'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 2.05e-54 Rstar-a/b^2=1.19e-56  O_p spread over members: 4.91e-53
  k813 Apol/Adag               spread=  1.3984e-43   value(member0)=8142390532.703729771043027
  k814R Apol/AdualR            spread=  1.3984e-43   value(member0)=16269249281379.46727450498
  k814P Apol/AdualP            spread=  1.3991e-43   value(member0)=520231952555808530.9384179
  k815(i) ApedX*AdualR         spread=     0.99788   value(member0)=4.246478916359044779526094e-11
  k815(ii) Apol*AdualR         spread=     0.99825   value(member0)=147104.7205392239911028839
  k815(iii) Aped*AdualR        spread=  1.1973e-45   value(member0)=7.772476035139020340136003e-12
  k815(i)P ApedX*AdualP        spread=     0.99788   value(member0)=1.328004243471685865104015e-15
  k816(i) ApedX/AdualR         spread=     0.17152   value(member0)=0.004696451874904047660533738
  k816(ii) Apol/AdualR         spread=  1.3984e-43   value(member0)=16269249281379.46727450498
  k816(iii) Aped/AdualR        spread=     0.99825   value(member0)=0.0008596076977387506270605112
  k816(i)P ApedX/AdualP        spread=     0.17152   value(member0)=150.1756034780332663221025
  k817 Adag*Aant               spread=     0.86477   value(member0)=2322816.542829603707947819
  k818 Adag/Aant               spread=     0.99737   value(member0)=1.554087099516049064348466e-8
  Aant/A                       spread=      0.9449   value(member0)=64117869.77016271262441526
  k804 A*Adag                  spread=      0.9632   value(member0)=0.03622728813599056459763236
  k805 A/Adag                  spread=     0.95235   value(member0)=1.003565122362782271630956
  k802 Ldag                    spread=  5.4332e-52   value(member0)=151.1158382788090172114308
  k803 sumcos_dag              spread=  7.0757e-52   value(member0)=3.031139981724734572698318
  k801 sum 1/d                 spread=  5.3697e-52   value(member0)=75.85199999231688831146918
  A                            spread=     0.63069   value(member0)=0.1906736553671406946635689
  Adag                         spread=     0.95813   value(member0)=0.1899962953258287976291375
  Apol                         spread=     0.95813   value(member0)=1547024036.309810306277102
  AdualR                       spread=     0.95813   value(member0)=0.00009508883966025495454177032
  Aped                         spread=     0.95813   value(member0)=8.173909854100096383196063e-8
  ApedX                        spread=     0.94946   value(member0)=0.0000004465801593048547476132033
  Aant                         spread=     0.96562   value(member0)=12225588.60343121360857768
  k908(i) ApedX1/ApedX2        0.99755 value0=0.0439189524982
  k908(ii) Apol1/Apol2         0.99825 value0=0.036382902751
  k908(iii) Aped1/Aped2        0.99825 value0=27.4854375102
  k907R AdualR1/AdualR2        0.99825 value0=0.036382902751
  k907R AdualR1*AdualR2        2.703e-53 value0=2.48520231874e-7
  k903a Adag1*Adag2            2.2033e-49 value0=0.992185601149
=== family a=1.7 b=0.3 N=7 tau=2
  J=0.58642093685544460480515 lambda=0.08944566289894675232502 caustic axes=(1.6734856847613,0.0235443645285) closure_err=9.8784e-57 worst tangency/closure=9.7493e-56
  checks: {'chk_polar_two_defs': '1.2419e-54', 'chk_polar_tangent_circle': '6.5217e-58', 'chk_polar_circumcircle': '4.266e-51', 'chk_dualR_on_circle': '1.7988e-60', 'chk_ant_is_polar_reciprocal_of_inv': '7.7195e-57', 'chk_invped_eq_polar': '1.2419e-54'}
  O_p(f1)=['-20.2657650871587', '-6.02688540837877e-59'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.45e-58 Rstar-a/b^2=-1.32e-58  O_p spread over members: 3.75e-58
  k813 Apol/Adag               spread=  1.9027e-54   value(member0)=16960.65423583758224752373
  k814R Apol/AdualR            spread=  1.6291e-54   value(member0)=40568627.54051635154383576
  k814P Apol/AdualP            spread=  1.6289e-54   value(member0)=84224250.36968668662274427
  k815(i) ApedX*AdualR         spread=       1.525   value(member0)=0.0000397852289696915146928863
  k815(ii) Apol*AdualR         spread=      0.5206   value(member0)=224.4539692413748758365269
  k815(iii) Aped*AdualR        spread=  6.7993e-56   value(member0)=0.00009106966264549696627091214
  k815(i)P ApedX*AdualP        spread=       1.525   value(member0)=0.00001916350847411621024599919
  k816(i) ApedX/AdualR         spread=      1.9131   value(member0)=7.190927124794425135684426
  k816(ii) Apol/AdualR         spread=   1.629e-54   value(member0)=40568627.54051635154383576
  k816(iii) Aped/AdualR        spread=      0.5206   value(member0)=16.46026237180304732110825
  k816(i)P ApedX/AdualP        spread=      1.9131   value(member0)=14.92903465723573880734236
  k817 Adag*Aant               spread=     0.77092   value(member0)=233.593758096224703219814
  k818 Adag/Aant               spread=     0.52215   value(member0)=0.1355099454488029338942495
  Aant/A                       spread=     0.66876   value(member0)=42.66214709773754448848241
  k804 A*Adag                  spread=      0.3084   value(member0)=5.475433703818733220320453
  k805 A/Adag                  spread=     0.30681   value(member0)=0.1729761078328291418955781
  k802 Ldag                    spread=  3.9321e-57   value(member0)=151.5920278565748753265945
  k803 sumcos_dag              spread=  1.2176e-56   value(member0)=3.84676014473554763785456
  k801 sum 1/d                 spread=  3.8629e-57   value(member0)=76.67862463179557264650299
  A                            spread=    0.016767   value(member0)=0.9732004987582241571177164
  Adag                         spread=     0.30761   value(member0)=5.626213417281669223146732
  Apol                         spread=     0.30761   value(member0)=95424.26042754458177652771
  AdualR                       spread=     0.30761   value(member0)=0.002352168811534067385394467
  Aped                         spread=     0.30761   value(member0)=0.03871731578062290303128372
  ApedX                        spread=      1.7583   value(member0)=0.01691427450895579123893246
  Aant                         spread=     0.66914   value(member0)=41.51882283361490349350232
  k908(i) ApedX1/ApedX2        0.99177 value0=-0.661347438094
  k908(ii) Apol1/Apol2         0.5206 value0=0.757358414121
  k908(iii) Aped1/Aped2        0.5206 value0=1.32037880791
  k907R AdualR1/AdualR2        0.5206 value0=0.757358414121
  k907R AdualR1*AdualR2        4.4701e-56 value0=7.30525734553e-6
  k903a Adag1*Adag2            1.1837e-54 value0=41.7956370809
=== family a=1.7 b=0.3 N=7 tau=3
  J=0.58823529411736362708472 lambda=0.08999999999991326988792 caustic axes=(1.6733200530681,0.0000002944997) closure_err=2.6843e-47 worst tangency/closure=2.6604e-46
  checks: {'chk_polar_two_defs': '2.0708e-35', 'chk_polar_tangent_circle': '7.21e-49', 'chk_polar_circumcircle': '4.715e-22', 'chk_dualR_on_circle': '2.0208e-51', 'chk_ant_is_polar_reciprocal_of_inv': '2.7077e-37', 'chk_invped_eq_polar': '2.0708e-35'}
  O_p(f1)=['-20.2657650871587', '4.68876676328757e-50'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 4.69e-50 Rstar-a/b^2=-1.55e-56  O_p spread over members: 1.41e-48
  k813 Apol/Adag               spread=  4.4247e-35   value(member0)=130165922719759.0693942726
  k814R Apol/AdualR            spread=  4.4247e-35   value(member0)=260083423533685882.8951983
  k814P Apol/AdualP            spread=  4.4267e-35   value(member0)=1.329413811764313388604288e+26
  k815(i) ApedX*AdualR         spread=     0.99788   value(member0)=2.656877736514183521723027e-15
  k815(ii) Apol*AdualR         spread=     0.99825   value(member0)=2351645064.487340462660717
  k815(iii) Aped*AdualR        spread=  3.7883e-37   value(member0)=4.861992023088427254634692e-16
