##############ECHO OF PROBLEM################# ##############temp/cospostode.ode################# diff ( y , x , 1 ) = cos ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.0); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=false; 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(1.0) + sin(c(x))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (closed_form) = 1.009999833334167 y[1] (numeric) = 1.009999833334167 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] = 0.02000000000000001 y[1] (closed_form) = 1.019998666693333 y[1] (numeric) = 1.019998666693333 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] = 0.03000000000000002 y[1] (closed_form) = 1.029995500202496 y[1] (numeric) = 1.029995500202496 absolute error = 4.440892098500626e-16 relative error = 4.311564562784549e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.04000000000000003 y[1] (closed_form) = 1.039989334186634 y[1] (numeric) = 1.039989334186634 absolute error = 2.220446049250313e-16 relative error = 2.135066174488129e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.05000000000000004 y[1] (closed_form) = 1.049979169270678 y[1] (numeric) = 1.049979169270679 absolute error = 4.440892098500626e-16 relative error = 4.229504954450949e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.06000000000000005 y[1] (closed_form) = 1.059964006479445 y[1] (numeric) = 1.059964006479445 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] = 0.07000000000000005 y[1] (closed_form) = 1.069942847337533 y[1] (numeric) = 1.069942847337533 absolute error = 2.220446049250313e-16 relative error = 2.075294072740161e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.08000000000000006 y[1] (closed_form) = 1.079914693969173 y[1] (numeric) = 1.079914693969173 absolute error = 2.220446049250313e-16 relative error = 2.056130971872578e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.09000000000000007 y[1] (closed_form) = 1.089878549198011 y[1] (numeric) = 1.089878549198011 absolute error = 2.220446049250313e-16 relative error = 2.037333472508686e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1000000000000001 y[1] (closed_form) = 1.099833416646828 y[1] (numeric) = 1.099833416646829 absolute error = 4.440892098500626e-16 relative error = 4.037786114955496e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1100000000000001 y[1] (closed_form) = 1.109778300837175 y[1] (numeric) = 1.109778300837175 absolute error = 4.440892098500626e-16 relative error = 4.001602928396225e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1200000000000001 y[1] (closed_form) = 1.119712207288919 y[1] (numeric) = 1.11971220728892 absolute error = 2.220446049250313e-16 relative error = 1.983050675696859e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1300000000000001 y[1] (closed_form) = 1.129634142619695 y[1] (numeric) = 1.129634142619695 absolute error = 2.220446049250313e-16 relative error = 1.965632911998352e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1400000000000001 y[1] (closed_form) = 1.139543114644237 y[1] (numeric) = 1.139543114644236 absolute error = 2.220446049250313e-16 relative error = 1.948540621864521e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1500000000000001 y[1] (closed_form) = 1.149438132473599 y[1] (numeric) = 1.149438132473599 absolute error = 4.440892098500626e-16 relative error = 3.863532949741099e-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) = 1.159318206614246 y[1] (numeric) = 1.159318206614246 absolute error = 4.440892098500626e-16 relative error = 3.830606707601115e-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) = 1.169182349066996 y[1] (numeric) = 1.169182349066995 absolute error = 6.661338147750939e-16 relative error = 5.697433042045722e-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) = 1.179029573425824 y[1] (numeric) = 1.179029573425824 absolute error = 4.440892098500626e-16 relative error = 3.766565486221889e-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) = 1.188858894976501 y[1] (numeric) = 1.1888588949765 absolute error = 6.661338147750939e-16 relative error = 5.603136062570831e-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) = 1.198669330795061 y[1] (numeric) = 1.198669330795061 absolute error = 6.661338147750939e-16 relative error = 5.557277538195261e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000002 y[1] (closed_form) = 1.2084598998461 y[1] (numeric) = 1.208459899846099 absolute error = 8.881784197001252e-16 relative error = 7.349672254852948e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000002 y[1] (closed_form) = 1.21822962308087 y[1] (numeric) = 1.218229623080869 absolute error = 8.881784197001252e-16 relative error = 7.290730769244851e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000002 y[1] (closed_form) = 1.227977523535189 y[1] (numeric) = 1.227977523535188 absolute error = 8.881784197001252e-16 relative error = 7.232855672660639e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000002 y[1] (closed_form) = 1.237702626427135 y[1] (numeric) = 1.237702626427134 absolute error = 4.440892098500626e-16 relative error = 3.588012179726976e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000002 y[1] (closed_form) = 1.247403959254523 y[1] (numeric) = 1.247403959254523 absolute error = 6.661338147750939e-16 relative error = 5.340161138923998e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000002 y[1] (closed_form) = 1.257080551892155 y[1] (numeric) = 1.257080551892155 absolute error = 4.440892098500626e-16 relative error = 3.532702889895325e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000002 y[1] (closed_form) = 1.266731436688831 y[1] (numeric) = 1.266731436688831 absolute error = 6.661338147750939e-16 relative error = 5.258682270618722e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000002 y[1] (closed_form) = 1.276355648564114 y[1] (numeric) = 1.276355648564113 absolute error = 6.661338147750939e-16 relative error = 5.219029786286347e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000002 y[1] (closed_form) = 1.285952225104836 y[1] (numeric) = 1.285952225104835 absolute error = 4.440892098500626e-16 relative error = 3.453388090011344e-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) = 1.29552020666134 y[1] (numeric) = 1.295520206661339 absolute error = 6.661338147750939e-16 relative error = 5.141824970000079e-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) = 1.305058636443444 y[1] (numeric) = 1.305058636443443 absolute error = 6.661338147750939e-16 relative error = 5.104244331813681e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 1.314566560616118 y[1] (numeric) = 1.314566560616118 absolute error = 4.440892098500626e-16 relative error = 3.378217757508791e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 1.324043028394869 y[1] (numeric) = 1.324043028394868 absolute error = 4.440892098500626e-16 relative error = 3.354039108445214e-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) = 1.333487092140815 y[1] (numeric) = 1.333487092140814 absolute error = 6.661338147750939e-16 relative error = 4.99542754257685e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000003 y[1] (closed_form) = 1.342897807455452 y[1] (numeric) = 1.342897807455451 absolute error = 6.661338147750939e-16 relative error = 4.960420748897468e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000003 y[1] (closed_form) = 1.35227423327509 y[1] (numeric) = 1.35227423327509 absolute error = 6.661338147750939e-16 relative error = 4.926026085417422e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000003 y[1] (closed_form) = 1.361615431964962 y[1] (numeric) = 1.361615431964962 absolute error = 6.661338147750939e-16 relative error = 4.892231676706167e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000003 y[1] (closed_form) = 1.370920469412983 y[1] (numeric) = 1.370920469412982 absolute error = 6.661338147750939e-16 relative error = 4.859025958379095e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000003 y[1] (closed_form) = 1.380188415123162 y[1] (numeric) = 1.380188415123161 absolute error = 4.440892098500626e-16 relative error = 3.217598445140073e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000003 y[1] (closed_form) = 1.389418342308651 y[1] (numeric) = 1.38941834230865 absolute error = 8.881784197001252e-16 relative error = 6.392447779437921e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = 1.398609327984423 y[1] (numeric) = 1.398609327984422 absolute error = 8.881784197001252e-16 relative error = 6.350439696981752e-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) = 1.40776045305957 y[1] (numeric) = 1.40776045305957 absolute error = 6.661338147750939e-16 relative error = 4.73186907138459e-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) = 1.416870802429211 y[1] (numeric) = 1.41687080242921 absolute error = 6.661338147750939e-16 relative error = 4.701443587044169e-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) = 1.425939465066 y[1] (numeric) = 1.425939465065999 absolute error = 8.881784197001252e-16 relative error = 6.228724580948572e-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) = 1.43496553411123 y[1] (numeric) = 1.43496553411123 absolute error = 8.881784197001252e-16 relative error = 6.189545313715379e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000004 y[1] (closed_form) = 1.44394810696552 y[1] (numeric) = 1.443948106965519 absolute error = 6.661338147750939e-16 relative error = 4.613280848263895e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000004 y[1] (closed_form) = 1.452886285379069 y[1] (numeric) = 1.452886285379068 absolute error = 8.881784197001252e-16 relative error = 6.113199832899469e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000004 y[1] (closed_form) = 1.461779175541483 y[1] (numeric) = 1.461779175541483 absolute error = 4.440892098500626e-16 relative error = 3.038004763514022e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000004 y[1] (closed_form) = 1.470625888171158 y[1] (numeric) = 1.470625888171158 absolute error = 4.440892098500626e-16 relative error = 3.01972930996287e-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) = 1.479425538604203 y[1] (numeric) = 1.479425538604202 absolute error = 8.881784197001252e-16 relative error = 6.003535808487508e-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) = 1.488177246882908 y[1] (numeric) = 1.488177246882907 absolute error = 8.881784197001252e-16 relative error = 5.968230071790693e-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) = 1.496880137843737 y[1] (numeric) = 1.496880137843736 absolute error = 8.881784197001252e-16 relative error = 5.933530663180222e-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) = 1.505533341204847 y[1] (numeric) = 1.505533341204846 absolute error = 8.881784197001252e-16 relative error = 5.899427102619556e-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) = 1.514135991653113 y[1] (numeric) = 1.514135991653113 absolute error = 8.881784197001252e-16 relative error = 5.865909169297429e-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) = 1.522687228930659 y[1] (numeric) = 1.522687228930658 absolute error = 1.110223024625157e-15 relative error = 7.291208618101007e-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) = 1.531186197920884 y[1] (numeric) = 1.531186197920883 absolute error = 1.110223024625157e-15 relative error = 7.250738193256113e-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) = 1.539632048733969 y[1] (numeric) = 1.539632048733968 absolute error = 1.110223024625157e-15 relative error = 7.210963330739228e-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) = 1.548023936791874 y[1] (numeric) = 1.548023936791872 absolute error = 1.554312234475219e-15 relative error = 1.004062144992652e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (closed_form) = 1.556361022912784 y[1] (numeric) = 1.556361022912783 absolute error = 1.332267629550188e-15 relative error = 8.560145171566958e-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) = 1.564642473395036 y[1] (numeric) = 1.564642473395034 absolute error = 1.554312234475219e-15 relative error = 9.933977000525867e-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) = 1.572867460100482 y[1] (numeric) = 1.57286746010048 absolute error = 1.554312234475219e-15 relative error = 9.882029312094249e-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) = 1.581035160537305 y[1] (numeric) = 1.581035160537304 absolute error = 1.332267629550188e-15 relative error = 8.426552823135348e-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) = 1.58914475794227 y[1] (numeric) = 1.589144757942268 absolute error = 1.77635683940025e-15 relative error = 1.117806814339806e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (closed_form) = 1.597195441362393 y[1] (numeric) = 1.597195441362391 absolute error = 1.332267629550188e-15 relative error = 8.341293714273165e-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) = 1.60518640573604 y[1] (numeric) = 1.605186405736039 absolute error = 8.881784197001252e-16 relative error = 5.533179302579885e-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) = 1.613116851973434 y[1] (numeric) = 1.613116851973433 absolute error = 8.881784197001252e-16 relative error = 5.505976945275582e-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) = 1.62098598703656 y[1] (numeric) = 1.620985987036559 absolute error = 6.661338147750939e-16 relative error = 4.109435985889678e-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) = 1.628793024018469 y[1] (numeric) = 1.628793024018468 absolute error = 4.440892098500626e-16 relative error = 2.726492582553123e-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) = 1.636537182221968 y[1] (numeric) = 1.636537182221968 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] = 0.7000000000000005 y[1] (closed_form) = 1.644217687237691 y[1] (numeric) = 1.644217687237691 absolute error = 2.220446049250313e-16 relative error = 1.350457464656455e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (closed_form) = 1.651833771021537 y[1] (numeric) = 1.651833771021537 absolute error = 4.440892098500626e-16 relative error = 2.688461863662142e-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) = 1.659384671971474 y[1] (numeric) = 1.659384671971473 absolute error = 2.220446049250313e-16 relative error = 1.338114113475724e-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) = 1.666869635003698 y[1] (numeric) = 1.666869635003698 absolute error = 2.220446049250313e-16 relative error = 1.332105404418976e-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) = 1.674287911628145 y[1] (numeric) = 1.674287911628145 absolute error = 2.220446049250313e-16 relative error = 1.326203237704238e-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) = 1.681638760023334 y[1] (numeric) = 1.681638760023335 absolute error = 2.220446049250313e-16 relative error = 1.320406083658242e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (closed_form) = 1.688921445110552 y[1] (numeric) = 1.688921445110552 absolute error = 2.220446049250313e-16 relative error = 1.314712448988395e-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) = 1.696135238627357 y[1] (numeric) = 1.696135238627357 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) = 1.703279419200411 y[1] (numeric) = 1.70327941920041 absolute error = 2.220446049250313e-16 relative error = 1.303629941288601e-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) = 1.710353272417608 y[1] (numeric) = 1.710353272417608 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) = 1.717356090899523 y[1] (numeric) = 1.717356090899523 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (closed_form) = 1.724287174370143 y[1] (numeric) = 1.724287174370143 absolute error = 2.220446049250313e-16 relative error = 1.287747239702928e-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) = 1.731145829726896 y[1] (numeric) = 1.731145829726896 absolute error = 2.220446049250313e-16 relative error = 1.282645292569378e-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) = 1.737931371109963 y[1] (numeric) = 1.737931371109963 absolute error = 2.220446049250313e-16 relative error = 1.277637360232575e-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) = 1.74464311997086 y[1] (numeric) = 1.74464311997086 absolute error = 2.220446049250313e-16 relative error = 1.272722211111806e-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) = 1.751280405140293 y[1] (numeric) = 1.751280405140293 absolute error = 4.440892098500626e-16 relative error = 2.53579728606903e-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) = 1.757842562895277 y[1] (numeric) = 1.757842562895277 absolute error = 4.440892098500626e-16 relative error = 2.526330965149801e-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) = 1.764328937025506 y[1] (numeric) = 1.764328937025505 absolute error = 6.661338147750939e-16 relative error = 3.775564753237758e-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) = 1.77073887889897 y[1] (numeric) = 1.770738878898969 absolute error = 6.661338147750939e-16 relative error = 3.761897492132156e-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) = 1.777071747526824 y[1] (numeric) = 1.777071747526824 absolute error = 6.661338147750939e-16 relative error = 3.748491391538703e-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) = 1.783326909627484 y[1] (numeric) = 1.783326909627483 absolute error = 6.661338147750939e-16 relative error = 3.735343257475106e-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) = 1.789503739689951 y[1] (numeric) = 1.78950373968995 absolute error = 8.881784197001252e-16 relative error = 4.963266630859407e-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) = 1.795601620036366 y[1] (numeric) = 1.795601620036366 absolute error = 6.661338147750939e-16 relative error = 3.709808497285732e-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) = 1.801619940883778 y[1] (numeric) = 1.801619940883777 absolute error = 8.881784197001252e-16 relative error = 4.929887816763578e-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) = 1.807558100405115 y[1] (numeric) = 1.807558100405114 absolute error = 1.110223024625157e-15 relative error = 6.14211529010509e-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) = 1.813415504789374 y[1] (numeric) = 1.813415504789373 absolute error = 1.554312234475219e-15 relative error = 8.571186417950862e-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) = 1.819191568300999 y[1] (numeric) = 1.819191568300997 absolute error = 1.77635683940025e-15 relative error = 9.764539756850605e-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) = 1.824885713338451 y[1] (numeric) = 1.824885713338449 absolute error = 1.554312234475219e-15 relative error = 8.517312745200665e-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) = 1.830497370491971 y[1] (numeric) = 1.83049737049197 absolute error = 1.110223024625157e-15 relative error = 6.06514405604838e-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) = 1.836025978600521 y[1] (numeric) = 1.83602597860052 absolute error = 8.881784197001252e-16 relative error = 4.83750464346438e-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) = 1.841470984807897 y[1] (numeric) = 1.841470984807896 absolute error = 8.881784197001252e-16 relative error = 4.823200729349425e-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) = 1.846831844618015 y[1] (numeric) = 1.846831844618015 absolute error = 2.220446049250313e-16 relative error = 1.202300066311437e-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) = 1.852108021949362 y[1] (numeric) = 1.852108021949362 absolute error = 2.220446049250313e-16 relative error = 1.198875023991998e-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) = 1.857298989188602 y[1] (numeric) = 1.857298989188603 absolute error = 8.881784197001252e-16 relative error = 4.782097146825798e-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) = 1.862404227243337 y[1] (numeric) = 1.862404227243338 absolute error = 1.332267629550188e-15 relative error = 7.153482633156187e-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) = 1.867423225594015 y[1] (numeric) = 1.867423225594016 absolute error = 1.77635683940025e-15 relative error = 9.512342007180528e-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) = 1.872355482344983 y[1] (numeric) = 1.872355482344986 absolute error = 2.664535259100376e-15 relative error = 1.423092614743888e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y[1] (closed_form) = 1.877200504274678 y[1] (numeric) = 1.877200504274682 absolute error = 3.33066907387547e-15 relative error = 1.774274546747146e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y[1] (closed_form) = 1.881957806884944 y[1] (numeric) = 1.881957806884947 absolute error = 3.774758283725532e-15 relative error = 2.005761377814092e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y[1] (closed_form) = 1.886626914449483 y[1] (numeric) = 1.886626914449487 absolute error = 4.218847493575595e-15 relative error = 2.236185364082253e-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) = 1.891207360061431 y[1] (numeric) = 1.891207360061435 absolute error = 4.662936703425657e-15 relative error = 2.465587223219243e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y[1] (closed_form) = 1.895698685680042 y[1] (numeric) = 1.895698685680048 absolute error = 5.551115123125783e-15 relative error = 2.928268698532349e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = 1.9001004421765 y[1] (numeric) = 1.900100442176506 absolute error = 5.995204332975845e-15 relative error = 3.155203903909704e-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) = 1.90441218937882 y[1] (numeric) = 1.904412189378826 absolute error = 6.217248937900877e-15 relative error = 3.264655084952389e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = 1.908633496115877 y[1] (numeric) = 1.908633496115884 absolute error = 6.661338147750939e-15 relative error = 3.49010858360547e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = 1.912763940260515 y[1] (numeric) = 1.912763940260522 absolute error = 7.105427357601002e-15 relative error = 3.714743470453159e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = 1.91680310877176 y[1] (numeric) = 1.916803108771768 absolute error = 7.549516567451064e-15 relative error = 3.938597831411389e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = 1.920750597736129 y[1] (numeric) = 1.920750597736137 absolute error = 7.993605777301127e-15 relative error = 4.161709378991058e-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) = 1.924606012408013 y[1] (numeric) = 1.924606012408022 absolute error = 8.43769498715119e-15 relative error = 4.384115467141341e-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) = 1.928368967249159 y[1] (numeric) = 1.928368967249168 absolute error = 8.659739592076221e-15 relative error = 4.49070677818957e-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) = 1.932039085967219 y[1] (numeric) = 1.932039085967228 absolute error = 9.103828801926284e-15 relative error = 4.712031380756833e-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) = 1.935616001553378 y[1] (numeric) = 1.935616001553387 absolute error = 9.547918011776346e-15 relative error = 4.932754226103687e-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) = 1.939099356319059 y[1] (numeric) = 1.939099356319069 absolute error = 9.547918011776346e-15 relative error = 4.923893136605905e-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) = 1.942488801931689 y[1] (numeric) = 1.942488801931699 absolute error = 9.992007221626409e-15 relative error = 5.143920115106947e-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) = 1.945783999449531 y[1] (numeric) = 1.945783999449541 absolute error = 1.043609643147647e-14 relative error = 5.363440358451339e-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) = 1.948984619355578 y[1] (numeric) = 1.948984619355589 absolute error = 1.088018564132653e-14 relative error = 5.582489227095089e-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) = 1.952090341590507 y[1] (numeric) = 1.952090341590518 absolute error = 1.13242748511766e-14 relative error = 5.801101829103823e-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) = 1.955100855584684 y[1] (numeric) = 1.955100855584695 absolute error = 1.176836406102666e-14 relative error = 6.019313033090186e-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) = 1.958015860289216 y[1] (numeric) = 1.958015860289229 absolute error = 1.243449787580175e-14 relative error = 6.350560344268645e-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) = 1.960835064206064 y[1] (numeric) = 1.960835064206077 absolute error = 1.310063169057685e-14 relative error = 6.681149235711599e-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) = 1.963558185417184 y[1] (numeric) = 1.963558185417198 absolute error = 1.332267629550188e-14 