OWR-13750332-001 part A: nested-cluster construction, exact certificates
columns: label | m | weights (float) | delta exponents | theta=2^-j | certified | numeric min|P|, max|P| on S^1, sign changes | seconds
uniform | m=3 | [1.0, 1.0, 1.0] | deltas 2^-[] | theta 2^-1 | True | 6.400e-01, 8.400e-01, 0 | 0.01
uniform | m=5 | [1.0, 1.0, 1.0, 1.0, 1.0] | deltas 2^-[1] | theta 2^-1 | True | 1.108e-01, 6.107e-01, 0 | 0.02
uniform | m=7 | [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0] | deltas 2^-[1, 1] | theta 2^-1 | True | 4.061e-03, 4.965e-01, 0 | 0.05
uniform | m=9 | [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0] | deltas 2^-[1, 1, 1] | theta 2^-1 | True | 4.425e-05, 4.290e-01, 0 | 0.09
uniform | m=11 | [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0] | deltas 2^-[1, 1, 1, 1] | theta 2^-1 | True | 1.545e-07, 3.861e-01, 0 | 0.21
uniform | m=13 | [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0] | deltas 2^-[1, 1, 1, 1, 1] | theta 2^-1 | True | 1.642e-10, 3.575e-01, 0 | 0.37
uniform | m=15 | [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0] | deltas 2^-[1, 1, 1, 1, 1, 1] | theta 2^-1 | True | 4.974e-14, 3.378e-01, 0 | 0.75
zero-sum (29) | m=3 | [-1.0, 0.5, 0.5] | deltas 2^-[] | theta 2^-1 | True | 2.353e-01, 8.435e-01, 0 | 0.01
zero-sum (29) | m=5 | [-0.5, -0.5, 0.3333, 0.3333, 0.3333] | deltas 2^-[1] | theta 2^-1 | True | 4.070e-02, 2.208e-01, 0 | 0.02
zero-sum (29) | m=7 | [-0.3333, -0.3333, -0.3333, 0.25, 0.25, 0.25, 0.25] | deltas 2^-[1, 1] | theta 2^-1 | True | 1.218e-03, 8.793e-02, 0 | 0.04
zero-sum (29) | m=9 | [-0.25, -0.25, -0.25, -0.25, 0.2, 0.2, 0.2, 0.2, 0.2] | deltas 2^-[1, 1, 1] | theta 2^-1 | True | 1.145e-05, 6.499e-02, 0 | 0.08
zero-sum (29) | m=11 | [-0.2, -0.2, -0.2, -0.2, -0.2, 0.1667, 0.1667, 0.1667, 0.1667, 0.1667, 0.1667] | deltas 2^-[1, 1, 1, 1] | theta 2^-1 | True | 3.420e-08, 5.363e-02, 0 | 0.18
zero-sum (29) | m=13 | [-0.1667, -0.1667, -0.1667, -0.1667, -0.1667, -0.1667, 0.1429, 0.1429, 0.1429, 0.1429, 0.1429, 0.1429, 0.1429] | deltas 2^-[1, 1, 1, 1, 1] | theta 2^-1 | True | 3.112e-11, 4.544e-02, 0 | 0.37
zero-sum (29) | m=15 | [-0.1429, -0.1429, -0.1429, -0.1429, -0.1429, -0.1429, -0.1429, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125] | deltas 2^-[1, 1, 1, 1, 1, 1] | theta 2^-1 | True | 8.182e-15, 3.932e-02, 0 | 0.80
1..m | m=5 | [1.0, 2.0, 3.0, 4.0, 5.0] | deltas 2^-[1] | theta 2^-1 | True | 1.321e-01, 2.387e+00, 0 | 0.03
alt 1..m | m=5 | [-1.0, 2.0, -3.0, 4.0, -5.0] | deltas 2^-[1] | theta 2^-1 | True | 1.321e-01, 2.387e+00, 0 | 0.02
1..m | m=9 | [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0] | deltas 2^-[1, 1, 1] | theta 2^-1 | True | 1.058e-04, 3.249e+00, 0 | 0.12
alt 1..m | m=9 | [-1.0, 2.0, -3.0, 4.0, -5.0, 6.0, -7.0, 8.0, -9.0] | deltas 2^-[1, 1, 1] | theta 2^-1 | True | 1.058e-04, 3.249e+00, 0 | 0.13