  k815(i)P ApedX*AdualP        spread=     0.99788   value(member0)=5.197853757107990185304415e-24
  k816(i) ApedX/AdualR         spread=     0.17148   value(member0)=0.0000002938410511254935048020828
  k816(ii) Apol/AdualR         spread=  4.4247e-35   value(member0)=260083423533685882.8951983
  k816(iii) Aped/AdualR        spread=     0.99825   value(member0)=5.377187015396714717632143e-8
  k816(i)P ApedX/AdualP        spread=     0.17148   value(member0)=150.196558674174700758603
  k817 Adag*Aant               spread=     0.86477   value(member0)=37132984782.81013072892914
  k818 Adag/Aant               spread=     0.99737   value(member0)=9.721426229464916861329074e-13
  Aant/A                       spread=      0.9449   value(member0)=1025000886011.475877433723
  k804 A*Adag                  spread=      0.9632   value(member0)=0.03622727091222669539056588
  k805 A/Adag                  spread=     0.95235   value(member0)=1.003565618615521924989396
  k802 Ldag                    spread=  7.1692e-48   value(member0)=226.6713926705489191287872
  k803 sumcos_dag              spread=   8.429e-48   value(member0)=5.031388141929325548806481
  k801 sum 1/d                 spread=  7.0945e-48   value(member0)=113.6297771881862611990004
  A                            spread=     0.63069   value(member0)=0.1906736571836311290002078
  Adag                         spread=     0.95813   value(member0)=0.1899962031846773573656832
  Apol                         spread=     0.95813   value(member0)=24731031100784.35488667614
  AdualR                       spread=     0.95813   value(member0)=0.00009508884020661625653676406
  Aped                         spread=     0.95813   value(member0)=5.113104768681499941299323e-12
  ApedX                        spread=     0.94946   value(member0)=2.794100475661620979954185e-11
  Aant                         spread=     0.96562   value(member0)=195440667552.2703194420724
  k908(i) ApedX1/ApedX2        0.99755 value0=0.0439170968492
  k908(ii) Apol1/Apol2         0.99825 value0=0.0363829028844
  k908(iii) Aped1/Aped2        0.99825 value0=27.4854374094
  k907R AdualR1/AdualR2        0.99825 value0=0.0363829028844
  k907R AdualR1*AdualR2        3.9453e-49 value0=2.48520233819e-7
  k903a Adag1*Adag2            4.3539e-45 value0=0.992184635165
=== family a=1.7 b=0.3 N=8 tau=3
  J=0.58823472123621378616344 lambda=0.08999982469836678160083 caustic axes=(1.6733201054495,0.0004186903787) closure_err=1.3549e-53 worst tangency/closure=1.3406e-52
  checks: {'chk_polar_two_defs': '1.2701e-47', 'chk_polar_tangent_circle': '1.4769e-54', 'chk_polar_circumcircle': '5.7998e-41', 'chk_dualR_on_circle': '2.0004e-57', 'chk_ant_is_polar_reciprocal_of_inv': '1.1115e-49', 'chk_invped_eq_polar': '1.2701e-47'}
  O_p(f1)=['-20.2657650871587', '-9.72558512137664e-58'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.27e-57 Rstar-a/b^2=8.21e-58  O_p spread over members: 6.21e-55
  k813 Apol/Adag               spread=  9.8716e-48   value(member0)=64395257.54441823802811953
  k814R Apol/AdualR            spread=   9.871e-48   value(member0)=128675600089.6733957072355
  k814P Apol/AdualP            spread=  9.8755e-48   value(member0)=32798013053850.17421029289
  k815(i) ApedX*AdualR         spread=     0.86361   value(member0)=0.000003526584573036071853760957
  k815(ii) Apol*AdualR         spread=     0.86361   value(member0)=944062.7150356443403939022
  k815(iii) Aped*AdualR        spread=     0.86361   value(member0)=2.901167277753291170010579e-8
  k815(i)P ApedX*AdualP        spread=     0.86361   value(member0)=1.383575844845671530643559e-8
  k816(i) ApedX/AdualR         spread=    6.94e-52   value(member0)=0.4806729245580553533433629
  k816(ii) Apol/AdualR         spread=   9.871e-48   value(member0)=128675600089.6733957072355
  k816(iii) Aped/AdualR        spread=  9.7119e-51   value(member0)=0.003954286452371271980107123
  k816(i)P ApedX/AdualP        spread=  3.8032e-51   value(member0)=122.5183083918070458540534
  k817 Adag*Aant               spread=  1.1041e-48   value(member0)=546304.8461191582028956019
  k818 Adag/Aant               spread=     0.86361   value(member0)=0.0000536233850803388359167269
  Aant/A                       spread=  1.1047e-48   value(member0)=264679.4626958843288603265
  k804 A*Adag                  spread=  6.6171e-52   value(member0)=2.064024312860497008223775
  k805 A/Adag                  spread=     0.86361   value(member0)=0.07045722422524699698699013
  k802 Ldag                    spread=  3.6027e-54   value(member0)=226.6763394151314023461295
  k803 sumcos_dag              spread=  5.2092e-54   value(member0)=4.03139012041412616160511
  k801 sum 1/d                 spread=  3.5559e-54   value(member0)=113.9263314135895288502477
  A                            spread=     0.63069   value(member0)=0.3813468549989279728552028
  Adag                         spread=     0.63069   value(member0)=5.412459250165572524414974
  Apol                         spread=     0.63069   value(member0)=348536707.363080863635979
  AdualR                       spread=     0.63069   value(member0)=0.00270864644983343647676068
  Aped                         spread=     0.63069   value(member0)=0.00001071076396083990004749716
  ApedX                        spread=     0.63069   value(member0)=0.001301973010635231875896858
  Aant                         spread=     0.63069   value(member0)=100934.6806818815666859909
  k908(i) ApedX1/ApedX2        2.9523e-51 value0=1.0
  k908(ii) Apol1/Apol2         4.3506e-47 value0=1.0
  k908(iii) Aped1/Aped2        1.9318e-50 value0=1.0
  k907R AdualR1/AdualR2        7.8928e-53 value0=1.0
  k907R AdualR1*AdualR2        0.86361 value0=7.3367655902e-6
  k903a Adag1*Adag2            0.86361 value0=29.2947151347
=== family a=1.7 b=0.3 N=9 tau=2
  J=0.56532420651331474547811 lambda=0.08312573834802331479838 caustic axes=(1.6753728724233,0.0829111672332) closure_err=1.666e-57 worst tangency/closure=1.6117e-56
  checks: {'chk_polar_two_defs': '1.4464e-56', 'chk_polar_tangent_circle': '1.0853e-57', 'chk_polar_circumcircle': '4.9684e-54', 'chk_dualR_on_circle': '2.6448e-60', 'chk_ant_is_polar_reciprocal_of_inv': '5.74e-59', 'chk_invped_eq_polar': '1.4464e-56'}
  O_p(f1)=['-20.2657650871587', '-5.88993515825747e-59'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.78e-58 Rstar-a/b^2=1.62e-58  O_p spread over members: 4.15e-58
  k813 Apol/Adag               spread=  2.3988e-56   value(member0)=441.7023845535101262214981
  k814R Apol/AdualR            spread=  1.3653e-56   value(member0)=3158045.109387538659361942
  k814P Apol/AdualP            spread=  1.3628e-56   value(member0)=6206843.382848902445273006
  k815(i) ApedX*AdualR         spread=      1.0552   value(member0)=0.00008164223582189404848048128
  k815(ii) Apol*AdualR         spread=    0.096234   value(member0)=63.29742979177411178414162
  k815(iii) Aped*AdualR        spread=  6.3984e-57   value(member0)=0.003030372986346308225126235
  k815(i)P ApedX*AdualP        spread=      1.0552   value(member0)=0.00004153961162758618156016687
  k816(i) ApedX/AdualR         spread=      1.0611   value(member0)=4.073306995322947307887716
  k816(ii) Apol/AdualR         spread=  1.3635e-56   value(member0)=3158045.109387538659361942
  k816(iii) Aped/AdualR        spread=    0.096234   value(member0)=151.1918354447111578072372
  k816(i)P ApedX/AdualP        spread=      1.0611   value(member0)=8.005705331782156126209174
  k817 Adag*Aant               spread=     0.40553   value(member0)=-389.3701428611617654092503
  k818 Adag/Aant               spread=     0.34223   value(member0)=-2.631372131041505426260934
  Aant/A                       spread=     0.37468   value(member0)=-7.826840207878312949744946