relative error = 6.784966391342917e-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) = 1.966184951612725 y[1] (numeric) = 1.966184951612739 absolute error = 1.354472090042691e-14 relative error = 6.888833570472153e-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) = 1.968715100118257 y[1] (numeric) = 1.96871510011827 absolute error = 1.354472090042691e-14 relative error = 6.879980196023947e-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) = 1.971148377921036 y[1] (numeric) = 1.97114837792105 absolute error = 1.376676550535194e-14 relative error = 6.984134558085224e-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) = 1.973484541695311 y[1] (numeric) = 1.973484541695325 absolute error = 1.4210854715202e-14 relative error = 7.200894871461343e-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) = 1.975723357826651 y[1] (numeric) = 1.975723357826665 absolute error = 1.4210854715202e-14 relative error = 7.19273508556093e-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) = 1.977864602435308 y[1] (numeric) = 1.977864602435322 absolute error = 1.4210854715202e-14 relative error = 7.184948200045868e-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) = 1.979908061398606 y[1] (numeric) = 1.979908061398621 absolute error = 1.465494392505207e-14 relative error = 7.401830524746599e-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) = 1.981853530372352 y[1] (numeric) = 1.981853530372367 absolute error = 1.48769885299771e-14 relative error = 7.506603440659915e-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) = 1.983700814811269 y[1] (numeric) = 1.983700814811284 absolute error = 1.509903313490213e-14 relative error = 7.611547579234454e-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) = 1.985449729988453 y[1] (numeric) = 1.985449729988468 absolute error = 1.509903313490213e-14 relative error = 7.604842825705762e-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) = 1.987100101013843 y[1] (numeric) = 1.987100101013858 absolute error = 1.509903313490213e-14 relative error = 7.598526680763799e-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) = 1.988651762851713 y[1] (numeric) = 1.988651762851728 absolute error = 1.554312234475219e-14 relative error = 7.815909570041294e-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) = 1.990104560337171 y[1] (numeric) = 1.990104560337187 absolute error = 1.554312234475219e-14 relative error = 7.810203872965758e-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) = 1.99145834819168 y[1] (numeric) = 1.991458348191695 absolute error = 1.532107773982716e-14 relative error = 7.693396024947888e-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) = 1.992712991037583 y[1] (numeric) = 1.992712991037598 absolute error = 1.48769885299771e-14 relative error = 7.465695560217541e-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) = 1.993868363411639 y[1] (numeric) = 1.993868363411655 absolute error = 1.509903313490213e-14 relative error = 7.572733191406224e-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) = 1.994924349777576 y[1] (numeric) = 1.994924349777591 absolute error = 1.554312234475219e-14 relative error = 7.791334215999305e-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) = 1.995880844537635 y[1] (numeric) = 1.995880844537651 absolute error = 1.554312234475219e-14 relative error = 7.787600340616978e-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) = 1.996737752043139 y[1] (numeric) = 1.996737752043154 absolute error = 1.532107773982716e-14 relative error = 7.673054573215758e-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) = 1.997494986604051 y[1] (numeric) = 1.997494986604066 absolute error = 1.576516694967722e-14 relative error = 7.892468844930444e-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) = 1.998152472497545 y[1] (numeric) = 1.99815247249756 absolute error = 1.554312234475219e-14 relative error = 7.778746896789323e-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) = 1.99871014397558 y[1] (numeric) = 1.998710143975595 absolute error = 1.532107773982716e-14 relative error = 7.66548255433998e-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) = 1.999167945271474 y[1] (numeric) = 1.999167945271489 absolute error = 1.532107773982716e-14 relative error = 7.663727190136924e-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) = 1.999525830605477 y[1] (numeric) = 1.999525830605492 absolute error = 1.509903313490213e-14 relative error = 7.551306866753496e-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) = 1.999783764189356 y[1] (numeric) = 1.999783764189371 absolute error = 1.509903313490213e-14 relative error = 7.550332893628009e-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) = 1.999941720229966 y[1] (numeric) = 1.999941720229981 absolute error = 1.48769885299771e-14 relative error = 7.438711028172586e-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) = 1.999999682931834 y[1] (numeric) = 1.99999968293185 absolute error = 1.509903313490213e-14 relative error = 7.549517764306938e-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) = 1.999957646498741 y[1] (numeric) = 1.999957646498755 absolute error = 1.48769885299771e-14 relative error = 7.438651791462558e-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) = 1.999815615134292 y[1] (numeric) = 1.999815615134307 absolute error = 1.48769885299771e-14 relative error = 7.439180101100508e-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) = 1.999573603041507 y[1] (numeric) = 1.999573603041522 absolute error = 1.48769885299771e-14 relative error = 7.440080478832106e-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) = 1.999231634421393 y[1] (numeric) = 1.999231634421408 absolute error = 1.465494392505207e-14 relative error = 7.330288133067393e-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) = 1.998789743470527 y[1] (numeric) = 1.998789743470542 absolute error = 1.465494392505207e-14 relative error = 7.331908707719541e-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) = 1.998247974377636 y[1] (numeric) = 1.998247974377651 absolute error = 1.48769885299771e-14 relative error = 7.445016194554434e-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) = 1.997606381319178 y[1] (numeric) = 1.997606381319193 absolute error = 1.48769885299771e-14 relative error = 7.4474073917168e-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) = 1.996865028453924 y[1] (numeric) = 1.996865028453939 absolute error = 1.465494392505207e-14 relative error = 7.338975702528416e-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) = 1.996023989916543 y[1] (numeric) = 1.996023989916558 absolute error = 1.48769885299771e-14 relative error = 7.453311485799892e-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) = 1.995083349810187 y[1] (numeric) = 1.995083349810202 absolute error = 1.443289932012704e-14 relative error = 7.234233758454344e-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) = 1.994043202198084 y[1] (numeric) = 1.994043202198098 absolute error = 1.443289932012704e-14 relative error = 7.238007333149696e-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) = 1.992903651094128 y[1] (numeric) = 1.992903651094142 absolute error = 1.443289932012704e-14 relative error = 7.242146057689845e-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) = 1.991664810452479 y[1] (numeric) = 1.991664810452493 absolute error = 1.4210854715202e-14 relative error = 7.135163829085023e-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) = 1.990326804156169 y[1] (numeric) = 1.990326804156183 absolute error = 1.4210854715202e-14 relative error = 7.139960475599847e-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) = 1.988889766004713 y[1] (numeric) = 1.988889766004727 absolute error = 1.398881011027697e-14 relative error = 7.033476841895431e-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) = 1.987353839700729 y[1] (numeric) = 1.987353839700743 absolute error = 1.376676550535194e-14 relative error = 6.927183891634036e-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) = 1.985719178835567 y[1] (numeric) = 1.985719178835581 absolute error = 1.376676550535194e-14 relative error = 6.932886408150029e-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) = 1.983985946873951 y[1] (numeric) = 1.983985946873965 absolute error = 1.398881011027697e-14 relative error = 7.050861490384198e-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) = 1.982154317137634 y[1] (numeric) = 1.982154317137648 absolute error = 1.354472090042691e-14 relative error = 6.833333198792721e-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) = 1.980224472788062 y[1] (numeric) = 1.980224472788076 absolute error = 1.376676550535194e-14 relative error = 6.952123708464722e-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) = 1.978196606808063 y[1] (numeric) = 1.978196606808076 absolute error = 1.354472090042691e-14 relative error = 6.847004414936349e-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) = 1.976070921982543 y[1] (numeric) = 1.976070921982557 absolute error = 1.376676550535194e-14 relative error = 6.966736543818016e-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) = 1.973847630878215 y[1] (numeric) = 1.973847630878228 absolute error = 1.332267629550188e-14 relative error = 6.749597125475324e-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) = 1.971526955822336 y[1] (numeric) = 1.97152695582235 absolute error = 1.332267629550188e-14 relative error = 6.757542044331271e-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) = 1.969109128880479 y[1] (numeric) = 1.969109128880491 absolute error = 1.287858708565182e-14 relative error = 6.540311502681335e-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) = 1.966594391833321 y[1] (numeric) = 1.966594391833334 absolute error = 1.265654248072678e-14 relative error = 6.435766588822599e-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) = 1.963982996152473 y[1] (numeric) = 1.963982996152485 absolute error = 1.243449787580175e-14 relative error = 6.331265545659749e-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) = 1.961275202975326 y[1] (numeric) = 1.961275202975338 absolute error = 1.221245327087672e-14 relative error = 6.226792268800415e-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) = 1.958471283078941 y[1] (numeric) = 1.958471283078953 absolute error = 1.199040866595169e-14 relative error = 6.122330600171679e-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) = 1.955571516852972 y[1] (numeric) = 1.955571516852983 absolute error = 1.13242748511766e-14 relative error = 5.790775102615694e-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) = 1.952576194271625 y[1] (numeric) = 1.952576194271636 absolute error = 1.088018564132653e-14 relative error = 5.572220778500889e-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) = 1.949485614864661 y[1] (numeric) = 1.949485614864671 absolute error = 1.021405182655144e-14 relative error = 5.23935737133435e-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) = 1.946300087687446 y[1] (numeric) = 1.946300087687457 absolute error = 1.021405182655144e-14 relative error = 5.247932675524649e-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) = 1.943019931290044 y[1] (numeric) = 1.943019931290054 absolute error = 9.992007221626409e-15 relative error = 5.142514011676833e-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) = 1.939645473685359 y[1] (numeric) = 1.939645473685369 absolute error = 9.547918011776346e-15 relative error = 4.92250678864274e-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) = 1.936177052316342 y[1] (numeric) = 1.936177052316351 absolute error = 9.325873406851315e-15 relative error = 4.816642876587306e-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) = 1.932615014022238 y[1] (numeric) = 1.932615014022246 absolute error = 8.881784197001252e-15 relative error = 4.595733828289019e-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) = 1.928959715003908 y[1] (numeric) = 1.928959715003916 absolute error = 8.43769498715119e-15 relative error = 4.37422042644063e-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) = 1.925211520788208 y[1] (numeric) = 1.925211520788216 absolute error = 7.771561172376096e-15 relative error = 4.036731075240144e-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) = 1.921370806191437 y[1] (numeric) = 1.921370806191444 absolute error = 7.327471962526033e-15 relative error = 3.813668834206257e-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) = 1.917437955281853 y[1] (numeric) = 1.917437955281859 absolute error = 6.661338147750939e-15 relative error = 3.474082762053054e-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) = 1.913413361341269 y[1] (numeric) = 1.913413361341276 absolute error = 6.439293542825908e-15 relative error = 3.365343669551924e-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) = 1.909297426825727 y[1] (numeric) = 1.909297426825733 absolute error = 5.995204332975845e-15 relative error = 3.140005453704025e-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) = 1.905090563325248 y[1] (numeric) = 1.905090563325253 absolute error = 5.551115123125783e-15 relative error = 2.913832670209949e-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) = 1.900793191522676 y[1] (numeric) = 1.900793191522681 absolute error = 5.10702591327572e-15 relative error = 2.686786724643419e-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) = 1.89640574115161 y[1] (numeric) = 1.896405741151614 absolute error = 4.662936703425657e-15 relative error = 2.458828615755005e-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) = 1.891928650953431 y[1] (numeric) = 1.891928650953435 absolute error = 4.440892098500626e-15 relative error = 2.347283073419631e-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) = 1.887362368633428 y[1] (numeric) = 1.887362368633433 absolute error = 4.440892098500626e-15 relative error = 2.352962087357987e-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) = 1.882707350816029 y[1] (numeric) = 1.882707350816033 absolute error = 3.996802888650564e-15 relative error = 2.122901834381331e-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) = 1.877964062999134 y[1] (numeric) = 1.877964062999138 absolute error = 3.552713678800501e-15 relative error = 1.891790023461242e-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) = 1.873132979507574 y[1] (numeric) = 1.873132979507577 absolute error = 2.664535259100376e-15 relative error = 1.422501919645263e-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) = 1.868214583445672 y[1] (numeric) = 1.868214583445674 absolute error = 1.77635683940025e-15 relative error = 9.508312669971766e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09999999999988 y[1] (closed_form) = 1.863209366648934 y[1] (numeric) = 1.863209366648936 absolute error = 1.332267629550188e-15 relative error = 7.15039143425052e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999879 y[1] (closed_form) = 1.858117829634871 y[1] (numeric) = 1.858117829634872 absolute error = 1.110223024625157e-15 relative error = 5.974987198972848e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999878 y[1] (closed_form) = 1.85294048155294 y[1] (numeric) = 1.852940481552941 absolute error = 6.661338147750939e-16 relative error = 3.595009237516418e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999876 y[1] (closed_form) = 1.847677840133635 y[1] (numeric) = 1.847677840133635 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] = 2.139999999999875 y[1] (closed_form) = 1.842330431636713 y[1] (numeric) = 1.842330431636712 absolute error = 1.110223024625157e-15 relative error = 6.026188383800633e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999874 y[1] (closed_form) = 1.836898790798567 y[1] (numeric) = 1.836898790798565 absolute error = 1.332267629550188e-15 relative error = 7.252809116233359e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999873 y[1] (closed_form) = 1.831383460778754 y[1] (numeric) = 1.831383460778752 absolute error = 1.554312234475219e-15 relative error = 8.487093324596716e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999872 y[1] (closed_form) = 1.82578499310568 y[1] (numeric) = 1.825784993105678 absolute error = 2.220446049250313e-15 relative error = 1.21615965605748e-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) = 1.820103947621448 y[1] (numeric) = 1.820103947621445 absolute error = 2.886579864025407e-15 relative error = 1.585942312689148e-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) = 1.814340892425871 y[1] (numeric) = 1.814340892425868 absolute error = 3.774758283725532e-15 relative error = 2.080512157050309e-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) = 1.808496403819667 y[1] (numeric) = 1.808496403819663 absolute error = 3.996802888650564e-15 relative error = 2.210014286016297e-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) = 1.802571066246826 y[1] (numeric) = 1.802571066246822 absolute error = 4.662936703425657e-15 relative error = 2.586825446574189e-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) = 1.796565472236167 y[1] (numeric) = 1.796565472236162 absolute error = 5.329070518200751e-15 relative error = 2.966254556572163e-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) = 1.790480222342087 y[1] (numeric) = 1.790480222342081 absolute error = 5.995204332975845e-15 relative error = 3.348377858725327e-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) = 1.784315925084504 y[1] (numeric) = 1.784315925084497 absolute error = 7.105427357601002e-15 relative error = 3.982157676065405e-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) = 1.778073196888007 y[1] (numeric) = 1.778073196887999 absolute error = 7.993605777301127e-15 relative error = 4.495656191933817e-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) = 1.771752662020214 y[1] (numeric) = 1.771752662020205 absolute error = 8.659739592076221e-15 relative error = 4.887668452662058e-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) = 1.765354952529343 y[1] (numeric) = 1.765354952529333 absolute error = 9.325873406851315e-15 relative error = 5.282718579336982e-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) = 1.758880708181013 y[1] (numeric) = 1.758880708181003 absolute error = 9.992007221626409e-15 relative error = 5.680889656217716e-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) = 1.752330576394264 y[1] (numeric) = 1.752330576394253 absolute error = 1.043609643147647e-14 relative error = 5.955552321041286e-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) = 1.745705212176815 y[1] (numeric) = 1.745705212176804 absolute error = 1.13242748511766e-14 relative error = 6.486934204117854e-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) = 1.739005278059568 y[1] (numeric) = 1.739005278059555 absolute error = 1.221245327087672e-14 relative error = 7.022666017726946e-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) = 1.73223144403035 y[1] (numeric) = 1.732231444030337 absolute error = 1.332267629550188e-14 relative error = 7.691048642151572e-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) = 1.72538438746692 y[1] (numeric) = 1.725384387466906 absolute error = 1.398881011027697e-14 relative error = 8.107648482211141e-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) = 1.718464793069228 y[1] (numeric) = 1.718464793069214 absolute error = 1.4210854715202e-14 relative error = 8.269505882527279e-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) = 1.711473352790948 y[1] (numeric) = 1.711473352790933 absolute error = 1.48769885299771e-14 relative error = 8.69250374580286e-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) = 1.704410765770282 y[1] (numeric) = 1.704410765770266 absolute error = 1.576516694967722e-14 relative error = 9.249628825567997e-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) = 1.697277738260045 y[1] (numeric) = 1.697277738260029 absolute error = 1.620925615952729e-14 relative error = 9.55014950949873e-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) = 1.690074983557046 y[1] (numeric) = 1.690074983557029 absolute error = 1.687538997430238e-14 relative error = 9.984994830694019e-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) = 1.682803221930751 y[1] (numeric) = 1.682803221930733 absolute error = 1.77635683940025e-14 relative error = 1.05559391392308e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999847 y[1] (closed_form) = 1.675463180551264 y[1] (numeric) = 1.675463180551245 absolute error = 1.865174681370263e-14 relative error = 1.113229286695862e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999846 y[1] (closed_form) = 1.668055593416606 y[1] (numeric) = 1.668055593416586 absolute error = 1.953992523340276e-14 relative error = 1.1714193046396e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999844 y[1] (closed_form) = 1.660581201279317 y[1] (numeric) = 1.660581201279297 absolute error = 2.065014825802791e-14 relative error = 1.243549441732748e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999843 y[1] (closed_form) = 1.653040751572384 y[1] (numeric) = 1.653040751572362 absolute error = 2.176037128265307e-14 relative error = 1.316384442546529e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999842 y[1] (closed_form) = 1.645434998334491 y[1] (numeric) = 1.645434998334469 absolute error = 2.242650509742816e-14 relative error = 1.362952965029203e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.449999999999841 y[1] (closed_form) = 1.637764702134626 y[1] (numeric) = 1.637764702134603 absolute error = 2.331468351712829e-14 relative error = 1.423567346807539e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45999999999984 y[1] (closed_form) = 1.630030629996016 y[1] (numeric) = 1.630030629995993 absolute error = 2.353672812205332e-14 relative error = 1.443943916692586e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999839 y[1] (closed_form) = 1.622233555319431 y[1] (numeric) = 1.622233555319406 absolute error = 2.442490654175344e-14 relative error = 1.505634405210166e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999838 y[1] (closed_form) = 1.61437425780584 y[1] (numeric) = 1.614374257805814 absolute error = 2.509104035652854e-14 relative error = 1.554226985174477e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999837 y[1] (closed_form) = 1.606453523378445 y[1] (numeric) = 1.606453523378419 absolute error = 2.620126338115369e-14 relative error = 1.631000399317575e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999836 y[1] (closed_form) = 1.598472144104088 y[1] (numeric) = 1.598472144104061 absolute error = 2.686739719592879e-14 relative error = 1.68081735393565e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999835 y[1] (closed_form) = 1.590430918114046 y[1] (numeric) = 1.590430918114019 absolute error = 2.775557561562891e-14 relative error = 1.74516071710564e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999833 y[1] (closed_form) = 1.582330649524217 y[1] (numeric) = 1.582330649524189 absolute error = 2.842170943040401e-14 relative error = 1.796192814627586e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999832 y[1] (closed_form) = 1.57417214835471 y[1] (numeric) = 1.57417214835468 absolute error = 2.97539770599542e-14 relative error = 1.890134893509099e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999831 y[1] (closed_form) = 1.565956230448842 y[1] (numeric) = 1.565956230448812 absolute error = 3.019806626980426e-14 relative error = 1.928410621103295e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54999999999983 y[1] (closed_form) = 1.557683717391558 y[1] (numeric) = 1.557683717391527 absolute error = 3.108624468950438e-14 relative error = 1.995671158555879e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999829 y[1] (closed_form) = 1.549355436427269 y[1] (numeric) = 1.549355436427237 absolute error = 3.219646771412954e-14 relative error = 2.078055619591904e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999828 y[1] (closed_form) = 1.540972220377133 y[1] (numeric) = 1.5409722203771 absolute error = 3.286260152890463e-14 relative error = 2.132588835434161e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999827 y[1] (closed_form) = 1.532534907555768 y[1] (numeric) = 1.532534907555734 absolute error = 3.397282455352979e-14 relative error = 2.21677329410479e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999826 y[1] (closed_form) = 1.524044341687425 y[1] (numeric) = 1.52404434168739 absolute error = 3.463895836830488e-14 relative error = 2.272831401345749e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999825 y[1] (closed_form) = 1.515501371821614 y[1] (numeric) = 1.515501371821579 absolute error = 3.530509218307998e-14 relative error = 2.329598167281345e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999824 y[1] (closed_form) = 1.506906852248205 y[1] (numeric) = 1.506906852248169 absolute error = 3.641531520770513e-14 relative error = 2.416560463135189e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999822 y[1] (closed_form) = 1.498261642411993 y[1] (numeric) = 1.498261642411955 absolute error = 3.774758283725532e-14 relative error = 2.519425297205565e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999821 y[1] (closed_form) = 1.489566606826755 y[1] (numeric) = 1.489566606826717 absolute error = 3.863576125695545e-14 relative error = 2.593758552312189e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999982 y[1] (closed_form) = 1.480822614988806 y[1] (numeric) = 1.480822614988766 absolute error = 3.952393967665557e-14 relative error = 2.669052949124115e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999819 y[1] (closed_form) = 1.472030541290042 y[1] (numeric) = 1.472030541290001 absolute error = 4.063416270128073e-14 relative error = 2.760415736053289e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999818 y[1] (closed_form) = 1.463191264930507 y[1] (numeric) = 1.463191264930465 absolute error = 4.152234112098085e-14 relative error = 2.837793124944122e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999817 y[1] (closed_form) = 1.454305669830469 y[1] (numeric) = 1.454305669830427 absolute error = 4.285460875053104e-14 relative error = 2.946740127577627e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999816 y[1] (closed_form) = 1.445374644542036 y[1] (numeric) = 1.445374644541992 absolute error = 4.39648317751562e-14 relative error = 3.04176027586857e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999815 y[1] (closed_form) = 1.436399082160293 y[1] (numeric) = 1.436399082160249 absolute error = 4.440892098500626e-14 relative error = 3.091684026852539e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999814 y[1] (closed_form) = 1.427379880233998 y[1] (numeric) = 1.427379880233953 absolute error = 4.551914400963142e-14 relative error = 3.188999974006164e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999813 y[1] (closed_form) = 1.418317940675829 y[1] (numeric) = 1.418317940675783 absolute error = 4.640732242933154e-14 relative error = 3.271997138188806e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999811 y[1] (closed_form) = 1.40921416967219 y[1] (numeric) = 1.409214169672142 absolute error = 4.729550084903167e-14 relative error = 3.356161317909081e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999981 y[1] (closed_form) = 1.400069477592593 y[1] (numeric) = 1.400069477592545 absolute error = 4.796163466380676e-14 relative error = 3.425661042641709e-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) = 1.390884778898628 y[1] (numeric) = 1.390884778898579 absolute error = 4.907185768843192e-14 relative error = 3.528103724543557e-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) = 1.381660992052509 y[1] (numeric) = 1.381660992052459 absolute error = 5.018208071305708e-14 relative error = 3.632011108492664e-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) = 1.372399039425235 y[1] (numeric) = 1.372399039425184 absolute error = 5.084821452783217e-14 relative error = 3.705060486571571e-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) = 1.363099847204349 y[1] (numeric) = 1.363099847204297 absolute error = 5.218048215738236e-14 relative error = 3.828074829910807e-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) = 1.353764345301326 y[1] (numeric) = 1.353764345301272 absolute error = 5.306866057708248e-14 relative error = 3.920081124995967e-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) = 1.344393467258574 y[1] (numeric) = 1.34439346725852 absolute error = 5.373479439185758e-14 relative error = 3.996954440832795e-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) = 1.334988150156091 y[1] (numeric) = 1.334988150156036 absolute error = 5.484501741648273e-14 relative error = 4.108277471232242e-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) = 1.325549334517748 y[1] (numeric) = 1.325549334517692 absolute error = 5.617728504603292e-14 relative error = 4.238038040769788e-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) = 1.316077964217243 y[1] (numeric) = 1.316077964217186 absolute error = 5.706546346573305e-14 relative error = 4.336024537852785e-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) = 1.306574986383714 y[1] (numeric) = 1.306574986383656 absolute error = 5.81756864903582e-14 relative error = 4.45253331011445e-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) = 1.297041351307025 y[1] (numeric) = 1.297041351306966 absolute error = 5.928590951498336e-14 relative error = 4.57085731732771e-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) = 1.287478012342739 y[1] (numeric) = 1.287478012342678 absolute error = 6.039613253960852e-14 relative error = 4.691041863286633e-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) = 1.277885925816783 y[1] (numeric) = 1.277885925816721 absolute error = 6.17284001691587e-14 relative error = 4.830509431403584e-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) = 1.268266050929816 y[1] (numeric) = 1.268266050929753 absolute error = 6.283862319378386e-14 relative error = 4.95468779186468e-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) = 1.25861934966131 y[1] (numeric) = 1.258619349661246 absolute error = 6.394884621840902e-14 relative error = 5.080872643155966e-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) = 1.248946786673353 y[1] (numeric) = 1.248946786673288 absolute error = 6.505906924303417e-14 relative error = 5.209114586564813e-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) = 1.239249329214185 y[1] (numeric) = 1.239249329214118 absolute error = 6.616929226765933e-14 relative error = 5.339465651324392e-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) = 1.229527947021468 y[1] (numeric) = 1.229527947021401 absolute error = 6.705747068735946e-14 relative error = 5.453920006438747e-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) = 1.219783612225322 y[1] (numeric) = 1.219783612225254 absolute error = 6.794564910705958e-14 relative error = 5.570303488755877e-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) = 1.210017299251106 y[1] (numeric) = 1.210017299251037 absolute error = 6.905587213168474e-14 relative error = 5.707015277750509e-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) = 1.200229984721979 y[1] (numeric) = 1.200229984721908 absolute error = 7.038813976123492e-14 relative error = 5.864554348518432e-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) = 1.190422647361237 y[1] (numeric) = 1.190422647361166 absolute error = 7.149836278586008e-14 relative error = 6.006132607133078e-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) = 1.180596267894444 y[1] (numeric) = 1.180596267894372 absolute error = 7.283063041541027e-14 relative error = 6.168970070124088e-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) = 1.170751828951358 y[1] (numeric) = 1.170751828951285 absolute error = 7.371880883511039e-14 relative error = 6.296706698390579e-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) = 1.16089031496767 y[1] (numeric) = 1.160890314967595 absolute error = 7.505107646466058e-14 relative error = 6.464958445858918e-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) = 1.15101271208656 y[1] (numeric) = 1.151012712086484 absolute error = 7.616129948928574e-14 relative error = 6.616894730139016e-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) = 1.141120008060085 y[1] (numeric) = 1.141120008060007 absolute error = 7.72715225139109e-14 relative error = 6.771550929623367e-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) = 1.131213192150403 y[1] (numeric) = 1.131213192150324 absolute error = 7.838174553853605e-14 relative error = 6.928998537360999e-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) = 1.12129325503085 y[1] (numeric) = 1.12129325503077 absolute error = 7.926992395823618e-14 relative error = 7.069508676929949e-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) = 1.111361188686871 y[1] (numeric) = 1.111361188686791 absolute error = 8.01581023779363e-14 relative error = 7.212605874121546e-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) = 1.101417986316825 y[1] (numeric) = 1.101417986316743 absolute error = 8.171241461241152e-14 relative error = 7.418837864239019e-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) = 1.091464642232661 y[1] (numeric) = 1.091464642232578 absolute error = 8.282263763703668e-14 relative error = 7.588210779564756e-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) = 1.081502151760494 y[1] (numeric) = 1.08150215176041 absolute error = 8.393286066166183e-14 relative error = 7.760766867179503e-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) = 1.07153151114107 y[1] (numeric) = 1.071531511140985 absolute error = 8.526512829121202e-14 relative error = 7.957314125126706e-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) = 1.061553717430141 y[1] (numeric) = 1.061553717430055 absolute error = 8.615330671091215e-14 relative error = 8.115774576106813e-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) = 1.051569768398763 y[1] (numeric) = 1.051569768398676 absolute error = 8.704148513061227e-14 relative error = 8.277290556113197e-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) = 1.041580662433521 y[1] (numeric) = 1.041580662433433 absolute error = 8.815170815523743e-14 relative error = 8.463262744268136e-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) = 1.031587398436685 y[1] (numeric) = 1.031587398436596 absolute error = 8.948397578478762e-14 relative error = 8.674395976569289e-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) = 1.021590975726329 y[1] (numeric) = 1.021590975726238 absolute error = 9.037215420448774e-14 relative error = 8.846216964694225e-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) = 1.011592393936392 y[1] (numeric) = 1.011592393936301 absolute error = 9.126033262418787e-14 relative error = 9.021453025073481e-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) = 1.001592652916722 y[1] (numeric) = 1.001592652916629 absolute error = 9.237055564881302e-14 relative error = 9.222367534328674e-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) = 0.9915927526330872 y[1] (numeric) = 0.9915927526329938 absolute error = 9.336975637097567e-14 relative error = 9.416139450700956e-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) = 0.9815936930671832 y[1] (numeric) = 0.9815936930670889 absolute error = 9.436895709313831e-14 relative error = 9.613851205406982e-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) = 0.9715964741166342 y[1] (numeric) = 0.9715964741165386 absolute error = 9.559020242022598e-14 relative error = 9.838467405631091e-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) = 0.9616020954950039 y[1] (numeric) = 0.9616020954949072 absolute error = 9.670042544485113e-14 relative error = 1.005617873524627e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18999999999976 y[1] (closed_form) = 0.9516115566318258 y[1] (numeric) = 0.9516115566317281 absolute error = 9.769962616701378e-14 relative error = 1.026675490499674e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999759 y[1] (closed_form) = 0.9416258565726611 y[1] (numeric) = 0.9416258565725623 absolute error = 9.880984919163893e-14 relative error = 1.049353610055781e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999757 y[1] (closed_form) = 0.9316459938791941 y[1] (numeric) = 0.9316459938790943 absolute error = 9.980904991380157e-14 relative error = 1.071319477242809e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999756 y[1] (closed_form) = 0.9216729665293778 y[1] (numeric) = 0.9216729665292769 absolute error = 1.009192729384267e-13 relative error = 1.094957502317173e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999755 y[1] (closed_form) = 0.9117077718176362 y[1] (numeric) = 0.9117077718175342 absolute error = 1.020294959630519e-13 relative error = 1.11910306259252e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999754 y[1] (closed_form) = 0.9017514062551362 y[1] (numeric) = 0.9017514062550329 absolute error = 1.032507412901396e-13 relative error = 1.145002276391531e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999753 y[1] (closed_form) = 0.891804865470137 y[1] (numeric) = 0.8918048654700328 absolute error = 1.042499420123022e-13 relative error = 1.168977049226394e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999752 y[1] (closed_form) = 0.8818691441084286 y[1] (numeric) = 0.8818691441083233 absolute error = 1.053601650369274e-13 relative error = 1.194736948682411e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.269999999999751 y[1] (closed_form) = 0.8719452357338674 y[1] (numeric) = 0.8719452357337609 absolute error = 1.064703880615525e-13 relative error = 1.221067375543859e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27999999999975 y[1] (closed_form) = 0.8620341327290207 y[1] (numeric) = 0.8620341327289133 absolute error = 1.074695887837152e-13 relative error = 1.246697603997289e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999749 y[1] (closed_form) = 0.8521368261959301 y[1] (numeric) = 0.8521368261958213 absolute error = 1.088018564132653e-13 relative error = 1.276812045537024e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999748 y[1] (closed_form) = 0.8422543058570009 y[1] (numeric) = 0.842254305856891 absolute error = 1.099120794378905e-13 relative error = 1.304974978145752e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999746 y[1] (closed_form) = 0.8323875599560316 y[1] (numeric) = 0.8323875599559207 absolute error = 1.109112801600531e-13 relative error = 1.332447594073988e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999745 y[1] (closed_form) = 0.8225375751593903 y[1] (numeric) = 0.8225375751592784 absolute error = 1.119104808822158e-13 relative error = 1.360551593774058e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999744 y[1] (closed_form) = 0.8127053364573481 y[1] (numeric) = 0.8127053364572353 absolute error = 1.127986593019159e-13 relative error = 1.387940428613584e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999743 y[1] (closed_form) = 0.8028918270655818 y[1] (numeric) = 0.8028918270654679 absolute error = 1.139088823265411e-13 relative error = 1.418732617354651e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999742 y[1] (closed_form) = 0.7930980283268527 y[1] (numeric) = 0.7930980283267377 absolute error = 1.150191053511662e-13 relative error = 1.450250804352831e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.359999999999741 y[1] (closed_form) = 0.7833249196128731 y[1] (numeric) = 0.783324919612757 absolute error = 1.161293283757914e-13 relative error = 1.482517987978522e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36999999999974 y[1] (closed_form) = 0.7735734782263703 y[1] (numeric) = 0.7735734782262532 absolute error = 1.17128529097954e-13 relative error = 1.514122864792409e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999739 y[1] (closed_form) = 0.7638446793033568 y[1] (numeric) = 0.7638446793032386 absolute error = 1.181277298201167e-13 relative error = 1.546488874254538e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999738 y[1] (closed_form) = 0.7541394957156173 y[1] (numeric) = 0.7541394957154982 absolute error = 1.191269305422793e-13 relative error = 1.579640520342162e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999737 y[1] (closed_form) = 0.7444588979734234 y[1] (numeric) = 0.744458897973303 absolute error = 1.20348175869367e-13 relative error = 1.616585901477979e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y[1] (closed_form) = 0.7348038541284818 y[1] (numeric) = 0.7348038541283605 absolute error = 1.213473765915296e-13 relative error = 1.65142542339349e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999734 y[1] (closed_form) = 0.7251753296771313 y[1] (numeric) = 0.7251753296770089 absolute error = 1.223465773136923e-13 relative error = 1.687130991730847e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999733 y[1] (closed_form) = 0.7155742874637934 y[1] (numeric) = 0.71557428746367 absolute error = 1.233457780358549e-13 relative error = 1.723731277056206e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999732 y[1] (closed_form) = 0.7060016875846884 y[1] (numeric) = 0.7060016875845641 absolute error = 1.243449787580175e-13 relative error = 1.761256112338991e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.449999999999731 y[1] (closed_form) = 0.6964584872918271 y[1] (numeric) = 0.6964584872917019 absolute error = 1.252331571777177e-13 relative error = 1.798142451600895e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45999999999973 y[1] (closed_form) = 0.6869456408972863 y[1] (numeric) = 0.6869456408971601 absolute error = 1.261213355974178e-13 relative error = 1.835972573210866e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999729 y[1] (closed_form) = 0.6774640996777779 y[1] (numeric) = 0.6774640996776509 absolute error = 1.270095140171179e-13 relative error = 1.87477851708345e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999728 y[1] (closed_form) = 0.6680148117795227 y[1] (numeric) = 0.6680148117793946 absolute error = 1.281197370417431e-13 relative error = 1.917917608749502e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999727 y[1] (closed_form) = 0.6585987221234362 y[1] (numeric) = 0.6585987221233069 absolute error = 1.292299600663682e-13 relative error = 1.962195730500486e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999726 y[1] (closed_form) = 0.6492167723106372 y[1] (numeric) = 0.649216772310507 absolute error = 1.302291607885309e-13 relative error = 2.005942642625056e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y[1] (closed_form) = 0.6398699005282886 y[1] (numeric) = 0.6398699005281575 absolute error = 1.31117339208231e-13 relative error = 2.049124972122896e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999723 y[1] (closed_form) = 0.63055904145578 y[1] (numeric) = 0.6305590414556478 absolute error = 1.322275622328561e-13 relative error = 2.096989394166494e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999722 y[1] (closed_form) = 0.6212851261712593 y[1] (numeric) = 0.6212851261711259 absolute error = 1.334488075599438e-13 relative error = 2.147947889600019e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.539999999999721 y[1] (closed_form) = 0.6120490820585267 y[1] (numeric) = 0.6120490820583921 absolute error = 1.34559030584569e-13 relative error = 2.198500651810501e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54999999999972 y[1] (closed_form) = 0.602851832714297 y[1] (numeric) = 0.6028518327141613 absolute error = 1.356692536091941e-13 relative error = 2.250457678769144e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999719 y[1] (closed_form) = 0.5936942978558402 y[1] (numeric) = 0.5936942978557033 absolute error = 1.368904989362818e-13 relative error = 2.305740503667787e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999718 y[1] (closed_form) = 0.5845773932290106 y[1] (numeric) = 0.5845773932288727 absolute error = 1.378896996584444e-13 relative error = 2.358792886204301e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999717 y[1] (closed_form) = 0.5755020305166739 y[1] (numeric) = 0.575502030516535 absolute error = 1.388889003806071e-13 relative error = 2.41335204770547e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999716 y[1] (closed_form) = 0.5664691172475385 y[1] (numeric) = 0.5664691172473986 absolute error = 1.398881011027697e-13 relative error = 2.46947444871281e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999715 y[1] (closed_form) = 0.5574795567054036 y[1] (numeric) = 0.5574795567052627 absolute error = 1.408873018249324e-13 relative error = 2.527219162215545e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y[1] (closed_form) = 0.5485342478388324 y[1] (numeric) = 0.5485342478386906 absolute error = 1.417754802446325e-13 relative error = 2.584624037664249e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999712 y[1] (closed_form) = 0.5396340851712571 y[1] (numeric) = 0.5396340851711143 absolute error = 1.427746809667951e-13 relative error = 2.645768399182651e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.629999999999711 y[1] (closed_form) = 0.5307799587115278 y[1] (numeric) = 0.5307799587113841 absolute error = 1.437738816889578e-13 relative error = 2.708728529200121e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63999999999971 y[1] (closed_form) = 0.5219727538649118 y[1] (numeric) = 0.5219727538647673 absolute error = 1.445510378061954e-13 relative error = 2.76932151603464e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999709 y[1] (closed_form) = 0.5132133513445547 y[1] (numeric) = 0.5132133513444093 absolute error = 1.454392162258955e-13 relative error = 2.833893854180975e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999708 y[1] (closed_form) = 0.5045026270834089 y[1] (numeric) = 0.5045026270832624 absolute error = 1.464384169480581e-13 relative error = 2.902629423252689e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999707 y[1] (closed_form) = 0.4958414521466417 y[1] (numeric) = 0.4958414521464944 absolute error = 1.472155730652958e-13 relative error = 2.969004959709536e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999706 y[1] (closed_form) = 0.4872306926445289 y[1] (numeric) = 0.4872306926443808 absolute error = 1.480482403337646e-13 relative error = 3.03856556183288e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999705 y[1] (closed_form) = 0.4786712096458455 y[1] (numeric) = 0.4786712096456964 absolute error = 1.491584633583898e-13 relative error = 3.116094311766686e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999704 y[1] (closed_form) = 0.4701638590917582 y[1] (numeric) = 0.4701638590916082 absolute error = 1.499911306268586e-13 relative error = 3.190188435933908e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999702 y[1] (closed_form) = 0.4617094917102331 y[1] (numeric) = 0.4617094917100821 absolute error = 1.509903313490213e-13 relative error = 3.270245339547452e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.719999999999701 y[1] (closed_form) = 0.4533089529309631 y[1] (numeric) = 0.4533089529308112 absolute error = 1.518785097687214e-13 relative error = 3.350441432641456e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7299999999997 y[1] (closed_form) = 0.4449630828008255 y[1] (numeric) = 0.4449630828006728 absolute error = 1.527666881884215e-13 relative error = 3.433244107057821e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999699 y[1] (closed_form) = 0.4366727158998787 y[1] (numeric) = 0.4366727158997251 absolute error = 1.535993554568904e-13 relative error = 3.517493762814071e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999698 y[1] (closed_form) = 0.4284386812579041 y[1] (numeric) = 0.4284386812577494 absolute error = 1.546540673302843e-13 relative error = 3.60971299034478e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999697 y[1] (closed_form) = 0.420261802271504 y[1] (numeric) = 0.4202618022713485 absolute error = 1.554867345987532e-13 relative error = 3.699758906432882e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999696 y[1] (closed_form) = 0.4121428966217633 y[1] (numeric) = 0.4121428966216069 absolute error = 1.563749130184533e-13 relative error = 3.794191633538296e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999695 y[1] (closed_form) = 0.4040827761924811 y[1] (numeric) = 0.4040827761923239 absolute error = 1.572630914381534e-13 relative error = 3.891853370242205e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999694 y[1] (closed_form) = 0.3960822469889836 y[1] (numeric) = 0.3960822469888255 absolute error = 1.580957587066223e-13 relative error = 3.991488129257645e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999693 y[1] (closed_form) = 0.3881421090575241 y[1] (numeric) = 0.3881421090573651 absolute error = 1.589839371263224e-13 relative error = 4.096023941137507e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999691 y[1] (closed_form) = 0.380263156405279 y[1] (numeric) = 0.3802631564051191 absolute error = 1.598721155460225e-13 relative error = 4.204249421830212e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81999999999969 y[1] (closed_form) = 0.3724461769209476 y[1] (numeric) = 0.3724461769207869 absolute error = 1.607047828144914e-13 relative error = 4.314845815925808e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999689 y[1] (closed_form) = 0.3646919522959644 y[1] (numeric) = 0.3646919522958028 absolute error = 1.615929612341915e-13 relative error = 4.430943984830555e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999688 y[1] (closed_form) = 0.35700125794633 y[1] (numeric) = 0.3570012579461675 absolute error = 1.624256285026604e-13 relative error = 4.549721461403892e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999687 y[1] (closed_form) = 0.3493748629350704 y[1] (numeric) = 0.3493748629349072 absolute error = 1.63202784619898e-13 relative error = 4.671280104379704e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999686 y[1] (closed_form) = 0.3418135298953314 y[1] (numeric) = 0.3418135298951674 absolute error = 1.639799407371356e-13 relative error = 4.797350789108577e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999685 y[1] (closed_form) = 0.3343180149541161 y[1] (numeric) = 0.3343180149539513 absolute error = 1.647570968543732e-13 relative error = 4.92815491492391e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999684 y[1] (closed_form) = 0.3268890676566721 y[1] (numeric) = 0.3268890676565065 absolute error = 1.656452752740734e-13 relative error = 5.067323800747252e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999683 y[1] (closed_form) = 0.3195274308915387 y[1] (numeric) = 0.3195274308913722 absolute error = 1.664779425425422e-13 relative error = 5.210129912102976e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999681 y[1] (closed_form) = 0.3122338408162574 y[1] (numeric) = 0.3122338408160901 absolute error = 1.673106098110111e-13 relative error = 5.358503401605005e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.90999999999968 y[1] (closed_form) = 0.305009026783758 y[1] (numeric) = 0.3050090267835898 absolute error = 1.6814327707948e-13 relative error = 5.512731175614956e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999679 y[1] (closed_form) = 0.2978537112694228 y[1] (numeric) = 0.297853711269254 absolute error = 1.688649220454863e-13 relative error = 5.66939123658392e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999678 y[1] (closed_form) = 0.2907686097988409 y[1] (numeric) = 0.2907686097986711 absolute error = 1.697531004651864e-13 relative error = 5.838082060598796e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999677 y[1] (closed_form) = 0.2837544308762548 y[1] (numeric) = 0.2837544308760843 absolute error = 1.705857677336553e-13 relative error = 6.011739348241144e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999676 y[1] (closed_form) = 0.2768118759137118 y[1] (numeric) = 0.2768118759135403 absolute error = 1.715294573045867e-13 relative error = 6.196607596346628e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999675 y[1] (closed_form) = 0.2699416391609226 y[1] (numeric) = 0.2699416391607503 absolute error = 1.723066134218243e-13 relative error = 6.383106139438742e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999674 y[1] (closed_form) = 0.2631444076358374 y[1] (numeric) = 0.2631444076356643 absolute error = 1.730282583878306e-13 relative error = 6.575410815010841e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999673 y[1] (closed_form) = 0.2564208610559442 y[1] (numeric) = 0.2564208610557703 absolute error = 1.738609256562995e-13 relative error = 6.780295680325622e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999672 y[1] (closed_form) = 0.2497716717702984 y[1] (numeric) = 0.2497716717701237 absolute error = 1.746935929247684e-13 relative error = 6.994131547689073e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99999999999967 y[1] (closed_form) = 0.2431975046922872 y[1] (numeric) = 0.2431975046921118 absolute error = 1.753874823151591e-13 relative error = 7.211730339794123e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999674 y[1] (closed_form) = 0.2366990172331372 y[1] (numeric) = 0.236699017232964 absolute error = 1.731947918415244e-13 relative error = 7.317089604598392e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999677 y[1] (closed_form) = 0.230276859236182 y[1] (numeric) = 0.230276859236011 absolute error = 1.71057612519121e-13 relative error = 7.4283457350648e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.029999999999681 y[1] (closed_form) = 0.2239316729118693 y[1] (numeric) = 0.2239316729117005 absolute error = 1.688371664698707e-13 relative error = 7.539673342069762e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999684 y[1] (closed_form) = 0.2176640927735441 y[1] (numeric) = 0.2176640927733774 absolute error = 1.667554982986985e-13 relative error = 7.661139518872757e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999687 y[1] (closed_form) = 0.2114747455739973 y[1] (numeric) = 0.2114747455738326 absolute error = 1.646738301275263e-13 relative error = 7.786926504181807e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.059999999999691 y[1] (closed_form) = 0.2053642502427908 y[1] (numeric) = 0.2053642502426282 absolute error = 1.626199175319698e-13 relative error = 7.918608878600499e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999694 y[1] (closed_form) = 0.1993332178243659 y[1] (numeric) = 0.1993332178242053 absolute error = 1.605660049364133e-13 relative error = 8.055155417091059e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999697 y[1] (closed_form) = 0.1933822514169385 y[1] (numeric) = 0.1933822514167799 absolute error = 1.586508702189349e-13 relative error = 8.204003679576485e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.089999999999701 y[1] (closed_form) = 0.1875119461121902 y[1] (numeric) = 0.1875119461120336 absolute error = 1.566524687746096e-13 relative error = 8.354266062647704e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.099999999999704 y[1] (closed_form) = 0.1817228889357597 y[1] (numeric) = 0.181722888935605 absolute error = 1.547373340571312e-13 relative error = 8.515016185541267e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.109999999999707 y[1] (closed_form) = 0.1760156587885403 y[1] (numeric) = 0.1760156587883875 absolute error = 1.527944437640372e-13 relative error = 8.680730158650238e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.119999999999711 y[1] (closed_form) = 0.1703908263887908 y[1] (numeric) = 0.1703908263886399 absolute error = 1.508793090465588e-13 relative error = 8.8548962549362e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.129999999999714 y[1] (closed_form) = 0.1648489542150638 y[1] (numeric) = 0.1648489542149147 absolute error = 1.491029522071585e-13 relative error = 9.0448224507774e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.139999999999717 y[1] (closed_form) = 0.1593905964499585 y[1] (numeric) = 0.1593905964498112 absolute error = 1.47271084216527e-13 relative error = 9.239634426160364e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.149999999999721 y[1] (closed_form) = 0.1540162989247027 y[1] (numeric) = 0.1540162989245572 absolute error = 1.454947273771268e-13 relative error = 9.446709756884753e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.159999999999724 y[1] (closed_form) = 0.1487265990645704 y[1] (numeric) = 0.1487265990644268 absolute error = 1.436351038108796e-13 relative error = 9.657660748937028e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.169999999999727 y[1] (closed_form) = 0.1435220258351396 y[1] (numeric) = 0.1435220258349977 absolute error = 1.41886502547095e-13 relative error = 9.886043742866109e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.179999999999731 y[1] (closed_form) = 0.1384030996893961 y[1] (numeric) = 0.138403099689256 absolute error = 1.40165656858926e-13 relative error = 1.012734954444557e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999734 y[1] (closed_form) = 0.1333703325156886 y[1] (numeric) = 0.1333703325155502 absolute error = 1.38444811170757e-13 relative error = 1.038048031817507e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999737 y[1] (closed_form) = 0.1284242275865407 y[1] (numeric) = 0.1284242275864039 absolute error = 1.367794766338193e-13 relative error = 1.065059757059066e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.209999999999741 y[1] (closed_form) = 0.1235652795083235 y[1] (numeric) = 0.1235652795081884 absolute error = 1.35155775460305e-13 relative error = 1.09380058862895e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999744 y[1] (closed_form) = 0.1187939741717956 y[1] (numeric) = 0.1187939741716621 absolute error = 1.334765631355594e-13 relative error = 1.12359708534147e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999747 y[1] (closed_form) = 0.1141107887035148 y[1] (numeric) = 0.1141107887033828 absolute error = 1.319638842645077e-13 relative error = 1.156454054553765e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.239999999999751 y[1] (closed_form) = 0.1095161914181251 y[1] (numeric) = 0.1095161914179946 absolute error = 1.304373276056481e-13 relative error = 1.191032357102774e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999754 y[1] (closed_form) = 0.1050106417715262 y[1] (numeric) = 0.1050106417713973 absolute error = 1.28869137583365e-13 relative error = 1.227200742794699e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999757 y[1] (closed_form) = 0.1005945903149283 y[1] (numeric) = 0.1005945903148009 absolute error = 1.274674810147758e-13 relative error = 1.267140515366853e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.269999999999761 y[1] (closed_form) = 0.09626847864979693 y[1] (numeric) = 0.09626847864967097 absolute error = 1.25954802143724e-13 relative error = 1.308370132262287e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999764 y[1] (closed_form) = 0.09203273938369361 y[1] (numeric) = 0.09203273938356904 absolute error = 1.245670233629426e-13 relative error = 1.353507721242658e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999767 y[1] (closed_form) = 0.08788779608701502 y[1] (numeric) = 0.0878877960868919 absolute error = 1.231237334309299e-13 relative error = 1.40091956918602e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.299999999999771 y[1] (closed_form) = 0.08383406325063691 y[1] (numeric) = 0.08383406325051511 absolute error = 1.218053435891875e-13 relative error = 1.452933794047757e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999774 y[1] (closed_form) = 0.0798719462444647 y[1] (numeric) = 0.07987194624434422 absolute error = 1.204730759596373e-13 relative error = 1.50832778746751e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999777 y[1] (closed_form) = 0.07600184127689724 y[1] (numeric) = 0.0760018412767781 absolute error = 1.191408083300871e-13 relative error = 1.567604236008202e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.329999999999781 y[1] (closed_form) = 0.07222413535520633 y[1] (numeric) = 0.07222413535508841 absolute error = 1.179195630029994e-13 relative error = 1.632689161636313e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999784 y[1] (closed_form) = 0.06853920624683596 y[1] (numeric) = 0.06853920624671925 absolute error = 1.167121954637196e-13 relative error = 1.702853036310257e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999787 y[1] (closed_form) = 0.06494742244162621 y[1] (numeric) = 0.06494742244151071 absolute error = 1.155048279244397e-13 relative error = 1.778435903722796e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.359999999999791 y[1] (closed_form) = 0.06144914311496452 y[1] (numeric) = 0.06144914311485015 absolute error = 1.143668493241989e-13 relative error = 1.861162638350079e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999794 y[1] (closed_form) = 0.05804471809186817 y[1] (numeric) = 0.05804471809175502 absolute error = 1.131525428910152e-13 relative error = 1.949402919175645e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y[1] (closed_form) = 0.05473448781200274 y[1] (numeric) = 0.05473448781189062 absolute error = 1.121255865932369e-13 relative error = 2.048536326463054e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999801 y[1] (closed_form) = 0.05151878329563742 y[1] (numeric) = 0.0515187832955264 absolute error = 1.110153635686117e-13 relative error = 2.154852200828517e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999804 y[1] (closed_form) = 0.04839792611054428 y[1] (numeric) = 0.04839792611043427 absolute error = 1.100022850586413e-13 relative error = 2.272871874868942e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y[1] (closed_form) = 0.045372228339841 y[1] (numeric) = 0.04537222833973205 absolute error = 1.089545120791513e-13 relative error = 2.401348050685868e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.419999999999811 y[1] (closed_form) = 0.0424419925507834 y[1] (numeric) = 0.04244199255067538 absolute error = 1.080247002960277e-13 relative error = 2.545231592667856e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999814 y[1] (closed_form) = 0.03960751176450839 y[1] (numeric) = 0.03960751176440131 absolute error = 1.070740718311924e-13 relative error = 2.703377896289352e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y[1] (closed_form) = 0.03686906942673251 y[1] (numeric) = 0.03686906942662641 absolute error = 1.061026266846454e-13 relative error = 2.877822205290432e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.449999999999821 y[1] (closed_form) = 0.03422693937940768 y[1] (numeric) = 0.03422693937930245 absolute error = 1.05235264946657e-13 relative error = 3.074632638931509e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999824 y[1] (closed_form) = 0.03168138583333679 y[1] (numeric) = 0.03168138583323238 absolute error = 1.04416475465996e-13 relative error = 3.295830429113475e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y[1] (closed_form) = 0.02923266334175312 y[1] (numeric) = 0.02923266334164951 absolute error = 1.036046248792388e-13 relative error = 3.544139090852525e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.479999999999831 y[1] (closed_form) = 0.02688101677486521 y[1] (numeric) = 0.02688101677476242 absolute error = 1.027823659516258e-13 relative error = 3.823604099965866e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999834 y[1] (closed_form) = 0.02462668129537016 y[1] (numeric) = 0.0246266812952681 absolute error = 1.020607209856195e-13 relative error = 4.144314849472105e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y[1] (closed_form) = 0.02246988233493719 y[1] (numeric) = 0.02246988233483587 absolute error = 1.013113204439975e-13 relative error = 4.5087606127102e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.509999999999841 y[1] (closed_form) = 0.02041083557166512 y[1] (numeric) = 0.02041083557156448 absolute error = 1.006451866292224e-13 relative error = 4.93096846897051e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999844 y[1] (closed_form) = 0.01844974690851431 y[1] (numeric) = 0.01844974690841435 absolute error = 9.995476668578362e-14 relative error = 5.417676848437192e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y[1] (closed_form) = 0.01658681245271698 y[1] (numeric) = 0.01658681245261761 absolute error = 9.937536904480737e-14 relative error = 5.991227629063191e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.539999999999851 y[1] (closed_form) = 0.01482221849616616 y[1] (numeric) = 0.01482221849606736 absolute error = 9.8804645021211e-14 relative error = 6.66598222437264e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999854 y[1] (closed_form) = 0.01315614149678701 y[1] (numeric) = 0.01315614149668878 absolute error = 9.823392099761463e-14 relative error = 7.46677291526587e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999858 y[1] (closed_form) = 0.01158874806089116 y[1] (numeric) = 0.01158874806079341 absolute error = 9.775513731824503e-14 relative error = 8.43534925469143e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.569999999999861 y[1] (closed_form) = 0.01012019492651595 y[1] (numeric) = 0.01012019492641869 absolute error = 9.725900640411567e-14 relative error = 9.610388644717418e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999864 y[1] (closed_form) = 0.008750628947751027 y[1] (numeric) = 0.00875062894765426 absolute error = 9.676634493693825e-14 relative error = 1.105821598821281e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999868 y[1] (closed_form) = 0.007480187080053047 y[1] (numeric) = 0.0074801870799567 absolute error = 9.634654185575187e-14 relative error = 1.288023158039366e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.599999999999871 y[1] (closed_form) = 0.006308996366550024 y[1] (numeric) = 0.006308996366454081 absolute error = 9.594235128584927e-14 relative error = 1.520722880655483e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999874 y[1] (closed_form) = 0.005237173925337402 y[1] (numeric) = 0.005237173925241764 absolute error = 9.563790731581534e-14 relative error = 1.826135787721694e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999878 y[1] (closed_form) = 0.004264826937765975 y[1] (numeric) = 0.004264826937670687 absolute error = 9.528836053540601e-14 relative error = 2.234284343207616e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.629999999999881 y[1] (closed_form) = 0.003392052637724352 y[1] (numeric) = 0.003392052637629323 absolute error = 9.502858569487849e-14 relative error = 2.80150681148129e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999884 y[1] (closed_form) = 0.002618938301915064 y[1] (numeric) = 0.002618938301820366 absolute error = 9.469768719183591e-14 relative error = 3.61588079881796e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999888 y[1] (closed_form) = 0.001945561241127658 y[1] (numeric) = 0.001945561241033136 absolute error = 9.452226328032776e-14 relative error = 4.858354560226649e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.659999999999891 y[1] (closed_form) = 0.001371988792506884 y[1] (numeric) = 0.001371988792412566 absolute error = 9.431799959103149e-14 relative error = 6.874545922397412e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999894 y[1] (closed_form) = 0.0008982783128197447 y[1] (numeric) = 0.0008982783127255438 absolute error = 9.420090575640305e-14 relative error = 1.048682845973441e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999898 y[1] (closed_form) = 0.0005244771727193065 y[1] (numeric) = 0.00052447717262528 absolute error = 9.402645762685014e-14 relative error = 1.792765491381489e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.689999999999901 y[1] (closed_form) = 0.0002506227520082671 y[1] (numeric) = 0.0002506227519142851 absolute error = 9.398200533777823e-14 relative error = 3.749939085126561e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999904 y[1] (closed_form) = 7.674243590027885e-05 y[1] (numeric) = 7.674243580641887e-05 absolute error = 9.385997838326499e-14 relative error = 1.22305185237056e-07 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999908 y[1] (closed_form) = 2.853612282249784e-06 y[1] (numeric) = 2.85361218839223e-06 absolute error = 9.385755459848642e-14 relative error = 3.28907872952135e-06 % Desired digits = 8 Estimated correct digits = 6 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.719999999999911 y[1] (closed_form) = 2.896366997484634e-05 y[1] (numeric) = 2.89636698809932e-05 absolute error = 9.385314113331475e-14 relative error = 3.240374621545613e-07 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999914 y[1] (closed_form) = 0.0001550699979940839 y[1] (numeric) = 0.0001550699979002108 absolute error = 9.387312433460637e-14 relative error = 6.053596798149679e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999918 y[1] (closed_form) = 0.0003811599858123405 y[1] (numeric) = 0.0003811599857183314 absolute error = 9.400900197187312e-14 relative error = 2.466392209862169e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.749999999999921 y[1] (closed_form) = 0.0007072110246191254 y[1] (numeric) = 0.000707211024524981 absolute error = 9.414441882321656e-14 relative error = 1.331206889399368e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999924 y[1] (closed_form) = 0.001133190509582271 y[1] (numeric) = 0.001133190509487987 absolute error = 9.428460616411893e-14 relative error = 8.320278485113251e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999928 y[1] (closed_form) = 0.001659055843108215 y[1] (numeric) = 0.001659055843013835 absolute error = 9.438023279573216e-14 relative error = 5.688791802144061e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.779999999999931 y[1] (closed_form) = 0.002284754439102032 y[1] (numeric) = 0.002284754439007392 absolute error = 9.464087499799767e-14 relative error = 4.142277759845123e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999934 y[1] (closed_form) = 0.003010223728225347 y[1] (numeric) = 0.003010223728130472 absolute error = 9.487593002899253e-14 relative error = 3.151789986218926e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999938 y[1] (closed_form) = 0.003835391164153878 y[1] (numeric) = 0.003835391164058718 absolute error = 9.516085835992172e-14 relative error = 2.481125243477351e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.809999999999941 y[1] (closed_form) = 0.004760174230831637 y[1] (numeric) = 0.004760174230736176 absolute error = 9.546183288300369e-14 relative error = 2.005427285932049e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999944 y[1] (closed_form) = 0.005784480450722662 y[1] (numeric) = 0.005784480450626826 absolute error = 9.583653315381468e-14 relative error = 1.656787225235444e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999948 y[1] (closed_form) = 0.006908207394058508 y[1] (numeric) = 0.006908207393962265 absolute error = 9.624245844719326e-14 relative error = 1.393161104716801e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.839999999999951 y[1] (closed_form) = 0.008131242689081164 y[1] (numeric) = 0.008131242688984597 absolute error = 9.656685173720092e-14 relative error = 1.18760262643339e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999954 y[1] (closed_form) = 0.009453464033280512 y[1] (numeric) = 0.009453464033183511 absolute error = 9.700053260619512e-14 relative error = 1.026084536469478e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999958 y[1] (closed_form) = 0.01087473920562398 y[1] (numeric) = 0.01087473920552644 absolute error = 9.754870522460379e-14 relative error = 8.970210998177819e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.869999999999961 y[1] (closed_form) = 0.01239492607977855 y[1] (numeric) = 0.01239492607968053 absolute error = 9.801361111616558e-14 relative error = 7.907559148421863e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999964 y[1] (closed_form) = 0.01401387263832377 y[1] (numeric) = 0.0140138726382252 absolute error = 9.857045735195413e-14 relative error = 7.033777164664199e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999968 y[1] (closed_form) = 0.01573141698795288 y[1] (numeric) = 0.01573141698785369 absolute error = 9.919148835635383e-14 relative error = 6.30531174860565e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.899999999999971 y[1] (closed_form) = 0.01754738737566208 y[1] (numeric) = 0.01754738737556234 absolute error = 9.974313042171445e-14 relative error = 5.684215449649013e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999974 y[1] (closed_form) = 0.01946160220592608 y[1] (numeric) = 0.01946160220582567 absolute error = 1.004023253425856e-13 relative error = 5.158995866846617e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999978 y[1] (closed_form) = 0.02147387005885693 y[1] (numeric) = 0.02147387005875584 absolute error = 1.010858063921205e-13 relative error = 4.707386517430636e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.929999999999981 y[1] (closed_form) = 0.02358398970934616 y[1] (numeric) = 0.02358398970924443 absolute error = 1.017345929721358e-13 relative error = 4.313714270822428e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y[1] (closed_form) = 0.02579175014718738 y[1] (numeric) = 0.02579175014708482 absolute error = 1.025533824527969e-13 relative error = 3.976208743786255e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999988 y[1] (closed_form) = 0.02809693059817631 y[1] (numeric) = 0.02809693059807303 absolute error = 1.032784968657552e-13 relative error = 3.675792859468383e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.959999999999991 y[1] (closed_form) = 0.03049930054618899 y[1] (numeric) = 0.03049930054608492 absolute error = 1.040730002177526e-13 relative error = 3.412307769489386e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y[1] (closed_form) = 0.03299861975623253 y[1] (numeric) = 0.03299861975612767 absolute error = 1.04860564675846e-13 relative error = 3.177725779152953e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999998 y[1] (closed_form) = 0.03559463829846876 y[1] (numeric) = 0.03559463829836303 absolute error = 1.057348653077383e-13 relative error = 2.970527876168556e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.990000000000001 y[1] (closed_form) = 0.03828709657320684 y[1] (numeric) = 0.03828709657310013 absolute error = 1.067063104542854e-13 relative error = 2.787004500334926e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 Finished! diff ( y , x , 1 ) = cos ( x ) ; Iterations = 5000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %