##############ECHO OF PROBLEM################# ##############temp/sub_sin_cpostode.ode################# diff ( y , x , 1 ) = sin ( x ) - 1 , 0 ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(5.0); 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)) - c(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.9049958347219743 y[1] (numeric) = 0.9049958347219743 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] = 0.11 y[1] (closed_form) = 0.8960439020433032 y[1] (numeric) = 0.8960439020433032 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] = 0.12 y[1] (closed_form) = 0.8871913641461339 y[1] (numeric) = 0.8871913641461339 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] = 0.13 y[1] (closed_form) = 0.8784381062852119 y[1] (numeric) = 0.878438106285212 absolute error = 1.110223024625157e-16 relative error = 1.263860272774515e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 0.8697840037873629 y[1] (numeric) = 0.8697840037873629 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] = 0.15 y[1] (closed_form) = 0.8612289220639576 y[1] (numeric) = 0.861228922063958 absolute error = 3.33066907387547e-16 relative error = 3.867344661270123e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 0.8527727166243732 y[1] (numeric) = 0.8527727166243734 absolute error = 2.220446049250313e-16 relative error = 2.603795836761472e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 0.8444152330904394 y[1] (numeric) = 0.8444152330904398 absolute error = 3.33066907387547e-16 relative error = 3.944349821456555e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 0.8361563072118786 y[1] (numeric) = 0.8361563072118788 absolute error = 2.220446049250313e-16 relative error = 2.655539436943649e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 0.8279957648827295 y[1] (numeric) = 0.82799576488273 absolute error = 4.440892098500626e-16 relative error = 5.363423687474534e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (closed_form) = 0.8199334221587583 y[1] (numeric) = 0.8199334221587586 absolute error = 3.33066907387547e-16 relative error = 4.062121367252394e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y[1] (closed_form) = 0.8119690852758515 y[1] (numeric) = 0.811969085275852 absolute error = 4.440892098500626e-16 relative error = 5.46928716749347e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (closed_form) = 0.8041025506693945 y[1] (numeric) = 0.8041025506693945 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] = 0.2300000000000001 y[1] (closed_form) = 0.7963336049946251 y[1] (numeric) = 0.7963336049946251 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] = 0.2400000000000001 y[1] (closed_form) = 0.7886620251479705 y[1] (numeric) = 0.7886620251479705 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] = 0.2500000000000001 y[1] (closed_form) = 0.7810875782893553 y[1] (numeric) = 0.7810875782893554 absolute error = 1.110223024625157e-16 relative error = 1.421380976326156e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = 0.7736100218654866 y[1] (numeric) = 0.7736100218654868 absolute error = 2.220446049250313e-16 relative error = 2.87023950891422e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = 0.7662291036341092 y[1] (numeric) = 0.7662291036341095 absolute error = 2.220446049250313e-16 relative error = 2.897887901567654e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = 0.7589445616892291 y[1] (numeric) = 0.7589445616892291 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] = 0.2900000000000001 y[1] (closed_form) = 0.7517561244873029 y[1] (numeric) = 0.7517561244873027 absolute error = 2.220446049250313e-16 relative error = 2.953678695686923e-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) = 0.7446635108743939 y[1] (numeric) = 0.7446635108743936 absolute error = 2.220446049250313e-16 relative error = 2.981811270224636e-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) = 0.7376664301142865 y[1] (numeric) = 0.7376664301142863 absolute error = 1.110223024625157e-16 relative error = 1.50504751104527e-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) = 0.7307645819175589 y[1] (numeric) = 0.7307645819175589 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] = 0.3300000000000002 y[1] (closed_form) = 0.7239576564716129 y[1] (numeric) = 0.7239576564716127 absolute error = 2.220446049250313e-16 relative error = 3.06709381329318e-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) = 0.7172453344716537 y[1] (numeric) = 0.7172453344716534 absolute error = 3.33066907387547e-16 relative error = 4.64369569769171e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (closed_form) = 0.7106272871526208 y[1] (numeric) = 0.7106272871526208 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] = 0.3600000000000002 y[1] (closed_form) = 0.704103176322065 y[1] (numeric) = 0.704103176322065 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] = 0.3700000000000002 y[1] (closed_form) = 0.6976726543939654 y[1] (numeric) = 0.6976726543939653 absolute error = 1.110223024625157e-16 relative error = 1.591323692612768e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (closed_form) = 0.6913353644234898 y[1] (numeric) = 0.6913353644234895 absolute error = 2.220446049250313e-16 relative error = 3.211821879099099e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (closed_form) = 0.6850909401426869 y[1] (numeric) = 0.6850909401426869 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] = 0.4000000000000002 y[1] (closed_form) = 0.6789390059971147 y[1] (numeric) = 0.6789390059971149 absolute error = 2.220446049250313e-16 relative error = 3.27046469511541e-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) = 0.6728791771833947 y[1] (numeric) = 0.6728791771833947 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] = 0.4200000000000003 y[1] (closed_form) = 0.6669110596876916 y[1] (numeric) = 0.6669110596876915 absolute error = 1.110223024625157e-16 relative error = 1.664724266448758e-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) = 0.6610342503251146 y[1] (numeric) = 0.6610342503251145 absolute error = 1.110223024625157e-16 relative error = 1.679524206316267e-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) = 0.6552483367800365 y[1] (numeric) = 0.6552483367800364 absolute error = 1.110223024625157e-16 relative error = 1.694354586355635e-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) = 0.6495528976473229 y[1] (numeric) = 0.6495528976473229 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] = 0.4600000000000003 y[1] (closed_form) = 0.6439475024744746 y[1] (numeric) = 0.6439475024744745 absolute error = 1.110223024625157e-16 relative error = 1.724089340138662e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (closed_form) = 0.6384317118046708 y[1] (numeric) = 0.6384317118046708 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] = 0.4800000000000003 y[1] (closed_form) = 0.6330050772207155 y[1] (numeric) = 0.6330050772207156 absolute error = 1.110223024625157e-16 relative error = 1.753892764177696e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (closed_form) = 0.6276671413898783 y[1] (numeric) = 0.6276671413898782 absolute error = 1.110223024625157e-16 relative error = 1.768808579284122e-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) = 0.6224174381096271 y[1] (numeric) = 0.622417438109627 absolute error = 1.110223024625157e-16 relative error = 1.783727377557201e-14 % 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) = 0.6172554923542485 y[1] (numeric) = 0.6172554923542486 absolute error = 1.110223024625157e-16 relative error = 1.79864422168315e-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) = 0.6121808203223499 y[1] (numeric) = 0.6121808203223501 absolute error = 2.220446049250313e-16 relative error = 3.627108160757332e-14 % 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) = 0.6071929294852388 y[1] (numeric) = 0.6071929294852388 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] = 0.5400000000000004 y[1] (closed_form) = 0.6022913186361757 y[1] (numeric) = 0.6022913186361758 absolute error = 1.110223024625157e-16 relative error = 1.843332271730461e-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) = 0.5974754779404939 y[1] (numeric) = 0.5974754779404942 absolute error = 2.220446049250313e-16 relative error = 3.716380221836418e-14 % 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) = 0.5927448889865837 y[1] (numeric) = 0.5927448889865838 absolute error = 1.110223024625157e-16 relative error = 1.87301998760935e-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) = 0.588099024837731 y[1] (numeric) = 0.5880990248377311 absolute error = 1.110223024625157e-16 relative error = 1.887816469227254e-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) = 0.583537350084813 y[1] (numeric) = 0.583537350084813 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] = 0.5900000000000004 y[1] (closed_form) = 0.5790593208998364 y[1] (numeric) = 0.5790593208998364 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] = 0.6000000000000004 y[1] (closed_form) = 0.5746643850903214 y[1] (numeric) = 0.5746643850903216 absolute error = 2.220446049250313e-16 relative error = 3.863900577206155e-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) = 0.5703519821545203 y[1] (numeric) = 0.5703519821545204 absolute error = 1.110223024625157e-16 relative error = 1.946557668531734e-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) = 0.5661215433374659 y[1] (numeric) = 0.566121543337466 absolute error = 1.110223024625157e-16 relative error = 1.961103649368367e-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) = 0.561972491687848 y[1] (numeric) = 0.5619724916878481 absolute error = 1.110223024625157e-16 relative error = 1.975582508123616e-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) = 0.5579042421157073 y[1] (numeric) = 0.5579042421157075 absolute error = 2.220446049250313e-16 relative error = 3.979976995388755e-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) = 0.5539162014509439 y[1] (numeric) = 0.5539162014509444 absolute error = 5.551115123125783e-16 relative error = 1.002157927243333e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (closed_form) = 0.5500077685026349 y[1] (numeric) = 0.5500077685026351 absolute error = 2.220446049250313e-16 relative error = 4.037117612530005e-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) = 0.5461783341191505 y[1] (numeric) = 0.546178334119151 absolute error = 4.440892098500626e-16 relative error = 8.130846320849907e-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) = 0.5424272812490719 y[1] (numeric) = 0.5424272812490724 absolute error = 4.440892098500626e-16 relative error = 8.187073644737009e-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) = 0.5387539850028932 y[1] (numeric) = 0.5387539850028937 absolute error = 5.551115123125783e-16 relative error = 1.030361775068072e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (closed_form) = 0.5351578127155113 y[1] (numeric) = 0.5351578127155118 absolute error = 4.440892098500626e-16 relative error = 8.298285090834307e-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) = 0.5316381240094915 y[1] (numeric) = 0.531638124009492 absolute error = 4.440892098500626e-16 relative error = 8.353223551780762e-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) = 0.5281942708591049 y[1] (numeric) = 0.5281942708591051 absolute error = 2.220446049250313e-16 relative error = 4.203843494248377e-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) = 0.5248255976551296 y[1] (numeric) = 0.5248255976551296 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] = 0.7400000000000005 y[1] (closed_form) = 0.5215314412704118 y[1] (numeric) = 0.521531441270412 absolute error = 1.110223024625157e-16 relative error = 2.128774867188708e-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) = 0.5183111311261789 y[1] (numeric) = 0.5183111311261791 absolute error = 2.220446049250313e-16 relative error = 4.284002244801805e-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) = 0.5151639892590946 y[1] (numeric) = 0.5151639892590947 absolute error = 1.110223024625157e-16 relative error = 2.155086628282912e-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) = 0.5120893303890565 y[1] (numeric) = 0.5120893303890565 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] = 0.7800000000000006 