  k804 A*Adag                  spread=    0.049332   value(member0)=49.74806339718433925896179
  k805 A/Adag                  spread=    0.049336   value(member0)=0.0485546985157946180386723
  k802 Ldag                    spread=  6.1998e-58   value(member0)=157.1301012884725822253582
  k803 sumcos_dag              spread=  2.8735e-57   value(member0)=4.377859966674260324153422
  k801 sum 1/d                 spread=  6.2067e-58   value(member0)=80.0984327772011960105051
  A                            spread=  0.00029986   value(member0)=1.554188605026726800046919
  Adag                         spread=    0.049334   value(member0)=32.00902595494762389058133
  Apol                         spread=    0.049334   value(member0)=14138.46309153556206415539
  AdualR                       spread=    0.049334   value(member0)=0.00447696679490355068086855
  Aped                         spread=    0.049334   value(member0)=0.6768808269464935622821294
  ApedX                        spread=      1.0581   value(member0)=0.01823606016350918771263567
  Aant                         spread=     0.37468   value(member0)=-12.16438586444949160635268
  k908(i) ApedX1/ApedX2        1.8095 value0=0.550460978495
  k908(ii) Apol1/Apol2         0.096234 value0=0.987056713619
  k908(iii) Aped1/Aped2        0.096234 value0=1.01311301185
  k907R AdualR1/AdualR2        0.096234 value0=0.987056713619
  k907R AdualR1*AdualR2        3.9875e-57 value0=2.03060588172e-5
  k903a Adag1*Adag2            5.2027e-56 value0=1038.01304266
=== family a=1.7 b=0.3 N=9 tau=4
  J=0.58823529411764704109375 lambda=0.08999999999999999457468 caustic axes=(1.6733200530681,0.0000000023292) closure_err=1.9067e-43 worst tangency/closure=1.8813e-42
  checks: {'chk_polar_two_defs': '7.3568e-27', 'chk_polar_tangent_circle': '1.4296e-44', 'chk_polar_circumcircle': '8.504e-10', 'chk_dualR_on_circle': '4.0068e-47', 'chk_ant_is_polar_reciprocal_of_inv': '3.9273e-29', 'chk_invped_eq_polar': '7.3568e-27'}
  O_p(f1)=['-20.2657650871587', '-8.78260301981205e-46'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 8.78e-46 Rstar-a/b^2=1.52e-55  O_p spread over members: 3.41e-44
  k813 Apol/Adag               spread=  4.9921e-27   value(member0)=2080858144300640900.221888
  k814R Apol/AdualR            spread=  4.9921e-27   value(member0)=4157744966831457887706.968
  k814P Apol/AdualP            spread=  4.9943e-27   value(member0)=3.397430109067189836438291e+34
  k815(i) ApedX*AdualR         spread=     0.99788   value(member0)=1.661982329051949693886054e-19
  k815(ii) Apol*AdualR         spread=     0.99825   value(member0)=37593862376188.40443765937
  k815(iii) Aped*AdualR        spread=   4.274e-29   value(member0)=3.041368676164373708582835e-20
  k815(i)P ApedX*AdualP        spread=     0.99788   value(member0)=2.033919298335714197314769e-32
  k816(i) ApedX/AdualR         spread=     0.17148   value(member0)=1.838092238150916519573295e-11
  k816(ii) Apol/AdualR         spread=  4.9921e-27   value(member0)=4157744966831457887706.968
  k816(iii) Aped/AdualR        spread=     0.99825   value(member0)=3.363643559436619887171387e-12
  k816(i)P ApedX/AdualP        spread=     0.17148   value(member0)=150.1965599851513894256155
  k817 Adag*Aant               spread=     0.86477   value(member0)=593615227306027.1333340891
  k818 Adag/Aant               spread=     0.99737   value(member0)=6.081137336423661862547848e-17
  Aant/A                       spread=      0.9449   value(member0)=16385866568914980.23573783
  k804 A*Adag                  spread=      0.9632   value(member0)=0.03622727091114928066193608
  k805 A/Adag                  spread=     0.95235   value(member0)=1.00356561864656451643947
  k802 Ldag                    spread=  3.7948e-44   value(member0)=302.2269482259952704461499
  k803 sumcos_dag              spread=  4.2629e-44   value(member0)=7.031388172858100143987525
  k801 sum 1/d                 spread=  3.7577e-44   value(member0)=151.4075549659094368216636
  A                            spread=     0.63069   value(member0)=0.19067365718374475767929
  Adag                         spread=     0.95813   value(member0)=0.189996203178913563024815
  Apol                         spread=     0.95813   value(member0)=395355146771041606.2546928
  AdualR                       spread=     0.95813   value(member0)=0.00009508884020665043360236874
  Aped                         spread=     0.95813   value(member0)=3.198449649353976386334506e-16
  ApedX                        spread=     0.94946   value(member0)=1.747820591186169547980972e-15
  Aant                         spread=     0.96562   value(member0)=3124353104819878.885701317
  k908(i) ApedX1/ApedX2        0.99755 value0=0.0439170967331
  k908(ii) Apol1/Apol2         0.99825 value0=0.0363829028844
  k908(iii) Aped1/Aped2        0.99825 value0=27.4854374094
  k907R AdualR1/AdualR2        0.99825 value0=0.0363829028844
  k907R AdualR1*AdualR2        6.2589e-45 value0=2.48520233819e-7
  k903a Adag1*Adag2            3.0884e-41 value0=0.992184635105
=== family a=1.7 b=0.3 N=10 tau=3
  J=0.58742307953697180356365 lambda=0.08975163392433914038161 caustic axes=(1.6733942649823,0.0157596343758) closure_err=2.1866e-56 worst tangency/closure=2.1608e-55
  checks: {'chk_polar_two_defs': '1.1595e-53', 'chk_polar_tangent_circle': '1.0604e-57', 'chk_polar_circumcircle': '4.6953e-50', 'chk_dualR_on_circle': '1.5363e-60', 'chk_ant_is_polar_reciprocal_of_inv': '4.4437e-56', 'chk_invped_eq_polar': '1.1595e-53'}
  O_p(f1)=['-20.2657650871587', '-2.30203970760991e-59'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 2.03e-58 Rstar-a/b^2=1.99e-58  O_p spread over members: 5.88e-58
  k813 Apol/Adag               spread=  5.9478e-54   value(member0)=41717.72556570082483711245
  k814R Apol/AdualR            spread=  5.4951e-54   value(member0)=90698507.10244149174038029
  k814P Apol/AdualP            spread=  5.4947e-54   value(member0)=197391575.4738326335370902
  k815(i) ApedX*AdualR         spread=     0.23432   value(member0)=-0.00004649653516329448996697783
  k815(ii) Apol*AdualR         spread=     0.23432   value(member0)=1290.213685255557848630919
  k815(iii) Aped*AdualR        spread=     0.23432   value(member0)=0.00007958774405171661493549678
  k815(i)P ApedX*AdualP        spread=     0.23432   value(member0)=-0.00002136446965694358000104854
  k816(i) ApedX/AdualR         spread=  2.8192e-55   value(member0)=-3.268579749959538411840716
  k816(ii) Apol/AdualR         spread=  5.4952e-54   value(member0)=90698507.10244149174038029
  k816(iii) Aped/AdualR        spread=   9.581e-56   value(member0)=5.594801583361069008109517
  k816(i)P ApedX/AdualP        spread=  2.8065e-55   value(member0)=-7.113569197755973910563127
  k817 Adag*Aant               spread=     0.23432   value(member0)=1900.460332386778703572185
  k818 Adag/Aant               spread=  1.2317e-54   value(member0)=0.03538031766450686595780964
  Aant/A                       spread=  7.7994e-55   value(member0)=171.7554518163392651864883
  k804 A*Adag                  spread=     0.23432   value(member0)=11.06491999112185411030993
  k805 A/Adag                  spread=  5.2463e-55   value(member0)=0.1645613118674972791327354
  k802 Ldag                    spread=  5.8092e-57   value(member0)=226.998726220889760065784
  k803 sumcos_dag              spread=  1.1711e-56   value(member0)=4.920462795701276388843063
  k801 sum 1/d                 spread=  5.7083e-57   value(member0)=114.6757970167964636597326
  A                            spread=     0.12497   value(member0)=1.349391621971882801293311
  Adag                         spread=     0.12497   value(member0)=8.199932333174374219660896
  Apol                         spread=     0.12497   value(member0)=342082.5267326854052281543