1..m | m=13 | [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0, 13.0] | deltas 2^-[1, 1, 1, 1, 1] | theta 2^-1 | True | 7.909e-10, 6.607e+00, 0 | 0.69
alt 1..m | m=13 | [-1.0, 2.0, -3.0, 4.0, -5.0, 6.0, -7.0, 8.0, -9.0, 10.0, -11.0, 12.0, -13.0] | deltas 2^-[1, 1, 1, 1, 1] | theta 2^-1 | True | 7.909e-10, 6.607e+00, 0 | 0.78
powers of 10, random signs | m=5 | [-1.0, -10.0, 100.0, -1000.0, -10000.0] | deltas 2^-[1] | theta 2^-3 | True | 6.818e-04, 1.023e+04, 0 | 0.04
powers of 10, random signs | m=7 | [1.0, 10.0, -100.0, -1000.0, -10000.0, 100000.0, 1000000.0] | deltas 2^-[3, 1] | theta 2^-3 | True | 1.217e-06, 9.178e+05, 0 | 0.13
powers of 10, random signs | m=9 | [-1.0, 10.0, 100.0, -1000.0, 10000.0, -100000.0, -1000000.0, 10000000.0, -100000000.0] | deltas 2^-[7, 3, 1] | theta 2^-3 | True | 4.347e-08, 8.544e+07, 0 | 0.56
powers of 10, random signs | m=11 | [1.0, 10.0, 100.0, -1000.0, -10000.0, 100000.0, 1000000.0, 10000000.0, -100000000.0, -1000000000.0, -10000000000.0] | deltas 2^-[10, 7, 3, 1] | theta 2^-3 | True | 2.291e-13, 8.168e+09, 0 | 1.77
one dominant 10^6 | m=5 | [1000000.0, 1.0, 1.0, 1.0, 1.0] | deltas 2^-[1] | theta 2^-1 | True | 2.043e-05, 3.323e+05, 0 | 0.07
one tiny 10^-6 | m=5 | [1e-06, 1.0, 1.0, 1.0, 1.0] | deltas 2^-[8] | theta 2^-1 | True | 5.454e-11, 7.219e-01, 0 | 0.05
k+1 equal big, k tiny | m=5 | [1.0, 1.0, 1.0, 0.001, 0.001] | deltas 2^-[3] | theta 2^-2 | True | 1.065e-06, 2.146e+00, 0 | 0.04
k+1 tiny, k big | m=5 | [0.001, 0.001, 0.001, -1.0, -1.0] | deltas 2^-[1] | theta 2^-2 | True | 1.961e-07, 1.183e+00, 0 | 0.04
one dominant 10^6 | m=9 | [1000000.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0] | deltas 2^-[1, 1, 1] | theta 2^-2 | True | 1.998e-08, 3.602e+05, 0 | 0.49
one tiny 10^-6 | m=9 | [1e-06, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0] | deltas 2^-[8, 1, 1] | theta 2^-1 | True | 5.274e-13, 3.268e-01, 0 | 0.22
k+1 equal big, k tiny | m=9 | [1.0, 1.0, 1.0, 1.0, 1.0, 0.001, 0.001, 0.001, 0.001] | deltas 2^-[3, 2, 12] | theta 2^-3 | True | 5.107e-30, 4.340e+00, 0 | 0.41
k+1 tiny, k big | m=9 | [0.001, 0.001, 0.001, 0.001, 0.001, -1.0, -1.0, -1.0, -1.0] | deltas 2^-[3, 2, 1] | theta 2^-2 | True | 2.249e-11, 1.297e+00, 0 | 0.24
random #0 | m=11 | [-0.01893, 0.0002181, 11260.0, 553100.0, -38.37, 0.003587, 0.4256, 0.5644, -135400.0, -0.0003791, -1.725] | deltas 2^-[10, 5, 1, 1] | theta 2^-3 | True | 7.223e-14, 5.013e+05, 0 | 2.49
random #1 | m=9 | [7.461e-05, 1.023, -9.062e-05, -34710.0, 794.2, -0.01404, -5.022e-05, 17.0, 3.571e-05] | deltas 2^-[8, 5, 2] | theta 2^-3 | True | 4.899e-14, 2.864e+04, 0 | 0.92
random #2 | m=15 | [7889.0, 8819.0, -0.000951, -7.113, 0.001113, 0.007523, -1544.0, 1.693e-05, 0.000288, -0.001346, -0.001909, 0.01602, -22620.0, 0.2397, 0.06945] | deltas 2^-[12, 8, 5, 2, 1, 1] | theta 2^-2 | True | 1.073e-26, 7.201e+03, 0 | 16.79