y[1] (closed_form) = 0.5090864619877223 y[1] (numeric) = 0.5090864619877226 absolute error = 2.220446049250313e-16 relative error = 4.361628554372879e-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) = 0.5061546843477637 y[1] (numeric) = 0.5061546843477639 absolute error = 2.220446049250313e-16 relative error = 4.386892224679504e-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) = 0.5032932906528346 y[1] (numeric) = 0.5032932906528347 absolute error = 1.110223024625157e-16 relative error = 2.205916600209508e-14 % 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) = 0.5005015670482528 y[1] (numeric) = 0.5005015670482531 absolute error = 3.33066907387547e-16 relative error = 6.654662628767281e-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) = 0.4977787927123863 y[1] (numeric) = 0.4977787927123866 absolute error = 2.220446049250313e-16 relative error = 4.460708414577384e-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) = 0.4951242399287329 y[1] (numeric) = 0.4951242399287331 absolute error = 1.665334536937735e-16 relative error = 3.363467999824528e-14 % 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) = 0.4925371741586916 y[1] (numeric) = 0.4925371741586921 absolute error = 4.996003610813204e-16 relative error = 1.014340413867631e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (closed_form) = 0.4900168541150177 y[1] (numeric) = 0.490016854115018 absolute error = 2.775557561562891e-16 relative error = 5.664208359885121e-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) = 0.4875625318359479 y[1] (numeric) = 0.4875625318359483 absolute error = 4.440892098500626e-16 relative error = 9.108353920835883e-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) = 0.4851734527599988 y[1] (numeric) = 0.485173452759999 absolute error = 2.220446049250313e-16 relative error = 4.576602525589345e-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) = 0.4828488558014198 y[1] (numeric) = 0.48284885580142 absolute error = 1.665334536937735e-16 relative error = 3.44897687325707e-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) = 0.4805879734263029 y[1] (numeric) = 0.4805879734263033 absolute error = 3.885780586188048e-16 relative error = 8.085471965693964e-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) = 0.4783900317293354 y[1] (numeric) = 0.4783900317293357 absolute error = 3.33066907387547e-16 relative error = 6.962245977064805e-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) = 0.4762542505111883 y[1] (numeric) = 0.4762542505111886 absolute error = 2.775557561562891e-16 relative error = 5.827890372807679e-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) = 0.4741798433565371 y[1] (numeric) = 0.4741798433565372 absolute error = 1.665334536937735e-16 relative error = 3.51203147976403e-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) = 0.4721660177127015 y[1] (numeric) = 0.4721660177127018 absolute error = 3.33066907387547e-16 relative error = 7.054021147074755e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (closed_form) = 0.4702119749689017 y[1] (numeric) = 0.4702119749689018 absolute error = 1.665334536937735e-16 relative error = 3.541667642658133e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (closed_form) = 0.4683169105361163 y[1] (numeric) = 0.4683169105361165 absolute error = 1.665334536937735e-16 relative error = 3.555999152435699e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (closed_form) = 0.4664800139275432 y[1] (numeric) = 0.4664800139275433 absolute error = 1.110223024625157e-16 relative error = 2.380001267959154e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (closed_form) = 0.4647004688396456 y[1] (numeric) = 0.4647004688396457 absolute error = 1.665334536937735e-16 relative error = 3.583673029416273e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = 0.4629774532337826 y[1] (numeric) = 0.4629774532337827 absolute error = 1.110223024625157e-16 relative error = 2.398006678015364e-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) = 0.4613101394184124 y[1] (numeric) = 0.4613101394184124 absolute error = 5.551115123125783e-17 relative error = 1.203336898279375e-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) = 0.45969769413186 y[1] (numeric) = 0.4596976941318603 absolute error = 2.775557561562891e-16 relative error = 6.037788740281887e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 0.4581392786256446 y[1] (numeric) = 0.4581392786256446 absolute error = 5.551115123125783e-17 relative error = 1.211665400045674e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = 0.4566340487483507 y[1] (numeric) = 0.4566340487483505 absolute error = 2.220446049250313e-16 relative error = 4.86263793805265e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y[1] (closed_form) = 0.4551811550300451 y[1] (numeric) = 0.4551811550300447 absolute error = 3.885780586188048e-16 relative error = 8.536778254652391e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = 0.4537797427672221 y[1] (numeric) = 0.4537797427672217 absolute error = 4.440892098500626e-16 relative error = 9.786448534302896e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y[1] (closed_form) = 0.4524289521082736 y[1] (numeric) = 0.4524289521082731 absolute error = 5.551115123125783e-16 relative error = 1.226958420158158e-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) = 0.4511279181394732 y[1] (numeric) = 0.4511279181394725 absolute error = 7.216449660063518e-16 relative error = 1.599645991723447e-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) = 0.4498757709714667 y[1] (numeric) = 0.449875770971466 absolute error = 7.216449660063518e-16 relative error = 1.604098314625888e-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) = 0.448671635826261 y[1] (numeric) = 0.4486716358262601 absolute error = 8.881784197001252e-16 relative error = 1.979573364526333e-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) = 0.4475146331247002 y[1] (numeric) = 0.4475146331246992 absolute error = 9.992007221626409e-16 relative error = 2.232777764574713e-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) = 0.4464038785744238 y[1] (numeric) = 0.4464038785744226 absolute error = 1.165734175856414e-15 relative error = 2.611388995048942e-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) = 0.4453384832582943 y[1] (numeric) = 0.4453384832582931 absolute error = 1.165734175856414e-15 relative error = 2.617636291675009e-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) = 0.4443175537232891 y[1] (numeric) = 0.4443175537232877 absolute error = 1.332267629550188e-15 relative error = 2.998458238676508e-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) = 0.4433401920698439 y[1] (numeric) = 0.4433401920698426 absolute error = 1.27675647831893e-15 relative error = 2.879857277000028e-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) = 0.4424054960416433 y[1] (numeric) = 0.4424054960416418 absolute error = 1.498801083243961e-15 relative error = 3.387844628184458e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = 0.441512559115844 y[1] (numeric) = 0.4415125591158425 absolute error = 1.498801083243961e-15 relative error = 3.394696373406461e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = 0.4406604705937283 y[1] (numeric) = 0.4406604705937265 absolute error = 1.77635683940025e-15 relative error = 4.031123638130869e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = 0.4398483156917712 y[1] (numeric) = 0.4398483156917694 absolute error = 1.831867990631508e-15 relative error = 4.164772093648782e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y[1] (closed_form) = 0.4390751756331197 y[1] (numeric) = 0.4390751756331177 absolute error = 1.998401444325282e-15 relative error = 4.551387906282127e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y[1] (closed_form) = 0.4383401277394685 y[1] (numeric) = 0.4383401277394665 absolute error = 1.998401444325282e-15 relative error = 4.55902008020824e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y[1] (closed_form) = 0.437642245523328 y[1] (numeric) = 0.4376422455233258 absolute error = 2.220446049250313e-15 relative error = 5.07365564445253e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y[1] (closed_form) = 0.4369805987806712 y[1] (numeric) = 0.4369805987806689 absolute error = 2.275957200481571e-15 relative error = 5.208371279714221e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y[1] (closed_form) = 0.4363542536839544 y[1] (numeric) = 0.4363542536839521 absolute error = 2.331468351712829e-15 relative error = 5.343063192415858e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y[1] (closed_form) = 0.4357622728754988 y[1] (numeric) = 0.4357622728754964 absolute error = 2.442490654175344e-15 relative error = 5.605098940892448e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y[1] (closed_form) = 0.4352037155612252 y[1] (numeric) = 0.4352037155612227 absolute error = 2.498001805406602e-15 relative error = 5.7398448498659e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y[1] (closed_form) = 0.4346776376047328 y[1] (numeric) = 0.4346776376047302 absolute error = 2.609024107869118e-15 relative error = 6.002204581413486e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y[1] (closed_form) = 0.434183091621712 y[1] (numeric) = 0.4341830916217094 absolute error = 2.55351295663786e-15 relative error = 5.881189309100603e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y[1] (closed_form) = 0.4337191270746825 y[1] (numeric) = 0.43371912707468 absolute error = 2.55351295663786e-15 relative error = 5.887480623371651e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y[1] (closed_form) = 0.4332847903680457 y[1] (numeric) = 0.4332847903680431 absolute error = 2.609024107869118e-15 relative error = 6.021499406090232e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y[1] (closed_form) = 0.4328791249434436 y[1] (numeric) = 0.4328791249434409 absolute error = 2.720046410331634e-15 relative error = 6.28361649614546e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y[1] (closed_form) = 0.4325011713754139 y[1] (numeric) = 0.432501171375411 absolute error = 2.886579864025407e-15 relative error = 6.674155019848111e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y[1] (closed_form) = 0.4321499674673315 y[1] (numeric) = 0.4321499674673286 absolute error = 2.831068712794149e-15 relative error = 6.55112559509371e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y[1] (closed_form) = 0.4318245483476282 y[1] (numeric) = 0.4318245483476252 absolute error = 2.942091015256665e-15 relative error = 6.813162953598964e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y[1] (closed_form) = 0.4315239465662779 y[1] (numeric) = 0.4315239465662749 absolute error = 3.05311331771918e-15 relative error = 7.075188623976519e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y[1] (closed_form) = 0.4312471921915415 y[1] (numeric) = 0.4312471921915386 absolute error = 2.942091015256665e-15 relative error = 6.822284454318056e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y[1] (closed_form) = 0.4309933129069594 y[1] (numeric) = 0.4309933129069564 absolute error = 3.05311331771918e-15 relative error = 7.083899509081874e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y[1] (closed_form) = 0.4307613341085814 y[1] (numeric) = 0.4307613341085785 absolute error = 2.942091015256665e-15 relative error = 6.829979346556337e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y[1] (closed_form) = 0.4305502790024278 y[1] (numeric) = 0.4305502790024248 absolute error = 3.05311331771918e-15 relative error = 7.091188803298777e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y[1] (closed_form) = 0.4303591687021664 y[1] (numeric) = 0.4303591687021632 absolute error = 3.219646771412954e-15 relative error = 7.481301679065973e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y[1] (closed_form) = 0.4301870223270012 y[1] (numeric) = 0.430187022326998 absolute error = 3.275157922644212e-15 relative error = 7.613335020958958e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y[1] (closed_form) = 0.4300328570997596 y[1] (numeric) = 0.4300328570997564 absolute error = 3.164135620181696e-15 relative error = 7.357892700388882e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999956 y[1] (closed_form) = 0.4298956884451695 y[1] (numeric) = 0.4298956884451661 absolute error = 3.33066907387547e-15 