##############ECHO OF PROBLEM################# ##############temp/mtest1postode.ode################# diff ( y1 , x , 1 ) = neg ( y2 ) + 1.0 ; diff ( y2 , x , 1 ) = y1 - 1.0 ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(10.0); array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y1 (double x) { return(c(1.0) + cos(c(x))); } double exact_soln_y2 (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] = 0.1 y1[1] (closed_form) = 1.995004165278026 y1[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 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] = 0.11 y1[1] (closed_form) = 1.993956097956697 y1[1] (numeric) = 1.993956097956697 absolute error = 2.220446049250313e-16 relative error = 1.113588233725763e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.109778300837175 y2[1] (numeric) = 1.109778300837175 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y1[1] (closed_form) = 1.992808635853866 y1[1] (numeric) = 1.992808635853866 absolute error = 2.220446049250313e-16 relative error = 1.114229439445855e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.119712207288919 y2[1] (numeric) = 1.119712207288919 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] = 0.13 y1[1] (closed_form) = 1.991561893714788 y1[1] (numeric) = 1.991561893714788 absolute error = 2.220446049250313e-16 relative error = 1.114926960722569e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.129634142619695 y2[1] (numeric) = 1.129634142619694 absolute error = 6.661338147750939e-16 relative error = 5.896898735995057e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y1[1] (closed_form) = 1.990215996212637 y1[1] (numeric) = 1.990215996212637 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.139543114644237 y2[1] (numeric) = 1.139543114644236 absolute error = 6.661338147750939e-16 relative error = 5.845621865593561e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y1[1] (closed_form) = 1.988771077936042 y1[1] (numeric) = 1.988771077936042 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.149438132473599 y2[1] (numeric) = 1.149438132473598 absolute error = 6.661338147750939e-16 relative error = 5.79529942461165e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y1[1] (closed_form) = 1.987227283375627 y1[1] (numeric) = 1.987227283375627 absolute error = 2.220446049250313e-16 relative error = 1.117358878788402e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.159318206614246 y2[1] (numeric) = 1.159318206614245 absolute error = 8.881784197001252e-16 relative error = 7.66121341520223e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y1[1] (closed_form) = 1.985584766909561 y1[1] (numeric) = 1.985584766909561 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.169182349066996 y2[1] (numeric) = 1.169182349066995 absolute error = 1.110223024625157e-15 relative error = 9.49572173674287e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y1[1] (closed_form) = 1.983843692788121 y1[1] (numeric) = 1.983843692788121 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.179029573425824 y2[1] (numeric) = 1.179029573425823 absolute error = 8.881784197001252e-16 relative error = 7.533130972443778e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y1[1] (closed_form) = 1.98200423511727 y1[1] (numeric) = 1.98200423511727 absolute error = 4.440892098500626e-16 relative error = 2.240606765523823e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.188858894976501 y2[1] (numeric) = 1.1888588949765 absolute error = 1.110223024625157e-15 relative error = 9.338560104284719e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y1[1] (closed_form) = 1.980066577841242 y1[1] (numeric) = 1.980066577841241 absolute error = 6.661338147750939e-16 relative error = 3.364199074060142e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.198669330795061 y2[1] (numeric) = 1.19866933079506 absolute error = 1.110223024625157e-15 relative error = 9.262129230325435e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y1[1] (closed_form) = 1.978030914724148 y1[1] (numeric) = 1.978030914724147 absolute error = 8.881784197001252e-16 relative error = 4.49021505725045e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.2084598998461 y2[1] (numeric) = 1.208459899846098 absolute error = 1.110223024625157e-15 relative error = 9.187090318566187e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y1[1] (closed_form) = 1.975897449330605 y1[1] (numeric) = 1.975897449330604 absolute error = 1.110223024625157e-15 relative error = 5.61882918064031e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.218229623080869 y2[1] (numeric) = 1.218229623080868 absolute error = 1.110223024625157e-15 relative error = 9.113413461556065e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y1[1] (closed_form) = 1.973666395005375 y1[1] (numeric) = 1.973666395005373 absolute error = 1.332267629550188e-15 relative error = 6.750216920760612e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.227977523535189 y2[1] (numeric) = 1.227977523535187 absolute error = 1.332267629550188e-15 relative error = 1.084928350899096e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y1[1] (closed_form) = 1.971337974852029 y1[1] (numeric) = 1.971337974852028 absolute error = 1.554312234475219e-15 relative error = 7.884554826738359e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.237702626427135 y2[1] (numeric) = 1.237702626427134 absolute error = 8.881784197001252e-16 relative error = 7.176024359453951e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y1[1] (closed_form) = 1.968912421710645 y1[1] (numeric) = 1.968912421710643 absolute error = 1.332267629550188e-15 relative error = 6.766515436947051e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.247403959254523 y2[1] (numeric) = 1.247403959254522 absolute error = 8.881784197001252e-16 relative error = 7.120214851898666e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y1[1] (closed_form) = 1.966389978134513 y1[1] (numeric) = 1.966389978134512 absolute error = 1.332267629550188e-15 relative error = 6.775195380186445e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.257080551892155 y2[1] (numeric) = 1.257080551892154 absolute error = 8.881784197001252e-16 relative error = 7.065405779790649e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y1[1] (closed_form) = 1.963770896365891 y1[1] (numeric) = 1.96377089636589 absolute error = 1.110223024625157e-15 relative error = 5.653526216727775e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.266731436688831 y2[1] (numeric) = 1.26673143668883 absolute error = 1.110223024625157e-15 relative error = 8.764470451031203e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y1[1] (closed_form) = 1.961055438310771 y1[1] (numeric) = 1.96105543831077 absolute error = 1.110223024625157e-15 relative error = 5.661354610053702e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.276355648564114 y2[1] (numeric) = 1.276355648564113 absolute error = 1.110223024625157e-15 relative error = 8.698382977143912e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y1[1] (closed_form) = 1.958243875512697 y1[1] (numeric) = 1.958243875512696 absolute error = 1.332267629550188e-15 relative error = 6.80337952902511e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.285952225104836 y2[1] (numeric) = 1.285952225104835 absolute error = 8.881784197001252e-16 relative error = 6.906776180022688e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y1[1] (closed_form) = 1.955336489125606 y1[1] (numeric) = 1.955336489125604 absolute error = 1.554312234475219e-15 relative error = 7.94907803909639e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.29552020666134 y2[1] (numeric) = 1.295520206661339 absolute error = 1.110223024625157e-15 relative error = 8.569708283333465e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y1[1] (closed_form) = 1.952333569885713 y1[1] (numeric) = 1.952333569885712 absolute error = 1.332267629550188e-15 relative error = 6.823975421516604e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.305058636443444 y2[1] (numeric) = 1.305058636443443 absolute error = 8.881784197001252e-16 relative error = 6.805659109084909e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y1[1] (closed_form) = 1.949235418082441 y1[1] (numeric) = 1.94923541808244 absolute error = 1.110223024625157e-15 relative error = 5.695684648072616e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.314566560616118 y2[1] (numeric) = 1.314566560616117 absolute error = 6.661338147750939e-16 relative error = 5.067326636263187e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y1[1] (closed_form) = 1.946042343528387 y1[1] (numeric) = 1.946042343528386 absolute error = 8.881784197001252e-16 relative error = 4.564024121334179e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.324043028394869 y2[1] (numeric) = 1.324043028394868 absolute error = 8.881784197001252e-16 relative error = 6.708078216890428e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y1[1] (closed_form) = 1.942754665528346 y1[1] (numeric) = 1.942754665528345 absolute error = 1.110223024625157e-15 relative error = 5.714684639932255e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.333487092140815 y2[1] (numeric) = 1.333487092140814 absolute error = 1.110223024625157e-15 relative error = 8.325712570961417e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y1[1] (closed_form) = 1.939372712847379 y1[1] (numeric) = 1.939372712847378 absolute error = 1.110223024625157e-15 relative error = 5.724650126664573e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.342897807455452 y2[1] (numeric) = 1.342897807455451 absolute error = 1.110223024625157e-15 relative error = 8.267367914829114e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y1[1] (closed_form) = 1.935896823677935 y1[1] (numeric) = 1.935896823677934 absolute error = 8.881784197001252e-16 relative error = 4.587942956653598e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.35227423327509 y2[1] (numeric) = 1.352274233275089 absolute error = 8.881784197001252e-16 relative error = 6.568034780556565e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y1[1] (closed_form) = 1.932327345606034 y1[1] (numeric) = 1.932327345606034 absolute error = 4.440892098500626e-16 relative error = 2.298209000974332e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.361615431964962 y2[1] (numeric) = 1.361615431964961 absolute error = 1.110223024625157e-15 relative error = 8.153719461176946e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y1[1] (closed_form) = 1.92866463557651 y1[1] (numeric) = 1.92866463557651 absolute error = 4.440892098500626e-16 relative error = 2.302573509454727e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.370920469412983 y2[1] (numeric) = 1.370920469412982 absolute error = 8.881784197001252e-16 relative error = 6.478701277838795e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y1[1] (closed_form) = 1.924909059857313 y1[1] (numeric) = 1.924909059857312 absolute error = 6.661338147750939e-16 relative error = 3.460598885770075e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.380188415123162 y2[1] (numeric) = 1.380188415123161 absolute error = 8.881784197001252e-16 relative error = 6.435196890280146e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y1[1] (closed_form) = 1.921060994002885 y1[1] (numeric) = 1.921060994002885 absolute error = 4.440892098500626e-16 relative error = 2.311687193880923e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.389418342308651 y2[1] (numeric) = 1.389418342308649 absolute error = 1.332267629550188e-15 relative error = 9.588671669156882e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y1[1] (closed_form) = 1.917120822816605 y1[1] (numeric) = 1.917120822816605 absolute error = 2.220446049250313e-16 relative error = 1.158219149687221e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.398609327984423 y2[1] (numeric) = 1.398609327984422 absolute error = 1.332267629550188e-15 relative error = 9.525659545472629e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y1[1] (closed_form) = 1.913088940312308 y1[1] (numeric) = 1.913088940312308 absolute error = 2.220446049250313e-16 relative error = 1.16066012534045e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.40776045305957 y2[1] (numeric) = 1.407760453059569 absolute error = 1.110223024625157e-15 relative error = 7.886448452307651e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y1[1] (closed_form) = 1.908965749674885 y1[1] (numeric) = 1.908965749674885 absolute error = 2.220446049250313e-16 relative error = 1.163167044578184e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.416870802429211 y2[1] (numeric) = 1.41687080242921 absolute error = 1.110223024625157e-15 relative error = 7.835739311740281e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y1[1] (closed_form) = 1.904751663219963 y1[1] (numeric) = 1.904751663219963 absolute error = 2.220446049250313e-16 relative error = 1.16574044382073e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.425939465066 y2[1] (numeric) = 1.425939465065999 absolute error = 1.110223024625157e-15 relative error = 7.785905726185717e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y1[1] (closed_form) = 1.900447102352677 y1[1] (numeric) = 1.900447102352677 absolute error = 2.220446049250313e-16 relative error = 1.168380875480033e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.43496553411123 y2[1] (numeric) = 1.434965534111229 absolute error = 1.332267629550188e-15 relative error = 9.284317970573069e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y1[1] (closed_form) = 1.896052497525525 y1[1] (numeric) = 1.896052497525524 absolute error = 6.661338147750939e-16 relative error = 3.513266724652629e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.44394810696552 y2[1] (numeric) = 1.443948106965519 absolute error = 1.110223024625157e-15 relative error = 7.688801413773159e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y1[1] (closed_form) = 1.891568288195329 y1[1] (numeric) = 1.891568288195328 absolute error = 6.661338147750939e-16 relative error = 3.521595381632381e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.452886285379068 y2[1] (numeric) = 1.452886285379067 absolute error = 1.110223024625157e-15 relative error = 7.641499791124336e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y1[1] (closed_form) = 1.886994922779284 y1[1] (numeric) = 1.886994922779283 absolute error = 6.661338147750939e-16 relative error = 3.530130403286779e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.461779175541483 y2[1] (numeric) = 1.461779175541482 absolute error = 6.661338147750939e-16 relative error = 4.557007145271034e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y1[1] (closed_form) = 1.882332858610121 y1[1] (numeric) = 1.882332858610121 absolute error = 6.661338147750939e-16 relative error = 3.538873646752118e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.470625888171158 y2[1] (numeric) = 1.470625888171158 absolute error = 6.661338147750939e-16 relative error = 4.529593964944307e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y1[1] (closed_form) = 1.877582561890373 y1[1] (numeric) = 1.877582561890372 absolute error = 6.661338147750939e-16 relative error = 3.547827021275818e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.479425538604203 y2[1] (numeric) = 1.479425538604202 absolute error = 1.332267629550188e-15 relative error = 9.005303712731262e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y1[1] (closed_form) = 1.872744507645751 y1[1] (numeric) = 1.87274450764575 absolute error = 8.881784197001252e-16 relative error = 4.74265665217016e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.488177246882908 y2[1] (numeric) = 1.488177246882906 absolute error = 1.332267629550188e-15 relative error = 8.952345107686039e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y1[1] (closed_form) = 1.86781917967765 y1[1] (numeric) = 1.867819179677649 absolute error = 6.661338147750939e-16 relative error = 3.566372066540488e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.496880137843737 y2[1] (numeric) = 1.496880137843736 absolute error = 1.332267629550188e-15 relative error = 8.900295994770334e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y1[1] (closed_form) = 1.862807070514761 y1[1] (numeric) = 1.86280707051476 absolute error = 1.110223024625157e-15 relative error = 5.959946374470019e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.505533341204847 y2[1] (numeric) = 1.505533341204846 absolute error = 1.332267629550188e-15 relative error = 8.849140653929334e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y1[1] (closed_form) = 1.857708681363824 y1[1] (numeric) = 1.857708681363823 absolute error = 8.881784197001252e-16 relative error = 4.781042520876175e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.514135991653113 y2[1] (numeric) = 1.514135991653112 absolute error = 1.332267629550188e-15 relative error = 8.798863753946143e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y1[1] (closed_form) = 1.852524522059506 y1[1] (numeric) = 1.852524522059505 absolute error = 8.881784197001252e-16 relative error = 4.794421931390745e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.522687228930659 y2[1] (numeric) = 1.522687228930658 absolute error = 1.554312234475219e-15 relative error = 1.020769206534141e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y1[1] (closed_form) = 1.847255111013416 y1[1] (numeric) = 1.847255111013415 absolute error = 4.440892098500626e-16 relative error = 2.40404916030484e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.531186197920884 y2[1] (numeric) = 1.531186197920882 absolute error = 1.554312234475219e-15 relative error = 1.015103347055856e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y1[1] (closed_form) = 1.841900975162269 y1[1] (numeric) = 1.841900975162268 absolute error = 6.661338147750939e-16 relative error = 3.616556067659438e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.539632048733969 y2[1] (numeric) = 1.539632048733968 absolute error = 1.554312234475219e-15 relative error = 1.009534866303492e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y1[1] (closed_form) = 1.836462649915187 y1[1] (numeric) = 1.836462649915186 absolute error = 4.440892098500626e-16 relative error = 2.418177194458989e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.548023936791874 y2[1] (numeric) = 1.548023936791872 absolute error = 1.998401444325282e-15 relative error = 1.290937043561982e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y1[1] (closed_form) = 1.830940679100163 y1[1] (numeric) = 1.830940679100163 absolute error = 6.661338147750939e-16 relative error = 3.638205335535355e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.556361022912784 y2[1] (numeric) = 1.556361022912782 absolute error = 1.77635683940025e-15 relative error = 1.141352689542261e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y1[1] (closed_form) = 1.825335614909678 y1[1] (numeric) = 1.825335614909677 absolute error = 8.881784197001252e-16 relative error = 4.865836246470622e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.564642473395036 y2[1] (numeric) = 1.564642473395034 absolute error = 1.998401444325282e-15 relative error = 1.277225614353326e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y1[1] (closed_form) = 1.819648017845479 y1[1] (numeric) = 1.819648017845479 absolute error = 6.661338147750939e-16 relative error = 3.660783889204118e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.572867460100482 y2[1] (numeric) = 1.57286746010048 absolute error = 1.998401444325282e-15 relative error = 1.270546625840689e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y1[1] (closed_form) = 1.813878456662534 y1[1] (numeric) = 1.813878456662533 absolute error = 6.661338147750939e-16 relative error = 3.672428063348602e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.581035160537305 y2[1] (numeric) = 1.581035160537304 absolute error = 1.77635683940025e-15 relative error = 1.123540376418046e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y1[1] (closed_form) = 1.808027508312152 y1[1] (numeric) = 1.808027508312151 absolute error = 4.440892098500626e-16 relative error = 2.456208259047084e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.58914475794227 y2[1] (numeric) = 1.589144757942268 absolute error = 2.220446049250313e-15 relative error = 1.397258517924757e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y1[1] (closed_form) = 1.802095757884292 y1[1] (numeric) = 1.802095757884292 absolute error = 2.220446049250313e-16 relative error = 1.232146538015924e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.597195441362393 y2[1] (numeric) = 1.597195441362391 absolute error = 1.77635683940025e-15 relative error = 1.112172495236422e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y1[1] (closed_form) = 1.796083798549056 y1[1] (numeric) = 1.796083798549055 absolute error = 2.220446049250313e-16 relative error = 1.236270852754239e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.60518640573604 y2[1] (numeric) = 1.605186405736039 absolute error = 1.332267629550188e-15 relative error = 8.299768953869826e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y1[1] (closed_form) = 1.789992231497365 y1[1] (numeric) = 1.789992231497365 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.613116851973434 y2[1] (numeric) = 1.613116851973433 absolute error = 1.332267629550188e-15 relative error = 8.258965417913373e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y1[1] (closed_form) = 1.783821665880849 y1[1] (numeric) = 1.783821665880849 absolute error = 2.220446049250313e-16 relative error = 1.244769077380759e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.62098598703656 y2[1] (numeric) = 1.620985987036559 absolute error = 1.110223024625157e-15 relative error = 6.849059976482797e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y1[1] (closed_form) = 1.777572718750928 y1[1] (numeric) = 1.777572718750928 absolute error = 2.220446049250313e-16 relative error = 1.249144986209389e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.628793024018469 y2[1] (numeric) = 1.628793024018468 absolute error = 8.881784197001252e-16 relative error = 5.452985165106246e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y1[1] (closed_form) = 1.771246014997106 y1[1] (numeric) = 1.771246014997107 absolute error = 4.440892098500626e-16 relative error = 2.507213600425733e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.636537182221968 y2[1] (numeric) = 1.636537182221968 absolute error = 4.440892098500626e-16 relative error = 2.713590712599095e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y1[1] (closed_form) = 1.764842187284488 y1[1] (numeric) = 1.764842187284489 absolute error = 4.440892098500626e-16 relative error = 2.516311163965147e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.644217687237691 y2[1] (numeric) = 1.644217687237691 absolute error = 4.440892098500626e-16 relative error = 2.70091492931291e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y1[1] (closed_form) = 1.758361875990508 y1[1] (numeric) = 1.758361875990508 absolute error = 4.440892098500626e-16 relative error = 2.525584840719442e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.651833771021537 y2[1] (numeric) = 1.651833771021537 absolute error = 6.661338147750939e-16 relative error = 4.032692795493213e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y1[1] (closed_form) = 1.751805729140895 y1[1] (numeric) = 1.751805729140895 absolute error = 6.661338147750939e-16 relative error = 3.802555293056231e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.659384671971474 y2[1] (numeric) = 1.659384671971473 absolute error = 4.440892098500626e-16 relative error = 2.676228226951448e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y1[1] (closed_form) = 1.74517440234487 y1[1] (numeric) = 1.745174402344871 absolute error = 6.661338147750939e-16 relative error = 3.817004271206683e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.666869635003698 y2[1] (numeric) = 1.666869635003698 absolute error = 4.440892098500626e-16 relative error = 2.664210808837953e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y1[1] (closed_form) = 1.738468558729588 y1[1] (numeric) = 1.738468558729588 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.674287911628145 y2[1] (numeric) = 1.674287911628145 absolute error = 4.440892098500626e-16 relative error = 2.652406475408475e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y1[1] (closed_form) = 1.731688868873821 y1[1] (numeric) = 1.731688868873821 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.681638760023334 y2[1] (numeric) = 1.681638760023334 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y1[1] (closed_form) = 1.724836010740905 y1[1] (numeric) = 1.724836010740905 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.688921445110552 y2[1] (numeric) = 1.688921445110552 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] = 0.7700000000000006 y1[1] (closed_form) = 1.717910669610943 y1[1] (numeric) = 1.717910669610943 absolute error = 2.220446049250313e-16 relative error = 1.292527072873457e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.696135238627357 y2[1] (numeric) = 1.696135238627357 absolute error = 2.220446049250313e-16 relative error = 1.309120875908025e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y1[1] (closed_form) = 1.710913538012277 y1[1] (numeric) = 1.710913538012277 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.703279419200411 y2[1] (numeric) = 1.70327941920041 absolute error = 4.440892098500626e-16 relative error = 2.607259882577201e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y1[1] (closed_form) = 1.703845315652236 y1[1] (numeric) = 1.703845315652236 absolute error = 2.220446049250313e-16 relative error = 1.303196967971427e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.710353272417608 y2[1] (numeric) = 1.710353272417608 absolute error = 2.220446049250313e-16 relative error = 1.298238255838036e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y1[1] (closed_form) = 1.696706709347165 y1[1] (numeric) = 1.696706709347165 absolute error = 2.220446049250313e-16 relative error = 1.308679948642783e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.717356090899523 y2[1] (numeric) = 1.717356090899523 absolute error = 2.220446049250313e-16 relative error = 1.292944463304218e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y1[1] (closed_form) = 1.689498432951747 y1[1] (numeric) = 1.689498432951747 absolute error = 2.220446049250313e-16 relative error = 1.314263455912735e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.724287174370143 y2[1] (numeric) = 1.724287174370143 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] = 0.8200000000000006 y1[1] (closed_form) = 1.682221207287613 y1[1] (numeric) = 1.682221207287614 absolute error = 6.661338147750939e-16 relative error = 3.959846730556664e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.731145829726896 y2[1] (numeric) = 1.731145829726896 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] = 0.8300000000000006 y1[1] (closed_form) = 1.674875760071266 y1[1] (numeric) = 1.674875760071268 absolute error = 1.110223024625157e-15 relative error = 6.62868883228638e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.737931371109963 y2[1] (numeric) = 1.737931371109963 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y1[1] (closed_form) = 1.667462825841308 y1[1] (numeric) = 1.667462825841309 absolute error = 8.881784197001252e-16 relative error = 5.326526060645463e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.74464311997086 y2[1] (numeric) = 1.744643119970859 absolute error = 4.440892098500626e-16 relative error = 2.545444422223613e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y1[1] (closed_form) = 1.659983145884982 y1[1] (numeric) = 1.659983145884983 absolute error = 1.554312234475219e-15 relative error = 9.363421781289071e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.751280405140293 y2[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 y1[1] (closed_form) = 1.652437468164051 y1[1] (numeric) = 1.652437468164053 absolute error = 1.554312234475219e-15 relative error = 9.406178838356559e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.757842562895277 y2[1] (numeric) = 1.757842562895277 absolute error = 2.220446049250313e-16 relative error = 1.263165482574901e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y1[1] (closed_form) = 1.644826547240001 y1[1] (numeric) = 1.644826547240002 absolute error = 1.77635683940025e-15 relative error = 1.079966056226996e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.764328937025506 y2[1] (numeric) = 1.764328937025505 absolute error = 4.440892098500626e-16 relative error = 2.517043168825172e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y1[1] (closed_form) = 1.63715114419858 y1[1] (numeric) = 1.637151144198582 absolute error = 2.220446049250313e-15 relative error = 1.356286532931734e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.77073887889897 y2[1] (numeric) = 1.770738878898969 absolute error = 4.440892098500626e-16 relative error = 2.507931661421437e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y1[1] (closed_form) = 1.629412026573696 y1[1] (numeric) = 1.629412026573699 absolute error = 2.220446049250313e-15 relative error = 1.362728403275281e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.777071747526824 y2[1] (numeric) = 1.777071747526824 absolute error = 4.440892098500626e-16 relative error = 2.498994261025802e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y1[1] (closed_form) = 1.621609968270664 y1[1] (numeric) = 1.621609968270666 absolute error = 2.220446049250313e-15 relative error = 1.369284903704845e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.783326909627484 y2[1] (numeric) = 1.783326909627483 absolute error = 4.440892098500626e-16 relative error = 2.490228838316737e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y1[1] (closed_form) = 1.613745749488811 y1[1] (numeric) = 1.613745749488813 absolute error = 2.220446049250313e-15 relative error = 1.375957798775729e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.789503739689951 y2[1] (numeric) = 1.78950373968995 absolute error = 6.661338147750939e-16 relative error = 3.722449973144555e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y1[1] (closed_form) = 1.605820156643462 y1[1] (numeric) = 1.605820156643465 absolute error = 2.664535259100376e-15 relative error = 1.659298675556467e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.795601620036366 y2[1] (numeric) = 1.795601620036366 absolute error = 4.440892098500626e-16 relative error = 2.473205664857155e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y1[1] (closed_form) = 1.597833982287298 y1[1] (numeric) = 1.5978339822873 absolute error = 2.220446049250313e-15 relative error = 1.38966004845619e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.801619940883778 y2[1] (numeric) = 1.801619940883777 absolute error = 6.661338147750939e-16 relative error = 3.697415862572683e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y1[1] (closed_form) = 1.589788025031098 y1[1] (numeric) = 1.5897880250311 absolute error = 2.664535259100376e-15 relative error = 1.676031783575836e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.807558100405115 y2[1] (numeric) = 1.807558100405114 absolute error = 8.881784197001252e-16 relative error = 4.913692232084072e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y1[1] (closed_form) = 1.581683089463883 y1[1] (numeric) = 1.581683089463885 absolute error = 2.442490654175344e-15 relative error = 1.544235169766679e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.813415504789374 y2[1] (numeric) = 1.813415504789373 absolute error = 1.332267629550188e-15 relative error = 7.346731215386454e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y1[1] (closed_form) = 1.573519986072456 y1[1] (numeric) = 1.573519986072458 absolute error = 2.220446049250313e-15 relative error = 1.411133044959029e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.819191568300999 y2[1] (numeric) = 1.819191568300997 absolute error = 1.332267629550188e-15 relative error = 7.323404817637954e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y1[1] (closed_form) = 1.565299531160354 y1[1] (numeric) = 1.565299531160356 absolute error = 2.664535259100376e-15 relative error = 1.702252639867055e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.824885713338451 y2[1] (numeric) = 1.82488571333845 absolute error = 1.110223024625157e-15 relative error = 6.083794818000474e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y1[1] (closed_form) = 1.557022546766217 y1[1] (numeric) = 1.557022546766219 absolute error = 2.664535259100376e-15 relative error = 1.71130165368148e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.830497370491971 y2[1] (numeric) = 1.83049737049197 absolute error = 6.661338147750939e-16 relative error = 3.639086433629027e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y1[1] (closed_form) = 1.548689860581587 y1[1] (numeric) = 1.54868986058159 absolute error = 2.886579864025407e-15 relative error = 1.863885040831478e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.836025978600521 y2[1] (numeric) = 1.83602597860052 absolute error = 4.440892098500626e-16 relative error = 2.41875232173219e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y1[1] (closed_form) = 1.540302305868139 y1[1] (numeric) = 1.540302305868142 absolute error = 2.442490654175344e-15 relative error = 1.585721611186394e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.841470984807897 y2[1] (numeric) = 1.841470984807897 absolute error = 2.220446049250313e-16 relative error = 1.205800182337356e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y1[1] (closed_form) = 1.531860721374356 y1[1] (numeric) = 1.531860721374357 absolute error = 1.554312234475219e-15 relative error = 1.014656367114577e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.846831844618015 y2[1] (numeric) = 1.846831844618015 absolute error = 4.440892098500626e-16 relative error = 2.404600132622874e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y1[1] (closed_form) = 1.523365951251651 y1[1] (numeric) = 1.523365951251652 absolute error = 8.881784197001252e-16 relative error = 5.830368067307575e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.852108021949362 y2[1] (numeric) = 1.852108021949363 absolute error = 8.881784197001252e-16 relative error = 4.795500095967991e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y1[1] (closed_form) = 1.514818844969958 y1[1] (numeric) = 1.514818844969958 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.857298989188602 y2[1] (numeric) = 1.857298989188604 absolute error = 1.554312234475219e-15 relative error = 8.368670006945146e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y1[1] (closed_form) = 1.506220257232782 y1[1] (numeric) = 1.506220257232781 absolute error = 8.881784197001252e-16 relative error = 5.896736652127365e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.862404227243337 y2[1] (numeric) = 1.862404227243339 absolute error = 1.998401444325282e-15 relative error = 1.073022394973428e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y1[1] (closed_form) = 1.497571047891731 y1[1] (numeric) = 1.497571047891729 absolute error = 1.77635683940025e-15 relative error = 1.1861586412885e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.867423225594015 y2[1] (numeric) = 1.867423225594017 absolute error = 2.442490654175344e-15 relative error = 1.307947025987323e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y1[1] (closed_form) = 1.488872081860533 y1[1] (numeric) = 1.48887208186053 absolute error = 2.664535259100376e-15 relative error = 1.789633435647946e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.872355482344983 y2[1] (numeric) = 1.872355482344986 absolute error = 3.108624468950438e-15 relative error = 1.660274717201203e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y1[1] (closed_form) = 1.48012422902854 y1[1] (numeric) = 1.480124229028537 absolute error = 3.552713678800501e-15 relative error = 2.40028073936218e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.877200504274678 y2[1] (numeric) = 1.877200504274682 absolute error = 3.774758283725532e-15 relative error = 2.010844486313433e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y1[1] (closed_form) = 1.471328364173747 y1[1] (numeric) = 1.471328364173743 absolute error = 4.440892098500626e-15 relative error = 3.01828756016302e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.881957806884944 y2[1] (numeric) = 1.881957806884948 absolute error = 3.996802888650564e-15 relative error = 2.123747341214921e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y1[1] (closed_form) = 1.462485366875309 y1[1] (numeric) = 1.462485366875304 absolute error = 5.551115123125783e-15 relative error = 3.795672250031523e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.886626914449483 y2[1] (numeric) = 1.886626914449487 absolute error = 4.440892098500626e-15 relative error = 2.353879330612898e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y1[1] (closed_form) = 1.453596121425587 y1[1] (numeric) = 1.45359612142558 absolute error = 6.661338147750939e-15 relative error = 4.582660925937227e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.891207360061431 y2[1] (numeric) = 1.891207360061435 absolute error = 4.884981308350689e-15 relative error = 2.582996138610635e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y1[1] (closed_form) = 1.444661516741717 y1[1] (numeric) = 1.44466151674171 absolute error = 7.549516567451064e-15 relative error = 5.225803054876279e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.895698685680042 y2[1] (numeric) = 1.895698685680048 absolute error = 5.773159728050814e-15 relative error = 3.045399446473643e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y1[1] (closed_form) = 1.435682446276723 y1[1] (numeric) = 1.435682446276715 absolute error = 8.43769498715119e-15 relative error = 5.8771318191104e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.9001004421765 y2[1] (numeric) = 1.900100442176506 absolute error = 6.217248937900877e-15 relative error = 3.272063307758211e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y1[1] (closed_form) = 1.42665980793017 y1[1] (numeric) = 1.42665980793016 absolute error = 9.547918011776346e-15 relative error = 6.692498070460596e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.90441218937882 y2[1] (numeric) = 1.904412189378826 absolute error = 6.439293542825908e-15 relative error = 3.381249909414974e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y1[1] (closed_form) = 1.417594503958371 y1[1] (numeric) = 1.417594503958361 absolute error = 1.043609643147647e-14 relative error = 7.361834715312168e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.908633496115877 y2[1] (numeric) = 1.908633496115884 absolute error = 6.883382752675971e-15 relative error = 3.606445536392319e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y1[1] (closed_form) = 1.408487440884172 y1[1] (numeric) = 1.40848744088416 absolute error = 1.154631945610163e-14 relative error = 8.197672993699877e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.912763940260515 y2[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 y1[1] (closed_form) = 1.399339529406289 y1[1] (numeric) = 1.399339529406276 absolute error = 1.243449787580175e-14 relative error = 8.885976287025535e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.91680310877176 y2[1] (numeric) = 1.916803108771767 absolute error = 7.105427357601002e-15 relative error = 3.706915606034249e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y1[1] (closed_form) = 1.390151684308247 y1[1] (numeric) = 1.390151684308234 absolute error = 1.332267629550188e-14 relative error = 9.583613389736943e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.920750597736129 y2[1] (numeric) = 1.920750597736136 absolute error = 7.327471962526033e-15 relative error = 3.814900264075136e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y1[1] (closed_form) = 1.380924824366899 y1[1] (numeric) = 1.380924824366885 absolute error = 1.4210854715202e-14 relative error = 1.029082428271729e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.924606012408013 y2[1] (numeric) = 1.924606012408021 absolute error = 7.771561172376096e-15 relative error = 4.038001088156498e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y1[1] (closed_form) = 1.371659872260552 y1[1] (numeric) = 1.371659872260536 absolute error = 1.554312234475219e-14 relative error = 1.133161555505483e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.928368967249159 y2[1] (numeric) = 1.928368967249167 absolute error = 7.771561172376096e-15 relative error = 4.030121467606024e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y1[1] (closed_form) = 1.362357754476693 y1[1] (numeric) = 1.362357754476677 absolute error = 1.620925615952729e-14 relative error = 1.189794391837521e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.932039085967219 y2[1] (numeric) = 1.932039085967227 absolute error = 8.215650382226158e-15 relative error = 4.25232100214641e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y1[1] (closed_form) = 1.353019401219351 y1[1] (numeric) = 1.353019401219334 absolute error = 1.731947918415244e-14 relative error = 1.280061406994164e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.935616001553378 y2[1] (numeric) = 1.935616001553386 absolute error = 8.43769498715119e-15 relative error = 4.359178153300933e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y1[1] (closed_form) = 1.343645746316069 y1[1] (numeric) = 1.34364574631605 absolute error = 1.865174681370263e-14 relative error = 1.388144670188621e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.939099356319059 y2[1] (numeric) = 1.939099356319068 absolute error = 8.43769498715119e-15 relative error = 4.351347423047079e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y1[1] (closed_form) = 1.334237727124526 y1[1] (numeric) = 1.334237727124506 absolute error = 1.998401444325282e-14 relative error = 1.49778514255636e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.942488801931689 y2[1] (numeric) = 1.942488801931698 absolute error = 8.881784197001252e-15 relative error = 4.572373435650619e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y1[1] (closed_form) = 1.324796284438801 y1[1] (numeric) = 1.32479628443878 absolute error = 2.109423746787797e-14 relative error = 1.592262728666524e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.945783999449531 y2[1] (numeric) = 1.94578399944954 absolute error = 9.325873406851315e-15 relative error = 4.792861596913963e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y1[1] (closed_form) = 1.315322362395294 y1[1] (numeric) = 1.315322362395272 absolute error = 2.220446049250313e-14 relative error = 1.688138294255657e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.948984619355578 y2[1] (numeric) = 1.948984619355587 absolute error = 9.547918011776346e-15 relative error = 4.898919117654874e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y1[1] (closed_form) = 1.305816908378316 y1[1] (numeric) = 1.305816908378293 absolute error = 2.331468351712829e-14 relative error = 1.785448125808281e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.952090341590507 y2[1] (numeric) = 1.952090341590517 absolute error = 9.992007221626409e-15 relative error = 5.118619260973961e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y1[1] (closed_form) = 1.296280872925347 y1[1] (numeric) = 1.296280872925322 absolute error = 2.442490654175344e-14 relative error = 1.884229494695328e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.955100855584684 y2[1] (numeric) = 1.955100855584694 absolute error = 9.992007221626409e-15 relative error = 5.110737480925629e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y1[1] (closed_form) = 1.286715209631984 y1[1] (numeric) = 1.286715209631959 absolute error = 2.531308496145357e-14 relative error = 1.967263989107069e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.958015860289216 y2[1] (numeric) = 1.958015860289226 absolute error = 9.992007221626409e-15 relative error = 5.103128848073019e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y1[1] (closed_form) = 1.277120875056588 y1[1] (numeric) = 1.277120875056561 absolute error = 2.620126338115369e-14 relative error = 2.051588372948077e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.960835064206064 y2[1] (numeric) = 1.960835064206074 absolute error = 1.021405182655144e-14 relative error = 5.209031607503958e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y1[1] (closed_form) = 1.267498828624618 y1[1] (numeric) = 1.267498828624591 absolute error = 2.708944180085382e-14 relative error = 2.13723604228092e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.963558185417184 y2[1] (numeric) = 1.963558185417194 absolute error = 1.021405182655144e-14 relative error = 5.201807566696237e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y1[1] (closed_form) = 1.257850032532702 y1[1] (numeric) = 1.257850032532674 absolute error = 2.819966482547898e-14 relative error = 2.241894033162163e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.966184951612725 y2[1] (numeric) = 1.966184951612736 absolute error = 1.021405182655144e-14 relative error = 5.194858102323263e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y1[1] (closed_form) = 1.248175451652406 y1[1] (numeric) = 1.248175451652377 absolute error = 2.953193245502916e-14 relative error = 2.366008113357228e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.968715100118257 y2[1] (numeric) = 1.968715100118267 absolute error = 1.021405182655144e-14 relative error = 5.1881817871656e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y1[1] (closed_form) = 1.238476053433758 y1[1] (numeric) = 1.238476053433727 absolute error = 3.086420008457935e-14 relative error = 2.492111171548799e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.971148377921036 y2[1] (numeric) = 1.971148377921046 absolute error = 9.992007221626409e-15 relative error = 5.069129921190888e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y1[1] (closed_form) = 1.228752807808495 y1[1] (numeric) = 1.228752807808463 absolute error = 3.241851231905457e-14 relative error = 2.638326611588675e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.973484541695311 y2[1] (numeric) = 1.973484541695321 absolute error = 1.043609643147647e-14 relative error = 5.288157171229424e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y1[1] (closed_form) = 1.219006687093078 y1[1] (numeric) = 1.219006687093045 absolute error = 3.352873534367973e-14 relative error = 2.75049642456306e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.975723357826651 y2[1] (numeric) = 1.975723357826661 absolute error = 1.021405182655144e-14 relative error = 5.169778342746919e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y1[1] (closed_form) = 1.209238665891458 y1[1] (numeric) = 1.209238665891423 absolute error = 3.463895836830488e-14 relative error = 2.864526196966159e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.977864602435308 y2[1] (numeric) = 1.977864602435318 absolute error = 9.992007221626409e-15 relative error = 5.051916703157251e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y1[1] (closed_form) = 1.199449720997612 y1[1] (numeric) = 1.199449720997577 absolute error = 3.552713678800501e-14 relative error = 2.961952982777486e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.979908061398606 y2[1] (numeric) = 1.979908061398616 absolute error = 9.769962616701378e-15 relative error = 4.934553683164399e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y1[1] (closed_form) = 1.189640831297875 y1[1] (numeric) = 1.189640831297838 absolute error = 3.641531520770513e-14 relative error = 3.061034410526809e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.981853530372352 y2[1] (numeric) = 1.981853530372361 absolute error = 9.547918011776346e-15 relative error = 4.81767086490114e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y1[1] (closed_form) = 1.179812977673041 y1[1] (numeric) = 1.179812977673004 absolute error = 3.752553823233029e-14 relative error = 3.180634468553003e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.983700814811269 y2[1] (numeric) = 1.983700814811278 absolute error = 9.103828801926284e-15 relative error = 4.58931545218548e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y1[1] (closed_form) = 1.169967142900284 y1[1] (numeric) = 1.169967142900245 absolute error = 3.885780586188048e-14 relative error = 3.321273259482666e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.985449729988453 y2[1] (numeric) = 1.985449729988461 absolute error = 8.659739592076221e-15 relative error = 4.36160103239007e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999956 y1[1] (closed_form) = 1.160104311554875 y1[1] (numeric) = 1.160104311554835 absolute error = 3.97459842815806e-14 relative error = 3.42606987024378e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.987100101013843 