##############ECHO OF PROBLEM################# ##############temp/sub_c_sinpostode.ode################# diff ( y , x , 1 ) = 1.0 - sin ( x ) ; ! // 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) = 3.095004165278026 y[1] (numeric) = 3.095004165278026 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) = 3.103956097956697 y[1] (numeric) = 3.103956097956697 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) = 3.112808635853866 y[1] (numeric) = 3.112808635853866 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) = 3.121561893714788 y[1] (numeric) = 3.121561893714788 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] = 0.14 y[1] (closed_form) = 3.130215996212637 y[1] (numeric) = 3.130215996212637 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) = 3.138771077936042 y[1] (numeric) = 3.138771077936043 absolute error = 4.440892098500626e-16 relative error = 1.414850585860762e-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) = 3.147227283375627 y[1] (numeric) = 3.147227283375627 absolute error = 4.440892098500626e-16 relative error = 1.411049059582837e-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) = 3.15558476690956 y[1] (numeric) = 3.155584766909561 absolute error = 4.440892098500626e-16 relative error = 1.407311933138097e-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) = 3.163843692788121 y[1] (numeric) = 3.163843692788122 absolute error = 8.881784197001252e-16 relative error = 2.807276546956789e-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) = 3.17200423511727 y[1] (numeric) = 3.172004235117272 absolute error = 1.332267629550188e-15 relative error = 4.20008149674155e-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) = 3.180066577841242 y[1] (numeric) = 3.180066577841243 absolute error = 1.332267629550188e-15 relative error = 4.189433135876624e-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) = 3.188030914724148 y[1] (numeric) = 3.188030914724149 absolute error = 8.881784197001252e-16 relative error = 2.785978064384538e-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) = 3.195897449330606 y[1] (numeric) = 3.195897449330606 absolute error = 4.440892098500626e-16 relative error = 1.389560262464238e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (closed_form) = 3.203666395005375 y[1] (numeric) = 3.203666395005376 absolute error = 8.881784197001252e-16 relative error = 2.772381110233031e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (closed_form) = 3.21133797485203 y[1] (numeric) = 3.21133797485203 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] = 0.2500000000000001 y[1] (closed_form) = 3.218912421710645 y[1] (numeric) = 3.218912421710645 absolute error = 4.440892098500626e-16 relative error = 1.379625015128737e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = 3.226389978134514 y[1] (numeric) = 3.226389978134514 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] = 0.2700000000000001 y[1] (closed_form) = 3.233770896365891 y[1] (numeric) = 3.233770896365891 absolute error = 4.440892098500626e-16 relative error = 1.373285937940532e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = 3.241055438310771 y[1] (numeric) = 3.241055438310771 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) = 3.248243875512697 y[1] (numeric) = 3.248243875512697 absolute error = 4.440892098500626e-16 relative error = 1.367167081258541e-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) = 3.255336489125606 y[1] (numeric) = 3.255336489125606 absolute error = 4.440892098500626e-16 relative error = 1.364188345301737e-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) = 3.262333569885713 y[1] (numeric) = 3.262333569885713 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] = 0.3200000000000002 y[1] (closed_form) = 3.269235418082441 y[1] (numeric) = 3.269235418082441 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) = 3.276042343528387 y[1] (numeric) = 3.276042343528387 absolute error = 4.440892098500626e-16 relative error = 1.355566147450239e-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) = 3.282754665528346 y[1] (numeric) = 3.282754665528346 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] = 0.3500000000000002 y[1] (closed_form) = 3.289372712847379 y[1] (numeric) = 3.289372712847379 absolute error = 4.440892098500626e-16 relative error = 1.350072638821296e-14 % 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) = 3.295896823677935 y[1] (numeric) = 3.295896823677935 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) = 3.302327345606034 y[1] (numeric) = 3.302327345606034 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] = 0.3800000000000002 y[1] (closed_form) = 3.30866463557651 y[1] (numeric) = 3.30866463557651 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] = 0.3900000000000002 y[1] (closed_form) = 3.314909059857313 y[1] (numeric) = 3.314909059857313 absolute error = 4.440892098500626e-16 relative error = 1.339672376620727e-14 % 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) = 3.321060994002885 y[1] (numeric) = 3.321060994002885 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] = 0.4100000000000003 y[1] (closed_form) = 3.327120822816605 y[1] (numeric) = 3.327120822816606 absolute error = 8.881784197001252e-16 relative error = 2.669510567843549e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 3.333088940312309 y[1] (numeric) = 3.333088940312309 absolute error = 4.440892098500626e-16 relative error = 1.332365315785578e-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) = 3.338965749674885 y[1] (numeric) = 3.338965749674887 absolute error = 1.332267629550188e-15 relative error = 3.990060783582194e-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) = 3.344751663219964 y[1] (numeric) = 3.344751663219965 absolute error = 8.881784197001252e-16 relative error = 2.655439055361986e-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) = 3.350447102352677 y[1] (numeric) = 3.350447102352679 absolute error = 1.77635683940025e-15 relative error = 5.30185012666786e-14 % 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) = 3.356052497525525 y[1] (numeric) = 3.356052497525526 absolute error = 8.881784197001252e-16 relative error = 2.64649739643523e-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) = 3.361568288195329 y[1] (numeric) = 3.361568288195329 absolute error = 4.440892098500626e-16 relative error = 1.321077460807657e-14 % 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) = 3.366994922779285 y[1] (numeric) = 3.366994922779285 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] = 0.4900000000000003 y[1] (closed_form) = 3.372332858610122 y[1] (numeric) = 3.372332858610121 absolute error = 4.440892098500626e-16 relative error = 1.316860548673983e-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) = 3.377582561890373 y[1] (numeric) = 3.377582561890372 absolute error = 8.881784197001252e-16 relative error = 2.629627561799785e-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) = 3.382744507645751 y[1] (numeric) = 3.382744507645751 absolute error = 8.881784197001252e-16 relative error = 2.62561484526143e-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) = 3.38781917967765 y[1] (numeric) = 3.387819179677649 absolute error = 8.881784197001252e-16 relative error = 2.621681892079716e-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) = 3.392807070514761 y[1] (numeric) = 3.392807070514759 absolute error = 2.220446049250313e-15 relative error = 6.544569152036765e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (closed_form) = 3.397708681363824 y[1] (numeric) = 3.397708681363822 absolute error = 2.220446049250313e-15 relative error = 6.5351278096009e-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) = 3.402524522059506 y[1] (numeric) = 3.402524522059504 absolute error = 2.220446049250313e-15 relative error = 6.525878167385858e-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) = 3.407255111013416 y[1] (numeric) = 3.407255111013415 absolute error = 1.77635683940025e-15 relative error = 5.213454177993471e-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) = 3.411900975162269 y[1] (numeric) = 3.411900975162267 absolute error = 1.77635683940025e-15 relative error = 5.206355202954762e-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) = 3.416462649915187 y[1] (numeric) = 3.416462649915186 absolute error = 1.332267629550188e-15 relative error = 3.899552742317441e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (closed_form) = 3.420940679100164 y[1] (numeric) = 3.420940679100162 absolute error = 1.332267629550188e-15 relative error = 3.894448207446335e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (closed_form) = 3.425335614909679 y[1] (numeric) = 3.425335614909677 absolute error = 1.332267629550188e-15 relative error = 3.889451368651705e-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) = 3.42964801784548 y[1] (numeric) = 3.429648017845479 absolute error = 4.440892098500626e-16 relative error = 1.29485360462454e-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) = 3.433878456662534 y[1] (numeric) = 3.433878456662534 absolute error = 4.440892098500626e-16 relative error = 1.293258382481258e-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) = 3.438027508312152 y[1] (numeric) = 3.438027508312152 absolute error = 4.440892098500626e-16 relative error = 1.291697663198982e-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) = 3.442095757884293 y[1] (numeric) = 3.442095757884294 absolute error = 8.881784197001252e-16 relative error = 2.580341983995384e-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) = 3.446083798549056 y[1] (numeric) = 3.446083798549056 absolute error = 4.440892098500626e-16 relative error = 1.288677919083229e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (closed_form) = 3.449992231497365 y[1] (numeric) = 3.449992231497366 absolute error = 4.440892098500626e-16 relative error = 1.287217999494796e-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) = 3.453821665880849 y[1] (numeric) = 3.45382166588085 absolute error = 4.440892098500626e-16 relative error = 1.285790792955733e-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) = 3.457572718750928 y[1] (numeric) = 3.457572718750928 absolute error = 4.440892098500626e-16 relative error = 1.284395863727467e-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) = 3.461246014997107 y[1] (numeric) = 3.461246014997108 absolute error = 8.881784197001252e-16 relative error = 2.566065560933171e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (closed_form) = 3.464842187284489 y[1] (numeric) = 3.464842187284489 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] = 0.7100000000000005 y[1] (closed_form) = 3.468361875990508 y[1] (numeric) = 3.468361875990509 absolute error = 4.440892098500626e-16 relative error = 1.280400447612572e-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) = 3.471805729140895 y[1] (numeric) = 3.471805729140896 absolute error = 8.881784197001252e-16 relative error = 2.558260712127768e-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) = 3.47517440234487 y[1] (numeric) = 3.475174402344871 absolute error = 4.440892098500626e-16 relative error = 1.277890426306127e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (closed_form) = 3.478468558729588 y[1] (numeric) = 3.478468558729587 absolute error = 8.881784197001252e-16 relative error = 2.553360493862009e-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) = 3.481688868873821 y[1] (numeric) = 3.481688868873821 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] = 0.7600000000000006 y[1] (closed_form) = 3.484836010740906 y[1] (numeric) = 3.484836010740905 absolute error = 4.440892098500626e-16 relative error = 1.274347511565244e-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) = 3.487910669610943 y[1] (numeric) = 3.487910669610943 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) = 3.490913538012278 y[1] (numeric) = 3.490913538012277 absolute error = 8.881784197001252e-16 relative error = 2.544257856944383e-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) = 