relative error = 7.747621489114507e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y[1] (closed_form) = 0.4297745300883147 y[1] (numeric) = 0.4297745300883115 absolute error = 3.164135620181696e-15 relative error = 7.362315350636287e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y[1] (closed_form) = 0.4296683941532637 y[1] (numeric) = 0.4296683941532605 absolute error = 3.275157922644212e-15 relative error = 7.622524642750324e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y[1] (closed_form) = 0.4295762912618548 y[1] (numeric) = 0.4295762912618515 absolute error = 3.275157922644212e-15 relative error = 7.6241589428123e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y[1] (closed_form) = 0.4294972306326337 y[1] (numeric) = 0.4294972306326304 absolute error = 3.275157922644212e-15 relative error = 7.625562376316197e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y[1] (closed_form) = 0.4294302201799307 y[1] (numeric) = 0.4294302201799274 absolute error = 3.275157922644212e-15 relative error = 7.626752307445724e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y[1] (closed_form) = 0.4293742666130687 y[1] (numeric) = 0.4293742666130652 absolute error = 3.441691376337985e-15 relative error = 8.015597682381537e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y[1] (closed_form) = 0.4293283755356905 y[1] (numeric) = 0.4293283755356872 absolute error = 3.275157922644212e-15 relative error = 7.628561514383167e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999947 y[1] (closed_form) = 0.4292915515451996 y[1] (numeric) = 0.4292915515451961 absolute error = 3.497202527569243e-15 relative error = 8.146450856023955e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999946 y[1] (closed_form) = 0.4292627983322972 y[1] (numeric) = 0.4292627983322939 absolute error = 3.33066907387547e-15 relative error = 7.759044312284338e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y[1] (closed_form) = 0.4292411187806142 y[1] (numeric) = 0.4292411187806108 absolute error = 3.386180225106727e-15 relative error = 7.888760132594401e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y[1] (closed_form) = 0.4292255150664208 y[1] (numeric) = 0.4292255150664175 absolute error = 3.275157922644212e-15 relative error = 7.630389638270677e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y[1] (closed_form) = 0.4292149887584089 y[1] (numeric) = 0.4292149887584056 absolute error = 3.275157922644212e-15 relative error = 7.630576770206157e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y[1] (closed_form) = 0.4292085409175339 y[1] (numeric) = 0.4292085409175306 absolute error = 3.33066907387547e-15 relative error = 7.760025154101975e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y[1] (closed_form) = 0.4292051721969075 y[1] (numeric) = 0.4292051721969042 absolute error = 3.219646771412954e-15 relative error = 7.501416525185464e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y[1] (closed_form) = 0.4292038829417326 y[1] (numeric) = 0.4292038829417293 absolute error = 3.275157922644212e-15 relative error = 7.630774214334955e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999938 y[1] (closed_form) = 0.4292036732892668 y[1] (numeric) = 0.4292036732892634 absolute error = 3.386180225106727e-15 relative error = 7.889448380430267e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999937 y[1] (closed_form) = 0.4292035432688082 y[1] (numeric) = 0.429203543268805 absolute error = 3.164135620181696e-15 relative error = 7.372109736288949e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999936 y[1] (closed_form) = 0.4292024929016927 y[1] (numeric) = 0.4292024929016893 absolute error = 3.386180225106727e-15 relative error = 7.889470077897055e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999935 y[1] (closed_form) = 0.4291995223012888 y[1] (numeric) = 0.4291995223012856 absolute error = 3.219646771412954e-15 relative error = 7.501515272313914e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999933 y[1] (closed_form) = 0.4291936317729876 y[1] (numeric) = 0.4291936317729845 absolute error = 3.164135620181696e-15 relative error = 7.372279982605369e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999932 y[1] (closed_form) = 0.4291838219141704 y[1] (numeric) = 0.4291838219141674 absolute error = 2.997602166487923e-15 relative error = 6.984424886097858e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999931 y[1] (closed_form) = 0.4291690937141486 y[1] (numeric) = 0.4291690937141452 absolute error = 3.33066907387547e-15 relative error = 7.760738419094754e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63999999999993 y[1] (closed_form) = 0.4291484486540622 y[1] (numeric) = 0.4291484486540591 absolute error = 3.108624468950438e-15 relative error = 7.243704314206456e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999929 y[1] (closed_form) = 0.4291208888067344 y[1] (numeric) = 0.429120888806731 absolute error = 3.33066907387547e-15 relative error = 7.761610214634697e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999928 y[1] (closed_form) = 0.4290854169364595 y[1] (numeric) = 0.4290854169364561 absolute error = 3.441691376337985e-15 relative error = 8.020993584239296e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999927 y[1] (closed_form) = 0.4290410365987285 y[1] (numeric) = 0.4290410365987253 absolute error = 3.219646771412954e-15 relative error = 7.504286296101345e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999926 y[1] (closed_form) = 0.4289867522398716 y[1] (numeric) = 0.4289867522398685 absolute error = 3.108624468950438e-15 relative error = 7.246434657292691e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999925 y[1] (closed_form) = 0.4289215692966126 y[1] (numeric) = 0.4289215692966096 absolute error = 2.997602166487923e-15 relative error = 6.988695325823047e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999924 y[1] (closed_form) = 0.4288444942955254 y[1] (numeric) = 0.4288444942955221 absolute error = 3.275157922644212e-15 relative error = 7.637169104909236e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999922 y[1] (closed_form) = 0.4287545349523783 y[1] (numeric) = 0.4287545349523753 absolute error = 2.997602166487923e-15 relative error = 6.991417984233954e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999921 y[1] (closed_form) = 0.4286507002713644 y[1] (numeric) = 0.4286507002713614 absolute error = 2.997602166487923e-15 relative error = 6.993111558176019e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72999999999992 y[1] (closed_form) = 0.4285320006441988 y[1] (numeric) = 0.4285320006441957 absolute error = 3.164135620181696e-15 relative error = 7.383662399599445e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999919 y[1] (closed_form) = 0.428397447949078 y[1] (numeric) = 0.4283974479490751 absolute error = 2.886579864025407e-15 relative error = 6.738088375280248e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999918 y[1] (closed_form) = 0.4282460556494934 y[1] (numeric) = 0.4282460556494903 absolute error = 3.108624468950438e-15 relative error = 7.25896812811454e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999917 y[1] (closed_form) = 0.4280768388928815 y[1] (numeric) = 0.4280768388928785 absolute error = 3.05311331771918e-15 relative error = 7.132161893213678e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999916 y[1] (closed_form) = 0.4278888146091104 y[1] (numeric) = 0.4278888146091074 absolute error = 2.997602166487923e-15 relative error = 7.005563277521812e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999915 y[1] (closed_form) = 0.4276810016087855 y[1] (numeric) = 0.4276810016087824 absolute error = 3.164135620181696e-15 relative error = 7.398354400310817e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999914 y[1] (closed_form) = 0.4274524206813666 y[1] (numeric) = 0.4274524206813633 absolute error = 3.275157922644212e-15 relative error = 7.662040882640349e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999913 y[1] (closed_form) = 0.4272020946930895 y[1] (numeric) = 0.427202094693086 absolute error = 3.497202527569243e-15 relative error = 8.186295364683789e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999911 y[1] (closed_form) = 0.4269290486846773 y[1] (numeric) = 0.4269290486846738 absolute error = 3.497202527569243e-15 relative error = 8.191530977673573e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81999999999991 y[1] (closed_form) = 0.4266323099688367 y[1] (numeric) = 0.4266323099688333 absolute error = 3.441691376337985e-15 relative error = 8.067113755611672e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.829999999999909 y[1] (closed_form) = 0.4263109082275258 y[1] (numeric) = 0.4263109082275223 absolute error = 3.552713678800501e-15 relative error = 8.333621331838844e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999908 y[1] (closed_form) = 0.4259638756089836 y[1] (numeric) = 0.4259638756089801 absolute error = 3.497202527569243e-15 relative error = 8.210091812526195e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.849999999999907 y[1] (closed_form) = 0.4255902468245163 y[1] (numeric) = 0.4255902468245129 absolute error = 3.441691376337985e-15 relative error = 8.08686618647325e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.859999999999906 y[1] (closed_form) = 0.4251890592450247 y[1] (numeric) = 0.425189059245021 absolute error = 3.719247132494274e-15 relative error = 8.747278537924409e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999905 y[1] (closed_form) = 0.4247593529972653 y[1] (numeric) = 0.4247593529972615 absolute error = 3.83026943495679e-15 relative error = 9.017504636281547e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999904 y[1] (closed_form) = 0.4243001710598377 y[1] (numeric) = 0.4243001710598341 absolute error = 3.663735981263017e-15 relative error = 8.634773754890453e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999903 y[1] (closed_form) = 0.4238105593588875 y[1] (numeric) = 0.4238105593588833 absolute error = 4.107825191113079e-15 relative error = 9.692597554263691e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999902 y[1] (closed_form) = 0.4232895668635088 y[1] (numeric) = 0.4232895668635046 absolute error = 4.218847493575595e-15 relative error = 9.966811903341753e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9099999999999 y[1] (closed_form) = 0.422736245680851 y[1] (numeric) = 0.4227362456808467 absolute error = 4.274358644806853e-15 relative error = 1.011117141829807e-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) = 0.4221496511509042 y[1] (numeric) = 0.4221496511509001 absolute error = 4.052314039881821e-15 relative error = 9.599235789568985e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999898 y[1] (closed_form) = 0.4215288419409664 y[1] (numeric) = 0.4215288419409621 absolute error = 4.274358644806853e-15 relative error = 1.014013329461679e-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) = 0.4208728801397743 y[1] (numeric) = 0.4208728801397698 absolute error = 4.496403249731884e-15 relative error = 1.068351861549882e-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) = 0.4201808313512945 y[1] (numeric) = 0.4201808313512899 absolute error = 4.551914400963142e-15 relative error = 1.083322717584299e-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) = 0.4194517647881624 y[1] (numeric) = 0.4194517647881579 absolute error = 4.440892098500626e-15 relative error = 1.058737254507304e-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) = 0.4186847533647604 y[1] (numeric) = 0.4186847533647559 absolute error = 4.551914400963142e-15 relative error = 1.087193733323623e-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) = 0.4178788737899251 y[1] (numeric) = 0.4178788737899202 absolute error = 4.829470157119431e-15 relative error = 1.155710532413105e-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) = 0.4170332066592748 y[1] (numeric) = 0.4170332066592702 absolute error = 4.6074255521944e-15 relative error = 1.104810235401414e-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) = 0.4161468365471521 y[1] (numeric) = 0.4161468365471475 absolute error = 4.662936703425657e-15 relative error = 1.120502739397207e-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) = 0.415218852098163 y[1] (numeric) = 0.415218852098158 absolute error = 5.051514762044462e-15 relative error = 1.216590898153685e-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) = 0.4142483461183115 y[1] (numeric) = 0.4142483461183064 absolute error = 5.10702591327572e-15 relative error = 1.232841593969123e-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) = 0.4132344156657206 y[1] (numeric) = 0.4132344156657156 absolute error = 5.051514762044462e-15 relative error = 1.222433217210738e-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) = 0.4121761621409243 y[1] (numeric) = 0.412176162140919 absolute error = 5.384581669432009e-15 relative error = 1.306378719590048e-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) = 0.411072691376726 y[1] (numeric) = 0.4110726913767204 absolute error = 5.551115123125783e-15 relative error = 1.35039744540911e-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) = 0.4099231137276158 y[1] (numeric) = 0.4099231137276102 absolute error = 5.606626274357041e-15 relative error = 1.367726309300654e-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) = 0.4087265441587342 y[1] (numeric) = 0.4087265441587286 absolute error = 5.662137425588298e-15 relative error = 1.385311892879982e-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) = 0.4074821023343742 y[1] (numeric) = 0.4074821023343685 absolute error = 5.662137425588298e-15 relative error = 1.389542606448522e-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) = 0.4061889127060145 y[1] (numeric) = 0.4061889127060087 absolute error = 5.828670879282072e-15 relative error = 1.434965528835264e-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) = 0.4048461045998737 y[1] (numeric) = 0.4048461045998678 absolute error = 5.88418203051333e-15 relative error = 1.453436741432627e-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) = 0.4034528123039767 y[1] (numeric) = 0.4034528123039706 absolute error = 6.050715484207103e-15 relative error = 1.499733128554391e-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) = 0.4020081751547253 y[1] (numeric) = 0.4020081751547189 absolute error = 6.439293542825908e-15 relative error = 1.601781739972712e-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) = 0.4005113376229636 y[1] (numeric) = 0.4005113376229571 absolute error = 6.550315845288424e-15 relative error = 1.635488244643603e-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) = 0.3989614493995308 y[1] (numeric) = 0.3989614493995244 absolute error = 6.439293542825908e-15 relative error = 1.614013973660253e-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) = 0.3973576654802917 y[1] (numeric) = 0.3973576654802847 absolute error = 7.049916206369744e-15 relative error = 1.774199120545067e-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) = 0.3956991462506338 y[1] (numeric) = 0.3956991462506269 absolute error = 6.938893903907228e-15 relative error = 1.753578184248133e-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) = 0.3939850575694326 y[1] (numeric) = 0.3939850575694252 absolute error = 7.382983113757291e-15 relative error = 1.873924650671854e-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) = 0.39221457085246 y[1] (numeric) = 0.3922145708524525 absolute error = 7.549516567451064e-15 relative error = 1.924843473061835e-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) = 0.3903868631552463 y[1] (numeric) = 0.3903868631552385 absolute error = 7.771561172376096e-15 relative error = 1.990733271494731e-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) = 0.388501117255371 y[1] (numeric) = 0.388501117255363 absolute error = 7.938094626069869e-15 relative error = 2.04326172396873e-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) = 0.3865565217341862 y[1] (numeric) = 0.386556521734178 absolute error = 8.215650382226158e-15 relative error = 2.125342587771838e-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) = 0.3845522710579568 y[1] (numeric) = 0.3845522710579484 absolute error = 8.382183835919932e-15 relative error = 2.179725479935245e-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) = 0.3824875656584132 y[1] (numeric) = 0.3824875656584049 absolute error = 8.326672684688674e-15 relative error = 2.176978660823956e-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) = 0.3803616120127087 y[1] (numeric) = 0.3803616120127002 absolute error = 8.43769498715119e-15 relative error = 2.21833505818386e-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) = 0.3781736227227697 y[1] (numeric) = 0.3781736227227604 absolute error = 9.214851104388799e-15 relative error = 2.436672086763701e-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) = 0.3759228165940343 y[1] (numeric) = 0.3759228165940248 absolute error = 9.492406860545088e-15 relative error = 2.525094631538715e-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) = 0.3736084187135731 y[1] (numeric) = 0.3736084187135636 absolute error = 9.492406860545088e-15 relative error = 2.54073687451418e-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) = 0.3712296605275793 y[1] (numeric) = 0.3712296605275697 absolute error = 9.658940314238862e-15 relative error = 2.601877312419459e-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) = 0.3687857799182228 y[1] (numeric) = 0.3687857799182126 absolute error = 1.021405182655144e-14 relative error = 2.7696436204282e-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) = 0.3662760212798606 y[1] (numeric) = 0.3662760212798501 absolute error = 1.049160758270773e-14 relative error = 2.864399243512423e-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) = 0.3636996355945983 y[1] (numeric) = 0.3636996355945877 absolute error = 1.060262988517024e-14 relative error = 2.915215977007076e-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) = 0.3610558805071911 y[1] (numeric) = 0.3610558805071803 absolute error = 1.071365218763276e-14 relative error = 2.967311368141359e-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) = 0.3583440203992785 y[1] (numeric) = 0.3583440203992671 absolute error = 1.137978600240785e-14 relative error = 3.175659521185293e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999853 y[1] (closed_form) = 0.3555633264629434 y[1] (numeric) = 0.3555633264629319 absolute error = 1.149080830487037e-14 relative error = 3.231719204333615e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999852 y[1] (closed_form) = 0.3527130767735964 y[1] (numeric) = 0.3527130767735847 absolute error = 1.176836406102666e-14 relative error = 3.336526155672043e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.359999999999851 y[1] (closed_form) = 0.3497925563621647 y[1] (numeric) = 0.3497925563621523 absolute error = 1.232347557333924e-14 relative error = 3.523081137432748e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36999999999985 y[1] (closed_form) = 0.3468010572865881 y[1] (numeric) = 0.3468010572865757 absolute error = 1.23789867245705e-14 relative error = 3.569477792664513e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999849 y[1] (closed_form) = 0.3437378787026155 y[1] (numeric) = 0.3437378787026025 absolute error = 1.298960938811433e-14 relative error = 3.778928710778564e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999848 y[1] (closed_form) = 0.3406023269338854 y[1] (numeric) = 0.3406023269338722 absolute error = 1.321165399303936e-14 relative error = 3.878908905870126e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999847 y[1] (closed_form) = 0.3373937155412952 y[1] (numeric) = 0.3373937155412816 absolute error = 1.360023205165817e-14 relative error = 4.030967805621019e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999846 y[1] (closed_form) = 0.3341113653916437 y[1] (numeric) = 0.3341113653916297 absolute error = 1.398881011027697e-14 relative error = 4.186870474723109e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999844 y[1] (closed_form) = 0.3307546047255436 y[1] (numeric) = 0.3307546047255293 absolute error = 1.432187701766452e-14 relative error = 4.330061263863174e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999843 y[1] (closed_form) = 0.3273227692245979 y[1] (numeric) = 0.3273227692245833 absolute error = 1.465494392505207e-14 relative error = 4.477214939788174e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999842 y[1] (closed_form) = 0.3238152020778298 y[1] (numeric) = 0.3238152020778149 absolute error = 1.48769885299771e-14 relative error = 4.594283540277203e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.449999999999841 y[1] (closed_form) = 0.3202312540473651 y[1] (numeric) = 0.3202312540473493 absolute error = 1.576516694967722e-14 relative error = 4.92305693164647e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45999999999984 y[1] (closed_form) = 0.3165702835333524 y[1] (numeric) = 0.3165702835333363 absolute error = 1.609823385706477e-14 relative error = 5.085200568223497e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999839 y[1] (closed_form) = 0.3128316566381262 y[1] (numeric) = 0.3128316566381097 absolute error = 1.648681191568357e-14 relative error = 5.270186557479699e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999838 y[1] (closed_form) = 0.3090147472295937 y[1] (numeric) = 0.3090147472295769 absolute error = 1.670885652060861e-14 relative error = 5.407138872952933e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999837 y[1] (closed_form) = 0.3051189370038485 y[1] (numeric) = 0.3051189370038313 absolute error = 1.720845688168993e-14 relative error = 5.639917682812612e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999836 y[1] (closed_form) = 0.3011436155469998 y[1] (numeric) = 0.3011436155469822 absolute error = 1.759703494030873e-14 relative error = 5.843402958533698e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999835 y[1] (closed_form) = 0.297088180396214 y[1] (numeric) = 0.2970881803961958 absolute error = 1.820765760385257e-14 relative error = 6.128704810662539e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999833 y[1] (closed_form) = 0.2929520370999597 y[1] (numeric) = 0.292952037099941 absolute error = 1.865174681370263e-14 relative error = 6.366826118822438e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999832 y[1] (closed_form) = 0.2887345992774533 y[1] (numeric) = 0.2887345992774341 absolute error = 1.915134717478395e-14 relative error = 6.632854954934195e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999831 y[1] (closed_form) = 0.2844352886772956 y[1] (numeric) = 0.284435288677276 absolute error = 1.959543638463401e-14 relative error = 6.889242356586035e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54999999999983 y[1] (closed_form) = 0.2800535352352975 y[1] (numeric) = 0.2800535352352774 absolute error = 2.015054789694659e-14 relative error = 7.195248537040017e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999829 y[1] (closed_form) = 0.2755887771314844 y[1] (numeric) = 0.2755887771314641 absolute error = 2.031708135064036e-14 relative error = 7.372245547193313e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999828 y[1] (closed_form) = 0.2710404608462804 y[1] (numeric) = 0.2710404608462595 absolute error = 2.09277040141842e-14 relative error = 7.721247207461498e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999827 y[1] (closed_form) = 0.2664080412158567 y[1] (numeric) = 0.2664080412158349 absolute error = 2.176037128265307e-14 relative error = 8.168060987701855e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999826 y[1] (closed_form) = 0.2616909814866486 y[1] (numeric) = 0.2616909814866266 absolute error = 2.203792703880936e-14 relative error = 8.421355185269817e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999825 y[1] (closed_form) = 0.2568887533690321 y[1] (numeric) = 0.2568887533690096 absolute error = 2.248201624865942e-14 relative error = 8.751654540657531e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999824 y[1] (closed_form) = 0.2520008370901508 y[1] (numeric) = 0.2520008370901274 absolute error = 2.337019466835955e-14 relative error = 9.273855967390733e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999822 y[1] (closed_form) = 0.2470267214458914 y[1] (numeric) = 0.2470267214458678 absolute error = 2.361999484890021e-14 relative error = 9.561716526312686e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999821 y[1] (closed_form) = 0.2419659038520079 y[1] (numeric) = 0.2419659038519835 absolute error = 2.434163981490656e-14 