  AdualR                       spread=     0.12497   value(member0)=0.003771644513909280942285699
  Aped                         spread=     0.12497   value(member0)=0.02110160269829473447787069
  ApedX                        spread=     0.12497   value(member0)=-0.01232792088220986229801093
  Aant                         spread=     0.12497   value(member0)=231.7653677089636049846064
  k908(i) ApedX1/ApedX2        7.0478e-55 value0=1.0
  k908(ii) Apol1/Apol2         3.29e-53 value0=1.0
  k908(iii) Aped1/Aped2        1.0049e-55 value0=1.0
  k907R AdualR1/AdualR2        1.0008e-55 value0=1.0
  k907R AdualR1*AdualR2        0.23432 value0=1.42253023393e-5
  k903a Adag1*Adag2            0.23432 value0=67.2388902686
=== family a=1.7 b=0.3 N=11 tau=3
  J=0.58479099859857562405356 lambda=0.08894913118210320407666 caustic axes=(1.6736340307301,0.0324171068711) closure_err=6.3412e-57 worst tangency/closure=6.3419e-56
  checks: {'chk_polar_two_defs': '7.166e-55', 'chk_polar_tangent_circle': '1.2396e-57', 'chk_polar_circumcircle': '7.8384e-52', 'chk_dualR_on_circle': '3.024e-60', 'chk_ant_is_polar_reciprocal_of_inv': '3.1008e-57', 'chk_invped_eq_polar': '7.166e-55'}
  O_p(f1)=['-20.2657650871587', '-1.51118152372284e-58'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.53e-58 Rstar-a/b^2=2.24e-59  O_p spread over members: 5.6e-58
  k813 Apol/Adag               spread=  3.8224e-55   value(member0)=7766.960939656198513236065
  k814R Apol/AdualR            spread=  2.9883e-55   value(member0)=21341822.43685582905516474
  k814P Apol/AdualP            spread=  2.9884e-55   value(member0)=43440852.91905077373535722
  k815(i) ApedX*AdualR         spread=      1.8003   value(member0)=0.00003055448401673083870292539
  k815(ii) Apol*AdualR         spread=    0.092877   value(member0)=433.2306917314753166313525
  k815(iii) Aped*AdualR        spread=  3.1036e-56   value(member0)=0.0004860892391010307593585229
  k815(i)P ApedX*AdualP        spread=      1.8003   value(member0)=0.00001501094773046799132306759
  k816(i) ApedX/AdualR         spread=      1.8822   value(member0)=1.505175845064541030256387
  k816(ii) Apol/AdualR         spread=  2.9887e-55   value(member0)=21341822.43685582905516474
  k816(iii) Aped/AdualR        spread=    0.092877   value(member0)=23.9457416737929978562371
  k816(i)P ApedX/AdualP        spread=      1.8822   value(member0)=3.063755342179187059462549
  k817 Adag*Aant               spread=     0.23639   value(member0)=612.6190791336585107308231
  k818 Adag/Aant               spread=     0.30731   value(member0)=0.2501830934181989146897681
  Aant/A                       spread=     0.27272   value(member0)=30.58159580505448648000351
  k804 A*Adag                  spread=    0.047571   value(member0)=20.03227964422986795559614
  k805 A/Adag                  spread=    0.047568   value(member0)=0.1307018990998117292809471
  k802 Ldag                    spread=  1.6991e-57   value(member0)=228.0211157576366791521482
  k803 sumcos_dag              spread=   9.259e-57   value(member0)=6.346598886609964482324221
  k801 sum 1/d                 spread=  1.6701e-57   value(member0)=115.4829616383277578105324
  A                            spread=   0.0002759   value(member0)=1.61810289932357040043257
  Adag                         spread=     0.04757   value(member0)=12.38010243514435063950791
  Apol                         spread=     0.04757   value(member0)=96155.7720427087570552295
  AdualR                       spread=     0.04757   value(member0)=0.004505508952068427357510065
  Aped                         spread=     0.04757   value(member0)=0.1078877534751923594625494
  ApedX                        spread=      1.8402   value(member0)=0.0067815832443754498352572
  Aant                         spread=     0.27272   value(member0)=49.48416883810020262675848
  k908(i) ApedX1/ApedX2        0.7079 value0=-0.574107161303
  k908(ii) Apol1/Apol2         0.092877 value0=0.984238208102
  k908(iii) Aped1/Aped2        0.092877 value0=1.01601420446
  k907R AdualR1/AdualR2        0.092877 value0=0.984238208102
  k907R AdualR1*AdualR2        2.422e-56 value0=2.06246930368e-5
  k903a Adag1*Adag2            4.7113e-55 value0=155.721384359
=== family a=1.7 b=0.3 N=12 tau=5
  J=0.58823529408181093177600 lambda=0.08999999998903414512379 caustic axes=(1.6733200530714,0.0000033114732) closure_err=1.6716e-49 worst tangency/closure=1.6489e-48
  checks: {'chk_polar_two_defs': '6.1753e-39', 'chk_polar_tangent_circle': '7.0006e-51', 'chk_polar_circumcircle': '1.857e-28', 'chk_dualR_on_circle': '2.1829e-53', 'chk_ant_is_polar_reciprocal_of_inv': '1.8106e-41', 'chk_invped_eq_polar': '6.1753e-39'}
  O_p(f1)=['-20.2657650871587', '2.51733378992945e-52'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 2.52e-52 Rstar-a/b^2=-1.09e-56  O_p spread over members: 8.39e-51
  k813 Apol/Adag               spread=   1.977e-39   value(member0)=1029496117639.833889561933
  k814R Apol/AdualR            spread=   1.977e-39   value(member0)=2057027447943423.998098213
  k814P Apol/AdualP            spread=  1.9779e-39   value(member0)=8316014283763291045860.815
  k815(i) ApedX*AdualR         spread=     0.86361   value(member0)=2.274566346979068101241309e-10
  k815(ii) Apol*AdualR         spread=     0.86361   value(member0)=15091936624.39300417499831
  k815(iii) Aped*AdualR        spread=     0.86361   value(member0)=1.814804974107495742036435e-12
  k815(i)P ApedX*AdualP        spread=     0.86361   value(member0)=5.626307565439877777018803e-17
  k816(i) ApedX/AdualR         spread=  1.4469e-43   value(member0)=0.00003100228634900281844733564
  k816(ii) Apol/AdualR         spread=   1.977e-39   value(member0)=2057027447943423.998098213
  k816(iii) Aped/AdualR        spread=  1.9378e-42   value(member0)=0.0000002473574954170945308516128
  k816(i)P ApedX/AdualP        spread=  7.5178e-43   value(member0)=125.333989279232031230789
  k817 Adag*Aant               spread=  2.2124e-40   value(member0)=8733271229.473561630672685
  k818 Adag/Aant               spread=     0.86361   value(member0)=3.353966225352913417361031e-9
  Aant/A                       spread=  2.2124e-40   value(member0)=4231442458.57621910346979
  k804 A*Adag                  spread=  8.2858e-48   value(member0)=2.063899323922769839681464
  k805 A/Adag                  spread=     0.86361   value(member0)=0.07046166083187412927018358
  k802 Ldag                    spread=  2.7083e-50   value(member0)=377.7872298083380190376525
  k803 sumcos_dag              spread=   3.316e-50   value(member0)=8.062770471741220351914482
  k801 sum 1/d                 spread=  2.6787e-50   value(member0)=189.4817766099926218249515
  A                            spread=     0.63069   value(member0)=0.3813473143387540990739877
  Adag                         spread=     0.63069   value(member0)=5.41212497458259354579041
  Apol                         spread=     0.63069   value(member0)=5571761649514.36472446295
  AdualR                       spread=     0.63069   value(member0)=0.002708647205988866879689904
  Aped                         spread=     0.63069   value(member0)=6.700041888419170448730192e-10
  ApedX                        spread=     0.63069   value(member0)=8.397425629849327288968945e-8
  Aant                         spread=     0.63069   value(member0)=1613649217.357015897222099
  k908(i) ApedX1/ApedX2        5.6255e-43 value0=1.0
  k908(ii) Apol1/Apol2         8.5916e-39 value0=1.0
  k908(iii) Aped1/Aped2        3.8575e-42 value0=1.0
  k907R AdualR1/AdualR2        9.7979e-49 value0=1.0
  k907R AdualR1*AdualR2        0.86361 value0=7.33676968651e-6
  k903a Adag1*Adag2            0.86361 value0=29.2910967405
=== family a=1.7 b=0.3 N=13 tau=5