3.493845315652236 y[1] (numeric) = 3.493845315652236 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] = 0.8000000000000006 y[1] (closed_form) = 3.496706709347166 y[1] (numeric) = 3.496706709347165 absolute error = 4.440892098500626e-16 relative error = 1.270021327962544e-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) = 3.499498432951747 y[1] (numeric) = 3.499498432951747 absolute error = 4.440892098500626e-16 relative error = 1.269008168909176e-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) = 3.502221207287614 y[1] (numeric) = 3.502221207287613 absolute error = 4.440892098500626e-16 relative error = 1.268021588487836e-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) = 3.504875760071267 y[1] (numeric) = 3.504875760071267 absolute error = 4.440892098500626e-16 relative error = 1.267061203450569e-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) = 3.507462825841309 y[1] (numeric) = 3.507462825841309 absolute error = 4.440892098500626e-16 relative error = 1.266126633127016e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (closed_form) = 3.509983145884982 y[1] (numeric) = 3.509983145884983 absolute error = 8.881784197001252e-16 relative error = 2.530434998644947e-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) = 3.512437468164052 y[1] (numeric) = 3.512437468164053 absolute error = 8.881784197001252e-16 relative error = 2.528666852436167e-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) = 3.514826547240001 y[1] (numeric) = 3.514826547240003 absolute error = 1.77635683940025e-15 relative error = 5.053896161092573e-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) = 3.51715114419858 y[1] (numeric) = 3.517151144198582 absolute error = 1.77635683940025e-15 relative error = 5.05055588051793e-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) = 3.519412026573697 y[1] (numeric) = 3.519412026573698 absolute error = 1.332267629550188e-15 relative error = 3.785483539553648e-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) = 3.521609968270665 y[1] (numeric) = 3.521609968270665 absolute error = 4.440892098500626e-16 relative error = 1.261040302166508e-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) = 3.523745749488812 y[1] (numeric) = 3.523745749488813 absolute error = 8.881784197001252e-16 relative error = 2.520551943422629e-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) = 3.525820156643463 y[1] (numeric) = 3.525820156643464 absolute error = 8.881784197001252e-16 relative error = 2.51906898321683e-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) = 3.527833982287298 y[1] (numeric) = 3.527833982287299 absolute error = 4.440892098500626e-16 relative error = 1.258815500048372e-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) = 3.529788025031098 y[1] (numeric) = 3.529788025031099 absolute error = 8.881784197001252e-16 relative error = 2.516237273744789e-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) = 3.531683089463884 y[1] (numeric) = 3.531683089463885 absolute error = 1.332267629550188e-15 relative error = 3.772330630471232e-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) = 3.533519986072457 y[1] (numeric) = 3.533519986072458 absolute error = 1.332267629550188e-15 relative error = 3.770369588403027e-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) = 3.535299531160354 y[1] (numeric) = 3.535299531160356 absolute error = 1.77635683940025e-15 relative error = 5.024628956452852e-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) = 3.537022546766218 y[1] (numeric) = 3.537022546766218 absolute error = 8.881784197001252e-16 relative error = 2.511090636140155e-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) = 3.538689860581588 y[1] (numeric) = 3.538689860581589 absolute error = 1.77635683940025e-15 relative error = 5.019814986296381e-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) = 3.54030230586814 y[1] (numeric) = 3.540302305868142 absolute error = 1.332267629550188e-15 relative error = 3.763146518143156e-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) = 3.541860721374356 y[1] (numeric) = 3.541860721374357 absolute error = 1.332267629550188e-15 relative error = 3.761490737086989e-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) = 3.54336595125165 y[1] (numeric) = 3.543365951251652 absolute error = 2.220446049250313e-15 relative error = 6.26648807884483e-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) = 3.544818844969955 y[1] (numeric) = 3.544818844969958 absolute error = 3.108624468950438e-15 relative error = 8.769487539148948e-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) = 3.546220257232778 y[1] (numeric) = 3.546220257232781 absolute error = 3.108624468950438e-15 relative error = 8.76602197116823e-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) = 3.547571047891727 y[1] (numeric) = 3.54757104789173 absolute error = 3.108624468950438e-15 relative error = 8.762684177383429e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y[1] (closed_form) = 3.548872081860527 y[1] (numeric) = 3.54887208186053 absolute error = 3.108624468950438e-15 relative error = 8.759471734243842e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y[1] (closed_form) = 3.550124229028533 y[1] (numeric) = 3.550124229028536 absolute error = 3.108624468950438e-15 relative error = 8.756382223280935e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y[1] (closed_form) = 3.551328364173739 y[1] (numeric) = 3.551328364173742 absolute error = 3.108624468950438e-15 relative error = 8.753413230695999e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y[1] (closed_form) = 3.5524853668753 y[1] (numeric) = 3.552485366875303 absolute error = 3.552713678800501e-15 relative error = 1.000064268223968e-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) = 3.553596121425576 y[1] (numeric) = 3.55359612142558 absolute error = 3.552713678800501e-15 relative error = 9.997516761627033e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y[1] (closed_form) = 3.554661516741706 y[1] (numeric) = 3.554661516741709 absolute error = 3.108624468950438e-15 relative error = 8.745205286943562e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = 3.555682446276711 y[1] (numeric) = 3.555682446276715 absolute error = 3.996802888650564e-15 relative error = 1.124060696937593e-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) = 3.556659807930156 y[1] (numeric) = 3.556659807930159 absolute error = 3.108624468950438e-15 relative error = 8.740291837918403e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = 3.557594503958357 y[1] (numeric) = 3.55759450395836 absolute error = 3.108624468950438e-15 relative error = 8.73799547838189e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = 3.558487440884156 y[1] (numeric) = 3.558487440884159 absolute error = 2.664535259100376e-15 relative error = 7.487831005069767e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = 3.559339529406272 y[1] (numeric) = 3.559339529406276 absolute error = 3.552713678800501e-15 relative error = 9.98138460646693e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = 3.560151684308229 y[1] (numeric) = 3.560151684308233 absolute error = 4.440892098500626e-15 relative error = 1.247388452035445e-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) = 3.560924824366881 y[1] (numeric) = 3.560924824366886 absolute error = 5.773159728050814e-15 relative error = 1.62125290838659e-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) = 3.561659872260532 y[1] (numeric) = 3.561659872260538 absolute error = 5.773159728050814e-15 relative error = 1.620918317612029e-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) = 3.562357754476672 y[1] (numeric) = 3.562357754476679 absolute error = 7.105427357601002e-15 relative error = 1.994585565885935e-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) = 3.563019401219329 y[1] (numeric) = 3.563019401219336 absolute error = 7.105427357601002e-15 relative error = 1.994215174682854e-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) = 3.563645746316046 y[1] (numeric) = 3.563645746316053 absolute error = 7.105427357601002e-15 relative error = 1.993864672139847e-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) = 3.564237727124501 y[1] (numeric) = 3.564237727124509 absolute error = 7.549516567451064e-15 relative error = 2.118129357645777e-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) = 3.564796284438775 y[1] (numeric) = 3.564796284438783 absolute error = 7.993605777301127e-15 relative error = 2.242373796279807e-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) = 3.565322362395268 y[1] (numeric) = 3.565322362395276 absolute error = 7.993605777301127e-15 relative error = 2.242042924817276e-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) = 3.565816908378288 y[1] (numeric) = 3.565816908378296 absolute error = 8.43769498715119e-15 relative error = 2.366272639328698e-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) = 3.566280872925318 y[1] (numeric) = 3.566280872925326 absolute error = 8.43769498715119e-15 relative error = 2.365964792960907e-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) = 3.566715209631954 y[1] (numeric) = 3.566715209631963 absolute error = 8.881784197001252e-15 relative error = 2.490185976445749e-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) = 3.567120875056556 y[1] (numeric) = 3.567120875056565 absolute error = 8.881784197001252e-15 relative error = 2.489902783813131e-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) = 3.567498828624586 y[1] (numeric) = 3.567498828624595 absolute error = 8.881784197001252e-15 relative error = 2.489638994618966e-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) = 3.567850032532669 y[1] (numeric) = 3.567850032532678 absolute error = 8.881784197001252e-15 relative error = 2.489393925197142e-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) = 3.568175451652372 y[1] (numeric) = 3.568175451652381 absolute error = 9.325873406851315e-15 relative error = 2.613625235982338e-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) = 3.568476053433722 y[1] (numeric) = 3.568476053433731 absolute error = 9.325873406851315e-15 relative error = 2.61340506905675e-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) = 3.568752807808458 y[1] (numeric) = 3.568752807808468 absolute error = 9.769962616701378e-15 relative error = 2.737640610838785e-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) = 3.569006687093041 y[1] (numeric) = 3.56900668709305 absolute error = 8.881784197001252e-15 relative error = 2.488587154829758e-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) = 3.569238665891419 y[1] (numeric) = 3.569238665891428 absolute error = 8.881784197001252e-15 relative error = 2.488425411805019e-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) = 3.569449720997572 y[1] (numeric) = 3.569449720997582 absolute error = 9.325873406851315e-15 relative error = 2.612692189496639e-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) = 3.569640831297834 y[1] (numeric) = 3.569640831297844 absolute error = 9.769962616701378e-15 relative error = 2.736959564962523e-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) = 3.569812977672999 y[1] (numeric) = 3.569812977673009 absolute error = 9.325873406851315e-15 relative error = 2.612426327423582e-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) = 3.56996714290024 y[1] (numeric) = 3.56996714290025 absolute error = 9.325873406851315e-15 relative error = 2.612313512576191e-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) = 3.570104311554831 y[1] (numeric) = 3.57010431155484 absolute error = 9.769962616701378e-15 relative error = 2.736604245730406e-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) = 3.570225469911685 y[1] (numeric) = 3.570225469911695 absolute error = 9.769962616701378e-15 relative error = 2.73651137695319e-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) = 3.570331605846736 y[1] (numeric) = 3.570331605846746 absolute error = 1.021405182655144e-14 relative error = 