relative error = 1.00599462268843e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999982 y[1] (closed_form) = 0.2368178903943745 y[1] (numeric) = 0.2368178903943499 absolute error = 2.461919557106285e-14 relative error = 1.039583433923186e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999819 y[1] (closed_form) = 0.2315821958783815 y[1] (numeric) = 0.231582195878356 absolute error = 2.550737399076297e-14 relative error = 1.101439335351951e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999818 y[1] (closed_form) = 0.2262583438774497 y[1] (numeric) = 0.2262583438774236 absolute error = 2.606248550307555e-14 relative error = 1.151890580317869e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999817 y[1] (closed_form) = 0.2208458667806763 y[1] (numeric) = 0.2208458667806498 absolute error = 2.653433028854124e-14 relative error = 1.201486388463529e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999816 y[1] (closed_form) = 0.2153443058395941 y[1] (numeric) = 0.2153443058395669 absolute error = 2.714495295208508e-14 relative error = 1.260537298455658e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999815 y[1] (closed_form) = 0.2097532112140459 y[1] (numeric) = 0.2097532112140179 absolute error = 2.794986464493832e-14 relative error = 1.332511883044138e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999814 y[1] (closed_form) = 0.2040721420171678 y[1] (numeric) = 0.2040721420171394 absolute error = 2.844946500601964e-14 relative error = 1.394088616153511e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999813 y[1] (closed_form) = 0.1983006663594793 y[1] (numeric) = 0.1983006663594501 absolute error = 2.922662112325725e-14 relative error = 1.473853903762242e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999811 y[1] (closed_form) = 0.1924383613920693 y[1] (numeric) = 0.1924383613920396 absolute error = 2.969846590872294e-14 relative error = 1.543271606237386e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999981 y[1] (closed_form) = 0.186484813348883 y[1] (numeric) = 0.1864848133488527 absolute error = 3.03368441478824e-14 relative error = 1.626772904618622e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999809 y[1] (closed_form) = 0.1804396175880969 y[1] (numeric) = 0.1804396175880657 absolute error = 3.116951141635127e-14 relative error = 1.727420609342249e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999808 y[1] (closed_form) = 0.1743023786325821 y[1] (numeric) = 0.1743023786325505 absolute error = 3.166911177743259e-14 relative error = 1.816906460249116e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999807 y[1] (closed_form) = 0.1680727102094539 y[1] (numeric) = 0.1680727102094214 absolute error = 3.255729019713272e-14 relative error = 1.937095567540946e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999806 y[1] (closed_form) = 0.1617502352886957 y[1] (numeric) = 0.1617502352886627 absolute error = 3.302913498259841e-14 relative error = 2.04198373644695e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999805 y[1] (closed_form) = 0.155334586120865 y[1] (numeric) = 0.1553345861208311 absolute error = 3.394506897791416e-14 relative error = 2.185287245140736e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999804 y[1] (closed_form) = 0.148825404273865 y[1] (numeric) = 0.1488254042738303 absolute error = 3.472222509515177e-14 relative error = 2.333084547262962e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999803 y[1] (closed_form) = 0.1422223406687895 y[1] (numeric) = 0.1422223406687541 absolute error = 3.538835890992686e-14 relative error = 2.488241913578124e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999802 y[1] (closed_form) = 0.1355250556148295 y[1] (numeric) = 0.1355250556147937 absolute error = 3.583244811977693e-14 relative error = 2.643972212903194e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8199999999998 y[1] (closed_form) = 0.1287332188432435 y[1] (numeric) = 0.1287332188432067 absolute error = 3.677613769070831e-14 relative error = 2.856771392898212e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999799 y[1] (closed_form) = 0.1218465095403816 y[1] (numeric) = 0.1218465095403439 absolute error = 3.766431611040844e-14 relative error = 3.091128030871166e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999798 y[1] (closed_form) = 0.1148646163797684 y[1] (numeric) = 0.1148646163797298 absolute error = 3.858025010572419e-14 relative error = 3.358758451616567e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999797 y[1] (closed_form) = 0.1077872375532349 y[1] (numeric) = 0.1077872375531957 absolute error = 3.923250613269147e-14 relative error = 3.639809964822131e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999796 y[1] (closed_form) = 0.1006140808010993 y[1] (numeric) = 0.1006140808010597 absolute error = 3.967659534254153e-14 relative error = 3.943443604178712e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999795 y[1] (closed_form) = 0.09334486344139314 y[1] (numeric) = 0.09334486344135259 absolute error = 4.055089597443384e-14 relative error = 4.344202185254023e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999794 y[1] (closed_form) = 0.08597931239812784 y[1] (numeric) = 0.08597931239808612 absolute error = 4.171663015029026e-14 relative error = 4.85193809844874e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999793 y[1] (closed_form) = 0.078517164228602 y[1] (numeric) = 0.07851716422855994 absolute error = 4.206357484548562e-14 relative error = 5.357245802079391e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999792 y[1] (closed_form) = 0.07095816514974906 y[1] (numeric) = 0.07095816514970586 absolute error = 4.32015534457264e-14 relative error = 6.088313213081888e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.909999999999791 y[1] (closed_form) = 0.06330207106350993 y[1] (numeric) = 0.06330207106346597 absolute error = 4.39648317751562e-14 relative error = 6.945243818491658e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999789 y[1] (closed_form) = 0.05554864758124722 y[1] (numeric) = 0.05554864758120209 absolute error = 4.513056595101261e-14 relative error = 8.124512101757871e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999788 y[1] (closed_form) = 0.04769767004718029 y[1] (numeric) = 0.04769767004713463 absolute error = 4.565792188770956e-14 relative error = 9.572358952239575e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999787 y[1] (closed_form) = 0.03974892356085435 y[1] (numeric) = 0.03974892356080784 absolute error = 4.651834473179406e-14 relative error = 1.170304515556904e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999786 y[1] (closed_form) = 0.03170220299862692 y[1] (numeric) = 0.0317022029985797 absolute error = 4.721917301608869e-14 relative error = 1.489460307163318e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999785 y[1] (closed_form) = 0.0235573130341824 y[1] (numeric) = 0.02355731303413417 absolute error = 4.823225152605914e-14 relative error = 2.047442824063705e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999784 y[1] (closed_form) = 0.0153140681580628 y[1] (numeric) = 0.01531406815801362 absolute error = 4.918114526741846e-14 relative error = 3.211501004161639e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999783 y[1] (closed_form) = 0.006972292696219906 y[1] (numeric) = 0.006972292696169607 absolute error = 5.029917454768551e-14 relative error = 7.214151318540554e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999782 y[1] (closed_form) = -0.001468179172418704 y[1] (numeric) = -0.001468179172469823 absolute error = 5.111904823051905e-14 relative error = 3.481799033172813e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.999999999999781 y[1] (closed_form) = -0.01000750339936607 y[1] (numeric) = -0.01000750339941821 absolute error = 5.213711407048294e-14 relative error = 5.209802284332533e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.00999999999978 y[1] (closed_form) = -0.01864582605098253 y[1] (numeric) = -0.01864582605103562 absolute error = 5.309641615269811e-14 relative error = 2.847630134890175e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999778 y[1] (closed_form) = -0.0273832832938683 y[1] (numeric) = -0.02738328329392219 absolute error = 5.388745005774354e-14 relative error = 1.967895868418747e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999777 y[1] (closed_form) = -0.03622000138124637 y[1] (numeric) = -0.03622000138130149 absolute error = 5.511563427873512e-14 relative error = 1.521690562587122e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999776 y[1] (closed_form) = -0.0451560966403397 y[1] (numeric) = -0.04515609664039539 absolute error = 5.568462357885551e-14 relative error = 1.23315848184075e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999775 y[1] (closed_form) = -0.05419167546073433 y[1] (numeric) = -0.0541916754607914 absolute error = 5.706546346573305e-14 relative error = 1.05303006376101e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999774 y[1] (closed_form) = -0.06332683428374608 y[1] (numeric) = -0.0633268342838038 absolute error = 5.771771949270033e-14 relative error = 9.114259404486697e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999773 y[1] (closed_form) = -0.0725616595927705 y[1] (numeric) = -0.07256165959282958 absolute error = 5.907774269786614e-14 relative error = 8.141729810125816e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999772 y[1] (closed_form) = -0.08189622790464046 y[1] (numeric) = -0.08189622790470021 absolute error = 5.974387651264124e-14 relative error = 7.295070608405394e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.089999999999771 y[1] (closed_form) = -0.09133060576196872 y[1] (numeric) = -0.09133060576202998 absolute error = 6.125655538369301e-14 relative error = 6.707122423269973e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09999999999977 y[1] (closed_form) = -0.1008648497264995 y[1] (numeric) = -0.1008648497265618 absolute error = 6.235290062051035e-14 relative error = 6.181826552023193e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.109999999999769 y[1] (closed_form) = -0.1104990063734479 y[1] (numeric) = -0.1104990063735111 absolute error = 6.317169010117141e-14 relative error = 5.716946439108533e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999767 y[1] (closed_form) = -0.1202331122868441 y[1] (numeric) = -0.1202331122869083 absolute error = 6.417089082333405e-14 relative error = 5.337206165822228e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.129999999999766 y[1] (closed_form) = -0.1300671940558753 y[1] (numeric) = -0.1300671940559404 absolute error = 6.50868248186498e-14 relative error = 5.004092330206592e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999765 y[1] (closed_form) = -0.140001268272226 y[1] (numeric) = -0.1400012682722924 absolute error = 6.636358129696873e-14 relative error = 4.740212864924038e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999764 y[1] (closed_form) = -0.1500353415284201 y[1] (numeric) = -0.1500353415284876 absolute error = 6.750155989720952e-14 relative error = 4.499043972544507e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.159999999999763 y[1] (closed_form) = -0.1601694104171605 y[1] (numeric) = -0.1601694104172289 absolute error = 6.838973831690964e-14 relative error = 4.269837676169806e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.169999999999762 y[1] (closed_form) = -0.1704034615316692 y[1] (numeric) = -0.170403461531739 absolute error = 6.980527267330672e-14 relative error = 4.09647034431478e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.179999999999761 y[1] (closed_form) = -0.1807374714670305 y[1] (numeric) = -0.1807374714671016 absolute error = 7.113754030285691e-14 relative error = 3.935959694768309e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18999999999976 y[1] (closed_form) = -0.1911714068225292 y[1] (numeric) = -0.1911714068226014 absolute error = 7.224776332748206e-14 relative error = 3.779213875564146e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999759 y[1] (closed_form) = -0.2017052242049915 y[1] (numeric) = -0.2017052242050646 absolute error = 7.313594174718219e-14 relative error = 3.625882375404153e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999757 y[1] (closed_form) = -0.2123388702331233 y[1] (numeric) = -0.2123388702331977 