random #3 | m=9 | [-12430.0, 10830.0, -0.006926, 0.0001842, 12.92, -609.7, -0.0003898, -9835.0, -68910.0] | deltas 2^-[10, 13, 2] | theta 2^-4 | True | 2.770e-21, 9.724e+04, 0 | 0.92
random #4 | m=7 | [74.13, -0.007538, -857.9, 0.01107, -0.06246, -6.662, 1.059] | deltas 2^-[3, 1] | theta 2^-2 | True | 2.077e-07, 4.379e+02, 0 | 0.15
random #5 | m=3 | [8342.0, 0.1316, 38.72] | deltas 2^-[] | theta 2^-3 | True | 1.280e-04, 8.376e+03, 0 | 0.01
random #6 | m=5 | [-80.38, -1985.0, -0.06382, -75.0, -110.4] | deltas 2^-[1] | theta 2^-3 | True | 1.938e-05, 1.958e+03, 0 | 0.04
random #7 | m=3 | [-21.79, -7991.0, -6028.0] | deltas 2^-[] | theta 2^-1 | True | 9.004e+00, 8.545e+03, 0 | 0.01
random #8 | m=11 | [-0.01846, 0.1468, -0.0002727, 237.9, -0.1114, 0.2896, 151.2, -377.3, -40810.0, 0.000512, 0.09755] | deltas 2^-[8, 5, 1, 1] | theta 2^-3 | True | 1.121e-15, 2.978e+04, 0 | 2.21
random #9 | m=15 | [18.62, -1504.0, 0.001755, -0.007444, -0.001578, -0.6225, -4.428, -4.281e-05, 114.8, 9948.0, 0.0006832, -0.002243, -13.52, 9.753, 0.00122] | deltas 2^-[7, 5, 5, 5, 4, 1] | theta 2^-3 | True | 2.572e-40, 8.150e+03, 0 | 19.80
random #10 | m=5 | [-8.571e-05, 815.1, 1392.0, 0.01581, -12230.0] | deltas 2^-[7] | theta 2^-4 | True | 3.700e-09, 1.402e+04, 0 | 0.08
random #11 | m=13 | [0.001176, -0.001494, -1256.0, 271.0, 0.000261, 23.58, -117.1, -0.007505, -8879.0, -0.0006279, -0.007856, -0.0009085, -662.5] | deltas 2^-[8, 7, 7, 5, 1] | theta 2^-3 | True | 1.012e-32, 8.052e+03, 0 | 6.91
random #12 | m=9 | [-103.4, -0.02815, -41670.0, 90.66, -0.6027, -1172.0, 1.009, 0.001549, -2.46] | deltas 2^-[4, 2, 1] | theta 2^-2 | True | 1.072e-09, 1.488e+04, 0 | 0.51
random #13 | m=9 | [11010.0, -0.004452, -433.3, -0.8015, -226.0, 8145.0, -2211.0, -0.115, -819.6] | deltas 2^-[6, 3, 1] | theta 2^-2 | True | 1.145e-10, 7.906e+03, 0 | 0.52
random #14 | m=13 | [-3.448, 0.03544, -61.43, -3.24, 5.484, 64.88, 476.9, -0.001825, -0.0009361, 0.004615, -2.247, -0.008715, -1829.0] | deltas 2^-[5, 5, 3, 2, 1] | theta 2^-2 | True | 1.032e-21, 5.754e+02, 0 | 5.41
random #15 | m=3 | [0.1514, 0.2711, -63.89] | deltas 2^-[] | theta 2^-1 | True | 3.162e-04, 6.385e+01, 0 | 0.01
random #16 | m=7 | [1.56, -0.005943, 0.4306, -0.004825, 191.6, -0.0009052, -8156.0] | deltas 2^-[2, 2] | theta 2^-3 | True | 5.312e-10, 7.057e+03, 0 | 0.20
random #17 | m=7 | [0.001797, 1.096, -0.3251, 0.07183, -0.0001311, 0.0001337, -0.1315] | deltas 2^-[2, 3] | theta 2^-2 | True | 1.180e-10, 8.496e-01, 0 | 0.14
random #18 | m=7 | [-0.001074, -0.1142, 557.6, 356.3, -0.0004818, 0.0006856, -0.1423] | deltas 2^-[1, 2] | theta 2^-4 | True | 7.156e-12, 8.757e+02, 0 | 0.19
random #19 | m=13 | [11930.0, 9551.0, -9.471e-05, 0.6694, -0.001324, -6.089, -0.3326, 921.5, -900.0, -0.5021, -5067.0, 0.06917, -9.77e-05] | deltas 2^-[10, 8, 5, 1, 1] | theta 2^-3 | True | 2.060e-25, 1.944e+04, 0 | 7.25
random #20 | m=5 | [-0.4977, 28.82, -1038.0, -209.7, 2.157e-05] | deltas 2^-[6] | theta 2^-3 | True | 1.959e-09, 1.130e+03, 0 | 0.05
random #21 | m=15 | [21.24, 0.1772, 8.631e-05, 8.098e-06, 5.506e-05, 0.1735, 0.002518, 11320.0, 13520.0, -11110.0, 12.7, 56.69, -24340.0, -0.001088, -0.004556] | deltas 2^-[13, 11, 6, 5, 4, 1] | theta 2^-3 | True | 4.955e-39, 4.238e+04, 0 | 21.18
random #22 | m=7 | [0.01888, 21070.0, -0.01, -16760.0, 47950.0, 5200.0, -0.002097] | deltas 2^-[9, 7] | theta 2^-5 | True | 2.103e-14, 9.009e+04, 0 | 0.30
random #23 | m=3 | [-0.0002847, -2500.0, 3.125] | deltas 2^-[] | theta 2^-4 | True | 7.586e-08, 2.503e+03, 0 | 0.02
random #24 | m=15 | [-0.002536, 102.3, -0.3107, 0.1044, 0.0008206, -3.757, 0.1158, -428.4, 0.002148, 0.00115, -139.2, -0.1709, -2993.0, 81.14, -0.01002] | deltas 2^-[7, 6, 6, 3, 1, 1] | theta 2^-2 | True | 3.024e-32, 6.746e+02, 0 | 14.50
random #25 | m=3 | [0.01086, -1428.0, -15.17] | deltas 2^-[] | theta 2^-3 | True | 1.721e-05, 1.441e+03, 0 | 0.01
random #26 | m=7 | [-10.39, 1319.0, 144.5, -168.7, -7263.0, 3.075, -0.005369] | deltas 2^-[3, 1] | theta 2^-3 | True | 1.189e-08, 7.347e+03, 0 | 0.15
random #27 | m=15 | [4.563, -0.4373, -82.35, -0.0735, -1.761, -0.02299, 3942.0, 4.017, -1693.0, 0.002939, 0.03063, -0.02985, -5066.0, -0.0006008, -18920.0] | deltas 2^-[8, 7, 4, 2, 1, 1] | theta 2^-2 | True | 4.439e-26, 5.231e+03, 0 | 15.04
random #28 | m=11 | [0.01487, -0.06, -0.2442, 109.3, 0.0008827, -0.01224, -0.0004637, 0.4907, -0.1016, 0.007439, 0.0002486] | deltas 2^-[3, 2, 1, 1] | theta 2^-2 | True | 5.174e-14, 2.853e+01, 0 | 1.66
random #29 | m=15 | [-0.03505, 762.3, -333.3, -0.00587, 2.254e-05, -0.0001102, -21220.0, 5.31, -0.0001655, -0.2531, -1.839, 29640.0, 1.599, 0.00213, 685.7] | deltas 2^-[8, 9, 8, 3, 1, 1] | theta 2^-2 | True | 1.567e-29, 9.481e+03, 0 | 16.04
random #30 | m=3 | [101.8, 87.34, 16.34] | deltas 2^-[] | theta 2^-1 | True | 1.028e+01, 1.083e+02, 0 | 0.01
random #31 | m=15 | [-0.01149, -0.00525, -0.01318, -26.16, -0.0003672, 0.001077, 6.377e-05, -4.494, -199.0, -26540.0, -17.8, 696.7, -1422.0, 0.002457, 0.000392] | deltas 2^-[9, 8, 6, 5, 3, 1] | theta 2^-2 | True | 1.293e-40, 6.404e+03, 0 | 19.50
random #32 | m=9 | [993.6, 21.03, 0.0003009, -0.008784, -0.02335, -0.1727, 1.207, 0.0695, 0.001454] | deltas 2^-[3, 1, 1] | theta 2^-2 | True | 7.357e-11, 3.490e+02, 0 | 0.59
random #33 | m=13 | [0.9533, 257.1, 45.57, 0.01127, 0.001451, 3.552, 0.0005108, 74.18, 0.3255, -0.2882, 0.00136, 93.45, -0.1275] | deltas 2^-[6, 5, 4, 1, 1] | theta 2^-2 | True | 4.609e-22, 1.005e+02, 0 | 4.81
random #34 | m=15 | [-0.1325, 80.34, 131.3, 7.778e-05, 0.6759, -5.64e-05, -182.4, 0.002312, 2053.0, 0.03489, 0.005876, -1.457e-05, -3.231e-05, 18860.0, 0.06162] | deltas 2^-[9, 9, 8, 2, 1, 1] | theta 2^-3 | True | 2.631e-31, 1.401e+04, 0 | 17.59
random #35 | m=9 | [-121.3, 0.3133, -0.000104, -15840.0, 25.69, 0.01075, -0.09702, 50.35, 0.8] | deltas 2^-[5, 2, 1] | theta 2^-2 | True | 1.094e-11, 5.537e+03, 0 | 0.70
random #36 | m=5 | [0.03942, 0.001049, 4315.0, 1660.0, 5.489] | deltas 2^-[1] | theta 2^-5 | True | 7.149e-09, 5.942e+03, 0 | 0.06
random #37 | m=9 | [0.107, 102.6, -0.1884, 35.7, -882.8, -0.5252, -224.3, 1.201, -62.26] | deltas 2^-[2, 2, 1] | theta 2^-2 | True | 1.918e-08, 4.616e+02, 0 | 0.37
random #38 | m=9 | [0.02187, -5.993, 436.2, 7.816e-05, -5.089e-05, -714.9, -0.2426, 0.03139, 2934.0] | deltas 2^-[9, 3, 1] | theta 2^-4 | True | 4.432e-16, 3.830e+03, 0 | 0.77
random #39 | m=7 | [-1.569, -653.5, -0.01329, 19120.0, 1.498, -0.004286, -0.006931] | deltas 2^-[2, 2] | theta 2^-3 | True | 5.233e-10, 1.672e+04, 0 | 0.21
random #40 | m=5 | [-0.1114, -2.172, 155.2, 1201.0, 2.772e-06] | deltas 2^-[3] | theta 2^-5 | True | 6.794e-10, 1.348e+03, 0 | 0.06
random #41 | m=15 | [15650.0, 63.96, -0.007364, -4476.0, -71.08, 3.163, 8367.0, 0.0001023, -74.3, 0.001079, 0.006451, 0.01112, -14.81, 32.05, 12.07] | deltas 2^-[10, 5, 5, 5, 1, 1] | theta 2^-3 | True | 7.251e-33, 1.908e+04, 0 | 16.35
random #42 | m=5 | [5.319e-07, 5.535e-05, -354.9, 0.01234, 8.575] | deltas 2^-[2] | theta 2^-6 | True | 4.742e-12, 3.630e+02, 0 | 0.07
random #43 | m=13 | [0.0007712, -336.8, -0.4536, -8.514, 26.18, 5.494e-05, 38.65, -1.312e-05, -36.01, 5.754, 0.002067, 0.06687, -177.1] | deltas 2^-[7, 6, 5, 2, 8] | theta 2^-2 | True | 4.365e-40, 2.623e+02, 0 | 7.52
random #44 | m=15 | [-111.6, -0.0002623, -0.1088, 9.358, -0.001452, 0.9914, 32.23, -0.00768, 0.2068, 0.1485, 4.119e-05, -19980.0, 62.54, -588.9, 2127.0] | deltas 2^-[9, 7, 5, 2, 1, 1] | theta 2^-2 | True | 1.376e-27, 4.036e+03, 0 | 15.42
random #45 | m=13 | [-96.94, 0.0007114, -1.643, 6.41, -164.1, -3.36e-05, 0.03022, 1.081, 16.64, 0.002122, -0.001394, -4.474, -2455.0] | deltas 2^-[7, 5, 4, 2, 1] | theta 2^-2 | True | 3.103e-24, 6.474e+02, 0 | 5.35
random #46 | m=13 | [0.01727, 4.524e-05, 2546.0, 0.5516, 7380.0, -15830.0, 22.22, 0.3344, -3067.0, 1342.0, -1.182, 4693.0, -0.00893] | deltas 2^-[11, 7, 6, 4, 1] | theta 2^-3 | True | 9.368e-32, 2.500e+04, 0 | 7.88
random #47 | m=7 | [0.102, -2.657, 0.2606, -147.2, 0.0002195, 8.598, -0.006887] | deltas 2^-[2, 1] | theta 2^-3 | True | 5.986e-10, 1.321e+02, 0 | 0.15
random #48 | m=7 | [855.3, 770.6, 4694.0, -0.1612, 54310.0, 0.7535, 2280.0] | deltas 2^-[4, 1] | theta 2^-3 | True | 4.707e-08, 5.066e+04, 0 | 0.15
random #49 | m=7 | [-0.0008611, -8028.0, 0.1411, -49.2, -480.6, 283.4, 938.6] | deltas 2^-[5, 1] | theta 2^-3 | True | 2.982e-09, 7.985e+03, 0 | 0.16
instances 82 ALL CERTIFIED