  J=0.58823517997663492052153 lambda=0.08999996507285367430677 caustic axes=(1.6733200635046,0.0001868880582) closure_err=4.576e-54 worst tangency/closure=3.2727e-53
  checks: {'chk_polar_two_defs': '3.9796e-46', 'chk_polar_tangent_circle': '2.5411e-54', 'chk_polar_circumcircle': '4.5519e-40', 'chk_dualR_on_circle': '7.859e-57', 'chk_ant_is_polar_reciprocal_of_inv': '1.8847e-48', 'chk_invped_eq_polar': '3.9796e-46'}
  O_p(f1)=['-20.2657650871587', '4.08123150586673e-57'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 4.14e-57 Rstar-a/b^2=-6.8e-58  O_p spread over members: 2.33e-54
  k813 Apol/Adag               spread=  1.0835e-47   value(member0)=323220318.2285044170702573
  k814R Apol/AdualR            spread=  1.0835e-47   value(member0)=645831753725.3586655233562
  k814P Apol/AdualP            spread=   1.084e-47   value(member0)=821026620293191.2884457894
  k815(i) ApedX*AdualR         spread=     0.51717   value(member0)=0.0000005448083174060552509408387
  k815(ii) Apol*AdualR         spread=     0.51991   value(member0)=3576440.676512737449501005
  k815(iii) Aped*AdualR        spread=  1.2015e-50   value(member0)=5.763387254395581200268124e-9
  k815(i)P ApedX*AdualP        spread=     0.51717   value(member0)=4.28554327445395271321317e-10
  k816(i) ApedX/AdualR         spread=   0.0056707   value(member0)=0.09838119597096059482034847
  k816(ii) Apol/AdualR         spread=  1.0835e-47   value(member0)=645831753725.3586655233562
  k816(iii) Aped/AdualR        spread=     0.51991   value(member0)=0.001040749402708964955148334
  k816(i)P ApedX/AdualP        spread=   0.0056707   value(member0)=125.0690762145291526149134
  k817 Adag*Aant               spread=     0.66077   value(member0)=4518851.526643526277263721
  k818 Adag/Aant               spread=      0.2934   value(member0)=0.00000489266004277490656970201
  Aant/A                       spread=     0.50985   value(member0)=983936.2401223031338292693
  k804 A*Adag                  spread=      0.3079   value(member0)=4.592626373922189998028819
  k805 A/Adag                  spread=     0.30633   value(member0)=0.2077246340867106596074665
  k802 Ldag                    spread=  6.7347e-55   value(member0)=377.7920290901597641909295
  k803 sumcos_dag              spread=  9.4641e-55   value(member0)=7.081629829721070387778751
  k801 sum 1/d                 spread=  6.6508e-55   value(member0)=189.7782571038624175809477
  A                            spread=    0.016695   value(member0)=0.9767300717291158144862869
  Adag                         spread=     0.30712   value(member0)=4.702042567187282188125518
  Apol                         spread=     0.30712   value(member0)=1519795694.890247210256332
  AdualR                       spread=     0.30712   value(member0)=0.002353237799355005978557182
  Aped                         spread=     0.30712   value(member0)=0.000002449130834110881588762897
  ApedX                        spread=     0.30316   value(member0)=0.0002315143491046168908180644
  Aant                         spread=     0.51041   value(member0)=961040.1143915336617079325
  k908(i) ApedX1/ApedX2        0.51445 value0=0.760229521141
  k908(ii) Apol1/Apol2         0.51991 value0=0.757006190904
  k908(iii) Aped1/Aped2        0.51991 value0=1.32099315965
  k907R AdualR1/AdualR2        0.51991 value0=0.757006190904
  k907R AdualR1*AdualR2        1.6718e-53 value0=7.31530099338e-6
  k903a Adag1*Adag2            5.0652e-52 value0=29.2061076505
=== family a=1.7 b=0.3 N=14 tau=3
  J=0.55936781280484858486924 lambda=0.08138330023554104141426 caustic axes=(1.6758928067643,0.0928261803827) closure_err=2.3777e-57 worst tangency/closure=2.3004e-56
  checks: {'chk_polar_two_defs': '9.6928e-57', 'chk_polar_tangent_circle': '1.3491e-57', 'chk_polar_circumcircle': '4.5976e-54', 'chk_dualR_on_circle': '4.5068e-60', 'chk_ant_is_polar_reciprocal_of_inv': '4.9839e-59', 'chk_invped_eq_polar': '9.6928e-57'}
  O_p(f1)=['-20.2657650871587', '-1.08295521195114e-58'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 3.77e-58 Rstar-a/b^2=3.46e-58  O_p spread over members: 7.57e-58
  k813 Apol/Adag               spread=  1.8305e-56   value(member0)=291.6241303894852949911109
  k814R Apol/AdualR            spread=  1.0155e-56   value(member0)=2494496.224998109725977481
  k814P Apol/AdualP            spread=  1.0145e-56   value(member0)=4872706.207455270436863379
  k815(i) ApedX*AdualR         spread=   0.0047768   value(member0)=0.0004432300856465583672437718
  k815(ii) Apol*AdualR         spread=   0.0047768   value(member0)=128.8604637018484023641619
  k815(iii) Aped*AdualR        spread=   0.0047768   value(member0)=0.00956756918981024288218416
  k815(i)P ApedX*AdualP        spread=   0.0047768   value(member0)=0.0002269038452922318967634572
  k816(i) ApedX/AdualR         spread=  1.9236e-56   value(member0)=8.580100860176162987842475
  k816(ii) Apol/AdualR         spread=  1.0155e-56   value(member0)=2494496.224998109725977481
  k816(iii) Aped/AdualR        spread=  8.3254e-57   value(member0)=185.2101454609892975086857
  k816(i)P ApedX/AdualP        spread=  1.9273e-56   value(member0)=16.76022208532481390452595
  k817 Adag*Aant               spread=   0.0047768   value(member0)=-1461.109121143530486164841
  k818 Adag/Aant               spread=  1.1794e-56   value(member0)=-2.58686029763066478489972
  Aant/A                       spread=  7.5932e-57   value(member0)=-9.686073586560255805933848
  k804 A*Adag                  spread=   0.0047768   value(member0)=150.8463783685132460731016
  k805 A/Adag                  spread=  1.1666e-56   value(member0)=0.03990977326012701019575662
  k802 Ldag                    spread=  5.6783e-58   value(member0)=238.0895721762364294503839
  k803 sumcos_dag              spread=  2.3303e-57   value(member0)=6.309299303192613683072521
  k801 sum 1/d                 spread=  5.7373e-58   value(member0)=121.5505087247349253325788
  A                            spread=   0.0023913   value(member0)=2.45361870668583944143998
  Adag                         spread=   0.0023913   value(member0)=61.47914423601090043616087
  Apol                         spread=   0.0023913   value(member0)=17928.80197491641613877579
  AdualR                       spread=   0.0023913   value(member0)=0.007187343799219420421472223
  Aped                         spread=   0.0023913   value(member0)=1.3311689905315683120324
  ApedX                        spread=   0.0023913   value(member0)=0.06166813471406436044529696
  Aant                         spread=   0.0023913   value(member0)=-23.76593134631984513993743
  k908(i) ApedX1/ApedX2        1.0316e-55 value0=1.0
  k908(ii) Apol1/Apol2         5.0725e-56 value0=1.0
  k908(iii) Aped1/Aped2        1.1884e-56 value0=1.0
  k907R AdualR1/AdualR2        6.6408e-57 value0=1.0
  k907R AdualR1*AdualR2        0.0047768 value0=5.16579108882e-5
  k903a Adag1*Adag2            0.0047768 value0=3779.68517599
=== family a=1.7 b=0.3 N=14 tau=5
  J=0.58822885260068962455850 lambda=0.08999802890660339101433 caustic axes=(1.6733206420448,0.0014039563371) closure_err=1.1381e-54 worst tangency/closure=1.0814e-53
  checks: {'chk_polar_two_defs': '1.6173e-49', 'chk_polar_tangent_circle': '8.0369e-56', 'chk_polar_circumcircle': '3.6493e-44', 'chk_dualR_on_circle': '2.4213e-58', 'chk_ant_is_polar_reciprocal_of_inv': '9.5318e-52', 'chk_invped_eq_polar': '1.6173e-49'}
  O_p(f1)=['-20.2657650871587', '2.55362620841603e-59'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.9e-58 Rstar-a/b^2=-1.89e-58  O_p spread over members: 6.63e-56
  k813 Apol/Adag               spread=  3.3773e-50   value(member0)=5723378.090020152612785569
  k814R Apol/AdualR            spread=  3.3749e-50   value(member0)=11443811544.47690959246786