absolute error = 7.446820937673237e-14 relative error = 3.507045568009992e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999756 y[1] (closed_form) = -0.2230722815428505 y[1] (numeric) = -0.223072281542926 absolute error = 7.543965452327939e-14 relative error = 3.381847982255384e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999755 y[1] (closed_form) = -0.233905384793653 y[1] (numeric) = -0.2339053847937295 absolute error = 7.657763312352017e-14 relative error = 3.273872176610023e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999754 y[1] (closed_form) = -0.2448380966758998 y[1] (numeric) = -0.2448380966759777 absolute error = 7.78543896018391e-14 relative error = 3.17983151555444e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999753 y[1] (closed_form) = -0.2558703239191802 y[1] (numeric) = -0.2558703239192594 absolute error = 7.921441280700492e-14 relative error = 3.095881210203407e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999752 y[1] (closed_form) = -0.2670019633016301 y[1] (numeric) = -0.2670019633017105 absolute error = 8.043565813409259e-14 relative error = 3.01254931384999e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.269999999999751 y[1] (closed_form) = -0.2782329016602541 y[1] (numeric) = -0.2782329016603358 absolute error = 8.176792576364278e-14 relative error = 2.938830212951894e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27999999999975 y[1] (closed_form) = -0.2895630159022424 y[1] (numeric) = -0.2895630159023252 absolute error = 8.282263763703668e-14 relative error = 2.860262985553304e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999749 y[1] (closed_form) = -0.3009921730172787 y[1] (numeric) = -0.300992173017363 absolute error = 8.432143872028064e-14 relative error = 2.801449548505041e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999748 y[1] (closed_form) = -0.312520230090843 y[1] (numeric) = -0.3125202300909285 absolute error = 8.554268404736831e-14 relative error = 2.737188694072793e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999746 y[1] (closed_form) = -0.3241470343185009 y[1] (numeric) = -0.3241470343185878 absolute error = 8.693046282814976e-14 relative error = 2.681821939568742e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999745 y[1] (closed_form) = -0.3358724230211858 y[1] (numeric) = -0.3358724230212739 absolute error = 8.809619700400617e-14 relative error = 2.622906525387746e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999744 y[1] (closed_form) = -0.3476962236614645 y[1] (numeric) = -0.3476962236615542 absolute error = 8.976153154094391e-14 relative error = 2.58160789311133e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999743 y[1] (closed_form) = -0.3596182538607939 y[1] (numeric) = -0.3596182538608846 absolute error = 9.070522111187529e-14 relative error = 2.522264099168524e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999742 y[1] (closed_form) = -0.3716383214177545 y[1] (numeric) = -0.3716383214178468 absolute error = 9.220402219511925e-14 relative error = 2.481014924493584e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.359999999999741 y[1] (closed_form) = -0.383756224327275 y[1] (numeric) = -0.3837562243273686 absolute error = 9.35918009759007e-14 relative error = 2.438834735253278e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36999999999974 y[1] (closed_form) = -0.3959717508008289 y[1] (numeric) = -0.3959717508009237 absolute error = 9.481304630298837e-14 relative error = 2.3944396566481e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999739 y[1] (closed_form) = -0.4082846792876151 y[1] (numeric) = -0.4082846792877112 absolute error = 9.60898027813073e-14 relative error = 2.353500085993114e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999738 y[1] (closed_form) = -0.4206947784967126 y[1] (numeric) = -0.4206947784968099 absolute error = 9.736655925962623e-14 relative error = 2.314422812841902e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999737 y[1] (closed_form) = -0.4332018074202084 y[1] (numeric) = -0.4332018074203071 absolute error = 9.869882688917642e-14 relative error = 2.278356765798023e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y[1] (closed_form) = -0.4458055153572995 y[1] (numeric) = -0.4458055153573999 absolute error = 1.003641614261142e-13 relative error = 2.251299231811328e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999734 y[1] (closed_form) = -0.4585056419393627 y[1] (numeric) = -0.4585056419394641 absolute error = 1.01418873299508e-13 relative error = 2.211943845893191e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999733 y[1] (closed_form) = -0.4713019171559889 y[1] (numeric) = -0.4713019171560918 absolute error = 1.028621632315208e-13 relative error = 2.182511029283083e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999732 y[1] (closed_form) = -0.4841940613819871 y[1] (numeric) = -0.4841940613820914 absolute error = 1.043609643147647e-13 relative error = 2.155354074705038e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.449999999999731 y[1] (closed_form) = -0.4971817854053446 y[1] (numeric) = -0.4971817854054505 absolute error = 1.059152765492399e-13 relative error = 2.130312888733219e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45999999999973 y[1] (closed_form) = -0.5102647904561493 y[1] (numeric) = -0.5102647904562566 absolute error = 1.073585664812526e-13 relative error = 2.103977552228909e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999729 y[1] (closed_form) = -0.5234427682364649 y[1] (numeric) = -0.5234427682365738 absolute error = 1.089128787157279e-13 relative error = 2.080702711447654e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999728 y[1] (closed_form) = -0.5367154009511617 y[1] (numeric) = -0.5367154009512719 absolute error = 1.10245146345278e-13 relative error = 2.05407085673157e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999727 y[1] (closed_form) = -0.5500823613396952 y[1] (numeric) = -0.550082361339807 absolute error = 1.117994585797533e-13 relative error = 2.032413079151854e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999726 y[1] (closed_form) = -0.5635433127088332 y[1] (numeric) = -0.5635433127089462 absolute error = 1.130207039068409e-13 relative error = 2.005537131894519e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y[1] (closed_form) = -0.5770979089663215 y[1] (numeric) = -0.5770979089664365 absolute error = 1.150191053511662e-13 relative error = 1.993060511294948e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999723 y[1] (closed_form) = -0.5907457946554979 y[1] (numeric) = -0.5907457946556144 absolute error = 1.164623952831789e-13 relative error = 1.971446878451258e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999722 y[1] (closed_form) = -0.6044866049908326 y[1] (numeric) = -0.6044866049909506 absolute error = 1.180167075176541e-13 relative error = 1.952346115584214e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.539999999999721 y[1] (closed_form) = -0.6183199658944094 y[1] (numeric) = -0.6183199658945291 absolute error = 1.196820420545919e-13 relative error = 1.935600476388789e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54999999999972 y[1] (closed_form) = -0.6322454940333331 y[1] (numeric) = -0.6322454940334541 absolute error = 1.210143096841421e-13 relative error = 1.914039891564051e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999719 y[1] (closed_form) = -0.6462627968580601 y[1] (numeric) = -0.6462627968581827 absolute error = 1.225686219186173e-13 relative error = 1.89657554967592e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999718 y[1] (closed_form) = -0.6603714726416561 y[1] (numeric) = -0.6603714726417803 absolute error = 1.24233956455555e-13 relative error = 1.881273822422812e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999717 y[1] (closed_form) = -0.6745711105199668 y[1] (numeric) = -0.6745711105200923 absolute error = 1.255662240851052e-13 relative error = 1.861423089825436e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999716 y[1] (closed_form) = -0.6888612905327038 y[1] (numeric) = -0.688861290532831 absolute error = 1.271205363195804e-13 relative error = 1.845372037399238e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999715 y[1] (closed_form) = -0.7032415836654411 y[1] (numeric) = -0.7032415836655697 absolute error = 1.285638262515931e-13 relative error = 1.828160183325505e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y[1] (closed_form) = -0.7177115518925157 y[1] (numeric) = -0.7177115518926459 absolute error = 1.302291607885309e-13 relative error = 1.814505569056717e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999712 y[1] (closed_form) = -0.7322707482208299 y[1] (numeric) = -0.7322707482209615 absolute error = 1.315614284180811e-13 relative error = 1.796622748317215e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.629999999999711 y[1] (closed_form) = -0.7469187167345499 y[1] (numeric) = -0.7469187167346831 absolute error = 1.332267629550188e-13 relative error = 1.783684890605931e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63999999999971 y[1] (closed_form) = -0.7616549926406977 y[1] (numeric) = -0.7616549926408326 absolute error = 1.348920974919565e-13 relative error = 1.771039365530561e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999709 y[1] (closed_form) = -0.7764791023156294 y[1] (numeric) = -0.7764791023157662 absolute error = 1.367794766338193e-13 relative error = 1.761534550329985e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999708 y[1] (closed_form) = -0.7913905633523983 y[1] (numeric) = -0.7913905633525365 absolute error = 1.38222766565832e-13 relative error = 1.746580929399872e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999707 y[1] (closed_form) = -0.8063888846089928 y[1] (numeric) = -0.8063888846091327 absolute error = 1.398881011027697e-13 relative error = 1.734747387677592e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999706 y[1] (closed_form) = -0.821473566257453 y[1] (numeric) = -0.8214735662575945 absolute error = 1.414424133372449e-13 relative error = 1.72181332604093e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999705 y[1] (closed_form) = -0.8366440998338511 y[1] (numeric) = -0.8366440998339942 absolute error = 1.431077478741827e-13 relative error = 1.710497305874773e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999704 y[1] (closed_form) = -0.8518999682891382 y[1] (numeric) = -0.8518999682892829 absolute error = 1.447730824111204e-13 relative error = 1.699414107290868e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999702 y[1] (closed_form) = -0.8672406460408486 y[1] (numeric) = -0.867240646040995 absolute error = 1.464384169480581e-13 relative error = 1.688555738439877e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.719999999999701 y[1] (closed_form) = -0.8826655990256578 y[1] (numeric) = -0.8826655990258059 absolute error = 1.481037514849959e-13 relative error = 1.677914621896245e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7299999999997 y[1] (closed_form) = -0.898174284752788 y[1] (numeric) = -0.8981742847529378 absolute error = 1.497690860219336e-13 relative error = 1.667483567102523e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999699 y[1] (closed_form) = -0.9137661523582574 y[1] (numeric) = -0.9137661523584085 absolute error = 1.511013536514838e-13 relative error = 1.653610754365543e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999698 y[1] (closed_form) = -0.9294406426599648 y[1] (numeric) = -0.9294406426601176 absolute error = 1.527666881884215e-13 relative error = 1.643641144755826e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999697 y[1] (closed_form) = -0.945197188213609 y[1] (numeric) = -0.9451971882137634 absolute error = 1.544320227253593e-13 relative error = 1.633860369572519e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999696 y[1] (closed_form) = -0.9610352133694313 y[1] (numeric) = -0.9610352133695879 absolute error = 1.565414464721471e-13 relative error = 1.628883565288996e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999695 y[1] (closed_form) = -0.9769541343297821 y[1] (numeric) = -0.9769541343299402 absolute error = 1.580957587066223e-13 relative error = 1.618251595967506e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999694 y[1] (closed_form) = -0.9929533592074971 