2.860813211250468e-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) = 3.570423708738145 y[1] (numeric) = 3.570423708738155 absolute error = 9.769962616701378e-15 relative error = 2.736359439018588e-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) = 3.570502769367367 y[1] (numeric) = 3.570502769367376 absolute error = 9.769962616701378e-15 relative error = 2.736298848588333e-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) = 3.570569779820069 y[1] (numeric) = 3.57056977982008 absolute error = 1.110223024625157e-14 relative error = 3.109372153710167e-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) = 3.570625733386931 y[1] (numeric) = 3.570625733386942 absolute error = 1.110223024625157e-14 relative error = 3.109323428227383e-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) = 3.57067162446431 y[1] (numeric) = 3.57067162446432 absolute error = 1.06581410364015e-14 relative error = 2.984912127841073e-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) = 3.5707084484548 y[1] (numeric) = 3.570708448454812 absolute error = 1.154631945610163e-14 relative error = 3.233621457136389e-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) = 3.570737201667702 y[1] (numeric) = 3.570737201667714 absolute error = 1.199040866595169e-14 relative error = 3.357964473093009e-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) = 3.570758881219386 y[1] (numeric) = 3.570758881219397 absolute error = 1.110223024625157e-14 relative error = 3.109207486577823e-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) = 3.570774484933579 y[1] (numeric) = 3.57077448493359 absolute error = 1.154631945610163e-14 relative error = 3.233561655831201e-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) = 3.570785011241591 y[1] (numeric) = 3.570785011241602 absolute error = 1.154631945610163e-14 relative error = 3.233552123623057e-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) = 3.570791459082466 y[1] (numeric) = 3.570791459082477 absolute error = 1.110223024625157e-14 relative error = 3.109179119943438e-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) = 3.570794827803092 y[1] (numeric) = 3.570794827803103 absolute error = 1.110223024625157e-14 relative error = 3.109176186715309e-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) = 3.570796117058268 y[1] (numeric) = 3.570796117058278 absolute error = 1.021405182655144e-14 relative error = 2.860441059000056e-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) = 3.570796326710734 y[1] (numeric) = 3.570796326710743 absolute error = 9.769962616701378e-15 relative error = 2.73607389579149e-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) = 3.570796456731192 y[1] (numeric) = 3.570796456731202 absolute error = 1.021405182655144e-14 relative error = 2.86044078689987e-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) = 3.570797507098307 y[1] (numeric) = 3.570797507098318 absolute error = 1.110223024625157e-14 relative error = 3.109173853790839e-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) = 3.570800477698711 y[1] (numeric) = 3.570800477698723 absolute error = 1.154631945610163e-14 relative error = 3.233538117913251e-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) = 3.570806368227013 y[1] (numeric) = 3.570806368227024 absolute error = 1.110223024625157e-14 relative error = 3.109166138225545e-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) = 3.570816178085829 y[1] (numeric) = 3.57081617808584 absolute error = 1.06581410364015e-14 relative error = 2.984791292761226e-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) = 3.570830906285852 y[1] (numeric) = 3.570830906285862 absolute error = 1.06581410364015e-14 relative error = 2.98477898173213e-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) = 3.570851551345938 y[1] (numeric) = 3.570851551345949 absolute error = 1.06581410364015e-14 relative error = 2.98476172508045e-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) = 3.570879111193266 y[1] (numeric) = 3.570879111193278 absolute error = 1.199040866595169e-14 relative error = 3.357831024961499e-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) = 3.570914583063541 y[1] (numeric) = 3.570914583063552 absolute error = 1.154631945610163e-14 relative error = 3.233434793110024e-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) = 3.570958963401272 y[1] (numeric) = 3.570958963401283 absolute error = 1.154631945610163e-14 relative error = 3.233394607566135e-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) = 3.571013247760129 y[1] (numeric) = 3.57101324776014 absolute error = 1.154631945610163e-14 relative error = 3.233345455479311e-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) = 3.571078430703387 y[1] (numeric) = 3.571078430703399 absolute error = 1.154631945610163e-14 relative error = 3.233286437180652e-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) = 3.571155505704475 y[1] (numeric) = 3.571155505704486 absolute error = 1.110223024625157e-14 relative error = 3.108862167586133e-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) = 3.571245465047622 y[1] (numeric) = 3.571245465047634 absolute error = 1.199040866595169e-14 relative error = 3.357486564086347e-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) = 3.571349299728635 y[1] (numeric) = 3.571349299728648 absolute error = 1.243449787580175e-14 relative error = 3.481736686116525e-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) = 3.571467999355801 y[1] (numeric) = 3.571467999355814 absolute error = 1.332267629550188e-14 relative error = 3.730308180811067e-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) = 3.571602552050922 y[1] (numeric) = 3.571602552050935 absolute error = 1.332267629550188e-14 relative error = 3.730167649211583e-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) = 3.571753944350506 y[1] (numeric) = 3.57175394435052 absolute error = 1.332267629550188e-14 relative error = 3.730009542391503e-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) = 3.571923161107119 y[1] (numeric) = 3.571923161107131 absolute error = 1.243449787580175e-14 relative error = 3.481177314001255e-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) = 3.572111185390889 y[1] (numeric) = 3.572111185390903 absolute error = 1.332267629550188e-14 relative error = 3.729636510192782e-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) = 3.572318998391214 y[1] (numeric) = 3.572318998391228 absolute error = 1.332267629550188e-14 relative error = 3.729419545539386e-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) = 3.572547579318633 y[1] (numeric) = 3.572547579318646 absolute error = 1.287858708565182e-14 relative error = 3.604874896615949e-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) = 3.572797905306911 y[1] (numeric) = 3.572797905306924 absolute error = 1.287858708565182e-14 relative error = 3.604622323172102e-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) = 3.573070951315323 y[1] (numeric) = 3.573070951315336 absolute error = 1.287858708565182e-14 relative error = 3.604346866079146e-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) = 3.573367690031163 y[1] (numeric) = 3.573367690031176 absolute error = 1.287858708565182e-14 relative error = 3.604047554798231e-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) = 3.573689091772474 y[1] (numeric) = 3.573689091772488 absolute error = 1.332267629550188e-14 relative error = 3.727989747673912e-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) = 3.574036124391016 y[1] (numeric) = 3.574036124391029 absolute error = 1.332267629550188e-14 relative error = 3.727627766429457e-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) = 3.574409753175483 y[1] (numeric) = 3.574409753175496 absolute error = 1.243449787580175e-14 relative error = 3.478755580485707e-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) = 3.574810940754976 y[1] (numeric) = 3.574810940754987 absolute error = 1.154631945610163e-14 relative error = 3.22991051763513e-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) = 3.575240647002735 y[1] (numeric) = 3.575240647002746 absolute error = 1.154631945610163e-14 relative error = 3.229522316429626e-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) = 3.575699828940162 y[1] (numeric) = 3.575699828940174 absolute error = 1.154631945610163e-14 relative error = 3.229107589694955e-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) = 3.576189440641113 y[1] (numeric) = 3.576189440641125 absolute error = 1.199040866595169e-14 relative error = 3.352844938718386e-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) = 3.576710433136491 y[1] (numeric) = 3.576710433136504 absolute error = 1.243449787580175e-14 relative error = 3.476517908914892e-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) = 3.577263754319149 y[1] (numeric) = 3.577263754319162 absolute error = 1.287858708565182e-14 relative error = 3.600122319776492e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.919999999999899 y[1] (closed_form) = 3.577850348849096 y[1] (numeric) = 3.577850348849109 absolute error = 1.287858708565182e-14 relative error = 3.599532073719777e-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) = 3.578471158059034 y[1] (numeric) = 3.578471158059047 absolute error = 1.287858708565182e-14 relative error = 3.598907610767827e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999897 y[1] (closed_form) = 3.579127119860226 y[1] (numeric) = 3.579127119860239 absolute error = 1.287858708565182e-14 relative error = 3.598248023712205e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.949999999999896 y[1] (closed_form) = 3.579819168648706 y[1] (numeric) = 3.579819168648719 absolute error = 1.332267629550188e-14 relative error = 3.721605943724488e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999895 y[1] (closed_form) = 3.580548235211838 y[1] (numeric) = 3.580548235211852 absolute error = 1.376676550535194e-14 relative error = 3.844876427013823e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999894 y[1] (closed_form) = 3.581315246635239 y[1] (numeric) = 3.581315246635254 absolute error = 1.4210854715202e-14 relative error = 3.96805467727354e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999893 y[1] (closed_form) = 3.582121126210075 y[1] (numeric) = 3.582121126210089 absolute error = 1.4210854715202e-14 relative error = 3.967161973173489e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999892 y[1] (closed_form) = 3.582966793340725 y[1] (numeric) = 3.58296679334074 absolute error = 1.4210854715202e-14 relative error = 3.966225626655036e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.999999999999891 y[1] (closed_form) = 3.583853163452848 y[1] (numeric) = 3.583853163452862 absolute error = 1.465494392505207e-14 relative error = 4.08915858342054e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.00999999999989 y[1] (closed_form) = 3.584781147901837 y[1] (numeric) = 3.584781147901852 absolute error = 1.509903313490213e-14 relative error = 4.211981851037002e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999889 y[1] (closed_form) = 3.585751653881688 y[1] (numeric) = 3.585751653881704 absolute error = 1.509903313490213e-14 relative error = 4.210841851960649e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999887 y[1] (closed_form) = 3.586765584334279 y[1] (numeric) = 3.586765584334295 absolute error = 1.554312234475219e-14 relative error = 4.333464783045494e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999886 y[1] (closed_form) = 3.587823837859076 y[1] (numeric) = 3.587823837859092 absolute error = 1.643130076445232e-14 relative error = 4.579740117412564e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999885 y[1] (closed_form) = 3.588927308623274 y[1] (numeric) = 3.58892730862329 absolute error = 1.598721155460225e-14 relative error = 4.454593303182562e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999884 y[1] (closed_form) = 3.590076886272384 y[1] (numeric) = 3.5900768862724 absolute error = 1.598721155460225e-14 relative error = 4.453166898941251e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999883 