  k814P Apol/AdualP            spread=  3.3764e-50   value(member0)=280262620924.9522326716263
  k815(i) ApedX*AdualR         spread=     0.23409   value(member0)=0.00005664593941846944805287101
  k815(ii) Apol*AdualR         spread=     0.23409   value(member0)=162915.6939542344666146312
  k815(iii) Aped*AdualR        spread=     0.23409   value(member0)=0.0000006329615494165720849817285
  k815(i)P ApedX*AdualP        spread=     0.23409   value(member0)=0.000002312992911168147757211261
  k816(i) ApedX/AdualR         spread=  4.5051e-54   value(member0)=3.979023995361198681218898
  k816(ii) Apol/AdualR         spread=  3.3749e-50   value(member0)=11443811544.47690959246786
  k816(iii) Aped/AdualR        spread=  3.9211e-53   value(member0)=0.04446160164568410726645318
  k816(i)P ApedX/AdualP        spread=  1.5127e-53   value(member0)=97.44757586482768397200313
  k817 Adag*Aant               spread=     0.23409   value(member0)=239910.2662907112465037686
  k818 Adag/Aant               spread=  4.0781e-51   value(member0)=0.0002372356291225974230724956
  Aant/A                       spread=  4.0747e-51   value(member0)=23525.86516951353101598319
  k804 A*Adag                  spread=     0.23409   value(member0)=10.19772342322202140958491
  k805 A/Adag                  spread=  2.7517e-53   value(member0)=0.1791737908867366659605425
  k802 Ldag                    spread=  1.7198e-55   value(member0)=377.8008184865426499607187
  k803 sumcos_dag              spread=  4.7685e-55   value(member0)=5.792571785053115961153567
  k801 sum 1/d                 spread=  1.6957e-55   value(member0)=190.0767326697011920834955
  A                            spread=     0.12484   value(member0)=1.351726586315871371051187
  Adag                         spread=     0.12484   value(member0)=7.54422050025360538159699
  Apol                         spread=     0.12484   value(member0)=43178426.31743236023904887
  AdualR                       spread=     0.12484   value(member0)=0.003773080861181380337417638
  Aped                         spread=     0.12484   value(member0)=0.0001677572182268012686875483
  ApedX                        spread=     0.12484   value(member0)=0.01501317928307880824099696
  Aant                         spread=     0.12484   value(member0)=31800.53741571398384729967
  k908(i) ApedX1/ApedX2        2.4455e-53 value0=1.0
  k908(ii) Apol1/Apol2         2.0753e-49 value0=1.0
  k908(iii) Aped1/Aped2        8.3053e-53 value0=1.0
  k907R AdualR1/AdualR2        6.0241e-54 value0=1.0
  k907R AdualR1*AdualR2        0.23409 value0=1.4236139185e-5
  k903a Adag1*Adag2            0.23409 value0=56.9152629564
=== family a=1.7 b=0.3 N=15 tau=4
  J=0.58370597118799072681355 lambda=0.08861936307421407127676 caustic axes=(1.6737325464140,0.0371569229859) closure_err=2.7576e-57 worst tangency/closure=2.549e-56
  checks: {'chk_polar_two_defs': '4.0708e-55', 'chk_polar_tangent_circle': '1.6777e-57', 'chk_polar_circumcircle': '1.942e-52', 'chk_dualR_on_circle': '5.0124e-60', 'chk_ant_is_polar_reciprocal_of_inv': '3.1376e-57', 'chk_invped_eq_polar': '4.0708e-55'}
  O_p(f1)=['-20.2657650871587', '1.24918953538126e-59'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 2.0e-59 Rstar-a/b^2=1.74e-59  O_p spread over members: 3.12e-58
  k813 Apol/Adag               spread=  9.4179e-56   value(member0)=5430.782002090608600713087
  k814R Apol/AdualR            spread=  7.0384e-56   value(member0)=16214823.31471515980873757
  k814P Apol/AdualP            spread=  7.0431e-56   value(member0)=32810990.65800574135849777
  k815(i) ApedX*AdualR         spread=      1.9486   value(member0)=-0.00002179126863164049726170167
  k815(ii) Apol*AdualR         spread=    0.012031   value(member0)=655.8710796974731492069311
  k815(iii) Aped*AdualR        spread=  1.0074e-56   value(member0)=0.001248808791169466641308073
  k815(i)P ApedX*AdualP        spread=      1.9486   value(member0)=-0.00001076900037394426007338437
  k816(i) ApedX/AdualR         spread=      1.9602   value(member0)=-0.5387363181625993546078148
  k816(ii) Apol/AdualR         spread=   7.036e-56   value(member0)=16214823.31471515980873757
  k816(iii) Aped/AdualR        spread=    0.012031   value(member0)=30.87377158330577369850187
  k816(i)P ApedX/AdualP        spread=      1.9602   value(member0)=-1.090142763770964512708787
  k817 Adag*Aant               spread=    0.074569   value(member0)=800.7619249297502835828614
  k818 Adag/Aant               spread=    0.063299   value(member0)=0.4503006222139200803674876
  Aant/A                       spread=     0.06895   value(member0)=18.65861175802221507970531
  k804 A*Adag                  spread=   0.0060346   value(member0)=42.91647928123404230891321
  k805 A/Adag                  spread=   0.0060329   value(member0)=0.1190195009131887327672093
  k802 Ldag                    spread=  5.4552e-58   value(member0)=304.5907756371342420394777
  k803 sumcos_dag              spread=  3.9332e-57   value(member0)=8.725613151064822884153999
  k801 sum 1/d                 spread=  5.3603e-58   value(member0)=154.3585799837342515438028
  A                            spread=   4.8785e-6   value(member0)=2.260065916074945020373554
  Adag                         spread=   0.0060337   value(member0)=18.98903876032388624020404
  Apol                         spread=   0.0060337   value(member0)=103125.3299365679233149551
  AdualR                       spread=   0.0060337   value(member0)=0.006359941637043948900239283
  Aped                         spread=   0.0060337   value(member0)=0.1963553853852506725549266
  ApedX                        spread=      1.9544   value(member0)=-0.003426331541270071840221776
  Aant                         spread=    0.068951   value(member0)=42.1696924755812179108104
  k908(i) ApedX1/ApedX2        0.70571 value0=-2.22492591522
  k908(ii) Apol1/Apol2         0.012031 value0=1.00110931698
  k908(iii) Aped1/Aped2        0.012031 value0=0.998891912241
  k907R AdualR1/AdualR2        0.012031 value0=1.00110931698
  k907R AdualR1*AdualR2        9.1432e-57 value0=4.04040367426e-5
  k903a Adag1*Adag2            1.3295e-55 value0=360.184034775
=== family a=1.7 b=0.3 N=16 tau=5
  J=0.58787223329599993595865 lambda=0.08988893767317895234668 caustic axes=(1.6733532389566,0.0105386112377) closure_err=9.7613e-56 worst tangency/closure=9.6635e-55
  checks: {'chk_polar_two_defs': '5.4465e-53', 'chk_polar_tangent_circle': '2.2403e-57', 'chk_polar_circumcircle': '1.0522e-48', 'chk_dualR_on_circle': '6.4078e-60', 'chk_ant_is_polar_reciprocal_of_inv': '2.8892e-55', 'chk_invped_eq_polar': '5.4465e-53'}
  O_p(f1)=['-20.2657650871587', '-1.42243028540402e-59'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 4.54e-58 Rstar-a/b^2=4.56e-58  O_p spread over members: 1.21e-57
  k813 Apol/Adag               spread=  3.5461e-53   value(member0)=97740.93392781553681518848
  k814R Apol/AdualR            spread=  3.4146e-53   value(member0)=202979419.4025109083573149
  k814P Apol/AdualP            spread=  3.4155e-53   value(member0)=486702749.5853811456674907
  k815(i) ApedX*AdualR         spread=    0.033139   value(member0)=-0.0001443747280563353931940716
  k815(ii) Apol*AdualR         spread=    0.033139   value(member0)=6053.508479231672198812686
  k815(iii) Aped*AdualR        spread=    0.033139   value(member0)=0.00007466906118688235498407644
  k815(i)P ApedX*AdualP        spread=    0.033139   value(member0)=-0.00006021149151558149187220965
  k816(i) ApedX/AdualR         spread=  3.3299e-55   value(member0)=-4.841010560703772783530514
  k816(ii) Apol/AdualR         spread=  3.4146e-53   value(member0)=202979419.4025109083573149
  k816(iii) Aped/AdualR        spread=   3.009e-55   value(member0)=2.503718750711590512724484
