[integrator checks] {'cube_L': 16, 'cheb_vs_dense_step_0p05': 1.1657341758564144e-15, 'cheb_vs_dense_step_2': 1.7486012637846216e-15, 'midpoint_step_0p2_vs_0p05_max_abs_phi': 7.76186975409536e-06, 'midpoint_step_0p2_vs_0p05_rel_gradient_d3': 5.4732819627028984e-05}
[ring L=1024] small checks: {'L': 1024, 'D': 1, 'g_s_over_t_f': 1e-05, 'sector_dim': 513, 'S2': 1491322.3110961812, 'static_sector_vs_fourier': 1.011841277431813e-09, 'exact_vs_first_order_rel': 3.726315205278744e-05, 'infinite_lambda_average_vs_static_rel': 0.0011086535721447658, 'sum_rule_max_abs': 8.98329188814273e-11, 'running_average': {'1.0L^2/t': {'max_dev_from_static_phi': 1.4317079589048944, 'max_dev_from_exact_average_phi': 1.337102944304334, 'bound_S2_over_tLambda': 1.4222357855760395}, '4.0L^2/t': {'max_dev_from_static_phi': 0.34670475364595177, 'max_dev_from_exact_average_phi': 0.2520997390453914, 'bound_S2_over_tLambda': 0.35555894639400987}, '16.0L^2/t': {'max_dev_from_static_phi': 0.06918124562714922, 'max_dev_from_exact_average_phi': 0.025423768973411143, 'bound_S2_over_tLambda': 0.08888973659850247}}}
[ring L=1024] gradual T=20.00 (0s): E=[0.8071, 1.0666, 1.1915, 1.3065, 1.3378]
[ring L=1024] gradual T=31.71 (0s): E=[0.6618, 0.9221, 1.0979, 1.2535, 1.3168]
[ring L=1024] gradual T=50.27 (0s): E=[0.5347, 0.7692, 0.9594, 1.1748, 1.272]
[ring L=1024] gradual T=79.71 (0s): E=[0.4281, 0.6277, 0.8057, 1.0683, 1.1968]
[ring L=1024] gradual T=126.38 (1s): E=[0.3408, 0.5053, 0.6599, 0.9219, 1.1006]
[ring L=1024] gradual T=200.37 (1s): E=[0.2702, 0.4034, 0.5322, 0.7676, 0.96]
[ring L=1024] gradual T=317.67 (2s): E=[0.2137, 0.3201, 0.425, 0.6249, 0.8042]
[ring L=1024] gradual T=503.66 (2s): E=[0.1685, 0.253, 0.337, 0.5014, 0.6566]
[ring L=1024] gradual T=798.54 (4s): E=[0.1326, 0.1993, 0.266, 0.3983, 0.5271]
[ring L=1024] gradual T=1266.07 (5s): E=[0.104, 0.1564, 0.209, 0.3141, 0.4183]
[ring L=1024] gradual T=2007.31 (12s): E=[0.0813, 0.1222, 0.1635, 0.2462, 0.3291]
[ring L=1024] gradual T=3182.53 (22s): E=[0.0632, 0.0951, 0.1272, 0.1919, 0.257]
[ring L=1024] gradual T=5045.82 (34s): E=[0.0489, 0.0736, 0.0984, 0.1485, 0.1991]
[ring L=1024] gradual T=8000.00 (55s): E=[0.0376, 0.0565, 0.0755, 0.114, 0.1529]
[ring L=1024] gradual: {'criterion': 'E(d,T) = max over lam in [0,2T] of |grad phi - f(lam/T) grad phi_st| / |grad phi_st|', 'eps': 0.2, 'd': [4, 6, 8, 12, 16], 'T_form': [361.1481825962641, 792.8787342230011, 1374.6990340941582, 2947.232545646591, 5005.553464179453], 'fit_exponent': 1.8965294439392304, 'fit_prefactor': 26.342322606071434, 'E_vs_nu_exponent_nu_lt_0p5': 0.520093915871649, 'E_vs_nu_prefactor': 0.972621239648678}
[ring L=16384] front (26s): {'criterion': 'first lam with |delta rho| >= eps (n g/t) rho^-p, i.e. |phi| >= (eps/2) rho^-p; eps=0.1, p=0.5', 'rho': [16, 24, 32, 48, 64, 96, 128, 160, 192, 256, 320, 384], 'arrival': [6.98, 10.34, 13.9, 21.54, 29.32, 44.980000000000004, 60.68, 76.38, 92.10000000000001, 123.54, 155.0, 186.46], 'arrival_times_2t_over_rho': [0.8725, 0.8616666666666667, 0.86875, 0.8975, 0.91625, 0.9370833333333334, 0.948125, 0.95475, 0.9593750000000001, 0.96515625, 0.96875, 0.9711458333333334], 'speed_linear_fit': 2.0360702950292646, 'fit_min_rho': 64, 'max_ratio_to_kapteyn_bound_ahead': 0.009476617339564673, 'front_peak_phi': [0.1674100375901452, 0.12204377600133479, 0.12691022406173483, 0.09721629770150894, 0.08492597222554239, 0.07822560580393277, 0.07059831347325946, 0.06266475217545564, 0.05948913604695868, 0.054734860499988894, 0.049979182561704104, 0.047550509581685156], 'front_peak_exponent': -0.33966603429607595, 'front_peak_prefactor': 0.35792690396462695, 'front_form_rel_dev': {64: 0.43657045062393335, 96: 0.4101579855372278, 128: 0.33304136099999126, 160: 0.3250214899987672, 192: 0.3163049499082327, 256: 0.2730170434845032, 320: 0.23867323731924736, 384: 0.2368827519256465}, 'front_peak_times_d13': [0.42184686064703186, 0.3520351669932374, 0.4029148463622355, 0.35330747302462334, 0.3397038889021695, 0.3581838603844977, 0.35579320492814565, 0.34019661448922156, 0.3431927236067404, 0.34754470054806, 0.3418528000603097, 0.3456200406421682], 'max_abs_phi_for_2tlam_le_0p8rho': {16: 0.0062214097159159765, 24: 0.0023345187086564736, 32: 0.0009023619947283656, 48: 0.00014259708600368532, 64: 2.357178066212203e-05, 96: 1.3017510287766479e-06, 128: 9.831789069008096e-08, 160: 5.398602538954514e-09, 192: 2.4047380273646905e-10, 256: 2.8427714976523403e-13, 320: 7.477058317984161e-16, 384: 3.065963628453758e-18}}
[ring L=16384] formation sudden (74s): {'window_end': 7372.8, 'eps': 0.2, 'zeta_star': 0.0604200987916, 'd': [6, 8, 12, 16, 24, 32, 40], 'lam_form': [148.0, 263.0, 589.5, 1045.0, 2334.5, 4122.5, 6397.0], 'lam_form_pred': [148.9570553507807, 264.81254284583235, 595.8282214031228, 1059.2501713833294, 2383.3128856124913, 4237.000685533318, 6620.31357114581], 'fit_exponent': 1.9805096044375017, 'fit_min_d': 12, 'fit_prefactor': 4.304176126675169, 'pred_prefactor': 4.1376959819661305, 'max_dev_from_scaling_fn_zeta_le_0p5': {6: 0.0056142199301002504, 8: 0.002969782745715688, 12: 0.0016758425134041355, 16: 0.0014784878513551813, 24: 0.002197879565406513, 32: 0.0029271254655802714, 40: 0.003630470467515745}}
[cube L=32] small checks: {'L': 32, 'D': 3, 'g_s_over_t_f': 0.001, 'sector_dim': 969, 'S2': 0.3511206004823627, 'static_sector_vs_fourier': 2.6281060661048627e-16, 'exact_vs_first_order_rel': 0.0007924266710725847, 'infinite_lambda_average_vs_static_rel': 0.00036877777109378413, 'sum_rule_max_abs': 2.1021958045847056e-12, 'running_average': {'1.0L^2/t': {'max_dev_from_static_phi': 0.0001920063806787886, 'max_dev_from_exact_average_phi': 0.00010140632972222008, 'bound_S2_over_tLambda': 0.00034289121140855733}, '4.0L^2/t': {'max_dev_from_static_phi': 0.00011942975113926613, 'max_dev_from_exact_average_phi': 2.8829700182697593e-05, 'bound_S2_over_tLambda': 8.572280285213933e-05}}}
[cube L=160] front (70s): {'criterion': 'first lam with |delta rho| >= eps (n g/t) rho^-p, i.e. |phi| >= (eps/2) rho^-p; eps=0.1, p=1.5', 'rho': [6, 8, 10, 12, 16, 20, 24, 32, 40, 48, 56, 64], 'arrival': [3.4000000000000004, 3.5500000000000003, 5.0, 6.550000000000001, 8.15, 9.75, 11.350000000000001, 16.0, 19.200000000000003, 23.85, 27.05, 31.700000000000003], 'arrival_times_2t_over_rho': [1.1333333333333335, 0.8875000000000001, 1.0, 1.0916666666666668, 1.01875, 0.975, 0.9458333333333334, 1.0, 0.9600000000000002, 0.99375, 0.9660714285714286, 0.9906250000000001], 'speed_linear_fit': 2.06060606060606, 'fit_min_rho': 12, 'max_ratio_to_kapteyn_bound_ahead': 0.019883584656335343, 'front_peak_phi': [0.00862912806508322, 0.004911684401296083, 0.0036820559721112366, 0.003407901423775105, 0.0020354836204727563, 0.0015134686193860128, 0.0013398425281674062, 0.0007958311642241178, 0.0006575362135385711, 0.0005172951630419191, 0.0003987845763149355, 0.0003593053169458446], 'front_peak_exponent': -1.3219039649855904, 'front_peak_prefactor': 0.08420233054477115}
[cube L=160] formation sudden (70s): {'window_end': 72.0, 'eps': 0.1, 'zeta_star': 0.406850091863, 'd': [3, 4, 5, 6, 7, 8, 9], 'lam_form': [5.4, 9.9, 14.9, 22.5, 30.5, 41.2, 49.5], 'lam_form_pred': [5.530292471354905, 9.831631060186497, 15.3619235315414, 22.12116988541962, 30.109370121821147, 39.32652424074599, 49.77263224219414], 'fit_exponent': 2.0303021166495148, 'fit_min_d': 4, 'fit_prefactor': 0.5858435040494757, 'pred_prefactor': 0.6144769412616561, 'max_dev_from_scaling_fn_zeta_le_0p5': {3: 0.03911795620843894, 4: 0.032423869745063616, 5: 0.016226510382659542, 6: 0.015007091061028044, 7: 0.009171727229514648, 8: 0.00928872610734377, 9: 0.007503161680561865}}
[cube L=128] gradual T=4.00 (6s): E=[0.7255, 1.2272, 1.5963, 1.9921, 2.3736]
[cube L=128] gradual T=5.92 (6s): E=[0.4922, 0.9367, 1.3584, 1.657, 1.9786]
[cube L=128] gradual T=8.75 (9s): E=[0.3214, 0.6511, 1.0321, 1.3777, 1.6385]
[cube L=128] gradual T=12.93 (12s): E=[0.2048, 0.4329, 0.7242, 1.0391, 1.3319]
[cube L=128] gradual T=19.13 (19s): E=[0.1279, 0.2793, 0.4836, 0.7243, 0.9821]
[cube L=128] gradual T=28.28 (24s): E=[0.0784, 0.1762, 0.3132, 0.4824, 0.6763]
[cube L=128] gradual T=41.83 (31s): E=[0.0474, 0.1091, 0.1983, 0.312, 0.4472]
[cube L=128] gradual T=61.85 (46s): E=[0.0282, 0.0664, 0.1231, 0.1974, 0.2878]
[cube L=128] gradual T=91.46 (82s): E=[0.0166, 0.0398, 0.0752, 0.1224, 0.1813]
[cube L=128] gradual T=135.25 (98s): E=[0.0097, 0.0236, 0.0452, 0.0746, 0.112]
[cube L=128] gradual T=200.00 (137s): E=[0.0056, 0.0138, 0.0268, 0.0448, 0.068]
[cube L=128] gradual: {'criterion': 'E(d,T) = max over lam in [0,2T] of |grad phi - f(lam/T) grad phi_st| / |grad phi_st|', 'eps': 0.1, 'd': [3, 4, 5, 6, 7], 'T_form': [23.28751540519407, 44.79207130775615, 72.93789653936413, 107.31734820324155, 147.8228217147121], 'fit_exponent': 2.1811508197459197, 'fit_prefactor': 2.1505239110933307, 'E_vs_nu_exponent_nu_lt_0p5': 1.373146161238009, 'E_vs_nu_prefactor': 0.4260301665208818}
total time 851s