y[1] (closed_form) = 3.591273455841266 y[1] (numeric) = 3.591273455841281 absolute error = 1.554312234475219e-14 relative error = 4.328025291271275e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999882 y[1] (closed_form) = 3.592517897665626 y[1] (numeric) = 3.592517897665642 absolute error = 1.643130076445232e-14 relative error = 4.573756132190511e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.089999999999881 y[1] (closed_form) = 3.593811087293985 y[1] (numeric) = 3.593811087294001 absolute error = 1.643130076445232e-14 relative error = 4.57211032114226e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09999999999988 y[1] (closed_form) = 3.595153895400126 y[1] (numeric) = 3.595153895400142 absolute error = 1.554312234475219e-14 relative error = 4.323353824891633e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999879 y[1] (closed_form) = 3.596547187696023 y[1] (numeric) = 3.596547187696039 absolute error = 1.554312234475219e-14 relative error = 4.321678969742432e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999878 y[1] (closed_form) = 3.597991824845275 y[1] (numeric) = 3.59799182484529 absolute error = 1.509903313490213e-14 relative error = 4.196516798798295e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999876 y[1] (closed_form) = 3.599488662377036 y[1] (numeric) = 3.599488662377051 absolute error = 1.509903313490213e-14 relative error = 4.194771688746202e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999875 y[1] (closed_form) = 3.601038550600469 y[1] (numeric) = 3.601038550600484 absolute error = 1.465494392505207e-14 relative error = 4.069643720589542e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999874 y[1] (closed_form) = 3.602642334519708 y[1] (numeric) = 3.602642334519722 absolute error = 1.4210854715202e-14 relative error = 3.944564404586265e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999873 y[1] (closed_form) = 3.604300853749366 y[1] (numeric) = 3.60430085374938 absolute error = 1.4210854715202e-14 relative error = 3.942749313065582e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999872 y[1] (closed_form) = 3.606014942430567 y[1] (numeric) = 3.606014942430582 absolute error = 1.465494392505207e-14 relative error = 4.064027509318687e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.179999999999871 y[1] (closed_form) = 3.60778542914754 y[1] (numeric) = 3.607785429147554 absolute error = 1.376676550535194e-14 relative error = 3.815849300274157e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.18999999999987 y[1] (closed_form) = 3.609613136844754 y[1] (numeric) = 3.609613136844768 absolute error = 1.4210854715202e-14 relative error = 3.936946752034497e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999869 y[1] (closed_form) = 3.611498882744629 y[1] (numeric) = 3.611498882744643 absolute error = 1.4210854715202e-14 relative error = 3.934891073371228e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999868 y[1] (closed_form) = 3.613443478265814 y[1] (numeric) = 3.613443478265828 absolute error = 1.376676550535194e-14 relative error = 3.809874317436113e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999867 y[1] (closed_form) = 3.615447728942043 y[1] (numeric) = 3.615447728942057 absolute error = 1.4210854715202e-14 relative error = 3.930593326365253e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999865 y[1] (closed_form) = 3.617512434341587 y[1] (numeric) = 3.617512434341601 absolute error = 1.4210854715202e-14 relative error = 3.928349929165753e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999864 y[1] (closed_form) = 3.619638387987291 y[1] (numeric) = 3.619638387987306 absolute error = 1.4210854715202e-14 relative error = 3.926042657289858e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999863 y[1] (closed_form) = 3.62182637727723 y[1] (numeric) = 3.621826377277245 absolute error = 1.509903313490213e-14 relative error = 4.168900317704651e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999862 y[1] (closed_form) = 3.624077183405966 y[1] (numeric) = 3.624077183405981 absolute error = 1.554312234475219e-14 relative error = 4.288849701082944e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.269999999999861 y[1] (closed_form) = 3.626391581286427 y[1] (numeric) = 3.626391581286442 absolute error = 1.554312234475219e-14 relative error = 4.286112516078151e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.27999999999986 y[1] (closed_form) = 3.628770339472421 y[1] (numeric) = 3.628770339472437 absolute error = 1.598721155460225e-14 relative error = 4.405682933609571e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999859 y[1] (closed_form) = 3.631214220081777 y[1] (numeric) = 3.631214220081794 absolute error = 1.643130076445232e-14 relative error = 4.525015537112066e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999858 y[1] (closed_form) = 3.633723978720139 y[1] (numeric) = 3.633723978720157 absolute error = 1.731947918415244e-14 relative error = 4.766316672807015e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999857 y[1] (closed_form) = 3.636300364405402 y[1] (numeric) = 3.636300364405419 absolute error = 1.731947918415244e-14 relative error = 4.762939649784535e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999856 y[1] (closed_form) = 3.638944119492809 y[1] (numeric) = 3.638944119492826 absolute error = 1.687538997430238e-14 relative error = 4.637441362153824e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999854 y[1] (closed_form) = 3.641655979600722 y[1] (numeric) = 3.641655979600739 absolute error = 1.77635683940025e-14 relative error = 4.877882066155556e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999853 y[1] (closed_form) = 3.644436673537057 y[1] (numeric) = 3.644436673537074 absolute error = 1.77635683940025e-14 relative error = 4.874160257190674e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999852 y[1] (closed_form) = 3.647286923226404 y[1] (numeric) = 3.647286923226423 absolute error = 1.909583602355269e-14 relative error = 5.235627584423889e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.359999999999851 y[1] (closed_form) = 3.650207443637835 y[1] (numeric) = 3.650207443637855 absolute error = 1.953992523340276e-14 relative error = 5.353099936131043e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36999999999985 y[1] (closed_form) = 3.653198942713412 y[1] (numeric) = 3.653198942713431 absolute error = 1.909583602355269e-14 relative error = 5.227154700031e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999849 y[1] (closed_form) = 3.656262121297384 y[1] (numeric) = 3.656262121297404 absolute error = 1.953992523340276e-14 relative error = 5.344235337938306e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999848 y[1] (closed_form) = 3.659397673066115 y[1] (numeric) = 3.659397673066134 absolute error = 1.953992523340276e-14 relative error = 5.339656134456345e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999847 y[1] (closed_form) = 3.662606284458705 y[1] (numeric) = 3.662606284458725 absolute error = 1.998401444325282e-14 relative error = 5.45622785830125e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999846 y[1] (closed_form) = 3.665888634608356 y[1] (numeric) = 3.665888634608377 absolute error = 2.042810365310288e-14 relative error = 5.572483424686824e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999844 y[1] (closed_form) = 3.669245395274456 y[1] (numeric) = 3.669245395274477 absolute error = 2.087219286295294e-14 relative error = 5.688415631681054e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999843 y[1] (closed_form) = 3.672677230775402 y[1] (numeric) = 3.672677230775423 absolute error = 2.087219286295294e-14 relative error = 5.683100243074248e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999842 y[1] (closed_form) = 3.67618479792217 y[1] (numeric) = 3.676184797922192 absolute error = 2.131628207280301e-14 relative error = 5.798479468401931e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.449999999999841 y[1] (closed_form) = 3.679768745952635 y[1] (numeric) = 3.679768745952658 absolute error = 2.264854970235319e-14 relative error = 6.154883979397959e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45999999999984 y[1] (closed_form) = 3.683429716466648 y[1] (numeric) = 3.68342971646667 absolute error = 2.220446049250313e-14 relative error = 6.028202572520617e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999839 y[1] (closed_form) = 3.687168343361874 y[1] (numeric) = 3.687168343361896 absolute error = 2.220446049250313e-14 relative error = 6.022090239649222e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999838 y[1] (closed_form) = 3.690985252770406 y[1] (numeric) = 3.690985252770429 absolute error = 2.220446049250313e-14 relative error = 6.015862695695343e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999837 y[1] (closed_form) = 3.694881062996151 y[1] (numeric) = 3.694881062996174 absolute error = 2.264854970235319e-14 relative error = 6.129710081652169e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999836 y[1] (closed_form) = 3.698856384453 y[1] (numeric) = 3.698856384453023 absolute error = 2.309263891220326e-14 relative error = 6.243183436173956e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999835 y[1] (closed_form) = 3.702911819603786 y[1] (numeric) = 3.702911819603809 absolute error = 2.309263891220326e-14 relative error = 6.236345891346174e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999833 y[1] (closed_form) = 3.70704796290004 y[1] (numeric) = 3.707047962900064 absolute error = 2.353672812205332e-14 relative error = 6.34918359773269e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999832 y[1] (closed_form) = 3.711265400722547 y[1] (numeric) = 3.711265400722571 absolute error = 2.398081733190338e-14 relative error = 6.461628243357253e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999831 y[1] (closed_form) = 3.715564711322704 y[1] (numeric) = 3.715564711322729 absolute error = 2.486899575160351e-14 relative error = 6.693194085899903e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54999999999983 y[1] (closed_form) = 3.719946464764702 y[1] (numeric) = 3.719946464764728 absolute error = 2.575717417130363e-14 relative error = 6.924071197065695e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999829 y[1] (closed_form) = 3.724411222868516 y[1] (numeric) = 3.724411222868542 absolute error = 2.620126338115369e-14 relative error = 7.035008169955428e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999828 y[1] (closed_form) = 3.72895953915372 y[1] (numeric) = 3.728959539153746 absolute error = 2.664535259100376e-14 relative error = 7.145519363036819e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999827 y[1] (closed_form) = 3.733591958784143 y[1] (numeric) = 3.733591958784171 absolute error = 2.797762022055394e-14 relative error = 7.493486307396309e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999826 y[1] (closed_form) = 3.738309018513351 y[1] (numeric) = 3.73830901851338 absolute error = 2.886579864025407e-14 relative error = 7.721619185920966e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999825 y[1] (closed_form) = 3.743111246630968 y[1] (numeric) = 3.743111246630997 absolute error = 2.886579864025407e-14 relative error = 7.711712727276026e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999824 y[1] (closed_form) = 3.747999162909849 y[1] (numeric) = 3.747999162909879 absolute error = 2.97539770599542e-14 relative error = 7.938629590529038e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999822 y[1] (closed_form) = 3.752973278554109 y[1] (numeric) = 3.752973278554139 absolute error = 3.019806626980426e-14 relative error = 8.04643785831551e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999821 y[1] (closed_form) = 3.758034096147992 y[1] (numeric) = 3.758034096148024 absolute error = 3.153033389935445e-14 relative error = 8.390113844808707e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999982 y[1] (closed_form) = 3.763182109605625 y[1] (numeric) = 3.763182109605657 absolute error = 3.197442310920451e-14 relative error = 8.496645173665371e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999819 y[1] (closed_form) = 3.768417804121619 y[1] (numeric) = 3.768417804121652 absolute error = 3.33066907387547e-14 relative error = 8.838375273125577e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999818 y[1] (closed_form) = 3.77374165612255 y[1] (numeric) = 3.773741656122584 absolute error = 3.375077994860476e-14 relative error = 8.943585179935995e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999817 y[1] (closed_form) = 3.779154133219324 y[1] (numeric) = 3.779154133219358 absolute error = 3.419486915845482e-14 relative error = 9.048286455923262e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999816 y[1] (closed_form) = 3.784655694160406 y[1] (numeric) = 3.784655694160441 absolute error = 3.463895836830488e-14 relative error = 9.152472818531845e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999815 y[1] (closed_form) = 3.790246788785954 y[1] (numeric) = 3.79024678878599 absolute error = 3.552713678800501e-14 relative error = 9.373304369815093e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999814 y[1] (closed_form) = 3.795927857982832 y[1] (numeric) = 3.795927857982868 absolute error = 3.597122599785507e-14 relative error = 9.476267027100535e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999813 y[1] (closed_form) = 3.801699333640521 y[1] (numeric) = 3.801699333640558 absolute error = 3.730349362740526e-14 relative error = 9.812320847499347e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999811 y[1] (closed_form) = 3.807561638607931 y[1] (numeric) = 3.807561638607968 absolute error = 3.774758283725532e-14 relative error = 9.913846818526116e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999981 y[1] (closed_form) = 3.813515186651117 y[1] (numeric) = 3.813515186651155 absolute error = 3.819167204710538e-14 relative error = 1.001482101888359e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999809 y[1] (closed_form) = 3.819560382411903 y[1] (numeric) = 3.819560382411942 absolute error = 3.863576125695545e-14 relative error = 1.011523772077625e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999808 y[1] (closed_form) = 3.825697621367418 y[1] (numeric) = 3.825697621367458 absolute error = 3.996802888650564e-14 relative error = 1.044725246011991e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999807 y[1] (closed_form) = 3.831927289790546 y[1] (numeric) = 3.831927289790587 absolute error = 4.085620730620576e-14 relative error = 1.066205181268953e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999806 y[1] (closed_form) = 3.838249764711304 y[1] (numeric) = 3.838249764711346 absolute error = 4.174438572590589e-14 relative error = 1.087589090988864e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999805 y[1] (closed_form) = 3.844665413879135 y[1] (numeric) = 3.844665413879177 absolute error = 4.218847493575595e-14 relative error = 1.097325004757416e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999804 y[1] (closed_form) = 3.851174595726135 y[1] (numeric) = 3.851174595726178 absolute error = 4.307665335545607e-14 relative error = 1.118532860163251e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999803 y[1] (closed_form) = 3.857777659331211 y[1] (numeric) = 3.857777659331254 absolute error = 4.307665335545607e-14 relative error = 1.116618352829694e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999802 y[1] (closed_form) = 3.86447494438517 y[1] (numeric) = 3.864474944385214 absolute error = 4.352074256530614e-14 relative error = 1.126174789373106e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8199999999998 y[1] (closed_form) = 3.871266781156756 y[1] (numeric) = 3.871266781156801 absolute error = 4.485301019485632e-14 relative error = 1.158613258408763e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999799 y[1] (closed_form) = 3.878153490459618 y[1] (numeric) = 3.878153490459664 absolute error = 4.574118861455645e-14 relative error = 1.179457923134843e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999798 y[1] (closed_form) = 3.885135383620232 y[1] (numeric) = 3.885135383620278 absolute error = 4.662936703425657e-14 relative error = 1.200199283423853e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999797 y[1] (closed_form) = 3.892212762446765 y[1] (numeric) = 3.892212762446813 absolute error = 4.75175454539567e-14 relative error = 1.220836278849404e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999796 y[1] (closed_form) = 3.899385919198901 y[1] (numeric) = 3.899385919198949 absolute error = 4.840572387365683e-14 relative error = 1.241367868600229e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999795 y[1] (closed_form) = 3.906655136558607 y[1] (numeric) = 3.906655136558657 absolute error = 4.973799150320701e-14 relative error = 1.273160536689232e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999794 y[1] (closed_form) = 3.914020687601872 y[1] (numeric) = 3.914020687601922 absolute error = 5.018208071305708e-14 relative error = 1.282110768397694e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999793 y[1] (closed_form) = 3.921482835771398 y[1] (numeric) = 3.921482835771448 absolute error = 5.018208071305708e-14 relative error = 1.279671053390846e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999792 y[1] (closed_form) = 3.929041834850251 y[1] (numeric) = 3.929041834850302 absolute error = 5.10702591327572e-14 relative error = 1.299814592956699e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.909999999999791 y[1] (closed_form) = 3.93669792893649 y[1] (numeric) = 3.936697928936542 absolute error = 5.195843755245733e-14 relative error = 1.319848220269571e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999789 y[1] (closed_form) = 3.944451352418753 y[1] (numeric) = 3.944451352418806 absolute error = 5.329070518200751e-14 relative error = 1.351029596279073e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999788 y[1] (closed_form) = 3.95230232995282 y[1] (numeric) = 3.952302329952874 absolute error = 5.417888360170764e-14 relative error = 1.370818299782102e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999787 y[1] (closed_form) = 3.960251076439146 y[1] (numeric) = 3.960251076439201 absolute error = 5.506706202140776e-14 relative error = 1.390494212577078e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999786 y[1] (closed_form) = 3.968297797001373 y[1] (numeric) = 3.968297797001429 absolute error = 5.595524044110789e-14 relative error = 1.41005648526152e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999785 y[1] (closed_form) = 3.976442686965818 y[1] (numeric) = 3.976442686965874 absolute error = 5.639932965095795e-14 relative error = 1.418336289262423e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999784 y[1] (closed_form) = 3.984685931841937 y[1] (numeric) = 3.984685931841995 absolute error = 5.773159728050814e-14 relative error = 1.448836828498086e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999783 y[1] (closed_form) = 3.99302770730378 y[1] (numeric) = 3.993027707303839 absolute error = 5.861977570020827e-14 relative error = 1.468053316859908e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999782 y[1] (closed_form) = 4.001468179172418 y[1] (numeric) = 4.001468179172478 absolute error = 5.950795411990839e-14 relative error = 1.487153001232058e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.999999999999781 y[1] (closed_form) = 4.010007503399367 y[1] (numeric) = 4.010007503399426 absolute error = 5.950795411990839e-14 relative error = 1.483986104002605e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.00999999999978 y[1] (closed_form) = 4.018645826050983 y[1] (numeric) = 4.018645826051043 absolute error = 6.039613253960852e-14 relative error = 1.50289762158409e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999778 y[1] (closed_form) = 4.027383283293869 y[1] (numeric) = 4.027383283293931 absolute error = 6.217248937900877e-14 relative error = 1.543744039384299e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999777 y[1] (closed_form) = 4.036220001381246 y[1] (numeric) = 4.03622000138131 absolute error = 6.394884621840902e-14 relative error = 1.584374642525058e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999776 y[1] (closed_form) = 4.04515609664034 y[1] (numeric) = 4.045156096640405 absolute error = 6.483702463810914e-14 relative error = 1.602831215634888e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999775 y[1] (closed_form) = 4.054191675460734 y[1] (numeric) = 4.054191675460801 absolute error = 6.750155989720952e-14 relative error = 1.664981956965278e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999774 y[1] (closed_form) = 4.063326834283746 y[1] (numeric) = 4.063326834283814 absolute error = 6.750155989720952e-14 relative error = 1.66123874967858e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999773 y[1] (closed_form) = 4.07256165959277 y[1] (numeric) = 4.072561659592838 absolute error = 6.838973831690964e-14 relative error = 1.679280610910337e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999772 y[1] (closed_form) = 4.08189622790464 y[1] (numeric) = 4.081896227904709 absolute error = 6.838973831690964e-14 relative error = 1.675440395798992e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.089999999999771 y[1] (closed_form) = 4.091330605761969 y[1] (numeric) = 4.09133060576204 absolute error = 7.105427357601002e-14 relative error = 1.736703298333841e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09999999999977 y[1] (closed_form) = 4.100864849726499 y[1] (numeric) = 4.100864849726572 absolute error = 7.283063041541027e-14 relative error = 1.775982215562836e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.109999999999769 y[1] (closed_form) = 4.110499006373448 y[1] (numeric) = 4.110499006373521 absolute error = 7.283063041541027e-14 relative error = 1.771819681807106e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999767 y[1] (closed_form) = 4.120233112286844 y[1] (numeric) = 4.120233112286917 absolute error = 7.371880883511039e-14 relative error = 1.789190243029585e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.129999999999766 y[1] (closed_form) = 4.130067194055876 y[1] (numeric) = 4.130067194055949 absolute error = 7.371880883511039e-14 relative error = 1.78493001133756e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999765 y[1] (closed_form) = 4.140001268272226 y[1] (numeric) = 4.1400012682723 absolute error = 7.460698725481052e-14 relative error = 1.80210058935433e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999764 y[1] (closed_form) = 4.150035341528421 y[1] (numeric) = 4.150035341528494 absolute error = 7.371880883511039e-14 relative error = 1.776341712019263e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.159999999999763 y[1] (closed_form) = 4.16016941041716 y[1] (numeric) = 4.160169410417235 absolute error = 7.460698725481052e-14 relative error = 1.793364161276531e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.169999999999762 y[1] (closed_form) = 4.170403461531669 y[1] (numeric) = 4.170403461531745 absolute error = 7.549516567451064e-14 relative error = 1.810260478893412e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.179999999999761 y[1] (closed_form) = 4.18073747146703 y[1] (numeric) = 4.180737471467107 absolute error = 7.638334409421077e-14 relative error = 1.827030389148249e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18999999999976 y[1] (closed_form) = 4.191171406822529 y[1] (numeric) = 4.191171406822606 absolute error = 7.638334409421077e-14 relative error = 1.822481990831284e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999759 y[1] (closed_form) = 4.201705224204991 y[1] (numeric) = 4.201705224205069 absolute error = 7.815970093361102e-14 relative error = 1.860190012458565e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999757 y[1] (closed_form) = 4.212338870233124 y[1] (numeric) = 4.212338870233201 absolute error = 7.72715225139109e-14 relative error = 1.834408980245088e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999756 y[1] (closed_form) = 4.223072281542851 y[1] (numeric) = 4.223072281542929 absolute error = 7.815970093361102e-14 relative error = 1.850778194709381e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999755 y[1] (closed_form) = 4.233905384793653 y[1] (numeric) = 4.233905384793732 absolute error = 7.904787935331115e-14 relative error = 1.867020449659002e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999754 y[1] (closed_form) = 4.2448380966759 y[1] (numeric) = 4.244838096675981 absolute error = 8.08242361927114e-14 relative error = 1.904059338706092e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999753 y[1] (closed_form) = 4.25587032391918 y[1] (numeric) = 4.255870323919262 absolute error = 8.171241461241152e-14 relative error = 1.919993054139007e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999752 y[1] (closed_form) = 4.26700196330163 y[1] (numeric) = 4.267001963301714 absolute error = 8.348877145181177e-14 relative error = 1.956614320074313e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.269999999999751 y[1] (closed_form) = 4.278232901660254 y[1] (numeric) = 4.278232901660338 absolute error = 8.43769498715119e-14 relative error = 1.972238347257059e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27999999999975 y[1] (closed_form) = 4.289563015902242 y[1] (numeric) = 4.289563015902328 absolute error = 8.526512829121202e-14 relative error = 1.987734600823385e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999749 y[1] (closed_form) = 4.300992173017279 y[1] (numeric) = 4.300992173017366 absolute error = 8.704148513061227e-14 relative error = 2.023753627748408e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999748 y[1] (closed_form) = 4.312520230090843 y[1] (numeric) = 4.312520230090931 absolute error = 8.79296635503124e-14 relative error = 2.038939155271166e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999746 y[1] (closed_form) = 4.324147034318501 y[1] (numeric) = 4.32414703431859 absolute error = 8.881784197001252e-14 relative error = 2.05399680596223e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999745 y[1] (closed_form) = 4.335872423021186 y[1] (numeric) = 4.335872423021276 absolute error = 8.970602038971265e-14 relative error = 2.068926657376292e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999744 y[1] (closed_form) = 4.347696223661464 y[1] (numeric) = 4.347696223661556 absolute error = 9.14823772291129e-14 relative error = 2.104157524420368e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999743 y[1] (closed_form) = 4.359618253860794 y[1] (numeric) = 4.359618253860886 absolute error = 9.237055564881302e-14 relative error = 2.118776238424349e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999742 y[1] (closed_form) = 4.371638321417755 y[1] (numeric) = 4.371638321417847 absolute error = 9.237055564881302e-14 relative error = 2.112950542963869e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.359999999999741 y[1] (closed_form) = 4.383756224327275 y[1] (numeric) = 4.383756224327368 absolute error = 9.325873406851315e-14 relative error = 2.127370439783624e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36999999999974 y[1] (closed_form) = 4.395971750800829 y[1] (numeric) = 4.395971750800922 absolute error = 9.325873406851315e-14 relative error = 2.121458902722109e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999739 y[1] (closed_form) = 4.408284679287615 y[1] (numeric) = 4.40828467928771 absolute error = 9.50350909079134e-14 relative error = 2.155829258360674e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999738 y[1] (closed_form) = 4.420694778496713 y[1] (numeric) = 4.420694778496808 absolute error = 9.50350909079134e-14 relative error = 2.149777256059074e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999737 y[1] (closed_form) = 4.433201807420208 y[1] (numeric) = 4.433201807420305 absolute error = 9.681144774731365e-14 relative error = 2.183781653821229e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y[1] (closed_form) = 4.4458055153573 y[1] (numeric) = 4.445805515357398 absolute error = 9.769962616701378e-14 relative error = 2.19756860324921e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999734 y[1] (closed_form) = 4.458505641939363 y[1] (numeric) = 4.45850564193946 absolute error = 9.769962616701378e-14 relative error = 2.191308792972982e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999733 y[1] (closed_form) = 4.471301917155989 y[1] (numeric) = 4.471301917156087 absolute error = 9.85878045867139e-14 relative error = 2.204901534571871e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999732 y[1] (closed_form) = 4.484194061381987 y[1] (numeric) = 4.484194061382086 absolute error = 9.85878045867139e-14 relative error = 2.198562400226052e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.449999999999731 y[1] (closed_form) = 4.497181785405345 y[1] (numeric) = 4.497181785405445 absolute error = 1.003641614261142e-13 relative error = 2.231712352652163e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45999999999973 y[1] (closed_form) = 4.51026479045615 y[1] (numeric) = 4.510264790456252 absolute error = 1.021405182655144e-13 relative error = 2.26462354231722e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999729 y[1] (closed_form) = 4.523442768236465 y[1] (numeric) = 4.523442768236569 absolute error = 1.039168751049147e-13 relative error = 2.297296117784824e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999728 y[1] (closed_form) = 4.536715400951161 y[1] (numeric) = 4.536715400951265 absolute error = 1.039168751049147e-13 relative error = 2.2905751390781e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999727 y[1] (closed_form) = 4.550082361339696 y[1] (numeric) = 4.5500823613398 absolute error = 1.048050535246148e-13 relative error = 2.303366075636413e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999726 y[1] (closed_form) = 4.563543312708833 y[1] (numeric) = 4.56354331270894 absolute error = 1.06581410364015e-13 relative error = 2.335496851036795e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y[1] (closed_form) = 4.577097908966321 y[1] (numeric) = 4.57709790896643 absolute error = 1.092459456231154e-13 relative error = 2.386795034668315e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999723 y[1] (closed_form) = 4.590745794655498 y[1] (numeric) = 4.590745794655608 absolute error = 1.101341240428155e-13 relative error = 2.399046450601395e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999722 y[1] (closed_form) = 4.604486604990832 y[1] (numeric) = 4.604486604990943 absolute error = 1.110223024625157e-13 relative error = 2.411176575954806e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.539999999999721 y[1] (closed_form) = 4.618319965894409 y[1] (numeric) = 4.618319965894522 absolute error = 1.127986593019159e-13 relative error = 2.442417592001352e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54999999999972 y[1] (closed_form) = 4.632245494033333 y[1] (numeric) = 4.632245494033447 absolute error = 1.145750161413162e-13 relative error = 2.473422798703071e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999719 y[1] (closed_form) = 4.646262796858061 y[1] (numeric) = 4.646262796858176 absolute error = 1.154631945610163e-13 relative error = 2.485076708082373e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999718 y[1] (closed_form) = 4.660371472641656 y[1] (numeric) = 4.660371472641775 absolute error = 1.190159082398168e-13 relative error = 2.553785871759157e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999717 y[1] (closed_form) = 4.674571110519967 y[1] (numeric) = 4.674571110520087 absolute error = 1.199040866595169e-13 relative error = 2.565028615987395e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999716 y[1] (closed_form) = 4.688861290532704 y[1] (numeric) = 4.688861290532825 absolute error = 1.20792265079217e-13 relative error = 2.576153517765798e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999715 y[1] (closed_form) = 4.703241583665442 y[1] (numeric) = 4.703241583665562 absolute error = 1.20792265079217e-13 relative error = 2.568276856088654e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y[1] (closed_form) = 4.717711551892515 y[1] (numeric) = 4.717711551892639 absolute error = 1.234568003383174e-13 relative error = 2.616878946081233e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999712 y[1] (closed_form) = 4.73227074822083 y[1] (numeric) = 4.732270748220954 absolute error = 1.243449787580175e-13 relative error = 2.627596462116352e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.629999999999711 y[1] (closed_form) = 4.74691871673455 y[1] (numeric) = 4.746918716734675 absolute error = 1.252331571777177e-13 relative error = 2.638198895974919e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63999999999971 y[1] (closed_form) = 4.761654992640698 y[1] (numeric) = 4.761654992640826 absolute error = 1.27897692436818e-13 relative error = 2.685992425626979e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999709 y[1] (closed_form) = 4.77647910231563 y[1] (numeric) = 4.77647910231576 absolute error = 1.305622276959184e-13 relative error = 2.733440781361778e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999708 y[1] (closed_form) = 4.791390563352398 y[1] (numeric) = 4.791390563352531 absolute error = 1.323385845353187e-13 relative error = 2.76200787194282e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999707 y[1] (closed_form) = 4.806388884608992 y[1] (numeric) = 4.806388884609127 absolute error = 1.35003119794419e-13 relative error = 2.808826398270138e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999706 y[1] (closed_form) = 4.821473566257453 y[1] (numeric) = 4.821473566257589 absolute error = 1.367794766338193e-13 relative error = 2.836881189001123e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999705 y[1] (closed_form) = 4.836644099833851 y[1] (numeric) = 4.836644099833989 absolute error = 1.376676550535194e-13 relative error = 2.846346603386604e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999704 y[1] (closed_form) = 4.851899968289138 y[1] (numeric) = 4.851899968289278 absolute error = 1.394440118929197e-13 relative error = 2.874008384432748e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999702 y[1] (closed_form) = 4.867240646040848 y[1] (numeric) = 4.86724064604099 absolute error = 1.4210854715202e-13 relative error = 2.919694288541397e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.719999999999701 y[1] (closed_form) = 4.882665599025658 y[1] (numeric) = 4.882665599025801 absolute error = 1.429967255717202e-13 relative error = 2.92866104941234e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7299999999997 y[1] (closed_form) = 4.898174284752788 y[1] (numeric) = 4.898174284752932 absolute error = 1.447730824111204e-13 relative error = 2.955653964004001e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999699 y[1] (closed_form) = 4.913766152358257 y[1] (numeric) = 4.913766152358403 absolute error = 1.456612608308205e-13 relative error = 2.964350689763971e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999698 y[1] (closed_form) = 4.929440642659965 y[1] (numeric) = 4.929440642660111 absolute error = 1.465494392505207e-13 relative error = 2.97294256841769e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999697 y[1] (closed_form) = 4.945197188213609 y[1] (numeric) = 4.945197188213757 absolute error = 1.483257960899209e-13 relative error = 2.99939093315512e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999696 y[1] (closed_form) = 4.961035213369431 y[1] (numeric) = 4.961035213369582 absolute error = 1.509903313490213e-13 relative error = 3.043524684971381e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999695 y[1] (closed_form) = 4.976954134329782 y[1] (numeric) = 4.976954134329936 absolute error = 1.536548666081217e-13 relative error = 3.087327358479133e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999694 y[1] (closed_form) = 4.992953359207497 y[1] (numeric) = 4.992953359207652 absolute error = 1.545430450278218e-13 relative error = 3.095223085607824e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999693 y[1] (closed_form) = 5.009032288085088 y[1] (numeric) = 5.009032288085245 absolute error = 1.572075802869222e-13 relative error = 3.138482070895601e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999691 y[1] (closed_form) = 5.025190313074733 y[1] (numeric) = 5.025190313074891 absolute error = 1.580957587066223e-13 relative error = 3.146065101162093e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81999999999969 y[1] (closed_form) = 5.041426818379064 y[1] (numeric) = 5.041426818379225 absolute error = 1.616484723854228e-13 relative error = 3.206403230849566e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999689 y[1] (closed_form) = 5.057741180352748 y[1] (numeric) = 5.057741180352911 absolute error = 1.63424829224823e-13 relative error = 3.231182130466888e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999688 y[1] (closed_form) = 5.07413276756485 y[1] (numeric) = 5.074132767565016 absolute error = 1.652011860642233e-13 relative error = 3.255752137985655e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999687 y[1] (closed_form) = 5.090600940861975 y[1] (numeric) = 5.090600940862142 absolute error = 1.669775429036235e-13 relative error = 3.280114564928945e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999686 y[1] (closed_form) = 5.107145053432184 y[1] (numeric) = 5.107145053432352 absolute error = 1.678657213233237e-13 relative error = 3.286879843181895e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999685 y[1] (closed_form) = 5.123764450869672 y[1] (numeric) = 5.123764450869843 absolute error = 1.714184350021242e-13 relative error = 3.345556507247885e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999684 y[1] (closed_form) = 5.140458471240212 y[1] (numeric) = 5.140458471240384 absolute error = 1.723066134218243e-13 relative error = 3.351969758842401e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999683 y[1] (closed_form) = 5.157226445147346 y[1] (numeric) = 5.157226445147519 absolute error = 1.731947918415244e-13 relative error = 3.358293332349034e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999681 y[1] (closed_form) = 5.174067695799322 y[1] (numeric) = 5.174067695799497 absolute error = 1.749711486809247e-13 relative error = 3.381694229145451e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.90999999999968 y[1] (closed_form) = 5.190981539076777 y[1] (numeric) = 5.190981539076954 absolute error = 1.77635683940025e-13 relative error = 3.422005695894226e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999679 y[1] (closed_form) = 5.207967283601144 y[1] (numeric) = 5.207967283601323 absolute error = 1.785238623597252e-13 relative error = 3.427899075362117e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999678 y[1] (closed_form) = 5.225024230803792 y[1] (numeric) = 5.225024230803973 absolute error = 1.803002191991254e-13 relative error = 3.450705895987566e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999677 y[1] (closed_form) = 5.242151674995882 y[1] (numeric) = 5.242151674996065 absolute error = 1.829647544582258e-13 relative error = 3.490260599114953e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999676 y[1] (closed_form) = 5.259348903438934 y[1] (numeric) = 5.25934890343912 absolute error = 1.865174681370263e-13 relative error = 3.546398452764144e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999675 y[1] (closed_form) = 5.276615196416101 y[1] (numeric) = 5.276615196416289 absolute error = 1.882938249764265e-13 relative error = 3.56845852819278e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999674 y[1] (closed_form) = 5.293949827304141 y[1] (numeric) = 5.293949827304331 absolute error = 1.900701818158268e-13 relative error = 3.590328356259035e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999673 y[1] (closed_form) = 5.311352062646078 y[1] (numeric) = 5.311352062646269 absolute error = 1.909583602355269e-13 relative error = 3.595287188332095e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999672 y[1] (closed_form) = 5.328821162224545 y[1] (numeric) = 5.328821162224739 absolute error = 1.936228954946273e-13 relative error = 3.633503350932467e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99999999999967 y[1] (closed_form) = 5.346356379135809 y[1] (numeric) = 5.346356379136005 absolute error = 1.962874307537277e-13 relative error = 3.671424365194596e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999674 y[1] (closed_form) = 5.363956959864466 y[1] (numeric) = 5.363956959864656 absolute error = 1.900701818158268e-13 relative error = 3.54346955499489e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999677 y[1] (closed_form) = 5.38162214435877 y[1] (numeric) = 5.381622144358954 absolute error = 1.84741111297626e-13 relative error = 3.432814611320846e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.029999999999681 y[1] (closed_form) = 5.399351166106657 y[1] (numeric) = 5.399351166106835 absolute error = 1.785238623597252e-13 relative error = 3.306394729062501e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999684 y[1] (closed_form) = 5.417143252212395 y[1] (numeric) = 5.417143252212567 absolute error = 1.714184350021242e-13 relative error = 3.16436961367259e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999687 y[1] (closed_form) = 5.434997623473866 y[1] (numeric) = 5.434997623474032 absolute error = 1.652011860642233e-13 relative error = 3.039581569469616e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.059999999999691 y[1] (closed_form) = 5.45291349446049 y[1] (numeric) = 5.452913494460648 absolute error = 1.580957587066223e-13 relative error = 2.899289689213459e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999694 y[1] (closed_form) = 5.470890073591764 y[1] (numeric) = 5.470890073591915 absolute error = 1.518785097687214e-13 relative error = 2.776120662739065e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999697 y[1] (closed_form) = 5.488926563216421 y[1] (numeric) = 5.488926563216568 absolute error = 1.465494392505207e-13 relative error = 2.669910729587992e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.089999999999701 y[1] (closed_form) = 5.507022159692198 y[1] (numeric) = 5.507022159692339 absolute error = 1.403321903126198e-13 relative error = 2.548240886694804e-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) = 5.525176053466192 y[1] (numeric) = 5.525176053466327 absolute error = 1.35003119794419e-13 relative error = 2.44341752168649e-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) = 5.543387429155822 y[1] (numeric) = 5.543387429155952 absolute error = 1.296740492762183e-13 relative error = 2.339256473292645e-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) = 5.56165546563036 y[1] (numeric) = 5.561655465630484 absolute error = 1.243449787580175e-13 relative error = 2.235754795068454e-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) = 5.57997933609305 y[1] (numeric) = 5.579979336093168 absolute error = 1.181277298201167e-13 relative error = 2.116992245043446e-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) = 5.598358208163781 y[1] (numeric) = 5.598358208163893 absolute error = 1.110223024625157e-13 relative error = 1.983122521538866e-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) = 5.61679124396233 y[1] (numeric) = 5.616791243962435 absolute error = 1.056932319443149e-13 relative error = 1.881736873484981e-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) = 5.635277600192143 y[1] (numeric) = 5.635277600192241 absolute error = 9.85878045867139e-14 relative error = 1.749475564138179e-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) = 5.653816428224669 y[1] (numeric) = 5.65381642822476 absolute error = 9.14823772291129e-14 relative error = 1.618064158794043e-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) = 5.672406874184222 y[1] (numeric) = 5.672406874184307 absolute error = 8.526512829121202e-14 relative error = 1.503156070825305e-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) = 5.691048079033362 y[1] (numeric) = 5.691048079033441 absolute error = 7.904787935331115e-14 relative error = 1.388986321246079e-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) = 5.709739178658809 y[1] (numeric) = 5.70973917865888 absolute error = 7.194245199571014e-14 relative error = 1.259995417384531e-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) = 5.728479303957839 y[1] (numeric) = 5.728479303957906 absolute error = 6.661338147750939e-14 relative error = 1.162845808511272e-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) = 5.747267580925209 y[1] (numeric) = 5.74726758092527 absolute error = 6.039613253960852e-14 relative error = 1.050866897863938e-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) = 5.766103130740543 y[1] (numeric) = 5.766103130740597 absolute error = 5.417888360170764e-14 relative error = 9.396100342511465e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.239999999999751 y[1] (closed_form) = 5.784985069856224 y[1] (numeric) = 5.784985069856271 absolute error = 4.707345624410664e-14 relative error = 8.137178519161946e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999754 y[1] (closed_form) = 5.803912510085741 y[1] (numeric) = 5.803912510085783 absolute error = 4.174438572590589e-14 relative error = 7.192456063623398e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999757 y[1] (closed_form) = 5.822884558692511 y[1] (numeric) = 5.822884558692547 absolute error = 3.552713678800501e-14 relative error = 6.101295059159199e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.269999999999761 y[1] (closed_form) = 5.841900318479151 y[1] (numeric) = 5.841900318479181 absolute error = 2.930988785010413e-14 relative error = 5.01718383612107e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999764 y[1] (closed_form) = 5.860958887877194 y[1] (numeric) = 5.860958887877217 absolute error = 2.309263891220326e-14 relative error = 3.940078637979881e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999767 y[1] (closed_form) = 5.880059361037249 y[1] (numeric) = 5.880059361037266 absolute error = 1.687538997430238e-14 relative error = 2.869935308157423e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.299999999999771 y[1] (closed_form) = 5.899200827919586 y[1] (numeric) = 5.899200827919596 absolute error = 9.769962616701378e-15 relative error = 1.656150197576314e-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) = 5.918382374385131 y[1] (numeric) = 5.918382374385135 absolute error = 3.552713678800501e-15 relative error = 6.002845801543191e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999777 y[1] (closed_form) = 5.937603082286891 y[1] (numeric) = 5.937603082286888 absolute error = 3.552713678800501e-15 relative error = 5.983413895413432e-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) = 5.956862029561759 y[1] (numeric) = 5.95686202956175 absolute error = 9.769962616701378e-15 relative error = 1.640119003632546e-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) = 5.976158290322725 y[1] (numeric) = 5.976158290322707 absolute error = 1.77635683940025e-14 relative error = 2.972405938906821e-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) = 5.995490934951457 y[1] (numeric) = 5.995490934951433 absolute error = 2.398081733190338e-14 relative error = 3.999808788318608e-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) = 6.014859030191271 y[1] (numeric) = 6.01485903019124 absolute error = 3.108624468950438e-14 relative error = 5.168241605242716e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999794 y[1] (closed_form) = 6.03426163924045 y[1] (numeric) = 6.034261639240412 absolute error = 3.819167204710538e-14 relative error = 6.329137569830777e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y[1] (closed_form) = 6.053697821845923 y[1] (numeric) = 6.053697821845877 absolute error = 4.529709940470639e-14 relative error = 7.482550457216938e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999801 y[1] (closed_form) = 6.073166634397293 y[1] (numeric) = 6.073166634397242 absolute error = 5.151434834260726e-14 relative error = 8.482287979855437e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999804 y[1] (closed_form) = 6.092667130021198 y[1] (numeric) = 6.092667130021139 absolute error = 5.861977570020827e-14 relative error = 9.621365232865481e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y[1] (closed_form) = 6.11219835867599 y[1] (numeric) = 6.112198358675925 absolute error = 6.572520305780927e-14 relative error = 1.075312010522618e-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) = 6.131759367246747 y[1] (numeric) = 6.131759367246675 absolute error = 7.194245199571014e-14 relative error = 1.17327585260433e-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) = 6.151349199640581 y[1] (numeric) = 6.151349199640503 absolute error = 7.815970093361102e-14 relative error = 1.270610696888706e-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) = 6.170966896882242 y[1] (numeric) = 6.170966896882159 absolute error = 8.348877145181177e-14 relative error = 1.352928525576645e-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) = 6.190611497210021 y[1] (numeric) = 6.190611497209931 absolute error = 9.059419880941277e-14 relative error = 1.463412763831839e-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) = 6.210282036171924 y[1] (numeric) = 6.210282036171826 absolute error = 9.769962616701378e-14 relative error = 1.573191452464802e-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) = 6.22997754672211 y[1] (numeric) = 6.229977546722006 absolute error = 1.039168751049147e-13 relative error = 1.668013637699069e-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) = 6.249697059317607 y[1] (numeric) = 6.249697059317495 absolute error = 1.119104808822158e-13 relative error = 1.790654488050259e-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) = 6.269439602015254 y[1] (numeric) = 6.269439602015136 absolute error = 1.181277298201167e-13 relative error = 1.884183233572353e-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) = 6.289204200568899 y[1] (numeric) = 6.289204200568774 absolute error = 1.252331571777177e-13 relative error = 1.991240118525481e-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) = 6.308989878526825 y[1] (numeric) = 6.308989878526693 absolute error = 1.323385845353187e-13 relative error = 2.097619224049544e-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) = 6.32879565732939 y[1] (numeric) = 6.328795657329252 absolute error = 1.385558334732195e-13 relative error = 2.189292259938236e-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) = 6.348620556406885 y[1] (numeric) = 6.348620556406743 absolute error = 1.4210854715202e-13 relative error = 2.238416139213223e-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) = 6.368463593277593 y[1] (numeric) = 6.368463593277442 absolute error = 1.509903313490213e-13 relative error = 2.370906720867546e-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) = 6.388323783646024 y[1] (numeric) = 6.388323783645867 absolute error = 1.572075802869222e-13 relative error = 2.46085805308382e-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) = 6.408200141501362 y[1] (numeric) = 6.408200141501197 absolute error = 1.643130076445232e-13 relative error = 2.564105427675152e-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) = 6.428091679216049 y[1] (numeric) = 6.428091679215878 absolute error = 1.70530256582424e-13 relative error = 2.652890859254537e-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) = 6.447997407644559 y[1] (numeric) = 6.447997407644381 absolute error = 1.77635683940025e-13 relative error = 2.754896950321744e-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) = 6.467916336222302 y[1] (numeric) = 6.467916336222117 absolute error = 1.84741111297626e-13 relative error = 2.856269340761561e-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) = 6.487847473064688 y[1] (numeric) = 6.487847473064494 absolute error = 1.945110739143274e-13 relative error = 2.998083335372333e-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) = 6.507789825066307 y[1] (numeric) = 6.507789825066106 absolute error = 2.007283228522283e-13 relative error = 3.084431554305507e-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) = 6.527742398000244 y[1] (numeric) = 6.527742398000036 absolute error = 2.078337502098293e-13 relative error = 3.183853429533289e-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) = 6.5477041966175 y[1] (numeric) = 6.547704196617286 absolute error = 2.140509991477302e-13 relative error = 3.269100019183938e-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) = 6.567674224746515 y[1] (numeric) = 6.567674224746293 absolute error = 2.220446049250313e-13 relative error = 3.380871177933636e-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) = 6.587651485392783 y[1] (numeric) = 6.587651485392555 absolute error = 2.282618538629322e-13 relative error = 3.464995899814549e-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) = 6.607634980838556 y[1] (numeric) = 6.60763498083832 absolute error = 2.362554596402333e-13 relative error = 3.575491992601728e-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) = 6.627623712742607 y[1] (numeric) = 6.627623712742365 absolute error = 2.415845301584341e-13 relative error = 3.645115363051637e-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) = 6.647616682240071 y[1] (numeric) = 6.647616682239822 absolute error = 2.486899575160351e-13 relative error = 3.741039374012659e-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) = 6.667612890042324 y[1] (numeric) = 6.667612890042069 absolute error = 2.549072064539359e-13 relative error = 3.82306547572107e-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) = 6.687611336536918 y[1] (numeric) = 6.687611336536657 absolute error = 2.611244553918368e-13 relative error = 3.904599747973038e-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) = 6.707611021887534 y[1] (numeric) = 6.707611021887266 absolute error = 2.673417043297377e-13 relative error = 3.985647102334615e-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) = 6.72761094613397 y[1] (numeric) = 6.727610946133694 absolute error = 2.753353101070388e-13 relative error = 4.092616417797771e-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) = 6.747610109292135 y[1] (numeric) = 6.747610109291852 absolute error = 2.833289158843399e-13 relative error = 4.198952092595979e-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) = 6.767607511454047 y[1] (numeric) = 6.767607511453757 absolute error = 2.90434343241941e-13 relative error = 4.291536451403045e-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) = 6.787602152887819 y[1] (numeric) = 6.787602152887522 absolute error = 2.966515921798418e-13 relative error = 4.370491750958473e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999924 y[1] (closed_form) = 6.807593034137637 y[1] (numeric) = 6.807593034137334 absolute error = 3.028688411177427e-13 relative error = 4.448985707561603e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999928 y[1] (closed_form) = 6.827579156123702 y[1] (numeric) = 6.827579156123393 absolute error = 3.099742684753437e-13 relative error = 4.540031852978602e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.779999999999931 y[1] (closed_form) = 6.847559520242137 y[1] (numeric) = 6.847559520241821 absolute error = 3.161915174132446e-13 relative error = 4.617579686288929e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999934 y[1] (closed_form) = 6.867533128464848 y[1] (numeric) = 6.867533128464523 absolute error = 3.241851231905457e-13 relative error = 4.720546914391271e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999938 y[1] (closed_form) = 6.887498983439322 y[1] (numeric) = 6.887498983438991 absolute error = 3.304023721284466e-13 relative error = 4.797131337846787e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.809999999999941 y[1] (closed_form) = 6.907456088588368 y[1] (numeric) = 6.907456088588032 absolute error = 3.366196210663475e-13 relative error = 4.873279203648766e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999944 y[1] (closed_form) = 6.927403448209769 y[1] (numeric) = 6.927403448209426 absolute error = 3.428368700042483e-13 relative error = 4.948995284702911e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999948 y[1] (closed_form) = 6.947340067575851 y[1] (numeric) = 6.9473400675755 absolute error = 3.508304757815495e-13 relative error = 5.049853215317923e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.839999999999951 y[1] (closed_form) = 6.967264953032959 y[1] (numeric) = 6.9672649530326 absolute error = 3.597122599785507e-13 relative error = 5.162890494382051e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999954 y[1] (closed_form) = 6.987177112100817 y[1] (numeric) = 6.987177112100452 absolute error = 3.650413304967515e-13 relative error = 5.224446505936579e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999958 y[1] (closed_form) = 7.007075553571779 y[1] (numeric) = 7.007075553571408 absolute error = 3.712585794346523e-13 relative error = 5.298338466543398e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.869999999999961 y[1] (closed_form) = 7.026959287609946 y[1] (numeric) = 7.026959287609569 absolute error = 3.774758283725532e-13 relative error = 5.371823187279952e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999964 y[1] (closed_form) = 7.046827325850151 y[1] (numeric) = 7.046827325849767 absolute error = 3.836930773104541e-13 relative error = 5.444905339214683e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999968 y[1] (closed_form) = 7.066678681496794 y[1] (numeric) = 7.066678681496403 absolute error = 3.907985046680551e-13 relative error = 5.530158116447429e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.899999999999971 y[1] (closed_form) = 7.086512369422518 y[1] (numeric) = 7.086512369422119 absolute error = 3.987921104453562e-13 relative error = 5.627480623135551e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999974 y[1] (closed_form) = 7.106327406266727 y[1] (numeric) = 7.106327406266322 absolute error = 4.050093593832571e-13 relative error = 5.699278069092326e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999978 y[1] (closed_form) = 7.126122810533914 y[1] (numeric) = 7.126122810533505 absolute error = 4.094502514817577e-13 relative error = 5.745764735860345e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.929999999999981 y[1] (closed_form) = 7.145897602691817 y[1] (numeric) = 7.145897602691399 absolute error = 4.18332035678759e-13 relative error = 5.85415659358421e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y[1] (closed_form) = 7.165650805269364 y[1] (numeric) = 7.16565080526894 absolute error = 4.245492846166599e-13 relative error = 5.924783333070897e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999988 y[1] (closed_form) = 7.185381442954426 y[1] (numeric) = 7.185381442953997 absolute error = 4.298783551348606e-13 relative error = 5.98267967466605e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.959999999999991 y[1] (closed_form) = 7.205088542691344 y[1] (numeric) = 7.205088542690907 absolute error = 4.369837824924616e-13 relative error = 6.064932858260662e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y[1] (closed_form) = 7.224771133778232 y[1] (numeric) = 7.224771133777789 absolute error = 4.423128530106624e-13 relative error = 6.122171136227433e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999998 y[1] (closed_form) = 7.244428247964051 y[1] (numeric) = 7.244428247963602 absolute error = 4.494182803682634e-13 relative error = 6.203640439044535e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.990000000000001 y[1] (closed_form) = 7.264058919545429 y[1] (numeric) = 7.264058919544975 absolute error = 4.547473508864641e-13 relative error = 6.260237642936428e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Finished! diff ( y , x , 1 ) = 1.0 - sin ( x ) ; 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 %