y[1] (numeric) = -0.9929533592076569 absolute error = 1.598721155460225e-13 relative error = 1.610066717268783e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999693 y[1] (closed_form) = -1.009032288085088 y[1] (numeric) = -1.009032288085249 absolute error = 1.616484723854228e-13 relative error = 1.602014864085218e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999691 y[1] (closed_form) = -1.025190313074732 y[1] (numeric) = -1.025190313074896 absolute error = 1.638689184346731e-13 relative error = 1.598424373940877e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81999999999969 y[1] (closed_form) = -1.041426818379064 y[1] (numeric) = -1.041426818379229 absolute error = 1.656452752740734e-13 relative error = 1.59056087620149e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999689 y[1] (closed_form) = -1.057741180352748 y[1] (numeric) = -1.057741180352915 absolute error = 1.671995875085486e-13 relative error = 1.580723059801727e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999688 y[1] (closed_form) = -1.07413276756485 y[1] (numeric) = -1.074132767565019 absolute error = 1.687538997430238e-13 relative error = 1.571071145381805e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999687 y[1] (closed_form) = -1.090600940861975 y[1] (numeric) = -1.090600940862146 absolute error = 1.709743457922741e-13 relative error = 1.567707668188344e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999686 y[1] (closed_form) = -1.107145053432184 y[1] (numeric) = -1.107145053432357 absolute error = 1.725286580267493e-13 relative error = 1.558320271511896e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999685 y[1] (closed_form) = -1.123764450869672 y[1] (numeric) = -1.123764450869847 absolute error = 1.745270594710746e-13 relative error = 1.553057309616882e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999684 y[1] (closed_form) = -1.140458471240212 y[1] (numeric) = -1.140458471240389 absolute error = 1.765254609153999e-13 relative error = 1.547846461462416e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999683 y[1] (closed_form) = -1.157226445147346 y[1] (numeric) = -1.157226445147525 absolute error = 1.785238623597252e-13 relative error = 1.542687372107144e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999681 y[1] (closed_form) = -1.174067695799322 y[1] (numeric) = -1.174067695799503 absolute error = 1.807443084089755e-13 relative error = 1.539470927065429e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.90999999999968 y[1] (closed_form) = -1.190981539076777 y[1] (numeric) = -1.190981539076959 absolute error = 1.825206652483757e-13 relative error = 1.532523043051211e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999679 y[1] (closed_form) = -1.207967283601144 y[1] (numeric) = -1.207967283601328 absolute error = 1.84519066692701e-13 relative error = 1.527517087570618e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999678 y[1] (closed_form) = -1.225024230803792 y[1] (numeric) = -1.225024230803978 absolute error = 1.860733789271762e-13 relative error = 1.518936313652223e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999677 y[1] (closed_form) = -1.242151674995882 y[1] (numeric) = -1.24215167499607 absolute error = 1.882938249764265e-13 relative error = 1.515868220980749e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999676 y[1] (closed_form) = -1.259348903438934 y[1] (numeric) = -1.259348903439124 absolute error = 1.900701818158268e-13 relative error = 1.509273413402732e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999675 y[1] (closed_form) = -1.276615196416101 y[1] (numeric) = -1.276615196416293 absolute error = 1.918465386552271e-13 relative error = 1.502774988060665e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999674 y[1] (closed_form) = -1.293949827304142 y[1] (numeric) = -1.293949827304335 absolute error = 1.934008508897023e-13 relative error = 1.494654945722587e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999673 y[1] (closed_form) = -1.311352062646078 y[1] (numeric) = -1.311352062646274 absolute error = 1.960653861488026e-13 relative error = 1.49513919056319e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999672 y[1] (closed_form) = -1.328821162224545 y[1] (numeric) = -1.328821162224743 absolute error = 1.976196983832779e-13 relative error = 1.487180547700247e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99999999999967 y[1] (closed_form) = -1.346356379135809 y[1] (numeric) = -1.346356379136009 absolute error = 1.998401444325282e-13 relative error = 1.484303469195878e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999674 y[1] (closed_form) = -1.363956959864466 y[1] (numeric) = -1.36395695986466 absolute error = 1.940669847044774e-13 relative error = 1.42282337650714e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999677 y[1] (closed_form) = -1.38162214435877 y[1] (numeric) = -1.381622144358957 absolute error = 1.876276911616515e-13 relative error = 1.358024637399918e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.029999999999681 y[1] (closed_form) = -1.399351166106657 y[1] (numeric) = -1.399351166106839 absolute error = 1.816324868286756e-13 relative error = 1.297976456717597e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999684 y[1] (closed_form) = -1.417143252212395 y[1] (numeric) = -1.417143252212571 absolute error = 1.754152378907747e-13 relative error = 1.237808793267177e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999687 y[1] (closed_form) = -1.434997623473866 y[1] (numeric) = -1.434997623474036 absolute error = 1.696420781627239e-13 relative error = 1.182176718537356e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.059999999999691 y[1] (closed_form) = -1.45291349446049 y[1] (numeric) = -1.452913494460654 absolute error = 1.638689184346731e-13 relative error = 1.127864246973097e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999694 y[1] (closed_form) = -1.470890073591764 y[1] (numeric) = -1.470890073591922 absolute error = 1.580957587066223e-13 relative error = 1.074830550189033e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999697 y[1] (closed_form) = -1.488926563216421 y[1] (numeric) = -1.488926563216573 absolute error = 1.521005543736464e-13 relative error = 1.021545038763191e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.089999999999701 y[1] (closed_form) = -1.507022159692198 y[1] (numeric) = -1.507022159692344 absolute error = 1.461053500406706e-13 relative error = 9.694970249841043e-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) = -1.525176053466192 y[1] (numeric) = -1.525176053466333 absolute error = 1.403321903126198e-13 relative error = 9.201048626071313e-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) = -1.543387429155822 y[1] (numeric) = -1.543387429155956 absolute error = 1.341149413747189e-13 relative error = 8.689648421464402e-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) = -1.56165546563036 y[1] (numeric) = -1.561655465630488 absolute error = 1.281197370417431e-13 relative error = 8.204097501751304e-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) = -1.57997933609305 y[1] (numeric) = -1.579979336093172 absolute error = 1.214583988939921e-13 relative error = 7.687340974618864e-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) = -1.598358208163781 y[1] (numeric) = -1.598358208163897 absolute error = 1.154631945610163e-13 relative error = 7.223862208813766e-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) = -1.61679124396233 y[1] (numeric) = -1.616791243962439 absolute error = 1.094679902280404e-13 relative error = 6.770694153424732e-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) = -1.635277600192143 y[1] (numeric) = -1.635277600192246 absolute error = 1.032507412901396e-13 relative error = 6.313958026331906e-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) = -1.653816428224669 y[1] (numeric) = -1.653816428224766 absolute error = 9.681144774731365e-14 relative error = 5.853820659602369e-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) = -1.672406874184222 y[1] (numeric) = -1.672406874184312 absolute error = 9.037215420448774e-14 relative error = 5.403718174057979e-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) = -1.691048079033363 y[1] (numeric) = -1.691048079033447 absolute error = 8.415490526658687e-14 relative error = 4.976493945381583e-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) = -1.709739178658809 y[1] (numeric) = -1.709739178658886 absolute error = 7.793765632868599e-14 relative error = 4.558452967652269e-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) = -1.728479303957839 y[1] (numeric) = -1.728479303957911 absolute error = 7.127631818093505e-14 relative error = 4.123643136352739e-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) = -1.747267580925209 y[1] (numeric) = -1.747267580925274 absolute error = 6.483702463810914e-14 relative error = 3.710766762110747e-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) = -1.766103130740543 y[1] (numeric) = -1.766103130740601 absolute error = 5.839773109528323e-14 relative error = 3.306586692408871e-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) = -1.784985069856224 y[1] (numeric) = -1.784985069856276 absolute error = 5.240252676230739e-14 relative error = 2.9357403401995e-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) = -1.803912510085741 y[1] (numeric) = -1.803912510085787 absolute error = 4.596323321948148e-14 relative error = 2.547974636380609e-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) = -1.822884558692512 y[1] (numeric) = -1.822884558692551 absolute error = 3.952393967665557e-14 relative error = 2.168208594898881e-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) = -1.841900318479151 y[1] (numeric) = -1.841900318479184 absolute error = 3.308464613382966e-14 relative error = 1.796223487335488e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999764 y[1] (closed_form) = -1.860958887877194 y[1] (numeric) = -1.860958887877221 absolute error = 2.664535259100376e-14 relative error = 1.431807696805073e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999767 y[1] (closed_form) = -1.88005936103725 y[1] (numeric) = -1.88005936103727 absolute error = 2.020605904817785e-14 relative error = 1.074756439447207e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.299999999999771 y[1] (closed_form) = -1.899200827919585 y[1] (numeric) = -1.899200827919599 absolute error = 1.354472090042691e-14 relative error = 7.131800229501801e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999774 y[1] (closed_form) = -1.918382374385131 y[1] (numeric) = -1.918382374385138 absolute error = 6.883382752675971e-15 relative error = 3.588118221156089e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999777 y[1] (closed_form) = -1.937603082286891 y[1] (numeric) = -1.937603082286892 absolute error = 6.661338147750939e-16 relative error = 3.43792710109068e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.329999999999781 y[1] (closed_form) = -1.956862029561759 y[1] (numeric) = -1.956862029561754 absolute error = 5.551115123125783e-15 relative error = 2.836743234457341e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999784 y[1] (closed_form) = -1.976158290322725 y[1] (numeric) = -1.976158290322712 absolute error = 1.243449787580175e-14 relative error = 6.292258032513724e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999787 y[1] (closed_form) = -1.995490934951457 y[1] (numeric) = -1.995490934951438 absolute error = 1.84297022087776e-14 relative error = 9.235673230069535e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.359999999999791 y[1] (closed_form) = -2.014859030191271 y[1] (numeric) = -2.014859030191246 absolute error = 2.442490654175344e-14 relative error = 1.212238979291508e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999794 y[1] (closed_form) = -2.034261639240449 y[1] (numeric) = -2.034261639240418 absolute error = 3.153033389935445e-14 relative error = 1.549964532149719e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y[1] (closed_form) = -2.053697821845923 y[1] (numeric) = -2.053697821845886 absolute error = 3.68594044175552e-14 relative error = 1.794782271542992e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999801 y[1] (closed_form) = -2.073166634397293 y[1] (numeric) = -2.073166634397251 absolute error = 4.263256414560601e-14 relative error = 2.056398334714665e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999804 y[1] (closed_form) = -2.092667130021198 y[1] (numeric) = -2.092667130021148 absolute error = 4.973799150320701e-14 relative error = 2.37677511103752e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y[1] (closed_form) = -2.11219835867599 y[1] (numeric) = -2.112198358675934 absolute error = 5.639932965095795e-14 relative error = 2.670172023346864e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.419999999999811 y[1] (closed_form) = -2.131759367246748 y[1] (numeric) = -2.131759367246685 absolute error = 6.261657858885883e-14 relative error = 2.937319265529047e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999814 y[1] (closed_form) = -2.151349199640581 y[1] (numeric) = -2.151349199640512 absolute error = 6.927791673660977e-14 relative error = 3.220207893176236e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y[1] (closed_form) = -2.170966896882242 y[1] (numeric) = -2.170966896882167 absolute error = 7.549516567451064e-14 relative error = 3.477490411435125e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.449999999999821 y[1] (closed_form) = -2.190611497210021 y[1] (numeric) = -2.19061149720994 absolute error = 8.171241461241152e-14 relative error = 3.730118951556725e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999824 y[1] (closed_form) = -2.210282036171923 y[1] (numeric) = -2.210282036171835 absolute error = 8.837375276016246e-14 relative error = 3.998302086064118e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y[1] (closed_form) = -2.22997754672211 y[1] (numeric) = -2.229977546722016 absolute error = 9.459100169806334e-14 relative error = 4.241791664544094e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.479999999999831 y[1] (closed_form) = -2.249697059317607 y[1] (numeric) = -2.249697059317505 absolute error = 1.016964290556643e-13 relative error = 4.520449926111899e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999834 y[1] (closed_form) = -2.269439602015253 y[1] (numeric) = -2.269439602015145 absolute error = 1.083577672034153e-13 relative error = 4.774648644854616e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y[1] (closed_form) = -2.289204200568899 y[1] (numeric) = -2.289204200568783 absolute error = 1.159072837708663e-13 relative error = 5.063212960296935e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.509999999999841 y[1] (closed_form) = -2.308989878526825 y[1] (numeric) = -2.308989878526703 absolute error = 1.216804434989172e-13 relative error = 5.269856079947452e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999844 y[1] (closed_form) = -2.32879565732939 y[1] (numeric) = -2.328795657329261 absolute error = 1.287858708565182e-13 relative error = 5.530149047263635e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y[1] (closed_form) = -2.348620556406886 y[1] (numeric) = -2.34862055640675 absolute error = 1.358912982141192e-13 relative error = 5.78600480368855e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.539999999999851 y[1] (closed_form) = -2.368463593277592 y[1] (numeric) = -2.36846359327745 absolute error = 1.4210854715202e-13 relative error = 6.000030887338382e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999854 y[1] (closed_form) = -2.388323783646024 y[1] (numeric) = -2.388323783645875 absolute error = 1.483257960899209e-13 relative error = 6.210455931711496e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999858 y[1] (closed_form) = -2.408200141501362 y[1] (numeric) = -2.408200141501207 absolute error = 1.549871342376719e-13 relative error = 6.435807870231546e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.569999999999861 y[1] (closed_form) = -2.428091679216049 y[1] (numeric) = -2.428091679215888 absolute error = 1.612043831755727e-13 relative error = 6.639139063629603e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999864 y[1] (closed_form) = -2.447997407644559 y[1] (numeric) = -2.447997407644391 absolute error = 1.687538997430238e-13 relative error = 6.893548956222027e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999868 y[1] (closed_form) = -2.467916336222303 y[1] (numeric) = -2.467916336222127 absolute error = 1.754152378907747e-13 relative error = 7.107827575682202e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.599999999999871 y[1] (closed_form) = -2.487847473064688 y[1] (numeric) = -2.487847473064507 absolute error = 1.816324868286756e-13 relative error = 7.300788685607369e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999874 y[1] (closed_form) = -2.507789825066307 y[1] (numeric) = -2.507789825066119 absolute error = 1.878497357665765e-13 relative error = 7.490649092238409e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999878 y[1] (closed_form) = -2.527742398000244 y[1] (numeric) = -2.52774239800005 absolute error = 1.940669847044774e-13 relative error = 7.677482676162266e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.629999999999881 y[1] (closed_form) = -2.5477041966175 y[1] (numeric) = -2.547704196617299 absolute error = 2.011724120620784e-13 relative error = 7.89622328719198e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999884 y[1] (closed_form) = -2.567674224746515 y[1] (numeric) = -2.567674224746307 absolute error = 2.078337502098293e-13 relative error = 8.094241403632388e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999888 y[1] (closed_form) = -2.587651485392783 y[1] (numeric) = -2.587651485392569 absolute error = 2.149391775674303e-13 relative error = 8.306341823107001e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.659999999999891 y[1] (closed_form) = -2.607634980838556 y[1] (numeric) = -2.607634980838334 absolute error = 2.216005157151812e-13 relative error = 8.498141700949248e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999894 y[1] (closed_form) = -2.627623712742607 y[1] (numeric) = -2.627623712742379 absolute error = 2.282618538629322e-13 relative error = 8.687006924012028e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999898 y[1] (closed_form) = -2.647616682240071 y[1] (numeric) = -2.647616682239836 absolute error = 2.349231920106831e-13 relative error = 8.873006186527027e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.689999999999901 y[1] (closed_form) = -2.667612890042324 y[1] (numeric) = -2.667612890042083 absolute error = 2.415845301584341e-13 relative error = 9.056206433108107e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999904 y[1] (closed_form) = -2.687611336536918 y[1] (numeric) = -2.687611336536669 absolute error = 2.486899575160351e-13 relative error = 9.253196477303182e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999908 y[1] (closed_form) = -2.707611021887534 y[1] (numeric) = -2.707611021887278 absolute error = 2.55351295663786e-13 relative error = 9.430870741757254e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.719999999999911 y[1] (closed_form) = -2.72761094613397 y[1] (numeric) = -2.727610946133709 absolute error = 2.611244553918368e-13 relative error = 9.573376135696568e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999914 y[1] (closed_form) = -2.747610109292135 y[1] (numeric) = -2.747610109291868 absolute error = 2.673417043297377e-13 relative error = 9.729972364915076e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999918 y[1] (closed_form) = -2.767607511454047 y[1] (numeric) = -2.767607511453772 absolute error = 2.744471316873387e-13 relative error = 9.916403628459208e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.749999999999921 y[1] (closed_form) = -2.787602152887819 y[1] (numeric) = -2.787602152887537 absolute error = 2.815525590449397e-13 relative error = 1.010017009612599e-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) = -2.807593034137637 y[1] (numeric) = -2.807593034137349 absolute error = 2.877698079828406e-13 relative error = 1.024969803257936e-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) = -2.827579156123702 y[1] (numeric) = -2.827579156123407 absolute error = 2.944311461305915e-13 relative error = 1.041283479166058e-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) = -2.847559520242137 y[1] (numeric) = -2.847559520241835 absolute error = 3.015365734881925e-13 relative error = 1.058929835688042e-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) = -2.867533128464848 y[1] (numeric) = -2.867533128464539 absolute error = 3.081979116359435e-13 relative error = 1.074784136150292e-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) = -2.887498983439322 y[1] (numeric) = -2.887498983439007 absolute error = 3.148592497836944e-13 relative error = 1.090422028161766e-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) = -2.907456088588368 y[1] (numeric) = -2.907456088588047 absolute error = 3.215205879314453e-13 relative error = 1.105848474181257e-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) = -2.927403448209769 y[1] (numeric) = -2.927403448209441 absolute error = 3.277378368693462e-13 relative error = 1.119551311144939e-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) = -2.947340067575851 y[1] (numeric) = -2.947340067575517 absolute error = 3.339550858072471e-13 relative error = 1.133072798355165e-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) = -2.967264953032958 y[1] (numeric) = -2.967264953032618 absolute error = 3.40172334745148e-13 relative error = 1.146417121927196e-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) = -2.987177112100817 y[1] (numeric) = -2.987177112100469 absolute error = 3.47721851312599e-13 relative error = 1.164048324767907e-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) = -3.007075553571779 y[1] (numeric) = -3.007075553571424 absolute error = 3.5438318946035e-13 relative error = 1.178497790118431e-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) = -3.026959287609946 y[1] (numeric) = -3.026959287609585 absolute error = 3.610445276081009e-13 relative error = 1.192763077739238e-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) = -3.046827325850151 y[1] (numeric) = -3.046827325849783 absolute error = 3.681499549657019e-13 relative error = 1.208305937925044e-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) = -3.066678681496794 y[1] (numeric) = -3.066678681496418 absolute error = 3.752553823233029e-13 relative error = 1.223654061273049e-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) = -3.086512369422518 y[1] (numeric) = -3.086512369422136 absolute error = 3.823608096809039e-13 relative error = 1.238811849480594e-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) = -3.106327406266727 y[1] (numeric) = -3.106327406266339 absolute error = 3.881339694089547e-13 relative error = 1.249494720440384e-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) = -3.126122810533914 y[1] (numeric) = -3.126122810533519 absolute error = 3.947953075567057e-13 relative error = 1.262891228157726e-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) = -3.145897602691817 y[1] (numeric) = -3.145897602691416 absolute error = 4.010125564946065e-13 relative error = 1.274715859001502e-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) = -3.165650805269364 y[1] (numeric) = -3.165650805268958 absolute error = 4.067857162226574e-13 relative error = 1.284998697726056e-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) = -3.185381442954427 y[1] (numeric) = -3.185381442954013 absolute error = 4.134470543704083e-13 relative error = 1.297951475434408e-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) = -3.205088542691344 y[1] (numeric) = -3.205088542690925 absolute error = 4.196643033083092e-13 relative error = 1.309368829342583e-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) = -3.224771133778232 y[1] (numeric) = -3.224771133777806 absolute error = 4.263256414560601e-13 relative error = 1.322033793314706e-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) = -3.244428247964051 y[1] (numeric) = -3.244428247963617 absolute error = 4.338751580235112e-13 relative error = 1.337293121818235e-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) = -3.264058919545429 y[1] (numeric) = -3.264058919544989 absolute error = 4.400924069614121e-13 relative error = 1.348297986675748e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 Finished! diff ( y , x , 1 ) = sin ( x ) - 1 , 0 ; Iterations = 4900 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %