D1/D2: chain inequality for the weight w
  gap=(1.0,1.0) k=2: max ratio random starts=0.998707253530, max ratio after SLSQP (repaired, feasible)=0.999999999993852
  gap=(1.0,1.0) k=3: max ratio random starts=0.982716906079, max ratio after SLSQP (repaired, feasible)=0.999999999987877
  gap=(1.0,1.0) k=4: max ratio random starts=0.957031132332, max ratio after SLSQP (repaired, feasible)=0.999999999983326
  gap=(1.0,1.0) k=5: max ratio random starts=0.962151809579, max ratio after SLSQP (repaired, feasible)=0.999999999980375
  gap=(1.0,1.0) k=6: max ratio random starts=0.929982117130, max ratio after SLSQP (repaired, feasible)=0.999999999976901
  gap=(1.0,1.0) k=7: max ratio random starts=0.936492381994, max ratio after SLSQP (repaired, feasible)=0.999999999977127
  gap=(1.0,1.0) k=8: max ratio random starts=0.969266884222, max ratio after SLSQP (repaired, feasible)=0.999999999975990
  gap=(0.3,2.0) k=2: max ratio random starts=0.991849037884, max ratio after SLSQP (repaired, feasible)=0.999999999991133
  gap=(0.3,2.0) k=3: max ratio random starts=0.997569573799, max ratio after SLSQP (repaired, feasible)=0.999999999983588
  gap=(0.3,2.0) k=4: max ratio random starts=0.990924249391, max ratio after SLSQP (repaired, feasible)=0.999999999977674
  gap=(0.3,2.0) k=5: max ratio random starts=0.988509579368, max ratio after SLSQP (repaired, feasible)=0.999999999973098
  gap=(0.3,2.0) k=6: max ratio random starts=0.959044885455, max ratio after SLSQP (repaired, feasible)=0.999999999960851
  gap=(0.3,2.0) k=7: max ratio random starts=0.924478776016, max ratio after SLSQP (repaired, feasible)=0.999999999961067
  gap=(0.3,2.0) k=8: max ratio random starts=0.927549911692, max ratio after SLSQP (repaired, feasible)=0.999999999956451
  gap=(5.0,0.7) k=2: max ratio random starts=0.999567721447, max ratio after SLSQP (repaired, feasible)=0.999999999998979
  gap=(5.0,0.7) k=3: max ratio random starts=0.996547222035, max ratio after SLSQP (repaired, feasible)=0.999999999997894
  gap=(5.0,0.7) k=4: max ratio random starts=0.994415042079, max ratio after SLSQP (repaired, feasible)=0.999999999996779
  gap=(5.0,0.7) k=5: max ratio random starts=0.989339300020, max ratio after SLSQP (repaired, feasible)=0.999999999995647
  gap=(5.0,0.7) k=6: max ratio random starts=0.993279871486, max ratio after SLSQP (repaired, feasible)=0.999999999994513
  gap=(5.0,0.7) k=7: max ratio random starts=0.982872969625, max ratio after SLSQP (repaired, feasible)=0.999999999981234
  gap=(5.0,0.7) k=8: max ratio random starts=0.972643735498, max ratio after SLSQP (repaired, feasible)=0.999999999985653
  gap=(20.0,20.0) k=2: max ratio random starts=0.999993928727, max ratio after SLSQP (repaired, feasible)=0.999999999999991
  gap=(20.0,20.0) k=3: max ratio random starts=0.999969693856, max ratio after SLSQP (repaired, feasible)=0.999999999999982
  gap=(20.0,20.0) k=4: max ratio random starts=0.999891932315, max ratio after SLSQP (repaired, feasible)=0.999999999999969
  gap=(20.0,20.0) k=5: max ratio random starts=0.999837209750, max ratio after SLSQP (repaired, feasible)=0.999999999999956
  gap=(20.0,20.0) k=6: max ratio random starts=0.999886015951, max ratio after SLSQP (repaired, feasible)=0.999999999999939
  gap=(20.0,20.0) k=7: max ratio random starts=0.999802122142, max ratio after SLSQP (repaired, feasible)=0.999999999999904
  gap=(20.0,20.0) k=8: max ratio random starts=0.999651012311, max ratio after SLSQP (repaired, feasible)=0.999999999999860
  gap=(0.05,0.08) k=2: max ratio random starts=0.579864179001, max ratio after SLSQP (repaired, feasible)=0.999999999832273
  gap=(0.05,0.08) k=3: max ratio random starts=0.868787816456, max ratio after SLSQP (repaired, feasible)=0.999999999674998
  gap=(0.05,0.08) k=4: max ratio random starts=0.262533365704, max ratio after SLSQP (repaired, feasible)=0.999999998089666
  gap=(0.05,0.08) k=5: max ratio random starts=0.791223802892, max ratio after SLSQP (repaired, feasible)=0.999999999674364
  gap=(0.05,0.08) k=6: max ratio random starts=0.962490779236, max ratio after SLSQP (repaired, feasible)=0.999999998552281
  gap=(0.05,0.08) k=7: max ratio random starts=0.265188033964, max ratio after SLSQP (repaired, feasible)=0.999999999674959
  gap=(0.05,0.08) k=8: max ratio random starts=0.511207114708, max ratio after SLSQP (repaired, feasible)=0.999999997669751
  gap=(100.0,3.0) k=2: max ratio random starts=0.999990650204, max ratio after SLSQP (repaired, feasible)=0.999999999999993
  gap=(100.0,3.0) k=3: max ratio random starts=0.999954623255, max ratio after SLSQP (repaired, feasible)=0.999999999999986
  gap=(100.0,3.0) k=4: max ratio random starts=0.999912813163, max ratio after SLSQP (repaired, feasible)=0.999999999999979
  gap=(100.0,3.0) k=5: max ratio random starts=0.999857132886, max ratio after SLSQP (repaired, feasible)=0.999999999999757
  gap=(100.0,3.0) k=6: max ratio random starts=0.999807182350, max ratio after SLSQP (repaired, feasible)=0.999999999999736
  gap=(100.0,3.0) k=7: max ratio random starts=0.999759366378, max ratio after SLSQP (repaired, feasible)=0.999999999999514
  gap=(100.0,3.0) k=8: max ratio random starts=0.999624977720, max ratio after SLSQP (repaired, feasible)=0.999999999999063
  gap=(0.6,0.6) k=2: max ratio random starts=0.997863809277, max ratio after SLSQP (repaired, feasible)=0.999999999982794
  gap=(0.6,0.6) k=3: max ratio random starts=0.947763141584, max ratio after SLSQP (repaired, feasible)=0.999999999971280
  gap=(0.6,0.6) k=4: max ratio random starts=0.909657536865, max ratio after SLSQP (repaired, feasible)=0.999999999967267
  gap=(0.6,0.6) k=5: max ratio random starts=0.943935311528, max ratio after SLSQP (repaired, feasible)=0.999999999965956
  gap=(0.6,0.6) k=6: max ratio random starts=0.896779254756, max ratio after SLSQP (repaired, feasible)=0.999999999965571
  gap=(0.6,0.6) k=7: max ratio random starts=0.769259070233, max ratio after SLSQP (repaired, feasible)=0.999999999966831
  gap=(0.6,0.6) k=8: max ratio random starts=0.802849479232, max ratio after SLSQP (repaired, feasible)=0.999999999965434
  runs=1225, repaired-feasible=1214, ended within 1e-6 of 1: 1148
  infeasible repaired outputs: 11; largest excess among them -8.392e-10 (min slack -3.140e-11)
  largest feasible ratio overall: 0.99999999999999325818537027600918092292123981702712
[OK] D2 no feasible chain with Phi > w(a)w(b) (50-digit re-evaluation)
  attained near: (100.0, 3.0, 2) [100.         2.830189   2.912621   3.      ]
D3: large-scale limit inequality
  max of sum(t+1/t) - 3k - (tau+1/tau) over optimised feasible chains: -1.972e-11
[OK] D3 limit inequality holds numerically
D4: area weight (p=4) directly
  check G4(1,1) = 0.11062653532618667  vs zeta(3)/zeta(4)-1 = 0.11062653532614841
  max Phi_4/G_4(a,b) over optimised feasible chains: 0.999999999992
[OK] D4 area version of the chain inequality
ALL PASSED   (112.4s)
