##############ECHO OF PROBLEM################# ##############temp/subpostode.ode################# diff ( y , x , 1 ) = sin ( x ) - cos ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.0); x_end=c(10.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(2.0) - cos(c(x)) - sin(c(x))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (closed_form) = 0.9900501662491681 y[1] (numeric) = 0.9900501662491682 absolute error = 1.110223024625157e-16 relative error = 1.121380574916993e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.02000000000000001 y[1] (closed_form) = 0.9802013266400892 y[1] (numeric) = 0.9802013266400893 absolute error = 1.110223024625157e-16 relative error = 1.132647951447641e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.03000000000000002 y[1] (closed_form) = 0.9704544660485168 y[1] (numeric) = 0.9704544660485172 absolute error = 3.33066907387547e-16 relative error = 3.432071457651426e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.04000000000000003 y[1] (closed_form) = 0.9608105591523879 y[1] (numeric) = 0.9608105591523882 absolute error = 3.33066907387547e-16 relative error = 3.466520056579868e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.05000000000000004 y[1] (closed_form) = 0.9512705703343554 y[1] (numeric) = 0.9512705703343556 absolute error = 2.220446049250313e-16 relative error = 2.33418978626645e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.06000000000000005 y[1] (closed_form) = 0.941835453585351 y[1] (numeric) = 0.9418354535853514 absolute error = 3.33066907387547e-16 relative error = 3.536359839923607e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.07000000000000005 y[1] (closed_form) = 0.9325061524091875 y[1] (numeric) = 0.9325061524091878 absolute error = 2.220446049250313e-16 relative error = 2.381159677621057e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.08000000000000006 y[1] (closed_form) = 0.9232835997282079 y[1] (numeric) = 0.9232835997282079 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.09000000000000007 y[1] (closed_form) = 0.9141687177899948 y[1] (numeric) = 0.9141687177899948 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1000000000000001 y[1] (closed_form) = 0.9051624180751461 y[1] (numeric) = 0.905162418075146 absolute error = 1.110223024625157e-16 relative error = 1.226545648002132e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1100000000000001 y[1] (closed_form) = 0.8962656012061283 y[1] (numeric) = 0.8962656012061281 absolute error = 2.220446049250313e-16 relative error = 2.477442006322903e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1200000000000001 y[1] (closed_form) = 0.8874791568572145 y[1] (numeric) = 0.8874791568572141 absolute error = 3.33066907387547e-16 relative error = 3.752954701122448e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1300000000000001 y[1] (closed_form) = 0.8788039636655172 y[1] (numeric) = 0.8788039636655168 absolute error = 3.33066907387547e-16 relative error = 3.790002334517417e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1400000000000001 y[1] (closed_form) = 0.8702408891431264 y[1] (numeric) = 0.870240889143126 absolute error = 3.33066907387547e-16 relative error = 3.827295540152082e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1500000000000001 y[1] (closed_form) = 0.8617907895903583 y[1] (numeric) = 0.8617907895903583 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 0.8534545100101271 y[1] (numeric) = 0.8534545100101268 absolute error = 2.220446049250313e-16 relative error = 2.601715760133443e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 0.8452328840234433 y[1] (numeric) = 0.8452328840234431 absolute error = 2.220446049250313e-16 relative error = 2.627022790074891e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 0.8371267337860544 y[1] (numeric) = 0.8371267337860543 absolute error = 1.110223024625157e-16 relative error = 1.326230521397848e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 0.8291368699062289 y[1] (numeric) = 0.8291368699062291 absolute error = 2.220446049250313e-16 relative error = 2.678021120326532e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (closed_form) = 0.821264091363697 y[1] (numeric) = 0.8212640913636972 absolute error = 1.110223024625157e-16 relative error = 1.351846545222314e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000002 y[1] (closed_form) = 0.8135091854297521 y[1] (numeric) = 0.8135091854297521 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000002 y[1] (closed_form) = 0.8058729275885251 y[1] (numeric) = 0.8058729275885254 absolute error = 2.220446049250313e-16 relative error = 2.755330242814736e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000002 y[1] (closed_form) = 0.7983560814594366 y[1] (numeric) = 0.7983560814594368 absolute error = 2.220446049250313e-16 relative error = 2.781272793953322e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000002 y[1] (closed_form) = 0.7909593987208358 y[1] (numeric) = 0.7909593987208358 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000002 y[1] (closed_form) = 0.7836836190348323 y[1] (numeric) = 0.7836836190348324 absolute error = 1.110223024625157e-16 relative error = 1.41667249086115e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000002 y[1] (closed_form) = 0.7765294699733314 y[1] (numeric) = 0.7765294699733317 absolute error = 3.33066907387547e-16 relative error = 4.289172790814823e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000002 y[1] (closed_form) = 0.7694976669452782 y[1] (numeric) = 0.7694976669452784 absolute error = 2.220446049250313e-16 relative error = 2.885578663370031e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000002 y[1] (closed_form) = 0.7625889131251153 y[1] (numeric) = 0.7625889131251153 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000002 y[1] (closed_form) = 0.7558038993824674 y[1] (numeric) = 0.7558038993824673 absolute error = 1.110223024625157e-16 relative error = 1.468930003579326e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 0.7491433042130542 y[1] (numeric) = 0.7491433042130543 absolute error = 1.110223024625157e-16 relative error = 1.481990185831538e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 0.7426077936708428 y[1] (numeric) = 0.7426077936708431 absolute error = 2.220446049250313e-16 relative error = 2.990065641883789e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 0.7361980213014411 y[1] (numeric) = 0.7361980213014414 absolute error = 3.33066907387547e-16 relative error = 4.524148364304969e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 0.7299146280767446 y[1] (numeric) = 0.7299146280767447 absolute error = 1.110223024625157e-16 relative error = 1.521031339720494e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (closed_form) = 0.7237582423308393 y[1] (numeric) = 0.7237582423308393 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000003 y[1] (closed_form) = 0.7177294796971694 y[1] (numeric) = 0.7177294796971696 absolute error = 2.220446049250313e-16 relative error = 3.093708858367059e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000003 y[1] (closed_form) = 0.711828943046975 y[1] (numeric) = 0.711828943046975 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000003 y[1] (closed_form) = 0.7060572224290034 y[1] (numeric) = 0.7060572224290034 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000003 y[1] (closed_form) = 0.700414895010507 y[1] (numeric) = 0.7004148950105068 absolute error = 2.220446049250313e-16 relative error = 3.170186792239768e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000003 y[1] (closed_form) = 0.6949025250195254 y[1] (numeric) = 0.6949025250195252 absolute error = 2.220446049250313e-16 relative error = 3.195334553127322e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000003 y[1] (closed_form) = 0.6895206636884641 y[1] (numeric) = 0.689520663688464 absolute error = 1.110223024625157e-16 relative error = 1.610137423128442e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = 0.6842698491989718 y[1] (numeric) = 0.6842698491989716 absolute error = 2.220446049250313e-16 relative error = 3.244985953786563e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 0.6791506066281214 y[1] (numeric) = 0.679150606628121 absolute error = 4.440892098500626e-16 relative error = 6.538891455238439e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = 0.6741634478959039 y[1] (numeric) = 0.6741634478959037 absolute error = 2.220446049250313e-16 relative error = 3.293631620314674e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = 0.6693088717140369 y[1] (numeric) = 0.6693088717140366 absolute error = 2.220446049250313e-16 relative error = 3.317520718893148e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (closed_form) = 0.6645873635360927 y[1] (numeric) = 0.6645873635360927 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000004 y[1] (closed_form) = 0.6599993955089549 y[1] (numeric) = 0.6599993955089548 absolute error = 1.110223024625157e-16 relative error = 1.682157638597554e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000004 y[1] (closed_form) = 0.6555454264256025 y[1] (numeric) = 0.6555454264256027 absolute error = 1.110223024625157e-16 relative error = 1.693586714011123e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000004 y[1] (closed_form) = 0.6512259016792326 y[1] (numeric) = 0.6512259016792328 absolute error = 2.220446049250313e-16 relative error = 3.409640254671588e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000004 y[1] (closed_form) = 0.6470412532187203 y[1] (numeric) = 0.6470412532187204 absolute error = 1.110223024625157e-16 relative error = 1.715845812152361e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (closed_form) = 0.6429918995054242 y[1] (numeric) = 0.6429918995054242 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (closed_form) = 0.6390782454713411 y[1] (numeric) = 0.6390782454713412 absolute error = 1.110223024625157e-16 relative error = 1.737225500151912e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (closed_form) = 0.6353006824786132 y[1] (numeric) = 0.6353006824786132 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (closed_form) = 0.6316595882803919 y[1] (numeric) = 0.6316595882803918 absolute error = 1.110223024625157e-16 relative error = 1.757628705752079e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (closed_form) = 0.6281553269830626 y[1] (numeric) = 0.6281553269830625 absolute error = 1.110223024625157e-16 relative error = 1.767433908357339e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (closed_form) = 0.6247882490098349 y[1] (numeric) = 0.6247882490098349 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (closed_form) = 0.6215586910657004 y[1] (numeric) = 0.6215586910657003 absolute error = 1.110223024625157e-16 relative error = 1.786191779768394e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (closed_form) = 0.6184669761037619 y[1] (numeric) = 0.618466976103762 absolute error = 1.110223024625157e-16 relative error = 1.795120948283084e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (closed_form) = 0.6155134132929395 y[1] (numeric) = 0.6155134132929396 absolute error = 1.110223024625157e-16 relative error = 1.803734899432275e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (closed_form) = 0.6126982979870527 y[1] (numeric) = 0.6126982979870529 absolute error = 2.220446049250313e-16 relative error = 3.624044748525211e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (closed_form) = 0.6100219116952861 y[1] (numeric) = 0.6100219116952864 absolute error = 3.33066907387547e-16 relative error = 5.459917111205642e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (closed_form) = 0.6074845220540391 y[1] (numeric) = 0.6074845220540392 absolute error = 1.110223024625157e-16 relative error = 1.827574175669938e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (closed_form) = 0.6050863828001609 y[1] (numeric) = 0.605086382800161 absolute error = 1.110223024625157e-16 relative error = 1.834817401587146e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (closed_form) = 0.6028277337455786 y[1] (numeric) = 0.6028277337455787 absolute error = 1.110223024625157e-16 relative error = 1.841692016601417e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (closed_form) = 0.6007088007533153 y[1] (numeric) = 0.6007088007533155 absolute error = 1.110223024625157e-16 relative error = 1.848188378849932e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (closed_form) = 0.5987297957149045 y[1] (numeric) = 0.5987297957149047 absolute error = 2.220446049250313e-16 relative error = 3.708594536537174e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (closed_form) = 0.5968909165292012 y[1] (numeric) = 0.5968909165292011 absolute error = 1.110223024625157e-16 relative error = 1.860009917860497e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (closed_form) = 0.5951923470825909 y[1] (numeric) = 0.5951923470825908 absolute error = 1.110223024625157e-16 relative error = 1.86531804393496e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (closed_form) = 0.5936342572306035 y[1] (numeric) = 0.5936342572306034 absolute error = 1.110223024625157e-16 relative error = 1.870213875129984e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (closed_form) = 0.5922168027809254 y[1] (numeric) = 0.5922168027809253 absolute error = 1.110223024625157e-16 relative error = 1.874690180035053e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (closed_form) = 0.5909401254778204 y[1] (numeric) = 0.5909401254778202 absolute error = 2.220446049250313e-16 relative error = 3.757480586472128e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (closed_form) = 0.589804352987955 y[1] (numeric) = 0.5898043529879546 absolute error = 3.33066907387547e-16 relative error = 5.647074418834425e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (closed_form) = 0.5888095988876318 y[1] (numeric) = 0.5888095988876314 absolute error = 4.440892098500626e-16 relative error = 7.542153026870277e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (closed_form) = 0.5879559626514319 y[1] (numeric) = 0.5879559626514315 absolute error = 4.440892098500626e-16 relative error = 7.553103260445029e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (closed_form) = 0.5872435296422669 y[1] (numeric) = 0.587243529642267 absolute error = 1.110223024625157e-16 relative error = 1.890566636471031e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y[1] (closed_form) = 0.5866723711028449 y[1] (numeric) = 0.586672371102845 absolute error = 1.110223024625157e-16 relative error = 1.892407209390354e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (closed_form) = 0.5862425441485434 y[1] (numeric) = 0.5862425441485435 absolute error = 1.110223024625157e-16 relative error = 1.893794702732878e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (closed_form) = 0.5859540917616999 y[1] (numeric) = 0.5859540917617 absolute error = 1.110223024625157e-16 relative error = 1.894726976455129e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (closed_form) = 0.5858070427873123 y[1] (numeric) = 0.5858070427873125 absolute error = 2.220446049250313e-16 relative error = 3.790405179639476e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (closed_form) = 0.585801411930156 y[1] (numeric) = 0.5858014119301562 absolute error = 2.220446049250313e-16 relative error = 3.790441613881007e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (closed_form) = 0.585937199753312 y[1] (numeric) = 0.585937199753312 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (closed_form) = 0.5862143926781105 y[1] (numeric) = 0.5862143926781107 absolute error = 2.220446049250313e-16 relative error = 3.787771294911821e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y[1] (closed_form) = 0.5866329629854906 y[1] (numeric) = 0.5866329629854907 absolute error = 1.110223024625157e-16 relative error = 1.892534335225578e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (closed_form) = 0.5871928688187704 y[1] (numeric) = 0.5871928688187704 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (closed_form) = 0.5878940541878325 y[1] (numeric) = 0.5878940541878329 absolute error = 4.440892098500626e-16 relative error = 7.553898643584102e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (closed_form) = 0.5887364489747252 y[1] (numeric) = 0.5887364489747255 absolute error = 3.33066907387547e-16 relative error = 5.657317598860704e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (closed_form) = 0.5897199689406711 y[1] (numeric) = 0.5897199689406717 absolute error = 5.551115123125783e-16 relative error = 9.413137447418291e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (closed_form) = 0.5908445157344939 y[1] (numeric) = 0.5908445157344944 absolute error = 4.440892098500626e-16 relative error = 7.516177234851778e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (closed_form) = 0.5921099769024507 y[1] (numeric) = 0.5921099769024512 absolute error = 4.440892098500626e-16 relative error = 7.50011361357665e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (closed_form) = 0.5935162258994793 y[1] (numeric) = 0.5935162258994798 absolute error = 5.551115123125783e-16 relative error = 9.352929003268642e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (closed_form) = 0.5950631221018522 y[1] (numeric) = 0.5950631221018526 absolute error = 4.440892098500626e-16 relative error = 7.462892479061262e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (closed_form) = 0.5967505108212382 y[1] (numeric) = 0.5967505108212386 absolute error = 4.440892098500626e-16 relative error = 7.441790192000245e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (closed_form) = 0.5985782233201713 y[1] (numeric) = 0.5985782233201719 absolute error = 5.551115123125783e-16 relative error = 9.273834073573651e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (closed_form) = 0.6005460768289247 y[1] (numeric) = 0.6005460768289255 absolute error = 7.771561172376096e-16 relative error = 1.294082414693711e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (closed_form) = 0.6026538745637877 y[1] (numeric) = 0.6026538745637884 absolute error = 6.661338147750939e-16 relative error = 1.105333995002113e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (closed_form) = 0.6049014057467429 y[1] (numeric) = 0.6049014057467438 absolute error = 8.881784197001252e-16 relative error = 1.468302786639552e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (closed_form) = 0.6072884456265453 y[1] (numeric) = 0.607288445626546 absolute error = 7.771561172376096e-16 relative error = 1.279714973723582e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (closed_form) = 0.6098147555011958 y[1] (numeric) = 0.6098147555011966 absolute error = 7.771561172376096e-16 relative error = 1.274413434943664e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = 0.6124800827418124 y[1] (numeric) = 0.612480082741813 absolute error = 5.551115123125783e-16 relative error = 9.063339820416372e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (closed_form) = 0.6152841608178922 y[1] (numeric) = 0.6152841608178927 absolute error = 5.551115123125783e-16 relative error = 9.022034820052464e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y[1] (closed_form) = 0.6182267093239638 y[1] (numeric) = 0.6182267093239645 absolute error = 6.661338147750939e-16 relative error = 1.077491160974777e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 0.6213074340076292 y[1] (numeric) = 0.6213074340076302 absolute error = 9.992007221626409e-16 relative error = 1.608222705010112e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = 0.6245260267989871 y[1] (numeric) = 0.6245260267989884 absolute error = 1.332267629550188e-15 relative error = 2.13324596955348e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y[1] (closed_form) = 0.6278821658414404 y[1] (numeric) = 0.6278821658414422 absolute error = 1.77635683940025e-15 relative error = 2.829124533294732e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = 0.6313755155238818 y[1] (numeric) = 0.631375515523884 absolute error = 2.220446049250313e-15 relative error = 3.516839019973565e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y[1] (closed_form) = 0.6350057265142542 y[1] (numeric) = 0.635005726514257 absolute error = 2.775557561562891e-15 relative error = 4.370917372350007e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y[1] (closed_form) = 0.6387724357944838 y[1] (numeric) = 0.6387724357944869 absolute error = 3.108624468950438e-15 relative error = 4.866560131205466e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y[1] (closed_form) = 0.6426752666967814 y[1] (numeric) = 0.642675266696785 absolute error = 3.552713678800501e-15 relative error = 5.528007475782782e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y[1] (closed_form) = 0.6467138289413092 y[1] (numeric) = 0.646713828941313 absolute error = 3.774758283725532e-15 relative error = 5.836829390064118e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y[1] (closed_form) = 0.650887718675208 y[1] (numeric) = 0.6508877186752124 absolute error = 4.440892098500626e-15 relative error = 6.822823616244362e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y[1] (closed_form) = 0.6551965185129828 y[1] (numeric) = 0.6551965185129879 absolute error = 5.10702591327572e-15 relative error = 7.794647512576067e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y[1] (closed_form) = 0.6596397975782403 y[1] (numeric) = 0.6596397975782461 absolute error = 5.773159728050814e-15 relative error = 8.751988205147758e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = 0.664217111546777 y[1] (numeric) = 0.6642171115467831 absolute error = 6.106226635438361e-15 relative error = 9.193118528998231e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = 0.6689280026910102 y[1] (numeric) = 0.6689280026910167 absolute error = 6.550315845288424e-15 relative error = 9.792258387954095e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = 0.6737719999257514 y[1] (numeric) = 0.6737719999257583 absolute error = 6.883382752675971e-15 relative error = 1.021618997737292e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = 0.6787486188553136 y[1] (numeric) = 0.678748618855321 absolute error = 7.438494264988549e-15 relative error = 1.095912987275512e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = 0.6838573618219511 y[1] (numeric) = 0.683857361821959 absolute error = 7.882583474838611e-15 relative error = 1.152664855992428e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = 0.6890977179556246 y[1] (numeric) = 0.6890977179556329 absolute error = 8.326672684688674e-15 relative error = 1.208344254773005e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y[1] (closed_form) = 0.6944691632250874 y[1] (numeric) = 0.6944691632250962 absolute error = 8.770761894538737e-15 relative error = 1.26294475823918e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y[1] (closed_form) = 0.6999711604902891 y[1] (numeric) = 0.6999711604902985 absolute error = 9.436895709313831e-15 relative error = 1.34818350268943e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y[1] (closed_form) = 0.705603159556088 y[1] (numeric) = 0.705603159556098 absolute error = 9.992007221626409e-15 relative error = 1.41609445568705e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y[1] (closed_form) = 0.7113645972272707 y[1] (numeric) = 0.7113645972272812 absolute error = 1.043609643147647e-14 relative error = 1.467053107809115e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y[1] (closed_form) = 0.7172548973648714 y[1] (numeric) = 0.7172548973648825 absolute error = 1.110223024625157e-14 relative error = 1.547877928340419e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y[1] (closed_form) = 0.7232734709437849 y[1] (numeric) = 0.7232734709437967 absolute error = 1.176836406102666e-14 relative error = 1.627097430474031e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y[1] (closed_form) = 0.7294197161116688 y[1] (numeric) = 0.7294197161116811 absolute error = 1.232347557333924e-14 relative error = 1.689490330619553e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y[1] (closed_form) = 0.7356930182491281 y[1] (numeric) = 0.7356930182491411 absolute error = 1.298960938811433e-14 relative error = 1.765629014534926e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y[1] (closed_form) = 0.7420927500311768 y[1] (numeric) = 0.7420927500311906 absolute error = 1.376676550535194e-14 relative error = 1.855127341531577e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y[1] (closed_form) = 0.7486182714899698 y[1] (numeric) = 0.7486182714899844 absolute error = 1.454392162258955e-14 relative error = 1.942768721586622e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y[1] (closed_form) = 0.7552689300787992 y[1] (numeric) = 0.7552689300788146 absolute error = 1.532107773982716e-14 relative error = 2.028559249515093e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y[1] (closed_form) = 0.7620440607373483 y[1] (numeric) = 0.7620440607373643 absolute error = 1.598721155460225e-14 relative error = 2.097937951138041e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y[1] (closed_form) = 0.7689429859581972 y[1] (numeric) = 0.768942985958214 absolute error = 1.676436767183986e-14 relative error = 2.180183443763312e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y[1] (closed_form) = 0.7759650158545726 y[1] (numeric) = 0.7759650158545901 absolute error = 1.754152378907747e-14 relative error = 2.260607557127938e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y[1] (closed_form) = 0.7831094482293369 y[1] (numeric) = 0.7831094482293551 absolute error = 1.820765760385257e-14 relative error = 2.325046345057042e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y[1] (closed_form) = 0.7903755686452062 y[1] (numeric) = 0.7903755686452251 absolute error = 1.887379141862766e-14 relative error = 2.387952280835235e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y[1] (closed_form) = 0.7977626504961938 y[1] (numeric) = 0.7977626504962135 absolute error = 1.976196983832779e-14 relative error = 2.477174110123632e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y[1] (closed_form) = 0.8052699550802708 y[1] (numeric) = 0.8052699550802912 absolute error = 2.042810365310288e-14 relative error = 2.53680191645379e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y[1] (closed_form) = 0.8128967316732344 y[1] (numeric) = 0.8128967316732558 absolute error = 2.142730437526552e-14 relative error = 2.635919611973394e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y[1] (closed_form) = 