# triples with max <= 119: 7021; phi_1 = 1/4 and the phi_2 closed form verified for all of them (2.8s)
# quadruples with max <= 119: 273819 (116437 distinct classes computed); phi_1 < 1/5 for 135180 of them (85.1s)
d=4 n=3: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.022977 ; term3 = 5.833975e-05 term4 = 0.000000e+00 ; E_lat = 465342589/179159040000 ; E_iid = 444229/174960000
d=4 n=4: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.054141 ; term3 = 6.213471e-05 term4 = 1.142358e-05 ; E_lat = 26936053043671/18807399383040000 ; E_iid = 281729/207360000
d=4 n=5: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.093952 ; term3 = 6.670163e-05 term4 = 1.248321e-05 ; E_lat = 231207711319021/250765325107200000 ; E_iid = 682687/810000000
d=4 n=6: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.133685 ; term3 = 6.024341e-05 term4 = 1.634848e-05 ; E_lat = 305394546198606317879/470184984576000000000000 ; E_iid = 200479/349920000
d=4 n=7: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.178996 ; term3 = 5.899637e-05 term4 = 1.518632e-05 ; E_lat = 13790251300741421495081/28222853699174400000000000 ; E_iid = 184229/444528000
d=4 n=8: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.222926 ; term3 = 5.394377e-05 term4 = 1.596072e-05 ; E_lat = 395975611161464993400799787/1032580140673794048000000000000 ; E_iid = 520187/1658880000
d=4 n=9: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.269587 ; term3 = 5.082900e-05 term4 = 1.534787e-05
d=4 n=10: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.316263 ; term3 = 4.740184e-05 term4 = 1.501294e-05
d=4 n=11: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.364517 ; term3 = 4.484889e-05 term4 = 1.423798e-05
d=4 n=12: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.411025 ; term3 = 4.169557e-05 term4 = 1.399974e-05
d=4 n=13: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.460736 ; term3 = 3.976967e-05 term4 = 1.319279e-05
d=4 n=14: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.508803 ; term3 = 3.744298e-05 term4 = 1.279734e-05
d=4 n=15: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.557482 ; term3 = 3.551911e-05 term4 = 1.227538e-05
d=4 n=16: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.606316 ; term3 = 3.373518e-05 term4 = 1.181961e-05
d=4 n=17: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.656271 ; term3 = 3.227263e-05 term4 = 1.129366e-05
d=4 n=18: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.704807 ; term3 = 3.068551e-05 term4 = 1.095359e-05
d=4 n=19: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.754926 ; term3 = 2.945183e-05 term4 = 1.049537e-05
d=4 n=20: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.803744 ; term3 = 2.813541e-05 term4 = 1.017765e-05
d=4 n=21: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.853730 ; term3 = 2.704880e-05 term4 = 9.801969e-06
d=4 n=22: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.903569 ; term3 = 2.600637e-05 term4 = 9.476641e-06
d=4 n=23: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 1.953597 ; term3 = 2.506644e-05 term4 = 9.148027e-06
d=4 n=24: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.002497 ; term3 = 2.409325e-05 term4 = 8.898641e-06
d=4 n=25: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.053090 ; term3 = 2.330979e-05 term4 = 8.592525e-06
d=4 n=26: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.102965 ; term3 = 2.251314e-05 term4 = 8.345742e-06
d=4 n=27: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.152945 ; term3 = 2.178507e-05 term4 = 8.096887e-06
d=4 n=28: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.202720 ; term3 = 2.108333e-05 term4 = 7.874774e-06
d=4 n=29: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.253145 ; term3 = 2.046014e-05 term4 = 7.642590e-06
d=4 n=30: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.302638 ; term3 = 1.982194e-05 term4 = 7.453441e-06
d=4 n=31: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.353347 ; term3 = 1.927878e-05 term4 = 7.239429e-06
d=4 n=32: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.403178 ; term3 = 1.872203e-05 term4 = 7.062582e-06
d=4 n=33: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.453510 ; term3 = 1.821833e-05 term4 = 6.880066e-06
d=4 n=34: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.503631 ; term3 = 1.772941e-05 term4 = 6.714138e-06
d=4 n=35: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.553804 ; term3 = 1.727272e-05 term4 = 6.549465e-06
d=4 n=36: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.603579 ; term3 = 1.682053e-05 term4 = 6.404790e-06
d=4 n=37: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.654485 ; term3 = 1.642672e-05 term4 = 6.245993e-06
d=4 n=38: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.704637 ; term3 = 1.602551e-05 term4 = 6.109971e-06
d=4 n=39: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.754821 ; term3 = 1.564829e-05 term4 = 5.974867e-06
d=4 n=40: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.804808 ; term3 = 1.528135e-05 term4 = 5.850035e-06
d=4 n=41: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.855459 ; term3 = 1.494769e-05 term4 = 5.720949e-06
d=4 n=42: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.905425 ; term3 = 1.460988e-05 term4 = 5.608272e-06
d=4 n=43: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 2.956130 ; term3 = 1.430539e-05 term4 = 5.488791e-06
d=4 n=44: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.006182 ; term3 = 1.399728e-05 term4 = 5.383789e-06
d=4 n=45: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.056554 ; term3 = 1.371027e-05 term4 = 5.277383e-06
d=4 n=46: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.107005 ; term3 = 1.343398e-05 term4 = 5.176438e-06
d=4 n=47: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.157475 ; term3 = 1.317111e-05 term4 = 5.076783e-06
d=4 n=48: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.207343 ; term3 = 1.290619e-05 term4 = 4.988015e-06
d=4 n=49: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.258078 ; term3 = 1.266709e-05 term4 = 4.893525e-06
d=4 n=50: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.308337 ; term3 = 1.242707e-05 term4 = 4.808490e-06
d=4 n=51: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.358829 ; term3 = 1.220085e-05 term4 = 4.723047e-06
d=4 n=52: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.409148 ; term3 = 1.197927e-05 term4 = 4.642756e-06
d=4 n=53: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.459724 ; term3 = 1.177027e-05 term4 = 4.562087e-06
d=4 n=54: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.509762 ; term3 = 1.155989e-05 term4 = 4.489202e-06
d=4 n=55: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.560327 ; term3 = 1.136512e-05 term4 = 4.413570e-06
d=4 n=56: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.610578 ; term3 = 1.117129e-05 term4 = 4.344025e-06
d=4 n=57: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.661207 ; term3 = 1.098902e-05 term4 = 4.273675e-06
d=4 n=58: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.711677 ; term3 = 1.081006e-05 term4 = 4.207175e-06
d=4 n=59: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.762153 ; term3 = 1.063810e-05 term4 = 4.141441e-06
d=4 n=60: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.812144 ; term3 = 1.046534e-05 term4 = 4.081356e-06
d=4 n=61: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.862971 ; term3 = 1.030734e-05 term4 = 4.017886e-06
d=4 n=62: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.913326 ; term3 = 1.014832e-05 term4 = 3.959747e-06
d=4 n=63: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 3.963685 ; term3 = 9.995204e-06 term4 = 3.902175e-06
d=4 n=64: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.014030 ; term3 = 9.845744e-06 term4 = 3.847055e-06
d=4 n=65: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.064621 ; term3 = 9.703469e-06 term4 = 3.791744e-06
d=4 n=66: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.114932 ; term3 = 9.561833e-06 term4 = 3.740193e-06
d=4 n=67: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.165656 ; term3 = 9.428663e-06 term4 = 3.687316e-06
d=4 n=68: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.215950 ; term3 = 9.294852e-06 term4 = 3.638454e-06
d=4 n=69: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.266424 ; term3 = 9.166862e-06 term4 = 3.589477e-06
d=4 n=70: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.316763 ; term3 = 9.040922e-06 term4 = 3.542693e-06
d=4 n=71: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.367358 ; term3 = 8.920697e-06 term4 = 3.495733e-06
d=4 n=72: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.417545 ; term3 = 8.800038e-06 term4 = 3.452114e-06
d=4 n=73: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.468354 ; term3 = 8.687415e-06 term4 = 3.406905e-06
d=4 n=74: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.518765 ; term3 = 8.574293e-06 term4 = 3.364842e-06
d=4 n=75: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.569177 ; term3 = 8.464706e-06 term4 = 3.323164e-06
d=4 n=76: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.619598 ; term3 = 8.357559e-06 term4 = 3.282849e-06
d=4 n=77: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.670179 ; term3 = 8.254547e-06 term4 = 3.242531e-06
d=4 n=78: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.720482 ; term3 = 8.151696e-06 term4 = 3.204675e-06
d=4 n=79: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.771123 ; term3 = 8.054011e-06 term4 = 3.166057e-06
d=4 n=80: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.821398 ; term3 = 7.956016e-06 term4 = 3.129905e-06
d=4 n=81: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.872016 ; term3 = 7.862547e-06 term4 = 3.093362e-06
d=4 n=82: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.922554 ; term3 = 7.770494e-06 term4 = 3.058184e-06
d=4 n=83: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 4.973091 ; term3 = 7.681015e-06 term4 = 3.023345e-06
d=4 n=84: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.023279 ; term3 = 7.591323e-06 term4 = 2.990612e-06
d=4 n=85: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.073995 ; term3 = 7.506766e-06 term4 = 2.956865e-06
d=4 n=86: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.124489 ; term3 = 7.422490e-06 term4 = 2.924886e-06
d=4 n=87: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.174981 ; term3 = 7.340475e-06 term4 = 2.893190e-06
d=4 n=88: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.225362 ; term3 = 7.259531e-06 term4 = 2.862623e-06
d=4 n=89: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.275942 ; term3 = 7.181507e-06 term4 = 2.832000e-06
d=4 n=90: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.326194 ; term3 = 7.103311e-06 term4 = 2.803103e-06
d=4 n=91: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.376904 ; term3 = 7.029124e-06 term4 = 2.773480e-06
d=4 n=92: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.427369 ; term3 = 6.955007e-06 term4 = 2.745399e-06
d=4 n=93: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.477960 ; term3 = 6.883255e-06 term4 = 2.717328e-06
d=4 n=94: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.528445 ; term3 = 6.812367e-06 term4 = 2.690199e-06
d=4 n=95: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.578930 ; term3 = 6.743223e-06 term4 = 2.663303e-06
d=4 n=96: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.629213 ; term3 = 6.674346e-06 term4 = 2.637652e-06
d=4 n=97: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.679935 ; term3 = 6.608825e-06 term4 = 2.611387e-06
d=4 n=98: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.730355 ; term3 = 6.543149e-06 term4 = 2.586484e-06
d=4 n=99: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.780841 ; term3 = 6.479229e-06 term4 = 2.561706e-06
d=4 n=100: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.831283 ; term3 = 6.416203e-06 term4 = 2.537657e-06
d=4 n=101: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.881960 ; term3 = 6.355398e-06 term4 = 2.513473e-06
d=4 n=102: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.932348 ; term3 = 6.294471e-06 term4 = 2.490490e-06
d=4 n=103: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 5.982986 ; term3 = 6.235863e-06 term4 = 2.467196e-06
d=4 n=104: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 6.033341 ; term3 = 6.177146e-06 term4 = 2.445035e-06
d=4 n=105: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 6.083856 ; term3 = 6.120212e-06 term4 = 2.422847e-06
d=4 n=106: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 6.134431 ; term3 = 6.064336e-06 term4 = 2.401137e-06
d=4 n=107: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 6.185004 ; term3 = 6.009676e-06 term4 = 2.379603e-06
d=4 n=108: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 6.235305 ; term3 = 5.954934e-06 term4 = 2.359073e-06
d=4 n=109: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 6.285990 ; term3 = 5.902552e-06 term4 = 2.338120e-06
d=4 n=110: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 6.336406 ; term3 = 5.850076e-06 term4 = 2.318131e-06
d=4 n=111: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 6.386951 ; term3 = 5.799041e-06 term4 = 2.298154e-06
d=4 n=112: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 6.437406 ; term3 = 5.748536e-06 term4 = 2.278738e-06
d=4 n=113: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 6.488059 ; term3 = 5.699562e-06 term4 = 2.259274e-06
d=4 n=114: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 6.538453 ; term3 = 5.650512e-06 term4 = 2.240671e-06
d=4 n=115: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 6.589069 ; term3 = 5.603130e-06 term4 = 2.221850e-06
d=4 n=116: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 6.639516 ; term3 = 5.555890e-06 term4 = 2.203754e-06
d=4 n=117: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 6.690060 ; term3 = 5.509847e-06 term4 = 2.185673e-06
d=4 n=118: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 6.740561 ; term3 = 5.464338e-06 term4 = 2.168051e-06
d=4 n=119: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 6.791061 ; term3 = 5.419725e-06 term4 = 2.150558e-06
d=4 n=120: E_lat-E_iid > 0 ; ratio E_lat/E_iid = 6.841369 ; term3 = 5.375175e-06 term4 = 2.133755e-06
# total time 158.0s