  k816(i)P ApedX/AdualP        spread=  3.4623e-55   value(member0)=-11.60774406391492474162247
  k817 Adag*Aant               spread=  4.7373e-54   value(member0)=8915.625075551019452347498
  k818 Adag/Aant               spread=    0.033139   value(member0)=0.01442628125911420857920913
  Aant/A                       spread=  4.8807e-54   value(member0)=402.724767142153603537925
  k804 A*Adag                  spread=  1.3535e-54   value(member0)=22.13825868922530459523325
  k805 A/Adag                  spread=    0.033139   value(member0)=0.1721223495820233118973757
  k802 Ldag                    spread=    1.57e-56   value(member0)=378.0393511124124508105835
  k803 sumcos_dag              spread=  3.4169e-56   value(member0)=6.773351530684546570128332
  k801 sum 1/d                 spread=  1.5438e-56   value(member0)=190.7841975538009686268497
  A                            spread=    0.016709   value(member0)=1.952047412652700671875328
  Adag                         spread=    0.016709   value(member0)=11.34104558410336219985228
  Apol                         spread=    0.016709   value(member0)=1108484.387108190886510878
  AdualR                       spread=    0.016709   value(member0)=0.005461067877576551219247439
  Aped                         spread=    0.016709   value(member0)=0.01367297804399715993899308
  ApedX                        spread=    0.016709   value(member0)=-0.02643708726806822260200886
  Aant                         spread=    0.016709   value(member0)=786.1378397110023039871991
  k908(i) ApedX1/ApedX2        1.5018e-54 value0=1.0
  k908(ii) Apol1/Apol2         2.275e-52 value0=1.0
  k908(iii) Aped1/Aped2        2.8957e-55 value0=1.0
  k907R AdualR1/AdualR2        3.4034e-55 value0=1.0
  k907R AdualR1*AdualR2        0.033139 value0=2.98232623635e-5
  k903a Adag1*Adag2            0.033139 value0=128.619314941
=== family a=1.7 b=0.3 N=16 tau=7
  J=0.58823529411764481713177 lambda=0.08999999999999931404232 caustic axes=(1.6733200530681,0.0000000261907) closure_err=5.1488e-45 worst tangency/closure=5.0847e-44
  checks: {'chk_polar_two_defs': '8.2804e-31', 'chk_polar_tangent_circle': '1.3017e-46', 'chk_polar_circumcircle': '1.4523e-15', 'chk_dualR_on_circle': '5.294e-49', 'chk_ant_is_polar_reciprocal_of_inv': '3.8666e-33', 'chk_invped_eq_polar': '8.2804e-31'}
  O_p(f1)=['-20.2657650871587', '2.61752018649702e-48'] R*=18.8888888888889  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 2.62e-48 Rstar-a/b^2=-6.4e-57  O_p spread over members: 1.28e-46
  k813 Apol/Adag               spread=  9.6721e-31   value(member0)=16457728288230465.87676874
  k814R Apol/AdualR            spread=  9.6721e-31   value(member0)=32884046970383059981.83188
  k814P Apol/AdualP            spread=  9.6765e-31   value(member0)=2.125227162936306655819249e+30
  k815(i) ApedX*AdualR         spread=     0.86361   value(member0)=1.422834113935592881407723e-14
  k815(ii) Apol*AdualR         spread=     0.86361   value(member0)=241262678990546.2699663255
  k815(iii) Aped*AdualR        spread=     0.86361   value(member0)=1.135232426940514662230105e-16
  k815(i)P ApedX*AdualP        spread=     0.86361   value(member0)=2.201578478277884576163871e-25
  k816(i) ApedX/AdualR         spread=  7.0784e-35   value(member0)=1.939319584342126079797945e-9
  k816(ii) Apol/AdualR         spread=  9.6721e-31   value(member0)=32884046970383059981.83188
  k816(iii) Aped/AdualR        spread=  9.4802e-34   value(member0)=1.547319154624683307025815e-11
  k816(i)P ApedX/AdualP        spread=  3.6779e-34   value(member0)=125.3341677187801309172639
  k817 Adag*Aant               spread=  1.0824e-31   value(member0)=139611798335447.3576814856
  k818 Adag/Aant               spread=     0.86361   value(member0)=2.098038766307124752705528e-13
  Aant/A                       spread=  1.0824e-31   value(member0)=67644674934520.77410515372
  k804 A*Adag                  spread=  2.5362e-43   value(member0)=2.063899316104185395596775
  k805 A/Adag                  spread=     0.86361   value(member0)=0.07046166110941937014345493
  k802 Ldag                    spread=  5.9201e-46   value(member0)=528.8983408964369826115061
  k803 sumcos_dag              spread=  6.7753e-46   value(member0)=12.06277634511087080390843
  k801 sum 1/d                 spread=  5.8606e-46   value(member0)=265.0373321540420945034956
  A                            spread=     0.63069   value(member0)=0.3813473143674877320602696
  Adag                         spread=     0.63069   value(member0)=5.412124953672273330198308
  Apol                         spread=     0.63069   value(member0)=89071281949490172.39030271
  AdualR                       spread=     0.63069   value(member0)=0.002708647206036167452924956
  Aped                         spread=     0.63069   value(member0)=4.191141705020393010895086e-14
  ApedX                        spread=     0.63069   value(member0)=5.252932573739521403917575e-12
  Aant                         spread=     0.63069   value(member0)=25796115117541.21125984233
  k908(i) ApedX1/ApedX2        2.7627e-34 value0=1.0
  k908(ii) Apol1/Apol2         4.2199e-30 value0=1.0
  k908(iii) Aped1/Aped2        1.8918e-33 value0=1.0
  k907R AdualR1/AdualR2        3.0165e-44 value0=1.0
  k907R AdualR1*AdualR2        0.86361 value0=7.33676968677e-6
  k903a Adag1*Adag2            0.86361 value0=29.2910965142
=== family a=1 b=0.5 N=6 tau=1  [J PERTURBED]
  J=0.66733333333333333333333 lambda=0.11133344444444444444444 caustic axes=(0.9426911241523,0.3723795853098) closure_err=6.6469e-60 worst tangency/closure=0.011249
  checks: {'chk_polar_two_defs': '8.3491e-60', 'chk_polar_tangent_circle': '3.7338e-60', 'chk_polar_circumcircle': '0.12016', 'chk_dualR_on_circle': '2.7226e-61', 'chk_ant_is_polar_reciprocal_of_inv': '1.3247e-60', 'chk_invped_eq_polar': '8.3491e-60'}
  O_p(f1)=['-4.33012701892219', '1.00479750670635e-60'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 2.47e-60 Rstar-a/b^2=-2.18e-60  O_p spread over members: 5.1e-60
  k813 Apol/Adag               spread=    0.019343   value(member0)=4.28349597155905197208668
  k814R Apol/AdualR            spread=   0.0091396   value(member0)=615.6898630679076244193465
  k814P Apol/AdualP            spread=    0.010224   value(member0)=985.6458073942800523816648
  k815(i) ApedX*AdualR         spread=    0.037773   value(member0)=0.183328676827290797618129
  k815(ii) Apol*AdualR         spread=    0.022374   value(member0)=8.512631878054081034207271
  k815(iii) Aped*AdualR        spread=    0.024536   value(member0)=0.1644830453028850663824519
  k815(i)P ApedX*AdualP        spread=    0.038782   value(member0)=0.1145174129341813648152091
  k816(i) ApedX/AdualR         spread=    0.023787   value(member0)=13.25954294149711979152942
  k816(ii) Apol/AdualR         spread=   0.0091396   value(member0)=615.6898630679076244193465
  k816(iii) Aped/AdualR        spread=   0.0095657   value(member0)=11.89650217350587255695543
  k816(i)P ApedX/AdualP        spread=    0.022763   value(member0)=21.22694182933069423835975
  k817 Adag*Aant               spread=      1.9452   value(member0)=0.05450690229825481374210305
  k818 Adag/Aant               spread=      1.1942   value(member0)=5240.55917846124765216311
  Aant/A                       spread=      1.9328   value(member0)=0.002569669010371334808430671
  k804 A*Adag                  spread=    0.021923   value(member0)=21.2116432420913977019559
  k805 A/Adag                  spread=    0.015183   value(member0)=0.07425833089698775005178661
  k802 Ldag                    spread=    0.002779   value(member0)=21.98780675583517466039538
  k803 sumcos_dag              spread=   0.0066023   value(member0)=-0.6667346994951850414416802
  k801 sum 1/d                 spread=   0.0034333   value(member0)=13.98861981351992017217261
  A                            spread=    0.011035   value(member0)=1.255046303026337370254433
  Adag                         spread=    0.018042   value(member0)=16.90108419979646566847384
  Apol                         spread=    0.012536   value(member0)=72.39572608480850416324676
  AdualR                       spread=    0.011101   value(member0)=0.1175847296300598740019831
  Aped                         spread=    0.014239   value(member0)=1.398846991615107665021569
  ApedX                        spread=    0.030806   value(member0)=1.559119771794107640011084
  Aant                         spread=       1.939   value(member0)=0.00322505359146789073265362
  k908(i) ApedX1/ApedX2        0.057767 value0=0.968867203856
  k908(ii) Apol1/Apol2         0.011879 value0=1.00677119093
  k908(iii) Aped1/Aped2        0.011058 value0=1.00475728724
  k907R AdualR1/AdualR2        0.0081708 value0=0.995783214363
  k907R AdualR1*AdualR2        0.024429 value0=0.0138847175196
  k903a Adag1*Adag2            0.037487 value0=290.654765129
=== family a=1 b=0.5 N=6 tau=1  [REGULAR INSCRIBED POLYGON, NOT A BILLIARD ORBIT]
  checks: {'chk_polar_two_defs': '2.1267e-57', 'chk_polar_tangent_circle': '1.4935e-59', 'chk_polar_circumcircle': '322.1', 'chk_dualR_on_circle': '1.1085e-60', 'chk_ant_is_polar_reciprocal_of_inv': '1.0047e-58', 'chk_invped_eq_polar': '2.1267e-57'}
  O_p(f1)=['-4.33012701892219', '-1.38260728702465e-60'] R*=4.0  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 1.51e-60 Rstar-a/b^2=1.24e-60  O_p spread over members: 8.84e-60
  k813 Apol/Adag               spread=     0.97338   value(member0)=23.73939989640139407180625
  k814R Apol/AdualR            spread=     0.94135   value(member0)=1757.336467847958711697508
  k814P Apol/AdualP            spread=     0.94135   value(member0)=2769.136252366480394190013
  k815(i) ApedX*AdualR         spread=     0.73686   value(member0)=0.03461564387339803003396605
  k815(ii) Apol*AdualR         spread=     0.92422   value(member0)=15.09406796808393542783214
  k815(iii) Aped*AdualR        spread=   0.0041996   value(member0)=0.1106551726748321733914763
  k815(i)P ApedX*AdualP        spread=     0.73686   value(member0)=0.02196762015042567290617076
  k816(i) ApedX/AdualR         spread=     0.65997   value(member0)=4.030148364601683363832743
  k816(ii) Apol/AdualR         spread=     0.94135   value(member0)=1757.336467847958711697508
  k816(iii) Aped/AdualR        spread=     0.22628   value(member0)=12.88309889081414931737243
  k816(i)P ApedX/AdualP        spread=     0.65997   value(member0)=6.350536816948107118766747
  k817 Adag*Aant               spread=     0.98713   value(member0)=2.13663215354316779295454
  k818 Adag/Aant               spread=     0.99795   value(member0)=22.0288583572421906092419
  Aant/A                       spread=     0.99486   value(member0)=0.2397435842240007822876995
  k804 A*Adag                  spread=     0.60076   value(member0)=8.91215571194112932594658
  k805 A/Adag                  spread=     0.60076   value(member0)=0.1893481279438340060190823
  k802 Ldag                    spread=     0.17086   value(member0)=18.29033957915422181467474
  k803 sumcos_dag              spread=     0.49866   value(member0)=-0.7159554189012163844630416
  k801 sum 1/d                 spread=      0.1203   value(member0)=11.9856911045040383019889
  A                            spread=  1.1976e-61   value(member0)=1.299038105676657970145585
  Adag                         spread=     0.60076   value(member0)=6.860580665798762491733947
  Apol                         spread=     0.93333   value(member0)=162.8660679469165494615978
  AdualR                       spread=      0.1203   value(member0)=0.09267779445012200175136172
  Aped                         spread=     0.12047   value(member0)=1.193977190883468484214695
  ApedX                        spread=     0.70088   value(member0)=0.3735052617380501520760045
  Aant                         spread=     0.99486   value(member0)=0.3114360514984782787979701
  k908(i) ApedX1/ApedX2        1.1279e-59 value0=1.0
  k908(ii) Apol1/Apol2         8.4166e-59 value0=1.0
  k908(iii) Aped1/Aped2        7.7788e-61 value0=1.0
  k907R AdualR1/AdualR2        1.3224e-59 value0=1.0
  k907R AdualR1*AdualR2        0.22612 value0=0.00858917358414
  k903a Adag1*Adag2            0.84061 value0=47.0675670719
=== family a=1 b=0.5 N=5 tau=1  [REGULAR INSCRIBED POLYGON, NOT A BILLIARD ORBIT]
  checks: {'chk_polar_two_defs': '3.3912e-58', 'chk_polar_tangent_circle': '8.0', 'chk_polar_circumcircle': '19.35', 'chk_dualR_on_circle': '0.52535', 'chk_ant_is_polar_reciprocal_of_inv': '7.5463e-59', 'chk_invped_eq_polar': '3.3912e-58'}
  O_p(f1)=['2.25939493229006', '3.16172542272377'] R*=3.30002429779052  |O_p - (-c-c/b^2,0)|, R*-a/b^2: 7.31 Rstar-a/b^2=-0.7  O_p spread over members: 7.31
  k813 Apol/Adag               spread=      1.5409   value(member0)=-68.7422520728185076017774
  k814R Apol/AdualR            spread=      1.1488   value(member0)=2359.003623785098665529198
  k814P Apol/AdualP            spread=      1.1488   value(member0)=3445.379697782588058154268
  k815(i) ApedX*AdualR         spread=      1.4351   value(member0)=-0.005008733759999727475506542
  k815(ii) Apol*AdualR         spread=      1.1053   value(member0)=8.297106761881757712903809
  k815(iii) Aped*AdualR        spread=      1.8495   value(member0)=-0.04675997295045717140704251
  k815(i)P ApedX*AdualP        spread=      1.5411   value(member0)=-0.003429410435667957130600121
  k816(i) ApedX/AdualR         spread=      1.7857   value(member0)=-1.42406521086325928997441
  k816(ii) Apol/AdualR         spread=      1.1488   value(member0)=2359.003623785098665529198
  k816(iii) Aped/AdualR        spread=      1.6729   value(member0)=-13.29462773035409164089772
  k816(i)P ApedX/AdualP        spread=      1.6473   value(member0)=-2.079880385242563281160634
  k817 Adag*Aant               spread=      1.3474   value(member0)=-2.497984074802244554698752
  k818 Adag/Aant               spread=      1.1389   value(member0)=-1.658128213659933794625522
  Aant/A                       spread=      1.5681   value(member0)=-1.032450977018781881828054
  k804 A*Adag                  spread=      0.9576   value(member0)=2.419469912281173962916163
  k805 A/Adag                  spread=      0.9576   value(member0)=0.5841339541697034405245925
  k802 Ldag                    spread=     0.30293   value(member0)=15.04893475482264219375519
  k803 sumcos_dag              spread=      1.0615   value(member0)=0.09961793614456637350984883
  k801 sum 1/d                 spread=     0.22275   value(member0)=9.580609898881871144815117
  A                            spread=  1.3087e-61   value(member0)=1.188820645368941965145549
  Adag                         spread=      0.9576   value(member0)=2.035184972355782751216043
  Apol                         spread=      1.4864   value(member0)=-139.9031983844933839218592
  AdualR                       spread=      1.9026   value(member0)=-0.0593060548843134521012066
  Aped                         spread=     0.25051   value(member0)=0.7884519218428953406058847
  ApedX                        spread=     0.61362   value(member0)=0.08445568955429786470294554
  Aant                         spread=      1.5681   value(member0)=-1.227399036811262946246893
  k908(i) ApedX1/ApedX2        0.83699 value0=0.730736315292
  k908(ii) Apol1/Apol2         1.1339 value0=-0.047148819409
  k908(iii) Aped1/Aped2        0.43858 value0=0.922682464486
  k907R AdualR1/AdualR2        1.685 value0=-0.79059616803
  k907R AdualR1*AdualR2        1.2396 value0=-0.0044488049502
  k903a Adag1*Adag2            0.74835 value0=7.8004088071