y2[1] (numeric) = 1.987100101013852 absolute error = 8.215650382226158e-15 relative error = 4.134492458650891e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y1[1] (closed_form) = 1.150225469911731 y1[1] (numeric) = 1.15022546991169 absolute error = 4.107825191113079e-14 relative error = 3.571321709150047e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.988651762851713 y2[1] (numeric) = 1.988651762851721 absolute error = 8.215650382226158e-15 relative error = 4.131266487021827e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y1[1] (closed_form) = 1.140331605846783 y1[1] (numeric) = 1.140331605846741 absolute error = 4.196643033083092e-14 relative error = 3.680195314736335e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.990104560337171 y2[1] (numeric) = 1.990104560337179 absolute error = 7.771561172376096e-15 relative error = 3.905101936482879e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y1[1] (closed_form) = 1.130423708738193 y1[1] (numeric) = 1.13042370873815 absolute error = 4.329869796038111e-14 relative error = 3.830306957088876e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.99145834819168 y2[1] (numeric) = 1.991458348191688 absolute error = 7.549516567451064e-15 relative error = 3.790948765916351e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y1[1] (closed_form) = 1.120502769367415 y1[1] (numeric) = 1.120502769367371 absolute error = 4.440892098500626e-14 relative error = 3.963303099204076e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.992712991037583 y2[1] (numeric) = 1.99271299103759 absolute error = 7.105427357601002e-15 relative error = 3.565705342193452e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y1[1] (closed_form) = 1.110569779820119 y1[1] (numeric) = 1.110569779820074 absolute error = 4.551914400963142e-14 relative error = 4.098719849643687e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.993868363411639 y2[1] (numeric) = 1.993868363411647 absolute error = 7.105427357601002e-15 relative error = 3.563639148897046e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y1[1] (closed_form) = 1.100625733386982 y1[1] (numeric) = 1.100625733386936 absolute error = 4.640732242933154e-14 relative error = 4.216448972760355e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.994924349777576 y2[1] (numeric) = 1.994924349777582 absolute error = 6.661338147750939e-15 relative error = 3.339143235428274e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y1[1] (closed_form) = 1.090671624464362 y1[1] (numeric) = 1.090671624464314 absolute error = 4.796163466380676e-14 relative error = 4.39744040167554e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.995880844537635 y2[1] (numeric) = 1.995880844537642 absolute error = 6.217248937900877e-15 relative error = 3.115040136246791e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999947 y1[1] (closed_form) = 1.080708448454854 y1[1] (numeric) = 1.080708448454805 absolute error = 4.907185768843192e-14 relative error = 4.540711952293199e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.996737752043139 y2[1] (numeric) = 1.996737752043145 absolute error = 5.773159728050814e-15 relative error = 2.891295926139271e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999946 y1[1] (closed_form) = 1.070737201667757 y1[1] (numeric) = 1.070737201667707 absolute error = 4.996003610813204e-14 relative error = 4.665947538790599e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.997494986604051 y2[1] (numeric) = 1.997494986604056 absolute error = 5.329070518200751e-15 relative error = 2.667876792652544e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y1[1] (closed_form) = 1.060758881219441 y1[1] (numeric) = 1.06075888121939 absolute error = 5.129230373768223e-14 relative error = 4.835434767109086e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.998152472497545 y2[1] (numeric) = 1.998152472497549 absolute error = 4.662936703425657e-15 relative error = 2.333624069036797e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y1[1] (closed_form) = 1.050774484933636 y1[1] (numeric) = 1.050774484933583 absolute error = 5.284661597215745e-14 relative error = 5.029301408617198e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.99871014397558 y2[1] (numeric) = 1.998710143975585 absolute error = 4.440892098500626e-15 relative error = 2.221879001257965e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y1[1] (closed_form) = 1.040785011241649 y1[1] (numeric) = 1.040785011241595 absolute error = 5.395683899678261e-14 relative error = 5.184244432230293e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.999167945271474 y2[1] (numeric) = 1.999167945271477 absolute error = 3.774758283725532e-15 relative error = 1.888164670033735e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y1[1] (closed_form) = 1.030791459082525 y1[1] (numeric) = 1.03079145908247 absolute error = 5.506706202140776e-14 relative error = 5.342211708896117e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.999525830605477 y2[1] (numeric) = 1.999525830605481 absolute error = 3.33066907387547e-15 relative error = 1.665729455901507e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y1[1] (closed_form) = 1.020794827803152 y1[1] (numeric) = 1.020794827803096 absolute error = 5.617728504603292e-14 relative error = 5.503288566511625e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.999783764189356 y2[1] (numeric) = 1.999783764189359 absolute error = 3.108624468950438e-15 relative error = 1.554480301629296e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y1[1] (closed_form) = 1.010796117058328 y1[1] (numeric) = 1.010796117058271 absolute error = 5.706546346573305e-14 relative error = 5.645595833095198e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.999941720229966 y2[1] (numeric) = 1.999941720229968 absolute error = 2.220446049250313e-15 relative error = 1.110255377339192e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999938 y1[1] (closed_form) = 1.000796326710795 y1[1] (numeric) = 1.000796326710737 absolute error = 5.81756864903582e-14 relative error = 5.812939649924344e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.999999682931834 y2[1] (numeric) = 1.999999682931836 absolute error = 1.332267629550188e-15 relative error = 6.66133920380024e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999937 y1[1] (closed_form) = 0.9907964567312549 y1[1] (numeric) = 0.9907964567311954 absolute error = 5.950795411990839e-14 relative error = 6.006072560678264e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.999957646498741 y2[1] (numeric) = 1.999957646498741 absolute error = 8.881784197001252e-16 relative error = 4.440986144156751e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999936 y1[1] (closed_form) = 0.9807975070983718 y1[1] (numeric) = 0.980797507098311 absolute error = 6.072919944699606e-14 relative error = 6.191818291490117e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.999815615134292 y2[1] (numeric) = 1.999815615134292 absolute error = 2.220446049250313e-16 relative error = 1.110325388223956e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999935 y1[1] (closed_form) = 0.9708004776987766 y1[1] (numeric) = 0.970800477698715 absolute error = 6.161737786669619e-14 relative error = 6.34706917458018e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.999573603041507 y2[1] (numeric) = 1.999573603041507 absolute error = 4.440892098500626e-16 relative error = 2.220919545920032e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999933 y1[1] (closed_form) = 0.9608063682270789 y1[1] (numeric) = 0.9608063682270161 absolute error = 6.272760089132134e-14 relative error = 6.528641250272831e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.999231634421393 y2[1] (numeric) = 1.999231634421392 absolute error = 1.110223024625157e-15 relative error = 5.553248585657116e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999932 y1[1] (closed_form) = 0.9508161780858971 y1[1] (numeric) = 0.9508161780858332 absolute error = 6.394884621840902e-14 relative error = 6.725679231409949e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.998789743470527 y2[1] (numeric) = 1.998789743470526 absolute error = 1.77635683940025e-15 relative error = 8.887162069963079e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999931 y1[1] (closed_form) = 0.9408309062859204 y1[1] (numeric) = 0.9408309062858555 absolute error = 6.483702463810914e-14 relative error = 6.89146415205083e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.998247974377636 y2[1] (numeric) = 1.998247974377634 absolute error = 2.442490654175344e-15 relative error = 1.222316091643265e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63999999999993 y1[1] (closed_form) = 0.9308515513460076 y1[1] (numeric) = 0.9308515513459417 absolute error = 6.59472476627343e-14 relative error = 7.084614895616261e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.997606381319178 y2[1] (numeric) = 1.997606381319175 absolute error = 3.108624468950438e-15 relative error = 1.556174678866197e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999929 y1[1] (closed_form) = 0.9208791111933368 y1[1] (numeric) = 0.9208791111932696 absolute error = 6.716849298982197e-14 relative error = 7.293953372748411e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.996865028453924 y2[1] (numeric) = 1.996865028453921 absolute error = 3.774758283725532e-15 relative error = 1.890342226408835e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999928 y1[1] (closed_form) = 0.9109145830636127 y1[1] (numeric) = 0.9109145830635444 absolute error = 6.827871601444713e-14 relative error = 7.495622233295496e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.996023989916543 y2[1] (numeric) = 1.996023989916539 absolute error = 4.440892098500626e-15 relative error = 2.224869100238774e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999927 y1[1] (closed_form) = 0.9009589634013446 y1[1] (numeric) = 0.9009589634012753 absolute error = 6.927791673660977e-14 relative error = 7.68935318375305e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.995083349810187 y2[1] (numeric) = 1.995083349810182 absolute error = 5.10702591327572e-15 relative error = 2.559805791453076e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999926 y1[1] (closed_form) = 0.8910132477602026 y1[1] (numeric) = 0.8910132477601322 absolute error = 7.038813976123492e-14 relative error = 7.899785995121186e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.994043202198084 y2[1] (numeric) = 1.994043202198078 absolute error = 5.773159728050814e-15 relative error = 2.895202933259879e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999925 y1[1] (closed_form) = 0.8810784307034625 y1[1] (numeric) = 0.8810784307033911 absolute error = 7.138734048339757e-14 relative error = 8.102268537705678e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.992903651094128 y2[1] (numeric) = 1.992903651094121 absolute error = 6.883382752675971e-15 relative error = 3.453946581359772e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999924 y1[1] (closed_form) = 0.8711555057045511 y1[1] (numeric) = 0.8711555057044787 absolute error = 7.238654120556021e-14 relative error = 8.309256009008088e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.991664810452479 y2[1] (numeric) = 1.991664810452471 absolute error = 7.771561172376096e-15 relative error = 3.902042719030872e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999922 y1[1] (closed_form) = 0.8612454650476992 y1[1] (numeric) = 0.8612454650476258 absolute error = 7.338574192772285e-14 relative error = 8.52088572955893e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.990326804156169 y2[1] (numeric) = 1.99032680415616 absolute error = 8.659739592076221e-15 relative error = 4.350913414818657e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999921 y1[1] (closed_form) = 0.8513492997287141 y1[1] (numeric) = 0.8513492997286396 absolute error = 7.4495964952348e-14 relative error = 8.750340779758256e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.988889766004713 y2[1] (numeric) = 1.988889766004704 absolute error = 9.325873406851315e-15 relative error = 4.688984561263621e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72999999999992 y1[1] (closed_form) = 0.8414679993558809 y1[1] (numeric) = 0.8414679993558054 absolute error = 7.549516567451064e-14 relative error = 8.97184037091131e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.987353839700729 y2[1] (numeric) = 1.987353839700719 absolute error = 1.021405182655144e-14 relative error = 5.139523532502672e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999919 y1[1] (closed_form) = 0.8316025520510026 y1[1] (numeric) = 0.831602552050926 absolute error = 7.66053886991358e-14 relative error = 9.211778933362093e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.985719178835567 y2[1] (numeric) = 1.985719178835556 absolute error = 1.154631945610163e-14 relative error = 5.814678922964541e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999918 y1[1] (closed_form) = 0.8217539443505886 y1[1] (numeric) = 0.8217539443505109 absolute error = 7.771561172376096e-14 relative error = 9.457284903594548e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.983985946873951 y2[1] (numeric) = 1.983985946873939 absolute error = 1.221245327087672e-14 relative error = 6.15551399954176e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999917 y1[1] (closed_form) = 0.8119231611072014 y1[1] (numeric) = 0.8119231611071228 absolute error = 7.860379014346108e-14 relative error = 9.681185844762805e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.982154317137634 y2[1] (numeric) = 1.982154317137621 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 y1[1] (closed_form) = 0.8021111853909735 y1[1] (numeric) = 0.8021111853908939 absolute error = 7.960299086562372e-14 relative error = 9.9241841175451e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.980224472788062 y2[1] (numeric) = 1.980224472788047 absolute error = 1.48769885299771e-14 relative error = 7.512778846244134e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999915 y1[1] (closed_form) = 0.7923189983912996 y1[1] (numeric) = 0.7923189983912191 absolute error = 8.049116928532385e-14 relative error = 1.015893465242543e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.978196606808063 y2[1] (numeric) = 1.978196606808046 absolute error = 1.620925615952729e-14 relative error = 8.193956103120549e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999914 y1[1] (closed_form) = 0.7825475793187197 y1[1] (numeric) = 0.7825475793186382 absolute error = 8.149037000748649e-14 relative error = 1.041347161004976e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.976070921982543 y2[1] (numeric) = 1.976070921982526 absolute error = 1.709743457922741e-14 relative error = 8.652237320548181e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999913 y1[1] (closed_form) = 0.7727979053069981 y1[1] (numeric) = 0.7727979053069157 absolute error = 8.237854842718662e-14 relative error = 1.06597789488652e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.973847630878215 y2[1] (numeric) = 1.973847630878197 absolute error = 1.84297022087776e-14 relative error = 9.336942690240865e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999911 y1[1] (closed_form) = 0.7630709513154114 y1[1] (numeric) = 0.7630709513153281 absolute error = 8.326672684688674e-14 relative error = 1.091205564873729e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.971526955822336 y2[1] (numeric) = 1.971526955822317 absolute error = 1.953992523340276e-14 relative error = 9.911061665019198e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81999999999991 y1[1] (closed_form) = 0.7533676900312529 y1[1] (numeric) = 0.7533676900311689 absolute error = 8.404388296412435e-14 relative error = 1.115575887793089e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.969109128880479 y2[1] (numeric) = 1.969109128880458 absolute error = 2.042810365310288e-14 relative error = 1.03742872111497e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.829999999999909 y1[1] (closed_form) = 0.7436890917725651 y1[1] (numeric) = 0.7436890917724801 absolute error = 8.504308368628699e-14 relative error = 1.143530066893799e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.966594391833321 y2[1] (numeric) = 1.9665943918333 absolute error = 2.109423746787797e-14 relative error = 1.072627764803766e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999908 y1[1] (closed_form) = 0.7340361243911082 y1[1] (numeric) = 0.7340361243910223 absolute error = 8.593126210598712e-14 relative error = 1.170668026417203e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.963982996152473 y2[1] (numeric) = 1.96398299615245 absolute error = 2.264854970235319e-14 relative error = 1.153194795816597e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.849999999999907 y1[1] (closed_form) = 0.7244097531755764 y1[1] (numeric) = 0.7244097531754899 absolute error = 8.648637361829969e-14 relative error = 1.193887482038606e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.961275202975326 y2[1] (numeric) = 1.961275202975302 absolute error = 2.375877272697835e-14 relative error = 1.211394132293899e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.859999999999906 y1[1] (closed_form) = 0.7148109407550693 y1[1] (numeric) = 0.714810940754982 absolute error = 8.737455203799982e-14 relative error = 1.22234491746453e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.958471283078941 y2[1] (numeric) = 1.958471283078916 absolute error = 2.464695114667848e-14 relative error = 1.258479067813067e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999905 y1[1] (closed_form) = 0.7052406470028301 y1[1] (numeric) = 0.7052406470027417 absolute error = 8.837375276016246e-14 relative error = 1.253100670469549e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.955571516852972 y2[1] (numeric) = 1.955571516852946 absolute error = 2.55351295663786e-14 relative error = 1.305763013334911e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999904 y1[1] (closed_form) = 0.6956998289402584 y1[1] (numeric) = 0.6956998289401694 absolute error = 8.903988657493755e-14 relative error = 1.279860693807697e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.952576194271625 y2[1] (numeric) = 1.952576194271598 absolute error = 2.664535259100376e-14 relative error = 1.364625496775728e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999903 y1[1] (closed_form) = 0.6861894406412101 y1[1] (numeric) = 0.6861894406411204 absolute error = 8.970602038971265e-14 relative error = 1.307306919586037e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.949485614864661 y2[1] (numeric) = 1.949485614864634 absolute error = 2.753353101070388e-14 relative error = 1.412348508794477e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999902 y1[1] (closed_form) = 0.6767104331365897 y1[1] (numeric) = 0.6767104331364996 absolute error = 9.015010959956271e-14 relative error = 1.332181464702887e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.946300087687446 y2[1] (numeric) = 1.946300087687417 absolute error = 2.90878432451791e-14 relative error = 1.494519957595063e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9099999999999 y1[1] (closed_form) = 0.6672637543192487 y1[1] (numeric) = 0.6672637543191577 absolute error = 9.092726571680032e-14 relative error = 1.362688519018473e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.943019931290044 y2[1] (numeric) = 1.943019931290013 absolute error = 3.064215547965432e-14 relative error = 1.577037630247562e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.919999999999899 y1[1] (closed_form) = 0.6578503488491964 y1[1] (numeric) = 0.6578503488491046 absolute error = 9.170442183403793e-14 relative error = 1.394001264793127e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.939645473685359 y2[1] (numeric) = 1.939645473685328 absolute error = 3.175237850427948e-14 relative error = 1.637019699478865e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999898 y1[1] (closed_form) = 0.6484711580591354 y1[1] (numeric) = 0.6484711580590428 absolute error = 9.259260025373806e-14 relative error = 1.427859961125586e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.936177052316342 y2[1] (numeric) = 1.936177052316309 absolute error = 3.308464613382966e-14 relative error = 1.708761401455973e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999897 y1[1] (closed_form) = 0.6391271198603288 y1[1] (numeric) = 0.6391271198602354 absolute error = 9.336975637097567e-14 relative error = 1.460894921676617e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.932615014022238 y2[1] (numeric) = 1.932615014022203 absolute error = 3.441691376337985e-14 relative error = 1.780846858461994e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.949999999999896 y1[1] (closed_form) = 0.6298191686488097 y1[1] (numeric) = 0.6298191686487159 absolute error = 9.381384558082573e-14 relative error = 1.489536207386168e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.928959715003908 y2[1] (numeric) = 1.928959715003872 absolute error = 3.597122599785507e-14 relative error = 1.864799234429953e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999895 y1[1] (closed_form) = 0.6205482352119427 y1[1] (numeric) = 0.620548235211848 absolute error = 9.470202400052585e-14 relative error = 1.526102543312869e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.925211520788208 y2[1] (numeric) = 1.925211520788171 absolute error = 3.730349362740526e-14 relative error = 1.937630916115269e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999894 y1[1] (closed_form) = 0.6113152466353458 y1[1] (numeric) = 0.6113152466352504 absolute error = 9.536815781530095e-14 relative error = 1.560048736559466e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.921370806191437 y2[1] (numeric) = 1.921370806191398 absolute error = 3.885780586188048e-14 relative error = 2.022400139351803e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999893 y1[1] (closed_form) = 0.6021211262101824 y1[1] (numeric) = 0.6021211262100865 absolute error = 9.592326932761353e-14 relative error = 1.593089249855179e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.917437955281853 y2[1] (numeric) = 1.917437955281813 absolute error = 3.996802888650564e-14 relative error = 2.084449657231833e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999892 y1[1] (closed_form) = 0.5929667933408335 y1[1] (numeric) = 0.592966793340737 absolute error = 9.64783808399261e-14 relative error = 1.627045256554037e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.913413361341269 y2[1] (numeric) = 1.913413361341228 absolute error = 4.107825191113079e-14 relative error = 2.146857168507262e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.999999999999891 y1[1] (closed_form) = 0.5838531634529571 y1[1] (numeric) = 0.5838531634528603 absolute error = 9.681144774731365e-14 relative error = 1.658147181643455e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.909297426825727 y2[1] (numeric) = 1.909297426825685 absolute error = 4.263256414560601e-14 relative error = 2.232892767078418e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.00999999999989 y1[1] (closed_form) = 0.5747811479019476 y1[1] (numeric) = 0.5747811479018502 absolute error = 9.736655925962623e-14 relative error = 1.693976213642902e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.905090563325248 y2[1] (numeric) = 1.905090563325204 absolute error = 4.39648317751562e-14 relative error = 2.30775547480628e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999889 y1[1] (closed_form) = 0.5657516538817999 y1[1] (numeric) = 0.5657516538817021 absolute error = 9.781064846947629e-14 relative error = 1.728861909609396e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.900793191522676 y2[1] (numeric) = 1.90079319152263 absolute error = 4.574118861455645e-14 relative error = 2.406426370767584e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999887 y1[1] (closed_form) = 0.5567655843343918 y1[1] (numeric) = 0.5567655843342936 absolute error = 9.825473767932635e-14 relative error = 1.76474157965042e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.89640574115161 y2[1] (numeric) = 1.896405741151563 absolute error = 4.707345624410664e-14 relative error = 2.482246031143148e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999886 y1[1] (closed_form) = 0.5478238378591894 y1[1] (numeric) = 0.5478238378590907 absolute error = 9.869882688917642e-14 relative error = 1.801652649415114e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.891928650953431 y2[1] (numeric) = 1.891928650953382 absolute error = 4.884981308350689e-14 relative error = 2.582011380761594e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999885 y1[1] (closed_form) = 0.538927308623389 y1[1] (numeric) = 0.5389273086232896 absolute error = 9.936496070395151e-14 relative error = 1.843754419455284e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.887362368633428 y2[1] (numeric) = 1.887362368633378 absolute error = 5.062616992290714e-14 relative error = 2.682376779588105e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999884 y1[1] (closed_form) = 0.5300768862725 y1[1] (numeric) = 0.5300768862724003 absolute error = 9.969802761133906e-14 relative error = 1.88082201267849e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.882707350816029 y2[1] (numeric) = 1.882707350815976 absolute error = 5.240252676230739e-14 relative error = 2.783360182855523e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999883 y1[1] (closed_form) = 0.5212734558413827 y1[1] (numeric) = 0.5212734558412826 absolute error = 1.001421168211891e-13 relative error = 1.921105241385266e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.877964062999134 y2[1] (numeric) = 1.87796406299908 absolute error = 5.395683899678261e-14 relative error = 2.873156098131761e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999882 y1[1] (closed_form) = 0.5125178976657437 y1[1] (numeric) = 0.5125178976656433 absolute error = 1.004751837285767e-13 relative error = 1.96042292739804e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.873132979507574 y2[1] (numeric) = 1.873132979507518 absolute error = 5.573319583618286e-14 relative error = 2.975399848591342e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.089999999999881 y1[1] (closed_form) = 0.5038110872941044 y1[1] (numeric) = 0.5038110872940036 absolute error = 1.008082506359642e-13 relative error = 2.000913699168285e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.868214583445672 y2[1] (numeric) = 1.868214583445615 absolute error = 5.706546346573305e-14 relative error = 3.05454544522843e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09999999999988 y1[1] (closed_form) = 0.4951538954002463 y1[1] (numeric) = 0.4951538954001451 absolute error = 1.01196828694583e-13 relative error = 2.043744977766617e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.863209366648934 y2[1] (numeric) = 1.863209366648876 absolute error = 5.861977570020827e-14 relative error = 3.146172231070229e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999879 y1[1] (closed_form) = 0.4865471876961446 y1[1] (numeric) = 0.4865471876960429 absolute error = 1.016964290556643e-13 relative error = 2.090165797426727e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.858117829634871 y2[1] (numeric) = 1.858117829634811 absolute error = 6.017408793468348e-14 relative error = 3.238443061843283e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999878 y1[1] (closed_form) = 0.4779918248453972 y1[1] (numeric) = 0.4779918248452952 absolute error = 1.019184736605894e-13 relative error = 2.132222108475477e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.85294048155294 y2[1] (numeric) = 1.852940481552878 absolute error = 6.217248937900877e-14 relative error = 3.355341955015323e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999876 y1[1] (closed_form) = 0.4694886623771599 y1[1] (numeric) = 0.4694886623770577 absolute error = 1.022515405679769e-13 relative error = 2.177934181631717e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.847677840133635 y2[1] (numeric) = 1.847677840133572 absolute error = 6.372680161348399e-14 relative error = 3.449021264923266e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999875 y1[1] (closed_form) = 0.4610385506005936 y1[1] (numeric) = 0.461038550600491 absolute error = 1.025846074753645e-13 relative error = 2.225076565543766e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.842330431636713 y2[1] (numeric) = 1.842330431636648 absolute error = 6.52811138479592e-14 relative error = 3.543398769674772e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999874 y1[1] (closed_form) = 0.4526423345198342 y1[1] (numeric) = 0.4526423345197313 absolute error = 1.028621632315208e-13 relative error = 2.272482164988778e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.836898790798567 y2[1] (numeric) = 1.836898790798499 absolute error = 6.705747068735946e-14 relative error = 3.650580588504124e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999873 y1[1] (closed_form) = 0.4443008537494929 y1[1] (numeric) = 0.4443008537493897 absolute error = 1.031952301389083e-13 relative error = 2.322643075475434e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.831383460778754 y2[1] (numeric) = 1.831383460778685 absolute error = 6.883382752675971e-14 relative error = 3.758569900892832e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999872 y1[1] (closed_form) = 0.4360149424306955 y1[1] (numeric) = 0.4360149424305921 absolute error = 1.033617635926021e-13 relative error = 2.370601406832093e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.82578499310568 y2[1] (numeric) = 1.82578499310561 absolute error = 7.061018436615996e-14 relative error = 3.867387706262788e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.179999999999871 y1[1] (closed_form) = 0.4277854291476691 y1[1] (numeric) = 0.4277854291475655 absolute error = 1.036393193487584e-13 relative error = 2.422694002347206e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.820103947621448 y2[1] (numeric) = 1.820103947621376 absolute error = 7.238654120556021e-14 relative error = 3.977055337974325e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.18999999999987 y1[1] (closed_form) = 0.4196131368448841 y1[1] (numeric) = 0.4196131368447804 absolute error = 1.037503416512209e-13 relative error = 2.47252367815104e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.814340892425871 y2[1] (numeric) = 1.814340892425798 absolute error = 7.394085344003543e-14 relative error = 4.07535616645737e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999869 y1[1] (closed_form) = 0.4114988827447604 y1[1] (numeric) = 0.4114988827446565 absolute error = 1.039168751049147e-13 relative error = 2.525325814052598e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.808496403819667 y2[1] (numeric) = 1.808496403819592 absolute error = 7.571721027943568e-14 relative error = 4.18674928628643e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999868 y1[1] (closed_form) = 0.4034434782659463 y1[1] (numeric) = 0.4034434782658423 absolute error = 1.040278974073772e-13 relative error = 2.578499914151616e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.802571066246826 y2[1] (numeric) = 1.802571066246748 absolute error = 7.771561172376096e-14 relative error = 4.311375744290314e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999867 y1[1] (closed_form) = 0.3954477289421768 y1[1] (numeric) = 0.3954477289420727 absolute error = 1.041389197098397e-13 relative error = 2.633443362752681e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.796565472236167 y2[1] (numeric) = 1.796565472236088 absolute error = 7.926992395823618e-14 relative error = 4.412303652901093e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999865 y1[1] (closed_form) = 0.3875124343417212 y1[1] (numeric) = 0.387512434341617 absolute error = 1.042499420123022e-13 relative error = 2.690234758257361e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.790480222342087 y2[1] (numeric) = 1.790480222342006 absolute error = 8.104628079763643e-14 relative error = 4.526510809017572e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999864 y1[1] (closed_form) = 0.3796383879874268 y1[1] (numeric) = 0.3796383879873226 absolute error = 1.041944308610709e-13 relative error = 2.744570469109719e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.784315925084504 y2[1] (numeric) = 1.784315925084421 absolute error = 8.282263763703668e-14 relative error = 4.641702541163737e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999863 y1[1] (closed_form) = 0.3718263772773673 y1[1] (numeric) = 0.371826377277263 absolute error = 1.043054531635335e-13 relative error = 2.805219304969476e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.778073196888007 y2[1] (numeric) = 1.778073196887923 absolute error = 8.459899447643693e-14 relative error = 4.757902803129956e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999862 y1[1] (closed_form) = 0.3640771834061038 y1[1] (numeric) = 0.3640771834059995 absolute error = 1.043054531635335e-13 relative error = 2.86492694180145e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.771752662020214 y2[1] (numeric) = 1.771752662020127 absolute error = 8.637535131583718e-14 relative error = 4.875135969450105e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.269999999999861 y1[1] (closed_form) = 0.3563915812865659 y1[1] (numeric) = 0.3563915812864616 absolute error = 1.043054531635335e-13 relative error = 2.926709233338033e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.765354952529343 y2[1] (numeric) = 1.765354952529255 absolute error = 8.79296635503124e-14 relative error = 4.980848946232011e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.27999999999986 y1[1] (closed_form) = 0.3487703394725606 y1[1] (numeric) = 0.3487703394724564 absolute error = 1.042499420123022e-13 relative error = 2.989071323265551e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.758880708181013 y2[1] (numeric) = 1.758880708180923 absolute error = 9.015010959956271e-14 relative error = 5.125424889831984e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999859 y1[1] (closed_form) = 0.3412142200819185 y1[1] (numeric) = 0.3412142200818144 absolute error = 1.040834085586084e-13 relative error = 3.050383085840331e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.752330576394264 y2[1] (numeric) = 1.752330576394172 absolute error = 9.170442183403793e-14 relative error = 5.233283209766066e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999858 y1[1] (closed_form) = 0.3337239787202819 y1[1] (numeric) = 0.333723978720178 absolute error = 1.039168751049147e-13 relative error = 3.113857011515941e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.745705212176815 y2[1] (numeric) = 1.745705212176721 absolute error = 9.348077867343818e-14 relative error = 5.354900588105131e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999857 y1[1] (closed_form) = 0.3263003644055451 y1[1] (numeric) = 0.3263003644054414 absolute error = 1.037503416512209e-13 relative error = 3.179596254519468e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.739005278059568 y2[1] (numeric) = 1.739005278059472 absolute error = 9.570122472268849e-14 relative error = 5.503216461164206e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999856 y1[1] (closed_form) = 0.3189441194929532 y1[1] (numeric) = 0.3189441194928496 absolute error = 1.035838081975271e-13 relative error = 3.247710237210242e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.73223144403035 y2[1] (numeric) = 1.732231444030252 absolute error = 9.747758156208874e-14 relative error = 5.627283923174233e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999854 y1[1] (closed_form) = 0.3116559796008673 y1[1] (numeric) = 0.311655979600764 absolute error = 1.033617635926021e-13 relative error = 3.316533946339672e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.72538438746692 y2[1] (numeric) = 1.725384387466821 absolute error = 9.925393840148899e-14 relative error = 5.752569637378381e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999853 y1[1] (closed_form) = 0.3044366735372033 y1[1] (numeric) = 0.3044366735371001 absolute error = 1.03139718987677e-13 relative error = 3.387887464059844e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.718464793069228 y2[1] (numeric) = 1.718464793069127 absolute error = 1.012523398458143e-13 relative error = 5.892022941300686e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999852 y1[1] (closed_form) = 0.2972869232265513 y1[1] (numeric) = 0.2972869232264483 absolute error = 1.02917674382752e-13 relative error = 3.461897121667955e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.711473352790948 y2[1] (numeric) = 1.711473352790845 absolute error = 1.032507412901396e-13 relative error = 6.03285707731094e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.359999999999851 y1[1] (closed_form) = 0.2902074436379843 y1[1] (numeric) = 0.2902074436378816 absolute error = 1.02695629777827e-13 relative error = 3.538697301849134e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.704410765770282 y2[1] (numeric) = 1.704410765770177 absolute error = 1.052491427344648e-13 relative error = 6.175104314534127e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36999999999985 y1[1] (closed_form) = 0.2831989427135617 y1[1] (numeric) = 0.2831989427134594 absolute error = 1.023070517192082e-13 relative error = 3.61255062391548e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.697277738260045 y2[1] (numeric) = 1.697277738259938 absolute error = 1.068034549689401e-13 relative error = 6.292632758998478e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999849 y1[1] (closed_form) = 0.2762621212975356 y1[1] (numeric) = 0.2762621212974336 absolute error = 1.019739848118206e-13 relative error = 3.69120400338902e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.690074983557046 y2[1] (numeric) = 1.690074983556937 absolute error = 1.088018564132653e-13 relative error = 6.437694035579038e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999848 y1[1] (closed_form) = 0.2693976730662667 y1[1] (numeric) = 0.2693976730661651 absolute error = 1.016409179044331e-13 relative error = 3.772895168230772e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.682803221930751 y2[1] (numeric) = 1.68280322193064 absolute error = 1.105782132526656e-13 relative error = 6.571072114171172e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999847 y1[1] (closed_form) = 0.262606284458858 y1[1] (numeric) = 0.2626062844587568 absolute error = 1.01196828694583e-13 relative error = 3.853557004666326e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.675463180551264 y2[1] (numeric) = 1.675463180551152 absolute error = 1.123545700920658e-13 relative error = 6.705881179382214e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999846 y1[1] (closed_form) = 0.2558886346085107 y1[1] (numeric) = 0.2558886346084099 absolute error = 1.008637617871955e-13 relative error = 3.941705419684192e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.668055593416606 y2[1] (numeric) = 1.668055593416492 absolute error = 1.143529715363911e-13 relative error = 6.855465248743113e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999844 y1[1] (closed_form) = 0.2492453952746118 y1[1] (numeric) = 0.2492453952745114 absolute error = 1.003641614261142e-13 relative error = 4.026720787179866e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.660581201279317 y2[1] (numeric) = 1.660581201279201 absolute error = 1.159072837708663e-13 relative error = 6.979922672951554e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999843 y1[1] (closed_form) = 0.2426772307755586 y1[1] (numeric) = 0.2426772307754587 absolute error = 9.989231664064846e-14 relative error = 4.11626242484341e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.653040751572384 y2[1] (numeric) = 1.653040751572266 absolute error = 1.176836406102666e-13 relative error = 7.119221985200614e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999842 y1[1] (closed_form) = 0.2361847979223277 y1[1] (numeric) = 0.2361847979222282 absolute error = 9.947598300641403e-14 relative error = 4.211786020162395e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.645434998334491 y2[1] (numeric) = 1.645434998334371 absolute error = 1.196820420545919e-13 relative error = 7.273580674759805e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.449999999999841 y1[1] (closed_form) = 0.229768745952794 y1[1] (numeric) = 0.229768745952695 absolute error = 9.892087149410145e-14 relative error = 4.305236166211429e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.637764702134626 y2[1] (numeric) = 1.637764702134504 absolute error = 1.219024881038422e-13 relative error = 7.443223556165131e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45999999999984 y1[1] (closed_form) = 0.2234297164668076 y1[1] (numeric) = 0.2234297164667093 absolute error = 9.83935155574045e-14 relative error = 4.403779278483831e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.630030629996016 y2[1] (numeric) = 1.630030629995892 absolute error = 1.239008895481675e-13 relative error = 7.601138731268521e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999839 y1[1] (closed_form) = 0.2171683433620349 y1[1] (numeric) = 0.2171683433619371 absolute error = 9.781064846947629e-14 relative error = 4.503909131287107e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.622233555319431 y2[1] (numeric) = 1.622233555319305 absolute error = 1.261213355974178e-13 relative error = 7.774548565085222e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999838 y1[1] (closed_form) = 0.2109852527705685 y1[1] (numeric) = 0.2109852527704713 absolute error = 9.720002580593246e-14 relative error = 4.606958284029008e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.61437425780584 y2[1] (numeric) = 1.614374257805712 absolute error = 1.27897692436818e-13 relative error = 7.922431358057511e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999837 y1[1] (closed_form) = 0.2048810629963148 y1[1] (numeric) = 0.2048810629962182 absolute error = 9.658940314238862e-14 relative error = 4.714413412826054e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.606453523378445 y2[1] (numeric) = 1.606453523378315 absolute error = 1.298960938811433e-13 relative error = 8.085891810176116e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999836 y1[1] (closed_form) = 0.1988563844531647 y1[1] (numeric) = 0.1988563844530686 absolute error = 9.603429163007604e-14 relative error = 4.829329060475519e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.598472144104088 y2[1] (numeric) = 1.598472144103956 absolute error = 1.316724507205436e-13 relative error = 8.237394139535873e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999835 y1[1] (closed_form) = 0.1929118196039517 y1[1] (numeric) = 0.1929118196038564 absolute error = 9.528489108845406e-14 relative error = 4.93929772079669e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.590430918114046 y2[1] (numeric) = 1.590430918113913 absolute error = 1.334488075599438e-13 relative error = 8.39073272784392e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999833 y1[1] (closed_form) = 0.187047962900207 y1[1] (numeric) = 0.1870479629001124 absolute error = 9.453549054683208e-14 relative error = 5.054077525413535e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.582330649524217 y2[1] (numeric) = 1.582330649524081 absolute error = 1.358912982141192e-13 relative error = 8.588046894938147e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999832 y1[1] (closed_form) = 0.1812654007227146 y1[1] (numeric) = 0.1812654007226207 absolute error = 9.386935673205699e-14 relative error = 5.178558972522885e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.57417214835471 y2[1] (numeric) = 1.574172148354572 absolute error = 1.376676550535194e-13 relative error = 8.745400253549564e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999831 y1[1] (closed_form) = 0.1755647113228732 y1[1] (numeric) = 0.1755647113227801 absolute error = 9.309220061481938e-14 relative error = 5.302443749280439e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.565956230448842 y2[1] (numeric) = 1.565956230448702 absolute error = 1.396660564978447e-13 relative error = 8.918899122602739e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54999999999983 y1[1] (closed_form) = 0.1699464647648725 y1[1] (numeric) = 0.1699464647647802 absolute error = 9.23428000731974e-14 relative error = 5.433640540917236e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.557683717391558 y2[1] (numeric) = 1.557683717391416 absolute error = 1.41886502547095e-13 relative error = 9.108813359408619e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999829 y1[1] (closed_form) = 0.1644112228686863 y1[1] (numeric) = 0.1644112228685948 absolute error = 9.145462165349727e-14 relative error = 5.562553459415678e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.549355436427269 y2[1] (numeric) = 1.549355436427126 absolute error = 1.434408147815702e-13 relative error = 9.258096070733586e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999828 y1[1] (closed_form) = 0.1589595391538915 y1[1] (numeric) = 0.1589595391538009 absolute error = 9.06219543850284e-14 relative error = 5.700944710043209e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.540972220377133 y2[1] (numeric) = 1.540972220376988 absolute error = 1.454392162258955e-13 relative error = 9.438146535198483e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999827 y1[1] (closed_form) = 0.1535919587843166 y1[1] (numeric) = 0.1535919587842269 absolute error = 8.976153154094391e-14 relative error = 5.844155660973932e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.532534907555768 y2[1] (numeric) = 1.53253490755562 absolute error = 1.474376176702208e-13 relative error = 9.620506322127978e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999826 y1[1] (closed_form) = 0.1483090185135256 y1[1] (numeric) = 0.1483090185134368 absolute error = 8.887335312124378e-14 relative error = 5.992444290442029e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.524044341687425 y2[1] (numeric) = 1.524044341687275 absolute error = 1.494360191145461e-13 relative error = 9.80522777631852e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999825 y1[1] (closed_form) = 0.1431112466311432 y1[1] (numeric) = 0.1431112466310552 absolute error = 8.795741912592803e-14 relative error = 6.146087131267234e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.515501371821614 y2[1] (numeric) = 1.515501371821464 absolute error = 1.507682867440963e-13 relative error = 9.948409783547381e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999824 y1[1] (closed_form) = 0.1379991629100259 y1[1] (numeric) = 0.137999162909939 absolute error = 8.693046282814976e-14 relative error = 6.299347111607305e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.506906852248205 y2[1] (numeric) = 1.506906852248053 absolute error = 1.525446435834965e-13 relative error = 1.012303072057241e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999822 y1[1] (closed_form) = 0.1329732785542861 y1[1] (numeric) = 0.1329732785542 absolute error = 8.604228440844963e-14 relative error = 6.470644729822393e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.498261642411993 y2[1] (numeric) = 1.498261642411838 absolute error = 1.540989558179717e-13 relative error = 1.028518327212154e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999821 y1[1] (closed_form) = 0.1280340961481709 y1[1] (numeric) = 0.1280340961480859 absolute error = 8.498757253505573e-14 relative error = 6.637885929752776e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.489566606826755 y2[1] (numeric) = 1.489566606826599 absolute error = 1.55875312657372e-13 relative error = 1.046447415932849e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999982 y1[1] (closed_form) = 0.123182109605805 y1[1] (numeric) = 0.123182109605721 absolute error = 8.398837181289309e-14 relative error = 6.818228075624312e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.480822614988806 y2[1] (numeric) = 1.480822614988648 absolute error = 1.576516694967722e-13 relative error = 1.064622243751754e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999819 y1[1] (closed_form) = 0.1184178041217995 y1[1] (numeric) = 0.1184178041217165 absolute error = 8.297529330292264e-14 relative error = 7.006994760481947e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.472030541290042 y2[1] (numeric) = 1.472030541289883 absolute error = 1.594280263361725e-13 relative error = 1.083048359828558e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999818 y1[1] (closed_form) = 0.1137416561227322 y1[1] (numeric) = 0.1137416561226504 absolute error = 8.182343691487404e-14 relative error = 7.193796864236174e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.463191264930507 y2[1] (numeric) = 1.463191264930346 absolute error = 1.609823385706477e-13 relative error = 1.100213912077267e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999817 y1[1] (closed_form) = 0.1091541332195066 y1[1] (numeric) = 0.1091541332194259 absolute error = 8.068545831463325e-14 relative error = 7.391883013021278e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.454305669830469 y2[1] (numeric) = 1.454305669830307 absolute error = 1.625366508051229e-13 relative error = 1.117623716780737e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999816 y1[1] (closed_form) = 0.10465569416059 y1[1] (numeric) = 0.1046556941605104 absolute error = 7.954747971439247e-14 relative error = 7.600874501136083e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.445374644542036 y2[1] (numeric) = 1.445374644541872 absolute error = 1.645350522494482e-13 relative error = 1.138355739605359e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999815 y1[1] (closed_form) = 0.1002467887861395 y1[1] (numeric) = 0.100246788786061 absolute error = 7.84233789019595e-14 relative error = 7.82303152565448e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.436399082160293 y2[1] (numeric) = 1.436399082160126 absolute error = 1.667554982986985e-13 relative error = 1.160927352083129e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999814 y1[1] (closed_form) = 0.09592785798301851 y1[1] (numeric) = 0.09592785798294125 absolute error = 7.725764472610308e-14 relative error = 8.053723532509139e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.427379880233998 y2[1] (numeric) = 1.42737988023383 absolute error = 1.683098105331737e-13 relative error = 1.179152185510572e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999813 y1[1] (closed_form) = 0.09169933364070826 y1[1] (numeric) = 0.09169933364063221 absolute error = 7.605027718682322e-14 relative error = 8.293438367262254e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.418317940675829 y2[1] (numeric) = 1.418317940675659 absolute error = 1.70086167372574e-13 relative error = 1.199210434379247e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999811 y1[1] (closed_form) = 0.08756163860811916 y1[1] (numeric) = 0.08756163860804442 absolute error = 7.474576513288866e-14 relative error = 8.536359794203057e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.40921416967219 y2[1] (numeric) = 1.409214169672018 absolute error = 1.716404796070492e-13 relative error = 1.217987182508788e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999981 y1[1] (closed_form) = 0.08351518665130653 y1[1] (numeric) = 0.08351518665123307 absolute error = 7.345513086676192e-14 relative error = 8.795421983962335e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.400069477592593 y2[1] (numeric) = 1.40006947759242 absolute error = 1.731947918415244e-13 relative error = 1.237044265398395e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999809 y1[1] (closed_form) = 0.07956038241209396 y1[1] (numeric) = 0.0795603824120218 absolute error = 7.215061881282736e-14 relative error = 9.068661641055632e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.390884778898628 y2[1] (numeric) = 1.390884778898453 absolute error = 1.747491040759996e-13 relative error = 1.25638806842343e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999808 y1[1] (closed_form) = 0.07569762136760971 y1[1] (numeric) = 0.07569762136753884 absolute error = 7.087386233450843e-14 relative error = 9.362759496804305e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.381660992052509 y2[1] (numeric) = 1.381660992052333 absolute error = 1.765254609153999e-13 relative error = 1.277632226217552e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999807 y1[1] (closed_form) = 0.07192728979073915 y1[1] (numeric) = 0.0719272897906697 absolute error = 6.944445019030354e-14 relative error = 9.654812574245599e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.372399039425235 y2[1] (numeric) = 1.372399039425056 absolute error = 1.783018177548001e-13 relative error = 1.299198065815272e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999806 y1[1] (closed_form) = 0.06824976471149824 y1[1] (numeric) = 0.06824976471143017 absolute error = 6.807054919732991e-14 relative error = 9.973741226079548e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.363099847204349 y2[1] (numeric) = 1.363099847204169 absolute error = 1.800781745942004e-13 relative error = 1.32109305832241e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999805 y1[1] (closed_form) = 0.06466541387933022 y1[1] (numeric) = 0.06466541387926354 absolute error = 6.668277041654846e-14 relative error = 1.031196839487995e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.353764345301326 y2[1] (numeric) = 1.353764345301144 absolute error = 1.818545314336006e-13 relative error = 1.343324870866819e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999804 y1[1] (closed_form) = 0.06117459572633133 y1[1] (numeric) = 0.06117459572626609 absolute error = 6.523254159063185e-14 relative error = 1.066333840315905e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.344393467258574 y2[1] (numeric) = 1.344393467258391 absolute error = 1.834088436680759e-13 relative error = 1.364249738895822e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999803 y1[1] (closed_form) = 0.05777765933140799 y1[1] (numeric) = 0.05777765933134414 absolute error = 6.385170170375432e-14 relative error = 1.105127871960096e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.334988150156091 y2[1] (numeric) = 1.334988150155906 absolute error = 1.84741111297626e-13 relative error = 1.383840832415071e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999802 y1[1] (closed_form) = 0.05447494438536871 y1[1] (numeric) = 0.05447494438530637 absolute error = 6.233208393879863e-14 relative error = 1.144234007800846e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.325549334517748 y2[1] (numeric) = 1.325549334517561 absolute error = 1.865174681370263e-13 relative error = 1.407095634089574e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8199999999998 y1[1] (closed_form) = 0.05126678115695593 y1[1] (numeric) = 0.05126678115689517 absolute error = 6.07638939165156e-14 relative error = 1.185248859890067e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.316077964217243 y2[1] (numeric) = 1.316077964217055 absolute error = 1.882938249764265e-13 relative error = 1.430719380583331e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999799 y1[1] (closed_form) = 0.0481534904598192 y1[1] (numeric) = 0.04815349045975989 absolute error = 5.931366509059899e-14 relative error = 1.231762526957255e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.306574986383714 y2[1] (numeric) = 1.306574986383524 absolute error = 1.898481372109018e-13 relative error = 1.453021366468647e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999798 y1[1] (closed_form) = 0.04513538362043357 y1[1] (numeric) = 0.04513538362037586 absolute error = 5.771078059879642e-14 relative error = 1.278615045883198e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.297041351307025 y2[1] (numeric) = 1.297041351306834 absolute error = 1.91180404840452e-13 relative error = 1.473973089969722e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999797 y1[1] (closed_form) = 0.04221276244696803 y1[1] (numeric) = 0.04221276244691193 absolute error = 5.610789610699385e-14 relative error = 1.329169020328444e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.287478012342739 y2[1] (numeric) = 1.287478012342546 absolute error = 1.927347170749272e-13 relative error = 1.49699424166647e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999796 y1[1] (closed_form) = 0.03938591919910439 y1[1] (numeric) = 0.03938591919904993 absolute error = 5.445643935786393e-14 relative error = 1.382637258827826e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.277885925816783 y2[1] (numeric) = 1.277885925816588 absolute error = 1.945110739143274e-13 relative error = 1.522131748888324e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999795 y1[1] (closed_form) = 0.03665513655881181 y1[1] (numeric) = 0.03665513655875896 absolute error = 5.284661597215745e-14 relative error = 1.441724705823071e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.268266050929816 y2[1] (numeric) = 1.26826605092962 absolute error = 1.960653861488026e-13 relative error = 1.545932621984633e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999794 y1[1] (closed_form) = 0.03402068760207855 y1[1] (numeric) = 0.03402068760202741 absolute error = 5.113964807179627e-14 relative error = 1.503192665296742e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.25861934966131 y2[1] (numeric) = 1.258619349661112 absolute error = 1.976196983832779e-13 relative error = 1.570130782086392e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999793 y1[1] (closed_form) = 0.03148283577160504 y1[1] (numeric) = 0.03148283577155558 absolute error = 4.946737464095463e-14 relative error = 1.571249013266149e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.248946786673353 y2[1] (numeric) = 1.248946786673154 absolute error = 1.991740106177531e-13 relative error = 1.594735762508067e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999792 y1[1] (closed_form) = 0.0290418348504593 y1[1] (numeric) = 0.02904183485041164 absolute error = 4.766673167289071e-14 relative error = 1.641312675949496e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.239249329214185 y2[1] (numeric) = 1.239249329213984 absolute error = 2.007283228522283e-13 relative error = 1.619757365368205e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.909999999999791 y1[1] (closed_form) = 0.02669792893669953 y1[1] (numeric) = 0.02669792893665355 absolute error = 4.598058045424125e-14 relative error = 1.722252709686233e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.229527947021468 y2[1] (numeric) = 1.229527947021266 absolute error = 2.022826350867035e-13 relative error = 1.645205670816457e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999789 y1[1] (closed_form) = 0.02445135241896357 y1[1] (numeric) = 0.02445135241891945 absolute error = 4.411748744104216e-14 relative error = 1.804296412121002e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.219783612225322 y2[1] (numeric) = 1.219783612225118 absolute error = 2.042810365310288e-13 relative error = 1.674731767861244e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999788 y1[1] (closed_form) = 0.02230232995303127 y1[1] (numeric) = 0.02230232995298896 absolute error = 4.230990557907433e-14 relative error = 1.897106969010817e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.210017299251106 y2[1] (numeric) = 1.2100172992509 absolute error = 2.05835348765504e-13 relative error = 1.701094264461326e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999787 y1[1] (closed_form) = 0.02025107643935831 y1[1] (numeric) = 0.02025107643931783 absolute error = 4.047803758844282e-14 relative error = 1.99880918476872e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.200229984721979 y2[1] (numeric) = 1.200229984721772 absolute error = 2.071676163950542e-13 relative error = 1.726065995951955e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999786 y1[1] (closed_form) = 0.01829779700158674 y1[1] (numeric) = 0.01829779700154805 absolute error = 3.868086406733084e-14 relative error = 2.113962902964578e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.190422647361237 y2[1] (numeric) = 1.190422647361028 absolute error = 2.087219286295294e-13 relative error = 1.753343059225184e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999785 y1[1] (closed_form) = 0.01644268696603246 y1[1] (numeric) = 0.01644268696599568 absolute error = 3.678307658461222e-14 relative error = 2.237047792772509e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.180596267894444 y2[1] (numeric) = 1.180596267894234 absolute error = 2.100541962590796e-13 relative error = 1.779221245834569e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999784 y1[1] (closed_form) = 0.01468593184215317 y1[1] (numeric) = 0.01468593184211834 absolute error = 3.482977795066233e-14 relative error = 2.371642353036809e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.170751828951358 y2[1] (numeric) = 1.170751828951147 absolute error = 2.111644192837048e-13 relative error = 1.803665081376338e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999783 y1[1] (closed_form) = 0.01302770730399738 y1[1] (numeric) = 0.01302770730396447 absolute error = 3.291637795665991e-14 relative error = 2.526643958800023e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.16089031496767 y2[1] (numeric) = 1.160890314967457 absolute error = 2.1271873151818e-13 relative error = 1.832375796193149e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999782 y1[1] (closed_form) = 0.01146817917263698 y1[1] (numeric) = 0.01146817917260603 absolute error = 3.095440570533015e-14 relative error = 2.699156094385689e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.15101271208656 y2[1] (numeric) = 1.151012712086345 absolute error = 2.144950883575802e-13 relative error = 1.863533617875886e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.999999999999781 y1[1] (closed_form) = 0.01000750339958545 y1[1] (numeric) = 0.01000750339955656 absolute error = 2.888661532196579e-14 relative error = 2.886495679148347e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.141120008060085 y2[1] (numeric) = 1.141120008059868 absolute error = 2.160494005920555e-13 relative error = 1.893310073138947e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.00999999999978 y1[1] (closed_form) = 0.00864582605120312 y1[1] (numeric) = 0.008645826051176144 absolute error = 2.697668477491533e-14 relative error = 3.120197493582624e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.131213192150403 y2[1] (numeric) = 1.131213192150185 absolute error = 2.171596236166806e-13 relative error = 1.91970554377877e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999778 y1[1] (closed_form) = 0.007383283294089771 y1[1] (numeric) = 0.007383283294064886 absolute error = 2.48846082628873e-14 relative error = 3.370398679244385e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.12129325503085 y2[1] (numeric) = 1.121293255030631 absolute error = 2.187139358511558e-13 relative error = 1.950550713382633e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999777 y1[1] (closed_form) = 0.006220001381469165 y1[1] (numeric) = 0.006220001381446381 absolute error = 2.278385813347938e-14 relative error = 3.662998886360028e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.111361188686871 y2[1] (numeric) = 1.111361188686651 absolute error = 2.20046203480706e-13 relative error = 1.979970199793477e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999776 y1[1] (closed_form) = 0.005156096640563268 y1[1] (numeric) = 0.005156096640542494 absolute error = 2.077418098656025e-14 relative error = 4.029051903940035e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.101417986316825 y2[1] (numeric) = 1.101417986316603 absolute error = 2.216005157151812e-13 relative error = 2.011956572964821e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999775 y1[1] (closed_form) = 0.004191675460959332 y1[1] (numeric) = 0.004191675460940731 absolute error = 1.86014398328993e-14 relative error = 4.437709933927486e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.091464642232661 y2[1] (numeric) = 1.091464642232438 absolute error = 2.229327833447314e-13 relative error = 2.042510354606706e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999774 y1[1] (closed_form) = 0.003326834283971847 y1[1] (numeric) = 0.00332683428395537 absolute error = 1.64772709365657e-14 relative error = 4.952837902371798e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.081502151760494 y2[1] (numeric) = 1.08150215176027 absolute error = 2.240430063693566e-13 relative error = 2.071590944175693e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999773 y1[1] (closed_form) = 0.0025616595929977 y1[1] (numeric) = 0.002561659592983409 absolute error = 1.429108567596593e-14 relative error = 5.578838700907267e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.07153151114107 y2[1] (numeric) = 1.071531511140845 absolute error = 2.253752739989068e-13 relative error = 2.103300478386356e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999772 y1[1] (closed_form) = 0.001896227904868431 y1[1] (numeric) = 0.001896227904856303 absolute error = 1.212766866098836e-14 relative error = 6.395680935741652e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.061553717430141 y2[1] (numeric) = 1.061553717429915 absolute error = 2.262634524186069e-13 relative error = 2.131436673467228e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.089999999999771 y1[1] (closed_form) = 0.001330605762198234 y1[1] (numeric) = 0.001330605762188337 absolute error = 9.896814270882182e-15 relative error = 7.437826103001465e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.051569768398763 y2[1] (numeric) = 1.051569768398536 absolute error = 2.273736754432321e-13 relative error = 2.162231002413243e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09999999999977 y1[1] (closed_form) = 0.0008648497267300659 y1[1] (numeric) = 0.0008648497267224304 absolute error = 7.635493799729165e-15 relative error = 8.828694238707127e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.041580662433521 y2[1] (numeric) = 1.041580662433292 absolute error = 2.284838984678572e-13 relative error = 2.193626540013076e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.109999999999769 y1[1] (closed_form) = 0.0004990063736793893 y1[1] (numeric) = 0.0004990063736740012 absolute error = 5.388051116383963e-15 relative error = 1.0797559711824e-09 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 11 h = 0.001 y2[1] (closed_form) = 1.031587398436685 y2[1] (numeric) = 1.031587398436455 absolute error = 2.298161660974074e-13 relative error = 2.227791522518415e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999767 y1[1] (closed_form) = 0.0002331122870766755 y1[1] (numeric) = 0.0002331122870734872 absolute error = 3.188367538736747e-15 relative error = 1.367738946204936e-09 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 11 h = 0.001 y2[1] (closed_form) = 1.021590975726329 y2[1] (numeric) = 1.021590975726098 absolute error = 2.307043445171075e-13 relative error = 2.258284871331032e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.129999999999766 y1[1] (closed_form) = 6.719405610888796e-05 y1[1] (numeric) = 6.71940561079666e-05 absolute error = 9.213550061781817e-16 relative error = 1.371185279669866e-09 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 11 h = 0.001 y2[1] (closed_form) = 1.011592393936392 y2[1] (numeric) = 1.01159239393616 absolute error = 2.315925229368077e-13 relative error = 2.289385767676798e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999765 y1[1] (closed_form) = 1.268272460830389e-06 y1[1] (numeric) = 1.268272462274112e-06 absolute error = 1.443723612881698e-15 relative error = 1.138338690991078e-07 % Desired digits = 8 Estimated correct digits = 5 Correct digits = 9 h = 0.001 y2[1] (closed_form) = 1.001592652916722 y2[1] (numeric) = 1.001592652916489 absolute error = 2.327027459614328e-13 relative error = 2.323327205763569e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999764 y1[1] (closed_form) = 3.534152865602991e-05 y1[1] (numeric) = 3.534152865983519e-05 absolute error = 3.805285351144577e-15 relative error = 1.076717814948088e-08 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 10 h = 0.001 y2[1] (closed_form) = 0.9915927526330872 y2[1] (numeric) = 0.9915927526328535 absolute error = 2.337019466835955e-13 relative error = 2.35683395288056e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.159999999999763 y1[1] (closed_form) = 0.0001694104173972644 y1[1] (numeric) = 0.0001694104174034265 absolute error = 6.162171467538613e-15 relative error = 3.637421808062979e-09 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 11 h = 0.001 y2[1] (closed_form) = 0.9815936930671832 y2[1] (numeric) = 0.9815936930669485 absolute error = 2.347011474057581e-13 relative error = 2.391021346850631e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.169999999999762 y1[1] (closed_form) = 0.0004034615319074009 y1[1] (numeric) = 0.0004034615319158974 absolute error = 8.496567165117153e-15 relative error = 2.105917539386931e-09 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 11 h = 0.001 y2[1] (closed_form) = 0.9715964741166342 y2[1] (numeric) = 0.9715964741163984 absolute error = 2.358113704303832e-13 relative error = 2.427050495883907e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.179999999999761 y1[1] (closed_form) = 0.000737471467269879 y1[1] (numeric) = 0.0007374714672808365 absolute error = 1.095748925622475e-14 relative error = 1.485818739101785e-09 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 11 h = 0.001 y2[1] (closed_form) = 0.9616020954950039 y2[1] (numeric) = 0.9616020954947672 absolute error = 2.366995488500834e-13 relative error = 2.461512406836401e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18999999999976 y1[1] (closed_form) = 0.001171406822769727 y1[1] (numeric) = 0.001171406822783049 absolute error = 1.332224261463288e-14 relative error = 1.137285728209536e-09 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 11 h = 0.001 y2[1] (closed_form) = 0.9516115566318258 y2[1] (numeric) = 0.9516115566315881 absolute error = 2.37698749572246e-13 relative error = 2.497854801317956e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999759 y1[1] (closed_form) = 0.00170522420523278 y1[1] (numeric) = 0.001705224205248597 absolute error = 1.581655813265304e-14 relative error = 9.275353988124931e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9416258565726611 y2[1] (numeric) = 0.9416258565724226 absolute error = 2.384759056894836e-13 relative error = 2.532597252134627e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999757 y1[1] (closed_form) = 0.002338870233365875 y1[1] (numeric) = 0.002338870233384079 absolute error = 1.820418815690061e-14 relative error = 7.783325426611168e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9316459938791941 y2[1] (numeric) = 0.9316459938789546 absolute error = 2.394751064116463e-13 relative error = 2.570451737945205e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999756 y1[1] (closed_form) = 0.003072281543094024 y1[1] (numeric) = 0.003072281543114719 absolute error = 2.069525106840331e-14 relative error = 6.736118021124326e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9216729665293778 y2[1] (numeric) = 0.9216729665291373 absolute error = 2.404743071338089e-13 relative error = 2.609106655686466e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999755 y1[1] (closed_form) = 0.00390538479389746 y1[1] (numeric) = 0.003905384793920719 absolute error = 2.325960604676602e-14 relative error = 5.955778309761282e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9117077718176362 y2[1] (numeric) = 0.9117077718173949 absolute error = 2.412514632510465e-13 relative error = 2.646149026130082e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999754 y1[1] (closed_form) = 0.004838096676145542 y1[1] (numeric) = 0.004838096676171247 absolute error = 2.570426510528634e-14 relative error = 5.312887861878081e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9017514062551362 y2[1] (numeric) = 0.9017514062548942 absolute error = 2.419175970658216e-13 relative error = 2.682752645437793e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999753 y1[1] (closed_form) = 0.005870323919427101 y1[1] (numeric) = 0.005870323919455334 absolute error = 2.823349193326052e-14 relative error = 4.809528796158135e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.891804865470137 y2[1] (numeric) = 0.8918048654698943 absolute error = 2.426947531830592e-13 relative error = 2.721388529934928e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999752 y1[1] (closed_form) = 0.007001963301877967 y1[1] (numeric) = 0.007001963301908839 absolute error = 3.087200634022125e-14 relative error = 4.409050006294834e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8818691441084286 y2[1] (numeric) = 0.8818691441081853 absolute error = 2.433608869978343e-13 relative error = 2.759603152278024e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.269999999999751 y1[1] (closed_form) = 0.008232901660503167 y1[1] (numeric) = 0.008232901660536546 absolute error = 3.337954912474572e-14 relative error = 4.05440882221174e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8719452357338674 y2[1] (numeric) = 0.8719452357336231 absolute error = 2.442490654175344e-13 relative error = 2.80119731615901e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27999999999975 y1[1] (closed_form) = 0.009563015902492422 y1[1] (numeric) = 0.009563015902528376 absolute error = 3.59538787630953e-14 relative error = 3.759679909527767e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8620341327290207 y2[1] (numeric) = 0.8620341327287757 absolute error = 2.45026221534772e-13 relative error = 2.842419020683903e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999749 y1[1] (closed_form) = 0.01099217301752997 y1[1] (numeric) = 0.01099217301756855 absolute error = 3.858025010572419e-14 relative error = 3.50979283570206e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8521368261959301 y2[1] (numeric) = 0.8521368261956844 absolute error = 2.456923553495471e-13 relative error = 2.883250057932077e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999748 y1[1] (closed_form) = 0.01252023009109526 y1[1] (numeric) = 0.01252023009113653 absolute error = 4.126386732306031e-14 relative error = 3.295775478791585e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8422543058570009 y2[1] (numeric) = 0.8422543058567544 absolute error = 2.464695114667848e-13 relative error = 2.926307526751079e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999746 y1[1] (closed_form) = 0.01414703431875441 y1[1] (numeric) = 0.01414703431879832 absolute error = 4.390932062392494e-14 relative error = 3.103782717605719e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8323875599560316 y2[1] (numeric) = 0.8323875599557845 absolute error = 2.471356452815598e-13 relative error = 2.968997341750447e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999745 y1[1] (closed_form) = 0.01587242302144032 y1[1] (numeric) = 0.01587242302148684 absolute error = 4.652528362569797e-14 relative error = 2.931202347798572e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8225375751593903 y2[1] (numeric) = 0.8225375751591424 absolute error = 2.479128013987975e-13 relative error = 3.01399971120781e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999744 y1[1] (closed_form) = 0.01769622366172041 y1[1] (numeric) = 0.01769622366176964 absolute error = 4.922451335431788e-14 relative error = 2.781639421793583e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8127053364573481 y2[1] (numeric) = 0.8127053364570995 absolute error = 2.485789352135725e-13 relative error = 3.058660058726196e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999743 y1[1] (closed_form) = 0.01961825386105054 y1[1] (numeric) = 0.0196182538611025 absolute error = 5.196190699940928e-14 relative error = 2.648650963915438e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8028918270655818 y2[1] (numeric) = 0.8028918270653327 absolute error = 2.491340467258851e-13 relative error = 3.102959057839997e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999742 y1[1] (closed_form) = 0.02163832141801258 y1[1] (numeric) = 0.02163832141806719 absolute error = 5.460215612984598e-14 relative error = 2.523400733126785e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.7930980283268527 y2[1] (numeric) = 0.793098028326603 absolute error = 2.496891582381977e-13 relative error = 3.148276118715749e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.359999999999741 y1[1] (closed_form) = 0.02375622432753399 y1[1] (numeric) = 0.02375622432759139 absolute error = 5.739853037312059e-14 relative error = 2.416147009800477e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.7833249196128731 y2[1] (numeric) = 0.783324919612623 absolute error = 2.501332474480478e-13 relative error = 3.193224691123909e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36999999999974 y1[1] (closed_form) = 0.02597175080108893 y1[1] (numeric) = 0.02597175080114907 absolute error = 6.013245457126004e-14 relative error = 2.315302307949868e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.7735734782263703 y2[1] (numeric) = 0.7735734782261195 absolute error = 2.507993812628229e-13 relative error = 3.242088674470191e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999739 y1[1] (closed_form) = 0.02828467928787626 y1[1] (numeric) = 0.02828467928793912 absolute error = 6.286290932244754e-14 relative error = 2.222507410553976e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.7638446793033568 y2[1] (numeric) = 0.7638446793031055 absolute error = 2.512434704726729e-13 relative error = 3.289195791765055e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999738 y1[1] (closed_form) = 0.03069477849697466 y1[1] (numeric) = 0.03069477849704031 absolute error = 6.564887522486629e-14 relative error = 2.138763608648838e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.7541394957156173 y2[1] (numeric) = 0.7541394957153659 absolute error = 2.51465515077598e-13 relative error = 3.334469504729726e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999737 y1[1] (closed_form) = 0.03320180742047163 y1[1] (numeric) = 0.03320180742054014 absolute error = 6.851463840717997e-14 relative error = 2.063581585770391e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.7444588979734234 y2[1] (numeric) = 0.7444588979731716 absolute error = 2.517985819849855e-13 relative error = 3.382303343682709e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y1[1] (closed_form) = 0.03580551535756415 y1[1] (numeric) = 0.03580551535763545 absolute error = 7.129019596874286e-14 relative error = 1.99103951603038e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.7348038541284818 y2[1] (numeric) = 0.7348038541282297 absolute error = 2.521316488923731e-13 relative error = 3.431278258487297e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999734 y1[1] (closed_form) = 0.03850564193962813 y1[1] (numeric) = 0.03850564193970226 absolute error = 7.412820357544092e-14 relative error = 1.925125769664205e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.7251753296771313 y2[1] (numeric) = 0.7251753296768788 absolute error = 2.524647157997606e-13 relative error = 3.481430013789425e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999733 y1[1] (closed_form) = 0.04130191715625553 y1[1] (numeric) = 0.04130191715633248 absolute error = 7.694539450042726e-14 relative error = 1.862998131765252e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.7155742874637934 y2[1] (numeric) = 0.7155742874635403 absolute error = 2.530198273120732e-13 relative error = 3.535898812251208e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999732 y1[1] (closed_form) = 0.0441940613822549 y1[1] (numeric) = 0.04419406138233466 absolute error = 7.975564653150968e-14 relative error = 1.804668863575723e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.7060016875846884 y2[1] (numeric) = 0.7060016875844353 absolute error = 2.531308496145357e-13 relative error = 3.585414228690089e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.449999999999731 y1[1] (closed_form) = 0.04718178540561369 y1[1] (numeric) = 0.04718178540569631 absolute error = 8.262140971382337e-14 relative error = 1.751129360695898e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.6964584872918271 y2[1] (numeric) = 0.6964584872915739 absolute error = 2.532418719169982e-13 relative error = 3.636137351153937e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45999999999973 y1[1] (closed_form) = 0.05026479045641929 y1[1] (numeric) = 0.05026479045650486 absolute error = 8.556350072908003e-14 relative error = 1.702255195975909e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.6869456408972863 y2[1] (numeric) = 0.6869456408970326 absolute error = 2.536859611268483e-13 relative error = 3.692955395939109e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999729 y1[1] (closed_form) = 0.05344276823673599 y1[1] (numeric) = 0.05344276823682438 absolute error = 8.838763054797028e-14 relative error = 1.653874480386919e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.6774640996777779 y2[1] (numeric) = 0.6774640996775239 absolute error = 2.540190280342358e-13 relative error = 3.7495570341669e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999728 y1[1] (closed_form) = 0.05671540095143379 y1[1] (numeric) = 0.05671540095152516 absolute error = 9.137135492665038e-14 relative error = 1.611050145001937e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.6680148117795227 y2[1] (numeric) = 0.6680148117792687 absolute error = 2.540190280342358e-13 relative error = 3.80259574421045e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999727 y1[1] (closed_form) = 0.06008236133996869 y1[1] (numeric) = 0.06008236134006291 absolute error = 9.421630142725235e-14 relative error = 1.56811915054638e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.6585987221234362 y2[1] (numeric) = 0.6585987221231822 absolute error = 2.540190280342358e-13 relative error = 3.856962054454563e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999726 y1[1] (closed_form) = 0.0635433127091074 y1[1] (numeric) = 0.06354331270920456 absolute error = 9.715839244250901e-14 relative error = 1.52901050166029e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.6492167723106372 y2[1] (numeric) = 0.6492167723103832 absolute error = 2.540190280342358e-13 relative error = 3.912699715538045e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y1[1] (closed_form) = 0.06709790896659718 y1[1] (numeric) = 0.06709790896669733 absolute error = 1.001559946089969e-13 relative error = 1.492684290040347e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.6398699005282886 y2[1] (numeric) = 0.6398699005280347 absolute error = 2.539080057317733e-13 relative error = 3.968119230520799e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999723 y1[1] (closed_form) = 0.07074579465577457 y1[1] (numeric) = 0.07074579465587762 absolute error = 1.030425744730223e-13 relative error = 1.45651872276498e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.63055904145578 y2[1] (numeric) = 0.630559041455526 absolute error = 2.540190280342358e-13 relative error = 4.028473328172073e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999722 y1[1] (closed_form) = 0.07448660499111037 y1[1] (numeric) = 0.07448660499121637 absolute error = 1.059985432760868e-13 relative error = 1.423055102172226e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.6212851261712593 y2[1] (numeric) = 0.6212851261710052 absolute error = 2.541300503366983e-13 relative error = 4.090393277283232e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.539999999999721 y1[1] (closed_form) = 0.07831996589468848 y1[1] (numeric) = 0.07831996589479742 absolute error = 1.089406342913435e-13 relative error = 1.390968867859679e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.6120490820585267 y2[1] (numeric) = 0.6120490820582726 absolute error = 2.541300503366983e-13 relative error = 4.152118805275772e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54999999999972 y1[1] (closed_form) = 0.08224549403361292 y1[1] (numeric) = 0.08224549403372484 absolute error = 1.119243586700236e-13 relative error = 1.360857029131361e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.602851832714297 y2[1] (numeric) = 0.6028518327140429 absolute error = 2.541300503366983e-13 relative error = 4.21546450630325e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999719 y1[1] (closed_form) = 0.08626279685834115 y1[1] (numeric) = 0.08626279685845603 absolute error = 1.148803274730881e-13 relative error = 1.331748235125532e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.5936942978558402 y2[1] (numeric) = 0.5936942978555859 absolute error = 2.542410726391608e-13 relative error = 4.282356653202946e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999718 y1[1] (closed_form) = 0.09037147264193834 y1[1] (numeric) = 0.09037147264205624 absolute error = 1.178918074273838e-13 relative error = 1.304524580389257e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.5845773932290106 y2[1] (numeric) = 0.5845773932287567 absolute error = 2.539080057317733e-13 relative error = 4.343445515901156e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999717 y1[1] (closed_form) = 0.09457111052025013 y1[1] (numeric) = 0.09457111052037101 absolute error = 1.208755318060639e-13 relative error = 1.278144362914945e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.5755020305166739 y2[1] (numeric) = 0.5755020305164201 absolute error = 2.537969834293108e-13 relative error = 4.410010216670427e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999716 y1[1] (closed_form) = 0.0988612905329882 y1[1] (numeric) = 0.09886129053311217 absolute error = 1.239702784872065e-13 relative error = 1.253981996581766e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.5664691172475385 y2[1] (numeric) = 0.566469117247285 absolute error = 2.534639165219232e-13 relative error = 4.474452513024878e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999715 y1[1] (closed_form) = 0.1032415836657267 y1[1] (numeric) = 0.1032415836658536 absolute error = 1.269540028658867e-13 relative error = 1.229678956465212e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.5574795567054036 y2[1] (numeric) = 0.5574795567051503 absolute error = 2.533528942194607e-13 relative error = 4.54461318217169e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y1[1] (closed_form) = 0.1077115518928023 y1[1] (numeric) = 0.1077115518929323 absolute error = 1.299516050323746e-13 relative error = 1.206477882351061e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.5485342478388324 y2[1] (numeric) = 0.5485342478385794 absolute error = 2.530198273120732e-13 relative error = 4.612653235580911e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999712 y1[1] (closed_form) = 0.1122707482211174 y1[1] (numeric) = 0.1122707482212505 absolute error = 1.330741072891328e-13 relative error = 1.185296342971218e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.5396340851712571 y2[1] (numeric) = 0.5396340851710043 absolute error = 2.527977827071481e-13 relative error = 4.684614809439267e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.629999999999711 y1[1] (closed_form) = 0.1169187167348384 y1[1] (numeric) = 0.1169187167349746 absolute error = 1.361133428190442e-13 relative error = 1.164170687296693e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.5307799587115278 y2[1] (numeric) = 0.5307799587112753 absolute error = 2.525757381022231e-13 relative error = 4.758577145892105e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63999999999971 y1[1] (closed_form) = 0.1216549926409874 y1[1] (numeric) = 0.1216549926411266 absolute error = 1.391109449855321e-13 relative error = 1.143487348653733e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.5219727538649118 y2[1] (numeric) = 0.5219727538646596 absolute error = 2.522426711948356e-13 relative error = 4.832487315230954e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999709 y1[1] (closed_form) = 0.1264791023159205 y1[1] (numeric) = 0.1264791023160627 absolute error = 1.421918138788669e-13 relative error = 1.124231681560319e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.5132133513445547 y2[1] (numeric) = 0.5132133513443029 absolute error = 2.517985819849855e-13 relative error = 4.906313939910268e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999708 y1[1] (closed_form) = 0.1313905633526904 y1[1] (numeric) = 0.1313905633528356 absolute error = 1.452449271965861e-13 relative error = 1.105444131529496e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.5045026270834089 y2[1] (numeric) = 0.5045026270831577 absolute error = 2.511324481702104e-13 relative error = 4.977822407428038e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999707 y1[1] (closed_form) = 0.1363888846092861 y1[1] (numeric) = 0.1363888846094344 absolute error = 1.483257960899209e-13 relative error = 1.087521145985104e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.4958414521466417 y2[1] (numeric) = 0.4958414521463911 absolute error = 2.505773366578978e-13 relative error = 5.053577823577996e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999706 y1[1] (closed_form) = 0.1414735662577474 y1[1] (numeric) = 0.1414735662578988 absolute error = 1.513511538320245e-13 relative error = 1.069819315618872e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.4872306926445289 y2[1] (numeric) = 0.487230692644279 absolute error = 2.499112028431227e-13 relative error = 5.129217157619657e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999705 y1[1] (closed_form) = 0.1466440998341466 y1[1] (numeric) = 0.146644099834301 absolute error = 1.544042671497436e-13 relative error = 1.052918373970543e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.4786712096458455 y2[1] (numeric) = 0.4786712096455962 absolute error = 2.493560913308102e-13 relative error = 5.209339653314459e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999704 y1[1] (closed_form) = 0.1518999682894348 y1[1] (numeric) = 0.1518999682895923 absolute error = 1.575406471943097e-13 relative error = 1.03713416775787e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.4701638590917582 y2[1] (numeric) = 0.4701638590915095 absolute error = 2.486899575160351e-13 relative error = 5.289431603620988e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999702 y1[1] (closed_form) = 0.1572406460411463 y1[1] (numeric) = 0.1572406460413069 absolute error = 1.606492716632602e-13 relative error = 1.021677764038326e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.4617094917102331 y2[1] (numeric) = 0.461709491709985 absolute error = 2.480793348524912e-13 relative error = 5.373061184719692e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.719999999999701 y1[1] (closed_form) = 0.1626655990259567 y1[1] (numeric) = 0.1626655990261203 absolute error = 1.636191182541324e-13 relative error = 1.005861837007243e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.4533089529309631 y2[1] (numeric) = 0.4533089529307157 absolute error = 2.474132010377161e-13 relative error = 5.457937670059565e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7299999999997 y1[1] (closed_form) = 0.1681742847530879 y1[1] (numeric) = 0.1681742847532547 absolute error = 1.667832538743141e-13 relative error = 9.917286350834428e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4449630828008255 y2[1] (numeric) = 0.4449630828005789 absolute error = 2.466360449204785e-13 relative error = 5.54284286615476e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999699 y1[1] (closed_form) = 0.1737661523585582 y1[1] (numeric) = 0.1737661523587281 absolute error = 1.69864122767649e-13 relative error = 9.775443632839519e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4366727158998787 y2[1] (numeric) = 0.4366727158996329 absolute error = 2.458033776520097e-13 relative error = 5.62900700460452e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999698 y1[1] (closed_form) = 0.1794406426602667 y1[1] (numeric) = 0.1794406426604396 absolute error = 1.728617249341369e-13 relative error = 9.63336523829857e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4284386812579041 y2[1] (numeric) = 0.428438681257659 absolute error = 2.450817326860033e-13 relative error = 5.720345603866549e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999697 y1[1] (closed_form) = 0.185197188213912 y1[1] (numeric) = 0.1851971882140879 absolute error = 1.759425938274717e-13 relative error = 9.500284292882959e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.420261802271504 y2[1] (numeric) = 0.4202618022712598 absolute error = 2.442490654175344e-13 relative error = 5.811831198966326e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999696 y1[1] (closed_form) = 0.1910352133697356 y1[1] (numeric) = 0.1910352133699146 absolute error = 1.790234627208065e-13 relative error = 9.371228453799185e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4121428966217633 y2[1] (numeric) = 0.4121428966215199 absolute error = 2.433608869978343e-13 relative error = 5.904769656170354e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999695 y1[1] (closed_form) = 0.1969541343300873 y1[1] (numeric) = 0.1969541343302694 absolute error = 1.8204882046291e-13 relative error = 9.243208886278234e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4040827761924811 y2[1] (numeric) = 0.4040827761922386 absolute error = 2.424727085781342e-13 relative error = 6.000570251047635e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999694 y1[1] (closed_form) = 0.2029533592078033 y1[1] (numeric) = 0.2029533592079884 absolute error = 1.851019337806292e-13 relative error = 9.120417346288115e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.3960822469889836 y2[1] (numeric) = 0.3960822469887421 absolute error = 2.415845301584341e-13 relative error = 6.099352646955503e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999693 y1[1] (closed_form) = 0.2090322880853952 y1[1] (numeric) = 0.2090322880855834 absolute error = 1.88182802673964e-13 relative error = 9.002571057208463e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.3881421090575241 y2[1] (numeric) = 0.3881421090572836 absolute error = 2.405298182850402e-13 relative error = 6.196952422119001e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999691 y1[1] (closed_form) = 0.2151903130750409 y1[1] (numeric) = 0.2151903130752322 absolute error = 1.913191827185301e-13 relative error = 8.890696796923825e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.380263156405279 y2[1] (numeric) = 0.3802631564050395 absolute error = 2.394751064116463e-13 relative error = 6.297615279783171e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81999999999969 y1[1] (closed_form) = 0.2214268183793733 y1[1] (numeric) = 0.2214268183795676 absolute error = 1.94316784885018e-13 relative error = 8.775666213660384e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.3724461769209476 y2[1] (numeric) = 0.3724461769207092 absolute error = 2.383648833870211e-13 relative error = 6.399982015055413e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999689 y1[1] (closed_form) = 0.2277411803530588 y1[1] (numeric) = 0.2277411803532562 absolute error = 1.974254093539685e-13 relative error = 8.668849834180499e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.3646919522959644 y2[1] (numeric) = 0.3646919522957271 absolute error = 2.373101715136272e-13 relative error = 6.507140341858683e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999688 y1[1] (closed_form) = 0.2341327675651622 y1[1] (numeric) = 0.2341327675653626 absolute error = 2.004230115204564e-13 relative error = 8.560229036060749e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.35700125794633 y2[1] (numeric) = 0.3570012579460938 absolute error = 2.361999484890021e-13 relative error = 6.616221742403813e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999687 y1[1] (closed_form) = 0.2406009408622884 y1[1] (numeric) = 0.240600940862492 absolute error = 2.035316359894068e-13 relative error = 8.459303411697846e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.3493748629350704 y2[1] (numeric) = 0.3493748629348353 absolute error = 2.350897254643769e-13 relative error = 6.728867769404097e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999686 y1[1] (closed_form) = 0.247145053432498 y1[1] (numeric) = 0.2471450534327046 absolute error = 2.065292381558947e-13 relative error = 8.356600113475605e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.3418135298953314 y2[1] (numeric) = 0.3418135298950975 absolute error = 2.339239912885205e-13 relative error = 6.843614158870528e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999685 y1[1] (closed_form) = 0.2537644508699873 y1[1] (numeric) = 0.253764450870197 absolute error = 2.096656182004608e-13 relative error = 8.262213934286645e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.3343180149541161 y2[1] (numeric) = 0.3343180149538834 absolute error = 2.326472348102016e-13 relative error = 6.958860258910413e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999684 y1[1] (closed_form) = 0.2604584712405287 y1[1] (numeric) = 0.2604584712407415 absolute error = 2.127742426694113e-13 relative error = 8.169219517261088e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.3268890676566721 y2[1] (numeric) = 0.3268890676564408 absolute error = 2.313704783318826e-13 relative error = 7.077950938845357e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999683 y1[1] (closed_form) = 0.2672264451476635 y1[1] (numeric) = 0.2672264451478792 absolute error = 2.157163336846679e-13 relative error = 8.0724171429017e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.3195274308915387 y2[1] (numeric) = 0.3195274308913086 absolute error = 2.300937218535637e-13 relative error = 7.201063182949929e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999681 y1[1] (closed_form) = 0.2740676957996409 y1[1] (numeric) = 0.2740676957998597 absolute error = 2.188804693048496e-13 relative error = 7.986365144794874e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.3122338408162574 y2[1] (numeric) = 0.3122338408160287 absolute error = 2.287059430727822e-13 relative error = 7.324828803786537e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.90999999999968 y1[1] (closed_form) = 0.2809815390770967 y1[1] (numeric) = 0.2809815390773186 absolute error = 2.219335826225688e-13 relative error = 7.898511174489436e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.305009026783758 y2[1] (numeric) = 0.3050090267835306 absolute error = 2.273181642920008e-13 relative error = 7.452833992784167e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999679 y1[1] (closed_form) = 0.2879672836014647 y1[1] (numeric) = 0.2879672836016897 absolute error = 2.24986695940288e-13 relative error = 7.812925590938331e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.2978537112694228 y2[1] (numeric) = 0.297853711269197 absolute error = 2.258193632087568e-13 relative error = 7.581552777916959e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999678 y1[1] (closed_form) = 0.295024230804114 y1[1] (numeric) = 0.295024230804342 absolute error = 2.280398092580072e-13 relative error = 7.72952813524723e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.2907686097988409 y2[1] (numeric) = 0.2907686097986165 absolute error = 2.243760732767441e-13 relative error = 7.716653920516787e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999677 y1[1] (closed_form) = 0.302151674996205 y1[1] (numeric) = 0.302151674996436 absolute error = 2.310374114244951e-13 relative error = 7.646405118468957e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.2837544308762548 y2[1] (numeric) = 0.283754430876032 absolute error = 2.228217610422689e-13 relative error = 7.852626665746811e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999676 y1[1] (closed_form) = 0.309348903439258 y1[1] (numeric) = 0.3093489034394921 absolute error = 2.34035013590983e-13 relative error = 7.565406277153227e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.2768118759137118 y2[1] (numeric) = 0.2768118759134906 absolute error = 2.212119376565624e-13 relative error = 7.991417887197836e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999675 y1[1] (closed_form) = 0.3166151964164264 y1[1] (numeric) = 0.3166151964166635 absolute error = 2.370881269087022e-13 relative error = 7.488210597348375e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.2699416391609226 y2[1] (numeric) = 0.2699416391607029 absolute error = 2.197131365733185e-13 relative error = 8.139282893008552e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999674 y1[1] (closed_form) = 0.3239498273044678 y1[1] (numeric) = 0.3239498273047078 absolute error = 2.400857290751901e-13 relative error = 7.411201020630363e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.2631444076358374 y2[1] (numeric) = 0.2631444076356193 absolute error = 2.180478020363807e-13 relative error = 8.286241155393837e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999673 y1[1] (closed_form) = 0.3313520626464054 y1[1] (numeric) = 0.3313520626466485 absolute error = 2.43083331241678e-13 relative error = 7.336104362841367e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.2564208610559442 y2[1] (numeric) = 0.256420861055728 absolute error = 2.162159340457492e-13 relative error = 8.432072693125255e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999672 y1[1] (closed_form) = 0.3388211622248736 y1[1] (numeric) = 0.3388211622251195 absolute error = 2.459699111057034e-13 relative error = 7.259579345355491e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.2497716717702984 y2[1] (numeric) = 0.2497716717700837 absolute error = 2.146338662356584e-13 relative error = 8.593202932678677e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99999999999967 y1[1] (closed_form) = 0.3463563791361387 y1[1] (numeric) = 0.3463563791363877 absolute error = 2.490230244234226e-13 relative error = 7.18979177009879e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.2431975046922872 y2[1] (numeric) = 0.2431975046920743 absolute error = 2.128575093962581e-13 relative error = 8.752454498477785e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999674 y1[1] (closed_form) = 0.3539569598647925 y1[1] (numeric) = 0.353956959865041 absolute error = 2.485234240623413e-13 relative error = 7.021289372506601e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.2366990172331372 y2[1] (numeric) = 0.2366990172329291 absolute error = 2.081668171172169e-13 relative error = 8.79457885168076e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999677 y1[1] (closed_form) = 0.3616221443590923 y1[1] (numeric) = 0.3616221443593404 absolute error = 2.4802382370126e-13 relative error = 6.85864589793957e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.230276859236182 y2[1] (numeric) = 0.2302768592359785 absolute error = 2.035316359894068e-13 relative error = 8.838562270847019e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.029999999999681 y1[1] (closed_form) = 0.3693511661069765 y1[1] (numeric) = 0.369351166107224 absolute error = 2.475242233401787e-13 relative error = 6.701595826787976e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.2239316729118693 y2[1] (numeric) = 0.2239316729116705 absolute error = 1.988409437103655e-13 relative error = 8.879536383788884e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999684 y1[1] (closed_form) = 0.3771432522127112 y1[1] (numeric) = 0.3771432522129581 absolute error = 2.469136006766348e-13 relative error = 6.546944674947386e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.2176640927735441 y2[1] (numeric) = 0.2176640927733499 absolute error = 1.942890293094024e-13 relative error = 8.926094645823785e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999687 y1[1] (closed_form) = 0.384997623474179 y1[1] (numeric) = 0.3849976234744252 absolute error = 2.461919557106285e-13 relative error = 6.394635724995327e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.2114747455739973 y2[1] (numeric) = 0.2114747455738075 absolute error = 1.897093593328236e-13 relative error = 8.970780828599805e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.059999999999691 y1[1] (closed_form) = 0.3929134944607993 y1[1] (numeric) = 0.3929134944610446 absolute error = 2.453592884421596e-13 relative error = 6.244613430212409e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.2053642502427908 y2[1] (numeric) = 0.2053642502426056 absolute error = 1.852129560830917e-13 relative error = 9.018753549564965e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999694 y1[1] (closed_form) = 0.4008900735920696 y1[1] (numeric) = 0.4008900735923142 absolute error = 2.44582132324922e-13 relative error = 6.100977510702832e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1993332178243659 y2[1] (numeric) = 0.1993332178241852 absolute error = 1.806887972577442e-13 relative error = 9.064660633580431e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999697 y1[1] (closed_form) = 0.4089265632167243 y1[1] (numeric) = 0.4089265632169679 absolute error = 2.436384427539906e-13 relative error = 5.957999911707039e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1933822514169385 y2[1] (numeric) = 0.1933822514167622 absolute error = 1.763589274617061e-13 relative error = 9.119705979711158e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.089999999999701 y1[1] (closed_form) = 0.4170221596924978 y1[1] (numeric) = 0.4170221596927404 absolute error = 2.425837308805967e-13 relative error = 5.817046534396929e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1875119461121902 y2[1] (numeric) = 0.1875119461120183 absolute error = 1.719180353632055e-13 relative error = 9.168377744868866e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.099999999999704 y1[1] (closed_form) = 0.4251760534664888 y1[1] (numeric) = 0.4251760534667304 absolute error = 2.415845301584341e-13 relative error = 5.681988159699476e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1817228889357597 y2[1] (numeric) = 0.1817228889355922 absolute error = 1.675604099915518e-13 relative error = 9.22065519499778e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.109999999999707 y1[1] (closed_form) = 0.4333874291561148 y1[1] (numeric) = 0.4333874291563553 absolute error = 2.404187959825776e-13 relative error = 5.547433538871151e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1760156587885403 y2[1] (numeric) = 0.1760156587883771 absolute error = 1.63202784619898e-13 relative error = 9.272060550928865e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.119999999999711 y1[1] (closed_form) = 0.4416554656306497 y1[1] (numeric) = 0.4416554656308889 absolute error = 2.3919755065549e-13 relative error = 5.415930952285045e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1703908263887908 y2[1] (numeric) = 0.1703908263886318 absolute error = 1.589284259750912e-13 relative error = 9.327287703415137e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.129999999999714 y1[1] (closed_form) = 0.4499793360933361 y1[1] (numeric) = 0.449979336093574 absolute error = 2.379763053284023e-13 relative error = 5.288605192284664e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1648489542150638 y2[1] (numeric) = 0.1648489542149091 absolute error = 1.547373340571312e-13 relative error = 9.38661302365674e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.139999999999717 y1[1] (closed_form) = 0.458358208164064 y1[1] (numeric) = 0.4583582081643007 absolute error = 2.366995488500834e-13 relative error = 5.164073526645769e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1593905964499585 y2[1] (numeric) = 0.159390596449808 absolute error = 1.5049073098794e-13 relative error = 9.441631711014229e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.149999999999721 y1[1] (closed_form) = 0.466791243962609 y1[1] (numeric) = 0.4667912439628444 absolute error = 2.354783035229957e-13 relative error = 5.044616979616225e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1540162989247027 y2[1] (numeric) = 0.1540162989245563 absolute error = 1.463829057968269e-13 relative error = 9.504377576842843e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.159999999999724 y1[1] (closed_form) = 0.4752776001924185 y1[1] (numeric) = 0.4752776001926526 absolute error = 2.341460358934455e-13 relative error = 4.926511070554353e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1487265990645704 y2[1] (numeric) = 0.1487265990644281 absolute error = 1.422750806057138e-13 relative error = 9.566216231700716e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.169999999999727 y1[1] (closed_form) = 0.4838164282249418 y1[1] (numeric) = 0.4838164282251743 absolute error = 2.32536212507739e-13 relative error = 4.806290132827518e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1435220258351396 y2[1] (numeric) = 0.1435220258350014 absolute error = 1.38222766565832e-13 relative error = 9.630770312885998e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.179999999999731 y1[1] (closed_form) = 0.4924068741844909 y1[1] (numeric) = 0.492406874184722 absolute error = 2.310374114244951e-13 relative error = 4.692002153851571e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1384030996893961 y2[1] (numeric) = 0.1384030996892619 absolute error = 1.342259636771814e-13 relative error = 9.698190573651239e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999734 y1[1] (closed_form) = 0.5010480790336287 y1[1] (numeric) = 0.5010480790338583 absolute error = 2.295941214924824e-13 relative error = 4.582277252420576e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1333703325156886 y2[1] (numeric) = 0.1333703325155585 absolute error = 1.30145894061684e-13 relative error = 9.758234204475319e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999737 y1[1] (closed_form) = 0.5097391786590715 y1[1] (numeric) = 0.5097391786592994 absolute error = 2.279287869555446e-13 relative error = 4.471478679648246e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1284242275865407 y2[1] (numeric) = 0.1284242275864145 absolute error = 1.262046023242647e-13 relative error = 9.827164600948812e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.209999999999741 y1[1] (closed_form) = 0.5184793039580989 y1[1] (numeric) = 0.5184793039583253 absolute error = 2.263744747210694e-13 relative error = 4.366123642600862e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1235652795083235 y2[1] (numeric) = 0.1235652795082012 absolute error = 1.223326995258844e-13 relative error = 9.90024867929376e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999744 y1[1] (closed_form) = 0.5272675809254648 y1[1] (numeric) = 0.5272675809256893 absolute error = 2.244870955792067e-13 relative error = 4.257555436751581e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1187939741717956 y2[1] (numeric) = 0.1187939741716772 absolute error = 1.184191633640808e-13 relative error = 9.968448668349726e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999747 y1[1] (closed_form) = 0.5361031307407956 y1[1] (numeric) = 0.5361031307410185 absolute error = 2.228217610422689e-13 relative error = 4.156322697358069e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1141107887035148 y2[1] (numeric) = 0.1141107887034001 absolute error = 1.146721606559709e-13 relative error = 1.004919534417685e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.239999999999751 y1[1] (closed_form) = 0.5449850698564731 y1[1] (numeric) = 0.5449850698566939 absolute error = 2.208233595979436e-13 relative error = 4.051915764519926e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1095161914181251 y2[1] (numeric) = 0.1095161914180141 absolute error = 1.10925157947861e-13 relative error = 1.012865371882378e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999754 y1[1] (closed_form) = 0.553912510085987 y1[1] (numeric) = 0.5539125100862061 absolute error = 2.191580250610059e-13 relative error = 3.956545863659674e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1050106417715262 y2[1] (numeric) = 0.105010641771419 absolute error = 1.07178155239751e-13 relative error = 1.020640893452882e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999757 y1[1] (closed_form) = 0.562884558692754 y1[1] (numeric) = 0.5628845586929713 absolute error = 2.172706459191431e-13 relative error = 3.859950367509345e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.1005945903149283 y2[1] (numeric) = 0.1005945903148248 absolute error = 1.035838081975271e-13 relative error = 1.029715493380315e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.269999999999761 y1[1] (closed_form) = 0.5719003184793903 y1[1] (numeric) = 0.5719003184796054 absolute error = 2.151612221723553e-13 relative error = 3.762215463429737e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.09626847864979693 y2[1] (numeric) = 0.09626847864969701 absolute error = 9.992007221626409e-14 relative error = 1.037931352169289e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999764 y1[1] (closed_form) = 0.5809588878774299 y1[1] (numeric) = 0.5809588878776429 absolute error = 2.130517984255675e-13 relative error = 3.667243980102719e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.09203273938369361 y2[1] (numeric) = 0.09203273938359718 absolute error = 9.642286968869485e-14 relative error = 1.047701832352271e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999767 y1[1] (closed_form) = 0.5900593610374821 y1[1] (numeric) = 0.5900593610376929 absolute error = 2.107203300738547e-13 relative error = 3.571171715729618e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.08788779608701502 y2[1] (numeric) = 0.08788779608692214 absolute error = 9.288403379770216e-14 relative error = 1.056847912146307e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.299999999999771 y1[1] (closed_form) = 0.5992008279198147 y1[1] (numeric) = 0.5992008279200233 absolute error = 2.086109063270669e-13 relative error = 3.4814856156204e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.08383406325063691 y2[1] (numeric) = 0.08383406325054746 absolute error = 8.945622020917199e-14 relative error = 1.067062918586287e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999774 y1[1] (closed_form) = 0.6083823743853569 y1[1] (numeric) = 0.6083823743855633 absolute error = 2.063904602778166e-13 relative error = 3.392446411458435e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.0798719462444647 y2[1] (numeric) = 0.07987194624437864 absolute error = 8.605616219625745e-14 relative error = 1.077426634038248e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999777 y1[1] (closed_form) = 0.6176030822871137 y1[1] (numeric) = 0.6176030822873179 absolute error = 2.041700142285663e-13 relative error = 3.305845130702423e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.07600184127689724 y2[1] (numeric) = 0.07600184127681459 absolute error = 8.26561041833429e-14 relative error = 1.087553969675579e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.329999999999781 y1[1] (closed_form) = 0.6268620295619789 y1[1] (numeric) = 0.6268620295621807 absolute error = 2.018385458768535e-13 relative error = 3.219824081830073e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.07222413535520633 y2[1] (numeric) = 0.07222413535512692 absolute error = 7.940870183631432e-14 relative error = 1.099475977743084e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999784 y1[1] (closed_form) = 0.6361582903229406 y1[1] (numeric) = 0.6361582903231401 absolute error = 1.995070775251406e-13 relative error = 3.136123203296816e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.06853920624683596 y2[1] (numeric) = 0.06853920624675978 absolute error = 7.617517727709355e-14 relative error = 1.111410263532343e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999787 y1[1] (closed_form) = 0.6454909349516695 y1[1] (numeric) = 0.6454909349518666 absolute error = 1.970645868709653e-13 relative error = 3.052941198712888e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.06494742244162621 y2[1] (numeric) = 0.06494742244155323 absolute error = 7.298328608129623e-14 relative error = 1.123728753776064e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.359999999999791 y1[1] (closed_form) = 0.6548590301914802 y1[1] (numeric) = 0.6548590301916749 absolute error = 1.947331185192525e-13 relative error = 2.973664705552166e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.06144914311496452 y2[1] (numeric) = 0.06144914311489463 absolute error = 6.989547829405751e-14 relative error = 1.137452448495349e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999794 y1[1] (closed_form) = 0.6642616392406552 y1[1] (numeric) = 0.6642616392408472 absolute error = 1.920685832601521e-13 relative error = 2.89145980911548e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.05804471809186817 y2[1] (numeric) = 0.05804471809180143 absolute error = 6.674522046168363e-14 relative error = 1.149893093735851e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y1[1] (closed_form) = 0.673697821846125 y1[1] (numeric) = 0.6736978218463148 absolute error = 1.897371149084393e-13 relative error = 2.816353396965203e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.05473448781200274 y2[1] (numeric) = 0.05473448781193892 absolute error = 6.381700723423478e-14 relative error = 1.165937780461706e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999801 y1[1] (closed_form) = 0.6831666343974928 y1[1] (numeric) = 0.68316663439768 absolute error = 1.871836019518014e-13 relative error = 2.739940631276362e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.05151878329563742 y2[1] (numeric) = 0.0515187832955766 absolute error = 6.081246617384295e-14 relative error = 1.180394067633047e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999804 y1[1] (closed_form) = 0.6926671300213938 y1[1] (numeric) = 0.6926671300215783 absolute error = 1.84519066692701e-13 relative error = 2.663892347353078e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.04839792611054428 y2[1] (numeric) = 0.04839792611048635 absolute error = 5.792588630981754e-14 relative error = 1.196867117353556e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y1[1] (closed_form) = 0.702198358676183 y1[1] (numeric) = 0.7021983586763648 absolute error = 1.818545314336006e-13 relative error = 2.589788614380149e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.045372228339841 y2[1] (numeric) = 0.04537222833978595 absolute error = 5.505318423359995e-14 relative error = 1.213367433074874e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.419999999999811 y1[1] (closed_form) = 0.7117593672469372 y1[1] (numeric) = 0.7117593672471164 absolute error = 1.791899961745003e-13 relative error = 2.517564283946153e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.0424419925507834 y2[1] (numeric) = 0.04244199255073108 absolute error = 5.232619892936441e-14 relative error = 1.232887425507985e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999814 y1[1] (closed_form) = 0.721349199640767 y1[1] (numeric) = 0.7213491996409437 absolute error = 1.766364832178624e-13 relative error = 2.44869590630762e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.03960751176450839 y2[1] (numeric) = 0.03960751176445879 absolute error = 4.959227473122496e-14 relative error = 1.252092659243082e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y1[1] (closed_form) = 0.7309668968824248 y1[1] (numeric) = 0.7309668968825985 absolute error = 1.73749903353837e-13 relative error = 2.376987304006251e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.03686906942673251 y2[1] (numeric) = 0.03686906942668566 absolute error = 4.685835053308551e-14 relative error = 1.27093933374706e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.449999999999821 y1[1] (closed_form) = 0.7406114972102006 y1[1] (numeric) = 0.7406114972103714 absolute error = 1.708633234898116e-13 relative error = 2.307057399641166e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.03422693937940768 y2[1] (numeric) = 0.03422693937936341 absolute error = 4.427014310692812e-14 relative error = 1.29342979271944e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999824 y1[1] (closed_form) = 0.7502820361720991 y1[1] (numeric) = 0.7502820361722672 absolute error = 1.680877659282487e-13 relative error = 2.240327741096188e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.03168138583333679 y2[1] (numeric) = 0.03168138583329504 absolute error = 4.17582635137137e-14 relative error = 1.318069346252319e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y1[1] (closed_form) = 0.7599775467222828 y1[1] (numeric) = 0.7599775467224482 absolute error = 1.654232306691483e-13 relative error = 2.17668576371242e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.02923266334175312 y2[1] (numeric) = 0.02923266334171384 absolute error = 3.927760894306687e-14 relative error = 1.343620609722773e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.479999999999831 y1[1] (closed_form) = 0.7696970593177762 y1[1] (numeric) = 0.7696970593179389 absolute error = 1.626476731075854e-13 relative error = 2.113138814012734e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.02688101677486521 y2[1] (numeric) = 0.0268810167748284 absolute error = 3.681083216022785e-14 relative error = 1.369398801709294e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999834 y1[1] (closed_form) = 0.7794396020154195 y1[1] (numeric) = 0.7794396020155792 absolute error = 1.596500709410975e-13 relative error = 2.048267377334764e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.02462668129537016 y2[1] (numeric) = 0.02462668129533568 absolute error = 3.447242491461111e-14 relative error = 1.399799855333815e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y1[1] (closed_form) = 0.7892042005690614 y1[1] (numeric) = 0.7892042005692181 absolute error = 1.567634910770721e-13 relative error = 1.986348919126845e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.02246988233493719 y2[1] (numeric) = 0.02246988233490504 absolute error = 3.214442600985024e-14 relative error = 1.430556045229958e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.509999999999841 y1[1] (closed_form) = 0.7989898785269839 y1[1] (numeric) = 0.7989898785271377 absolute error = 1.537658889105842e-13 relative error = 1.924503589382968e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.02041083557166512 y2[1] (numeric) = 0.02041083557163519 absolute error = 2.992744940755188e-14 relative error = 1.466253025383144e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999844 y1[1] (closed_form) = 0.8087956573295458 y1[1] (numeric) = 0.8087956573296965 absolute error = 1.506572644416337e-13 relative error = 1.862735823026904e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.01844974690851431 y2[1] (numeric) = 0.0184497469084866 absolute error = 2.771047280525352e-14 relative error = 1.501943248471637e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y1[1] (closed_form) = 0.8186205564070383 y1[1] (numeric) = 0.8186205564071861 absolute error = 1.477706845776083e-13 relative error = 1.805118176193625e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.01658681245271698 y2[1] (numeric) = 0.01658681245269134 absolute error = 2.564268242188916e-14 relative error = 1.545968069210838e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.539999999999851 y1[1] (closed_form) = 0.8284635932777412 y1[1] (numeric) = 0.8284635932778858 absolute error = 1.445510378061954e-13 relative error = 1.744808570697625e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.01482221849616616 y2[1] (numeric) = 0.01482221849614255 absolute error = 2.361652540194825e-14 relative error = 1.593319205762402e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999854 y1[1] (closed_form) = 0.8383237836461698 y1[1] (numeric) = 0.838323783646311 absolute error = 1.412203687323199e-13 relative error = 1.684556390826729e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.01315614149678701 y2[1] (numeric) = 0.0131561414967654 absolute error = 2.161465451067102e-14 relative error = 1.642932657417051e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999858 y1[1] (closed_form) = 0.8482001415015039 y1[1] (numeric) = 0.848200141501642 absolute error = 1.381117442633695e-13 relative error = 1.628291926701177e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.01158874806089116 y2[1] (numeric) = 0.01158874806087142 absolute error = 1.973941843314009e-14 relative error = 1.703326220349478e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.569999999999861 y1[1] (closed_form) = 0.8580916792161886 y1[1] (numeric) = 0.8580916792163233 absolute error = 1.34781075189494e-13 relative error = 1.570707168639694e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.01012019492651595 y2[1] (numeric) = 0.01012019492649807 absolute error = 1.787979486689295e-14 relative error = 1.766744118736889e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999864 y1[1] (closed_form) = 0.867997407644695 y1[1] (numeric) = 0.8679974076448267 absolute error = 1.316724507205436e-13 relative error = 1.516968248532399e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.008750628947751027 y2[1] (numeric) = 0.00875062894773497 absolute error = 1.605660049364133e-14 relative error = 1.834908163688964e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999868 y1[1] (closed_form) = 0.8779163362224353 y1[1] (numeric) = 0.8779163362225637 absolute error = 1.284528039491306e-13 relative error = 1.46315541298442e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.007480187080053047 y2[1] (numeric) = 0.007480187080038712 absolute error = 1.433488744373435e-14 relative error = 1.916380872606824e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.599999999999871 y1[1] (closed_form) = 0.8878474730648171 y1[1] (numeric) = 0.8878474730649425 absolute error = 1.253441794801802e-13 relative error = 1.411776045805443e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.006308996366550024 y2[1] (numeric) = 0.006308996366537364 absolute error = 1.266001192767874e-14 relative error = 2.006660202691108e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999874 y1[1] (closed_form) = 0.8977898250664325 y1[1] (numeric) = 0.8977898250665546 absolute error = 1.221245327087672e-13 relative error = 1.360279759237977e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.005237173925337402 y2[1] (numeric) = 0.005237173925326285 absolute error = 1.111697539579737e-14 relative error = 2.122705022648482e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999878 y1[1] (closed_form) = 0.9077423980003663 y1[1] (numeric) = 0.9077423980004852 absolute error = 1.189048859373543e-13 relative error = 1.309896796704502e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.004264826937765975 y2[1] (numeric) = 0.004264826937756415 absolute error = 9.560061076108184e-15 relative error = 2.241605864812884e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.629999999999881 y1[1] (closed_form) = 0.917704196617619 y1[1] (numeric) = 0.9177041966177348 absolute error = 1.157962614684038e-13 relative error = 1.261803769615459e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.003392052637724352 y2[1] (numeric) = 0.003392052637716227 absolute error = 8.12501108060637e-15 relative error = 2.39530807695757e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999884 y1[1] (closed_form) = 0.9276742247466303 y1[1] (numeric) = 0.9276742247467429 absolute error = 1.125766146969909e-13 relative error = 1.213536085124476e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.002618938301915064 y2[1] (numeric) = 0.002618938301908413 absolute error = 6.650929806895078e-15 relative error = 2.539551925309457e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999888 y1[1] (closed_form) = 0.9376514853928958 y1[1] (numeric) = 0.9376514853930048 absolute error = 1.090239010181904e-13 relative error = 1.162733731206185e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.001945561241127658 y2[1] (numeric) = 0.001945561241122292 absolute error = 5.366150232499756e-15 relative error = 2.758150254571018e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.659999999999891 y1[1] (closed_form) = 0.9476349808386649 y1[1] (numeric) = 0.9476349808387707 absolute error = 1.058042542467774e-13 relative error = 1.116508533202729e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.001371988792506884 y2[1] (numeric) = 0.001371988792502798 absolute error = 4.085707466794375e-15 relative error = 2.977945220185809e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999894 y1[1] (closed_form) = 0.957623712742713 y1[1] (numeric) = 0.9576237127428153 absolute error = 1.023625628704394e-13 relative error = 1.068922599851508e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.0008982783128197447 y2[1] (numeric) = 0.000898278312816819 absolute error = 2.925719562452134e-15 relative error = 3.257030166149887e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999898 y1[1] (closed_form) = 0.9676166822401732 y1[1] (numeric) = 0.9676166822402724 absolute error = 9.925393840148899e-14 relative error = 1.025756792159698e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.0005244771727193065 y2[1] (numeric) = 0.0005244771727175654 absolute error = 1.741120268794472e-15 relative error = 3.319725546427732e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.689999999999901 y1[1] (closed_form) = 0.9776128900424234 y1[1] (numeric) = 0.9776128900425194 absolute error = 9.603429163007604e-14 relative error = 9.823345478383438e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.0002506227520082671 y2[1] (numeric) = 0.0002506227520075479 absolute error = 7.192597212268836e-16 relative error = 2.869889965948335e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999904 y1[1] (closed_form) = 0.9876113365370135 y1[1] (numeric) = 0.9876113365371062 absolute error = 9.270362255620057e-14 relative error = 9.38665030732221e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 7.674243590027885e-05 y2[1] (numeric) = 7.674243590062711e-05 absolute error = 3.482592903295001e-16 relative error = 4.538027575539007e-10 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999908 y1[1] (closed_form) = 0.9976110218876261 y1[1] (numeric) = 0.9976110218877154 absolute error = 8.93729534823251e-14 relative error = 8.958697480428634e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 2.853612282249784e-06 y2[1] (numeric) = 2.853612283512045e-06 absolute error = 1.26226035645962e-15 relative error = 4.423377220203354e-08 % Desired digits = 8 Estimated correct digits = 6 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.719999999999911 y1[1] (closed_form) = 1.007610946134059 y1[1] (numeric) = 1.007610946134145 absolute error = 8.615330671091215e-14 relative error = 8.550255139789813e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 2.896366997484634e-05 y2[1] (numeric) = 2.896366997699087e-05 absolute error = 2.144528180253805e-15 relative error = 7.404200441850884e-09 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999914 y1[1] (closed_form) = 1.017610109292221 y1[1] (numeric) = 1.017610109292304 absolute error = 8.237854842718662e-14 relative error = 8.095295798946358e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.0001550699979940839 y2[1] (numeric) = 0.0001550699979970525 absolute error = 2.968518443210999e-15 relative error = 1.914308687438205e-09 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999918 y1[1] (closed_form) = 1.027607511454129 y1[1] (numeric) = 1.027607511454208 absolute error = 7.904787935331115e-14 relative error = 7.69241937920962e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.0003811599858123405 y2[1] (numeric) = 0.0003811599858159826 absolute error = 3.642106147921931e-15 relative error = 9.555321344027644e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.749999999999921 y1[1] (closed_form) = 1.037602152887898 y1[1] (numeric) = 1.037602152887973 absolute error = 7.549516567451064e-14 relative error = 7.275926082496008e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.0007072110246191254 y2[1] (numeric) = 0.000707211024623407 absolute error = 4.281514379145257e-15 relative error = 6.054083194547347e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999924 y1[1] (closed_form) = 1.047593034137712 y1[1] (numeric) = 1.047593034137785 absolute error = 7.216449660063518e-14 relative error = 6.888600272150026e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.001133190509582271 y2[1] (numeric) = 0.001133190509587154 absolute error = 4.882379223136724e-15 relative error = 4.308524631870167e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999928 y1[1] (closed_form) = 1.057579156123774 y1[1] (numeric) = 1.057579156123843 absolute error = 6.861178292183467e-14 relative error = 6.4876262476002e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.001659055843108215 y2[1] (numeric) = 0.001659055843113708 absolute error = 5.49300188668056e-15 relative error = 3.310920430736983e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.779999999999931 y1[1] (closed_form) = 1.067559520242206 y1[1] (numeric) = 1.067559520242271 absolute error = 6.461498003318411e-14 relative error = 6.052588057902792e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.002284754439102032 y2[1] (numeric) = 0.002284754439107933 absolute error = 5.900228222666115e-15 relative error = 2.582434296521187e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999934 y1[1] (closed_form) = 1.077533128464913 y1[1] (numeric) = 1.077533128464975 absolute error = 6.128431095930864e-14 relative error = 5.687464203222796e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.003010223728225347 y2[1] (numeric) = 0.003010223728231644 absolute error = 6.29704621779581e-15 relative error = 2.091886446429741e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999938 y1[1] (closed_form) = 1.087498983439384 y1[1] (numeric) = 1.087498983439442 absolute error = 5.795364188543317e-14 relative error = 5.329075499652034e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.003835391164153878 y2[1] (numeric) = 0.003835391164160488 absolute error = 6.609730124340629e-15 relative error = 1.723352284407422e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.809999999999941 y1[1] (closed_form) = 1.097456088588427 y1[1] (numeric) = 1.097456088588482 absolute error = 5.484501741648273e-14 relative error = 4.997468052414345e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.004760174230831637 y2[1] (numeric) = 0.004760174230838511 absolute error = 6.873841773558098e-15 relative error = 1.444031550155505e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999944 y1[1] (closed_form) = 1.107403448209825 y1[1] (numeric) = 1.107403448209876 absolute error = 5.195843755245733e-14 relative error = 4.691915817713125e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.005784480450722662 y2[1] (numeric) = 0.005784480450729697 absolute error = 7.035171056823941e-15 relative error = 1.216214855725725e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999948 y1[1] (closed_form) = 1.117340067575903 y1[1] (numeric) = 1.117340067575952 absolute error = 4.862776847858186e-14 relative error = 4.352101020066432e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.006908207394058508 y2[1] (numeric) = 0.006908207394065641 absolute error = 7.133182933216631e-15 relative error = 1.03256641358967e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.839999999999951 y1[1] (closed_form) = 1.127264953033008 y1[1] (numeric) = 1.127264953033053 absolute error = 4.485301019485632e-14 relative error = 3.978923506330545e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.008131242689081164 y2[1] (numeric) = 0.008131242689088443 absolute error = 7.278899705198683e-15 relative error = 8.95176787057773e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999954 y1[1] (closed_form) = 1.137177112100862 y1[1] (numeric) = 1.137177112100904 absolute error = 4.107825191113079e-14 relative error = 3.612300271788036e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.009453464033280512 y2[1] (numeric) = 0.009453464033287787 absolute error = 7.275430258246729e-15 relative error = 7.696046901573741e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999958 y1[1] (closed_form) = 1.147075553571821 y1[1] (numeric) = 1.147075553571859 absolute error = 3.774758283725532e-14 relative error = 3.290766917638077e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.01087473920562398 y2[1] (numeric) = 0.01087473920563111 absolute error = 7.1279787627887e-15 relative error = 6.554620417106087e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.869999999999961 y1[1] (closed_form) = 1.156959287609985 y1[1] (numeric) = 1.156959287610019 absolute error = 3.419486915845482e-14 relative error = 2.955581023865901e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.01239492607977855 y2[1] (numeric) = 0.01239492607978557 absolute error = 7.020425907278138e-15 relative error = 5.6639514121278e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999964 y1[1] (closed_form) = 1.166827325850187 y1[1] (numeric) = 1.166827325850217 absolute error = 3.042011087472929e-14 relative error = 2.607079059668426e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.01401387263832377 y2[1] (numeric) = 0.01401387263833056 absolute error = 6.789707684973223e-15 relative error = 4.84499028941179e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999968 y1[1] (closed_form) = 1.176678681496826 y1[1] (numeric) = 1.176678681496853 absolute error = 2.708944180085382e-14 relative error = 2.302195342435708e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.01573141698795288 y2[1] (numeric) = 0.01573141698795934 absolute error = 6.456640777585676e-15 relative error = 4.104297014394933e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.899999999999971 y1[1] (closed_form) = 1.186512369422547 y1[1] (numeric) = 1.186512369422571 absolute error = 2.353672812205332e-14 relative error = 1.983690075941492e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.01754738737566208 y2[1] (numeric) = 0.01754738737566825 absolute error = 6.168676680573526e-15 relative error = 3.515438822037617e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999974 y1[1] (closed_form) = 1.196327406266752 y1[1] (numeric) = 1.196327406266773 absolute error = 2.042810365310288e-14 relative error = 1.707567973958786e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.01946160220592608 y2[1] (numeric) = 0.01946160220593181 absolute error = 5.731526364627371e-15 relative error = 2.945043426528426e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999978 y1[1] (closed_form) = 1.206122810533937 y1[1] (numeric) = 1.206122810533954 absolute error = 1.731947918415244e-14 relative error = 1.435963156727407e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.02147387005885693 y2[1] (numeric) = 0.02147387005886216 absolute error = 5.238864897449957e-15 relative error = 2.439646362342209e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.929999999999981 y1[1] (closed_form) = 1.215897602691836 y1[1] (numeric) = 1.21589760269185 absolute error = 1.398881011027697e-14 relative error = 1.150492449307212e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.02358398970934616 y2[1] (numeric) = 0.02358398970935092 absolute error = 4.756611771128405e-15 relative error = 2.016881719229802e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y1[1] (closed_form) = 1.22565080526938 y1[1] (numeric) = 1.225650805269391 absolute error = 1.110223024625157e-14 relative error = 9.058232735229556e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 0.02579175014718738 y2[1] (numeric) = 0.02579175014719143 absolute error = 4.059252933785729e-15 relative error = 1.573857109587577e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999988 y1[1] (closed_form) = 1.235381442954439 y1[1] (numeric) = 1.235381442954447 absolute error = 7.993605777301127e-15 relative error = 6.470556784618895e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 0.02809693059817631 y2[1] (numeric) = 0.02809693059817973 absolute error = 3.427813588530171e-15 relative error = 1.219995748842637e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.959999999999991 y1[1] (closed_form) = 1.245088542691353 y1[1] (numeric) = 1.245088542691358 absolute error = 4.662936703425657e-15 relative error = 3.745064341646231e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 0.03049930054618899 y2[1] (numeric) = 0.03049930054619169 absolute error = 2.702699175571865e-15 relative error = 8.861511992640037e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y1[1] (closed_form) = 1.254771133778238 y1[1] (numeric) = 1.254771133778239 absolute error = 1.554312234475219e-15 relative error = 1.238721702016713e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 0.03299861975623253 y2[1] (numeric) = 0.03299861975623448 absolute error = 1.949829186997931e-15 relative error = 5.908820433708178e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999998 y1[1] (closed_form) = 1.264428247964053 y1[1] (numeric) = 1.264428247964051 absolute error = 1.77635683940025e-15 relative error = 1.404869625667166e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 0.03559463829846876 y2[1] (numeric) = 0.03559463829846984 absolute error = 1.07552855510562e-15 relative error = 3.021602709057134e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.990000000000001 y1[1] (closed_form) = 1.274058919545428 y1[1] (numeric) = 1.274058919545423 absolute error = 4.884981308350689e-15 relative error = 3.834187911885269e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 0.03828709657320684 y2[1] (numeric) = 0.03828709657320688 absolute error = 4.85722573273506e-17 relative error = 1.268632559653042e-13 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.000000000000004 y1[1] (closed_form) = 1.283662185463231 y1[1] (numeric) = 1.283662185463223 absolute error = 7.993605777301127e-15 relative error = 6.227188015526455e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 0.04107572533686277 y2[1] (numeric) = 0.04107572533686187 absolute error = 8.951173136040325e-16 relative error = 2.179188088008573e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.010000000000008 y1[1] (closed_form) = 1.293237085398871 y1[1] (numeric) = 1.29323708539886 absolute error = 1.088018564132653e-14 relative error = 8.413140764495458e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 0.04396024572888424 y2[1] (numeric) = 0.04396024572888228 absolute error = 1.956768080901838e-15 relative error = 4.451221890272867e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.020000000000011 y1[1] (closed_form) = 1.302782661870335 y1[1] (numeric) = 1.30278266187032 absolute error = 1.443289932012704e-14 relative error = 1.107851658035309e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.04694036929963574 y2[1] (numeric) = 0.04694036929963265 absolute error = 3.087807787238717e-15 relative error = 6.578149753207583e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.030000000000014 y1[1] (closed_form) = 1.312297960327929 y1[1] (numeric) = 1.312297960327912 absolute error = 1.731947918415244e-14 relative error = 1.319782527119412e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.05001579803924361 y2[1] (numeric) = 0.05001579803923936 absolute error = 4.253541963095131e-15 relative error = 8.504396870280263e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.040000000000018 y1[1] (closed_form) = 1.321782029249739 y1[1] (numeric) = 1.321782029249718 absolute error = 2.087219286295294e-14 relative error = 1.579094918910366e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.05318622440739684 y2[1] (numeric) = 0.05318622440739127 absolute error = 5.571931804837504e-15 relative error = 1.047626874612779e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.050000000000021 y1[1] (closed_form) = 1.331233920236774 y1[1] (numeric) = 1.33123392023675 absolute error = 2.398081733190338e-14 relative error = 1.801397708348518e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.05645133136410041 y2[1] (numeric) = 0.05645133136409359 absolute error = 6.820932707540805e-15 relative error = 1.208285534232502e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.060000000000024 y1[1] (closed_form) = 1.340652688107813 y1[1] (numeric) = 1.340652688107785 absolute error = 2.731148640577885e-14 relative error = 2.03717835708263e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.05981079240137976 y2[1] (numeric) = 0.05981079240137156 absolute error = 8.201772594418344e-15 relative error = 1.371286395836003e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.070000000000028 y1[1] (closed_form) = 1.350037390993917 y1[1] (numeric) = 1.350037390993887 absolute error = 3.042011087472929e-14 relative error = 2.253279137130681e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.06326427157593073 y2[1] (numeric) = 0.06326427157592102 absolute error = 9.71445146547012e-15 relative error = 1.535535180202097e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.080000000000031 y1[1] (closed_form) = 1.359387090432619 y1[1] (numeric) = 1.359387090432585 absolute error = 3.352873534367973e-14 relative error = 2.466459743486998e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.06681142354271352 y2[1] (numeric) = 0.06681142354270235 absolute error = 1.117161918529064e-14 relative error = 1.672112131864464e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.090000000000034 y1[1] (closed_form) = 1.368700851461765 y1[1] (numeric) = 1.368700851461729 absolute error = 3.663735981263017e-14 relative error = 2.676798204187691e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.07045189358948767 y2[1] (numeric) = 0.07045189358947487 absolute error = 1.279532035880493e-14 relative error = 1.816178346228888e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.100000000000038 y1[1] (closed_form) = 1.377977742713016 y1[1] (numeric) = 1.377977742712976 absolute error = 3.97459842815806e-14 relative error = 2.884370556183817e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.07418531767228198 y2[1] (numeric) = 0.0741853176722676 absolute error = 1.437738816889578e-14 relative error = 1.938036881153322e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.110000000000041 y1[1] (closed_form) = 1.387216836504975 y1[1] (numeric) = 1.387216836504932 absolute error = 4.263256414560601e-14 relative error = 3.073244428968774e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.07801132245179954 y2[1] (numeric) = 0.07801132245178344 absolute error = 1.609823385706477e-14 relative error = 2.063576587489759e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.120000000000045 y1[1] (closed_form) = 1.396417208935963 y1[1] (numeric) = 1.396417208935918 absolute error = 4.507505479978136e-14 relative error = 3.227907427045208e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.0819295253307506 y2[1] (numeric) = 0.08192952533073276 absolute error = 1.783295733304158e-14 relative error = 2.176621585569999e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.130000000000048 y1[1] (closed_form) = 1.405577939976405 y1[1] (numeric) = 1.405577939976357 absolute error = 4.796163466380676e-14 relative error = 3.412235871076057e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.08593953449211245 y2[1] (numeric) = 0.08593953449209285 absolute error = 1.959543638463401e-14 relative error = 2.280142253555316e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.140000000000051 y1[1] (closed_form) = 1.414698113560829 y1[1] (numeric) = 1.414698113560778 absolute error = 5.10702591327572e-14 relative error = 3.609975771029492e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.09004094893831072 y2[1] (numeric) = 0.09004094893828919 absolute error = 2.152444888992022e-14 relative error = 2.390517774825669e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.150000000000055 y1[1] (closed_form) = 1.423776817679477 y1[1] (numeric) = 1.423776817679423 absolute error = 5.373479439185758e-14 relative error = 3.774102354007736e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.09423335853131853 y2[1] (numeric) = 0.09423335853129501 absolute error = 2.35228503342455e-14 relative error = 2.496233892207892e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.160000000000058 y1[1] (closed_form) = 1.432813144469504 y1[1] (numeric) = 1.432813144469447 absolute error = 5.684341886080801e-14 relative error = 3.967259728193948e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.09851634403367016 y2[1] (numeric) = 0.0985163440336447 absolute error = 2.545186283953171e-14 relative error = 2.583516784873074e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.170000000000061 y1[1] (closed_form) = 1.44180619030576 y1[1] (numeric) = 1.441806190305701 absolute error = 5.928590951498336e-14 relative error = 4.111919473893418e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1028894771503847 y2[1] (numeric) = 0.1028894771503572 absolute error = 2.749189764728044e-14 relative error = 2.671983414503886e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.180000000000065 y1[1] (closed_form) = 1.450755055891157 y1[1] (numeric) = 1.450755055891095 absolute error = 6.17284001691587e-14 relative error = 4.254915391712404e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1073523205717946 y2[1] (numeric) = 0.107352320571765 absolute error = 2.958744360626042e-14 relative error = 2.756106570278849e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.190000000000068 y1[1] (closed_form) = 1.459658846346592 y1[1] (numeric) = 1.459658846346527 absolute error = 6.461498003318411e-14 relative error = 4.426717941312806e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1119044280172767 y2[1] (numeric) = 0.111904428017245 absolute error = 3.171074514085603e-14 relative error = 2.833734616467569e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.200000000000071 y1[1] (closed_form) = 1.46851667130044 y1[1] (numeric) = 1.468516671300373 absolute error = 6.683542608243442e-14 relative error = 4.551220111328293e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1165453442798801 y2[1] (numeric) = 0.1165453442798462 absolute error = 3.38895578266829e-14 relative error = 2.907843126302684e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.210000000000075 y1[1] (closed_form) = 1.477327644977587 y1[1] (numeric) = 1.477327644977518 absolute error = 6.927791673660977e-14 relative error = 4.689407726994833e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1212746052718457 y2[1] (numeric) = 0.1212746052718096 absolute error = 3.617939281497229e-14 relative error = 2.98326205505873e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.220000000000078 y1[1] (closed_form) = 1.486090886288008 y1[1] (numeric) = 1.486090886287937 absolute error = 7.194245199571014e-14 relative error = 4.841053307002618e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1260917380710156 y2[1] (numeric) = 0.1260917380709771 absolute error = 3.852473895449293e-14 relative error = 3.055294466065301e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.230000000000081 y1[1] (closed_form) = 1.494805518914875 y1[1] (numeric) = 1.494805518914801 absolute error = 7.438494264988549e-14 relative error = 4.976228794223598e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1309962609681239 y2[1] (numeric) = 0.130996260968083 absolute error = 4.091171845743702e-14 relative error = 3.123121084150052e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.240000000000085 y1[1] (closed_form) = 1.503470671402187 y1[1] (numeric) = 1.50347067140211 absolute error = 7.704947790898586e-14 relative error = 5.124774255631268e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1359876835149681 y2[1] (numeric) = 0.1359876835149248 absolute error = 4.338196468722799e-14 relative error = 3.190139251283955e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.250000000000088 y1[1] (closed_form) = 1.512085477241916 y1[1] (numeric) = 1.512085477241837 absolute error = 7.882583474838611e-14 relative error = 5.21305415168503e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.141065506573453 y2[1] (numeric) = 0.1410655065734072 absolute error = 4.576894419017208e-14 relative error = 3.244517054659293e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.260000000000091 y1[1] (closed_form) = 1.520649074960658 y1[1] (numeric) = 1.520649074960576 absolute error = 8.149037000748649e-14 relative error = 5.358920170953632e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1462292223655043 y2[1] (numeric) = 0.1462292223654559 absolute error = 4.835021272242557e-14 relative error = 3.306467198572169e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.270000000000095 y1[1] (closed_form) = 1.529160608205776 y1[1] (numeric) = 1.529160608205692 absolute error = 8.393286066166183e-14 relative error = 5.488819173817429e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1514783145238457 y2[1] (numeric) = 0.1514783145237948 absolute error = 5.093148125467906e-14 relative error = 3.362295217950911e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.280000000000098 y1[1] (closed_form) = 1.537619225831039 y1[1] (numeric) = 1.537619225830952 absolute error = 8.637535131583718e-14 relative error = 5.617473420258114e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1568122581436359 y2[1] (numeric) = 0.1568122581435822 absolute error = 5.362377208939506e-14 relative error = 3.419616088958881e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.290000000000101 y1[1] (closed_form) = 1.546024081981733 y1[1] (numeric) = 1.546024081981645 absolute error = 8.815170815523743e-14 relative error = 5.70183279695374e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1622305198349575 y2[1] (numeric) = 0.1622305198349013 absolute error = 5.620504062164855e-14 relative error = 3.464517075999498e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.300000000000105 y1[1] (closed_form) = 1.554374336179248 y1[1] (numeric) = 1.554374336179158 absolute error = 9.059419880941277e-14 relative error = 5.828338560458938e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1677325577761568 y2[1] (numeric) = 0.1677325577760979 absolute error = 5.892508703198018e-14 relative error = 3.513038125288541e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.310000000000108 y1[1] (closed_form) = 1.562669153405122 y1[1] (numeric) = 1.562669153405029 absolute error = 9.281464485866309e-14 relative error = 5.939494272118705e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1733178217680247 y2[1] (numeric) = 0.1733178217679629 absolute error = 6.175615574477433e-14 relative error = 3.563174006850327e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.320000000000111 y1[1] (closed_form) = 1.570907704184545 y1[1] (numeric) = 1.57090770418445 absolute error = 9.459100169806334e-14 relative error = 6.021423247597182e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1789857532888164 y2[1] (numeric) = 0.1789857532887517 absolute error = 6.467049118441537e-14 relative error = 3.613164176260513e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.330000000000115 y1[1] (closed_form) = 1.579089164669304 y1[1] (numeric) = 1.579089164669207 absolute error = 9.658940314238862e-14 relative error = 6.116779552636382e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1847357855501028 y2[1] (numeric) = 0.1847357855500354 absolute error = 6.747380432159389e-14 relative error = 3.652449043409301e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.340000000000118 y1[1] (closed_form) = 1.587212716720169 y1[1] (numeric) = 1.58721271672007 absolute error = 9.85878045867139e-14 relative error = 6.211379454572206e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1905673435534498 y2[1] (numeric) = 0.1905673435533794 absolute error = 7.041589533685055e-14 relative error = 3.695066217738428e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.350000000000121 y1[1] (closed_form) = 1.595277547988704 y1[1] (numeric) = 1.595277547988603 absolute error = 1.008082506359642e-13 relative error = 6.31916689124481e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1964798441479166 y2[1] (numeric) = 0.1964798441478432 absolute error = 7.344125307895411e-14 relative error = 3.737851757642125e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.360000000000125 y1[1] (closed_form) = 1.603282851998503 y1[1] (numeric) = 1.6032828519984 absolute error = 1.025846074753645e-13 relative error = 6.39840982191583e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2024726960883707 y2[1] (numeric) = 0.2024726960882943 absolute error = 7.643885524544203e-14 relative error = 3.775267318615628e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.370000000000128 y1[1] (closed_form) = 1.611227828225836 y1[1] (numeric) = 1.611227828225732 absolute error = 1.043609643147647e-13 relative error = 6.47710786063565e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2085453000946121 y2[1] (numeric) = 0.2085453000945327 absolute error = 7.943645741192995e-14 relative error = 3.809074449335059e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.380000000000131 y1[1] (closed_form) = 1.619111682179702 y1[1] (numeric) = 1.619111682179595 absolute error = 1.0635936575909e-13 relative error = 6.568995019287706e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2146970489113008 y2[1] (numeric) = 0.2146970489112183 absolute error = 8.251732630526476e-14 relative error = 3.84343085867732e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.390000000000135 y1[1] (closed_form) = 1.626933625481274 y1[1] (numeric) = 1.626933625481166 absolute error = 1.079136779935652e-13 relative error = 6.632949021607599e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2209273273686815 y2[1] (numeric) = 0.2209273273685957 absolute error = 8.573697307667771e-14 relative error = 3.880777181249319e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.400000000000138 y1[1] (closed_form) = 1.634692875942741 y1[1] (numeric) = 1.634692875942631 absolute error = 1.099120794378905e-13 relative error = 6.723714347534749e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2272355124441002 y2[1] (numeric) = 0.2272355124440114 absolute error = 8.887335312124378e-14 relative error = 3.911067956119163e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.410000000000141 y1[1] (closed_form) = 1.642388657645523 y1[1] (numeric) = 1.642388657645411 absolute error = 1.116884362772907e-13 relative error = 6.800365781714775e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2336209733243064 y2[1] (numeric) = 0.2336209733242143 absolute error = 9.214851104388799e-14 relative error = 3.944359521007983e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.420000000000145 y1[1] (closed_form) = 1.650020201017862 y1[1] (numeric) = 1.650020201017748 absolute error = 1.13464793116691e-13 relative error = 6.876569938155728e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.240083071468533 y2[1] (numeric) = 0.2400830714684377 absolute error = 9.528489108845406e-14 relative error = 3.968830059762992e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.430000000000148 y1[1] (closed_form) = 1.657586742911781 y1[1] (numeric) = 1.657586742911666 absolute error = 1.152411499560912e-13 relative error = 6.952345055176672e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.246621160672351 y2[1] (numeric) = 0.2466211606722523 absolute error = 9.867107131356079e-14 relative error = 4.000916670919834e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.440000000000151 y1[1] (closed_form) = 1.665087526679396 y1[1] (numeric) = 1.665087526679279 absolute error = 1.167954621905665e-13 relative error = 7.014373738267445e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2532345871322881 y2[1] (numeric) = 0.2532345871321861 absolute error = 1.020294959630519e-13 relative error = 4.029050577903577e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.450000000000155 y1[1] (closed_form) = 1.67252180224858 y1[1] (numeric) = 1.672521802248462 absolute error = 1.181277298201167e-13 relative error = 7.062851417619954e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2599226895112096 y2[1] (numeric) = 0.2599226895111042 absolute error = 1.053601650369274e-13 relative error = 4.05351934588933e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.460000000000158 y1[1] (closed_form) = 1.679888826197973 y1[1] (numeric) = 1.679888826197853 absolute error = 1.201261312644419e-13 relative error = 7.150838162089496e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.266684799004451 y2[1] (numeric) = 0.2666847990043421 absolute error = 1.088573675644966e-13 relative error = 4.081873731493776e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.470000000000161 y1[1] (closed_form) = 1.687187861831318 y1[1] (numeric) = 1.687187861831196 absolute error = 1.219024881038422e-13 relative error = 7.225187595382889e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.273520239406698 y2[1] (numeric) = 0.2735202394065857 absolute error = 1.123545700920658e-13 relative error = 4.107724179233607e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.480000000000165 y1[1] (closed_form) = 1.694418179251135 y1[1] (numeric) = 1.694418179251011 absolute error = 1.234568003383174e-13 relative error = 7.286088041907128e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2804283271796066 y2[1] (numeric) = 0.2804283271794908 absolute error = 1.158517726196351e-13 relative error = 4.131243579591558e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.490000000000168 y1[1] (closed_form) = 1.701579055431706 y1[1] (numeric) = 1.701579055431581 absolute error = 1.247890679678676e-13 relative error = 7.333721437715247e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2874083715201563 y2[1] (numeric) = 0.2874083715200369 absolute error = 1.194044862984356e-13 relative error = 4.154523602318299e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.500000000000171 y1[1] (closed_form) = 1.708669774291381 y1[1] (numeric) = 1.708669774291255 absolute error = 1.258992909924928e-13 relative error = 7.368263481146068e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2944596744297295 y2[1] (numeric) = 0.2944596744296066 absolute error = 1.229016888260048e-13 relative error = 4.173803732685113e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.510000000000175 y1[1] (closed_form) = 1.715689626764183 y1[1] (numeric) = 1.715689626764056 absolute error = 1.270095140171179e-13 relative error = 7.402825781295874e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3015815307839116 y2[1] (numeric) = 0.3015815307837851 absolute error = 1.265099136560366e-13 relative error = 4.194882668285252e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.520000000000178 y1[1] (closed_form) = 1.722637910870715 y1[1] (numeric) = 1.722637910870587 absolute error = 1.283417816466681e-13 relative error = 7.450305188151652e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3087732284030019 y2[1] (numeric) = 0.3087732284028716 absolute error = 1.302846719397621e-13 relative error = 4.219429016356247e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.530000000000181 y1[1] (closed_form) = 1.729513931788356 y1[1] (numeric) = 1.729513931788227 absolute error = 1.290079154614432e-13 relative error = 7.459200708955616e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3160340481232315 y2[1] (numeric) = 0.3160340481230975 absolute error = 1.340039190722564e-13 relative error = 4.240173483459734e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.540000000000185 y1[1] (closed_form) = 1.736317001920744 y1[1] (numeric) = 1.736317001920614 absolute error = 1.301181384860683e-13 relative error = 7.49391605001445e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3233632638686792 y2[1] (numeric) = 0.3233632638685415 absolute error = 1.377231662047507e-13 relative error = 4.259085109330209e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.550000000000188 y1[1] (closed_form) = 1.743046440966536 y1[1] (numeric) = 1.743046440966405 absolute error = 1.312283615106935e-13 relative error = 7.528678434862936e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3307601427238779 y2[1] (numeric) = 0.3307601427237364 absolute error = 1.414979244884762e-13 relative error = 4.277961767799822e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.560000000000191 y1[1] (closed_form) = 1.749701575987434 y1[1] (numeric) = 1.749701575987302 absolute error = 1.321165399303936e-13 relative error = 7.550804191042374e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3382239450071063 y2[1] (numeric) = 0.338223945006961 absolute error = 1.452726827722017e-13 relative error = 4.295162566599165e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.570000000000195 y1[1] (closed_form) = 1.756281741475483 y1[1] (numeric) = 1.75628174147535 absolute error = 1.325606291402437e-13 relative error = 7.547799764112858e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3457539243443557 y2[1] (numeric) = 0.3457539243442066 absolute error = 1.491029522071585e-13 relative error = 4.312400863993045e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.580000000000198 y1[1] (closed_form) = 1.762786279419617 y1[1] (numeric) = 1.762786279419483 absolute error = 1.334488075599438e-13 relative error = 7.570333915004194e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3533493277439677 y2[1] (numeric) = 0.3533493277438146 absolute error = 1.530442439445778e-13 relative error = 4.331244803031625e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.590000000000201 y1[1] (closed_form) = 1.769214539371462 y1[1] (numeric) = 1.769214539371327 absolute error = 1.343369859796439e-13 relative error = 7.59302973099967e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3610093956719314 y2[1] (numeric) = 0.3610093956717744 absolute error = 1.569300245307659e-13 relative error = 4.346978954347677e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.600000000000205 y1[1] (closed_form) = 1.775565878510379 y1[1] (numeric) = 1.775565878510244 absolute error = 1.34781075189494e-13 relative error = 7.590880001736086e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3687333621278376 y2[1] (numeric) = 0.3687333621276767 absolute error = 1.608713162681852e-13 relative error = 4.362808815016095e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.610000000000208 y1[1] (closed_form) = 1.781839661707748 y1[1] (numeric) = 1.781839661707613 absolute error = 1.354472090042691e-13 relative error = 7.601537439931826e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3765204547214772 y2[1] (numeric) = 0.3765204547213125 absolute error = 1.647570968543732e-13 relative error = 4.375780778663106e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.620000000000211 y1[1] (closed_form) = 1.788035261590478 y1[1] (numeric) = 1.788035261590342 absolute error = 1.358912982141192e-13 relative error = 7.600034581714137e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3843698947500802 y2[1] (numeric) = 0.3843698947499115 absolute error = 1.686983885917925e-13 relative error = 4.388959460560284e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.630000000000215 y1[1] (closed_form) = 1.794152058603742 y1[1] (numeric) = 1.794152058603606 absolute error = 1.358912982141192e-13 relative error = 7.574123807536887e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3922808972761849 y2[1] (numeric) = 0.3922808972760122 absolute error = 1.726396803292118e-13 relative error = 4.400919890005888e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.640000000000218 y1[1] (closed_form) = 1.800189441072937 y1[1] (numeric) = 1.8001894410728 absolute error = 1.367794766338193e-13 relative error = 7.598060154841087e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.4002526712061311 y2[1] (numeric) = 0.4002526712059544 absolute error = 1.766919943690937e-13 relative error = 4.414511309484725e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.650000000000222 y1[1] (closed_form) = 1.806146805264847 y1[1] (numeric) = 1.80614680526471 absolute error = 1.367794766338193e-13 relative error = 7.572998841241061e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.4082844193691689 y2[1] (numeric) = 0.4082844193689882 absolute error = 1.807443084089755e-13 relative error = 4.426921524172768e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.660000000000225 y1[1] (closed_form) = 1.812023555448017 y1[1] (numeric) = 1.81202355544788 absolute error = 1.370015212387443e-13 relative error = 7.560692068645386e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.4163753385971752 y2[1] (numeric) = 0.4163753385969903 absolute error = 1.849076447513198e-13 relative error = 4.440888487159173e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.670000000000228 y1[1] (closed_form) = 1.817819103952326 y1[1] (numeric) = 1.817819103952189 absolute error = 1.370015212387443e-13 relative error = 7.536587163204184e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.4245246198049696 y2[1] (numeric) = 0.4245246198047806 absolute error = 1.889599587912016e-13 relative error = 4.451095412982444e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.680000000000232 y1[1] (closed_form) = 1.823532871227753 y1[1] (numeric) = 1.823532871227616 absolute error = 1.370015212387443e-13 relative error = 7.512972395529318e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.4327314480712222 y2[1] (numeric) = 0.4327314480710291 absolute error = 1.930677839823147e-13 relative error = 4.461607420557476e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.690000000000235 y1[1] (closed_form) = 1.829164285902333 y1[1] (numeric) = 1.829164285902197 absolute error = 1.367794766338193e-13 relative error = 7.477703216053416e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.4409950027199456 y2[1] (numeric) = 0.4409950027197483 absolute error = 1.972866314758903e-13 relative error = 4.473670455653155e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.700000000000238 y1[1] (closed_form) = 1.834712784839291 y1[1] (numeric) = 1.834712784839155 absolute error = 1.363353874239692e-13 relative error = 7.430884471430297e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.449314457402561 y2[1] (numeric) = 0.4493144574023596 absolute error = 2.014499678182347e-13 relative error = 4.483496235193397e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.710000000000242 y1[1] (closed_form) = 1.840177813193356 y1[1] (numeric) = 1.84017781319322 absolute error = 1.354472090042691e-13 relative error = 7.360550052998439e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.4576889801805333 y2[1] (numeric) = 0.4576889801803276 absolute error = 2.057243264630415e-13 relative error = 4.494849895269371e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.720000000000245 y1[1] (closed_form) = 1.845558824466248 y1[1] (numeric) = 1.845558824466113 absolute error = 1.352251643993441e-13 relative error = 7.3270579407542e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.466117733608563 y2[1] (numeric) = 0.4661177336083532 absolute error = 2.097766405029233e-13 relative error = 4.500507605211387e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.730000000000248 y1[1] (closed_form) = 1.850855280561323 y1[1] (numeric) = 1.850855280561188 absolute error = 1.35003119794419e-13 relative error = 7.294093774499519e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.4745998748183317 y2[1] (numeric) = 0.4745998748181176 absolute error = 2.141065102989614e-13 relative error = 4.511305663131866e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.740000000000252 y1[1] (closed_form) = 1.856066651837385 y1[1] (numeric) = 1.856066651837251 absolute error = 1.34559030584569e-13 relative error = 7.249687421050548e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.4831345556027864 y2[1] (numeric) = 0.4831345556025681 absolute error = 2.18325357792537e-13 relative error = 4.518934844561921e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.750000000000255 y1[1] (closed_form) = 1.861192417161651 y1[1] (numeric) = 1.861192417161516 absolute error = 1.341149413747189e-13 relative error = 7.205861153208782e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.4917209225009612 y2[1] (numeric) = 0.4917209225007387 absolute error = 2.225442052861126e-13 relative error = 4.525823390923082e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.760000000000258 y1[1] (closed_form) = 1.866232063961857 y1[1] (numeric) = 1.866232063961724 absolute error = 1.332267629550188e-13 relative error = 7.138810093755935e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.5003581168833214 y2[1] (numeric) = 0.5003581168830947 absolute error = 2.26707541628457e-13 relative error = 4.530905644952751e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.770000000000262 y1[1] (closed_form) = 1.871185088277526 y1[1] (numeric) = 1.871185088277393 absolute error = 1.330047183500938e-13 relative error = 7.108047150617689e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.5090452750376265 y2[1] (numeric) = 0.5090452750373956 absolute error = 2.309263891220326e-13 relative error = 4.536460712752189e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.780000000000265 y1[1] (closed_form) = 1.876050994810351 y1[1] (numeric) = 1.876050994810219 absolute error = 1.318944953254686e-13 relative error = 7.03043231182539e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.5177815282553003 y2[1] (numeric) = 0.5177815282550652 absolute error = 2.351452366156082e-13 relative error = 4.541398713236176e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.790000000000268 y1[1] (closed_form) = 1.880829296973736 y1[1] (numeric) = 1.880829296973604 absolute error = 1.316724507205436e-13 relative error = 7.000765616125036e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.5265660029183012 y2[1] (numeric) = 0.526566002918062 absolute error = 2.392530618067212e-13 relative error = 4.543648098828026e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.800000000000272 y1[1] (closed_form) = 1.885519516941445 y1[1] (numeric) = 1.885519516941315 absolute error = 1.305622276959184e-13 relative error = 6.924469703061314e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.5353978205864833 y2[1] (numeric) = 0.5353978205862399 absolute error = 2.434719093002968e-13 relative error = 4.547495337832974e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.810000000000275 y1[1] (closed_form) = 1.890121185695391 y1[1] (numeric) = 1.890121185695261 absolute error = 1.296740492762183e-13 relative error = 6.860620909262501e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.5442760980854395 y2[1] (numeric) = 0.5442760980851918 absolute error = 2.476907567938724e-13 relative error = 4.55082921453204e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.820000000000278 y1[1] (closed_form) = 1.894633843072532 y1[1] (numeric) = 1.894633843072403 absolute error = 1.285638262515931e-13 relative error = 6.785681925912445e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.5531999475948186 y2[1] (numeric) = 0.5531999475945667 absolute error = 2.51909604287448e-13 relative error = 4.553680913794205e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.830000000000282 y1[1] (closed_form) = 1.899057037810891 y1[1] (numeric) = 1.899057037810763 absolute error = 1.27675647831893e-13 relative error = 6.72310758917853e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.5621684767371062 y2[1] (numeric) = 0.56216847673685 absolute error = 2.562394740834861e-13 relative error = 4.558054830301603e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.840000000000285 y1[1] (closed_form) = 1.903390327594681 y1[1] (numeric) = 1.903390327594554 absolute error = 1.270095140171179e-13 relative error = 6.672804425649265e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.5711807886668616 y2[1] (numeric) = 0.571180788666601 absolute error = 2.605693438795242e-13 relative error = 4.561941666275125e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.850000000000288 y1[1] (closed_form) = 1.907633279098534 y1[1] (numeric) = 1.907633279098409 absolute error = 1.254552017826427e-13 relative error = 6.576484230864721e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.5802359821604024 y2[1] (numeric) = 0.5802359821601376 absolute error = 2.647881913730998e-13 relative error = 4.563456929837573e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.860000000000292 y1[1] (closed_form) = 1.911785468030836 y1[1] (numeric) = 1.911785468030712 absolute error = 1.245670233629426e-13 relative error = 6.515742767479461e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.5893331517059248 y2[1] (numeric) = 0.5893331517056557 absolute error = 2.691180611691379e-13 relative error = 4.566484345741115e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.870000000000295 y1[1] (closed_form) = 1.915846479176154 y1[1] (numeric) = 1.91584647917603 absolute error = 1.234568003383174e-13 relative error = 6.443981899395505e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.5984713875940555 y2[1] (numeric) = 0.598471387593782 absolute error = 2.734479309651761e-13 relative error = 4.569106170045617e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.880000000000298 y1[1] (closed_form) = 1.919815906436756 y1[1] (numeric) = 1.919815906436634 absolute error = 1.216804434989172e-13 relative error = 6.33813081196729e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.6076497760088206 y2[1] (numeric) = 0.6076497760085429 absolute error = 2.777778007612142e-13 relative error = 4.571347044439327e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.890000000000302 y1[1] (closed_form) = 1.923693352873226 y1[1] (numeric) = 1.923693352873106 absolute error = 1.201261312644419e-13 relative error = 6.244557173575596e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.6168673991190275 y2[1] (numeric) = 0.6168673991187454 absolute error = 2.821076705572523e-13 relative error = 4.573230340266665e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.900000000000305 y1[1] (closed_form) = 1.92747843074415 y1[1] (numeric) = 1.927478430744032 absolute error = 1.183497744250417e-13 relative error = 6.140134827830466e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.6261233351700466 y2[1] (numeric) = 0.6261233351697599 absolute error = 2.866595849582154e-13 relative error = 4.578324570515529e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.910000000000308 y1[1] (closed_form) = 1.931170761544895 y1[1] (numeric) = 1.931170761544779 absolute error = 1.161293283757914e-13 relative error = 6.013415835008313e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.6354166585759856 y2[1] (numeric) = 0.635416658575695 absolute error = 2.90656387846866e-13 relative error = 4.574264522718807e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.920000000000312 y1[1] (closed_form) = 1.93476997604546 y1[1] (numeric) = 1.934769976045345 absolute error = 1.147970607462412e-13 relative error = 5.933369969947471e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.6447464400122487 y2[1] (numeric) = 0.6447464400119537 absolute error = 2.949862576429041e-13 relative error = 4.575228947945801e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.930000000000315 y1[1] (closed_form) = 1.938275714327392 y1[1] (numeric) = 1.938275714327279 absolute error = 1.130207039068409e-13 relative error = 5.830992106613722e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.6541117465084669 y2[1] (numeric) = 0.6541117465081675 absolute error = 2.994271497414047e-13 relative error = 4.577614625325015e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.940000000000318 y1[1] (closed_form) = 1.941687625819785 y1[1] (numeric) = 1.941687625819674 absolute error = 1.110223024625157e-13 relative error = 5.717825101534641e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.6635116415417952 y2[1] (numeric) = 0.6635116415414914 absolute error = 3.037570195374428e-13 relative error = 4.578020949739567e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.950000000000322 y1[1] (closed_form) = 1.945005369334333 y1[1] (numeric) = 1.945005369334223 absolute error = 1.092459456231154e-13 relative error = 5.616742624237805e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.6729451851305632 y2[1] (numeric) = 0.6729451851302551 absolute error = 3.080868893334809e-13 relative error = 4.578186992655377e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.960000000000325 y1[1] (closed_form) = 1.948228613099449 y1[1] (numeric) = 1.948228613099342 absolute error = 1.068034549689401e-13 relative error = 5.482080195867044e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.6824114339282734 y2[1] (numeric) = 0.682411433927961 absolute error = 3.124167591295191e-13 relative error = 4.578129023001634e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.970000000000328 y1[1] (closed_form) = 1.951357034793443 y1[1] (numeric) = 1.951357034793338 absolute error = 1.048050535246148e-13 relative error = 5.370880451701074e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.6919094413179345 y2[1] (numeric) = 0.6919094413176179 absolute error = 3.166356066230946e-13 relative error = 4.576257927915737e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.980000000000332 y1[1] (closed_form) = 1.954390321576753 y1[1] (numeric) = 1.95439032157665 absolute error = 1.028066520802895e-13 relative error = 5.26029273401987e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.7014382575067226 y2[1] (numeric) = 0.7014382575064017 absolute error = 3.209654764191328e-13 relative error = 4.575819368051173e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.990000000000335 y1[1] (closed_form) = 1.957328170123227 y1[1] (numeric) = 1.957328170123127 absolute error = 1.003641614261142e-13 relative error = 5.127610329125112e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.7109969296209594 y2[1] (numeric) = 0.7109969296206343 absolute error = 3.250733016102458e-13 relative error = 4.572077431945397e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.000000000000338 y1[1] (closed_form) = 1.96017028665046 y1[1] (numeric) = 1.960170286650362 absolute error = 9.836575998178887e-14 relative error = 5.018225235414435e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.720584501801399 y2[1] (numeric) = 0.7205845018010696 absolute error = 3.294031714062839e-13 relative error = 4.571333002344687e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.010000000000342 y1[1] (closed_form) = 1.962916386949168 y1[1] (numeric) = 1.962916386949072 absolute error = 9.592326932761353e-14 relative error = 4.886773067124921e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.7302000152988131 y2[1] (numeric) = 0.7302000152984794 absolute error = 3.336220188998595e-13 relative error = 4.568912789783145e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.020000000000345 y1[1] (closed_form) = 1.965566196411608 y1[1] (numeric) = 1.965566196411515 absolute error = 9.303668946358812e-14 relative error = 4.733327711548891e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.7398425085698648 y2[1] (numeric) = 0.7398425085695269 absolute error = 3.378408663934351e-13 relative error = 4.566388960895076e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.030000000000348 y1[1] (closed_form) = 1.968119450059042 y1[1] (numeric) = 1.968119450058952 absolute error = 9.037215420448774e-14 relative error = 4.591802301520706e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.7495110173732622 y2[1] (numeric) = 0.7495110173729204 absolute error = 3.418376692820857e-13 relative error = 4.560809132333914e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.040000000000352 y1[1] (closed_form) = 1.970575892568234 y1[1] (numeric) = 1.970575892568146 absolute error = 8.79296635503124e-14 relative error = 4.462130277850626e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.7592045748661822 y2[1] (numeric) = 0.7592045748658365 absolute error = 3.457234498682737e-13 relative error = 4.553758780091797e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.050000000000355 y1[1] (closed_form) = 1.97293527829698 y1[1] (numeric) = 1.972935278296895 absolute error = 8.504308368628699e-14 relative error = 4.310485225835459e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.7689222117009534 y2[1] (numeric) = 0.7689222117006036 absolute error = 3.498312750593868e-13 relative error = 4.549631545764762e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.060000000000358 y1[1] (closed_form) = 1.975197371308672 y1[1] (numeric) = 1.97519737130859 absolute error = 8.237854842718662e-14 relative error = 4.170648950013866e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.7786629561219904 y2[1] (numeric) = 0.7786629561216365 absolute error = 3.539391002504999e-13 relative error = 4.545472434097013e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.070000000000362 y1[1] (closed_form) = 1.977361945395895 y1[1] (numeric) = 1.977361945395816 absolute error = 7.971401316808624e-14 relative error = 4.031331408682814e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.7884258340629683 y2[1] (numeric) = 0.7884258340626102 absolute error = 3.58046925441613e-13 relative error = 4.541288602841714e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.080000000000365 y1[1] (closed_form) = 1.979428784103045 y1[1] (numeric) = 1.979428784102968 absolute error = 7.66053886991358e-14 relative error = 3.870075514429212e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.7982098692442287 y2[1] (numeric) = 0.7982098692438666 absolute error = 3.620437283302635e-13 relative error = 4.535695965185928e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.090000000000368 y1[1] (closed_form) = 1.981397680747972 y1[1] (numeric) = 1.981397680747898 absolute error = 7.394085344003543e-14 relative error = 3.731752295789656e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.8080140832704067 y2[1] (numeric) = 0.8080140832700407 absolute error = 3.660405312189141e-13 relative error = 4.530125635154511e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.100000000000372 y1[1] (closed_form) = 1.983268438442652 y1[1] (numeric) = 1.983268438442581 absolute error = 7.083222897108499e-14 relative error = 3.571489748846379e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.81783749572827 y2[1] (numeric) = 0.8178374957279 absolute error = 3.700373341075647e-13 relative error = 4.524582646801403e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.110000000000375 y1[1] (closed_form) = 1.985040870112876 y1[1] (numeric) = 1.985040870112809 absolute error = 6.750155989720952e-14 relative error = 3.400512347807285e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.827679124284759 y2[1] (numeric) = 0.8276791242843849 absolute error = 3.740341369962152e-13 relative error = 4.519071775785547e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.120000000000378 y1[1] (closed_form) = 1.986714798516954 y1[1] (numeric) = 1.986714798516889 absolute error = 6.439293542825908e-14 relative error = 3.241176613589793e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.8375379847852191 y2[1] (numeric) = 0.8375379847848413 absolute error = 3.778088952799408e-13 relative error = 4.510946394590417e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.130000000000382 y1[1] (closed_form) = 1.988290056263439 y1[1] (numeric) = 1.988290056263378 absolute error = 6.106226635438361e-14 relative error = 3.071094489560388e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.8474130913518163 y2[1] (numeric) = 0.8474130913514345 absolute error = 3.818056981685913e-13 relative error = 4.505544014661428e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.140000000000385 y1[1] (closed_form) = 1.98976648582787 y1[1] (numeric) = 1.989766485827812 absolute error = 5.81756864903582e-14 relative error = 2.923744414468485e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.8573034564821229 y2[1] (numeric) = 0.8573034564817372 absolute error = 3.856914787547794e-13 relative error = 4.498890980067127e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.150000000000388 y1[1] (closed_form) = 1.99114393956852 y1[1] (numeric) = 1.991143939568466 absolute error = 5.440092820663267e-14 relative error = 2.732144428414418e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.8672080911478679 y2[1] (numeric) = 0.8672080911474782 absolute error = 3.896882816434299e-13 relative error = 4.493596007938815e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.160000000000392 y1[1] (closed_form) = 1.992422279741165 y1[1] (numeric) = 1.992422279741114 absolute error = 5.084821452783217e-14 relative error = 2.552080201313441e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.8771260048938386 y2[1] (numeric) = 0.8771260048934451 absolute error = 3.93574062229618e-13 relative error = 4.487086918341379e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.170000000000395 y1[1] (closed_form) = 1.993601378512851 y1[1] (numeric) = 1.993601378512804 absolute error = 4.75175454539567e-14 relative error = 2.383502838937789e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.8870562059369254 y2[1] (numeric) = 0.8870562059365279 absolute error = 3.97459842815806e-13 relative error = 4.480661317238647e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.180000000000399 y1[1] (closed_form) = 1.994681117974684 y1[1] (numeric) = 1.994681117974641 absolute error = 4.352074256530614e-14 relative error = 2.181839601985869e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.8969977012652988 y2[1] (numeric) = 0.8969977012648974 absolute error = 4.013456234019941e-13 relative error = 4.474321649162074e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.190000000000402 y1[1] (closed_form) = 1.995661390153618 y1[1] (numeric) = 1.995661390153578 absolute error = 3.952393967665557e-14 relative error = 1.980493277650332e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.9069494967377109 y2[1] (numeric) = 0.9069494967373057 absolute error = 4.051203816857196e-13 relative error = 4.466846093888733e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.200000000000405 y1[1] (closed_form) = 1.996542097023251 y1[1] (numeric) = 1.996542097023216 absolute error = 3.552713678800501e-14 relative error = 1.779433393414257e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.9169105971829072 y2[1] (numeric) = 0.9169105971824985 absolute error = 4.087841176669826e-13 relative error = 4.458276727555778e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.210000000000409 y1[1] (closed_form) = 1.997323150513631 y1[1] (numeric) = 1.9973231505136 absolute error = 3.153033389935445e-14 relative error = 1.578629571847005e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.9268800064991444 y2[1] (numeric) = 0.9268800064987321 absolute error = 4.122258090433206e-13 relative error = 4.447456047739241e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.220000000000412 y1[1] (closed_form) = 1.998004472520059 y1[1] (numeric) = 1.998004472520031 absolute error = 2.797762022055394e-14 relative error = 1.400278157799422e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.9368567277537985 y2[1] (numeric) = 0.9368567277533827 absolute error = 4.157785227221211e-13 relative error = 4.43801608511676e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.230000000000415 y1[1] (closed_form) = 1.998585994910903 y1[1] (numeric) = 1.998585994910879 absolute error = 2.420286193682841e-14 relative error = 1.21099927641129e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.9468397632830581 y2[1] (numeric) = 0.9468397632826387 absolute error = 4.193312364009216e-13 relative error = 4.428745524447967e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.240000000000419 y1[1] (closed_form) = 1.999067659534408 y1[1] (numeric) = 1.999067659534388 absolute error = 2.042810365310288e-14 relative error = 1.02188155341679e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.9568281147916893 y2[1] (numeric) = 0.9568281147912665 absolute error = 4.227729277772596e-13 relative error = 4.418483542044554e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.250000000000422 y1[1] (closed_form) = 1.999449418224513 y1[1] (numeric) = 1.999449418224497 absolute error = 1.643130076445232e-14 relative error = 8.217912698708382e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 0.9668207834528648 y2[1] (numeric) = 0.9668207834524386 absolute error = 4.262146191535976e-13 relative error = 4.408413911329377e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.260000000000425 y1[1] (closed_form) = 1.999731232805668 y1[1] (numeric) = 1.999731232805656 absolute error = 1.199040866595169e-14 relative error = 5.99601009838151e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 0.9768167700080459 y2[1] (numeric) = 0.9768167700076161 absolute error = 4.297673328323981e-13 relative error = 4.39967193467469e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.270000000000429 y1[1] (closed_form) = 1.999913075096648 y1[1] (numeric) = 1.99991307509664 absolute error = 7.549516567451064e-15 relative error = 3.774922351105798e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 0.9868150748669068 y2[1] (numeric) = 0.9868150748664736 absolute error = 4.332090242087361e-13 relative error = 4.389971690158499e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.280000000000432 y1[1] (closed_form) = 1.999994926913377 y1[1] (numeric) = 1.999994926913373 absolute error = 3.552713678800501e-15 relative error = 1.77636134521774e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 0.9968146982072936 y2[1] (numeric) = 0.996814698206857 absolute error = 4.366507155850741e-13 relative error = 4.380460243717935e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.290000000000435 y1[1] (closed_form) = 1.99997678007074 y1[1] (numeric) = 1.999976780070741 absolute error = 6.661338147750939e-16 relative error = 3.330707743274562e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.006814640075205 y2[1] (numeric) = 1.006814640074765 absolute error = 4.400924069614121e-13 relative error = 4.371136348678231e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.300000000000439 y1[1] (closed_form) = 1.999858636383408 y1[1] (numeric) = 1.999858636383413 absolute error = 5.329070518200751e-15 relative error = 2.664723606583498e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.016813900484788 y2[1] (numeric) = 1.016813900484345 absolute error = 4.436451206402126e-13 relative error = 4.36309063466476e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.310000000000442 y1[1] (closed_form) = 1.99964050766565 y1[1] (numeric) = 1.99964050766566 absolute error = 1.021405182655144e-14 relative error = 5.107944046640249e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.026811479518335 y2[1] (numeric) = 1.026811479517888 absolute error = 4.46975789714088e-13 relative error = 4.353046285806614e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.320000000000445 y1[1] (closed_form) = 1.999322415730156 y1[1] (numeric) = 1.999322415730171 absolute error = 1.48769885299771e-14 relative error = 7.441015222421741e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.036806377426272 y2[1] (numeric) = 1.036806377425821 absolute error = 4.503064587879635e-13 relative error = 4.343206876348378e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.330000000000449 y1[1] (closed_form) = 1.998904392385855 y1[1] (numeric) = 1.998904392385875 absolute error = 1.953992523340276e-14 relative error = 9.775317572883144e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.046797594727138 y2[1] (numeric) = 1.046797594726685 absolute error = 4.534150832569139e-13 relative error = 4.331449418118913e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.340000000000452 y1[1] (closed_form) = 1.998386479434733 y1[1] (numeric) = 1.998386479434757 absolute error = 2.420286193682841e-14 relative error = 1.211120180500544e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.056784132307529 y2[1] (numeric) = 1.056784132307073 absolute error = 4.567457523307894e-13 relative error = 4.322034542035253e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.350000000000455 y1[1] (closed_form) = 1.997768728667654 y1[1] (numeric) = 1.997768728667682 absolute error = 2.886579864025407e-14 relative error = 1.444901916124454e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.06676499152201 y2[1] (numeric) = 1.06676499152155 absolute error = 4.598543767997398e-13 relative error = 4.310737420653834e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.360000000000459 y1[1] (closed_form) = 1.997051201859179 y1[1] (numeric) = 1.997051201859212 absolute error = 3.352873534367973e-14 relative error = 1.678912153702707e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.076739174292976 y2[1] (numeric) = 1.076739174292513 absolute error = 4.629630012686903e-13 relative error = 4.299676396307283e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.370000000000462 y1[1] (closed_form) = 1.996233970761391 y1[1] (numeric) = 1.996233970761429 absolute error = 3.885780586188048e-14 relative error = 1.946555685907879e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.086705683210461 y2[1] (numeric) = 1.086705683209996 absolute error = 4.654054919228656e-13 relative error = 4.282718854914933e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.380000000000465 y1[1] (closed_form) = 1.995317117096719 y1[1] (numeric) = 1.995317117096762 absolute error = 4.374278717023117e-14 relative error = 2.192272436066654e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.096663521631881 y2[1] (numeric) = 1.096663521631412 absolute error = 4.68292071786891e-13 relative error = 4.270152718219834e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.390000000000469 y1[1] (closed_form) = 1.994300732549765 y1[1] (numeric) = 1.994300732549814 absolute error = 4.862776847858186e-14 relative error = 2.438336790681012e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.106611693781689 y2[1] (numeric) = 1.106611693781218 absolute error = 4.709566070459914e-13 relative error = 4.25584339739411e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.400000000000472 y1[1] (closed_form) = 1.993184918758138 y1[1] (numeric) = 1.993184918758191 absolute error = 5.351274978693255e-14 relative error = 2.684786006723044e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.116549204850962 y2[1] (numeric) = 1.116549204850489 absolute error = 4.733990977001667e-13 relative error = 4.239840892308517e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.410000000000475 y1[1] (closed_form) = 1.991969787302286 y1[1] (numeric) = 1.991969787302345 absolute error = 5.88418203051333e-14 relative error = 2.953951444455514e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.126475061096874 y2[1] (numeric) = 1.126475061096398 absolute error = 4.762856775641922e-13 relative error = 4.228106719916392e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.420000000000479 y1[1] (closed_form) = 1.990655459694342 y1[1] (numeric) = 1.990655459694406 absolute error = 6.417089082333405e-14 relative error = 3.223606099730953e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.136388269942072 y2[1] (numeric) = 1.136388269941593 absolute error = 4.787281682183675e-13 relative error = 4.212716558951906e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.430000000000482 y1[1] (closed_form) = 1.989242067365973 y1[1] (numeric) = 1.989242067366042 absolute error = 6.905587213168474e-14 relative error = 3.471466508001417e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.146287840073932 y2[1] (numeric) = 1.146287840073451 absolute error = 4.813927034774679e-13 relative error = 4.199579605122737e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.440000000000485 y1[1] (closed_form) = 1.987729751655232 y1[1] (numeric) = 1.987729751655307 absolute error = 7.438494264988549e-14 relative error = 3.742206031174172e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.156172781543691 y2[1] (numeric) = 1.156172781543207 absolute error = 4.838351941316432e-13 relative error = 4.184800073615636e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.450000000000489 y1[1] (closed_form) = 1.986118663792432 y1[1] (numeric) = 1.986118663792511 absolute error = 7.949196856316121e-14 relative error = 4.002377602724592e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.166042105865439 y2[1] (numeric) = 1.166042105864952 absolute error = 4.864997293907436e-13 relative error = 4.172231233705429e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.460000000000492 y1[1] (closed_form) = 1.984408964885014 y1[1] (numeric) = 1.984408964885099 absolute error = 8.482103908136196e-14 relative error = 4.27437290308134e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.175894826114968 y2[1] (numeric) = 1.175894826114479 absolute error = 4.889422200449189e-13 relative error = 4.15804380788316e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.470000000000495 y1[1] (closed_form) = 1.982600825901446 y1[1] (numeric) = 1.982600825901537 absolute error = 9.015010959956271e-14 relative error = 4.547063050807183e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.185729957028465 y2[1] (numeric) = 1.185729957027974 absolute error = 4.907185768843192e-13 relative error = 4.138535709379391e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.480000000000499 y1[1] (closed_form) = 1.98069442765412 y1[1] (numeric) = 1.980694427654216 absolute error = 9.570122472268849e-14 relative error = 4.831700608964423e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.195546515101033 y2[1] (numeric) = 1.195546515100539 absolute error = 4.936051567483446e-13 relative error = 4.128698888028051e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.490000000000502 y1[1] (closed_form) = 1.97868996078127 y1[1] (numeric) = 1.978689960781372 absolute error = 1.014743844507393e-13 relative error = 5.128362020428554e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.205343518685046 y2[1] (numeric) = 1.20534351868455 absolute error = 4.960476474025199e-13 relative error = 4.115404776421554e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.500000000000505 y1[1] (closed_form) = 1.976587625727915 y1[1] (numeric) = 1.976587625728022 absolute error = 1.072475441787901e-13 relative error = 5.425893736398064e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.215119988088309 y2[1] (numeric) = 1.215119988087811 absolute error = 4.982680934517703e-13 relative error = 4.100567008494955e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.510000000000509 y1[1] (closed_form) = 1.974387632725807 y1[1] (numeric) = 1.97438763272592 absolute error = 1.13242748511766e-13 relative error = 5.735588424215609e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.22487494567203 y2[1] (numeric) = 1.224874945671529 absolute error = 5.004885395010206e-13 relative error = 4.086037854471966e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.520000000000512 y1[1] (closed_form) = 1.972090201772413 y1[1] (numeric) = 1.972090201772532 absolute error = 1.185718190299667e-13 relative error = 6.01249470857877e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.234607415948578 y2[1] (numeric) = 1.234607415948076 absolute error = 5.022648963404208e-13 relative error = 4.0682154493177e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.530000000000515 y1[1] (closed_form) = 1.969695562608915 y1[1] (numeric) = 1.969695562609039 absolute error = 1.243449787580175e-13 relative error = 6.312903431295711e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.244316425679037 y2[1] (numeric) = 1.244316425678533 absolute error = 5.044853423896711e-13 relative error = 4.054317149388813e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.540000000000519 y1[1] (closed_form) = 1.967203954697232 y1[1] (numeric) = 1.967203954697362 absolute error = 1.303401830909934e-13 relative error = 6.625656825250423e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.254001003970525 y2[1] (numeric) = 1.254001003970019 absolute error = 5.062616992290714e-13 relative error = 4.037171402782792e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.550000000000522 y1[1] (closed_form) = 1.96461562719608 y1[1] (numeric) = 1.964615627196217 absolute error = 1.361133428190442e-13 relative error = 6.928242905881114e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.263660182373282 y2[1] (numeric) = 1.263660182372774 absolute error = 5.078160114635466e-13 relative error = 4.018612112235875e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.560000000000525 y1[1] (closed_form) = 1.961930838936053 y1[1] (numeric) = 1.961930838936194 absolute error = 1.4166445794217e-13 relative error = 7.220665230941272e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.273292994977518 y2[1] (numeric) = 1.273292994977008 absolute error = 5.100364575127969e-13 relative error = 4.005648813938557e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.570000000000529 y1[1] (closed_form) = 1.959149858393738 y1[1] (numeric) = 1.959149858393886 absolute error = 1.476596622751458e-13 relative error = 7.53692534762035e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.28289847851 y2[1] (numeric) = 1.282898478509488 absolute error = 5.120348589571222e-13 relative error = 3.991234439312892e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.580000000000532 y1[1] (closed_form) = 1.956272963664872 y1[1] (numeric) = 1.956272963665026 absolute error = 1.538769112130467e-13 relative error = 7.8658200604467e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.292475672430379 y2[1] (numeric) = 1.292475672429865 absolute error = 5.138112157965224e-13 relative error = 3.975403380942165e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.590000000000535 y1[1] (closed_form) = 1.953300442436531 y1[1] (numeric) = 1.953300442436692 absolute error = 1.603162047558726e-13 relative error = 8.207452436548647e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.302023619027243 y2[1] (numeric) = 1.302023619026727 absolute error = 5.155875726359227e-13 relative error = 3.95989416091487e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.600000000000539 y1[1] (closed_form) = 1.950232591958362 y1[1] (numeric) = 1.950232591958528 absolute error = 1.660893644839234e-13 relative error = 8.516387489819446e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.31154136351389 y2[1] (numeric) = 1.311541363513373 absolute error = 5.173639294753229e-13 relative error = 3.944701584471557e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.610000000000542 y1[1] (closed_form) = 1.947069719012854 y1[1] (numeric) = 1.947069719013026 absolute error = 1.723066134218243e-13 relative error = 8.849534854313392e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.321027954123803 y2[1] (numeric) = 1.321027954123284 absolute error = 5.186961971048731e-13 relative error = 3.926458902596867e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.620000000000545 y1[1] (closed_form) = 1.943812139884666 y1[1] (numeric) = 1.943812139884845 absolute error = 1.785238623597252e-13 relative error = 9.1842137774856e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.330482442205826 y2[1] (numeric) = 1.330482442205305 absolute error = 5.202505093393484e-13 relative error = 3.910239570518628e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.630000000000549 y1[1] (closed_form) = 1.940460180328998 y1[1] (numeric) = 1.940460180329183 absolute error = 1.84519066692701e-13 relative error = 9.50903649367422e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.339903882319029 y2[1] (numeric) = 1.339903882318508 absolute error = 5.213607323639735e-13 relative error = 3.891030836194251e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.640000000000552 y1[1] (closed_form) = 1.937014175539011 y1[1] (numeric) = 1.937014175539202 absolute error = 1.91180404840452e-13 relative error = 9.869850580068799e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.349291332327252 y2[1] (numeric) = 1.34929133232673 absolute error = 5.220268661787486e-13 relative error = 3.868896610180981e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.650000000000555 y1[1] (closed_form) = 1.933474470112313 y1[1] (numeric) = 1.93347447011251 absolute error = 1.976196983832779e-13 relative error = 1.022096238859562e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.358643853493319 y2[1] (numeric) = 1.358643853492795 absolute error = 5.233591338082988e-13 relative error = 3.852070080489806e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.660000000000559 y1[1] (closed_form) = 1.929841418016496 y1[1] (numeric) = 1.9298414180167 absolute error = 2.045030811359538e-13 relative error = 1.05968852791098e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.367960510572904 y2[1] (numeric) = 1.36796051057238 absolute error = 5.244693568329239e-13 relative error = 3.833951000627024e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.670000000000562 y1[1] (closed_form) = 1.926115382553742 y1[1] (numeric) = 1.926115382553953 absolute error = 2.109423746787797e-13 relative error = 1.09516998093386e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.377240371908065 y2[1] (numeric) = 1.37724037190754 absolute error = 5.253575352526241e-13 relative error = 3.814566766764032e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.680000000000565 y1[1] (closed_form) = 1.922296736324494 y1[1] (numeric) = 1.922296736324711 absolute error = 2.173816682216057e-13 relative error = 1.130843454675202e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.386482509520401 y2[1] (numeric) = 1.386482509519875 absolute error = 5.260236690673992e-13 relative error = 3.793943778269199e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.690000000000569 y1[1] (closed_form) = 1.918385861190191 y1[1] (numeric) = 1.918385861190415 absolute error = 2.242650509742816e-13 relative error = 1.169029940802132e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.395685999203853 y2[1] (numeric) = 1.395685999203326 absolute error = 5.269118474870993e-13 relative error = 3.775289340064082e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.700000000000572 y1[1] (closed_form) = 1.914383148235088 y1[1] (numeric) = 1.914383148235319 absolute error = 2.311484337269576e-13 relative error = 1.20743036178551e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.404849920617121 y2[1] (numeric) = 1.404849920616594 absolute error = 5.273559366969494e-13 relative error = 3.753824013210556e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.710000000000576 y1[1] (closed_form) = 1.910288997727144 y1[1] (numeric) = 1.910288997727382 absolute error = 2.378097718747085e-13 relative error = 1.24488897835696e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.413973357375702 y2[1] (numeric) = 1.413973357375174 absolute error = 5.280220705117245e-13 relative error = 3.734314142182423e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.720000000000579 y1[1] (closed_form) = 1.906103819078 y1[1] (numeric) = 1.906103819078245 absolute error = 2.444711100224595e-13 relative error = 1.282569750795171e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.423055397143522 y2[1] (numeric) = 1.423055397142993 absolute error = 5.289102489314246e-13 relative error = 3.716722834494696e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.730000000000582 y1[1] (closed_form) = 1.901828030802032 y1[1] (numeric) = 1.901828030802283 absolute error = 2.511324481702104e-13 relative error = 1.320479265753086e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.432095131724172 y2[1] (numeric) = 1.432095131723642 absolute error = 5.295763827461997e-13 relative error = 3.697913434763345e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.740000000000586 y1[1] (closed_form) = 1.897462060474504 y1[1] (numeric) = 1.897462060474762 absolute error = 2.577937863179613e-13 relative error = 1.358624194327733e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.441091657151728 y2[1] (numeric) = 1.441091657151198 absolute error = 5.300204719560497e-13 relative error = 3.677909516203977e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.750000000000589 y1[1] (closed_form) = 1.893006344688812 y1[1] (numeric) = 1.893006344689076 absolute error = 2.644551244657123e-13 relative error = 1.397011294799361e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.450044073781144 y2[1] (numeric) = 1.450044073780613 absolute error = 5.304645611658998e-13 relative error = 3.658265088333882e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.760000000000592 y1[1] (closed_form) = 1.88846132901282 y1[1] (numeric) = 1.888461329013091 absolute error = 2.711164626134632e-13 relative error = 1.435647415428875e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.458951486378217 y2[1] (numeric) = 1.458951486377686 absolute error = 5.304645611658998e-13 relative error = 3.635930091704111e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.770000000000596 y1[1] (closed_form) = 1.883827467944308 y1[1] (numeric) = 1.883827467944586 absolute error = 2.779998453661392e-13 relative error = 1.475718185962653e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.46781300420911 y2[1] (numeric) = 1.46781300420858 absolute error = 5.302425165609748e-13 relative error = 3.612466404374725e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.780000000000599 y1[1] (closed_form) = 1.879105224865523 y1[1] (numeric) = 1.879105224865807 absolute error = 2.846611835138901e-13 relative error = 1.514876228042321e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.476627741129426 y2[1] (numeric) = 1.476627741128895 absolute error = 5.304645611658998e-13 relative error = 3.592405495241233e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.790000000000602 y1[1] (closed_form) = 1.874295071996836 y1[1] (numeric) = 1.874295071997127 absolute error = 2.915445662665661e-13 relative error = 1.555489157616791e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.485394815672817 y2[1] (numeric) = 1.485394815672286 absolute error = 5.304645611658998e-13 relative error = 3.571202454517948e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.800000000000606 y1[1] (closed_form) = 1.869397490349526 y1[1] (numeric) = 1.869397490349824 absolute error = 2.98205904414317e-13 relative error = 1.595197949894331e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.494113351139135 y2[1] (numeric) = 1.494113351138604 absolute error = 5.304645611658998e-13 relative error = 3.550363570216848e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.810000000000609 y1[1] (closed_form) = 1.864412969677677 y1[1] (numeric) = 1.864412969677982 absolute error = 3.05089287166993e-13 relative error = 1.636382561851291e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.502782475682099 y2[1] (numeric) = 1.502782475681568 absolute error = 5.304645611658998e-13 relative error = 3.529882532900358e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.820000000000612 y1[1] (closed_form) = 1.859342008429201 y1[1] (numeric) = 1.859342008429513 absolute error = 3.11972669919669e-13 relative error = 1.67786597896117e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.511401322396478 y2[1] (numeric) = 1.511401322395948 absolute error = 5.300204719560497e-13 relative error = 3.506814927987818e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.830000000000616 y1[1] (closed_form) = 1.854185113695999 y1[1] (numeric) = 1.854185113696318 absolute error = 3.18856052672345e-13 relative error = 1.71965598427635e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.519969029404785 y2[1] (numeric) = 1.519969029404255 absolute error = 5.297984273511247e-13 relative error = 3.485586989615126e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.840000000000619 y1[1] (closed_form) = 1.848942801163245 y1[1] (numeric) = 1.848942801163571 absolute error = 3.25961480029946e-13 relative error = 1.762961405971403e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.528484739943456 y2[1] (numeric) = 1.528484739942927 absolute error = 5.291322935363496e-13 relative error = 3.461809462068453e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.850000000000622 y1[1] (closed_form) = 1.843615595057825 y1[1] (numeric) = 1.843615595058158 absolute error = 3.328448627826219e-13 relative error = 1.80539188144686e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.536947602448536 y2[1] (numeric) = 1.536947602448008 absolute error = 5.286882043264995e-13 relative error = 3.439858349655107e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.860000000000626 y1[1] (closed_form) = 1.83820402809591 y1[1] (numeric) = 1.83820402809625 absolute error = 3.40172334745148e-13 relative error = 1.850568976815446e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.545356770640826 y2[1] (numeric) = 1.545356770640298 absolute error = 5.282441151166495e-13 relative error = 3.418266416871477e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.870000000000629 y1[1] (closed_form) = 1.832708641429686 y1[1] (numeric) = 1.832708641430034 absolute error = 3.47277762102749e-13 relative error = 1.894888004848602e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.553711403610514 y2[1] (numeric) = 1.553711403609987 absolute error = 5.271338920920243e-13 relative error = 3.392740060136463e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.880000000000632 y1[1] (closed_form) = 1.827129984593241 y1[1] (numeric) = 1.827129984593596 absolute error = 3.5438318946035e-13 relative error = 1.939562004064223e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.562010665901266 y2[1] (numeric) = 1.562010665900739 absolute error = 5.266898028821743e-13 relative error = 3.371870720090628e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.890000000000636 y1[1] (closed_form) = 1.821468615447609 y1[1] (numeric) = 1.821468615447971 absolute error = 3.61488616817951e-13 relative error = 1.984599755121877e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.570253727593768 y2[1] (numeric) = 1.570253727593242 absolute error = 5.260236690673992e-13 relative error = 3.349927848115791e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.900000000000639 y1[1] (closed_form) = 1.815725100124987 y1[1] (numeric) = 1.815725100125356 absolute error = 3.683719995706269e-13 relative error = 2.028787284734179e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.578439764388721 y2[1] (numeric) = 1.578439764388196 absolute error = 5.25135490647699e-13 relative error = 3.326927656634823e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.910000000000642 y1[1] (closed_form) = 1.809900012972122 y1[1] (numeric) = 1.809900012972497 absolute error = 3.754774269282279e-13 relative error = 2.0745755248194e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.586567957689266 y2[1] (numeric) = 1.586567957688742 absolute error = 5.242473122279989e-13 relative error = 3.304285263592057e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.920000000000646 y1[1] (closed_form) = 1.803993936492873 y1[1] (numeric) = 1.803993936493256 absolute error = 3.825828542858289e-13 relative error = 2.120754657466335e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.594637494682848 y2[1] (numeric) = 1.594637494682325 absolute error = 5.231370892033738e-13 relative error = 3.280601960932938e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.930000000000649 y1[1] (closed_form) = 1.798007461289968 y1[1] (numeric) = 1.798007461290357 absolute error = 3.892441924335799e-13 relative error = 2.164864166661018e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.60264756842249 y2[1] (numeric) = 1.602647568421968 absolute error = 5.220268661787486e-13 relative error = 3.257277997136871e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.940000000000652 y1[1] (closed_form) = 1.791941186005938 y1[1] (numeric) = 1.791941186006335 absolute error = 3.967937090010309e-13 relative error = 2.21432328303947e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.610597377907495 y2[1] (numeric) = 1.610597377906975 absolute error = 5.206945985491984e-13 relative error = 3.232928388506941e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.950000000000656 y1[1] (closed_form) = 1.785795717263256 y1[1] (numeric) = 1.78579571726366 absolute error = 4.04343225568482e-13 relative error = 2.264218811030305e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.618486128163539 y2[1] (numeric) = 1.61848612816302 absolute error = 5.193623309196482e-13 relative error = 3.208939031865274e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.960000000000659 y1[1] (closed_form) = 1.779571669603675 y1[1] (numeric) = 1.779571669604087 absolute error = 4.121147867408581e-13 relative error = 2.315808875697822e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.62631303032217 y2[1] (numeric) = 1.626313030321652 absolute error = 5.18030063290098e-13 relative error = 3.185303527866816e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.970000000000662 y1[1] (closed_form) = 1.773269665426774 y1[1] (numeric) = 1.773269665427194 absolute error = 4.194422587033841e-13 relative error = 2.365360818386507e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.634077301699694 y2[1] (numeric) = 1.634077301699178 absolute error = 5.160316618457728e-13 relative error = 3.157939109178127e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.980000000000666 y1[1] (closed_form) = 1.76689033492772 y1[1] (numeric) = 1.766890334928147 absolute error = 4.265476860609851e-13 relative error = 2.414115226219936e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.641778165875444 y2[1] (numeric) = 1.64177816587493 absolute error = 5.144773496112975e-13 relative error = 3.133659347558464e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.990000000000669 y1[1] (closed_form) = 1.760434316034247 y1[1] (numeric) = 1.76043431603468 absolute error = 4.336531134185861e-13 relative error = 2.463330267246109e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.64941485276942 y2[1] (numeric) = 1.649414852768907 absolute error = 5.124789481669723e-13 relative error = 3.107034881530889e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.000000000000672 y1[1] (closed_form) = 1.753902254342863 y1[1] (numeric) = 1.753902254343304 absolute error = 4.409805853811122e-13 relative error = 2.514282562150734e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.656986598719296 y2[1] (numeric) = 1.656986598718785 absolute error = 5.10924635932497e-13 relative error = 3.083456657569811e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.010000000000676 y1[1] (closed_form) = 1.747294803054294 y1[1] (numeric) = 1.747294803054743 absolute error = 4.483080573436382e-13 relative error = 2.565726496524741e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.664492646556787 y2[1] (numeric) = 1.664492646556278 absolute error = 5.089262344881718e-13 relative error = 3.057545706440637e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.020000000000679 y1[1] (closed_form) = 1.740612622908164 y1[1] (numeric) = 1.74061262290862 absolute error = 4.554134847012392e-13 relative error = 2.6163976907185e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.671932245683365 y2[1] (numeric) = 1.671932245682858 absolute error = 5.069278330438465e-13 relative error = 3.031987895159299e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.030000000000682 y1[1] (closed_form) = 1.733856382116918 y1[1] (numeric) = 1.733856382117381 absolute error = 4.627409566637652e-13 relative error = 2.668854014879772e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.679304652145315 y2[1] (numeric) = 1.679304652144811 absolute error = 5.042632977847461e-13 relative error = 3.00281010441166e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.040000000000686 y1[1] (closed_form) = 1.727026756299005 y1[1] (numeric) = 1.727026756299475 absolute error = 4.696243394164412e-13 relative error = 2.719264989402016e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.686609128708137 y2[1] (numeric) = 1.686609128707635 absolute error = 5.013767179207207e-13 relative error = 2.972690645311232e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.050000000000689 y1[1] (closed_form) = 1.720124428411316 y1[1] (numeric) = 1.720124428411793 absolute error = 4.769518113789672e-13 relative error = 2.772775059182629e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.69384494493026 y2[1] (numeric) = 1.693844944929761 absolute error = 4.996003610813204e-13 relative error = 2.94950469094968e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.060000000000692 y1[1] (closed_form) = 1.713150088680887 y1[1] (numeric) = 1.713150088681371 absolute error = 4.840572387365683e-13 relative error = 2.825538999383812e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.701011377236092 y2[1] (numeric) = 1.701011377235595 absolute error = 4.971578704271451e-13 relative error = 2.922719254441189e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.070000000000696 y1[1] (closed_form) = 1.70610443453588 y1[1] (numeric) = 1.706104434536371 absolute error = 4.911626660941693e-13 relative error = 2.878854636045669e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.708107708988375 y2[1] (numeric) = 1.70810770898788 absolute error = 4.944933351680447e-13 relative error = 2.894977480435985e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.080000000000699 y1[1] (closed_form) = 1.698988170535838 y1[1] (numeric) = 1.698988170536336 absolute error = 4.984901380566953e-13 relative error = 2.934041252915129e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.715133230559847 y2[1] (numeric) = 1.715133230559355 absolute error = 4.920508445138694e-13 relative error = 2.868878264070811e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.090000000000702 y1[1] (closed_form) = 1.69180200830123 y1[1] (numeric) = 1.691802008301736 absolute error = 5.062616992290714e-13 relative error = 2.992440585511647e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.722087239404204 y2[1] (numeric) = 1.722087239403715 absolute error = 4.89386309254769e-13 relative error = 2.84182065842427e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.100000000000706 y1[1] (closed_form) = 1.684546666442292 y1[1] (numeric) = 1.684546666442805 absolute error = 5.131450819817474e-13 relative error = 3.046190955727532e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.728969040126359 y2[1] (numeric) = 1.728969040125873 absolute error = 4.864997293907436e-13 relative error = 2.813814001870088e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.110000000000709 y1[1] (closed_form) = 1.677222870487163 y1[1] (numeric) = 1.677222870487683 absolute error = 5.200284647344233e-13 relative error = 3.10053287422307e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.735777944551974 y2[1] (numeric) = 1.73577794455149 absolute error = 4.836131495267182e-13 relative error = 2.786146413742715e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.120000000000712 y1[1] (closed_form) = 1.669831352809336 y1[1] (numeric) = 1.669831352809864 absolute error = 5.275779813018744e-13 relative error = 3.159468651814888e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.742513271796279 y2[1] (numeric) = 1.742513271795798 absolute error = 4.807265696626928e-13 relative error = 2.758811524959768e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.130000000000716 y1[1] (closed_form) = 1.662372852554419 y1[1] (numeric) = 1.662372852554954 absolute error = 5.346834086594754e-13 relative error = 3.216386792156016e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.749174348332164 y2[1] (numeric) = 1.749174348331686 absolute error = 4.776179451937423e-13 relative error = 2.7305336694947e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.140000000000719 y1[1] (closed_form) = 1.654848115566222 y1[1] (numeric) = 1.654848115566764 absolute error = 5.420108806220014e-13 relative error = 3.275290798736217e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.755760508057525 y2[1] (numeric) = 1.75576050805705 absolute error = 4.747313653297169e-13 relative error = 2.70385034377458e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.150000000000722 y1[1] (closed_form) = 1.647257894312173 y1[1] (numeric) = 1.647257894312722 absolute error = 5.491163079796024e-13 relative error = 3.333517537694914e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.762271092361879 y2[1] (numeric) = 1.762271092361407 absolute error = 4.716227408607665e-13 relative error = 2.676221285731218e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.160000000000726 y1[1] (closed_form) = 1.639602947808073 y1[1] (numeric) = 1.63960294780863 absolute error = 5.566658245470535e-13 relative error = 3.395125785125236e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.76870545019222 y2[1] (numeric) = 1.768705450191752 absolute error = 4.68070027181966e-13 relative error = 2.646398964457858e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.170000000000729 y1[1] (closed_form) = 1.631884041542193 y1[1] (numeric) = 1.631884041542757 absolute error = 5.639932965095795e-13 relative error = 3.456086842889795e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.775062938118128 y2[1] (numeric) = 1.775062938117663 absolute error = 4.645173135031655e-13 relative error = 2.616906158807156e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.180000000000732 y1[1] (closed_form) = 1.624101947398726 y1[1] (numeric) = 1.624101947399297 absolute error = 5.710987238671805e-13 relative error = 3.516397014250809e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.781342920396107 y2[1] (numeric) = 1.781342920395646 absolute error = 4.60964599824365e-13 relative error = 2.587736446174344e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.190000000000736 y1[1] (closed_form) = 1.616257443580603 y1[1] (numeric) = 1.616257443581181 absolute error = 5.779821066198565e-13 relative error = 3.576052249073725e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.787544769033164 y2[1] (numeric) = 1.787544769032707 absolute error = 4.576339307504895e-13 relative error = 2.56012570246289e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.200000000000739 y1[1] (closed_form) = 1.608351314531668 y1[1] (numeric) = 1.608351314532253 absolute error = 5.850875339774575e-13 relative error = 3.637809281412051e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.793667863849603 y2[1] (numeric) = 1.793667863849149 absolute error = 4.53637127861839e-13 relative error = 2.52910328051613e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.210000000000742 y1[1] (closed_form) = 1.600384350858238 y1[1] (numeric) = 1.60038435085883 absolute error = 5.919709167301335e-13 relative error = 3.698929675316291e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.799711592541044 y2[1] (numeric) = 1.799711592540594 absolute error = 4.500844141830385e-13 relative error = 2.500869672943299e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.220000000000746 y1[1] (closed_form) = 1.59235734925004 y1[1] (numeric) = 1.592357349250639 absolute error = 5.990763440877345e-13 relative error = 3.762197878320996e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.805675350739655 y2[1] (numeric) = 1.805675350739209 absolute error = 4.458655666894629e-13 relative error = 2.469245462684219e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.230000000000749 y1[1] (closed_form) = 1.584271112400546 y1[1] (numeric) = 1.584271112401153 absolute error = 6.066258606551855e-13 relative error = 3.829053347668528e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.811558542074586 y2[1] (numeric) = 1.811558542074144 absolute error = 4.420908084057373e-13 relative error = 2.440389300913552e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.240000000000753 y1[1] (closed_form) = 1.576126448926704 y1[1] (numeric) = 1.576126448927318 absolute error = 6.137312880127865e-13 relative error = 3.893921635733729e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.817360578231606 y2[1] (numeric) = 1.817360578231168 absolute error = 4.380940055170868e-13 relative error = 2.410605857552917e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.250000000000756 y1[1] (closed_form) = 1.567924173288073 y1[1] (numeric) = 1.567924173288693 absolute error = 6.203926261605375e-13 relative error = 3.956776971296516e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.823080879011935 y2[1] (numeric) = 1.823080879011501 absolute error = 4.336531134185861e-13 relative error = 2.378682802342897e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.260000000000759 y1[1] (closed_form) = 1.559665105705381 y1[1] (numeric) = 1.559665105706008 absolute error = 6.272760089132134e-13 relative error = 4.021863454010653e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.82871887239026 y2[1] (numeric) = 1.828718872389831 absolute error = 4.294342659250105e-13 relative error = 2.348279292178522e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.270000000000763 y1[1] (closed_form) = 1.551350072078505 y1[1] (numeric) = 1.55135007207914 absolute error = 6.346034808757395e-13 relative error = 4.090652988628771e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.834273994571944 y2[1] (numeric) = 1.834273994571519 absolute error = 4.247713292215849e-13 relative error = 2.315746341487614e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.280000000000766 y1[1] (closed_form) = 1.542979903903878 y1[1] (numeric) = 1.542979903904519 absolute error = 6.414868636284154e-13 relative error = 4.157454429609848e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.839745690049396 y2[1] (numeric) = 1.839745690048975 absolute error = 4.203304371230843e-13 relative error = 2.284720325186894e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.290000000000769 y1[1] (closed_form) = 1.534555438191342 y1[1] (numeric) = 1.534555438191991 absolute error = 6.485922909860165e-13 relative error = 4.226581033465043e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.845133411657629 y2[1] (numeric) = 1.845133411657213 absolute error = 4.158895450245836e-13 relative error = 2.25398089047099e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.300000000000773 y1[1] (closed_form) = 1.526077517380448 y1[1] (numeric) = 1.526077517381104 absolute error = 6.559197629485425e-13 relative error = 4.298076313151156e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.850436620628971 y2[1] (numeric) = 1.85043662062856 absolute error = 4.11004563716233e-13 relative error = 2.221122080779675e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.310000000000776 y1[1] (closed_form) = 1.517546989256213 y1[1] (numeric) = 1.517546989256876 absolute error = 6.632472349110685e-13 relative error = 4.370521898871431e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.855654786646945 y2[1] (numeric) = 1.855654786646539 absolute error = 4.061195824078823e-13 relative error = 2.188551369200063e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.320000000000779 y1[1] (closed_form) = 1.50896470686434 y1[1] (numeric) = 1.50896470686501 absolute error = 6.699085730588195e-13 relative error = 4.439524463437607e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.860787387899298 y2[1] (numeric) = 1.860787387898897 absolute error = 4.012346010995316e-13 relative error = 2.156262470977396e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.330000000000783 y1[1] (closed_form) = 1.500331528425916 y1[1] (numeric) = 1.500331528426593 absolute error = 6.767919558114954e-13 relative error = 4.510949366781332e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.865833911130181 y2[1] (numeric) = 1.865833911129785 absolute error = 3.959055305813308e-13 relative error = 2.121869091453704e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.340000000000786 y1[1] (closed_form) = 1.491648317251591 y1[1] (numeric) = 1.491648317252274 absolute error = 6.834532939592464e-13 relative error = 4.581866154741693e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.870793851691477 y2[1] (numeric) = 1.870793851691087 absolute error = 3.907985046680551e-13 relative error = 2.088944777719441e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.350000000000789 y1[1] (closed_form) = 1.482915941655246 y1[1] (numeric) = 1.482915941655937 absolute error = 6.903366767119223e-13 relative error = 4.655265057986774e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.875666713593263 y2[1] (numeric) = 1.875666713592878 absolute error = 3.852473895449293e-13 relative error = 2.053922409311732e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.360000000000793 y1[1] (closed_form) = 1.474135274867165 y1[1] (numeric) = 1.474135274867862 absolute error = 6.972200594645983e-13 relative error = 4.729688457712438e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.88045200955341 y2[1] (numeric) = 1.88045200955303 absolute error = 3.801403636316536e-13 relative error = 2.021537171384307e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.370000000000796 y1[1] (closed_form) = 1.465307194946708 y1[1] (numeric) = 1.465307194947413 absolute error = 7.045475314271243e-13 relative error = 4.808189940354099e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.885149261046309 y2[1] (numeric) = 1.885149261045934 absolute error = 3.750333377183779e-13 relative error = 1.989409249802449e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.380000000000799 y1[1] (closed_form) = 1.456432584694511 y1[1] (numeric) = 1.456432584695222 absolute error = 7.109868249699502e-13 relative error = 4.881700893276023e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.889757998350724 y2[1] (numeric) = 1.889757998350355 absolute error = 3.692601779903271e-13 relative error = 1.954007752911202e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.390000000000803 y1[1] (closed_form) = 1.447512331564204 y1[1] (numeric) = 1.447512331564922 absolute error = 7.176481631177012e-13 relative error = 4.957803449882872e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.894277760596768 y2[1] (numeric) = 1.894277760596405 absolute error = 3.630429290524262e-13 relative error = 1.916524263780905e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.400000000000806 y1[1] (closed_form) = 1.438547327573666 y1[1] (numeric) = 1.438547327574391 absolute error = 7.243095012654521e-13 relative error = 5.035006408076353e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.89870809581198 y2[1] (numeric) = 1.898708095811623 absolute error = 3.574918139293004e-13 relative error = 1.882816082776639e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.410000000000809 y1[1] (closed_form) = 1.429538469215826 y1[1] (numeric) = 1.429538469216556 absolute error = 7.30526750203353e-13 relative error = 5.110227992703714e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.903048560966532 y2[1] (numeric) = 1.903048560966181 absolute error = 3.514966095963246e-13 relative error = 1.847018603759666e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.420000000000813 y1[1] (closed_form) = 1.420486657369012 y1[1] (numeric) = 1.420486657369749 absolute error = 7.369660437461789e-13 relative error = 5.188123661162493e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.907298722017526 y2[1] (numeric) = 1.90729872201718 absolute error = 3.455014052633487e-13 relative error = 1.811469809500423e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.430000000000816 y1[1] (closed_form) = 1.411392797206865 y1[1] (numeric) = 1.411392797207608 absolute error = 7.434053372890048e-13 relative error = 5.267175365781929e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.911458153952397 y2[1] (numeric) = 1.911458153952058 absolute error = 3.392841563254478e-13 relative error = 1.775001747351343e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.440000000000819 y1[1] (closed_form) = 1.402257798107823 y1[1] (numeric) = 1.402257798108573 absolute error = 7.498446308318307e-13 relative error = 5.347409241322496e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.915526440831419 y2[1] (numeric) = 1.915526440831085 absolute error = 3.33510996597397e-13 relative error = 1.74109315062568e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.450000000000823 y1[1] (closed_form) = 1.393082573564185 y1[1] (numeric) = 1.393082573564941 absolute error = 7.565059689795817e-13 relative error = 5.430446000369314e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.919503175829294 y2[1] (numeric) = 1.919503175828967 absolute error = 3.272937476594961e-13 relative error = 1.705096150820868e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.460000000000826 y1[1] (closed_form) = 1.383868041090757 y1[1] (numeric) = 1.38386804109152 absolute error = 7.629452625224076e-13 relative error = 5.51313593398008e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.923387961275836 y2[1] (numeric) = 1.923387961275515 absolute error = 3.206324095117452e-13 relative error = 1.667018906050867e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.470000000000829 y1[1] (closed_form) = 1.37461512213311 y1[1] (numeric) = 1.374615122133879 absolute error = 7.693845560652335e-13 relative error = 5.597090732359416e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.927180408695738 y2[1] (numeric) = 1.927180408695424 absolute error = 3.139710713639943e-13 relative error = 1.629173220873915e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.480000000000833 y1[1] (closed_form) = 1.365324741975427 y1[1] (numeric) = 1.365324741976203 absolute error = 7.756018050031344e-13 relative error = 5.680713028615821e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.930880138847418 y2[1] (numeric) = 1.93088013884711 absolute error = 3.077538224260934e-13 relative error = 1.593852545450066e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.490000000000836 y1[1] (closed_form) = 1.355997829647983 y1[1] (numeric) = 1.355997829648765 absolute error = 7.813749647311852e-13 relative error = 5.762361470254196e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.934486781760944 y2[1] (numeric) = 1.934486781760642 absolute error = 3.015365734881925e-13 relative error = 1.558741968832203e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.500000000000839 y1[1] (closed_form) = 1.346635317834239 y1[1] (numeric) = 1.346635317835026 absolute error = 7.87592213669086e-13 relative error = 5.848593180637442e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.93799997677503 y2[1] (numeric) = 1.937999976774735 absolute error = 2.946531907355165e-13 relative error = 1.520398319229294e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.510000000000843 y1[1] (closed_form) = 1.337238142777572 y1[1] (numeric) = 1.337238142778366 absolute error = 7.935874180020619e-13 relative error = 5.934525740895369e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.941419372573102 y2[1] (numeric) = 1.941419372572815 absolute error = 2.875477633779155e-13 relative error = 1.481121325150927e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.520000000000846 y1[1] (closed_form) = 1.327807244187659 y1[1] (numeric) = 1.327807244188458 absolute error = 7.995826223350377e-13 relative error = 6.02182753434378e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.944744627218431 y2[1] (numeric) = 1.944744627218151 absolute error = 2.806643806252396e-13 relative error = 1.443194014767244e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.530000000000849 y1[1] (closed_form) = 1.318343565146498 y1[1] (numeric) = 1.318343565147304 absolute error = 8.053557820630886e-13 relative error = 6.108846004596647e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.947975408188323 y2[1] (numeric) = 1.947975408188049 absolute error = 2.735589532676386e-13 relative error = 1.404324469999633e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.540000000000853 y1[1] (closed_form) = 1.308848052014109 y1[1] (numeric) = 1.30884805201492 absolute error = 8.113509863960644e-13 relative error = 6.198970041996277e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.951111392407372 y2[1] (numeric) = 1.951111392407106 absolute error = 2.662314813051125e-13 relative error = 1.364511951194256e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.550000000000856 y1[1] (closed_form) = 1.29932165433389 y1[1] (numeric) = 1.299321654334707 absolute error = 8.171241461241152e-13 relative error = 6.288851905135236e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.954152266279771 y2[1] (numeric) = 1.954152266279512 absolute error = 2.595701431573616e-13 relative error = 1.328300499589624e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.560000000000859 y1[1] (closed_form) = 1.289765324737672 y1[1] (numeric) = 1.289765324738495 absolute error = 8.22897305852166e-13 relative error = 6.380209562693406e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.957097725720666 y2[1] (numeric) = 1.957097725720414 absolute error = 2.522426711948356e-13 relative error = 1.288860887628653e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.570000000000863 y1[1] (closed_form) = 1.28018001885045 y1[1] (numeric) = 1.280180018851279 absolute error = 8.286704655802168e-13 relative error = 6.473077640473792e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.959947476186568 y2[1] (numeric) = 1.959947476186322 absolute error = 2.453592884421596e-13 relative error = 1.251866651649005e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.580000000000866 y1[1] (closed_form) = 1.270566695194826 y1[1] (numeric) = 1.27056669519566 absolute error = 8.339995360984176e-13 relative error = 6.563996516298844e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.962701232704804 y2[1] (numeric) = 1.962701232704566 absolute error = 2.382538610845586e-13 relative error = 1.213907940314585e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.590000000000869 y1[1] (closed_form) = 1.260926315095154 y1[1] (numeric) = 1.260926315095994 absolute error = 8.395506512215434e-13 relative error = 6.658205488860684e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.965358719902019 y2[1] (numeric) = 1.965358719901788 absolute error = 2.304822999121825e-13 relative error = 1.172723826842527e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.600000000000873 y1[1] (closed_form) = 1.251259842581411 y1[1] (numeric) = 1.251259842582256 absolute error = 8.453238109495942e-13 relative error = 6.755781510622522e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.967919672031706 y2[1] (numeric) = 1.967919672031483 absolute error = 2.224886941348814e-13 relative error = 1.130578129264703e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.610000000000876 y1[1] (closed_form) = 1.241568244292791 y1[1] (numeric) = 1.241568244293642 absolute error = 8.504308368628699e-13 relative error = 6.849650357699694e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.970383833000787 y2[1] (numeric) = 1.970383833000572 absolute error = 2.147171329625053e-13 relative error = 1.089722364578595e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.620000000000879 y1[1] (closed_form) = 1.231852489381049 y1[1] (numeric) = 1.231852489381905 absolute error = 8.559819519859957e-13 relative error = 6.948737445147257e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.972750956395218 y2[1] (numeric) = 1.972750956395011 absolute error = 2.069455717901292e-13 relative error = 1.049020258331433e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.630000000000883 y1[1] (closed_form) = 1.222113549413578 y1[1] (numeric) = 1.222113549414439 absolute error = 8.610889778992714e-13 relative error = 7.045899935504835e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.975020805504632 y2[1] (numeric) = 1.975020805504433 absolute error = 1.991740106177531e-13 relative error = 1.008465379517167e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.640000000000886 y1[1] (closed_form) = 1.21235239827626 y1[1] (numeric) = 1.212352398277126 absolute error = 8.661960038125471e-13 relative error = 7.144754322622013e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.977193153346011 y2[1] (numeric) = 1.97719315334582 absolute error = 1.91402449445377e-13 relative error = 9.680513465336754e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.650000000000889 y1[1] (closed_form) = 1.202570012076074 y1[1] (numeric) = 1.202570012076945 absolute error = 8.715250743307479e-13 relative error = 7.247187819245371e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.97926778268638 y2[1] (numeric) = 1.979267782686197 absolute error = 1.834088436680759e-13 relative error = 9.266499726436332e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.660000000000893 y1[1] (closed_form) = 1.192767369043488 y1[1] (numeric) = 1.192767369044364 absolute error = 8.766321002440236e-13 relative error = 7.349564743266061e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.981244486064534 y2[1] (numeric) = 1.981244486064359 absolute error = 1.751931932858497e-13 relative error = 8.842583261081854e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.670000000000896 y1[1] (closed_form) = 1.182945449434636 y1[1] (numeric) = 1.182945449435518 absolute error = 8.817391261572993e-13 relative error = 7.453759821120305e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.983123065811783 y2[1] (numeric) = 1.983123065811616 absolute error = 1.667554982986985e-13 relative error = 8.408731720864629e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.680000000000899 y1[1] (closed_form) = 1.173105235433296 y1[1] (numeric) = 1.173105235434182 absolute error = 8.86402062860725e-13 relative error = 7.556031940589929e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.984903334071717 y2[1] (numeric) = 1.984903334071558 absolute error = 1.585398479164724e-13 relative error = 7.98728306789897e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.690000000000903 y1[1] (closed_form) = 1.163247711052665 y1[1] (numeric) = 1.163247711053556 absolute error = 8.908429549592256e-13 relative error = 7.658239483257348e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.986585112818993 y2[1] (numeric) = 1.986585112818843 absolute error = 1.503241975342462e-13 relative error = 7.56696486670707e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.700000000000906 y1[1] (closed_form) = 1.153373862036969 y1[1] (numeric) = 1.153373862037865 absolute error = 8.955058916626513e-13 relative error = 7.764229111981971e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.988168233877139 y2[1] (numeric) = 1.988168233876997 absolute error = 1.41886502547095e-13 relative error = 7.13654408763997e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.710000000000909 y1[1] (closed_form) = 1.14348467576288 y1[1] (numeric) = 1.14348467576378 absolute error = 9.001688283660769e-13 relative error = 7.872154716594919e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.989652538935369 y2[1] (numeric) = 1.989652538935235 absolute error = 1.334488075599438e-13 relative error = 6.707141319828142e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.720000000000913 y1[1] (closed_form) = 1.133581141140785 y1[1] (numeric) = 1.13358114114169 absolute error = 9.046097204645775e-13 relative error = 7.980105593096042e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.991037879564412 y2[1] (numeric) = 1.991037879564287 absolute error = 1.252331571777177e-13 relative error = 6.289843024237965e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.730000000000916 y1[1] (closed_form) = 1.123664248515894 y1[1] (numeric) = 1.123664248516803 absolute error = 9.092726571680032e-13 relative error = 8.092031568762171e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.992324117231361 y2[1] (numeric) = 1.992324117231244 absolute error = 1.165734175856414e-13 relative error = 5.851127162363423e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.740000000000919 y1[1] (closed_form) = 1.113734989569203 y1[1] (numeric) = 1.113734989570117 absolute error = 9.137135492665038e-13 relative error = 8.20404816068436e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.993511123313521 y2[1] (numeric) = 1.993511123313413 absolute error = 1.079136779935652e-13 relative error = 5.413246845304588e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.750000000000923 y1[1] (closed_form) = 1.103794357218335 y1[1] (numeric) = 1.103794357219253 absolute error = 9.181544413650045e-13 relative error = 8.318165746732384e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.994598779111272 y2[1] (numeric) = 1.994598779111173 absolute error = 9.85878045867139e-14 relative error = 4.942738640933161e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.760000000000926 y1[1] (closed_form) = 1.09384334551824 y1[1] (numeric) = 1.093843345519163 absolute error = 9.223732888585801e-13 relative error = 8.432407553035658e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.995586975859942 y2[1] (numeric) = 1.995586975859852 absolute error = 8.948397578478762e-14 relative error = 4.484092994555e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.770000000000929 y1[1] (closed_form) = 1.083882949561796 y1[1] (numeric) = 1.083882949562722 absolute error = 9.268141809570807e-13 relative error = 8.550869642628694e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.996475614740679 y2[1] (numeric) = 1.996475614740598 absolute error = 8.038014698286133e-14 relative error = 4.026102116619235e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.780000000000933 y1[1] (closed_form) = 1.073914165380297 y1[1] (numeric) = 1.073914165381228 absolute error = 9.308109838457312e-13 relative error = 8.667461645001303e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.997264606890335 y2[1] (numeric) = 1.997264606890264 absolute error = 7.105427357601002e-14 relative error = 3.557579367845447e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.790000000000936 y1[1] (closed_form) = 1.063937989843856 y1[1] (numeric) = 1.06393798984479 absolute error = 9.345857421294568e-13 relative error = 8.784212529779269e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.997953873410353 y2[1] (numeric) = 1.997953873410291 absolute error = 6.17284001691587e-14 relative error = 3.089580845217066e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.80000000000094 y1[1] (closed_form) = 1.053955420561711 y1[1] (numeric) = 1.05395542056265 absolute error = 9.388045896230324e-13 relative error = 8.907441162195373e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.998543345374656 y2[1] (numeric) = 1.998543345374603 absolute error = 5.306866057708248e-14 relative error = 2.655367005169157e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.810000000000943 y1[1] (closed_form) = 1.043967455782474 y1[1] (numeric) = 1.043967455783416 absolute error = 9.425793479067579e-13 relative error = 9.028819267170322e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.999032963836537 y2[1] (numeric) = 1.999032963836494 absolute error = 4.374278717023117e-14 relative error = 2.188197391516754e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.820000000000946 y1[1] (closed_form) = 1.033975094294297 y1[1] (numeric) = 1.033975094295243 absolute error = 9.463541061904834e-13 relative error = 9.152581250870302e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.99942267983456 y2[1] (numeric) = 1.999422679834526 absolute error = 3.463895836830488e-14 relative error = 1.732448007000253e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.83000000000095 y1[1] (closed_form) = 1.023979335325003 y1[1] (numeric) = 1.023979335325954 absolute error = 9.50350909079134e-13 relative error = 9.280957889423617e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.999712454397449 y2[1] (numeric) = 1.999712454397424 absolute error = 2.509104035652854e-14 relative error = 1.254732414220471e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.840000000000953 y1[1] (closed_form) = 1.01398117844216 y1[1] (numeric) = 1.013981178443114 absolute error = 9.539036227579345e-13 relative error = 9.407508177059793e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.999902258547988 y2[1] (numeric) = 1.999902258547973 absolute error = 1.532107773982716e-14 relative error = 7.660913264306674e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.850000000000956 y1[1] (closed_form) = 1.003981623453123 y1[1] (numeric) = 1.003981623454081 absolute error = 9.57456336436735e-13 relative error = 9.5365922450217e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.999992073305922 y2[1] (numeric) = 1.999992073305916 absolute error = 5.995204332975845e-15 relative error = 2.99761404707268e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.86000000000096 y1[1] (closed_form) = 0.9939816703050592 y1[1] (numeric) = 0.9939816703060201 absolute error = 9.60898027813073e-13 relative error = 9.667160436853602e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.99998188968985 y2[1] (numeric) = 1.999981889689853 absolute error = 3.552713678800501e-15 relative error = 1.776372924732555e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.870000000000963 y1[1] (closed_form) = 0.9839823189849495 y1[1] (numeric) = 0.9839823189859135 absolute error = 9.640066522820234e-13 relative error = 9.796991609325537e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.999871708718123 y2[1] (numeric) = 1.999871708718137 absolute error = 1.332267629550188e-14 relative error = 6.661765470966854e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.880000000000966 y1[1] (closed_form) = 0.9739845694195932 y1[1] (numeric) = 0.9739845694205603 absolute error = 9.671152767509739e-13 relative error = 9.929472263891071e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 1.999661541408749 y2[1] (numeric) = 1.999661541408772 absolute error = 2.309263891220326e-14 relative error = 1.154827376233612e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.89000000000097 y1[1] (closed_form) = 0.9639894213756155 y1[1] (numeric) = 0.9639894213765858 absolute error = 9.703349235223868e-13 relative error = 1.006582543341312e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.999351408778282 y2[1] (numeric) = 1.999351408778315 absolute error = 3.26405569239796e-14 relative error = 1.632557277358503e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.900000000000973 y1[1] (closed_form) = 0.9539978743594916 y1[1] (numeric) = 0.9539978743604649 absolute error = 9.733325256888747e-13 relative error = 1.020266975272208e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.998941341839727 y2[1] (numeric) = 1.99894134183977 absolute error = 4.263256414560601e-14 relative error = 2.132757137654129e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.910000000000976 y1[1] (closed_form) = 0.9440109275175966 y1[1] (numeric) = 0.9440109275185729 absolute error = 9.762191055529001e-13 relative error = 1.034118437717664e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.998431381599437 y2[1] (numeric) = 1.998431381599489 absolute error = 5.240252676230739e-14 relative error = 2.622182940320284e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.92000000000098 y1[1] (closed_form) = 0.9340295795362926 y1[1] (numeric) = 0.9340295795372716 absolute error = 9.78994663114463e-13 relative error = 1.048140963159318e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.99782157905301 y2[1] (numeric) = 1.997821579053073 absolute error = 6.306066779870889e-14 relative error = 3.156471451699925e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.930000000000983 y1[1] (closed_form) = 0.9240548285420598 y1[1] (numeric) = 0.9240548285430413 absolute error = 9.815481760711009e-13 relative error = 1.062218545645989e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.997111995180192 y2[1] (numeric) = 1.997111995180265 absolute error = 7.283063041541027e-14 relative error = 3.646797505156391e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.940000000000986 y1[1] (closed_form) = 0.9140876720016853 y1[1] (numeric) = 0.9140876720026696 absolute error = 9.843237336326638e-13 relative error = 1.076837336048056e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.996302700938781 y2[1] (numeric) = 1.996302700938864 absolute error = 8.304468224196171e-14 relative error = 4.15992435430304e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.95000000000099 y1[1] (closed_form) = 0.9041291066225173 y1[1] (numeric) = 0.9041291066235042 absolute error = 9.868772465893016e-13 relative error = 1.091522482088758e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.995393777257525 y2[1] (numeric) = 1.995393777257618 absolute error = 9.281464485866309e-14 relative error = 4.65144503889492e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.960000000000993 y1[1] (closed_form) = 0.8941801282527949 y1[1] (numeric) = 0.8941801282537842 absolute error = 9.89319737243477e-13 relative error = 1.106398706462626e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.994385315028035 y2[1] (numeric) = 1.994385315028138 absolute error = 1.030286966852145e-13 relative error = 5.165937389774967e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.970000000000996 y1[1] (closed_form) = 0.8842417317820643 y1[1] (numeric) = 0.884241731783056 absolute error = 9.916512055951898e-13 relative error = 1.121470713213972e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.993277415095694 y2[1] (numeric) = 1.993277415095808 absolute error = 1.13242748511766e-13 relative error = 5.6812337135887e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.980000000001 y1[1] (closed_form) = 0.8743149110416907 y1[1] (numeric) = 0.8743149110426844 absolute error = 9.937606293419776e-13 relative error = 1.136616357323673e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.992070188249572 y2[1] (numeric) = 1.992070188249696 absolute error = 1.232347557333924e-13 relative error = 6.186265748079815e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.990000000001003 y1[1] (closed_form) = 0.8644006587054756 y1[1] (numeric) = 0.8644006587064714 absolute error = 9.958700530887654e-13 relative error = 1.152093121470058e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.990763755211348 y2[1] (numeric) = 1.990763755211481 absolute error = 1.334488075599438e-13 relative error = 6.703397488054847e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.000000000001005 y1[1] (closed_form) = 0.8544999661903918 y1[1] (numeric) = 0.8544999661913886 absolute error = 9.967582315084655e-13 relative error = 1.166481300113214e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.989358246623235 y2[1] (numeric) = 1.989358246623379 absolute error = 1.438849039914203e-13 relative error = 7.232729662224114e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.010000000001 y1[1] (closed_form) = 0.8446138235574472 y1[1] (numeric) = 0.8446138235584371 absolute error = 9.898748487557896e-13 relative error = 1.17198513823337e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.987853803034925 y2[1] (numeric) = 1.987853803035077 absolute error = 1.527666881884215e-13 relative error = 7.685006208967047e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.020000000000994 y1[1] (closed_form) = 0.8347432194126588 y1[1] (numeric) = 0.8347432194136416 absolute error = 9.827694213981886e-13 relative error = 1.177331421858909e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.986250574889519 y2[1] (numeric) = 1.986250574889681 absolute error = 1.618705169903478e-13 relative error = 8.149551674735274e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.030000000000989 y1[1] (closed_form) = 0.8248891408082156 y1[1] (numeric) = 0.8248891408091914 absolute error = 9.757750163430501e-13 relative error = 1.182916549716e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.984548722508498 y2[1] (numeric) = 1.984548722508668 absolute error = 1.70530256582424e-13 relative error = 8.592898458389643e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.040000000000983 y1[1] (closed_form) = 0.8150525731437663 y1[1] (numeric) = 0.815052573144735 absolute error = 9.686695889854491e-13 relative error = 1.188474978060816e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.98274841607568 y2[1] (numeric) = 1.982748416075859 absolute error = 1.789679515695752e-13 relative error = 9.026256186541024e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.050000000000978 y1[1] (closed_form) = 0.8052345000678803 y1[1] (numeric) = 0.8052345000688418 absolute error = 9.614531393253856e-13 relative error = 1.194003907239861e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.980849835620209 y2[1] (numeric) = 1.980849835620397 absolute error = 1.876276911616515e-13 relative error = 9.472080507450721e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.060000000000972 y1[1] (closed_form) = 0.7954359033796835 y1[1] (numeric) = 0.7954359033806375 absolute error = 9.54014645060397e-13 relative error = 1.199360804568837e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.978853170998549 y2[1] (numeric) = 1.978853170998744 absolute error = 1.956212969389526e-13 relative error = 9.885589279988881e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.070000000000967 y1[1] (closed_form) = 0.7856577629306791 y1[1] (numeric) = 0.7856577629316257 absolute error = 9.465761507954085e-13 relative error = 1.20481995527476e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.976758621875496 y2[1] (numeric) = 1.976758621875701 absolute error = 2.042810365310288e-13 relative error = 1.033414167366638e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.080000000000961 y1[1] (closed_form) = 0.7759010565267638 y1[1] (numeric) = 0.7759010565277029 absolute error = 9.391376565304199e-13 relative error = 1.210383268112002e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.97456639770422 y2[1] (numeric) = 1.974566397704433 absolute error = 2.131628207280301e-13 relative error = 1.079542430053855e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.090000000000956 y1[1] (closed_form) = 0.7661667598304471 y1[1] (numeric) = 0.7661667598313788 absolute error = 9.316991622654314e-13 relative error = 1.21605270694805e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.972276717705308 y2[1] (numeric) = 1.97227671770553 absolute error = 2.213784711102562e-13 relative error = 1.12245137369884e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.10000000000095 y1[1] (closed_form) = 0.7564558462632871 y1[1] (numeric) = 0.7564558462642113 absolute error = 9.241496456979803e-13 relative error = 1.221683526227024e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.969889810844855 y2[1] (numeric) = 1.969889810845084 absolute error = 2.291500322826323e-13 relative error = 1.163263198891076e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.110000000000944 y1[1] (closed_form) = 0.746769286908548 y1[1] (numeric) = 0.7467692869094642 absolute error = 9.161560399206792e-13 relative error = 1.226826084014988e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.967405915811556 y2[1] (numeric) = 1.967405915811793 absolute error = 2.369215934550084e-13 relative error = 1.20423340984658e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.120000000000939 y1[1] (closed_form) = 0.737108050414093 y1[1] (numeric) = 0.7371080504150016 absolute error = 9.086065233532281e-13 relative error = 1.232663953192196e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.964825280992844 y2[1] (numeric) = 1.964825280993089 absolute error = 2.446931546273845e-13 relative error = 1.24536851695912e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.130000000000933 y1[1] (closed_form) = 0.7274731028955208 y1[1] (numeric) = 0.7274731028964215 absolute error = 9.007239398783895e-13 relative error = 1.238154285420709e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.962148164450052 y2[1] (numeric) = 1.962148164450304 absolute error = 2.520206265899105e-13 relative error = 1.284411805163279e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.140000000000928 y1[1] (closed_form) = 0.7178654078395539 y1[1] (numeric) = 0.7178654078404466 absolute error = 8.927303341010884e-13 relative error = 1.243590127553016e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.959374833892602 y2[1] (numeric) = 1.959374833892862 absolute error = 2.593480985524366e-13 relative error = 1.323626771490176e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.150000000000922 y1[1] (closed_form) = 0.7082859260076917 y1[1] (numeric) = 0.7082859260085762 absolute error = 8.845146837188622e-13 relative error = 1.248810192663996e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.95650556665124 y2[1] (numeric) = 1.956505566651507 absolute error = 2.664535259100376e-13 relative error = 1.361884834123422e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.160000000000917 y1[1] (closed_form) = 0.6987356153401344 y1[1] (numeric) = 0.698735615341011 absolute error = 8.766321002440236e-13 relative error = 1.254597706197203e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.953540649650298 y2[1] (numeric) = 1.953540649650572 absolute error = 2.735589532676386e-13 relative error = 1.400323834144983e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.170000000000911 y1[1] (closed_form) = 0.6892154308599903 y1[1] (numeric) = 0.6892154308608588 absolute error = 8.6852747216426e-13 relative error = 1.260168349801059e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.950480379379006 y2[1] (numeric) = 1.950480379379286 absolute error = 2.802202914153895e-13 relative error = 1.436673213316845e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.180000000000906 y1[1] (closed_form) = 0.6797263245777738 y1[1] (numeric) = 0.6797263245786342 absolute error = 8.604228440844963e-13 relative error = 1.265837165595971e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.94732506186184 y2[1] (numeric) = 1.947325061862127 absolute error = 2.871036741680655e-13 relative error = 1.47434899180913e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.1900000000009 y1[1] (closed_form) = 0.6702692453962057 y1[1] (numeric) = 0.670269245397058 absolute error = 8.523182160047327e-13 relative error = 1.271605734350701e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.944075012627923 y2[1] (numeric) = 1.944075012628217 absolute error = 2.939870569207415e-13 relative error = 1.512220747713544e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.200000000000895 y1[1] (closed_form) = 0.6608451390153232 y1[1] (numeric) = 0.6608451390161674 absolute error = 8.44213587924969e-13 relative error = 1.277475671808481e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.940730556679469 y2[1] (numeric) = 1.94073055667977 absolute error = 3.006483950684924e-13 relative error = 1.549150622860767e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.210000000000889 y1[1] (closed_form) = 0.651454947837911 y1[1] (numeric) = 0.651454947838747 absolute error = 8.359979375427429e-13 relative error = 1.283278207214949e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.937292028459288 y2[1] (numeric) = 1.937292028459595 absolute error = 3.073097332162433e-13 relative error = 1.586285024156343e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.220000000000883 y1[1] (closed_form) = 0.6420996108752619 y1[1] (numeric) = 0.6420996108760897 absolute error = 8.277822871605167e-13 relative error = 1.289180484056276e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.933759771817335 y2[1] (numeric) = 1.933759771817649 absolute error = 3.139710713639943e-13 relative error = 1.623630173405285e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.230000000000878 y1[1] (closed_form) = 0.6327800636532758 y1[1] (numeric) = 0.6327800636540954 absolute error = 8.196776590807531e-13 relative error = 1.295359487700114e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.93013413997633 y2[1] (numeric) = 1.93013413997665 absolute error = 3.199662756969701e-13 relative error = 1.657741133478391e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.240000000000872 y1[1] (closed_form) = 0.6234972381189087 y1[1] (numeric) = 0.62349723811972 absolute error = 8.113509863960644e-13 relative error = 1.301290425670386e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.926415495496438 y2[1] (numeric) = 1.926415495496764 absolute error = 3.25961480029946e-13 relative error = 1.692062178652408e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.250000000000867 y1[1] (closed_form) = 0.6142520625469784 y1[1] (numeric) = 0.6142520625477813 absolute error = 8.029132914089132e-13 relative error = 1.307139756404979e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.922604210239006 y2[1] (numeric) = 1.922604210239338 absolute error = 3.317346397579968e-13 relative error = 1.725444259360889e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.260000000000861 y1[1] (closed_form) = 0.6050454614473378 y1[1] (numeric) = 0.6050454614481324 absolute error = 7.945866187242245e-13 relative error = 1.313267629218278e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.918700665329384 y2[1] (numeric) = 1.918700665329722 absolute error = 3.377298440909726e-13 relative error = 1.76020079730881e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.270000000000856 y1[1] (closed_form) = 0.5958783554724248 y1[1] (numeric) = 0.5958783554732109 absolute error = 7.860379014346108e-13 relative error = 1.31912477473934e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.914705251118812 y2[1] (numeric) = 1.914705251119155 absolute error = 3.435030038190234e-13 relative error = 1.794025496186976e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.28000000000085 y1[1] (closed_form) = 0.5867516613251976 y1[1] (numeric) = 0.5867516613259751 absolute error = 7.774891841449971e-13 relative error = 1.32507368174981e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.910618367145379 y2[1] (numeric) = 1.910618367145728 absolute error = 3.490541189421492e-13 relative error = 1.82691700731248e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.290000000000845 y1[1] (closed_form) = 0.5776662916674654 y1[1] (numeric) = 0.5776662916682345 absolute error = 7.690514891578459e-13 relative error = 1.331307539060202e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.906440422094078 y2[1] (numeric) = 1.906440422094433 absolute error = 3.550493232751251e-13 relative error = 1.862367788473195e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.300000000000839 y1[1] (closed_form) = 0.5686231550286227 y1[1] (numeric) = 0.5686231550293831 absolute error = 7.603917495657697e-13 relative error = 1.337250765891681e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.902171833755932 y2[1] (numeric) = 1.902171833756292 absolute error = 3.601563491884008e-13 relative error = 1.893395448282159e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.310000000000834 y1[1] (closed_form) = 0.5596231557147977 y1[1] (numeric) = 0.5596231557155493 absolute error = 7.51620987671231e-13 relative error = 1.343084145099746e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.897813028986218 y2[1] (numeric) = 1.897813028986583 absolute error = 3.650413304967515e-13 relative error = 1.923484162671972e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.320000000000828 y1[1] (closed_form) = 0.5506671937184217 y1[1] (numeric) = 0.5506671937191646 absolute error = 7.429612480791548e-13 relative error = 1.349201943668104e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.89336444366178 y2[1] (numeric) = 1.89336444366215 absolute error = 3.701483564100272e-13 relative error = 1.954976801477046e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.330000000000823 y1[1] (closed_form) = 0.541756164628231 y1[1] (numeric) = 0.5417561646289654 absolute error = 7.344125307895411e-13 relative error = 1.355614534249955e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.888826522637444 y2[1] (numeric) = 1.888826522637819 absolute error = 3.748112931134528e-13 relative error = 1.984360599670576e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.340000000000817 y1[1] (closed_form) = 0.5328909595397089 y1[1] (numeric) = 0.5328909595404344 absolute error = 7.255307465925398e-13 relative error = 1.361499446752157e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.884199719701531 y2[1] (numeric) = 1.884199719701911 absolute error = 3.799183190267286e-13 relative error = 2.016337838575361e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.350000000000811 y1[1] (closed_form) = 0.5240724649659765 y1[1] (numeric) = 0.5240724649666932 absolute error = 7.167599846980011e-13 relative error = 1.367673428033534e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.879484497530479 y2[1] (numeric) = 1.879484497530863 absolute error = 3.843592111252292e-13 relative error = 2.045024641758165e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.360000000000806 y1[1] (closed_form) = 0.5153015627491424 y1[1] (numeric) = 0.5153015627498504 absolute error = 7.079892228034623e-13 relative error = 1.373931837167984e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.874681327642574 y2[1] (numeric) = 1.874681327642963 absolute error = 3.890221478286549e-13 relative error = 2.075137475860247e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.3700000000008 y1[1] (closed_form) = 0.5065791299721194 y1[1] (numeric) = 0.5065791299728185 absolute error = 6.991074386064611e-13 relative error = 1.380055744982897e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.869790690350805 y2[1] (numeric) = 1.869790690351198 absolute error = 3.934630399271555e-13 relative error = 2.104315964121819e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.380000000000795 y1[1] (closed_form) = 0.4979060388709163 y1[1] (numeric) = 0.4979060388716067 absolute error = 6.903366767119223e-13 relative error = 1.386479823135654e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.864813074714823 y2[1] (numeric) = 1.864813074715221 absolute error = 3.976818874207311e-13 relative error = 2.132556301824228e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.390000000000789 y1[1] (closed_form) = 0.4892831567474161 y1[1] (numeric) = 0.4892831567480976 absolute error = 6.815104036661523e-13 relative error = 1.392875258973957e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.859748978492045 y2[1] (numeric) = 1.859748978492447 absolute error = 4.014566457044566e-13 relative error = 2.158660390984448e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.400000000000784 y1[1] (closed_form) = 0.480711345882645 y1[1] (numeric) = 0.4807113458833177 absolute error = 6.726841306203823e-13 relative error = 1.399351474397285e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.854598908087874 y2[1] (numeric) = 1.854598908088279 absolute error = 4.056754931980322e-13 relative error = 2.187402847208032e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.410000000000778 y1[1] (closed_form) = 0.4721914634505464 y1[1] (numeric) = 0.4721914634512104 absolute error = 6.639688798770749e-13 relative error = 1.406143336487094e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.849363378505056 y2[1] (numeric) = 1.849363378505466 absolute error = 4.094502514817577e-13 relative error = 2.214006485911596e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.420000000000773 y1[1] (closed_form) = 0.4637243614322638 y1[1] (numeric) = 0.463724361432919 absolute error = 6.551981179825361e-13 relative error = 1.412904243285568e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.84404291329219 y2[1] (numeric) = 1.844042913292602 absolute error = 4.127809205556332e-13 relative error = 2.238456152946522e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.430000000000767 y1[1] (closed_form) = 0.455310886530943 y1[1] (numeric) = 0.4553108865315894 absolute error = 6.464273560879974e-13 relative error = 1.419749395875836e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.83863804449136 y2[1] (numeric) = 1.838638044491776 absolute error = 4.158895450245836e-13 relative error = 2.261943541691671e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.440000000000762 y1[1] (closed_form) = 0.446951880087063 y1[1] (numeric) = 0.4469518800877005 absolute error = 6.375455718909961e-13 relative error = 1.426430003531492e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.833149312584945 y2[1] (numeric) = 1.833149312585364 absolute error = 4.194422587033841e-13 relative error = 2.288096533238331e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.450000000000756 y1[1] (closed_form) = 0.4386481779943023 y1[1] (numeric) = 0.4386481779949311 absolute error = 6.287192988452261e-13 relative error = 1.43331109163616e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.827577266441559 y2[1] (numeric) = 1.827577266441982 absolute error = 4.225508831723346e-13 relative error = 2.312082180771899e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.46000000000075 y1[1] (closed_form) = 0.4304006106159505 y1[1] (numeric) = 0.4304006106165705 absolute error = 6.200040481019187e-13 relative error = 1.440527807836111e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.821922463261175 y2[1] (numeric) = 1.821922463261601 absolute error = 4.2543746303636e-13 relative error = 2.335101913584414e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.470000000000745 y1[1] (closed_form) = 0.4222100027018725 y1[1] (numeric) = 0.4222100027024836 absolute error = 6.111222639049174e-13 relative error = 1.44743672578605e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.816185468519398 y2[1] (numeric) = 1.816185468519827 absolute error = 4.283240429003854e-13 relative error = 2.358371709963995e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.480000000000739 y1[1] (closed_form) = 0.4140771733060341 y1[1] (numeric) = 0.4140771733066364 absolute error = 6.022959908591474e-13 relative error = 1.454550092801192e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.810366855910922 y2[1] (numeric) = 1.810366855911353 absolute error = 4.312106227644108e-13 relative error = 2.381896361814681e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.490000000000734 y1[1] (closed_form) = 0.4060029357045977 y1[1] (numeric) = 0.4060029357051912 absolute error = 5.935807401158399e-13 relative error = 1.462010955870825e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.804467207292158 y2[1] (numeric) = 1.804467207292592 absolute error = 4.336531134185861e-13 relative error = 2.40321969646287e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.500000000000728 y1[1] (closed_form) = 0.3979880973145948 y1[1] (numeric) = 0.3979880973151796 absolute error = 5.848099782213012e-13 relative error = 1.469415749283152e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.798487112623052 y2[1] (numeric) = 1.798487112623488 absolute error = 4.363176486776865e-13 relative error = 2.426025994933749e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.510000000000723 y1[1] (closed_form) = 0.3900334596131856 y1[1] (numeric) = 0.3900334596137616 absolute error = 5.760392163267625e-13 relative error = 1.476896922889763e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.792427169908087 y2[1] (numeric) = 1.792427169908526 absolute error = 4.389821839367869e-13 relative error = 2.449093560433461e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.520000000000717 y1[1] (closed_form) = 0.3821398180575112 y1[1] (numeric) = 0.3821398180580785 absolute error = 5.672684544322237e-13 relative error = 1.484452620812341e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.786287985136486 y2[1] (numeric) = 1.786287985136927 absolute error = 4.407585407761871e-13 relative error = 2.467455104908573e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.530000000000712 y1[1] (closed_form) = 0.3743079620051492 y1[1] (numeric) = 0.3743079620057077 absolute error = 5.58497692537685e-13 relative error = 1.492080717561659e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.780070172221609 y2[1] (numeric) = 1.780070172222052 absolute error = 4.432010314303625e-13 relative error = 2.489795280807539e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.540000000000706 y1[1] (closed_form) = 0.3665386746351782 y1[1] (numeric) = 0.366538674635728 absolute error = 5.498379529456088e-13 relative error = 1.500081685767188e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.773774352939566 y2[1] (numeric) = 1.773774352940011 absolute error = 4.454214774796128e-13 relative error = 2.511150737642833e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.550000000000701 y1[1] (closed_form) = 0.3588327328698611 y1[1] (numeric) = 0.3588327328704021 absolute error = 5.4106719105107e-13 relative error = 1.507853496875104e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.767401156867038 y2[1] (numeric) = 1.767401156867486 absolute error = 4.471978343190131e-13 relative error = 2.530256544087211e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.560000000000695 y1[1] (closed_form) = 0.3511909072969526 y1[1] (numeric) = 0.3511909072974849 absolute error = 5.322964291565313e-13 relative error = 1.515689666493681e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.760951221318324 y2[1] (numeric) = 1.760951221318773 absolute error = 4.489741911584133e-13 relative error = 2.549611742353045e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.57000000000069 y1[1] (closed_form) = 0.3436139620926419 y1[1] (numeric) = 0.3436139620931654 absolute error = 5.234701561107613e-13 relative error = 1.52342516271102e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.754425191281601 y2[1] (numeric) = 1.754425191282051 absolute error = 4.503064587879635e-13 relative error = 2.56668942640419e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.580000000000684 y1[1] (closed_form) = 0.3361026549451354 y1[1] (numeric) = 0.3361026549456502 absolute error = 5.148104165186851e-13 relative error = 1.531705890876469e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.747823719354436 y2[1] (numeric) = 1.747823719354888 absolute error = 4.518607710224387e-13 relative error = 2.585276570049838e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.590000000000678 y1[1] (closed_form) = 0.3286577369788882 y1[1] (numeric) = 0.3286577369793945 absolute error = 5.062616992290714e-13 relative error = 1.540391849231262e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.74114746567852 y2[1] (numeric) = 1.741147465678973 absolute error = 4.534150832569139e-13 relative error = 2.604116493258769e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.600000000000673 y1[1] (closed_form) = 0.3212799526794932 y1[1] (numeric) = 0.3212799526799908 absolute error = 4.976019596369952e-13 relative error = 1.548811108464647e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.734397097873656 y2[1] (numeric) = 1.734397097874111 absolute error = 4.547473508864641e-13 relative error = 2.621933301456611e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.610000000000667 y1[1] (closed_form) = 0.3139700398192319 y1[1] (numeric) = 0.3139700398197209 absolute error = 4.889977311961502e-13 relative error = 1.55746622027277e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.727573290971002 y2[1] (numeric) = 1.727573290971457 absolute error = 4.558575739110893e-13 relative error = 2.638716263405934e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.620000000000662 y1[1] (closed_form) = 0.3067287293832989 y1[1] (numeric) = 0.3067287293837793 absolute error = 4.804490139065365e-13 relative error = 1.566364568694022e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.720676727345559 y2[1] (numeric) = 1.720676727346016 absolute error = 4.571898415406395e-13 relative error = 2.657035073903358e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.630000000000656 y1[1] (closed_form) = 0.2995567454967033 y1[1] (numeric) = 0.2995567454971753 absolute error = 4.720113189193853e-13 relative error = 1.575699182259209e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.713708096647943 y2[1] (numeric) = 1.713708096648401 absolute error = 4.578559753554146e-13 relative error = 2.671726744192856e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.640000000000651 y1[1] (closed_form) = 0.2924548053518573 y1[1] (numeric) = 0.2924548053523208 absolute error = 4.634626016297716e-13 relative error = 1.584732386503863e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.706668095735418 y2[1] (numeric) = 1.706668095735877 absolute error = 4.587441537751147e-13 relative error = 2.68795177528316e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.650000000000645 y1[1] (closed_form) = 0.285423619136857 y1[1] (numeric) = 0.285423619137312 absolute error = 4.549693954913892e-13 relative error = 1.594014527834983e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.699557428602207 y2[1] (numeric) = 1.699557428602666 absolute error = 4.591882429849647e-13 relative error = 2.701810690578558e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.66000000000064 y1[1] (closed_form) = 0.2784638899644645 y1[1] (numeric) = 0.278463889964911 absolute error = 4.46531700504238e-13 relative error = 1.6035533388592e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.692376806309099 y2[1] (numeric) = 1.692376806309559 absolute error = 4.596323321948148e-13 relative error = 2.715898318160162e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.670000000000634 y1[1] (closed_form) = 0.2715763138017975 y1[1] (numeric) = 0.2715763138022356 absolute error = 4.380940055170868e-13 relative error = 1.613152485149414e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.685126946912339 y2[1] (numeric) = 1.685126946912798 absolute error = 4.596323321948148e-13 relative error = 2.727582827139522e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.680000000000629 y1[1] (closed_form) = 0.2647615794007324 y1[1] (numeric) = 0.2647615794011621 absolute error = 4.297118216811668e-13 relative error = 1.623014270627131e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.677808575391824 y2[1] (numeric) = 1.677808575392284 absolute error = 4.600764214046649e-13 relative error = 2.742127011105672e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.690000000000623 y1[1] (closed_form) = 0.2580203682290306 y1[1] (numeric) = 0.258020368229452 absolute error = 4.213851489964782e-13 relative error = 1.63314683987443e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.67042242357861 y2[1] (numeric) = 1.67042242357907 absolute error = 4.605205106145149e-13 relative error = 2.75691049230484e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.700000000000617 y1[1] (closed_form) = 0.2513533544021915 y1[1] (numeric) = 0.2513533544026046 absolute error = 4.131139874630207e-13 relative error = 1.643558680350831e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.66296923008172 y2[1] (numeric) = 1.662969230082181 absolute error = 4.602984660095899e-13 relative error = 2.767931346432491e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.710000000000612 y1[1] (closed_form) = 0.2447612046160419 y1[1] (numeric) = 0.2447612046164468 absolute error = 4.049538482320258e-13 relative error = 1.654485435579053e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.655449740214296 y2[1] (numeric) = 1.655449740214756 absolute error = 4.598543767997398e-13 relative error = 2.777821432018904e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.720000000000606 y1[1] (closed_form) = 0.2382445780800672 y1[1] (numeric) = 0.2382445780804638 absolute error = 3.966826866985684e-13 relative error = 1.665022935234458e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.647864705919056 y2[1] (numeric) = 1.647864705919516 absolute error = 4.600764214046649e-13 relative error = 2.791955066165875e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.730000000000601 y1[1] (closed_form) = 0.2318041264514902 y1[1] (numeric) = 0.2318041264518787 absolute error = 3.885503030431892e-13 relative error = 1.676200976191428e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.64021488569311 y2[1] (numeric) = 1.64021488569357 absolute error = 4.598543767997398e-13 relative error = 2.803622749743659e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.740000000000595 y1[1] (closed_form) = 0.2254404937701069 y1[1] (numeric) = 0.2254404937704873 absolute error = 3.804179193878099e-13 relative error = 1.687442717259754e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.632501044512105 y2[1] (numeric) = 1.632501044512565 absolute error = 4.594102875898898e-13 relative error = 2.814150037663165e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.75000000000059 y1[1] (closed_form) = 0.2191543163938825 y1[1] (numeric) = 0.2191543163942548 absolute error = 3.722855357324306e-13 relative error = 1.698736953295174e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.624723953753732 y2[1] (numeric) = 1.624723953754191 absolute error = 4.587441537751147e-13 relative error = 2.823520590776302e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.760000000000584 y1[1] (closed_form) = 0.212946222935316 y1[1] (numeric) = 0.2129462229356802 absolute error = 3.642641743795139e-13 relative error = 1.710592324007371e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.616884391120585 y2[1] (numeric) = 1.616884391121043 absolute error = 4.580780199603396e-13 relative error = 2.833090742145564e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.770000000000579 y1[1] (closed_form) = 0.2068168341985799 y1[1] (numeric) = 0.2068168341989361 absolute error = 3.562428130265971e-13 relative error = 1.722503946098229e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.608983140562394 y2[1] (numeric) = 1.608983140562851 absolute error = 4.571898415406395e-13 relative error = 2.841483108274435e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.780000000000573 y1[1] (closed_form) = 0.20076676311744 y1[1] (numeric) = 0.2007667631177884 absolute error = 3.483879851273741e-13 relative error = 1.735287154694933e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.601020992197632 y2[1] (numeric) = 1.601020992198088 absolute error = 4.563016631209393e-13 relative error = 2.850066709585111e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.790000000000568 y1[1] (closed_form) = 0.1947966146939629 y1[1] (numeric) = 0.1947966146943035 absolute error = 3.405609128037668e-13 relative error = 1.748289688395295e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.592998742234499 y2[1] (numeric) = 1.592998742234954 absolute error = 4.547473508864641e-13 relative error = 2.854662334815093e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.800000000000562 y1[1] (closed_form) = 0.1889069859380157 y1[1] (numeric) = 0.1889069859383485 absolute error = 3.327893516313907e-13 relative error = 1.761657198535716e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.584917192891306 y2[1] (numeric) = 1.58491719289176 absolute error = 4.53637127861839e-13 relative error = 2.8622134323263e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.810000000000556 y1[1] (closed_form) = 0.1830984658075661 y1[1] (numeric) = 0.1830984658078911 absolute error = 3.250177904590146e-13 relative error = 1.775098382313065e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.576777152316254 y2[1] (numeric) = 1.576777152316707 absolute error = 4.525269048372138e-13 relative error = 2.869948389171297e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.820000000000551 y1[1] (closed_form) = 0.1773716351497865 y1[1] (numeric) = 0.1773716351501038 absolute error = 3.173294960134854e-13 relative error = 1.789065629042138e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.568579434506617 y2[1] (numeric) = 1.568579434507068 absolute error = 4.511946372076636e-13 relative error = 2.87645386189564e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.830000000000545 y1[1] (closed_form) = 0.1717270666429705 y1[1] (numeric) = 0.1717270666432803 absolute error = 3.097522238704187e-13 relative error = 1.803747248035218e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.560324859227343 y2[1] (numeric) = 1.560324859227793 absolute error = 4.498623695781134e-13 relative error = 2.883132745836535e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.84000000000054 y1[1] (closed_form) = 0.166165324739265 y1[1] (numeric) = 0.1661653247395672 absolute error = 3.021471961517364e-13 relative error = 1.818352876124092e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.552014251929083 y2[1] (numeric) = 1.552014251929531 absolute error = 4.483080573436382e-13 relative error = 2.888556318258108e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.850000000000534 y1[1] (closed_form) = 0.1606869656082256 y1[1] (numeric) = 0.1606869656085202 absolute error = 2.946531907355165e-13 relative error = 1.833709346742641e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.543648443665639 y2[1] (numeric) = 1.543648443666087 absolute error = 4.471978343190131e-13 relative error = 2.897018658322684e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.860000000000529 y1[1] (closed_form) = 0.1552925370812001 y1[1] (numeric) = 0.1552925370814873 absolute error = 2.87214696470528e-13 relative error = 1.849507399833051e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.535228271010869 y2[1] (numeric) = 1.535228271011314 absolute error = 4.451994328746878e-13 relative error = 2.899890793318617e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.870000000000523 y1[1] (closed_form) = 0.1499825785965457 y1[1] (numeric) = 0.1499825785968256 absolute error = 2.798317133567707e-13 relative error = 1.865761450264968e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.526754575975019 y2[1] (numeric) = 1.526754575975463 absolute error = 4.432010314303625e-13 relative error = 2.902896368575312e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.880000000000518 y1[1] (closed_form) = 0.1447576211456862 y1[1] (numeric) = 0.1447576211459587 absolute error = 2.725042413942447e-13 relative error = 1.88248631911402e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.518228205920533 y2[1] (numeric) = 1.518228205920975 absolute error = 4.414246745909622e-13 relative error = 2.907498838906878e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.890000000000512 y1[1] (closed_form) = 0.1396181872200125 y1[1] (numeric) = 0.1396181872202777 absolute error = 2.652045250073343e-13 relative error = 1.8994984126919e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.50965001347731 y2[1] (numeric) = 1.50965001347775 absolute error = 4.39648317751562e-13 relative error = 2.912253262853164e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.900000000000507 y1[1] (closed_form) = 0.1345647907586341 y1[1] (numeric) = 0.1345647907588922 absolute error = 2.58043586498502e-13 relative error = 1.917615930911296e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.501020856457447 y2[1] (numeric) = 1.501020856457884 absolute error = 4.374278717023117e-13 relative error = 2.91420248972878e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.910000000000501 y1[1] (closed_form) = 0.1295979370969862 y1[1] (numeric) = 0.1295979370972372 absolute error = 2.509659147165166e-13 relative error = 1.936496215435152e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.492341597769453 y2[1] (numeric) = 1.492341597769888 absolute error = 4.349853810481363e-13 relative error = 2.914784267209951e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.920000000000496 y1[1] (closed_form) = 0.1247181229162959 y1[1] (numeric) = 0.1247181229165398 absolute error = 2.438604873589156e-13 relative error = 1.955293117445182e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.483613105331966 y2[1] (numeric) = 1.483613105332399 absolute error = 4.32542890393961e-13 relative error = 2.915469598101031e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.93000000000049 y1[1] (closed_form) = 0.1199258361939146 y1[1] (numeric) = 0.1199258361941516 absolute error = 2.369909823940475e-13 relative error = 1.97614617429762e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.474836251986956 y2[1] (numeric) = 1.474836251987386 absolute error = 4.303224443447107e-13 relative error = 2.917764217993448e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.940000000000484 y1[1] (closed_form) = 0.1152215561545212 y1[1] (numeric) = 0.1152215561547513 absolute error = 2.300937218535637e-13 relative error = 1.996967664149491e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.466011915412442 y2[1] (numeric) = 1.46601191541287 absolute error = 4.278799536905353e-13 relative error = 2.918666275438541e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.950000000000479 y1[1] (closed_form) = 0.1106057532221995 y1[1] (numeric) = 0.1106057532224227 absolute error = 2.231964613130799e-13 relative error = 2.017946217179981e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.457140978034729 y2[1] (numeric) = 1.457140978035155 absolute error = 4.25215418431435e-13 relative error = 2.918148791649043e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.960000000000473 y1[1] (closed_form) = 0.1060788889733959 y1[1] (numeric) = 0.1060788889736124 absolute error = 2.164657342262899e-13 relative error = 2.040610872919102e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.448224326940162 y2[1] (numeric) = 1.448224326940585 absolute error = 4.227729277772596e-13 relative error = 2.919250284039233e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.970000000000468 y1[1] (closed_form) = 0.101641416090763 y1[1] (numeric) = 0.1016414160909729 absolute error = 2.09873785017578e-13 relative error = 2.064845149640245e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.439262853786421 y2[1] (numeric) = 1.439262853786841 absolute error = 4.196643033083092e-13 relative error = 2.915828072712735e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.980000000000462 y1[1] (closed_form) = 0.09729377831789143 y1[1] (numeric) = 0.0972937783180947 absolute error = 2.032679580210583e-13 relative error = 2.089218463249661e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.430257454713352 y2[1] (numeric) = 1.430257454713768 absolute error = 4.165556788393587e-13 relative error = 2.912452422230819e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.990000000000457 y1[1] (closed_form) = 0.09303641041493527 y1[1] (numeric) = 0.09303641041513201 absolute error = 1.967453977513856e-13 relative error = 2.114713979977475e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.421209030253358 y2[1] (numeric) = 1.421209030253772 absolute error = 4.134470543704083e-13 relative error = 2.909122061352954e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.000000000000451 y1[1] (closed_form) = 0.0888697381151371 y1[1] (numeric) = 0.08886973811532735 absolute error = 1.902505930573284e-13 relative error = 2.140780394906139e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.412118485241346 y2[1] (numeric) = 1.412118485241756 absolute error = 4.105604745063829e-13 relative error = 2.907408116226266e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.010000000000446 y1[1] (closed_form) = 0.08479417808225453 y1[1] (numeric) = 0.08479417808243846 absolute error = 1.83922321816965e-13 relative error = 2.169044219504684e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.40298672872424 y2[1] (numeric) = 1.402986728724647 absolute error = 4.074518500374325e-13 relative error = 2.90417465607772e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.02000000000044 y1[1] (closed_form) = 0.08081013786889468 y1[1] (numeric) = 0.08081013786907235 absolute error = 1.776634395156407e-13 relative error = 2.198529097968865e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.393814673870083 y2[1] (numeric) = 1.393814673870487 absolute error = 4.04121180963557e-13 relative error = 2.899389628618769e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.030000000000435 y1[1] (closed_form) = 0.07691801587575886 y1[1] (numeric) = 0.07691801587593032 absolute error = 1.714600683655476e-13 relative error = 2.229127551112303e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.384603237876717 y2[1] (numeric) = 1.384603237877118 absolute error = 4.010125564946065e-13 relative error = 2.896227204477419e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.040000000000429 y1[1] (closed_form) = 0.07311820131180291 y1[1] (numeric) = 0.07311820131196826 absolute error = 1.653538417301093e-13 relative error = 2.261459373500992e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.375353341880064 y2[1] (numeric) = 1.375353341880462 absolute error = 3.976818874207311e-13 relative error = 2.891488865523914e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.050000000000423 y1[1] (closed_form) = 0.06941107415531678 y1[1] (numeric) = 0.06941107415547611 absolute error = 1.593308818215178e-13 relative error = 2.295467744311133e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.366065910862018 y2[1] (numeric) = 1.366065910862412 absolute error = 3.941291737419306e-13 relative error = 2.88514024548952e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.060000000000418 y1[1] (closed_form) = 0.06579700511592679 y1[1] (numeric) = 0.06579700511608022 absolute error = 1.534328220031966e-13 relative error = 2.33191194238804e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.356741873557939 y2[1] (numeric) = 1.356741873558329 absolute error = 3.905764600631301e-13 relative error = 2.87878238060772e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.070000000000412 y1[1] (closed_form) = 0.0622763555975252 y1[1] (numeric) = 0.06227635559767283 absolute error = 1.476249678056263e-13 relative error = 2.370481804678576e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.347382162363788 y2[1] (numeric) = 1.347382162364175 absolute error = 3.870237463843296e-13 relative error = 2.872412573024955e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.080000000000407 y1[1] (closed_form) = 0.05884947766213 y1[1] (numeric) = 0.05884947766227189 absolute error = 1.41886502547095e-13 relative error = 2.411006999275371e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.337987713242885 y2[1] (numeric) = 1.337987713243268 absolute error = 3.83248988100604e-13 relative error = 2.864368516297675e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.090000000000401 y1[1] (closed_form) = 0.05551671399467906 y1[1] (numeric) = 0.05551671399481523 absolute error = 1.361688539702754e-13 relative error = 2.452754209900219e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.328559465632313 y2[1] (numeric) = 1.328559465632692 absolute error = 3.794742298168785e-13 relative error = 2.856283362794544e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.100000000000396 y1[1] (closed_form) = 0.05227839786876165 y1[1] (numeric) = 0.05227839786889231 absolute error = 1.306593722105731e-13 relative error = 2.499299472385842e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.319098362348977 y2[1] (numeric) = 1.319098362349352 absolute error = 3.75699471533153e-13 relative error = 2.84815357411352e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.11000000000039 y1[1] (closed_form) = 0.04913485311329202 y1[1] (numeric) = 0.04913485311341714 absolute error = 1.251151959813512e-13 relative error = 2.546363488517378e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.30960534949532 y2[1] (numeric) = 1.309605349495691 absolute error = 3.714806240395774e-13 relative error = 2.836584503741789e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.120000000000385 y1[1] (closed_form) = 0.04608639408012583 y1[1] (numeric) = 0.04608639408024564 absolute error = 1.198138810387661e-13 relative error = 2.599766881966457e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.300081376364717 y2[1] (numeric) = 1.300081376365085 absolute error = 3.677058657558518e-13 relative error = 2.828329614135614e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.130000000000379 y1[1] (closed_form) = 0.04313332561262628 y1[1] (numeric) = 0.04313332561274076 absolute error = 1.144778716266615e-13 relative error = 2.654046957908358e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.290527395346545 y2[1] (numeric) = 1.290527395346909 absolute error = 3.634870182622763e-13 relative error = 2.816577312290756e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.140000000000374 y1[1] (closed_form) = 0.04027594301517912 y1[1] (numeric) = 0.04027594301528838 absolute error = 1.092598234109232e-13 relative error = 2.712781259267985e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.280944361830944 y2[1] (numeric) = 1.280944361831303 absolute error = 3.592681707687007e-13 relative error = 2.804713315222946e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.150000000000368 y1[1] (closed_form) = 0.03751453202366295 y1[1] (numeric) = 0.03751453202376707 absolute error = 1.04118103028128e-13 relative error = 2.77540721985959e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.271333234113279 y2[1] (numeric) = 1.271333234113634 absolute error = 3.552713678800501e-13 relative error = 2.794478727898924e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.160000000000363 y1[1] (closed_form) = 0.03484936877687572 y1[1] (numeric) = 0.03484936877697484 absolute error = 9.911516052341085e-14 relative error = 2.844102031173048e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.261694973298313 y2[1] (numeric) = 1.261694973298664 absolute error = 3.510525203864745e-13 relative error = 2.782388198541806e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.170000000000357 y1[1] (closed_form) = 0.03228071978892111 y1[1] (numeric) = 0.03228071978901539 absolute error = 9.428569036629142e-14 relative error = 2.920805080642926e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.252030543204095 y2[1] (numeric) = 1.252030543204442 absolute error = 3.468336728928989e-13 relative error = 2.770169424184415e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.180000000000351 y1[1] (closed_form) = 0.02980884192255762 y1[1] (numeric) = 0.02980884192264701 absolute error = 8.939030071708487e-14 relative error = 2.998784754849514e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.242340910265582 y2[1] (numeric) = 1.242340910265925 absolute error = 3.421707361894732e-13 relative error = 2.754241878071337e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.190000000000346 y1[1] (closed_form) = 0.02743398236351169 y1[1] (numeric) = 0.02743398236359642 absolute error = 8.473083346061117e-14 relative error = 3.08853568314991e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.232627043437993 y2[1] (numeric) = 1.232627043438331 absolute error = 3.377298440909726e-13 relative error = 2.739919149826458e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.20000000000034 y1[1] (closed_form) = 0.02515637859576036 y1[1] (numeric) = 0.02515637859584049 absolute error = 8.012687735536872e-14 relative error = 3.185151513376914e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.222889914099915 y2[1] (numeric) = 1.222889914100248 absolute error = 3.328448627826219e-13 relative error = 2.72178925465753e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.210000000000335 y1[1] (closed_form) = 0.02297625837778239 y1[1] (numeric) = 0.022976258377858 absolute error = 7.561659631782902e-14 relative error = 3.29107529496399e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.213130495956168 y2[1] (numeric) = 1.213130495956496 absolute error = 3.281819260791963e-13 relative error = 2.705248340332332e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.220000000000329 y1[1] (closed_form) = 0.02089383971978287 y1[1] (numeric) = 0.020893839719854 absolute error = 7.1130601408953e-14 relative error = 3.404381500141622e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.203349764940434 y2[1] (numeric) = 1.203349764940757 absolute error = 3.235189893757706e-13 relative error = 2.688486745927813e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.230000000000324 y1[1] (closed_form) = 0.01890933086189206 y1[1] (numeric) = 0.01890933086195893 absolute error = 6.687012055195396e-14 relative error = 3.536355730424982e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.193548699117663 y2[1] (numeric) = 1.193548699117982 absolute error = 3.18856052672345e-13 relative error = 2.671495959134813e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.240000000000318 y1[1] (closed_form) = 0.01702293025334223 y1[1] (numeric) = 0.01702293025340483 absolute error = 6.260270080105101e-14 relative error = 3.677551389177536e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.18372827858627 y2[1] (numeric) = 1.183728278586584 absolute error = 3.139710713639943e-13 relative error = 2.652391406404269e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.250000000000313 y1[1] (closed_form) = 0.01523482653262198 y1[1] (numeric) = 0.01523482653268055 absolute error = 5.857293816635689e-14 relative error = 3.844673783514109e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.173889485380126 y2[1] (numeric) = 1.173889485380435 absolute error = 3.093081346605686e-13 relative error = 2.634899950231766e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.260000000000307 y1[1] (closed_form) = 0.01354519850861358 y1[1] (numeric) = 0.01354519850866811 absolute error = 5.453450191428288e-14 relative error = 4.026113155861367e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.16403330337035 y2[1] (numeric) = 1.164033303370654 absolute error = 3.042011087472929e-13 relative error = 2.613336816622917e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.270000000000302 y1[1] (closed_form) = 0.01195421514271122 y1[1] (numeric) = 0.01195421514276187 absolute error = 5.064698660461886e-14 relative error = 4.236747122248303e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.154160718166932 y2[1] (numeric) = 1.154160718167231 absolute error = 2.993161274389422e-13 relative error = 2.593366094752591e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.280000000000296 y1[1] (closed_form) = 0.01046203553192571 y1[1] (numeric) = 0.01046203553197261 absolute error = 4.690171861998493e-14 relative error = 4.483039507642727e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.144272717020164 y2[1] (numeric) = 1.144272717020458 absolute error = 2.942091015256665e-13 relative error = 2.571144947786797e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.29000000000029 y1[1] (closed_form) = 0.009068808892974789 y1[1] (numeric) = 0.00906880889301793 absolute error = 4.314083812406722e-14 relative error = 4.757056702064429e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.13437028872192 y2[1] (numeric) = 1.13437028872221 absolute error = 2.893241202173158e-13 relative error = 2.5505262531452e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.300000000000285 y1[1] (closed_form) = 0.007774674547361138 y1[1] (numeric) = 0.007774674547400707 absolute error = 3.956904248703097e-14 relative error = 5.089478954519248e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.12445442350678 y2[1] (numeric) = 1.124454423507064 absolute error = 2.844391389089651e-13 relative error = 2.529574636043487e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.310000000000279 y1[1] (closed_form) = 0.006579761907440917 y1[1] (numeric) = 0.006579761907477062 absolute error = 3.614469834545275e-14 relative error = 5.493314021678726e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.114526112953 y2[1] (numeric) = 1.114526112953279 absolute error = 2.793321129956894e-13 relative error = 2.506285942960844e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.320000000000274 y1[1] (closed_form) = 0.005484190463482475 y1[1] (numeric) = 0.00548419046351523 absolute error = 3.275504867339407e-14 relative error = 5.972631492560259e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.104586349883363 y2[1] (numeric) = 1.104586349883637 absolute error = 2.740030424774886e-13 relative error = 2.480594138307263e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.330000000000268 y1[1] (closed_form) = 0.004488069771717229 y1[1] (numeric) = 0.004488069771746635 absolute error = 2.940616500302085e-14 relative error = 6.552073942417663e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.094636128265893 y2[1] (numeric) = 1.094636128266162 absolute error = 2.691180611691379e-13 relative error = 2.458516160940814e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.340000000000263 y1[1] (closed_form) = 0.003591499443384105 y1[1] (numeric) = 0.003591499443410354 absolute error = 2.624896827674306e-14 relative error = 7.308637712612272e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.08467644311446 y2[1] (numeric) = 1.084676443114723 absolute error = 2.637889906509372e-13 relative error = 2.431960169555384e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.350000000000257 y1[1] (closed_form) = 0.002794569134768832 y1[1] (numeric) = 0.002794569134792082 absolute error = 2.325049874851715e-14 relative error = 8.319886761520552e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.074708290389278 y2[1] (numeric) = 1.074708290389536 absolute error = 2.584599201327364e-13 relative error = 2.4049309235264e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.360000000000252 y1[1] (closed_form) = 0.002097358538238225 y1[1] (numeric) = 0.002097358538258575 absolute error = 2.034960741581493e-14 relative error = 9.70249341960795e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 1.064732666897314 y2[1] (numeric) = 1.064732666897567 absolute error = 2.531308496145357e-13 relative error = 2.377412260226523e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.370000000000246 y1[1] (closed_form) = 0.00149993737427101 y1[1] (numeric) = 0.001499937374288479 absolute error = 1.746931592438994e-14 relative error = 1.164669687151456e-09 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 11 h = 0.001 y2[1] (closed_form) = 1.054750570192604 y2[1] (numeric) = 1.054750570192852 absolute error = 2.4802382370126e-13 relative error = 2.35149267239523e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.380000000000241 y1[1] (closed_form) = 0.001002365384485615 y1[1] (numeric) = 0.001002365384500342 absolute error = 1.47269349493051e-14 relative error = 1.469218228925826e-09 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 11 h = 0.001 y2[1] (closed_form) = 1.044762998476501 y2[1] (numeric) = 1.044762998476743 absolute error = 2.424727085781342e-13 relative error = 2.320839357172047e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.390000000000235 y1[1] (closed_form) = 0.0006046923256664005 y1[1] (numeric) = 0.0006046923256785002 absolute error = 1.209969624493823e-14 relative error = 2.000967389755405e-09 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 11 h = 0.001 y2[1] (closed_form) = 1.034770950497852 y2[1] (numeric) = 1.034770950498089 absolute error = 2.371436380599334e-13 relative error = 2.291750052954601e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.40000000000023 y1[1] (closed_form) = 0.0003069579647878573 y1[1] (numeric) = 0.0003069579647974437 absolute error = 9.586352978790957e-15 relative error = 3.123018158338459e-09 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 11 h = 0.001 y2[1] (closed_form) = 1.024775425453129 y2[1] (numeric) = 1.024775425453361 absolute error = 2.318145675417327e-13 relative error = 2.262101156838635e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.410000000000224 y1[1] (closed_form) = 0.0001091920750379005 y1[1] (numeric) = 0.0001091920750451487 absolute error = 7.248135468554406e-15 relative error = 6.637968429520716e-09 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 11 h = 0.001 y2[1] (closed_form) = 1.014777422886507 y2[1] (numeric) = 1.014777422886733 absolute error = 2.262634524186069e-13 relative error = 2.229685518377091e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.420000000000218 y1[1] (closed_form) = 1.141443284091714e-05 y1[1] (numeric) = 1.14144328457878e-05 absolute error = 4.870659675278513e-15 relative error = 4.267106165642093e-08 % Desired digits = 8 Estimated correct digits = 6 Correct digits = 10 h = 0.001 y2[1] (closed_form) = 1.00477794258991 y2[1] (numeric) = 1.004777942590131 absolute error = 2.209343819004062e-13 relative error = 2.198837897764027e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.430000000000213 y1[1] (closed_form) = 1.363481587934867e-05 y1[1] (numeric) = 1.363481588209865e-05 absolute error = 2.7499805546876e-15 relative error = 2.016881327200559e-08 % Desired digits = 8 Estimated correct digits = 6 Correct digits = 10 h = 0.001 y2[1] (closed_form) = 0.9947779845030362 y2[1] (numeric) = 0.9947779845032516 absolute error = 2.153832667772804e-13 relative error = 2.165139057484067e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.440000000000207 y1[1] (closed_form) = 0.0001158530021169168 y1[1] (numeric) = 0.0001158530021176273 absolute error = 7.104370260482828e-16 relative error = 6.132228022294339e-10 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9847785486133604 y2[1] (numeric) = 0.9847785486135703 absolute error = 2.098321516541546e-13 relative error = 2.130754695556818e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.450000000000202 y1[1] (closed_form) = 0.000318058769820273 y1[1] (numeric) = 0.0003180587698189339 absolute error = 1.339152313345471e-15 relative error = 4.210392670833104e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9747806348561389 y2[1] (numeric) = 0.974780634856343 absolute error = 2.041700142285663e-13 relative error = 2.094522674413801e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.460000000000196 y1[1] (closed_form) = 0.0006202318985808475 y1[1] (numeric) = 0.0006202318985777511 absolute error = 3.096372984401352e-15 relative error = 4.992282711492528e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9647852430144156 y2[1] (numeric) = 0.9647852430146142 absolute error = 1.986188991054405e-13 relative error = 2.058685086070215e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.470000000000191 y1[1] (closed_form) = 0.001022342171337898 y1[1] (numeric) = 0.001022342171333012 absolute error = 4.88563182965418e-15 relative error = 4.778861683129584e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9547933726190453 y2[1] (numeric) = 0.9547933726192385 absolute error = 1.931788062847772e-13 relative error = 2.023252483989057e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.480000000000185 y1[1] (closed_form) = 0.001524349377399092 y1[1] (numeric) = 0.001524349377392532 absolute error = 6.56029050527529e-15 relative error = 4.303665945971473e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.944806022848741 y2[1] (numeric) = 0.9448060228489287 absolute error = 1.876276911616515e-13 relative error = 1.985885849837451e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.49000000000018 y1[1] (closed_form) = 0.002126203316462072 y1[1] (numeric) = 0.002126203316454046 absolute error = 8.026131842475692e-15 relative error = 3.774865639769058e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.934824192430157 y2[1] (numeric) = 0.9348241924303389 absolute error = 1.818545314336006e-13 relative error = 1.945334030785552e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.500000000000174 y1[1] (closed_form) = 0.002827843803634655 y1[1] (numeric) = 0.002827843803625191 absolute error = 9.46465128492946e-15 relative error = 3.346949811288888e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9248488795380171 y2[1] (numeric) = 0.9248488795381932 absolute error = 1.760813717055498e-13 relative error = 1.903893442499562e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.510000000000169 y1[1] (closed_form) = 0.003629200675452693 y1[1] (numeric) = 0.003629200675441945 absolute error = 1.074747929541431e-14 relative error = 2.961390194846061e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9148810816952976 y2[1] (numeric) = 0.9148810816954682 absolute error = 1.706412788848866e-13 relative error = 1.865174417736172e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.520000000000163 y1[1] (closed_form) = 0.004530193796896786 y1[1] (numeric) = 0.004530193796884924 absolute error = 1.18629064904674e-14 relative error = 2.61863112756756e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9049217956734763 y2[1] (numeric) = 0.9049217956736413 absolute error = 1.649791414592983e-13 relative error = 1.82313148216874e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.530000000000157 y1[1] (closed_form) = 0.005530733069405769 y1[1] (numeric) = 0.005530733069392807 absolute error = 1.29618538124987e-14 relative error = 2.343605024838298e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8949720173928561 y2[1] (numeric) = 0.8949720173930154 absolute error = 1.592059817312474e-13 relative error = 1.778893402667835e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.540000000000152 y1[1] (closed_form) = 0.006630718439886052 y1[1] (numeric) = 0.006630718439872126 absolute error = 1.392636006514181e-14 relative error = 2.100279206755329e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8850327418229738 y2[1] (numeric) = 0.8850327418231272 absolute error = 1.534328220031966e-13 relative error = 1.733640064967072e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.550000000000146 y1[1] (closed_form) = 0.007830039910717179 y1[1] (numeric) = 0.007830039910702481 absolute error = 1.469831201195149e-14 relative error = 1.877169488221066e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8751049628831031 y2[1] (numeric) = 0.875104962883251 absolute error = 1.478817068800709e-13 relative error = 1.689873936868816e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.560000000000141 y1[1] (closed_form) = 0.009128577550751693 y1[1] (numeric) = 0.009128577550736225 absolute error = 1.546852923528519e-14 relative error = 1.694516933146001e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8651896733428655 y2[1] (numeric) = 0.8651896733430077 absolute error = 1.422195694544826e-13 relative error = 1.643796427955312e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.570000000000135 y1[1] (closed_form) = 0.01052620150730754 y1[1] (numeric) = 0.01052620150729146 absolute error = 1.6080886622305e-14 relative error = 1.52770081507002e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8552878647229518 y2[1] (numeric) = 0.8552878647230884 absolute error = 1.365574320288943e-13 relative error = 1.596625389664899e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.58000000000013 y1[1] (closed_form) = 0.0120227720191538 y1[1] (numeric) = 0.01202277201913722 absolute error = 1.658916060076621e-14 relative error = 1.379811625333789e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8454005271959729 y2[1] (numeric) = 0.8454005271961037 absolute error = 1.307842723008434e-13 relative error = 1.547009590053476e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.590000000000124 y1[1] (closed_form) = 0.0136181394304864 y1[1] (numeric) = 0.01361813943046945 absolute error = 1.694998308376938e-14 relative error = 1.244662177993575e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8355286494874419 y2[1] (numeric) = 0.8355286494875669 absolute error = 1.250111125727926e-13 relative error = 1.496191814002801e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.600000000000119 y1[1] (closed_form) = 0.01531214420589377 y1[1] (numeric) = 0.01531214420587649 absolute error = 1.728304999115693e-14 relative error = 1.128715205314259e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8256732187769031 y2[1] (numeric) = 0.8256732187770223 absolute error = 1.191269305422793e-13 relative error = 1.442785448688113e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.610000000000113 y1[1] (closed_form) = 0.01710461694630994 y1[1] (numeric) = 0.01710461694629247 absolute error = 1.746519595613449e-14 relative error = 1.02108080005278e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.8158352205992149 y2[1] (numeric) = 0.8158352205993284 absolute error = 1.135758154191535e-13 relative error = 1.392141605945062e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.620000000000108 y1[1] (closed_form) = 0.01899537840595455 y1[1] (numeric) = 0.01899537840593706 absolute error = 1.749642097870208e-14 relative error = 9.210883092077495e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8060156387459965 y2[1] (numeric) = 0.8060156387461044 absolute error = 1.079136779935652e-13 relative error = 1.338853401919818e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.630000000000102 y1[1] (closed_form) = 0.02098423951025741 y1[1] (numeric) = 0.02098423951023994 absolute error = 1.746866540308645e-14 relative error = 8.324659749783882e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7962154551672503 y2[1] (numeric) = 0.7962154551673527 absolute error = 1.023625628704394e-13 relative error = 1.285613865017698e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.640000000000096 y1[1] (closed_form) = 0.02307100137476537 y1[1] (numeric) = 0.02307100137474804 absolute error = 1.73229486311044e-14 relative error = 7.508537817544373e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7864356498731676 y2[1] (numeric) = 0.7864356498732645 absolute error = 9.692247004977617e-14 relative error = 1.232427218494067e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.650000000000091 y1[1] (closed_form) = 0.02525545532503093 y1[1] (numeric) = 0.02525545532501389 absolute error = 1.70384539810442e-14 relative error = 6.746444980604733e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7766772008361278 y2[1] (numeric) = 0.7766772008362192 absolute error = 9.137135492665038e-14 relative error = 1.176439257239494e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.660000000000085 y1[1] (closed_form) = 0.02753738291747942 y1[1] (numeric) = 0.02753738291746282 absolute error = 1.660477311205e-14 relative error = 6.029902391889999e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7669410838929027 y2[1] (numeric) = 0.7669410838929883 absolute error = 8.559819519859957e-14 relative error = 1.116098706879976e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.67000000000008 y1[1] (closed_form) = 0.02991655596125331 y1[1] (numeric) = 0.02991655596123718 absolute error = 1.612945887963235e-14 relative error = 5.39148252911283e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7572282726470732 y2[1] (numeric) = 0.7572282726471532 absolute error = 8.004708007547379e-14 relative error = 1.057106330639901e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.680000000000074 y1[1] (closed_form) = 0.03239273654103081 y1[1] (numeric) = 0.03239273654101525 absolute error = 1.555700013256001e-14 relative error = 4.802619906118295e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7475397383716698 y2[1] (numeric) = 0.7475397383717444 absolute error = 7.460698725481052e-14 relative error = 9.980337288466212e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.690000000000069 y1[1] (closed_form) = 0.03496567704081732 y1[1] (numeric) = 0.03496567704080251 absolute error = 1.481453848484193e-14 relative error = 4.236880203277094e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7378764499120463 y2[1] (numeric) = 0.7378764499121154 absolute error = 6.916689443414725e-14 relative error = 9.373777201100785e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.700000000000063 y1[1] (closed_form) = 0.03763512016870718 y1[1] (numeric) = 0.0376351201686931 absolute error = 1.407901573102777e-14 relative error = 3.740924877591908e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.728239373588996 y2[1] (numeric) = 0.7282393735890597 absolute error = 6.361577931102147e-14 relative error = 8.735558886016092e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.710000000000058 y1[1] (closed_form) = 0.04040079898261195 y1[1] (numeric) = 0.04040079898259878 absolute error = 1.317002062961592e-14 relative error = 3.259841627212409e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7186294731021203 y2[1] (numeric) = 0.7186294731021786 absolute error = 5.828670879282072e-14 relative error = 8.110815235731075e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.720000000000052 y1[1] (closed_form) = 0.04326243691695497 y1[1] (numeric) = 0.04326243691694286 absolute error = 1.211530875622202e-14 relative error = 2.800422172120848e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.70904770943346 y2[1] (numeric) = 0.7090477094335126 absolute error = 5.262457136723242e-14 relative error = 7.421866070095658e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.730000000000047 y1[1] (closed_form) = 0.04621974781032756 y1[1] (numeric) = 0.04621974781031659 absolute error = 1.097039126207733e-14 relative error = 2.373529017747269e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.6994950407513966 y2[1] (numeric) = 0.699495040751444 absolute error = 4.740652315149418e-14 relative error = 6.777249356989031e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.740000000000041 y1[1] (closed_form) = 0.0492724359341048 y1[1] (numeric) = 0.04927243593409507 absolute error = 9.728329253277934e-15 relative error = 1.974395839955681e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.6899724223148381 y2[1] (numeric) = 0.6899724223148801 absolute error = 4.196643033083092e-14 relative error = 6.082334448967499e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.750000000000036 y1[1] (closed_form) = 0.0524201960220182 y1[1] (numeric) = 0.0524201960220098 absolute error = 8.396061623727746e-15 relative error = 1.601684514915039e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.6804808063776927 y2[1] (numeric) = 0.6804808063777292 absolute error = 3.652633751016765e-14 relative error = 5.367724874505005e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.76000000000003 y1[1] (closed_form) = 0.05566271330068207 y1[1] (numeric) = 0.05566271330067513 absolute error = 6.931955010003321e-15 relative error = 1.245349821981887e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.6710211420936443 y2[1] (numeric) = 0.6710211420936756 absolute error = 3.130828929442941e-14 relative error = 4.665767936423707e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.770000000000024 y1[1] (closed_form) = 0.05899966352107067 y1[1] (numeric) = 0.05899966352106529 absolute error = 5.377642775528102e-15 relative error = 9.114700753517982e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.6615943754212386 y2[1] (numeric) = 0.6615943754212645 absolute error = 2.597921877622866e-14 relative error = 3.926759316792504e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.780000000000019 y1[1] (closed_form) = 0.06243071299094261 y1[1] (numeric) = 0.06243071299093899 absolute error = 3.615163723935666e-15 relative error = 5.790681462279873e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.6522014490292867 y2[1] (numeric) = 0.6522014490293075 absolute error = 2.087219286295294e-14 relative error = 3.200267784442732e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.790000000000013 y1[1] (closed_form) = 0.06595551860821036 y1[1] (numeric) = 0.06595551860820849 absolute error = 1.873501354054952e-15 relative error = 2.840552835592035e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.6428433022026008 y2[1] (numeric) = 0.6428433022026167 absolute error = 1.587618925213974e-14 relative error = 2.469682611258839e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.800000000000008 y1[1] (closed_form) = 0.06957372789524929 y1[1] (numeric) = 0.06957372789524935 absolute error = 5.551115123125783e-17 relative error = 7.978751881002527e-14 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 0.633520870748065 y2[1] (numeric) = 0.6335208707480758 absolute error = 1.088018564132653e-14 relative error = 1.717415501793832e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.810000000000002 y1[1] (closed_form) = 0.0732849790341461 y1[1] (numeric) = 0.073284979034148 absolute error = 1.901256929670581e-15 relative error = 2.594333729405471e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.624235086901056 y2[1] (numeric) = 0.6242350869010618 absolute error = 5.773159728050814e-15 relative error = 9.248374289101575e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.819999999999997 y1[1] (closed_form) = 0.07708890090287934 y1[1] (numeric) = 0.07708890090288333 absolute error = 3.982925100842749e-15 relative error = 5.166664791161892e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.6149868792322206 y2[1] (numeric) = 0.6149868792322211 absolute error = 4.440892098500626e-16 relative error = 7.221116821296823e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.829999999999991 y1[1] (closed_form) = 0.08098511311243217 y1[1] (numeric) = 0.08098511311243835 absolute error = 6.175615574477433e-15 relative error = 7.625618261351052e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.6057771725546187 y2[1] (numeric) = 0.6057771725546144 absolute error = 4.329869796038111e-15 relative error = 7.147627860882652e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.839999999999986 y1[1] (closed_form) = 0.08497322604483049 y1[1] (numeric) = 0.08497322604483895 absolute error = 8.465450562766819e-15 relative error = 9.96249166566959e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.5966068878312434 y2[1] (numeric) = 0.5966068878312342 absolute error = 9.214851104388799e-15 relative error = 1.544543197931586e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.84999999999998 y1[1] (closed_form) = 0.08905284089210441 y1[1] (numeric) = 0.08905284089211525 absolute error = 1.083855227790309e-14 relative error = 1.217092253242654e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5874769420829251 y2[1] (numeric) = 0.5874769420829109 absolute error = 1.4210854715202e-14 relative error = 2.41896382602129e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.859999999999975 y1[1] (closed_form) = 0.09322354969616897 y1[1] (numeric) = 0.09322354969618227 absolute error = 1.329492071988625e-14 relative error = 1.426133285335798e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5783882482966304 y2[1] (numeric) = 0.5783882482966113 absolute error = 1.909583602355269e-14 relative error = 3.301560168241742e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.869999999999969 y1[1] (closed_form) = 0.09748493538961922 y1[1] (numeric) = 0.09748493538963515 absolute error = 1.5931700403371e-14 relative error = 1.634273063801764e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.569341715334164 y2[1] (numeric) = 0.5693417153341401 absolute error = 2.386979502944087e-14 relative error = 4.192525224579927e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.879999999999963 y1[1] (closed_form) = 0.1018365718374371 y1[1] (numeric) = 0.1018365718374557 absolute error = 1.856848008685574e-14 relative error = 1.823360679942842e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5603382478412835 y2[1] (numeric) = 0.5603382478412549 absolute error = 2.864375403532904e-14 relative error = 5.11186843762313e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.889999999999958 y1[1] (closed_form) = 0.1062780238796041 y1[1] (numeric) = 0.1062780238796254 absolute error = 2.137179322403426e-14 relative error = 2.010932499859526e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5513787461572351 y2[1] (numeric) = 0.5513787461572018 absolute error = 3.33066907387547e-14 relative error = 6.040619260514028e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.899999999999952 y1[1] (closed_form) = 0.1108088473746172 y1[1] (numeric) = 0.1108088473746414 absolute error = 2.425837308805967e-14 relative error = 2.189209044477121e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5424641062247213 y2[1] (numeric) = 0.5424641062246833 absolute error = 3.796962744218035e-14 relative error = 6.999472777365853e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.909999999999947 y1[1] (closed_form) = 0.1154285892439025 y1[1] (numeric) = 0.1154285892439298 absolute error = 2.722821967893196e-14 relative error = 2.358880053657962e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5335952195003062 y2[1] (numeric) = 0.5335952195002638 absolute error = 4.241051954068098e-14 relative error = 7.948069621087871e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.919999999999941 y1[1] (closed_form) = 0.1201367875171231 y1[1] (numeric) = 0.1201367875171533 absolute error = 3.022582184541989e-14 relative error = 2.51595056519318e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5247729728652718 y2[1] (numeric) = 0.5247729728652247 absolute error = 4.707345624410664e-14 relative error = 8.970251647504738e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.929999999999936 y1[1] (closed_form) = 0.1249329713783748 y1[1] (numeric) = 0.1249329713784083 absolute error = 3.347322419244847e-14 relative error = 2.679294650814853e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5159982485369295 y2[1] (numeric) = 0.515998248536878 absolute error = 5.151434834260726e-14 relative error = 9.983434728445678e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.93999999999993 y1[1] (closed_form) = 0.1298166612132686 y1[1] (numeric) = 0.1298166612133053 absolute error = 3.663735981263017e-14 relative error = 2.822238645657407e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5072719239804 y2[1] (numeric) = 0.5072719239803442 absolute error = 5.584421813864537e-14 relative error = 1.100873427026154e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.949999999999925 y1[1] (closed_form) = 0.1347873686568906 y1[1] (numeric) = 0.1347873686569306 absolute error = 4.005129561335252e-14 relative error = 2.971442800052394e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4985948718208671 y2[1] (numeric) = 0.4985948718208069 absolute error = 6.0285110237146e-14 relative error = 1.209100085947233e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.959999999999919 y1[1] (closed_form) = 0.1398445966426386 y1[1] (numeric) = 0.1398445966426821 absolute error = 4.349298698969051e-14 relative error = 3.110094206988438e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4899679597563159 y2[1] (numeric) = 0.4899679597562512 absolute error = 6.467049118441537e-14 relative error = 1.319892247986563e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.969999999999914 y1[1] (closed_form) = 0.1449878394519286 y1[1] (numeric) = 0.1449878394519755 absolute error = 4.687916721479723e-14 relative error = 3.233317179703215e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4813920504707637 y2[1] (numeric) = 0.4813920504706947 absolute error = 6.900036098045348e-14 relative error = 1.433350652819807e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.979999999999908 y1[1] (closed_form) = 0.1502165827647655 y1[1] (numeric) = 0.150216582764816 absolute error = 5.054290319606025e-14 relative error = 3.364668684762246e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4728680015479925 y2[1] (numeric) = 0.4728680015479192 absolute error = 7.327471962526033e-14 relative error = 1.549580842547738e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.989999999999903 y1[1] (closed_form) = 0.1555303037111753 y1[1] (numeric) = 0.1555303037112295 absolute error = 5.42343947529389e-14 relative error = 3.487062871918125e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4643966653857912 y2[1] (numeric) = 0.4643966653857138 absolute error = 7.738254481637341e-14 relative error = 1.666302766237327e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.999999999999897 y1[1] (closed_form) = 0.1609284709234915 y1[1] (numeric) = 0.1609284709235495 absolute error = 5.79813974610488e-14 relative error = 3.602929744396458e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4559788891107166 y2[1] (numeric) = 0.4559788891106351 absolute error = 8.149037000748649e-14 relative error = 1.787152255368992e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 Finished! diff ( y1 , x , 1 ) = neg ( y2 ) + 1.0 ; diff ( y2 , x , 1 ) = y1 - 1.0 ; Iterations = 9901 Total Elapsed Time = 1.0 Seconds Elapsed Time(since restart) = 1.0 Seconds Time to Timeout = 2 Minutes 59.0 Seconds Percent Done = 100 %