0.8206422176037815 y[1] (numeric) = 0.8206422176038037 absolute error = 2.220446049250313e-14 relative error = 2.705741919705108e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y[1] (closed_form) = 0.8285056383297733 y[1] (numeric) = 0.8285056383297963 absolute error = 2.298161660974074e-14 relative error = 2.77386363429832e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y[1] (closed_form) = 0.83648620751569 y[1] (numeric) = 0.8364862075157138 absolute error = 2.375877272697835e-14 relative error = 2.840306572123929e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y[1] (closed_form) = 0.8445831271112634 y[1] (numeric) = 0.8445831271112881 absolute error = 2.475797344914099e-14 relative error = 2.931383857243389e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999956 y[1] (closed_form) = 0.8527955874312817 y[1] (numeric) = 0.8527955874313071 absolute error = 2.542410726391608e-14 relative error = 2.981266277478806e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y[1] (closed_form) = 0.8611227672365561 y[1] (numeric) = 0.8611227672365825 absolute error = 2.642330798607873e-14 relative error = 3.068471650200844e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y[1] (closed_form) = 0.8695638338160459 y[1] (numeric) = 0.8695638338160732 absolute error = 2.731148640577885e-14 relative error = 3.140825934068979e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y[1] (closed_form) = 0.8781179430701268 y[1] (numeric) = 0.8781179430701551 absolute error = 2.831068712794149e-14 relative error = 3.224018749572526e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y[1] (closed_form) = 0.8867842395950022 y[1] (numeric) = 0.8867842395950315 absolute error = 2.930988785010413e-14 relative error = 3.305188177846967e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y[1] (closed_form) = 0.8955618567682414 y[1] (numeric) = 0.8955618567682716 absolute error = 3.019806626980426e-14 relative error = 3.371968786028711e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y[1] (closed_form) = 0.9044499168354418 y[1] (numeric) = 0.9044499168354729 absolute error = 3.108624468950438e-14 relative error = 3.437033285189665e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y[1] (closed_form) = 0.9134475309980029 y[1] (numeric) = 0.9134475309980351 absolute error = 3.219646771412954e-14 relative error = 3.524719989001747e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999947 y[1] (closed_form) = 0.9225537995020072 y[1] (numeric) = 0.9225537995020402 absolute error = 3.297362383136715e-14 relative error = 3.574168124305189e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999946 y[1] (closed_form) = 0.9317678117281922 y[1] (numeric) = 0.9317678117282264 absolute error = 3.419486915845482e-14 relative error = 3.669891654127012e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y[1] (closed_form) = 0.9410886462830139 y[1] (numeric) = 0.9410886462830491 absolute error = 3.519406988061746e-14 relative error = 3.739718890417209e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y[1] (closed_form) = 0.9505153710907841 y[1] (numeric) = 0.9505153710908202 absolute error = 3.608224830031759e-14 relative error = 3.796072046568867e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y[1] (closed_form) = 0.9600470434868775 y[1] (numeric) = 0.9600470434869149 absolute error = 3.741451592986778e-14 relative error = 3.897154434638825e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y[1] (closed_form) = 0.9696827103119978 y[1] (numeric) = 0.9696827103120363 absolute error = 3.852473895449293e-14 relative error = 3.972922126465213e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y[1] (closed_form) = 0.9794214080074918 y[1] (numeric) = 0.9794214080075315 absolute error = 3.97459842815806e-14 relative error = 4.058108589073906e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y[1] (closed_form) = 0.989262162711706 y[1] (numeric) = 0.9892621627117465 absolute error = 4.052314039881821e-14 relative error = 4.096299436717423e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999938 y[1] (closed_form) = 0.9992039903573701 y[1] (numeric) = 0.9992039903574116 absolute error = 4.152234112098085e-14 relative error = 4.155541963571442e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999937 y[1] (closed_form) = 1.009245896770004 y[1] (numeric) = 1.009245896770047 absolute error = 4.263256414560601e-14 relative error = 4.22419989836446e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999936 y[1] (closed_form) = 1.019386877767336 y[1] (numeric) = 1.01938687776738 absolute error = 4.329869796038111e-14 relative error = 4.247523575662855e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999935 y[1] (closed_form) = 1.029625919259716 y[1] (numeric) = 1.029625919259761 absolute error = 4.440892098500626e-14 relative error = 4.313112185145411e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999933 y[1] (closed_form) = 1.039961997351528 y[1] (numeric) = 1.039961997351573 absolute error = 4.529709940470639e-14 relative error = 4.355649487199008e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999932 y[1] (closed_form) = 1.050394078443575 y[1] (numeric) = 1.050394078443622 absolute error = 4.662936703425657e-14 relative error = 4.439226000145562e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999931 y[1] (closed_form) = 1.060921119336443 y[1] (numeric) = 1.060921119336491 absolute error = 4.773959005888173e-14 relative error = 4.499824651312494e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63999999999993 y[1] (closed_form) = 1.071542067334814 y[1] (numeric) = 1.071542067334863 absolute error = 4.884981308350689e-14 relative error = 4.558832972839626e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999929 y[1] (closed_form) = 1.082255860352739 y[1] (numeric) = 1.082255860352789 absolute error = 4.951594689828198e-14 relative error = 4.575253293813838e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999928 y[1] (closed_form) = 1.093061427019844 y[1] (numeric) = 1.093061427019895 absolute error = 5.084821452783217e-14 relative error = 4.651908234148036e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999927 y[1] (closed_form) = 1.103957686788468 y[1] (numeric) = 1.10395768678852 absolute error = 5.240252676230739e-14 relative error = 4.746787615995681e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999926 y[1] (closed_form) = 1.114943550041713 y[1] (numeric) = 1.114943550041767 absolute error = 5.395683899678261e-14 relative error = 4.839423394553376e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999925 y[1] (closed_form) = 1.12601791820241 y[1] (numeric) = 1.126017918202465 absolute error = 5.551115123125783e-14 relative error = 4.929863933237988e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999924 y[1] (closed_form) = 1.13717968384297 y[1] (numeric) = 1.137179683843027 absolute error = 5.684341886080801e-14 relative error = 4.99863123378287e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999922 y[1] (closed_form) = 1.148427730796132 y[1] (numeric) = 1.14842773079619 absolute error = 5.839773109528323e-14 relative error = 5.085015759311193e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999921 y[1] (closed_form) = 1.159760934266573 y[1] (numeric) = 1.159760934266632 absolute error = 5.972999872483342e-14 relative error = 5.150199231586153e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72999999999992 y[1] (closed_form) = 1.17117816094339 y[1] (numeric) = 1.171178160943451 absolute error = 6.084022174945858e-14 relative error = 5.194787930510202e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999919 y[1] (closed_form) = 1.18267826911343 y[1] (numeric) = 1.182678269113492 absolute error = 6.261657858885883e-14 relative error = 5.294472742430454e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999918 y[1] (closed_form) = 1.19426010877546 y[1] (numeric) = 1.194260108775523 absolute error = 6.306066779870889e-14 relative error = 5.280312666841768e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999917 y[1] (closed_form) = 1.205922521755164 y[1] (numeric) = 1.205922521755229 absolute error = 6.461498003318411e-14 relative error = 5.358136933966537e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999916 y[1] (closed_form) = 1.217664341820964 y[1] (numeric) = 1.21766434182103 absolute error = 6.616929226765933e-14 relative error = 5.434115954213296e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999915 y[1] (closed_form) = 1.229484394800638 y[1] (numeric) = 1.229484394800705 absolute error = 6.772360450213455e-14 relative error = 5.508293133978004e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999914 y[1] (closed_form) = 1.241381498698737 y[1] (numeric) = 1.241381498698806 absolute error = 6.861178292183467e-14 relative error = 5.527050547616194e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999913 y[1] (closed_form) = 1.253354463814787 y[1] (numeric) = 1.253354463814857 absolute error = 6.994405055138486e-14 relative error = 5.580548246383456e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999911 y[1] (closed_form) = 1.265402092862252 y[1] (numeric) = 1.265402092862324 absolute error = 7.105427357601002e-14 relative error = 5.615153789993356e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81999999999991 y[1] (closed_form) = 1.277523181088269 y[1] (numeric) = 1.277523181088341 absolute error = 7.238654120556021e-14 relative error = 5.666162640109367e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.829999999999909 y[1] (closed_form) = 1.289716516394114 y[1] (numeric) = 1.289716516394188 absolute error = 7.371880883511039e-14 relative error = 5.715892438225025e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999908 y[1] (closed_form) = 1.301980879456419 y[1] (numeric) = 1.301980879456494 absolute error = 7.527312106958561e-14 relative error = 5.781430607568704e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.849999999999907 y[1] (closed_form) = 1.314315043849098 y[1] (numeric) = 1.314315043849175 absolute error = 7.704947790898586e-14 relative error = 5.862329452102981e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.859999999999906 y[1] (closed_form) = 1.32671777616599 y[1] (numeric) = 1.326717776166068 absolute error = 7.838174553853605e-14 relative error = 5.907944172199701e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999905 y[1] (closed_form) = 1.339187836144198 y[1] (numeric) = 1.339187836144278 absolute error = 7.949196856316121e-14 relative error = 5.93583412406397e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999904 y[1] (closed_form) = 1.351723976788117 y[1] (numeric) = 1.351723976788198 absolute error = 8.104628079763643e-14 relative error = 5.995771488067675e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999903 y[1] (closed_form) = 1.364324944494129 y[1] (numeric) = 1.364324944494211 absolute error = 8.171241461241152e-14 relative error = 5.989219426220287e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999902 y[1] (closed_form) = 1.376989479175964 y[1] (numeric) = 1.376989479176047 absolute error = 8.304468224196171e-14 relative error = 6.03088719978154e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9099999999999 y[1] (closed_form) = 1.389716314390708 y[1] (numeric) = 1.389716314390792 absolute error = 8.459899447643693e-14 relative error = 6.087500995735782e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.919999999999899 y[1] (closed_form) = 1.402504177465444 y[1] (numeric) = 1.40250417746553 absolute error = 8.615330671091215e-14 relative error = 6.142819971246386e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999898 y[1] (closed_form) = 1.415351789624523 y[1] (numeric) = 1.41535178962461 absolute error = 8.704148513061227e-14 relative error = 6.149812772251018e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999897 y[1] (closed_form) = 1.428257866117434 y[1] (numeric) = 1.428257866117522 absolute error = 8.815170815523743e-14 relative error = 6.171974280447579e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.949999999999896 y[1] (closed_form) = 1.441221116347283 y[1] (numeric) = 1.441221116347372 absolute error = 8.970602038971265e-14 relative error = 6.224306553117191e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999895 y[1] (closed_form) = 1.454240243999849 y[1] (numeric) = 1.454240243999941 absolute error = 9.14823772291129e-14 relative error = 6.290733433252614e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999894 y[1] (closed_form) = 1.467313947173218 y[1] (numeric) = 1.467313947173311 absolute error = 9.303668946358812e-14 relative error = 6.340612357895421e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999893 y[1] (closed_form) = 1.480440918507965 y[1] (numeric) = 1.480440918508059 absolute error = 9.414691248821327e-14 relative error = 6.359383296639591e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999892 y[1] (closed_form) = 1.493619845317897 y[1] (numeric) = 1.493619845317993 absolute error = 9.570122472268849e-14 relative error = 6.407334839764381e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.999999999999891 y[1] (closed_form) = 1.506849409721315 y[1] (numeric) = 1.506849409721413 absolute error = 9.747758156208874e-14 relative error = 6.468966370044685e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.00999999999989 y[1] (closed_form) = 1.520128288772805 y[1] (numeric) = 1.520128288772903 absolute error = 9.836575998178887e-14 relative error = 6.470885431728875e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999889 y[1] (closed_form) = 1.533455154595524 y[1] (numeric) = 1.533455154595624 absolute error = 9.992007221626409e-14 relative error = 6.51600876079221e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999887 y[1] (closed_form) = 1.546828674513998 y[1] (numeric) = 1.5468286745141 absolute error = 1.016964290556643e-13 relative error = 6.574511497701358e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999886 y[1] (closed_form) = 1.56024751118738 y[1] (numeric) = 1.560247511187483 absolute error = 1.028066520802895e-13 relative error = 6.589124567938043e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999885 y[1] (closed_form) = 1.573710322743183 y[1] (numeric) = 1.573710322743287 absolute error = 1.039168751049147e-13 relative error = 6.603303899269971e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999884 y[1] (closed_form) = 1.587215762911471 y[1] (numeric) = 1.587215762911577 absolute error = 1.056932319443149e-13 relative error = 6.659033662218617e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999883 y[1] (closed_form) = 1.600762481159483 y[1] (numeric) = 1.60076248115959 absolute error = 1.070254995738651e-13 relative error = 6.685907549278836e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999882 y[1] (closed_form) = 1.614349122826682 y[1] (numeric) = 1.614349122826791 absolute error = 1.085798118083403e-13 relative error = 6.725918840790768e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.089999999999881 y[1] (closed_form) = 1.627974329260224 y[1] (numeric) = 1.627974329260334 absolute error = 1.103561686477406e-13 relative error = 6.778741326829649e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09999999999988 y[1] (closed_form) = 1.641636737950819 y[1] (numeric) = 1.64163673795093 absolute error = 1.114663916723657e-13 relative error = 6.789954750373349e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999879 y[1] (closed_form) = 1.655334982668984 y[1] (numeric) = 1.655334982669097 absolute error = 1.127986593019159e-13 relative error = 6.814249712770805e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999878 y[1] (closed_form) = 1.669067693601663 y[1] (numeric) = 1.669067693601777 absolute error = 1.143529715363911e-13 relative error = 6.851308186885465e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999876 y[1] (closed_form) = 1.682833497489205 y[1] (numeric) = 1.682833497489321 absolute error = 1.161293283757914e-13 relative error = 6.900821058592954e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999875 y[1] (closed_form) = 1.696631017762693 y[1] (numeric) = 1.696631017762811 absolute error = 1.179056852151916e-13 relative error = 6.949400546187765e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999874 y[1] (closed_form) = 1.710458874681599 y[1] (numeric) = 1.710458874681718 absolute error = 1.190159082398168e-13 relative error = 6.958127435947357e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999873 y[1] (closed_form) = 1.724315685471753 y[1] (numeric) = 1.724315685471874 absolute error = 1.210143096841421e-13 relative error = 7.018106411937783e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999872 y[1] (closed_form) = 1.738200064463624 y[1] (numeric) = 1.738200064463747 absolute error = 1.223465773136923e-13 relative error = 7.038693635732092e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.179999999999871 y[1] (closed_form) = 1.752110623230883 y[1] (numeric) = 1.752110623231007 absolute error = 1.239008895481675e-13 relative error = 7.071522077738155e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.18999999999987 y[1] (closed_form) = 1.766045970729245 y[1] (numeric) = 1.76604597072937 absolute error = 1.252331571777177e-13 relative error = 7.091160663615441e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999869 y[1] (closed_form) = 1.780004713435572 y[1] (numeric) = 1.780004713435699 absolute error = 1.270095140171179e-13 relative error = 7.13534706163659e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999868 y[1] (closed_form) = 1.793985455487228 y[1] (numeric) = 1.793985455487356 absolute error = 1.285638262515931e-13 relative error = 7.16638063359753e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999867 y[1] (closed_form) = 1.807986798821656 y[1] (numeric) = 1.807986798821786 absolute error = 1.303401830909934e-13 relative error = 7.209133560927645e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999865 y[1] (closed_form) = 1.822007343316192 y[1] (numeric) = 1.822007343316324 absolute error = 1.321165399303936e-13 relative error = 7.25115298876521e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999864 y[1] (closed_form) = 1.836045686928069 y[1] (numeric) = 1.836045686928203 absolute error = 1.341149413747189e-13 relative error = 7.304553602863215e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999863 y[1] (closed_form) = 1.850100425834626 y[1] (numeric) = 1.850100425834761 absolute error = 1.352251643993441e-13 relative error = 7.309071578551779e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999862 y[1] (closed_form) = 1.864170154573683 y[1] (numeric) = 1.864170154573819 absolute error = 1.365574320288943e-13 relative error = 7.32537379669205e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.269999999999861 y[1] (closed_form) = 1.878253466184091 y[1] (numeric) = 1.87825346618423 absolute error = 1.383337888682945e-13 relative error = 7.365022418903719e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.27999999999986 y[1] (closed_form) = 1.892348952346426 y[1] (numeric) = 1.892348952346566 absolute error = 1.398881011027697e-13 relative error = 7.392299445052926e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999859 y[1] (closed_form) = 1.906455203523818 y[1] (numeric) = 1.906455203523959 absolute error = 1.409983241273949e-13 relative error = 7.395837251605967e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999858 y[1] (closed_form) = 1.920570809102903 y[1] (numeric) = 1.920570809103046 absolute error = 1.425526363618701e-13 relative error = 7.422409821403892e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999857 y[1] (closed_form) = 1.934694357534887 y[1] (numeric) = 1.934694357535032 absolute error = 1.445510378061954e-13 relative error = 7.471518032976368e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999856 y[1] (closed_form) = 1.948824436476697 y[1] (numeric) = 1.948824436476843 absolute error = 1.465494392505207e-13 relative error = 7.519889247461878e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999854 y[1] (closed_form) = 1.962959632932213 y[1] (numeric) = 1.962959632932361 absolute error = 1.478817068800709e-13 relative error = 7.533609168476347e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999853 y[1] (closed_form) = 1.977098533393569 y[1] (numeric) = 1.977098533393718 absolute error = 1.496580637194711e-13 relative error = 7.56958043272594e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999852 y[1] (closed_form) = 1.9912397239825 y[1] (numeric) = 1.991239723982651 absolute error = 1.509903313490213e-13 relative error = 7.582729971208039e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.359999999999851 y[1] (closed_form) = 2.005381790591734 y[1] (numeric) = 2.005381790591886 absolute error = 1.523225989785715e-13 relative error = 7.595690740446245e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36999999999985 y[1] (closed_form) = 2.019523319026393 y[1] (numeric) = 2.019523319026547 absolute error = 1.545430450278218e-13 relative error = 7.652451624194496e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999849 y[1] (closed_form) = 2.033662895145419 y[1] (numeric) = 2.033662895145574 absolute error = 1.554312234475219e-13 relative error = 7.64291976898205e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999848 y[1] (closed_form) = 2.047799105002982 y[1] (numeric) = 2.047799105003139 absolute error = 1.572075802869222e-13 relative error = 7.676904433782006e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999847 y[1] (closed_form) = 2.061930534989878 y[1] (numeric) = 2.061930534990036 absolute error = 1.580957587066223e-13 relative error = 7.667365899278386e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999846 y[1] (closed_form) = 2.076055771974883 y[1] (numeric) = 2.076055771975043 absolute error = 1.598721155460225e-13 relative error = 7.700762075093074e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999844 y[1] (closed_form) = 2.090173403446071 y[1] (numeric) = 2.090173403446232 absolute error = 1.616484723854228e-13 relative error = 7.733735015425648e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999843 y[1] (closed_form) = 2.104282017652058 y[1] (numeric) = 2.104282017652221 absolute error = 1.63424829224823e-13 relative error = 7.76629880661962e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999842 y[1] (closed_form) = 2.118380203743181 y[1] (numeric) = 2.118380203743346 absolute error = 1.656452752740734e-13 relative error = 7.819430854828511e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.449999999999841 y[1] (closed_form) = 2.13246655191258 y[1] (numeric) = 2.132466551912747 absolute error = 1.665334536937735e-13 relative error = 7.809428642358395e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45999999999984 y[1] (closed_form) = 2.146539653537176 y[1] (numeric) = 2.146539653537344 absolute error = 1.678657213233237e-13 relative error = 7.820294446771859e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999839 y[1] (closed_form) = 2.160598101318534 y[1] (numeric) = 2.160598101318704 absolute error = 1.70086167372574e-13 relative error = 7.872179803767141e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999838 y[1] (closed_form) = 2.174640489423592 y[1] (numeric) = 2.174640489423763 absolute error = 1.714184350021242e-13 relative error = 7.882610290566243e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999837 y[1] (closed_form) = 2.188665413625241 y[1] (numeric) = 2.188665413625414 absolute error = 1.731947918415244e-13 relative error = 7.913260325827952e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999836 y[1] (closed_form) = 2.202671471442748 y[1] (numeric) = 2.202671471442923 absolute error = 1.749711486809247e-13 relative error = 7.943588090616108e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999835 y[1] (closed_form) = 2.216657262282002 y[1] (numeric) = 2.216657262282179 absolute error = 1.767475055203249e-13 relative error = 7.973605506264287e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999833 y[1] (closed_form) = 2.230621387575576 y[1] (numeric) = 2.230621387575754 absolute error = 1.785238623597252e-13 relative error = 8.003324246512301e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999832 y[1] (closed_form) = 2.244562450922576 y[1] (numeric) = 2.244562450922756 absolute error = 1.798561299892754e-13 relative error = 8.012970631106727e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999831 y[1] (closed_form) = 2.258479058228285 y[1] (numeric) = 2.258479058228467 absolute error = 1.820765760385257e-13 relative error = 8.061911195287318e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54999999999983 y[1] (closed_form) = 2.27236981784357 y[1] (numeric) = 2.272369817843753 absolute error = 1.829647544582258e-13 relative error = 8.051715571185301e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999829 y[1] (closed_form) = 2.286233340704044 y[1] (numeric) = 2.286233340704229 absolute error = 1.851852005074761e-13 relative error = 8.10001311810318e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999828 y[1] (closed_form) = 2.300068240468975 y[1] (numeric) = 2.300068240469162 absolute error = 1.865174681370263e-13 relative error = 8.109214537869366e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999827 y[1] (closed_form) = 2.313873133659916 y[1] (numeric) = 2.313873133660103 absolute error = 1.869615573468764e-13 relative error = 8.080026282649048e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999826 y[1] (closed_form) = 2.32764663979905 y[1] (numeric) = 2.327646639799239 absolute error = 1.891820033961267e-13 relative error = 8.127608381848678e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999825 y[1] (closed_form) = 2.341387381547242 y[1] (numeric) = 2.341387381547433 absolute error = 1.905142710256769e-13 relative error = 8.136811214032455e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999824 y[1] (closed_form) = 2.355093984841769 y[1] (numeric) = 2.35509398484196 absolute error = 1.909583602355269e-13 relative error = 8.108311662490055e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999822 y[1] (closed_form) = 2.368765079033721 y[1] (numeric) = 2.368765079033914 absolute error = 1.931788062847772e-13 relative error = 8.155253891347458e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999821 y[1] (closed_form) = 2.382399297025074 y[1] (numeric) = 2.382399297025268 absolute error = 1.936228954946273e-13 relative error = 8.127222658955874e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999982 y[1] (closed_form) = 2.395995275405389 y[1] (numeric) = 2.395995275405584 absolute error = 1.949551631241775e-13 relative error = 8.136708996272631e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999819 y[1] (closed_form) = 2.409551654588159 y[1] (numeric) = 2.409551654588355 absolute error = 1.958433415438776e-13 relative error = 8.127791789437741e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999818 y[1] (closed_form) = 2.423067078946761 y[1] (numeric) = 2.423067078946959 absolute error = 1.976196983832779e-13 relative error = 8.155766718153653e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999817 y[1] (closed_form) = 2.436540196950024 y[1] (numeric) = 2.436540196950223 absolute error = 1.989519660128281e-13 relative error = 8.165347169805333e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999816 y[1] (closed_form) = 2.449969661297374 y[1] (numeric) = 2.449969661297575 absolute error = 2.011724120620784e-13 relative error = 8.211220540402455e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999815 y[1] (closed_form) = 2.463354129053568 y[1] (numeric) = 2.46335412905377 absolute error = 2.025046796916286e-13 relative error = 8.220688909614136e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999814 y[1] (closed_form) = 2.476692261782983 y[1] (numeric) = 2.476692261783187 absolute error = 2.038369473211787e-13 relative error = 8.230208914790063e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999813 y[1] (closed_form) = 2.489982725683463 y[1] (numeric) = 2.489982725683668 absolute error = 2.05613304160579e-13 relative error = 8.25761970313032e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999811 y[1] (closed_form) = 2.503224191719691 y[1] (numeric) = 2.503224191719898 absolute error = 2.069455717901292e-13 relative error = 8.267160906908603e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999981 y[1] (closed_form) = 2.5164153357561 y[1] (numeric) = 2.516415335756308 absolute error = 2.082778394196794e-13 relative error = 8.276767211685218e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999809 y[1] (closed_form) = 2.529554838689278 y[1] (numeric) = 2.529554838689488 absolute error = 2.096101070492296e-13 relative error = 8.286442493487975e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999808 y[1] (closed_form) = 2.542641386579881 y[1] (numeric) = 2.542641386580093 absolute error = 2.113864638886298e-13 relative error = 8.31365622396978e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999807 y[1] (closed_form) = 2.555673670784026 y[1] (numeric) = 2.555673670784238 absolute error = 2.122746423083299e-13 relative error = 8.306015151113116e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999806 y[1] (closed_form) = 2.568650388084153 y[1] (numeric) = 2.568650388084366 absolute error = 2.131628207280301e-13 relative error = 8.298631130062785e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999805 y[1] (closed_form) = 2.581570240819345 y[1] (numeric) = 2.58157024081956 absolute error = 2.149391775674303e-13 relative error = 8.32590855630612e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999804 y[1] (closed_form) = 2.594431937015095 y[1] (numeric) = 2.594431937015311 absolute error = 2.167155344068306e-13 relative error = 8.353101552402363e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999803 y[1] (closed_form) = 2.607234190512501 y[1] (numeric) = 2.607234190512719 absolute error = 2.176037128265307e-13 relative error = 8.346151397460638e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999802 y[1] (closed_form) = 2.619975721096883 y[1] (numeric) = 2.619975721097102 absolute error = 2.189359804560809e-13 relative error = 8.356412568755438e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8199999999998 y[1] (closed_form) = 2.632655254625801 y[1] (numeric) = 2.632655254626021 absolute error = 2.19824158875781e-13 relative error = 8.349902954043493e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999799 y[1] (closed_form) = 2.645271523156467 y[1] (numeric) = 2.645271523156688 absolute error = 2.216005157151812e-13 relative error = 8.377231364542749e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999798 y[1] (closed_form) = 2.657823265072542 y[1] (numeric) = 2.657823265072764 absolute error = 2.224886941348814e-13 relative error = 8.371086861142696e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999797 y[1] (closed_form) = 2.670309225210293 y[1] (numeric) = 2.670309225210517 absolute error = 2.233768725545815e-13 relative error = 8.365206188320382e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999796 y[1] (closed_form) = 2.682728154984113 y[1] (numeric) = 2.682728154984338 absolute error = 2.251532293939817e-13 relative error = 8.392696404057202e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999795 y[1] (closed_form) = 2.695078812511372 y[1] (numeric) = 2.695078812511599 absolute error = 2.26929586233382e-13 relative error = 8.420146571592122e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999794 y[1] (closed_form) = 2.707359962736612 y[1] (numeric) = 2.70735996273684 absolute error = 2.282618538629322e-13 relative error = 8.431160134029761e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999793 y[1] (closed_form) = 2.719570377555041 y[1] (numeric) = 2.719570377555271 absolute error = 2.295941214924824e-13 relative error = 8.442293804468224e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999792 y[1] (closed_form) = 2.731708835935356 y[1] (numeric) = 2.731708835935587 absolute error = 2.309263891220326e-13 relative error = 8.4535506157984e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.909999999999791 y[1] (closed_form) = 2.743774124041832 y[1] (numeric) = 2.743774124042064 absolute error = 2.322586567515827e-13 relative error = 8.464933564190201e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999789 y[1] (closed_form) = 2.755765035355714 y[1] (numeric) = 2.755765035355948 absolute error = 2.335909243811329e-13 relative error = 8.476445610718804e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999788 y[1] (closed_form) = 2.767680370795862 y[1] (numeric) = 2.767680370796097 absolute error = 2.344791028008331e-13 relative error = 8.472044144801564e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999787 y[1] (closed_form) = 2.779518938838663 y[1] (numeric) = 2.779518938838898 absolute error = 2.353672812205332e-13 relative error = 8.467914282997267e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999786 y[1] (closed_form) = 2.791279555637176 y[1] (numeric) = 2.791279555637413 absolute error = 2.375877272697835e-13 relative error = 8.511785456600332e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999785 y[1] (closed_form) = 2.802961045139523 y[1] (numeric) = 2.802961045139762 absolute error = 2.384759056894836e-13 relative error = 8.507999285363348e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999784 y[1] (closed_form) = 2.814562239206488 y[1] (numeric) = 2.814562239206728 absolute error = 2.398081733190338e-13 relative error = 8.520265424531635e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999783 y[1] (closed_form) = 2.826081977728333 y[1] (numeric) = 2.826081977728574 absolute error = 2.41140440948584e-13 relative error = 8.532676788888411e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999782 y[1] (closed_form) = 2.837519108740803 y[1] (numeric) = 2.837519108741046 absolute error = 2.424727085781342e-13 relative error = 8.545236147704236e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.999999999999781 y[1] (closed_form) = 2.84887248854033 y[1] (numeric) = 2.848872488540574 absolute error = 2.438049762076844e-13 relative error = 8.557946246748381e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.00999999999978 y[1] (closed_form) = 2.860140981798394 y[1] (numeric) = 2.860140981798639 absolute error = 2.446931546273845e-13 relative error = 8.555282980265076e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999778 y[1] (closed_form) = 2.87132346167506 y[1] (numeric) = 2.871323461675306 absolute error = 2.460254222569347e-13 relative error = 8.568363179584423e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999777 y[1] (closed_form) = 2.88241880993166 y[1] (numeric) = 2.882418809931906 absolute error = 2.464695114667848e-13 relative error = 8.550787644652804e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999776 y[1] (closed_form) = 2.893425917042612 y[1] (numeric) = 2.89342591704286 absolute error = 2.478017790963349e-13 relative error = 8.564303569576601e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999775 y[1] (closed_form) = 2.90434368230638 y[1] (numeric) = 2.904343682306628 absolute error = 2.486899575160351e-13 relative error = 8.562690394772664e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999774 y[1] (closed_form) = 2.915171013955534 y[1] (numeric) = 2.915171013955783 absolute error = 2.495781359357352e-13 relative error = 8.56135488247353e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999773 y[1] (closed_form) = 2.925906829265932 y[1] (numeric) = 2.925906829266183 absolute error = 2.504663143554353e-13 relative error = 8.560296994086913e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999772 y[1] (closed_form) = 2.93655005466499 y[1] (numeric) = 2.936550054665243 absolute error = 2.522426711948356e-13 relative error = 8.589762357162072e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.089999999999771 y[1] (closed_form) = 2.947099625839039 y[1] (numeric) = 2.947099625839292 absolute error = 2.531308496145357e-13 relative error = 8.5891514285836e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09999999999977 y[1] (closed_form) = 2.95755448783975 y[1] (numeric) = 2.957554487840004 absolute error = 2.544631172440859e-13 relative error = 8.603835306850095e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.109999999999769 y[1] (closed_form) = 2.967913595189636 y[1] (numeric) = 2.967913595189891 absolute error = 2.557953848736361e-13 relative error = 8.618693795136983e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999767 y[1] (closed_form) = 2.978175911986595 y[1] (numeric) = 2.978175911986852 absolute error = 2.566835632933362e-13 relative error = 8.618818057732364e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.129999999999766 y[1] (closed_form) = 2.988340412007499 y[1] (numeric) = 2.988340412007758 absolute error = 2.584599201327364e-13 relative error = 8.648945049707671e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999765 y[1] (closed_form) = 2.998406078810818 y[1] (numeric) = 2.998406078811077 absolute error = 2.597921877622866e-13 relative error = 8.664343018718849e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999764 y[1] (closed_form) = 3.008371905838257 y[1] (numeric) = 3.008371905838518 absolute error = 2.615685446016869e-13 relative error = 8.694687784248639e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.159999999999763 y[1] (closed_form) = 3.018236896515419 y[1] (numeric) = 3.018236896515682 absolute error = 2.629008122312371e-13 relative error = 8.710410125022272e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.169999999999762 y[1] (closed_form) = 3.028000064351458 y[1] (numeric) = 3.028000064351721 absolute error = 2.629008122312371e-13 relative error = 8.682325186394788e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.179999999999761 y[1] (closed_form) = 3.037660433037726 y[1] (numeric) = 3.03766043303799 absolute error = 2.637889906509372e-13 relative error = 8.683952550520681e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18999999999976 y[1] (closed_form) = 3.047217036545405 y[1] (numeric) = 3.047217036545669 absolute error = 2.646771690706373e-13 relative error = 8.685865361618575e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999759 y[1] (closed_form) = 3.056668919222106 y[1] (numeric) = 3.056668919222372 absolute error = 2.655653474903374e-13 relative error = 8.688063853442176e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999757 y[1] (closed_form) = 3.06601513588744 y[1] (numeric) = 3.066015135887707 absolute error = 2.664535259100376e-13 relative error = 8.690548288272365e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999756 y[1] (closed_form) = 3.075254751927528 y[1] (numeric) = 3.075254751927796 absolute error = 2.682298827494378e-13 relative error = 8.722200415471758e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999755 y[1] (closed_form) = 3.084386843388466 y[1] (numeric) = 3.084386843388735 absolute error = 2.691180611691379e-13 relative error = 8.725172127679304e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999754 y[1] (closed_form) = 3.093410497068718 y[1] (numeric) = 3.093410497068988 absolute error = 2.69562150378988e-13 relative error = 8.714076280352127e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999753 y[1] (closed_form) = 3.102324810610436 y[1] (numeric) = 3.102324810610706 absolute error = 2.704503287986881e-13 relative error = 8.717666437560172e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999752 y[1] (closed_form) = 3.111128892589693 y[1] (numeric) = 3.111128892589965 absolute error = 2.717825964282383e-13 relative error = 8.735819241548922e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.269999999999751 y[1] (closed_form) = 3.11982186260563 y[1] (numeric) = 3.119821862605902 absolute error = 2.726707748479384e-13 relative error = 8.739946921847897e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27999999999975 y[1] (closed_form) = 3.128402851368487 y[1] (numeric) = 3.12840285136876 absolute error = 2.735589532676386e-13 relative error = 8.744364657127618e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999749 y[1] (closed_form) = 3.13687100078654 y[1] (numeric) = 3.136871000786814 absolute error = 2.740030424774886e-13 relative error = 8.734915857514862e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999748 y[1] (closed_form) = 3.145225464051904 y[1] (numeric) = 3.145225464052178 absolute error = 2.744471316873387e-13 relative error = 8.725833324959041e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999746 y[1] (closed_form) = 3.153465405725214 y[1] (numeric) = 3.15346540572549 absolute error = 2.757793993168889e-13 relative error = 8.745280630515333e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999745 y[1] (closed_form) = 3.161590001819169 y[1] (numeric) = 3.161590001819446 absolute error = 2.771116669464391e-13 relative error = 8.764946333553366e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999744 y[1] (closed_form) = 3.169598439880932 y[1] (numeric) = 3.169598439881209 absolute error = 2.771116669464391e-13 relative error = 8.742800458876076e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999743 y[1] (closed_form) = 3.177489919073368 y[1] (numeric) = 3.177489919073646 absolute error = 2.784439345759893e-13 relative error = 8.763015514371489e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999742 y[1] (closed_form) = 3.185263650255135 y[1] (numeric) = 3.185263650255414 absolute error = 2.788880237858393e-13 relative error = 8.755571105189387e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.359999999999741 y[1] (closed_form) = 3.192918856059593 y[1] (numeric) = 3.192918856059873 absolute error = 2.802202914153895e-13 relative error = 8.776304818507404e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36999999999974 y[1] (closed_form) = 3.200454770972541 y[1] (numeric) = 3.200454770972821 absolute error = 2.806643806252396e-13 relative error = 8.769515606682124e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999739 y[1] (closed_form) = 3.207870641408767 y[1] (numeric) = 3.207870641409048 absolute error = 2.815525590449397e-13 relative error = 8.776929948811565e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999738 y[1] (closed_form) = 3.215165725787408 y[1] (numeric) = 3.21516572578769 absolute error = 2.819966482547898e-13 relative error = 8.770827767695476e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999737 y[1] (closed_form) = 3.222339294606105 y[1] (numeric) = 3.222339294606387 absolute error = 2.824407374646398e-13 relative error = 8.76508373706702e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y[1] (closed_form) = 3.229390630513954 y[1] (numeric) = 3.229390630514238 absolute error = 2.833289158843399e-13 relative error = 8.773448253897004e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999734 y[1] (closed_form) = 3.23631902838324 y[1] (numeric) = 3.236319028383525 absolute error = 2.851052727237402e-13 relative error = 8.809554009456525e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999733 y[1] (closed_form) = 3.243123795379951 y[1] (numeric) = 3.243123795380237 absolute error = 2.859934511434403e-13 relative error = 8.81845619186222e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999732 y[1] (closed_form) = 3.249804251033057 y[1] (numeric) = 3.249804251033343 absolute error = 2.859934511434403e-13 relative error = 8.800328544481654e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.449999999999731 y[1] (closed_form) = 3.256359727302559 y[1] (numeric) = 3.256359727302846 absolute error = 2.868816295631405e-13 relative error = 8.809887530478149e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45999999999973 y[1] (closed_form) = 3.262789568646295 y[1] (numeric) = 3.262789568646583 absolute error = 2.886579864025407e-13 relative error = 8.846969144942516e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999729 y[1] (closed_form) = 3.269093132085486 y[1] (numeric) = 3.269093132085776 absolute error = 2.895461648222408e-13 relative error = 8.85707910797658e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999728 y[1] (closed_form) = 3.275269787269043 y[1] (numeric) = 3.275269787269334 absolute error = 2.90434343241941e-13 relative error = 8.867493736572716e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999727 y[1] (closed_form) = 3.281318916536595 y[1] (numeric) = 3.281318916536886 absolute error = 2.90878432451791e-13 relative error = 8.864680326739188e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999726 y[1] (closed_form) = 3.287239914980255 y[1] (numeric) = 3.287239914980546 absolute error = 2.90878432451791e-13 relative error = 8.848713205453341e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y[1] (closed_form) = 3.293032190505114 y[1] (numeric) = 3.293032190505405 absolute error = 2.913225216616411e-13 relative error = 8.846634493935982e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999723 y[1] (closed_form) = 3.298695163888445 y[1] (numeric) = 3.298695163888737 absolute error = 2.917666108714911e-13 relative error = 8.844909771158171e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999722 y[1] (closed_form) = 3.304228268837631 y[1] (numeric) = 3.304228268837922 absolute error = 2.917666108714911e-13 relative error = 8.830098502066551e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.539999999999721 y[1] (closed_form) = 3.309630952046785 y[1] (numeric) = 3.309630952047077 absolute error = 2.922107000813412e-13 relative error = 8.829102226658489e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54999999999972 y[1] (closed_form) = 3.31490267325209 y[1] (numeric) = 3.314902673252383 absolute error = 2.926547892911913e-13 relative error = 8.828457971107848e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999719 y[1] (closed_form) = 3.320042905285819 y[1] (numeric) = 3.320042905286113 absolute error = 2.939870569207415e-13 relative error = 8.854917400395235e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999718 y[1] (closed_form) = 3.325051134129051 y[1] (numeric) = 3.325051134129346 absolute error = 2.944311461305915e-13 relative error = 8.854935886804443e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999717 y[1] (closed_form) = 3.329926858963076 y[1] (numeric) = 3.329926858963371 absolute error = 2.953193245502916e-13 relative error = 8.868642978009815e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999716 y[1] (closed_form) = 3.334669592219473 y[1] (numeric) = 3.334669592219769 absolute error = 2.957634137601417e-13 relative error = 8.869346889725554e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999715 y[1] (closed_form) = 3.33927885962887 y[1] (numeric) = 3.339278859629167 absolute error = 2.970956813896919e-13 relative error = 8.897001235252073e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y[1] (closed_form) = 3.343754200268365 y[1] (numeric) = 3.343754200268663 absolute error = 2.97539770599542e-13 relative error = 8.898374485052215e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999712 y[1] (closed_form) = 3.348095166607625 y[1] (numeric) = 3.348095166607924 absolute error = 2.984279490192421e-13 relative error = 8.913365187334768e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.629999999999711 y[1] (closed_form) = 3.352301324553633 y[1] (numeric) = 3.352301324553932 absolute error = 2.988720382290921e-13 relative error = 8.915428814230703e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63999999999971 y[1] (closed_form) = 3.356372253494101 y[1] (numeric) = 3.3563722534944 absolute error = 2.988720382290921e-13 relative error = 8.904615330375107e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999709 y[1] (closed_form) = 3.360307546339525 y[1] (numeric) = 3.360307546339825 absolute error = 3.002043058586423e-13 relative error = 8.933834231502503e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999708 y[1] (closed_form) = 3.364106809563901 y[1] (numeric) = 3.364106809564202 absolute error = 3.015365734881925e-13 relative error = 8.963347199052863e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999707 y[1] (closed_form) = 3.367769663244072 y[1] (numeric) = 3.367769663244375 absolute error = 3.024247519078926e-13 relative error = 8.979971380126272e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999706 y[1] (closed_form) = 3.371295741097724 y[1] (numeric) = 3.371295741098026 absolute error = 3.028688411177427e-13 relative error = 8.983751779045228e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999705 y[1] (closed_form) = 3.374684690520008 y[1] (numeric) = 3.374684690520312 absolute error = 3.037570195374428e-13 relative error = 9.001048909568989e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999704 y[1] (closed_form) = 3.377936172618807 y[1] (numeric) = 3.377936172619111 absolute error = 3.037570195374428e-13 relative error = 8.99238481767847e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999702 y[1] (closed_form) = 3.381049862248621 y[1] (numeric) = 3.381049862248925 absolute error = 3.037570195374428e-13 relative error = 8.984103515569699e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.719999999999701 y[1] (closed_form) = 3.38402544804308 y[1] (numeric) = 3.384025448043384 absolute error = 3.042011087472929e-13 relative error = 8.989326865825043e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7299999999997 y[1] (closed_form) = 3.386862632446086 y[1] (numeric) = 3.386862632446391 absolute error = 3.04645197957143e-13 relative error = 8.994908592945197e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999699 y[1] (closed_form) = 3.389561131741563 y[1] (numeric) = 3.389561131741868 absolute error = 3.05089287166993e-13 relative error = 9.000849234137799e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999698 y[1] (closed_form) = 3.392120676081829 y[1] (numeric) = 3.392120676082135 absolute error = 3.064215547965432e-13 relative error = 9.033332951777076e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999697 y[1] (closed_form) = 3.394541009514584 y[1] (numeric) = 3.39454100951489 absolute error = 3.055333763768431e-13 relative error = 9.000727212323002e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999696 y[1] (closed_form) = 3.396821890008501 y[1] (numeric) = 3.396821890008806 absolute error = 3.05089287166993e-13 relative error = 8.981609782496706e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999695 y[1] (closed_form) = 3.398963089477431 y[1] (numeric) = 3.398963089477737 absolute error = 3.055333763768431e-13 relative error = 8.9890171894693e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999694 y[1] (closed_form) = 3.400964393803213 y[1] (numeric) = 3.400964393803519 absolute error = 3.059774655866931e-13 relative error = 8.996785327838327e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999693 y[1] (closed_form) = 3.402825602857081 y[1] (numeric) = 3.402825602857386 absolute error = 3.055333763768431e-13 relative error = 8.978813845773087e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999691 y[1] (closed_form) = 3.40454653051968 y[1] (numeric) = 3.404546530519986 absolute error = 3.055333763768431e-13 relative error = 8.974275241590119e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81999999999969 y[1] (closed_form) = 3.406127004699679 y[1] (numeric) = 3.406127004699986 absolute error = 3.068656440063933e-13 relative error = 9.00922495206399e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999689 y[1] (closed_form) = 3.407566867350977 y[1] (numeric) = 3.407566867351284 absolute error = 3.068656440063933e-13 relative error = 9.005418116562123e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999688 y[1] (closed_form) = 3.408865974488508 y[1] (numeric) = 3.408865974488815 absolute error = 3.073097332162433e-13 relative error = 9.015013658973624e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999687 y[1] (closed_form) = 3.410024196202642 y[1] (numeric) = 3.410024196202948 absolute error = 3.064215547965432e-13 relative error = 8.985905587936011e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999686 y[1] (closed_form) = 3.411041416672171 y[1] (numeric) = 3.411041416672477 absolute error = 3.064215547965432e-13 relative error = 8.983225864653665e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999685 y[1] (closed_form) = 3.411917534175896 y[1] (numeric) = 3.411917534176204 absolute error = 3.073097332162433e-13 relative error = 9.006950787586076e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999684 y[1] (closed_form) = 3.412652461102799 y[1] (numeric) = 3.412652461103106 absolute error = 3.073097332162433e-13 relative error = 9.005011108483521e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999683 y[1] (closed_form) = 3.413246123960798 y[1] (numeric) = 3.413246123961105 absolute error = 3.077538224260934e-13 relative error = 9.01645563341239e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999681 y[1] (closed_form) = 3.413698463384102 y[1] (numeric) = 3.413698463384409 absolute error = 3.073097332162433e-13 relative error = 9.002251854183921e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.90999999999968 y[1] (closed_form) = 3.414009434139146 y[1] (numeric) = 3.414009434139453 absolute error = 3.073097332162433e-13 relative error = 9.00143186902858e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999679 y[1] (closed_form) = 3.414179005129113 y[1] (numeric) = 3.41417900512942 absolute error = 3.073097332162433e-13 relative error = 9.000984797650407e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999678 y[1] (closed_form) = 3.414207159397045 y[1] (numeric) = 3.414207159397353 absolute error = 3.077538224260934e-13 relative error = 9.013917669847639e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999677 y[1] (closed_form) = 3.41409389412754 y[1] (numeric) = 3.414093894127848 absolute error = 3.073097332162433e-13 relative error = 9.001209185981549e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999676 y[1] (closed_form) = 3.41383922064703 y[1] (numeric) = 3.413839220647337 absolute error = 3.068656440063933e-13 relative error = 8.988872180929263e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999675 y[1] (closed_form) = 3.413443164422651 y[1] (numeric) = 3.413443164422957 absolute error = 3.064215547965432e-13 relative error = 8.976905137612603e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999674 y[1] (closed_form) = 3.412905765059695 y[1] (numeric) = 3.412905765060001 absolute error = 3.064215547965432e-13 relative error = 8.97831864956821e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999673 y[1] (closed_form) = 3.412227076297651 y[1] (numeric) = 3.412227076297957 absolute error = 3.068656440063933e-13 relative error = 8.993119072818272e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999672 y[1] (closed_form) = 3.411407166004828 y[1] (numeric) = 3.411407166005135 absolute error = 3.068656440063933e-13 relative error = 8.995280512521471e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99999999999967 y[1] (closed_form) = 3.410446116171574 y[1] (numeric) = 3.41044611617188 absolute error = 3.064215547965432e-13 relative error = 8.984793905511675e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999674 y[1] (closed_form) = 3.40934402290207 y[1] (numeric) = 3.409344022902378 absolute error = 3.073097332162433e-13 relative error = 9.013749599685689e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999677 y[1] (closed_form) = 3.408100996404726 y[1] (numeric) = 3.408100996405033 absolute error = 3.073097332162433e-13 relative error = 9.017037157655555e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.029999999999681 y[1] (closed_form) = 3.406717160981154 y[1] (numeric) = 3.406717160981462 absolute error = 3.081979116359435e-13 relative error = 9.046771336519779e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999684 y[1] (closed_form) = 3.405192655013745 y[1] (numeric) = 3.405192655014054 absolute error = 3.090860900556436e-13 relative error = 9.076904638583393e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999687 y[1] (closed_form) = 3.403527630951824 y[1] (numeric) = 3.403527630952133 absolute error = 3.095301792654936e-13 relative error = 9.094393018896428e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.059999999999691 y[1] (closed_form) = 3.40172225529641 y[1] (numeric) = 3.40172225529672 absolute error = 3.104183576851938e-13 relative error = 9.125329300529428e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999694 y[1] (closed_form) = 3.399776708583564 y[1] (numeric) = 3.399776708583875 absolute error = 3.104183576851938e-13 relative error = 9.130551335958831e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999697 y[1] (closed_form) = 3.397691185366337 y[1] (numeric) = 3.397691185366649 absolute error = 3.113065361048939e-13 relative error = 9.162296368948226e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.089999999999701 y[1] (closed_form) = 3.395465894195312 y[1] (numeric) = 3.395465894195624 absolute error = 3.113065361048939e-13 relative error = 9.168301075769459e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.099999999999704 y[1] (closed_form) = 3.393101057597752 y[1] (numeric) = 3.393101057598064 absolute error = 3.126388037344441e-13 relative error = 9.213954975917698e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.109999999999707 y[1] (closed_form) = 3.390596912055345 y[1] (numeric) = 3.390596912055658 absolute error = 3.130828929442941e-13 relative error = 9.233857667690334e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.119999999999711 y[1] (closed_form) = 3.38795370798056 y[1] (numeric) = 3.387953707980873 absolute error = 3.135269821541442e-13 relative error = 9.254169601420752e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.129999999999714 y[1] (closed_form) = 3.3851717096916 y[1] (numeric) = 3.385171709691916 absolute error = 3.157474282033945e-13 relative error = 9.327368159772319e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.139999999999717 y[1] (closed_form) = 3.382251195385977 y[1] (numeric) = 3.382251195386294 absolute error = 3.170796958329447e-13 relative error = 9.374812144807596e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.149999999999721 y[1] (closed_form) = 3.379192457112688 y[1] (numeric) = 3.379192457113006 absolute error = 3.179678742526448e-13 relative error = 9.409581676337215e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.159999999999724 y[1] (closed_form) = 3.375995800743011 y[1] (numeric) = 3.37599580074333 absolute error = 3.18856052672345e-13 relative error = 9.444800038026382e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.169999999999727 y[1] (closed_form) = 3.372661545939919 y[1] (numeric) = 3.372661545940238 absolute error = 3.197442310920451e-13 relative error = 9.480471928081843e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.179999999999731 y[1] (closed_form) = 3.369190026126113 y[1] (numeric) = 3.369190026126434 absolute error = 3.206324095117452e-13 relative error = 9.516602121739261e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999734 y[1] (closed_form) = 3.365581588450683 y[1] (numeric) = 3.365581588451004 absolute error = 3.210764987215953e-13 relative error = 9.540000451137485e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999737 y[1] (closed_form) = 3.361836593754388 y[1] (numeric) = 3.36183659375471 absolute error = 3.219646771412954e-13 relative error = 9.57704719317532e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.209999999999741 y[1] (closed_form) = 3.357955416533578 y[1] (numeric) = 3.357955416533901 absolute error = 3.232969447708456e-13 relative error = 9.627791458428161e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999744 y[1] (closed_form) = 3.35393844490274 y[1] (numeric) = 3.353938444903065 absolute error = 3.250733016102458e-13 relative error = 9.692285858862045e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999747 y[1] (closed_form) = 3.34978608055569 y[1] (numeric) = 3.349786080556016 absolute error = 3.268496584496461e-13 relative error = 9.757329291768554e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.239999999999751 y[1] (closed_form) = 3.345498738725402 y[1] (numeric) = 3.34549873872573 absolute error = 3.286260152890463e-13 relative error = 9.822930479245951e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999754 y[1] (closed_form) = 3.341076848142487 y[1] (numeric) = 3.341076848142817 absolute error = 3.304023721284466e-13 relative error = 9.889098250228453e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999757 y[1] (closed_form) = 3.336520850992318 y[1] (numeric) = 3.33652085099265 absolute error = 3.321787289678468e-13 relative error = 9.955841542817071e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.269999999999761 y[1] (closed_form) = 3.331831202870813 y[1] (numeric) = 3.331831202871147 absolute error = 3.339550858072471e-13 relative error = 1.002316940664643e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999764 y[1] (closed_form) = 3.327008372738876 y[1] (numeric) = 3.327008372739213 absolute error = 3.361755318564974e-13 relative error = 1.010443900926373e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999767 y[1] (closed_form) = 3.322052842875503 y[1] (numeric) = 3.32205284287584 absolute error = 3.366196210663475e-13 relative error = 1.013287978811849e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.299999999999771 y[1] (closed_form) = 3.316965108829549 y[1] (numeric) = 3.316965108829887 absolute error = 3.388400671155978e-13 relative error = 1.021536422597956e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999774 y[1] (closed_form) = 3.311745679370178 y[1] (numeric) = 3.311745679370519 absolute error = 3.410605131648481e-13 relative error = 1.029851160641388e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999777 y[1] (closed_form) = 3.306395076435989 y[1] (numeric) = 3.306395076436331 absolute error = 3.423927807943983e-13 relative error = 1.035547092465031e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.329999999999781 y[1] (closed_form) = 3.300913835082815 y[1] (numeric) = 3.300913835083159 absolute error = 3.437250484239485e-13 relative error = 1.041302698576271e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999784 y[1] (closed_form) = 3.295302503430223 y[1] (numeric) = 3.295302503430569 absolute error = 3.455014052633487e-13 relative error = 1.048466430331362e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999787 y[1] (closed_form) = 3.289561642606704 y[1] (numeric) = 3.289561642607052 absolute error = 3.47277762102749e-13 relative error = 1.055696168160449e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.359999999999791 y[1] (closed_form) = 3.283691826693556 y[1] (numeric) = 3.283691826693904 absolute error = 3.486100297322992e-13 relative error = 1.061640519668756e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999794 y[1] (closed_form) = 3.277693642667477 y[1] (numeric) = 3.277693642667828 absolute error = 3.512745649913995e-13 relative error = 1.071712622615708e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y[1] (closed_form) = 3.271567690341872 y[1] (numeric) = 3.271567690342226 absolute error = 3.534950110406498e-13 relative error = 1.080506486490305e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999801 y[1] (closed_form) = 3.26531458230687 y[1] (numeric) = 3.265314582307225 absolute error = 3.552713678800501e-13 relative error = 1.088015745267211e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999804 y[1] (closed_form) = 3.258934943868062 y[1] (numeric) = 3.25893494386842 absolute error = 3.579359031391505e-13 relative error = 1.09832171953182e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y[1] (closed_form) = 3.252429412983976 y[1] (numeric) = 3.252429412984337 absolute error = 3.606004383982508e-13 relative error = 1.108711035998823e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.419999999999811 y[1] (closed_form) = 3.245798640202279 y[1] (numeric) = 3.245798640202643 absolute error = 3.632649736573512e-13 relative error = 1.119185180368159e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999814 y[1] (closed_form) = 3.239043288594725 y[1] (numeric) = 3.23904328859509 absolute error = 3.654854197066015e-13 relative error = 1.128374606765966e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y[1] (closed_form) = 3.232164033690843 y[1] (numeric) = 3.232164033691211 absolute error = 3.681499549657019e-13 relative error = 1.139020022276863e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.449999999999821 y[1] (closed_form) = 3.225161563410392 y[1] (numeric) = 3.225161563410762 absolute error = 3.703704010149522e-13 relative error = 1.148377821492175e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999824 y[1] (closed_form) = 3.218036577994564 y[1] (numeric) = 3.218036577994938 absolute error = 3.734790254839027e-13 relative error = 1.160580423596831e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y[1] (closed_form) = 3.210789789935964 y[1] (numeric) = 3.21078978993634 absolute error = 3.76143560743003e-13 relative error = 1.171498557526261e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.479999999999831 y[1] (closed_form) = 3.203421923907358 y[1] (numeric) = 3.203421923907737 absolute error = 3.788080960021034e-13 relative error = 1.182510780659371e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999834 y[1] (closed_form) = 3.19593371668921 y[1] (numeric) = 3.195933716689591 absolute error = 3.810285420513537e-13 relative error = 1.192229175660363e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y[1] (closed_form) = 3.188325917096001 y[1] (numeric) = 3.188325917096385 absolute error = 3.841371665203042e-13 relative error = 1.204824025236996e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.509999999999841 y[1] (closed_form) = 3.180599285901351 y[1] (numeric) = 3.180599285901739 absolute error = 3.876898801991047e-13 relative error = 1.218920855316853e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999844 y[1] (closed_form) = 3.17275459576194 y[1] (numeric) = 3.17275459576233 absolute error = 3.90354415458205e-13 relative error = 1.230332834375616e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y[1] (closed_form) = 3.164792631140245 y[1] (numeric) = 3.164792631140638 absolute error = 3.934630399271555e-13 relative error = 1.243250619505501e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.539999999999851 y[1] (closed_form) = 3.156714188226093 y[1] (numeric) = 3.156714188226489 absolute error = 3.965716643961059e-13 relative error = 1.256279918768821e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999854 y[1] (closed_form) = 3.148520074857043 y[1] (numeric) = 3.148520074857442 absolute error = 3.992361996552063e-13 relative error = 1.268012241190279e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999858 y[1] (closed_form) = 3.140211110437605 y[1] (numeric) = 3.140211110438007 absolute error = 4.023448241241567e-13 relative error = 1.281266800142261e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.569999999999861 y[1] (closed_form) = 3.131788125857295 y[1] (numeric) = 3.131788125857701 absolute error = 4.054534485931072e-13 relative error = 1.294638820696462e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999864 y[1] (closed_form) = 3.123251963407554 y[1] (numeric) = 3.123251963407962 absolute error = 4.081179838522075e-13 relative error = 1.306708484085734e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999868 y[1] (closed_form) = 3.114603476697512 y[1] (numeric) = 3.114603476697922 absolute error = 4.098943406916078e-13 relative error = 1.316040207873358e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.599999999999871 y[1] (closed_form) = 3.105843530568633 y[1] (numeric) = 3.105843530569045 absolute error = 4.125588759507082e-13 relative error = 1.328331166364891e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999874 y[1] (closed_form) = 3.09697300100823 y[1] (numeric) = 3.096973001008646 absolute error = 4.161115896295087e-13 relative error = 1.343607417610816e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999878 y[1] (closed_form) = 3.087992775061868 y[1] (numeric) = 3.087992775062287 absolute error = 4.192202140984591e-13 relative error = 1.35758158984054e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.629999999999881 y[1] (closed_form) = 3.078903750744657 y[1] (numeric) = 3.07890375074508 absolute error = 4.232170169871097e-13 relative error = 1.374570468091935e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999884 y[1] (closed_form) = 3.069706836951455 y[1] (numeric) = 3.06970683695188 absolute error = 4.2543746303636e-13 relative error = 1.385922127530799e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999888 y[1] (closed_form) = 3.060402953365976 y[1] (numeric) = 3.060402953366406 absolute error = 4.294342659250105e-13 relative error = 1.403195175500332e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.659999999999891 y[1] (closed_form) = 3.050993030368828 y[1] (numeric) = 3.050993030369261 absolute error = 4.320988011841109e-13 relative error = 1.416256270935746e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999894 y[1] (closed_form) = 3.041478008944468 y[1] (numeric) = 3.041478008944903 absolute error = 4.352074256530614e-13 relative error = 1.430907684925522e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999898 y[1] (closed_form) = 3.031858840587107 y[1] (numeric) = 3.031858840587546 absolute error = 4.383160501220118e-13 relative error = 1.44570071750812e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.689999999999901 y[1] (closed_form) = 3.022136487205568 y[1] (numeric) = 3.022136487206009 absolute error = 4.414246745909622e-13 relative error = 1.460637785420233e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999904 y[1] (closed_form) = 3.012311921027086 y[1] (numeric) = 3.012311921027531 absolute error = 4.445332990599127e-13 relative error = 1.475721341992842e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999908 y[1] (closed_form) = 3.002386124500092 y[1] (numeric) = 3.00238612450054 absolute error = 4.480860127387132e-13 relative error = 1.492432998814638e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.719999999999911 y[1] (closed_form) = 2.992360090195966 y[1] (numeric) = 2.992360090196418 absolute error = 4.516387264175137e-13 relative error = 1.509306075486177e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999914 y[1] (closed_form) = 2.982234820709785 y[1] (numeric) = 2.98223482071024 absolute error = 4.551914400963142e-13 relative error = 1.526343388304938e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999918 y[1] (closed_form) = 2.972011328560058 y[1] (numeric) = 2.972011328560517 absolute error = 4.587441537751147e-13 relative error = 1.543547796627601e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.749999999999921 y[1] (closed_form) = 2.961690636087483 y[1] (numeric) = 2.961690636087945 absolute error = 4.622968674539152e-13 relative error = 1.560922203760716e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999924 y[1] (closed_form) = 2.951273775352705 y[1] (numeric) = 2.951273775353171 absolute error = 4.654054919228656e-13 relative error = 1.576964820443489e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999928 y[1] (closed_form) = 2.940761788033118 y[1] (numeric) = 2.940761788033587 absolute error = 4.694022948115162e-13 relative error = 1.596192852891592e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.779999999999931 y[1] (closed_form) = 2.930155725318692 y[1] (numeric) = 2.930155725319165 absolute error = 4.733990977001667e-13 relative error = 1.615610711777711e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999934 y[1] (closed_form) = 2.919456647806861 y[1] (numeric) = 2.919456647807338 absolute error = 4.769518113789672e-13 relative error = 1.633700612534392e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999938 y[1] (closed_form) = 2.908665625396462 y[1] (numeric) = 2.908665625396942 absolute error = 4.805045250577678e-13 relative error = 1.651975809327596e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.809999999999941 y[1] (closed_form) = 2.897783737180741 y[1] (numeric) = 2.897783737181225 absolute error = 4.840572387365683e-13 relative error = 1.670439489758157e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999944 y[1] (closed_form) = 2.886812071339453 y[1] (numeric) = 2.886812071339941 absolute error = 4.876099524153688e-13 relative error = 1.689094892100553e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999948 y[1] (closed_form) = 2.875751725030038 y[1] (numeric) = 2.87575172503053 absolute error = 4.916067553040193e-13 relative error = 1.709489560677858e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.839999999999951 y[1] (closed_form) = 2.864603804277911 y[1] (numeric) = 2.864603804278407 absolute error = 4.956035581926699e-13 relative error = 1.7300946031439e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999954 y[1] (closed_form) = 2.853369423865857 y[1] (numeric) = 2.853369423866357 absolute error = 5.000444502911705e-13 relative error = 1.752470066121654e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999958 y[1] (closed_form) = 2.842049707222555 y[1] (numeric) = 2.842049707223058 absolute error = 5.031530747601209e-13 relative error = 1.770388017779733e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.869999999999961 y[1] (closed_form) = 2.830645786310237 y[1] (numeric) = 2.830645786310744 absolute error = 5.071498776487715e-13 relative error = 1.791640197800391e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999964 y[1] (closed_form) = 2.819158801511489 y[1] (numeric) = 2.819158801512 absolute error = 5.10702591327572e-13 relative error = 1.811542475201323e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999968 y[1] (closed_form) = 2.807589901515221 y[1] (numeric) = 2.807589901515736 absolute error = 5.146993942162226e-13 relative error = 1.833242789263652e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.899999999999971 y[1] (closed_form) = 2.795940243201791 y[1] (numeric) = 2.795940243202309 absolute error = 5.182521078950231e-13 relative error = 1.853587926834741e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999974 y[1] (closed_form) = 2.784210991527321 y[1] (numeric) = 2.784210991527844 absolute error = 5.226929999935237e-13 relative error = 1.877346945271531e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999978 y[1] (closed_form) = 2.772403319407207 y[1] (numeric) = 2.772403319407732 absolute error = 5.258016244624741e-13 relative error = 1.896555312792299e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.929999999999981 y[1] (closed_form) = 2.760518407598818 y[1] (numeric) = 2.760518407599348 absolute error = 5.302425165609748e-13 relative error = 1.920807755171594e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y[1] (closed_form) = 2.748557444583432 y[1] (numeric) = 2.748557444583966 absolute error = 5.342393194496253e-13 relative error = 1.943708036746505e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999988 y[1] (closed_form) = 2.736521626447384 y[1] (numeric) = 2.736521626447922 absolute error = 5.377920331284258e-13 relative error = 1.965239477484415e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.959999999999991 y[1] (closed_form) = 2.724412156762458 y[1] (numeric) = 2.724412156763 absolute error = 5.417888360170764e-13 relative error = 1.988644907020634e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y[1] (closed_form) = 2.71223024646553 y[1] (numeric) = 2.712230246466075 absolute error = 5.45785638905727e-13 relative error = 2.012313075620969e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999998 y[1] (closed_form) = 2.699977113737478 y[1] (numeric) = 2.699977113738028 absolute error = 5.502265310042276e-13 relative error = 2.037893314742099e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.990000000000001 y[1] (closed_form) = 2.687653983881365 y[1] (numeric) = 2.687653983881919 absolute error = 5.542233338928781e-13 relative error = 2.062108207443053e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.000000000000004 y[1] (closed_form) = 2.675262089199907 y[1] (numeric) = 2.675262089200465 absolute error = 5.582201367815287e-13 relative error = 2.086599810295507e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.010000000000008 y[1] (closed_form) = 2.662802668872245 y[1] (numeric) = 2.662802668872807 absolute error = 5.622169396701793e-13 relative error = 2.111372901350931e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.020000000000011 y[1] (closed_form) = 2.650276968830029 y[1] (numeric) = 2.650276968830596 absolute error = 5.662137425588298e-13 relative error = 2.136432339782155e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.030000000000014 y[1] (closed_form) = 2.637686241632827 y[1] (numeric) = 2.637686241633397 absolute error = 5.702105454474804e-13 relative error = 2.16178306747545e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.040000000000018 y[1] (closed_form) = 2.625031746342865 y[1] (numeric) = 2.625031746343439 absolute error = 5.74207348336131e-13 relative error = 2.187430110649533e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.050000000000021 y[1] (closed_form) = 2.612314748399126 y[1] (numeric) = 2.612314748399704 absolute error = 5.782041512247815e-13 relative error = 2.213378581501772e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.060000000000024 y[1] (closed_form) = 2.599536519490807 y[1] (numeric) = 2.599536519491389 absolute error = 5.81756864903582e-13 relative error = 2.237925339927656e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.070000000000028 y[1] (closed_form) = 2.586698337430152 y[1] (numeric) = 2.586698337430739 absolute error = 5.861977570020827e-13 relative error = 2.266200694992759e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.080000000000031 y[1] (closed_form) = 2.573801486024668 y[1] (numeric) = 2.573801486025258 absolute error = 5.897504706808832e-13 relative error = 2.291359585745576e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.090000000000034 y[1] (closed_form) = 2.560847254948747 y[1] (numeric) = 2.560847254949341 absolute error = 5.941913627793838e-13 relative error = 2.320292089390064e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.100000000000038 y[1] (closed_form) = 2.547836939614703 y[1] (numeric) = 2.547836939615301 absolute error = 5.981881656680343e-13 relative error = 2.347827509552065e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.110000000000041 y[1] (closed_form) = 2.534771841043225 y[1] (numeric) = 2.534771841043828 absolute error = 6.03073146976385e-13 relative error = 2.379200909570546e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.120000000000045 y[1] (closed_form) = 2.521653265733286 y[1] (numeric) = 2.521653265733893 absolute error = 6.070699498650356e-13 relative error = 2.407428325355041e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.130000000000048 y[1] (closed_form) = 2.508482525531483 y[1] (numeric) = 2.508482525532095 absolute error = 6.115108419635362e-13 relative error = 2.437771982621138e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.140000000000051 y[1] (closed_form) = 2.495260937500861 y[1] (numeric) = 2.495260937501477 absolute error = 6.163958232718869e-13 relative error = 2.470265991055993e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.150000000000055 y[1] (closed_form) = 2.481989823789204 y[1] (numeric) = 2.481989823789824 absolute error = 6.199485369506874e-13 relative error = 2.49778839142952e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.160000000000058 y[1] (closed_form) = 2.468670511496826 y[1] (numeric) = 2.468670511497451 absolute error = 6.252776074688882e-13 relative error = 2.532851608008897e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.170000000000061 y[1] (closed_form) = 2.455304332543855 y[1] (numeric) = 2.455304332544484 absolute error = 6.292744103575387e-13 relative error = 2.562918176850075e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.180000000000065 y[1] (closed_form) = 2.441892623537049 y[1] (numeric) = 2.441892623537683 absolute error = 6.341593916658894e-13 relative error = 2.596999497657346e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.190000000000068 y[1] (closed_form) = 2.428436725636131 y[1] (numeric) = 2.42843672563677 absolute error = 6.390443729742401e-13 relative error = 2.631505141674391e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.200000000000071 y[1] (closed_form) = 2.41493798441968 y[1] (numeric) = 2.414937984420323 absolute error = 6.430411758628907e-13 relative error = 2.662764758397786e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.210000000000075 y[1] (closed_form) = 2.401397749750567 y[1] (numeric) = 2.401397749751215 absolute error = 6.474820679613913e-13 relative error = 2.696271652743263e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.220000000000078 y[1] (closed_form) = 2.387817375640976 y[1] (numeric) = 2.387817375641628 absolute error = 6.519229600598919e-13 relative error = 2.730204439880551e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.230000000000081 y[1] (closed_form) = 2.374198220117001 y[1] (numeric) = 2.374198220117658 absolute error = 6.572520305780927e-13 relative error = 2.768311529378972e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.240000000000085 y[1] (closed_form) = 2.360541645082844 y[1] (numeric) = 2.360541645083507 absolute error = 6.625811010962934e-13 relative error = 2.806902824512718e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.250000000000088 y[1] (closed_form) = 2.346849016184631 y[1] (numeric) = 2.346849016185298 absolute error = 6.66577903984944e-13 relative error = 2.84031013238605e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.260000000000091 y[1] (closed_form) = 2.333121702673838 y[1] (numeric) = 2.333121702674509 absolute error = 6.714628852932947e-13 relative error = 2.877959107421508e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.270000000000095 y[1] (closed_form) = 2.319361077270379 y[1] (numeric) = 2.319361077271055 absolute error = 6.759037773917953e-13 relative error = 2.914180909629027e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.280000000000098 y[1] (closed_form) = 2.305568516025326 y[1] (numeric) = 2.305568516026006 absolute error = 6.803446694902959e-13 relative error = 2.950875954288155e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.290000000000101 y[1] (closed_form) = 2.29174539818331 y[1] (numeric) = 2.291745398183994 absolute error = 6.843414723789465e-13 relative error = 2.98611474434041e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.300000000000105 y[1] (closed_form) = 2.277893106044595 y[1] (numeric) = 2.277893106045284 absolute error = 6.892264536872972e-13 relative error = 3.025719037729964e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.310000000000108 y[1] (closed_form) = 2.264013024826853 y[1] (numeric) = 2.264013024827548 absolute error = 6.945555242054979e-13 relative error = 3.067807104416354e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.320000000000111 y[1] (closed_form) = 2.250106542526639 y[1] (numeric) = 2.250106542527337 absolute error = 6.981082378842984e-13 relative error = 3.102556366510514e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.330000000000115 y[1] (closed_form) = 2.236175049780593 y[1] (numeric) = 2.236175049781296 absolute error = 7.029932191926491e-13 relative error = 3.143730716705853e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.340000000000118 y[1] (closed_form) = 2.222219939726382 y[1] (numeric) = 2.222219939727088 absolute error = 7.065459328714496e-13 relative error = 3.179459963618387e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.350000000000121 y[1] (closed_form) = 2.208242607863379 y[1] (numeric) = 2.208242607864091 absolute error = 7.114309141798003e-13 relative error = 3.221706309109563e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.360000000000125 y[1] (closed_form) = 2.194244451913126 y[1] (numeric) = 2.194244451913842 absolute error = 7.154277170684509e-13 relative error = 3.260474084574674e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.370000000000128 y[1] (closed_form) = 2.180226871679551 y[1] (numeric) = 2.180226871680272 absolute error = 7.203126983768016e-13 relative error = 3.303842860270336e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.380000000000131 y[1] (closed_form) = 2.166191268908997 y[1] (numeric) = 2.166191268909722 absolute error = 7.251976796851523e-13 relative error = 3.347800769460207e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.390000000000135 y[1] (closed_form) = 2.152139047150044 y[1] (numeric) = 2.152139047150775 absolute error = 7.309708394132031e-13 relative error = 3.396485187056971e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.400000000000138 y[1] (closed_form) = 2.138071611613159 y[1] (numeric) = 2.138071611613895 absolute error = 7.358558207215538e-13 relative error = 3.441679954612727e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.410000000000141 y[1] (closed_form) = 2.123990369030171 y[1] (numeric) = 2.123990369030911 absolute error = 7.402967128200544e-13 relative error = 3.485405224121045e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.420000000000145 y[1] (closed_form) = 2.109896727513605 y[1] (numeric) = 2.10989672751435 absolute error = 7.44737604918555e-13 relative error = 3.529734869043502e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.430000000000148 y[1] (closed_form) = 2.095792096415868 y[1] (numeric) = 2.095792096416618 absolute error = 7.491784970170556e-13 relative error = 3.574679465097076e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.440000000000151 y[1] (closed_form) = 2.081677886188317 y[1] (numeric) = 2.081677886189071 absolute error = 7.545075675352564e-13 relative error = 3.62451641794018e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.450000000000155 y[1] (closed_form) = 2.06755550824021 y[1] (numeric) = 2.067555508240969 absolute error = 7.58948459633757e-13 relative error = 3.670752522043446e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.460000000000158 y[1] (closed_form) = 2.053426374797576 y[1] (numeric) = 2.05342637479834 absolute error = 7.638334409421077e-13 relative error = 3.719799503487946e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.470000000000161 y[1] (closed_form) = 2.039291898761984 y[1] (numeric) = 2.039291898762753 absolute error = 7.691625114603085e-13 relative error = 3.771713661625649e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.480000000000165 y[1] (closed_form) = 2.025153493569259 y[1] (numeric) = 2.025153493570033 absolute error = 7.740474927686591e-13 relative error = 3.822167036852248e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.490000000000168 y[1] (closed_form) = 2.011012573048138 y[1] (numeric) = 2.011012573048917 absolute error = 7.789324740770098e-13 relative error = 3.873334679834269e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.500000000000171 y[1] (closed_form) = 1.99687055127889 y[1] (numeric) = 1.996870551279673 absolute error = 7.835954107804355e-13 relative error = 3.924117215703262e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.510000000000175 y[1] (closed_form) = 1.982728842451905 y[1] (numeric) = 1.982728842452694 absolute error = 7.884803920887862e-13 relative error = 3.976743441698898e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.520000000000178 y[1] (closed_form) = 1.968588860726283 y[1] (numeric) = 1.968588860727076 absolute error = 7.931433287922118e-13 relative error = 4.028994294418555e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.530000000000181 y[1] (closed_form) = 1.954452020088413 y[1] (numeric) = 1.95445202008921 absolute error = 7.978062654956375e-13 relative error = 4.081994632232248e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.540000000000185 y[1] (closed_form) = 1.940319734210577 y[1] (numeric) = 1.940319734211379 absolute error = 8.026912468039882e-13 relative error = 4.136901937610632e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.550000000000188 y[1] (closed_form) = 1.926193416309586 y[1] (numeric) = 1.926193416310394 absolute error = 8.073541835074138e-13 relative error = 4.191449190259574e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.560000000000191 y[1] (closed_form) = 1.91207447900546 y[1] (numeric) = 1.912074479006272 absolute error = 8.122391648157645e-13 relative error = 4.247947314469884e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.570000000000195 y[1] (closed_form) = 1.897964334180162 y[1] (numeric) = 1.897964334180978 absolute error = 8.166800569142652e-13 relative error = 4.302926257394798e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.580000000000198 y[1] (closed_form) = 1.883864392836416 y[1] (numeric) = 1.883864392837237 absolute error = 8.213429936176908e-13 relative error = 4.359883846952733e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.590000000000201 y[1] (closed_form) = 1.869776064956607 y[1] (numeric) = 1.869776064957433 absolute error = 8.262279749260415e-13 relative error = 4.418860581281514e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.600000000000205 y[1] (closed_form) = 1.855700759361783 y[1] (numeric) = 1.855700759362614 absolute error = 8.306688670245421e-13 relative error = 4.476308277797049e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.610000000000208 y[1] (closed_form) = 1.841639883570775 y[1] (numeric) = 1.84163988357161 absolute error = 8.351097591230427e-13 relative error = 4.534598574743287e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.620000000000211 y[1] (closed_form) = 1.827594843659442 y[1] (numeric) = 1.827594843660282 absolute error = 8.397726958264684e-13 relative error = 4.594960960521037e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.630000000000215 y[1] (closed_form) = 1.813567044120073 y[1] (numeric) = 1.813567044120918 absolute error = 8.446576771348191e-13 relative error = 4.657438388469611e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.640000000000218 y[1] (closed_form) = 1.799557887720932 y[1] (numeric) = 1.799557887721782 absolute error = 8.497647030480948e-13 relative error = 4.722074843195446e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.650000000000222 y[1] (closed_form) = 1.785568775365984 y[1] (numeric) = 1.785568775366839 absolute error = 8.542055951465954e-13 relative error = 4.783941156069504e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.660000000000225 y[1] (closed_form) = 1.771601105954808 y[1] (numeric) = 1.771601105955667 absolute error = 8.590905764549461e-13 relative error = 4.849232558996047e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.670000000000228 y[1] (closed_form) = 1.757656276242705 y[1] (numeric) = 1.757656276243568 absolute error = 8.635314685534468e-13 relative error = 4.912971211865128e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.680000000000232 y[1] (closed_form) = 1.743735680701024 y[1] (numeric) = 1.743735680701892 absolute error = 8.677503160470224e-13 relative error = 4.976386763492535e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.690000000000235 y[1] (closed_form) = 1.729840711377721 y[1] (numeric) = 1.729840711378594 absolute error = 8.728573419602981e-13 relative error = 5.045882757985943e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.700000000000238 y[1] (closed_form) = 1.715972757758148 y[1] (numeric) = 1.715972757759025 absolute error = 8.772982340587987e-13 relative error = 5.112541735248495e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.710000000000242 y[1] (closed_form) = 1.702133206626111 y[1] (numeric) = 1.702133206626993 absolute error = 8.817391261572993e-13 relative error = 5.180200484455865e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.720000000000245 y[1] (closed_form) = 1.688323441925189 y[1] (numeric) = 1.688323441926075 absolute error = 8.859579736508749e-13 relative error = 5.247560696311958e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.730000000000248 y[1] (closed_form) = 1.674544844620346 y[1] (numeric) = 1.674544844621237 absolute error = 8.908429549592256e-13 relative error = 5.3199110063917e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.740000000000252 y[1] (closed_form) = 1.660798792559828 y[1] (numeric) = 1.660798792560724 absolute error = 8.952838470577262e-13 relative error = 5.3906821890074e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.750000000000255 y[1] (closed_form) = 1.647086660337388 y[1] (numeric) = 1.647086660338288 absolute error = 8.997247391562269e-13 relative error = 5.462522166088868e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.760000000000258 y[1] (closed_form) = 1.633409819154821 y[1] (numeric) = 1.633409819155726 absolute error = 9.043876758596525e-13 relative error = 5.536808125272639e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.770000000000262 y[1] (closed_form) = 1.619769636684848 y[1] (numeric) = 1.619769636685757 absolute error = 9.090506125630782e-13 relative error = 5.612221589877528e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.780000000000265 y[1] (closed_form) = 1.606167476934349 y[1] (numeric) = 1.606167476935262 absolute error = 9.134915046615788e-13 relative error = 5.687398840905041e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.790000000000268 y[1] (closed_form) = 1.592604700107963 y[1] (numeric) = 1.592604700108881 absolute error = 9.183764859699295e-13 relative error = 5.766506188934849e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.800000000000272 y[1] (closed_form) = 1.579082662472072 y[1] (numeric) = 1.579082662472994 absolute error = 9.225953334635051e-13 relative error = 5.842603147951557e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.810000000000275 y[1] (closed_form) = 1.56560271621917 y[1] (numeric) = 1.565602716220097 absolute error = 9.268141809570807e-13 relative error = 5.91985547390514e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.820000000000278 y[1] (closed_form) = 1.55216620933265 y[1] (numeric) = 1.552166209333581 absolute error = 9.312550730555813e-13 relative error = 5.999712321117802e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.830000000000282 y[1] (closed_form) = 1.538774485452003 y[1] (numeric) = 1.538774485452939 absolute error = 9.35918009759007e-13 relative error = 6.082229843342435e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.840000000000285 y[1] (closed_form) = 1.525428883738457 y[1] (numeric) = 1.525428883739398 absolute error = 9.403589018575076e-13 relative error = 6.16455419116567e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.850000000000288 y[1] (closed_form) = 1.512130738741063 y[1] (numeric) = 1.512130738742008 absolute error = 9.447997939560082e-13 relative error = 6.248135625776703e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.860000000000292 y[1] (closed_form) = 1.498881380263239 y[1] (numeric) = 1.498881380264188 absolute error = 9.492406860545088e-13 relative error = 6.332994048453652e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.870000000000295 y[1] (closed_form) = 1.485682133229791 y[1] (numeric) = 1.485682133230745 absolute error = 9.536815781530095e-13 relative error = 6.419149539610861e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.880000000000298 y[1] (closed_form) = 1.472534317554423 y[1] (numeric) = 1.472534317555381 absolute error = 9.579004256465851e-13 relative error = 6.505114442680431e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.890000000000302 y[1] (closed_form) = 1.459439248007746 y[1] (numeric) = 1.459439248008709 absolute error = 9.625633623500107e-13 relative error = 6.595432894270783e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.900000000000305 y[1] (closed_form) = 1.446398234085803 y[1] (numeric) = 1.44639823408677 absolute error = 9.667822098435863e-13 relative error = 6.684066580423069e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.910000000000308 y[1] (closed_form) = 1.433412579879119 y[1] (numeric) = 1.43341257988009 absolute error = 9.707790127322369e-13 relative error = 6.772502392954466e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.920000000000312 y[1] (closed_form) = 1.420483583942292 y[1] (numeric) = 1.420483583943267 absolute error = 9.754419494356625e-13 relative error = 6.866970941885174e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.930000000000315 y[1] (closed_form) = 1.407612539164141 y[1] (numeric) = 1.407612539165121 absolute error = 9.798828415341632e-13 relative error = 6.961310831431143e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.940000000000318 y[1] (closed_form) = 1.39480073263842 y[1] (numeric) = 1.394800732639405 absolute error = 9.843237336326638e-13 relative error = 7.057092175243602e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.950000000000322 y[1] (closed_form) = 1.382049445535104 y[1] (numeric) = 1.382049445536093 absolute error = 9.887646257311644e-13 relative error = 7.154336112398155e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.960000000000325 y[1] (closed_form) = 1.369359952972278 y[1] (numeric) = 1.369359952973271 absolute error = 9.9298347322474e-13 relative error = 7.251442333109055e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.970000000000328 y[1] (closed_form) = 1.356733523888622 y[1] (numeric) = 1.356733523889619 absolute error = 9.972023207183156e-13 relative error = 7.35002344351431e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.980000000000332 y[1] (closed_form) = 1.344171420916525 y[1] (numeric) = 1.344171420917526 absolute error = 1.001421168211891e-12 relative error = 7.450100133278174e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.990000000000335 y[1] (closed_form) = 1.331674900255813 y[1] (numeric) = 1.331674900256819 absolute error = 1.005640015705467e-12 relative error = 7.551693101013502e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.000000000000338 y[1] (closed_form) = 1.319245211548141 y[1] (numeric) = 1.31924521154915 absolute error = 1.009636818594117e-12 relative error = 7.653139914825264e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.010000000000342 y[1] (closed_form) = 1.306883597752019 y[1] (numeric) = 1.306883597753033 absolute error = 1.014077710692618e-12 relative error = 7.759510582556404e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.020000000000345 y[1] (closed_form) = 1.294591295018528 y[1] (numeric) = 1.294591295019546 absolute error = 1.018296558186194e-12 relative error = 7.865776342730778e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.030000000000348 y[1] (closed_form) = 1.282369532567696 y[1] (numeric) = 1.282369532568718 absolute error = 1.022515405679769e-12 relative error = 7.97364082436036e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.040000000000352 y[1] (closed_form) = 1.270219532565584 y[1] (numeric) = 1.27021953256661 absolute error = 1.026290163963495e-12 relative error = 8.079628266230471e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.050000000000355 y[1] (closed_form) = 1.258142510002067 y[1] (numeric) = 1.258142510003097 absolute error = 1.030286966852145e-12 relative error = 8.188952830553771e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.060000000000358 y[1] (closed_form) = 1.246139672569337 y[1] (numeric) = 1.246139672570372 absolute error = 1.034727858950646e-12 relative error = 8.303466150124289e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.070000000000362 y[1] (closed_form) = 1.234212220541136 y[1] (numeric) = 1.234212220542175 absolute error = 1.038502617234371e-12 relative error = 8.41429536955195e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.080000000000365 y[1] (closed_form) = 1.222361346652727 y[1] (numeric) = 1.222361346653769 absolute error = 1.042277375518097e-12 relative error = 8.526753389022275e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.090000000000368 y[1] (closed_form) = 1.210588235981622 y[1] (numeric) = 1.210588235982668 absolute error = 1.046718267616598e-12 relative error = 8.646360806305474e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.100000000000372 y[1] (closed_form) = 1.198894065829078 y[1] (numeric) = 1.198894065830128 absolute error = 1.050493025900323e-12 relative error = 8.762183881307893e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.110000000000375 y[1] (closed_form) = 1.187280005602365 y[1] (numeric) = 1.18728000560342 absolute error = 1.055155962603749e-12 relative error = 8.887170318920827e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.120000000000378 y[1] (closed_form) = 1.175747216697827 y[1] (numeric) = 1.175747216698886 absolute error = 1.058930720887474e-12 relative error = 9.006448885004033e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.130000000000382 y[1] (closed_form) = 1.164296852384745 y[1] (numeric) = 1.164296852385807 absolute error = 1.062483434566275e-12 relative error = 9.125537292229786e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.140000000000385 y[1] (closed_form) = 1.152930057690007 y[1] (numeric) = 1.152930057691074 absolute error = 1.066480237454925e-12 relative error = 9.250172899401275e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.150000000000388 y[1] (closed_form) = 1.141647969283612 y[1] (numeric) = 1.141647969284682 absolute error = 1.070254995738651e-12 relative error = 9.37464984420933e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.160000000000392 y[1] (closed_form) = 1.130451715364996 y[1] (numeric) = 1.13045171536607 absolute error = 1.074029754022376e-12 relative error = 9.500890125816628e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.170000000000395 y[1] (closed_form) = 1.119342415550224 y[1] (numeric) = 1.119342415551301 absolute error = 1.077582467701177e-12 relative error = 9.626924279211566e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.180000000000399 y[1] (closed_form) = 1.108321180760017 y[1] (numeric) = 1.108321180761098 absolute error = 1.081135181379977e-12 relative error = 9.754710098011506e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.190000000000402 y[1] (closed_form) = 1.097389113108671 y[1] (numeric) = 1.097389113109756 absolute error = 1.084687895058778e-12 relative error = 9.884259667804489e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.200000000000405 y[1] (closed_form) = 1.086547305793842 y[1] (numeric) = 1.08654730579493 absolute error = 1.088240608737578e-12 relative error = 1.001558425422167e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.210000000000409 y[1] (closed_form) = 1.075796842987224 y[1] (numeric) = 1.075796842988316 absolute error = 1.092015367021304e-12 relative error = 1.01507582415751e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.220000000000412 y[1] (closed_form) = 1.065138799726142 y[1] (numeric) = 1.065138799727237 absolute error = 1.095346036095179e-12 relative error = 1.028359906123788e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.230000000000415 y[1] (closed_form) = 1.054574241806039 y[1] (numeric) = 1.054574241807137 absolute error = 1.098676705169055e-12 relative error = 1.041820159847151e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.240000000000419 y[1] (closed_form) = 1.044104225673902 y[1] (numeric) = 1.044104225675005 absolute error = 1.102229418847855e-12 relative error = 1.055669914693082e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.250000000000422 y[1] (closed_form) = 1.033729798322622 y[1] (numeric) = 1.033729798323727 absolute error = 1.105560087921731e-12 relative error = 1.069486523185908e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.260000000000425 y[1] (closed_form) = 1.023451997186286 y[1] (numeric) = 1.023451997187396 absolute error = 1.109334846205456e-12 relative error = 1.083914877547049e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.270000000000429 y[1] (closed_form) = 1.013271850036445 y[1] (numeric) = 1.013271850037558 absolute error = 1.112665515279332e-12 relative error = 1.098091805510349e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.280000000000432 y[1] (closed_form) = 1.00319037487933 y[1] (numeric) = 1.003190374880446 absolute error = 1.116218228958132e-12 relative error = 1.112668399646875e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.290000000000435 y[1] (closed_form) = 0.9932085798540544 y[1] (numeric) = 0.9932085798551741 absolute error = 1.11965992033447e-12 relative error = 1.127315996906709e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.300000000000439 y[1] (closed_form) = 0.9833274631318037 y[1] (numeric) = 0.9833274631329267 absolute error = 1.122990589408346e-12 relative error = 1.142031145791178e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.310000000000442 y[1] (closed_form) = 0.9735480128160157 y[1] (numeric) = 0.9735480128171419 absolute error = 1.126210236179759e-12 relative error = 1.156810163807087e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.320000000000445 y[1] (closed_form) = 0.9638712068435725 y[1] (numeric) = 0.9638712068447017 absolute error = 1.129207838346247e-12 relative error = 1.171533945955403e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.330000000000449 y[1] (closed_form) = 0.9542980128870069 y[1] (numeric) = 0.9542980128881395 absolute error = 1.132649529722585e-12 relative error = 1.18689289344323e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.340000000000452 y[1] (closed_form) = 0.9448293882577373 y[1] (numeric) = 0.9448293882588731 absolute error = 1.135758154191535e-12 relative error = 1.202077505533428e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.350000000000455 y[1] (closed_form) = 0.9354662798103364 y[1] (numeric) = 0.9354662798114751 absolute error = 1.138755756358023e-12 relative error = 1.21731352688512e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.360000000000459 y[1] (closed_form) = 0.9262096238478456 y[1] (numeric) = 0.9262096238489876 absolute error = 1.142086425431899e-12 relative error = 1.23307553282292e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.370000000000462 y[1] (closed_form) = 0.917060346028148 y[1] (numeric) = 0.9170603460292932 absolute error = 1.145195049900849e-12 relative error = 1.24876738467732e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.380000000000465 y[1] (closed_form) = 0.9080193612714009 y[1] (numeric) = 0.9080193612725492 absolute error = 1.148303674369799e-12 relative error = 1.264624658181247e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.390000000000469 y[1] (closed_form) = 0.899087573668546 y[1] (numeric) = 0.8990875736696972 absolute error = 1.151190254233825e-12 relative error = 1.28039835934627e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.400000000000472 y[1] (closed_form) = 0.8902658763909003 y[1] (numeric) = 0.8902658763920543 absolute error = 1.15407683409785e-12 relative error = 1.296328282036854e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.410000000000475 y[1] (closed_form) = 0.8815551516008402 y[1] (numeric) = 0.8815551516019972 absolute error = 1.156963413961876e-12 relative error = 1.312411834768266e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.420000000000479 y[1] (closed_form) = 0.8729562703635859 y[1] (numeric) = 0.8729562703647459 absolute error = 1.159961016128364e-12 relative error = 1.328773336658937e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.430000000000482 y[1] (closed_form) = 0.8644700925600952 y[1] (numeric) = 0.864470092561258 absolute error = 1.162736573689926e-12 relative error = 1.345028108776472e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.440000000000485 y[1] (closed_form) = 0.856097466801077 y[1] (numeric) = 0.8560974668022424 absolute error = 1.165401108949027e-12 relative error = 1.361294892395494e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.450000000000489 y[1] (closed_form) = 0.8478392303421296 y[1] (numeric) = 0.8478392303432979 absolute error = 1.168287688813052e-12 relative error = 1.37795898916073e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.460000000000492 y[1] (closed_form) = 0.8396962090000173 y[1] (numeric) = 0.8396962090011884 absolute error = 1.171063246374615e-12 relative error = 1.394627287610621e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.470000000000495 y[1] (closed_form) = 0.8316692170700887 y[1] (numeric) = 0.8316692170712623 absolute error = 1.173616759331253e-12 relative error = 1.411158108587716e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.480000000000499 y[1] (closed_form) = 0.8237590572448472 y[1] (numeric) = 0.8237590572460235 absolute error = 1.176281294590353e-12 relative error = 1.427943382528085e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.490000000000502 y[1] (closed_form) = 0.815966520533684 y[1] (numeric) = 0.8159665205348626 absolute error = 1.178612762942066e-12 relative error = 1.444437649440804e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.500000000000505 y[1] (closed_form) = 0.8082923861837763 y[1] (numeric) = 0.8082923861849574 absolute error = 1.181055253596242e-12 relative error = 1.461173300385032e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.510000000000509 y[1] (closed_form) = 0.8007374216021637 y[1] (numeric) = 0.8007374216033473 absolute error = 1.183608766552879e-12 relative error = 1.478148434957172e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.520000000000512 y[1] (closed_form) = 0.7933023822790087 y[1] (numeric) = 0.7933023822801951 absolute error = 1.186384324114442e-12 relative error = 1.495500770722739e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.530000000000515 y[1] (closed_form) = 0.785988011712048 y[1] (numeric) = 0.7859880117132367 absolute error = 1.188715792466155e-12 relative error = 1.512384126415466e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.540000000000519 y[1] (closed_form) = 0.7787950413322432 y[1] (numeric) = 0.778795041333434 absolute error = 1.190825216212943e-12 relative error = 1.529061117512846e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.550000000000522 y[1] (closed_form) = 0.7717241904306374 y[1] (numeric) = 0.7717241904318308 absolute error = 1.193378729169581e-12 relative error = 1.54637983876552e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.560000000000525 y[1] (closed_form) = 0.764776166086429 y[1] (numeric) = 0.7647761660876249 absolute error = 1.195932242126219e-12 relative error = 1.563767668448841e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.570000000000529 y[1] (closed_form) = 0.7579516630962623 y[1] (numeric) = 0.7579516630974605 absolute error = 1.198263710477931e-12 relative error = 1.580923650966049e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.580000000000532 y[1] (closed_form) = 0.7512513639047493 y[1] (numeric) = 0.7512513639059495 absolute error = 1.200151089619794e-12 relative error = 1.59753598766439e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.590000000000535 y[1] (closed_form) = 0.7446759385362256 y[1] (numeric) = 0.7446759385374278 absolute error = 1.20214949106412e-12 relative error = 1.614325680277958e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.600000000000539 y[1] (closed_form) = 0.7382260445277482 y[1] (numeric) = 0.7382260445289528 absolute error = 1.204591981718295e-12 relative error = 1.6317386668319e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.610000000000542 y[1] (closed_form) = 0.7319023268633436 y[1] (numeric) = 0.7319023268645501 absolute error = 1.20659038316262e-12 relative error = 1.648567491694705e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.620000000000545 y[1] (closed_form) = 0.7257054179095079 y[1] (numeric) = 0.7257054179107167 absolute error = 1.20881082921187e-12 relative error = 1.66570456741802e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.630000000000549 y[1] (closed_form) = 0.7196359373519728 y[1] (numeric) = 0.7196359373531838 absolute error = 1.210920252958658e-12 relative error = 1.682684521585251e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.640000000000552 y[1] (closed_form) = 0.7136944921337364 y[1] (numeric) = 0.7136944921349491 absolute error = 1.212696609798058e-12 relative error = 1.699181685110744e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.650000000000555 y[1] (closed_form) = 0.7078816763943687 y[1] (numeric) = 0.7078816763955833 absolute error = 1.214583988939921e-12 relative error = 1.715800859723431e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.660000000000559 y[1] (closed_form) = 0.7021980714106001 y[1] (numeric) = 0.7021980714118164 absolute error = 1.216360345779322e-12 relative error = 1.732218294669842e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.670000000000562 y[1] (closed_form) = 0.6966442455381925 y[1] (numeric) = 0.6966442455394106 absolute error = 1.218136702618722e-12 relative error = 1.748577857953381e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.680000000000565 y[1] (closed_form) = 0.6912207541551048 y[1] (numeric) = 0.6912207541563248 absolute error = 1.220024081760585e-12 relative error = 1.765028139601868e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.690000000000569 y[1] (closed_form) = 0.6859281396059562 y[1] (numeric) = 0.6859281396071778 absolute error = 1.22157839399506e-12 relative error = 1.780913077420643e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.700000000000572 y[1] (closed_form) = 0.680766931147791 y[1] (numeric) = 0.6807669311490141 absolute error = 1.223132706229535e-12 relative error = 1.796698180047173e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.710000000000576 y[1] (closed_form) = 0.6757376448971537 y[1] (numeric) = 0.6757376448983785 absolute error = 1.224798040766473e-12 relative error = 1.812534864700168e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.720000000000579 y[1] (closed_form) = 0.6708407837784782 y[1] (numeric) = 0.6708407837797048 absolute error = 1.226574397605873e-12 relative error = 1.828413577804933e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.730000000000582 y[1] (closed_form) = 0.6660768374737963 y[1] (numeric) = 0.6660768374750243 absolute error = 1.228017687537886e-12 relative error = 1.843657696002972e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.740000000000586 y[1] (closed_form) = 0.6614462823737681 y[1] (numeric) = 0.6614462823749977 absolute error = 1.229571999772361e-12 relative error = 1.858914370732766e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.750000000000589 y[1] (closed_form) = 0.6569495815300448 y[1] (numeric) = 0.656949581531276 absolute error = 1.231237334309299e-12 relative error = 1.874173253055021e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.760000000000592 y[1] (closed_form) = 0.6525871846089637 y[1] (numeric) = 0.6525871846101964 absolute error = 1.232680624241311e-12 relative error = 1.888913318118475e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.770000000000596 y[1] (closed_form) = 0.6483595278465817 y[1] (numeric) = 0.6483595278478157 absolute error = 1.234012891870861e-12 relative error = 1.903284888816904e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.780000000000599 y[1] (closed_form) = 0.6442670340050516 y[1] (numeric) = 0.6442670340062872 absolute error = 1.235567204105337e-12 relative error = 1.917787406294094e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.790000000000602 y[1] (closed_form) = 0.6403101123303476 y[1] (numeric) = 0.6403101123315845 absolute error = 1.236899471734887e-12 relative error = 1.931719408949063e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.800000000000606 y[1] (closed_form) = 0.6364891585113391 y[1] (numeric) = 0.6364891585125777 absolute error = 1.238564806271825e-12 relative error = 1.945932290769348e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.810000000000609 y[1] (closed_form) = 0.6328045546402248 y[1] (numeric) = 0.6328045546414645 absolute error = 1.23967502929645e-12 relative error = 1.959017235584304e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.820000000000612 y[1] (closed_form) = 0.6292566691743207 y[1] (numeric) = 0.6292566691755613 absolute error = 1.240674230018612e-12 relative error = 1.971650505741264e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.830000000000616 y[1] (closed_form) = 0.6258458568992167 y[1] (numeric) = 0.6258458569004587 absolute error = 1.242006497648163e-12 relative error = 1.984524598120284e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.840000000000619 y[1] (closed_form) = 0.6225724588932985 y[1] (numeric) = 0.6225724588945415 absolute error = 1.243005698370325e-12 relative error = 1.996563902906861e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.850000000000622 y[1] (closed_form) = 0.6194368024936383 y[1] (numeric) = 0.6194368024948825 absolute error = 1.244226943697413e-12 relative error = 2.008642267764178e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.860000000000626 y[1] (closed_form) = 0.6164392012632637 y[1] (numeric) = 0.6164392012645087 absolute error = 1.245004099814651e-12 relative error = 2.019670548633627e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.870000000000629 y[1] (closed_form) = 0.6135799549597992 y[1] (numeric) = 0.6135799549610451 absolute error = 1.245892278234351e-12 relative error = 2.030529628882644e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.880000000000632 y[1] (closed_form) = 0.6108593495054927 y[1] (numeric) = 0.6108593495067396 absolute error = 1.246891478956513e-12 relative error = 2.041208798663565e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.890000000000636 y[1] (closed_form) = 0.6082776569586225 y[1] (numeric) = 0.60827765695987 absolute error = 1.247557612771288e-12 relative error = 2.050967347722509e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.900000000000639 y[1] (closed_form) = 0.6058351354862914 y[1] (numeric) = 0.60583513548754 absolute error = 1.248556813493451e-12 relative error = 2.060885446155677e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.910000000000642 y[1] (closed_form) = 0.6035320293386117 y[1] (numeric) = 0.6035320293398612 absolute error = 1.249444991913151e-12 relative error = 2.070221514643343e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.920000000000646 y[1] (closed_form) = 0.601368568824279 y[1] (numeric) = 0.6013685688255291 absolute error = 1.250111125727926e-12 relative error = 2.07877696064493e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.930000000000649 y[1] (closed_form) = 0.5993449702875415 y[1] (numeric) = 0.5993449702887923 absolute error = 1.250777259542701e-12 relative error = 2.08690707614119e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.940000000000652 y[1] (closed_form) = 0.5974614360865669 y[1] (numeric) = 0.5974614360878184 absolute error = 1.251554415659939e-12 relative error = 2.094786943669114e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.950000000000656 y[1] (closed_form) = 0.5957181545732053 y[1] (numeric) = 0.5957181545744575 absolute error = 1.252220549474714e-12 relative error = 2.102035232368991e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.960000000000659 y[1] (closed_form) = 0.5941153000741556 y[1] (numeric) = 0.5941153000754084 absolute error = 1.252775660987027e-12 relative error = 2.108640630582413e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.970000000000662 y[1] (closed_form) = 0.5926530328735319 y[1] (numeric) = 0.5926530328747851 absolute error = 1.253219750196877e-12 relative error = 2.114592654863381e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.980000000000666 y[1] (closed_form) = 0.5913314991968358 y[1] (numeric) = 0.5913314991980894 absolute error = 1.253552817104264e-12 relative error = 2.119881688709087e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.990000000000669 y[1] (closed_form) = 0.5901508311963334 y[1] (numeric) = 0.5901508311975874 absolute error = 1.253996906314114e-12 relative error = 2.124875269212203e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.000000000000672 y[1] (closed_form) = 0.5891111469378412 y[1] (numeric) = 0.5891111469390955 absolute error = 1.254329973221502e-12 relative error = 2.129190696427019e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.010000000000676 y[1] (closed_form) = 0.5882125503889185 y[1] (numeric) = 0.588212550390173 absolute error = 1.254440995523964e-12 relative error = 2.132632149202774e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.020000000000679 y[1] (closed_form) = 0.5874551314084712 y[1] (numeric) = 0.5874551314097262 absolute error = 1.254996107036277e-12 relative error = 2.136326742141689e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.030000000000682 y[1] (closed_form) = 0.5868389657377666 y[1] (numeric) = 0.5868389657390217 absolute error = 1.255107129338739e-12 relative error = 2.138759016727586e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.040000000000686 y[1] (closed_form) = 0.5863641149928579 y[1] (numeric) = 0.5863641149941132 absolute error = 1.255329173943665e-12 relative error = 2.140869711917747e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.050000000000689 y[1] (closed_form) = 0.586030626658424 y[1] (numeric) = 0.5860306266596794 absolute error = 1.255440196246127e-12 relative error = 2.142277449567286e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.060000000000692 y[1] (closed_form) = 0.5858385340830206 y[1] (numeric) = 0.5858385340842758 absolute error = 1.255218151641202e-12 relative error = 2.142600868012076e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.070000000000696 y[1] (closed_form) = 0.5857878564757452 y[1] (numeric) = 0.5857878564770003 absolute error = 1.255107129338739e-12 relative error = 2.142596701969543e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.080000000000699 y[1] (closed_form) = 0.5858785989043157 y[1] (numeric) = 0.585878598905571 absolute error = 1.255329173943665e-12 relative error = 2.14264384514356e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.090000000000702 y[1] (closed_form) = 0.5861107522945657 y[1] (numeric) = 0.5861107522958208 absolute error = 1.255107129338739e-12 relative error = 2.141416318375186e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.100000000000706 y[1] (closed_form) = 0.5864842934313489 y[1] (numeric) = 0.5864842934326039 absolute error = 1.254996107036277e-12 relative error = 2.139863114992663e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.110000000000709 y[1] (closed_form) = 0.5869991849608631 y[1] (numeric) = 0.586999184962118 absolute error = 1.254885084733814e-12 relative error = 2.13779697976494e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.120000000000712 y[1] (closed_form) = 0.5876553753943851 y[1] (numeric) = 0.5876553753956395 absolute error = 1.254440995523964e-12 relative error = 2.134654166452725e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.130000000000716 y[1] (closed_form) = 0.5884527991134174 y[1] (numeric) = 0.5884527991146716 absolute error = 1.254218950919039e-12 relative error = 2.131384119182859e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.140000000000719 y[1] (closed_form) = 0.5893913763762534 y[1] (numeric) = 0.589391376377507 absolute error = 1.253663839406727e-12 relative error = 2.127048154512559e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.150000000000722 y[1] (closed_form) = 0.5904710133259482 y[1] (numeric) = 0.5904710133272015 absolute error = 1.253330772499339e-12 relative error = 2.122594918656038e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.160000000000726 y[1] (closed_form) = 0.5916916019997072 y[1] (numeric) = 0.59169160200096 absolute error = 1.252886683289489e-12 relative error = 2.117465718720999e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.170000000000729 y[1] (closed_form) = 0.5930530203396795 y[1] (numeric) = 0.5930530203409323 absolute error = 1.252775660987027e-12 relative error = 2.112417638931308e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.180000000000732 y[1] (closed_form) = 0.5945551322051665 y[1] (numeric) = 0.5945551322064184 absolute error = 1.251887482567327e-12 relative error = 2.105586874549643e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.190000000000736 y[1] (closed_form) = 0.5961977873862329 y[1] (numeric) = 0.5961977873874842 absolute error = 1.251332371055014e-12 relative error = 2.098854436446218e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.200000000000739 y[1] (closed_form) = 0.5979808216187291 y[1] (numeric) = 0.59798082161998 absolute error = 1.250888281845164e-12 relative error = 2.091853512055821e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.210000000000742 y[1] (closed_form) = 0.5999040566007184 y[1] (numeric) = 0.5999040566019684 absolute error = 1.250000103425464e-12 relative error = 2.083666695818717e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.220000000000746 y[1] (closed_form) = 0.6019673000103051 y[1] (numeric) = 0.6019673000115542 absolute error = 1.249111925005764e-12 relative error = 2.07504946694676e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.230000000000749 y[1] (closed_form) = 0.6041703455248674 y[1] (numeric) = 0.6041703455261158 absolute error = 1.248445791190989e-12 relative error = 2.066380451206047e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.240000000000753 y[1] (closed_form) = 0.6065129728416895 y[1] (numeric) = 0.6065129728429373 absolute error = 1.247779657376213e-12 relative error = 2.057300854637953e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.250000000000756 y[1] (closed_form) = 0.6089949476999924 y[1] (numeric) = 0.6089949477012393 absolute error = 1.246891478956513e-12 relative error = 2.047457837976624e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.260000000000759 y[1] (closed_form) = 0.6116160219043585 y[1] (numeric) = 0.6116160219056043 absolute error = 1.245781255931888e-12 relative error = 2.036868249548076e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.270000000000763 y[1] (closed_form) = 0.6143759333495514 y[1] (numeric) = 0.6143759333507963 absolute error = 1.244893077512188e-12 relative error = 2.026272531095227e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.280000000000766 y[1] (closed_form) = 0.6172744060467265 y[1] (numeric) = 0.6172744060479705 absolute error = 1.244004899092488e-12 relative error = 2.015319097805457e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.290000000000769 y[1] (closed_form) = 0.6203111501510296 y[1] (numeric) = 0.6203111501522727 absolute error = 1.243116720672788e-12 relative error = 2.004021240582442e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.300000000000773 y[1] (closed_form) = 0.6234858619905809 y[1] (numeric) = 0.6234858619918227 absolute error = 1.241784453043238e-12 relative error = 1.99168021080484e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.310000000000776 y[1] (closed_form) = 0.6267982240968419 y[1] (numeric) = 0.6267982240980824 absolute error = 1.240452185413687e-12 relative error = 1.979029514962433e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.320000000000779 y[1] (closed_form) = 0.6302479052363622 y[1] (numeric) = 0.6302479052376014 absolute error = 1.2392309400866e-12 relative error = 1.966259514376093e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.330000000000783 y[1] (closed_form) = 0.6338345604439025 y[1] (numeric) = 0.6338345604451407 absolute error = 1.238231739364437e-12 relative error = 1.953556679675606e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.340000000000786 y[1] (closed_form) = 0.6375578310569316 y[1] (numeric) = 0.6375578310581683 absolute error = 1.236677427129962e-12 relative error = 1.939710198649463e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.350000000000789 y[1] (closed_form) = 0.64141734475149 y[1] (numeric) = 0.6414173447527257 absolute error = 1.235678226407799e-12 relative error = 1.926480842027353e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.360000000000793 y[1] (closed_form) = 0.645412715579425 y[1] (numeric) = 0.6454127155806595 absolute error = 1.234456981080712e-12 relative error = 1.912662938430748e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.370000000000796 y[1] (closed_form) = 0.6495435440069833 y[1] (numeric) = 0.6495435440082165 absolute error = 1.233124713451161e-12 relative error = 1.898448109951354e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.380000000000799 y[1] (closed_form) = 0.6538094169547644 y[1] (numeric) = 0.6538094169559961 absolute error = 1.231792445821611e-12 relative error = 1.884023713758831e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.390000000000803 y[1] (closed_form) = 0.6582099078390281 y[1] (numeric) = 0.6582099078402585 absolute error = 1.230349155889598e-12 relative error = 1.869235241275786e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.400000000000806 y[1] (closed_form) = 0.6627445766143536 y[1] (numeric) = 0.6627445766155822 absolute error = 1.228572799050198e-12 relative error = 1.853765149352699e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.410000000000809 y[1] (closed_form) = 0.6674129698176418 y[1] (numeric) = 0.6674129698188689 absolute error = 1.227129509118186e-12 relative error = 1.838635993923636e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.420000000000813 y[1] (closed_form) = 0.6722146206134627 y[1] (numeric) = 0.672214620614688 absolute error = 1.225242129976323e-12 relative error = 1.822694854298419e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.430000000000816 y[1] (closed_form) = 0.6771490488407382 y[1] (numeric) = 0.6771490488419618 absolute error = 1.223576795439385e-12 relative error = 1.806953428545926e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.440000000000819 y[1] (closed_form) = 0.682215761060758 y[1] (numeric) = 0.6822157610619796 absolute error = 1.22157839399506e-12 relative error = 1.790604180846925e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.450000000000823 y[1] (closed_form) = 0.6874142506065215 y[1] (numeric) = 0.6874142506077416 absolute error = 1.220135104063047e-12 relative error = 1.774963354318729e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.460000000000826 y[1] (closed_form) = 0.6927439976334069 y[1] (numeric) = 0.6927439976346249 absolute error = 1.218025680316259e-12 relative error = 1.758262337136591e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.470000000000829 y[1] (closed_form) = 0.6982044691711525 y[1] (numeric) = 0.6982044691723688 absolute error = 1.216249323476859e-12 relative error = 1.741967256269047e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.480000000000833 y[1] (closed_form) = 0.7037951191771553 y[1] (numeric) = 0.7037951191783698 absolute error = 1.214472966637459e-12 relative error = 1.725605838326023e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.490000000000836 y[1] (closed_form) = 0.7095153885910731 y[1] (numeric) = 0.7095153885922858 absolute error = 1.212696609798058e-12 relative error = 1.709190003907008e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.500000000000839 y[1] (closed_form) = 0.7153647053907317 y[1] (numeric) = 0.7153647053919425 absolute error = 1.210809230656196e-12 relative error = 1.692576138481493e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.510000000000843 y[1] (closed_form) = 0.7213424846493254 y[1] (numeric) = 0.7213424846505343 absolute error = 1.208921851514333e-12 relative error = 1.675933245637182e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.520000000000846 y[1] (closed_form) = 0.7274481285939099 y[1] (numeric) = 0.727448128595117 absolute error = 1.20703447237247e-12 relative error = 1.659272221519844e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.530000000000849 y[1] (closed_form) = 0.7336810266651789 y[1] (numeric) = 0.7336810266663839 absolute error = 1.205036070928145e-12 relative error = 1.642452274396994e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.540000000000853 y[1] (closed_form) = 0.7400405555785192 y[1] (numeric) = 0.7400405555797221 absolute error = 1.202926647181357e-12 relative error = 1.625487465671366e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.550000000000856 y[1] (closed_form) = 0.7465260793863387 y[1] (numeric) = 0.7465260793875398 absolute error = 1.201039268039494e-12 relative error = 1.608837656451032e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.560000000000859 y[1] (closed_form) = 0.753136949541662 y[1] (numeric) = 0.7531369495428607 absolute error = 1.198707799687782e-12 relative error = 1.591619957588433e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.570000000000863 y[1] (closed_form) = 0.7598725049629818 y[1] (numeric) = 0.7598725049641785 absolute error = 1.196709398243456e-12 relative error = 1.574881826131814e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.580000000000866 y[1] (closed_form) = 0.7667320721003692 y[1] (numeric) = 0.7667320721015636 absolute error = 1.194377929891743e-12 relative error = 1.557751362376026e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.590000000000869 y[1] (closed_form) = 0.7737149650028269 y[1] (numeric) = 0.7737149650040189 absolute error = 1.192046461540031e-12 relative error = 1.5406790813923e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.600000000000873 y[1] (closed_form) = 0.7808204853868838 y[1] (numeric) = 0.7808204853880731 absolute error = 1.18938192628093e-12 relative error = 1.52324631402519e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.610000000000876 y[1] (closed_form) = 0.7880479227064222 y[1] (numeric) = 0.7880479227076094 absolute error = 1.18716148023168e-12 relative error = 1.506458485614133e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.620000000000879 y[1] (closed_form) = 0.7953965542237336 y[1] (numeric) = 0.7953965542249181 absolute error = 1.18449694497258e-12 relative error = 1.48919044052006e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.630000000000883 y[1] (closed_form) = 0.8028656450817897 y[1] (numeric) = 0.8028656450829716 absolute error = 1.181943432015942e-12 relative error = 1.472155944467563e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.640000000000886 y[1] (closed_form) = 0.8104544483777291 y[1] (numeric) = 0.8104544483789085 absolute error = 1.179389919059304e-12 relative error = 1.455220489467441e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.650000000000889 y[1] (closed_form) = 0.8181622052375462 y[1] (numeric) = 0.8181622052387231 absolute error = 1.176836406102666e-12 relative error = 1.438390087648918e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.660000000000893 y[1] (closed_form) = 0.8259881448919781 y[1] (numeric) = 0.8259881448931523 absolute error = 1.174171870843566e-12 relative error = 1.421535984632228e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.670000000000896 y[1] (closed_form) = 0.8339314847535809 y[1] (numeric) = 0.8339314847547524 absolute error = 1.171507335584465e-12 relative error = 1.404800462631094e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.680000000000899 y[1] (closed_form) = 0.8419914304949878 y[1] (numeric) = 0.8419914304961567 absolute error = 1.168842800325365e-12 relative error = 1.388188475550432e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.690000000000903 y[1] (closed_form) = 0.8501671761283415 y[1] (numeric) = 0.8501671761295078 absolute error = 1.166289287368727e-12 relative error = 1.371835234430015e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.700000000000906 y[1] (closed_form) = 0.8584579040858915 y[1] (numeric) = 0.858457904087055 absolute error = 1.163513729807164e-12 relative error = 1.355353272733977e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.710000000000909 y[1] (closed_form) = 0.8668627853017512 y[1] (numeric) = 0.8668627853029119 absolute error = 1.160738172245601e-12 relative error = 1.339010270052778e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.720000000000913 y[1] (closed_form) = 0.8753809792948027 y[1] (numeric) = 0.8753809792959609 absolute error = 1.158184659288963e-12 relative error = 1.323063542255606e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.730000000000916 y[1] (closed_form) = 0.8840116342527456 y[1] (numeric) = 0.8840116342539009 absolute error = 1.155298079424938e-12 relative error = 1.306881080135908e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.740000000000919 y[1] (closed_form) = 0.8927538871172761 y[1] (numeric) = 0.8927538871184285 absolute error = 1.152411499560912e-12 relative error = 1.290850161719348e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.750000000000923 y[1] (closed_form) = 0.901606863670393 y[1] (numeric) = 0.9016068636715423 absolute error = 1.149302875091962e-12 relative error = 1.274727291242229e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.760000000000926 y[1] (closed_form) = 0.9105696786218181 y[1] (numeric) = 0.9105696786229646 absolute error = 1.146416295227937e-12 relative error = 1.259009960624959e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.770000000000929 y[1] (closed_form) = 0.9196414356975258 y[1] (numeric) = 0.9196414356986691 absolute error = 1.143307670758986e-12 relative error = 1.243210262586543e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.780000000000933 y[1] (closed_form) = 0.9288212277293679 y[1] (numeric) = 0.928821227730508 absolute error = 1.140088023987573e-12 relative error = 1.227456899079144e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.790000000000936 y[1] (closed_form) = 0.9381081367457911 y[1] (numeric) = 0.9381081367469281 absolute error = 1.136979399518623e-12 relative error = 1.211991832266478e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.80000000000094 y[1] (closed_form) = 0.947501234063633 y[1] (numeric) = 0.9475012340647668 absolute error = 1.133870775049672e-12 relative error = 1.196695829288517e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.810000000000943 y[1] (closed_form) = 0.956999580380989 y[1] (numeric) = 0.9569995803821199 absolute error = 1.130873172883184e-12 relative error = 1.181686174233196e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.820000000000946 y[1] (closed_form) = 0.966602225871143 y[1] (numeric) = 0.9666022258722706 absolute error = 1.127653526111771e-12 relative error = 1.166615900450138e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.83000000000095 y[1] (closed_form) = 0.976308210277548 y[1] (numeric) = 0.9763082102786723 absolute error = 1.124322857037896e-12 relative error = 1.151606475498419e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.840000000000953 y[1] (closed_form) = 0.9861165630098515 y[1] (numeric) = 0.9861165630109727 absolute error = 1.121214232568946e-12 relative error = 1.136999696209082e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.850000000000956 y[1] (closed_form) = 0.9960263032409543 y[1] (numeric) = 0.9960263032420721 absolute error = 1.117772541192608e-12 relative error = 1.122231950657834e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.86000000000096 y[1] (closed_form) = 1.006036440005091 y[1] (numeric) = 1.006036440006205 absolute error = 1.114441872118732e-12 relative error = 1.107754975667773e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.870000000000963 y[1] (closed_form) = 1.016145972296927 y[1] (numeric) = 1.016145972298038 absolute error = 1.110667113835007e-12 relative error = 1.093019255220213e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.880000000000966 y[1] (closed_form) = 1.026353889171658 y[1] (numeric) = 1.026353889172765 absolute error = 1.107336444761131e-12 relative error = 1.078903150700615e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.89000000000097 y[1] (closed_form) = 1.036659169846102 y[1] (numeric) = 1.036659169847207 absolute error = 1.104449864897106e-12 relative error = 1.065393426328412e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.900000000000973 y[1] (closed_form) = 1.047060783800781 y[1] (numeric) = 1.047060783801882 absolute error = 1.10111919582323e-12 relative error = 1.051628723813167e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.910000000000976 y[1] (closed_form) = 1.057557690882967 y[1] (numeric) = 1.057557690884064 absolute error = 1.096900348329655e-12 relative error = 1.037201429090682e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.92000000000098 y[1] (closed_form) = 1.068148841410698 y[1] (numeric) = 1.068148841411791 absolute error = 1.093347634650854e-12 relative error = 1.023591087930102e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.930000000000983 y[1] (closed_form) = 1.078833176277748 y[1] (numeric) = 1.078833176278838 absolute error = 1.089794920972054e-12 relative error = 1.010160741192745e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.940000000000986 y[1] (closed_form) = 1.089609627059534 y[1] (numeric) = 1.08960962706062 absolute error = 1.086020162688328e-12 relative error = 9.967057336113187e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.95000000000099 y[1] (closed_form) = 1.100477116119958 y[1] (numeric) = 1.10047711612104 absolute error = 1.082245404404603e-12 relative error = 9.834329024672169e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.960000000000993 y[1] (closed_form) = 1.11143455671917 y[1] (numeric) = 1.111434556720248 absolute error = 1.078470646120877e-12 relative error = 9.70341114194255e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.970000000000996 y[1] (closed_form) = 1.122480853122241 y[1] (numeric) = 1.122480853123316 absolute error = 1.075139977047002e-12 relative error = 9.578247807581232e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.980000000001 y[1] (closed_form) = 1.133614900708737 y[1] (numeric) = 1.133614900709808 absolute error = 1.071365218763276e-12 relative error = 9.450874526203365e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.990000000001003 y[1] (closed_form) = 1.144835586083177 y[1] (numeric) = 1.144835586084244 absolute error = 1.067590460479551e-12 relative error = 9.325273196058618e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.000000000001005 y[1] (closed_form) = 1.156141787186373 y[1] (numeric) = 1.156141787187437 absolute error = 1.0644818360106e-12 relative error = 9.207191088570204e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.010000000001 y[1] (closed_form) = 1.167532373407628 y[1] (numeric) = 1.167532373408699 absolute error = 1.070699084948501e-12 relative error = 9.170615816189283e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.020000000000994 y[1] (closed_form) = 1.179006205697822 y[1] (numeric) = 1.179006205698899 absolute error = 1.077138378491327e-12 relative error = 9.135985657122116e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.030000000000989 y[1] (closed_form) = 1.190562136683287 y[1] (numeric) = 1.19056213668437 absolute error = 1.083577672034153e-12 relative error = 9.10139537154125e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.040000000000983 y[1] (closed_form) = 1.202199010780554 y[1] (numeric) = 1.202199010781644 absolute error = 1.090683099391754e-12 relative error = 9.07240057271054e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.050000000000978 y[1] (closed_form) = 1.21391566431191 y[1] (numeric) = 1.213915664313008 absolute error = 1.097344437539505e-12 relative error = 9.039709016042047e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.060000000000972 y[1] (closed_form) = 1.225710925621768 y[1] (numeric) = 1.225710925622872 absolute error = 1.104005775687256e-12 relative error = 9.007064819359631e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.070000000000967 y[1] (closed_form) = 1.237583615193824 y[1] (numeric) = 1.237583615194935 absolute error = 1.110889158439932e-12 relative error = 8.976275580910543e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.080000000000961 y[1] (closed_form) = 1.249532545769017 y[1] (numeric) = 1.249532545770134 absolute error = 1.117772541192608e-12 relative error = 8.945525628583622e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.090000000000956 y[1] (closed_form) = 1.261556522464244 y[1] (numeric) = 1.261556522465368 absolute error = 1.123989790130508e-12 relative error = 8.909547611350605e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.10000000000095 y[1] (closed_form) = 1.273654342891858 y[1] (numeric) = 1.273654342892989 absolute error = 1.13153930669796e-12 relative error = 8.884194624805164e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.110000000000944 y[1] (closed_form) = 1.285824797279896 y[1] (numeric) = 1.285824797281034 absolute error = 1.137978600240785e-12 relative error = 8.850183964783752e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.120000000000939 y[1] (closed_form) = 1.298066668593063 y[1] (numeric) = 1.298066668594207 absolute error = 1.144417893783611e-12 relative error = 8.816326013701694e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.130000000000933 y[1] (closed_form) = 1.310378732654427 y[1] (numeric) = 1.310378732655579 absolute error = 1.151745365746137e-12 relative error = 8.789408260717519e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.140000000000928 y[1] (closed_form) = 1.322759758267844 y[1] (numeric) = 1.322759758269002 absolute error = 1.158406703893888e-12 relative error = 8.757498832674076e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.150000000000922 y[1] (closed_form) = 1.335208507341068 y[1] (numeric) = 1.335208507342234 absolute error = 1.165512131251489e-12 relative error = 8.72906459810152e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.160000000000917 y[1] (closed_form) = 1.347723735009567 y[1] (numeric) = 1.34772373501074 absolute error = 1.172839603214015e-12 relative error = 8.702374030725885e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.170000000000911 y[1] (closed_form) = 1.360304189761004 y[1] (numeric) = 1.360304189762184 absolute error = 1.179945030571616e-12 relative error = 8.674126268617349e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.180000000000906 y[1] (closed_form) = 1.372948613560386 y[1] (numeric) = 1.372948613561574 absolute error = 1.187494547139067e-12 relative error = 8.649227912904973e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.1900000000009 y[1] (closed_form) = 1.385655741975871 y[1] (numeric) = 1.385655741977066 absolute error = 1.194377929891743e-12 relative error = 8.619586335265525e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.200000000000895 y[1] (closed_form) = 1.398424304305207 y[1] (numeric) = 1.398424304306409 absolute error = 1.201483357249344e-12 relative error = 8.591693905422282e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.210000000000889 y[1] (closed_form) = 1.411253023702801 y[1] (numeric) = 1.411253023704009 absolute error = 1.20836674000202e-12 relative error = 8.56236776613981e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.220000000000883 y[1] (closed_form) = 1.424140617307403 y[1] (numeric) = 1.424140617308619 absolute error = 1.215250122754696e-12 relative error = 8.533217211740984e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.230000000000878 y[1] (closed_form) = 1.437085796370394 y[1] (numeric) = 1.437085796371616 absolute error = 1.222355550112297e-12 relative error = 8.505793830817655e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.240000000000872 y[1] (closed_form) = 1.450087266384654 y[1] (numeric) = 1.450087266385883 absolute error = 1.229016888260048e-12 relative error = 8.475468454558763e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.250000000000867 y[1] (closed_form) = 1.463143727214016 y[1] (numeric) = 1.463143727215252 absolute error = 1.236344360222574e-12 relative error = 8.449917374670416e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.260000000000861 y[1] (closed_form) = 1.476253873223278 y[1] (numeric) = 1.476253873224522 absolute error = 1.2436718321851e-12 relative error = 8.424511899634486e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.270000000000856 y[1] (closed_form) = 1.489416393408764 y[1] (numeric) = 1.489416393410015 absolute error = 1.250999304147626e-12 relative error = 8.399258324829618e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.28000000000085 y[1] (closed_form) = 1.502629971529423 y[1] (numeric) = 1.502629971530682 absolute error = 1.258770865320002e-12 relative error = 8.377118047491003e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.290000000000845 y[1] (closed_form) = 1.515893286238457 y[1] (numeric) = 1.515893286239723 absolute error = 1.265876292677603e-12 relative error = 8.350695290819273e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.300000000000839 y[1] (closed_form) = 1.529205011215445 y[1] (numeric) = 1.529205011216719 absolute error = 1.27320376464013e-12 relative error = 8.325919384923801e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.310000000000834 y[1] (closed_form) = 1.542563815298985 y[1] (numeric) = 1.542563815300265 absolute error = 1.280087147392805e-12 relative error = 8.298438837324179e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.320000000000828 y[1] (closed_form) = 1.555968362619799 y[1] (numeric) = 1.555968362621085 absolute error = 1.286748485540556e-12 relative error = 8.269759954335098e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.330000000000823 y[1] (closed_form) = 1.569417312734325 y[1] (numeric) = 1.569417312735619 absolute error = 1.294520046712933e-12 relative error = 8.248411918290546e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.340000000000817 y[1] (closed_form) = 1.58290932075876 y[1] (numeric) = 1.582909320760062 absolute error = 1.301847518675459e-12 relative error = 8.224397327140786e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.350000000000811 y[1] (closed_form) = 1.596443037503545 y[1] (numeric) = 1.596443037504855 absolute error = 1.30939703524291e-12 relative error = 8.201965272061903e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.360000000000806 y[1] (closed_form) = 1.610017109608283 y[1] (numeric) = 1.6100171096096 absolute error = 1.316946551810361e-12 relative error = 8.179705320838319e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.3700000000008 y[1] (closed_form) = 1.623630179677076 y[1] (numeric) = 1.6236301796784 absolute error = 1.324051979167962e-12 relative error = 8.154886474402086e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.380000000000795 y[1] (closed_form) = 1.637280886414261 y[1] (numeric) = 1.637280886415592 absolute error = 1.331379451130488e-12 relative error = 8.131649628221614e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.390000000000789 y[1] (closed_form) = 1.650967864760538 y[1] (numeric) = 1.650967864761878 absolute error = 1.339595101512714e-12 relative error = 8.113998643498812e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.400000000000784 y[1] (closed_form) = 1.664689746029481 y[1] (numeric) = 1.664689746030829 absolute error = 1.347144618080165e-12 relative error = 8.092466607025687e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.410000000000778 y[1] (closed_form) = 1.678445158044397 y[1] (numeric) = 1.678445158045752 absolute error = 1.354694134647616e-12 relative error = 8.071125399330936e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.420000000000773 y[1] (closed_form) = 1.692232725275547 y[1] (numeric) = 1.692232725276909 absolute error = 1.362243651215067e-12 relative error = 8.049978178936662e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.430000000000767 y[1] (closed_form) = 1.706051068977697 y[1] (numeric) = 1.706051068979067 absolute error = 1.370015212387443e-12 relative error = 8.030329439132126e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.440000000000762 y[1] (closed_form) = 1.719898807327992 y[1] (numeric) = 1.71989880732937 absolute error = 1.378008818164744e-12 relative error = 8.012150553820065e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.450000000000756 y[1] (closed_form) = 1.733774555564138 y[1] (numeric) = 1.733774555565524 absolute error = 1.38622446854697e-12 relative error = 7.995413614176144e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.46000000000075 y[1] (closed_form) = 1.747676926122874 y[1] (numeric) = 1.747676926124268 absolute error = 1.393107851299646e-12 relative error = 7.971197825390874e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.470000000000745 y[1] (closed_form) = 1.761604528778729 y[1] (numeric) = 1.761604528780131 absolute error = 1.401101457076948e-12 relative error = 7.953552765036835e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.480000000000739 y[1] (closed_form) = 1.775555970783044 y[1] (numeric) = 1.775555970784453 absolute error = 1.409317107459174e-12 relative error = 7.937328536242347e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.490000000000734 y[1] (closed_form) = 1.789529857003244 y[1] (numeric) = 1.789529857004661 absolute error = 1.41708866863155e-12 relative error = 7.918776337180614e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.500000000000728 y[1] (closed_form) = 1.803524790062353 y[1] (numeric) = 1.803524790063778 absolute error = 1.425082274408851e-12 relative error = 7.901650602538053e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.510000000000723 y[1] (closed_form) = 1.817539370478727 y[1] (numeric) = 1.81753937048016 absolute error = 1.432631790976302e-12 relative error = 7.882260017283459e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.520000000000717 y[1] (closed_form) = 1.831572196806003 y[1] (numeric) = 1.831572196807443 absolute error = 1.440403352148678e-12 relative error = 7.86430016059718e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.530000000000712 y[1] (closed_form) = 1.845621865773242 y[1] (numeric) = 1.845621865774691 absolute error = 1.448396957925979e-12 relative error = 7.847744897187585e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.540000000000706 y[1] (closed_form) = 1.859686972425256 y[1] (numeric) = 1.859686972426712 absolute error = 1.45594647449343e-12 relative error = 7.828986792302471e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.550000000000701 y[1] (closed_form) = 1.8737661102631 y[1] (numeric) = 1.873766110264564 absolute error = 1.464162124875656e-12 relative error = 7.814006864869969e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.560000000000695 y[1] (closed_form) = 1.887857871384724 y[1] (numeric) = 1.887857871386196 absolute error = 1.471711641443108e-12 relative error = 7.7956697045399e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.57000000000069 y[1] (closed_form) = 1.901960846625757 y[1] (numeric) = 1.901960846627236 absolute error = 1.479483202615484e-12 relative error = 7.778725861997711e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.580000000000684 y[1] (closed_form) = 1.916073625700429 y[1] (numeric) = 1.916073625701916 absolute error = 1.48725476378786e-12 relative error = 7.761991730584923e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.590000000000678 y[1] (closed_form) = 1.930194797342592 y[1] (numeric) = 1.930194797344087 absolute error = 1.495026324960236e-12 relative error = 7.745468628443734e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.600000000000673 y[1] (closed_form) = 1.94432294944685 y[1] (numeric) = 1.944322949448353 absolute error = 1.502797886132612e-12 relative error = 7.729157785028202e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.610000000000667 y[1] (closed_form) = 1.958456669209767 y[1] (numeric) = 1.958456669211277 absolute error = 1.510569447304988e-12 relative error = 7.713060345187519e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.620000000000662 y[1] (closed_form) = 1.972594543271143 y[1] (numeric) = 1.972594543272661 absolute error = 1.518341008477364e-12 relative error = 7.697177373103281e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.630000000000656 y[1] (closed_form) = 1.986735157855353 y[1] (numeric) = 1.98673515785688 absolute error = 1.526778703464515e-12 relative error = 7.684862763050144e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.640000000000651 y[1] (closed_form) = 2.000877098912725 y[1] (numeric) = 2.000877098914259 absolute error = 1.534772309241816e-12 relative error = 7.670497653633053e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.650000000000645 y[1] (closed_form) = 2.015018952260935 y[1] (numeric) = 2.015018952262478 absolute error = 1.542765915019118e-12 relative error = 7.656334513817201e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.66000000000064 y[1] (closed_form) = 2.029159303726437 y[1] (numeric) = 2.029159303727987 absolute error = 1.549871342376719e-12 relative error = 7.63799736930692e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.670000000000634 y[1] (closed_form) = 2.043296739285864 y[1] (numeric) = 2.043296739287422 absolute error = 1.55830903736387e-12 relative error = 7.626445084567119e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.680000000000629 y[1] (closed_form) = 2.057429845207444 y[1] (numeric) = 2.057429845209009 absolute error = 1.565858553931321e-12 relative error = 7.610750653679959e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.690000000000623 y[1] (closed_form) = 2.07155720819236 y[1] (numeric) = 2.071557208193934 absolute error = 1.574296248918472e-12 relative error = 7.599578919146542e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.700000000000617 y[1] (closed_form) = 2.085677415516088 y[1] (numeric) = 2.08567741551767 absolute error = 1.582289854695773e-12 relative error = 7.586455330649709e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.710000000000612 y[1] (closed_form) = 2.099789055169662 y[1] (numeric) = 2.099789055171252 absolute error = 1.589839371263224e-12 relative error = 7.571424221633377e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.720000000000606 y[1] (closed_form) = 2.113890716000877 y[1] (numeric) = 2.113890716002474 absolute error = 1.596944798620825e-12 relative error = 7.554528654357186e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.730000000000601 y[1] (closed_form) = 2.1279809878554 y[1] (numeric) = 2.127980987857005 absolute error = 1.604938404398126e-12 relative error = 7.542071163030449e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.740000000000595 y[1] (closed_form) = 2.142058461717788 y[1] (numeric) = 2.142058461719401 absolute error = 1.612932010175427e-12 relative error = 7.529822546869068e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.75000000000059 y[1] (closed_form) = 2.156121729852386 y[1] (numeric) = 2.156121729854006 absolute error = 1.620481526742878e-12 relative error = 7.515723738166774e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.760000000000584 y[1] (closed_form) = 2.170169385944099 y[1] (numeric) = 2.170169385945728 absolute error = 1.62847513252018e-12 relative error = 7.503907957911479e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.770000000000579 y[1] (closed_form) = 2.184200025239026 y[1] (numeric) = 2.184200025240663 absolute error = 1.636912827507331e-12 relative error = 7.494335722884158e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.780000000000573 y[1] (closed_form) = 2.198212244684928 y[1] (numeric) = 2.198212244686574 absolute error = 1.645350522494482e-12 relative error = 7.484948400559526e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.790000000000568 y[1] (closed_form) = 2.212204643071538 y[1] (numeric) = 2.212204643073191 absolute error = 1.652455949852083e-12 relative error = 7.469724625284795e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.800000000000562 y[1] (closed_form) = 2.226175821170678 y[1] (numeric) = 2.226175821172337 absolute error = 1.659561377209684e-12 relative error = 7.454763282519938e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.810000000000556 y[1] (closed_form) = 2.24012438187618 y[1] (numeric) = 2.240124381877847 absolute error = 1.667110893777135e-12 relative error = 7.442046108086523e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.820000000000551 y[1] (closed_form) = 2.254048930343597 y[1] (numeric) = 2.254048930345272 absolute error = 1.675104499554436e-12 relative error = 7.431535655701543e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.830000000000545 y[1] (closed_form) = 2.267948074129686 y[1] (numeric) = 2.26794807413137 absolute error = 1.683098105331737e-12 relative error = 7.421237393089865e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.84000000000054 y[1] (closed_form) = 2.281820423331652 y[1] (numeric) = 2.281820423333343 absolute error = 1.690647621899188e-12 relative error = 7.409205407280469e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.850000000000534 y[1] (closed_form) = 2.295664590726135 y[1] (numeric) = 2.295664590727833 absolute error = 1.698197138466639e-12 relative error = 7.397409644801324e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.860000000000529 y[1] (closed_form) = 2.309479191907931 y[1] (numeric) = 2.309479191909638 absolute error = 1.706634833453791e-12 relative error = 7.38969564841105e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.870000000000523 y[1] (closed_form) = 2.323262845428435 y[1] (numeric) = 2.323262845430149 absolute error = 1.714628439231092e-12 relative error = 7.380260234458731e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.880000000000518 y[1] (closed_form) = 2.337014172933781 y[1] (numeric) = 2.337014172935503 absolute error = 1.722177955798543e-12 relative error = 7.369137832983698e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.890000000000512 y[1] (closed_form) = 2.350731799302678 y[1] (numeric) = 2.350731799304406 absolute error = 1.728395204736444e-12 relative error = 7.3525835880093e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.900000000000507 y[1] (closed_form) = 2.364414352783919 y[1] (numeric) = 2.364414352785655 absolute error = 1.735944721303895e-12 relative error = 7.341964910930061e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.910000000000501 y[1] (closed_form) = 2.378060465133561 y[1] (numeric) = 2.378060465135304 absolute error = 1.743494237871346e-12 relative error = 7.331580771111406e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.920000000000496 y[1] (closed_form) = 2.391668771751738 y[1] (numeric) = 2.391668771753489 absolute error = 1.751487843648647e-12 relative error = 7.323287674010975e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.93000000000049 y[1] (closed_form) = 2.40523791181913 y[1] (numeric) = 2.405237911820889 absolute error = 1.758593271006248e-12 relative error = 7.311514850005787e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.940000000000484 y[1] (closed_form) = 2.418766528433037 y[1] (numeric) = 2.418766528434803 absolute error = 1.766586876783549e-12 relative error = 7.303668444295891e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.950000000000479 y[1] (closed_form) = 2.432253268743072 y[1] (numeric) = 2.432253268744846 absolute error = 1.774136393351e-12 relative error = 7.294209102935362e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.960000000000473 y[1] (closed_form) = 2.445696784086441 y[1] (numeric) = 2.445696784088223 absolute error = 1.781685909918451e-12 relative error = 7.284982838066645e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.970000000000468 y[1] (closed_form) = 2.459095730122816 y[1] (numeric) = 2.459095730124604 absolute error = 1.788347248066202e-12 relative error = 7.272377509178489e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.980000000000462 y[1] (closed_form) = 2.472448766968756 y[1] (numeric) = 2.472448766970552 absolute error = 1.795896764633653e-12 relative error = 7.263635908765212e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.990000000000457 y[1] (closed_form) = 2.485754559331706 y[1] (numeric) = 2.485754559333509 absolute error = 1.803002191991254e-12 relative error = 7.253339575392312e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.000000000000451 y[1] (closed_form) = 2.499011776643518 y[1] (numeric) = 2.499011776645327 absolute error = 1.809219440929155e-12 relative error = 7.239739555606099e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.010000000000446 y[1] (closed_form) = 2.512219093193506 y[1] (numeric) = 2.512219093195323 absolute error = 1.816324868286756e-12 relative error = 7.229962041160444e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.02000000000044 y[1] (closed_form) = 2.525375188261023 y[1] (numeric) = 2.525375188262846 absolute error = 1.823430295644357e-12 relative error = 7.22043324144629e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.030000000000435 y[1] (closed_form) = 2.538478746247525 y[1] (numeric) = 2.538478746249356 absolute error = 1.830979812211808e-12 relative error = 7.212901880381831e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.040000000000429 y[1] (closed_form) = 2.551528456808133 y[1] (numeric) = 2.551528456809971 absolute error = 1.837641150359559e-12 relative error = 7.2021189709104e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.050000000000423 y[1] (closed_form) = 2.564523014982666 y[1] (numeric) = 2.564523014984511 absolute error = 1.84563475613686e-12 relative error = 7.196795448331492e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.060000000000418 y[1] (closed_form) = 2.577461121326134 y[1] (numeric) = 2.577461121327988 absolute error = 1.853184272704311e-12 relative error = 7.189960140895649e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.070000000000412 y[1] (closed_form) = 2.590341482038687 y[1] (numeric) = 2.590341482040547 absolute error = 1.860733789271762e-12 relative error = 7.18335324579407e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.080000000000407 y[1] (closed_form) = 2.603162809094985 y[1] (numeric) = 2.603162809096853 absolute error = 1.867839216629363e-12 relative error = 7.175268523749138e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.090000000000401 y[1] (closed_form) = 2.615923820373008 y[1] (numeric) = 2.615923820374883 absolute error = 1.875388733196814e-12 relative error = 7.16912594545433e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.100000000000396 y[1] (closed_form) = 2.628623239782262 y[1] (numeric) = 2.628623239784143 absolute error = 1.881605982134715e-12 relative error = 7.158142535065525e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.11000000000039 y[1] (closed_form) = 2.641259797391388 y[1] (numeric) = 2.641259797393277 absolute error = 1.888267320282466e-12 relative error = 7.149116198820703e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.120000000000385 y[1] (closed_form) = 2.653832229555157 y[1] (numeric) = 2.653832229557052 absolute error = 1.895372747640067e-12 relative error = 7.142021739474372e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.130000000000379 y[1] (closed_form) = 2.666339279040828 y[1] (numeric) = 2.666339279042731 absolute error = 1.902922264207518e-12 relative error = 7.136834682539213e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.140000000000374 y[1] (closed_form) = 2.678779695153877 y[1] (numeric) = 2.678779695155787 absolute error = 1.909583602355269e-12 relative error = 7.128557849717377e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.150000000000368 y[1] (closed_form) = 2.691152233863058 y[1] (numeric) = 2.691152233864975 absolute error = 1.91713311892272e-12 relative error = 7.123837495327199e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.160000000000363 y[1] (closed_form) = 2.703455657924811 y[1] (numeric) = 2.703455657926735 absolute error = 1.923794457070471e-12 relative error = 7.116057004416294e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.170000000000357 y[1] (closed_form) = 2.715688737006984 y[1] (numeric) = 2.715688737008914 absolute error = 1.930011706008372e-12 relative error = 7.106895866628212e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.180000000000351 y[1] (closed_form) = 2.72785024781186 y[1] (numeric) = 2.727850247813796 absolute error = 1.936228954946273e-12 relative error = 7.098003112522087e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.190000000000346 y[1] (closed_form) = 2.739938974198495 y[1] (numeric) = 2.739938974200438 absolute error = 1.942890293094024e-12 relative error = 7.090998417811006e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.20000000000034 y[1] (closed_form) = 2.751953707304324 y[1] (numeric) = 2.751953707306275 absolute error = 1.950439809661475e-12 relative error = 7.087473181269564e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.210000000000335 y[1] (closed_form) = 2.76389324566605 y[1] (numeric) = 2.763893245668006 absolute error = 1.956657058599376e-12 relative error = 7.079351062735623e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.220000000000329 y[1] (closed_form) = 2.775756395339783 y[1] (numeric) = 2.775756395341747 absolute error = 1.963318396747127e-12 relative error = 7.073093301859419e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.230000000000324 y[1] (closed_form) = 2.787541970020445 y[1] (numeric) = 2.787541970022415 absolute error = 1.969979734894878e-12 relative error = 7.067085468422307e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.240000000000318 y[1] (closed_form) = 2.799248791160387 y[1] (numeric) = 2.799248791162364 absolute error = 1.976641073042629e-12 relative error = 7.061326879141891e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.250000000000313 y[1] (closed_form) = 2.810875688087252 y[1] (numeric) = 2.810875688089236 absolute error = 1.98330241119038e-12 relative error = 7.055816874420296e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.260000000000307 y[1] (closed_form) = 2.822421498121036 y[1] (numeric) = 2.822421498123026 absolute error = 1.990407838547981e-12 relative error = 7.052128251832869e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.270000000000302 y[1] (closed_form) = 2.833885066690357 y[1] (numeric) = 2.833885066692353 absolute error = 1.995736909066181e-12 relative error = 7.042405962486567e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.280000000000296 y[1] (closed_form) = 2.845265247447911 y[1] (numeric) = 2.845265247449913 absolute error = 2.002398247213932e-12 relative error = 7.037650528399782e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.29000000000029 y[1] (closed_form) = 2.856560902385105 y[1] (numeric) = 2.856560902387113 absolute error = 2.008615496151833e-12 relative error = 7.031586459349514e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.300000000000285 y[1] (closed_form) = 2.867770901945859 y[1] (numeric) = 2.867770901947873 absolute error = 2.013944566670034e-12 relative error = 7.022682897380396e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.310000000000279 y[1] (closed_form) = 2.878894125139559 y[1] (numeric) = 2.87889412514158 absolute error = 2.021494083237485e-12 relative error = 7.021772928657076e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.320000000000274 y[1] (closed_form) = 2.889929459653155 y[1] (numeric) = 2.889929459655182 absolute error = 2.027711332175386e-12 relative error = 7.016473448520605e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.330000000000268 y[1] (closed_form) = 2.90087580196239 y[1] (numeric) = 2.900875801964425 absolute error = 2.034816759532987e-12 relative error = 7.014491134561743e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.340000000000263 y[1] (closed_form) = 2.911732057442157 y[1] (numeric) = 2.911732057444198 absolute error = 2.041034008470888e-12 relative error = 7.009690343086915e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.350000000000257 y[1] (closed_form) = 2.922497140475953 y[1] (numeric) = 2.922497140478 absolute error = 2.046807168198939e-12 relative error = 7.00362419470357e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.360000000000252 y[1] (closed_form) = 2.933169974564448 y[1] (numeric) = 2.933169974566501 absolute error = 2.05346850634669e-12 relative error = 7.000850697892519e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.370000000000246 y[1] (closed_form) = 2.943749492433124 y[1] (numeric) = 2.943749492435184 absolute error = 2.05924166607474e-12 relative error = 6.99530198261774e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.380000000000241 y[1] (closed_form) = 2.954234636139014 y[1] (numeric) = 2.954234636141079 absolute error = 2.065014825802791e-12 relative error = 6.990016299117076e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.390000000000235 y[1] (closed_form) = 2.964624357176482 y[1] (numeric) = 2.964624357178553 absolute error = 2.071232074740692e-12 relative error = 6.986490783315767e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.40000000000023 y[1] (closed_form) = 2.974917616582084 y[1] (numeric) = 2.974917616584161 absolute error = 2.077005234468743e-12 relative error = 6.981723537121131e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.410000000000224 y[1] (closed_form) = 2.985113385038456 y[1] (numeric) = 2.985113385040538 absolute error = 2.081890215777094e-12 relative error = 6.974241669383936e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.420000000000218 y[1] (closed_form) = 2.995210642977249 y[1] (numeric) = 2.995210642979337 absolute error = 2.087663375505144e-12 relative error = 6.970005199467374e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.430000000000213 y[1] (closed_form) = 3.005208380681085 y[1] (numeric) = 3.005208380683178 absolute error = 2.092992446023345e-12 relative error = 6.964550143937108e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.440000000000207 y[1] (closed_form) = 3.015105598384523 y[1] (numeric) = 3.015105598386621 absolute error = 2.098321516541546e-12 relative error = 6.959363272934173e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.450000000000202 y[1] (closed_form) = 3.024901306374041 y[1] (numeric) = 3.024901306376144 absolute error = 2.103206497849897e-12 relative error = 6.952975600949497e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.460000000000196 y[1] (closed_form) = 3.034594525087003 y[1] (numeric) = 3.034594525089112 absolute error = 2.108979657577947e-12 relative error = 6.949790623238146e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.470000000000191 y[1] (closed_form) = 3.044184285209617 y[1] (numeric) = 3.044184285211731 absolute error = 2.113864638886298e-12 relative error = 6.943944389821135e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.480000000000185 y[1] (closed_form) = 3.05366962777386 y[1] (numeric) = 3.053669627775979 absolute error = 2.118749620194649e-12 relative error = 6.938372117678059e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.49000000000018 y[1] (closed_form) = 3.063049604253381 y[1] (numeric) = 3.063049604255505 absolute error = 2.124078690712849e-12 relative error = 6.93452266578815e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.500000000000174 y[1] (closed_form) = 3.072323276658348 y[1] (numeric) = 3.072323276660478 absolute error = 2.13029593965075e-12 relative error = 6.933827425764239e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.510000000000169 y[1] (closed_form) = 3.08148971762925 y[1] (numeric) = 3.081489717631385 absolute error = 2.135180920959101e-12 relative error = 6.929054180332644e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.520000000000163 y[1] (closed_form) = 3.090548010529627 y[1] (numeric) = 3.090548010531767 absolute error = 2.140065902267452e-12 relative error = 6.924551551945342e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.530000000000157 y[1] (closed_form) = 3.099497249537738 y[1] (numeric) = 3.099497249539883 absolute error = 2.145394972785652e-12 relative error = 6.921751497297243e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.540000000000152 y[1] (closed_form) = 3.10833653973714 y[1] (numeric) = 3.10833653973929 absolute error = 2.149835864884153e-12 relative error = 6.916354897227301e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.550000000000146 y[1] (closed_form) = 3.117064997206179 y[1] (numeric) = 3.117064997208335 absolute error = 2.155609024612204e-12 relative error = 6.915508744746334e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.560000000000141 y[1] (closed_form) = 3.125681749106383 y[1] (numeric) = 3.125681749108543 absolute error = 2.160494005920555e-12 relative error = 6.912072883102156e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.570000000000135 y[1] (closed_form) = 3.134185933769741 y[1] (numeric) = 3.134185933771905 absolute error = 2.164490808809205e-12 relative error = 6.906070203071187e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.58000000000013 y[1] (closed_form) = 3.142576700784873 y[1] (numeric) = 3.142576700787042 absolute error = 2.168487611697856e-12 relative error = 6.900349038915313e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.590000000000124 y[1] (closed_form) = 3.150853211082072 y[1] (numeric) = 3.150853211084244 absolute error = 2.172928503796356e-12 relative error = 6.896317785144061e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.600000000000119 y[1] (closed_form) = 3.159014637017203 y[1] (numeric) = 3.15901463701938 absolute error = 2.177369395894857e-12 relative error = 6.892558744048009e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.610000000000113 y[1] (closed_form) = 3.167060162454475 y[1] (numeric) = 3.167060162456656 absolute error = 2.180922109573658e-12 relative error = 6.886266751192501e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.620000000000108 y[1] (closed_form) = 3.174988982848049 y[1] (numeric) = 3.174988982850234 absolute error = 2.185363001672158e-12 relative error = 6.883056960127873e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.630000000000102 y[1] (closed_form) = 3.182800305322492 y[1] (numeric) = 3.182800305324683 absolute error = 2.190247982980509e-12 relative error = 6.881512419481138e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.640000000000096 y[1] (closed_form) = 3.190493348752067 y[1] (numeric) = 3.190493348754262 absolute error = 2.19557705349871e-12 relative error = 6.881622412275173e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.650000000000091 y[1] (closed_form) = 3.198067343838841 y[1] (numeric) = 3.198067343841041 absolute error = 2.20046203480706e-12 relative error = 6.880599431548266e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.660000000000085 y[1] (closed_form) = 3.205521533189618 y[1] (numeric) = 3.205521533191822 absolute error = 2.204458837695711e-12 relative error = 6.87706763118259e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.67000000000008 y[1] (closed_form) = 3.212855171391674 y[1] (numeric) = 3.212855171393883 absolute error = 2.208899729794211e-12 relative error = 6.875192350601377e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.680000000000074 y[1] (closed_form) = 3.2200675250873 y[1] (numeric) = 3.220067525089513 absolute error = 2.212896532682862e-12 relative error = 6.872205366633943e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.690000000000069 y[1] (closed_form) = 3.227157873047136 y[1] (numeric) = 3.227157873049353 absolute error = 2.216449246361663e-12 relative error = 6.86811533105709e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.700000000000063 y[1] (closed_form) = 3.234125506242297 y[1] (numeric) = 3.234125506244518 absolute error = 2.220890138460163e-12 relative error = 6.867049946495728e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.710000000000058 y[1] (closed_form) = 3.240969727915267 y[1] (numeric) = 3.240969727917492 absolute error = 2.224886941348814e-12 relative error = 6.864880354127706e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.720000000000052 y[1] (closed_form) = 3.247689853649585 y[1] (numeric) = 3.247689853651813 absolute error = 2.227995565817764e-12 relative error = 6.860247333390097e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.730000000000047 y[1] (closed_form) = 3.254285211438276 y[1] (numeric) = 3.254285211440508 absolute error = 2.231992368706415e-12 relative error = 6.858625546591091e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.740000000000041 y[1] (closed_form) = 3.260755141751057 y[1] (numeric) = 3.260755141753292 absolute error = 2.235545082385215e-12 relative error = 6.855912158999789e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.750000000000036 y[1] (closed_form) = 3.267098997600289 y[1] (numeric) = 3.267098997602527 absolute error = 2.238209617644316e-12 relative error = 6.850755423353559e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.76000000000003 y[1] (closed_form) = 3.273316144605674 y[1] (numeric) = 3.273316144607915 absolute error = 2.241762331323116e-12 relative error = 6.848597056588845e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.770000000000024 y[1] (closed_form) = 3.279405961057691 y[1] (numeric) = 3.279405961059936 absolute error = 2.245315045001917e-12 relative error = 6.846712702436347e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.780000000000019 y[1] (closed_form) = 3.285367837979771 y[1] (numeric) = 3.285367837982019 absolute error = 2.247979580261017e-12 relative error = 6.842398450102739e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.790000000000013 y[1] (closed_form) = 3.291201179189189 y[1] (numeric) = 3.29120117919144 absolute error = 2.251532293939817e-12 relative error = 6.84106553004608e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.800000000000008 y[1] (closed_form) = 3.296905401356686 y[1] (numeric) = 3.296905401358941 absolute error = 2.254640918408768e-12 relative error = 6.838658208030405e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.810000000000002 y[1] (closed_form) = 3.302479934064797 y[1] (numeric) = 3.302479934067055 absolute error = 2.257749542877718e-12 relative error = 6.836527663920756e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.819999999999997 y[1] (closed_form) = 3.3079242198649 y[1] (numeric) = 3.30792421986716 absolute error = 2.259969988926969e-12 relative error = 6.831988397301521e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.829999999999991 y[1] (closed_form) = 3.313237714332949 y[1] (numeric) = 3.313237714335212 absolute error = 2.263522702605769e-12 relative error = 6.831754609136103e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.839999999999986 y[1] (closed_form) = 3.318419886123926 y[1] (numeric) = 3.318419886126192 absolute error = 2.26663132707472e-12 relative error = 6.830453664265658e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.84999999999998 y[1] (closed_form) = 3.32347021702497 y[1] (numeric) = 3.32347021702724 absolute error = 2.26929586233382e-12 relative error = 6.828091465086747e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.859999999999975 y[1] (closed_form) = 3.328388202007201 y[1] (numeric) = 3.328388202009473 absolute error = 2.27240448680277e-12 relative error = 6.827342091383409e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.869999999999969 y[1] (closed_form) = 3.333173349276217 y[1] (numeric) = 3.333173349278492 absolute error = 2.275069022061871e-12 relative error = 6.825534659203644e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.879999999999963 y[1] (closed_form) = 3.33782518032128 y[1] (numeric) = 3.337825180323557 absolute error = 2.277733557320971e-12 relative error = 6.824004956130536e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.889999999999958 y[1] (closed_form) = 3.342343229963161 y[1] (numeric) = 3.342343229965441 absolute error = 2.280842181789922e-12 relative error = 6.824081265331511e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.899999999999952 y[1] (closed_form) = 3.346727046400662 y[1] (numeric) = 3.346727046402945 absolute error = 2.283506717049022e-12 relative error = 6.823104141417473e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.909999999999947 y[1] (closed_form) = 3.350976191255791 y[1] (numeric) = 3.350976191258077 absolute error = 2.285727163098272e-12 relative error = 6.82107849367228e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.919999999999941 y[1] (closed_form) = 3.355090239617605 y[1] (numeric) = 3.355090239619893 absolute error = 2.287947609147523e-12 relative error = 6.81933255365522e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.929999999999936 y[1] (closed_form) = 3.359068780084696 y[1] (numeric) = 3.359068780086985 absolute error = 2.289723965986923e-12 relative error = 6.816543857518719e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.93999999999993 y[1] (closed_form) = 3.362911414806331 y[1] (numeric) = 3.362911414808623 absolute error = 2.291944412036173e-12 relative error = 6.815357674737219e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.949999999999925 y[1] (closed_form) = 3.366617759522242 y[1] (numeric) = 3.366617759524537 absolute error = 2.294608947295274e-12 relative error = 6.815769152304662e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.959999999999919 y[1] (closed_form) = 3.370187443601046 y[1] (numeric) = 3.370187443603341 absolute error = 2.295497125714974e-12 relative error = 6.811185324642462e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.969999999999914 y[1] (closed_form) = 3.373620110077308 y[1] (numeric) = 3.373620110079606 absolute error = 2.298161660974074e-12 relative error = 6.812153075887998e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.979999999999908 y[1] (closed_form) = 3.376915415687242 y[1] (numeric) = 3.376915415689541 absolute error = 2.299493928603624e-12 relative error = 6.80945077250521e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.989999999999903 y[1] (closed_form) = 3.380073030903034 y[1] (numeric) = 3.380073030905334 absolute error = 2.299938017813474e-12 relative error = 6.804403327341757e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.999999999999897 y[1] (closed_form) = 3.383092639965792 y[1] (numeric) = 3.383092639968094 absolute error = 2.302158463862725e-12 relative error = 6.804893359012489e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 Finished! diff ( y , x , 1 ) = sin ( x ) - cos ( x ) ; Iterations = 10001 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %