##############ECHO OF PROBLEM################# ##############temp/mtest4postode.ode################# diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ; diff ( y1 , x , 1 ) = neg ( y2 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.1); x_end=c(5.0); array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(x_start); array_y2_init[2 + 1] = exact_soln_y2pp(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_y2 (double x) { return(sin(c(x))); } double exact_soln_y2p (double x) { return( cos(c(x))); } double exact_soln_y2pp (double x) { return( neg( sin(c(x)))); } double exact_soln_y1 (double x) { return( cos(c(x))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (closed_form) = 0.09983341664682815 y2[1] (numeric) = 0.09983341664682815 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9950041652780258 y1[1] (numeric) = 0.9950041652780258 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 y2[1] (closed_form) = 0.1097783008371748 y2[1] (numeric) = 0.1097783008371748 absolute error = 1.387778780781446e-17 relative error = 1.264164930772452e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9939560979566968 y1[1] (numeric) = 0.9939560979566969 absolute error = 1.110223024625157e-16 relative error = 1.116973905494893e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y2[1] (closed_form) = 0.1197122072889194 y2[1] (numeric) = 0.1197122072889194 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9928086358538663 y1[1] (numeric) = 0.9928086358538663 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y2[1] (closed_form) = 0.1296341426196949 y2[1] (numeric) = 0.1296341426196949 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9915618937147881 y1[1] (numeric) = 0.9915618937147881 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y2[1] (closed_form) = 0.1395431146442365 y2[1] (numeric) = 0.1395431146442365 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9902159962126371 y1[1] (numeric) = 0.9902159962126372 absolute error = 1.110223024625157e-16 relative error = 1.121192779021467e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y2[1] (closed_form) = 0.1494381324735993 y2[1] (numeric) = 0.1494381324735993 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9887710779360422 y1[1] (numeric) = 0.9887710779360421 absolute error = 1.110223024625157e-16 relative error = 1.122831208759294e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y2[1] (closed_form) = 0.159318206614246 y2[1] (numeric) = 0.159318206614246 absolute error = 2.775557561562891e-17 relative error = 1.742147128409054e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9872272833756269 y1[1] (numeric) = 0.9872272833756267 absolute error = 2.220446049250313e-16 relative error = 2.249174112832397e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y2[1] (closed_form) = 0.1691823490669961 y2[1] (numeric) = 0.1691823490669961 absolute error = 2.775557561562891e-17 relative error = 1.640571594418383e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9855847669095607 y1[1] (numeric) = 0.9855847669095603 absolute error = 3.33066907387547e-16 relative error = 3.379383677285567e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y2[1] (closed_form) = 0.1790295734258243 y2[1] (numeric) = 0.1790295734258242 absolute error = 5.551115123125783e-17 relative error = 3.100669356968404e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9838436927881214 y1[1] (numeric) = 0.9838436927881212 absolute error = 2.220446049250313e-16 relative error = 2.256909370387664e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y2[1] (closed_form) = 0.1888588949765007 y2[1] (numeric) = 0.1888588949765006 absolute error = 8.326672684688674e-17 relative error = 4.408938581222105e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9820042351172703 y1[1] (numeric) = 0.9820042351172701 absolute error = 2.220446049250313e-16 relative error = 2.261136937953377e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y2[1] (closed_form) = 0.1986693307950613 y2[1] (numeric) = 0.1986693307950612 absolute error = 8.326672684688674e-17 relative error = 4.191221992526924e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9800665778412416 y1[1] (numeric) = 0.9800665778412414 absolute error = 2.220446049250313e-16 relative error = 2.265607357146299e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y2[1] (closed_form) = 0.2084598998460997 y2[1] (numeric) = 0.2084598998460996 absolute error = 1.110223024625157e-16 relative error = 5.325834970873556e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9780309147241483 y1[1] (numeric) = 0.978030914724148 absolute error = 2.220446049250313e-16 relative error = 2.27032296814113e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y2[1] (closed_form) = 0.2182296230808694 y2[1] (numeric) = 0.2182296230808693 absolute error = 1.387778780781446e-16 relative error = 6.359259394711854e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9758974493306055 y1[1] (numeric) = 0.9758974493306055 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y2[1] (closed_form) = 0.2279775235351885 y2[1] (numeric) = 0.2279775235351884 absolute error = 1.110223024625157e-16 relative error = 4.869879308316079e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9736663950053748 y1[1] (numeric) = 0.9736663950053749 absolute error = 1.110223024625157e-16 relative error = 1.140249915494956e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y2[1] (closed_form) = 0.2377026264271347 y2[1] (numeric) = 0.2377026264271346 absolute error = 1.110223024625157e-16 relative error = 4.670638441454007e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9713379748520296 y1[1] (numeric) = 0.9713379748520296 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y2[1] (closed_form) = 0.247403959254523 y2[1] (numeric) = 0.2474039592545229 absolute error = 1.110223024625157e-16 relative error = 4.487490935757365e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9689124217106447 y1[1] (numeric) = 0.9689124217106446 absolute error = 1.110223024625157e-16 relative error = 1.145844556998272e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y2[1] (closed_form) = 0.2570805518921552 y2[1] (numeric) = 0.2570805518921551 absolute error = 1.665334536937735e-16 relative error = 6.477870553336681e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9663899781345132 y1[1] (numeric) = 0.9663899781345132 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] = 0.2700000000000001 y2[1] (closed_form) = 0.2667314366888313 y2[1] (numeric) = 0.266731436688831 absolute error = 2.220446049250313e-16 relative error = 8.324650730392475e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9637708963658905 y1[1] (numeric) = 0.9637708963658905 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] = 0.2800000000000001 y2[1] (closed_form) = 0.2763556485641139 y2[1] (numeric) = 0.2763556485641137 absolute error = 2.220446049250313e-16 relative error = 8.034740960741299e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9610554383107709 y1[1] (numeric) = 0.961055438310771 absolute error = 1.110223024625157e-16 relative error = 1.155212259738704e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y2[1] (closed_form) = 0.2859522251048357 y2[1] (numeric) = 0.2859522251048353 absolute error = 3.885780586188048e-16 relative error = 1.358891536781518e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9582438755126971 y1[1] (numeric) = 0.9582438755126974 absolute error = 3.33066907387547e-16 relative error = 3.475805229742204e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y2[1] (closed_form) = 0.2955202066613397 y2[1] (numeric) = 0.2955202066613393 absolute error = 3.885780586188048e-16 relative error = 1.314895055768919e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.955336489125606 y1[1] (numeric) = 0.9553364891256064 absolute error = 4.440892098500626e-16 relative error = 4.64851091636336e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y2[1] (closed_form) = 0.3050586364434437 y2[1] (numeric) = 0.3050586364434433 absolute error = 3.33066907387547e-16 relative error = 1.091812745479494e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9523335698857134 y1[1] (numeric) = 0.9523335698857137 absolute error = 3.33066907387547e-16 relative error = 3.49737652771725e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y2[1] (closed_form) = 0.3145665606161179 y2[1] (numeric) = 0.3145665606161176 absolute error = 3.33066907387547e-16 relative error = 1.058812185043425e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9492354180824408 y1[1] (numeric) = 0.9492354180824413 absolute error = 4.440892098500626e-16 relative error = 4.678388536609509e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y2[1] (closed_form) = 0.3240430283948685 y2[1] (numeric) = 0.3240430283948683 absolute error = 2.775557561562891e-16 relative error = 8.565398167371418e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9460423435283869 y1[1] (numeric) = 0.9460423435283875 absolute error = 5.551115123125783e-16 relative error = 5.86772374524187e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y2[1] (closed_form) = 0.3334870921408146 y2[1] (numeric) = 0.3334870921408142 absolute error = 3.33066907387547e-16 relative error = 9.987400269360645e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9427546655283462 y1[1] (numeric) = 0.9427546655283467 absolute error = 5.551115123125783e-16 relative error = 5.888186318351214e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y2[1] (closed_form) = 0.3428978074554516 y2[1] (numeric) = 0.3428978074554511 absolute error = 4.440892098500626e-16 relative error = 1.29510658917747e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9393727128473789 y1[1] (numeric) = 0.9393727128473793 absolute error = 4.440892098500626e-16 relative error = 4.727508088924171e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y2[1] (closed_form) = 0.3522742332750902 y2[1] (numeric) = 0.3522742332750897 absolute error = 4.440892098500626e-16 relative error = 1.260634948294031e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9358968236779348 y1[1] (numeric) = 0.9358968236779351 absolute error = 3.33066907387547e-16 relative error = 3.558799420631045e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y2[1] (closed_form) = 0.3616154319649622 y2[1] (numeric) = 0.3616154319649617 absolute error = 4.996003610813204e-16 relative error = 1.381579205197548e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9323273456060344 y1[1] (numeric) = 0.9323273456060348 absolute error = 4.440892098500626e-16 relative error = 4.763232698719078e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y2[1] (closed_form) = 0.3709204694129829 y2[1] (numeric) = 0.3709204694129824 absolute error = 4.996003610813204e-16 relative error = 1.346920437882508e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9286646355765101 y1[1] (numeric) = 0.9286646355765106 absolute error = 4.440892098500626e-16 relative error = 4.782019179338884e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y2[1] (closed_form) = 0.3801884151231616 y2[1] (numeric) = 0.3801884151231611 absolute error = 4.996003610813204e-16 relative error = 1.314086229901233e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.924909059857313 y1[1] (numeric) = 0.9249090598573132 absolute error = 2.220446049250313e-16 relative error = 2.400718238821084e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y2[1] (closed_form) = 0.3894183423086507 y2[1] (numeric) = 0.3894183423086502 absolute error = 4.440892098500626e-16 relative error = 1.140391095132546e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.921060994002885 y1[1] (numeric) = 0.9210609940028852 absolute error = 2.220446049250313e-16 relative error = 2.410748108657132e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y2[1] (closed_form) = 0.3986093279844231 y2[1] (numeric) = 0.3986093279844226 absolute error = 4.996003610813204e-16 relative error = 1.253358428934819e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.917120822816605 y1[1] (numeric) = 0.9171208228166053 absolute error = 3.33066907387547e-16 relative error = 3.631657891755771e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y2[1] (closed_form) = 0.4077604530595704 y2[1] (numeric) = 0.4077604530595698 absolute error = 6.106226635438361e-16 relative error = 1.497503396815751e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9130889403123081 y1[1] (numeric) = 0.9130889403123086 absolute error = 4.440892098500626e-16 relative error = 4.863592036260659e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y2[1] (closed_form) = 0.416870802429211 y2[1] (numeric) = 0.4168708024292104 absolute error = 5.551115123125783e-16 relative error = 1.331615236849892e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.908965749674885 y1[1] (numeric) = 0.9089657496748855 absolute error = 5.551115123125783e-16 relative error = 6.107067428130578e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y2[1] (closed_form) = 0.4259394650659998 y2[1] (numeric) = 0.4259394650659993 absolute error = 4.996003610813204e-16 relative error = 1.172937475995343e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9047516632199633 y1[1] (numeric) = 0.9047516632199637 absolute error = 4.440892098500626e-16 relative error = 4.908409985891296e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y2[1] (closed_form) = 0.4349655341112305 y2[1] (numeric) = 0.4349655341112299 absolute error = 5.551115123125783e-16 relative error = 1.276219536444062e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9004471023526768 y1[1] (numeric) = 0.9004471023526771 absolute error = 3.33066907387547e-16 relative error = 3.698905871508875e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y2[1] (closed_form) = 0.44394810696552 y2[1] (numeric) = 0.4439481069655195 absolute error = 4.996003610813204e-16 relative error = 1.125357565991655e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.8960524975255251 y1[1] (numeric) = 0.8960524975255255 absolute error = 4.440892098500626e-16 relative error = 4.956062407910562e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y2[1] (closed_form) = 0.4528862853790686 y2[1] (numeric) = 0.452886285379068 absolute error = 5.551115123125783e-16 relative error = 1.225719413975953e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.8915682881953289 y1[1] (numeric) = 0.8915682881953292 absolute error = 3.33066907387547e-16 relative error = 3.735741970609178e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y2[1] (closed_form) = 0.4617791755414832 y2[1] (numeric) = 0.4617791755414826 absolute error = 6.106226635438361e-16 relative error = 1.322326115784279e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.886994922779284 y1[1] (numeric) = 0.8869949227792844 absolute error = 3.33066907387547e-16 relative error = 3.755003538734188e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y2[1] (closed_form) = 0.4706258881711583 y2[1] (numeric) = 0.4706258881711577 absolute error = 5.551115123125783e-16 relative error = 1.179517587674e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.8823328586101213 y1[1] (numeric) = 0.8823328586101219 absolute error = 5.551115123125783e-16 relative error = 6.2914070001542e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y2[1] (closed_form) = 0.4794255386042033 y2[1] (numeric) = 0.4794255386042027 absolute error = 5.551115123125783e-16 relative error = 1.157868047515213e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.8775825618903725 y1[1] (numeric) = 0.8775825618903731 absolute error = 5.551115123125783e-16 relative error = 6.325461972681297e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y2[1] (closed_form) = 0.4881772468829078 y2[1] (numeric) = 0.4881772468829073 absolute error = 5.551115123125783e-16 relative error = 1.137110579931893e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.8727445076457511 y1[1] (numeric) = 0.8727445076457516 absolute error = 5.551115123125783e-16 relative error = 6.360527135369831e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y2[1] (closed_form) = 0.496880137843737 y2[1] (numeric) = 0.4968801378437365 absolute error = 5.551115123125783e-16 relative error = 1.117194007233902e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.8678191796776498 y1[1] (numeric) = 0.8678191796776501 absolute error = 3.33066907387547e-16 relative error = 3.837975873168236e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y2[1] (closed_form) = 0.5055333412048473 y2[1] (numeric) = 0.5055333412048468 absolute error = 4.440892098500626e-16 relative error = 8.78456817094707e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8628070705147608 y1[1] (numeric) = 0.8628070705147614 absolute error = 5.551115123125783e-16 relative error = 6.433784924611156e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y2[1] (closed_form) = 0.5141359916531134 y2[1] (numeric) = 0.514135991653113 absolute error = 4.440892098500626e-16 relative error = 8.637582605764911e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8577086813638239 y1[1] (numeric) = 0.8577086813638244 absolute error = 4.440892098500626e-16 relative error = 5.177622886408542e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y2[1] (closed_form) = 0.5226872289306594 y2[1] (numeric) = 0.522687228930659 absolute error = 4.440892098500626e-16 relative error = 8.496270527952314e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8525245220595056 y1[1] (numeric) = 0.852524522059506 absolute error = 4.440892098500626e-16 relative error = 5.209107754193908e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y2[1] (closed_form) = 0.5311861979208837 y2[1] (numeric) = 0.5311861979208832 absolute error = 5.551115123125783e-16 relative error = 1.045041295284668e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.8472551110134159 y1[1] (numeric) = 0.8472551110134163 absolute error = 4.440892098500626e-16 relative error = 5.24150523351674e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y2[1] (closed_form) = 0.5396320487339695 y2[1] (numeric) = 0.5396320487339691 absolute error = 4.440892098500626e-16 relative error = 8.229481753204616e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8419009751622685 y1[1] (numeric) = 0.841900975162269 absolute error = 5.551115123125783e-16 relative error = 6.593548750856189e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y2[1] (closed_form) = 0.5480239367918739 y2[1] (numeric) = 0.5480239367918734 absolute error = 4.440892098500626e-16 relative error = 8.103463736452024e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8364626499151867 y1[1] (numeric) = 0.8364626499151873 absolute error = 5.551115123125783e-16 relative error = 6.636417207258015e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y2[1] (closed_form) = 0.5563610229127841 y2[1] (numeric) = 0.5563610229127838 absolute error = 3.33066907387547e-16 relative error = 5.986524822386038e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8309406791001632 y1[1] (numeric) = 0.8309406791001639 absolute error = 6.661338147750939e-16 relative error = 8.016622985607819e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y2[1] (closed_form) = 0.5646424733950357 y2[1] (numeric) = 0.5646424733950353 absolute error = 4.440892098500626e-16 relative error = 7.864962888460721e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8253356149096781 y1[1] (numeric) = 0.8253356149096787 absolute error = 5.551115123125783e-16 relative error = 6.725888260296725e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y2[1] (closed_form) = 0.5728674601004816 y2[1] (numeric) = 0.5728674601004813 absolute error = 3.33066907387547e-16 relative error = 5.814030828860948e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8196480178454792 y1[1] (numeric) = 0.8196480178454798 absolute error = 5.551115123125783e-16 relative error = 6.772559686921958e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y2[1] (closed_form) = 0.5810351605373054 y2[1] (numeric) = 0.5810351605373052 absolute error = 2.220446049250313e-16 relative error = 3.82153473672227e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8138784566625337 y1[1] (numeric) = 0.8138784566625342 absolute error = 5.551115123125783e-16 relative error = 6.820570169517947e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y2[1] (closed_form) = 0.5891447579422698 y2[1] (numeric) = 0.5891447579422696 absolute error = 2.220446049250313e-16 relative error = 3.768931182559879e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8080275083121516 y1[1] (numeric) = 0.8080275083121521 absolute error = 4.440892098500626e-16 relative error = 5.495966477399989e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y2[1] (closed_form) = 0.5971954413623924 y2[1] (numeric) = 0.5971954413623919 absolute error = 5.551115123125783e-16 relative error = 9.295307262329275e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8020957578842923 y1[1] (numeric) = 0.8020957578842927 absolute error = 3.33066907387547e-16 relative error = 4.152458158687757e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y2[1] (closed_form) = 0.6051864057360399 y2[1] (numeric) = 0.6051864057360393 absolute error = 5.551115123125783e-16 relative error = 9.172570749295673e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.7960837985490555 y1[1] (numeric) = 0.7960837985490558 absolute error = 2.220446049250313e-16 relative error = 2.789211453991783e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y2[1] (closed_form) = 0.6131168519734341 y2[1] (numeric) = 0.6131168519734334 absolute error = 7.771561172376096e-16 relative error = 1.267549757825419e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7899922314973647 y1[1] (numeric) = 0.7899922314973651 absolute error = 3.33066907387547e-16 relative error = 4.216078261380448e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y2[1] (closed_form) = 0.62098598703656 y2[1] (numeric) = 0.6209859870365592 absolute error = 8.881784197001252e-16 relative error = 1.43027127542547e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.783821665880849 y1[1] (numeric) = 0.7838216658808494 absolute error = 4.440892098500626e-16 relative error = 5.665691944748691e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y2[1] (closed_form) = 0.6287930240184689 y2[1] (numeric) = 0.6287930240184679 absolute error = 9.992007221626409e-16 relative error = 1.589077302061946e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7775727187509276 y1[1] (numeric) = 0.7775727187509281 absolute error = 5.551115123125783e-16 relative error = 7.139030201629178e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y2[1] (closed_form) = 0.6365371822219683 y2[1] (numeric) = 0.6365371822219672 absolute error = 1.110223024625157e-15 relative error = 1.744160522955921e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7712460149971063 y1[1] (numeric) = 0.7712460149971068 absolute error = 4.440892098500626e-16 relative error = 5.758074611921708e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y2[1] (closed_form) = 0.6442176872376915 y2[1] (numeric) = 0.6442176872376904 absolute error = 1.110223024625157e-15 relative error = 1.723366257430196e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7648421872844881 y1[1] (numeric) = 0.7648421872844888 absolute error = 7.771561172376096e-16 relative error = 1.01609996174092e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y2[1] (closed_form) = 0.6518337710215371 y2[1] (numeric) = 0.6518337710215361 absolute error = 9.992007221626409e-16 relative error = 1.532907263452643e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7583618759905079 y1[1] (numeric) = 0.7583618759905086 absolute error = 7.771561172376096e-16 relative error = 1.024782682044181e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y2[1] (closed_form) = 0.6593846719714735 y2[1] (numeric) = 0.6593846719714724 absolute error = 1.110223024625157e-15 relative error = 1.683725861120999e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7518057291408946 y1[1] (numeric) = 0.7518057291408955 absolute error = 8.881784197001252e-16 relative error = 1.181393523982674e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y2[1] (closed_form) = 0.6668696350036982 y2[1] (numeric) = 0.6668696350036971 absolute error = 1.110223024625157e-15 relative error = 1.664827675980478e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.74517440234487 y1[1] (numeric) = 0.745174402344871 absolute error = 9.992007221626409e-16 relative error = 1.340895123367652e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y2[1] (closed_form) = 0.6742879116281455 y2[1] (numeric) = 0.6742879116281443 absolute error = 1.221245327087672e-15 relative error = 1.811163015126336e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7384685587295875 y1[1] (numeric) = 0.7384685587295887 absolute error = 1.221245327087672e-15 relative error = 1.653753992165383e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y2[1] (closed_form) = 0.6816387600233346 y2[1] (numeric) = 0.6816387600233332 absolute error = 1.332267629550188e-15 relative error = 1.954506855661466e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7316888688738205 y1[1] (numeric) = 0.7316888688738217 absolute error = 1.221245327087672e-15 relative error = 1.669077362031423e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y2[1] (closed_form) = 0.6889214451105518 y2[1] (numeric) = 0.6889214451105504 absolute error = 1.332267629550188e-15 relative error = 1.93384548994029e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7248360107409048 y1[1] (numeric) = 0.7248360107409061 absolute error = 1.332267629550188e-15 relative error = 1.838026270505497e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y2[1] (closed_form) = 0.6961352386273572 y2[1] (numeric) = 0.6961352386273557 absolute error = 1.443289932012704e-15 relative error = 2.073289573529692e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.717910669610943 y1[1] (numeric) = 0.7179106696109443 absolute error = 1.332267629550188e-15 relative error = 1.855756831518026e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y2[1] (closed_form) = 0.7032794192004106 y2[1] (numeric) = 0.7032794192004094 absolute error = 1.221245327087672e-15 relative error = 1.736500875393396e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.710913538012277 y1[1] (numeric) = 0.7109135380122783 absolute error = 1.332267629550188e-15 relative error = 1.874022027031901e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y2[1] (closed_form) = 0.7103532724176083 y2[1] (numeric) = 0.710353272417607 absolute error = 1.221245327087672e-15 relative error = 1.719208419961662e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7038453156522356 y1[1] (numeric) = 0.703845315652237 absolute error = 1.332267629550188e-15 relative error = 1.892841509239298e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y2[1] (closed_form) = 0.7173560908995231 y2[1] (numeric) = 0.7173560908995219 absolute error = 1.221245327087672e-15 relative error = 1.702425535352047e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6967067093471649 y1[1] (numeric) = 0.6967067093471663 absolute error = 1.332267629550188e-15 relative error = 1.912235969133357e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y2[1] (closed_form) = 0.7242871743701429 y2[1] (numeric) = 0.7242871743701417 absolute error = 1.221245327087672e-15 relative error = 1.686134133397703e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6894984329517466 y1[1] (numeric) = 0.689498432951748 absolute error = 1.332267629550188e-15 relative error = 1.932227204414001e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y2[1] (closed_form) = 0.7311458297268963 y2[1] (numeric) = 0.7311458297268949 absolute error = 1.443289932012704e-15 relative error = 1.974011029443761e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6822212072876132 y1[1] (numeric) = 0.6822212072876146 absolute error = 1.443289932012704e-15 relative error = 2.115574708899714e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y2[1] (closed_form) = 0.7379313711099631 y2[1] (numeric) = 0.7379313711099617 absolute error = 1.443289932012704e-15 relative error = 1.955859296023385e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6748757600712666 y1[1] (numeric) = 0.6748757600712681 absolute error = 1.554312234475219e-15 relative error = 2.303108700053302e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y2[1] (closed_form) = 0.7446431199708597 y2[1] (numeric) = 0.7446431199708582 absolute error = 1.554312234475219e-15 relative error = 2.087325045769636e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6674628258413077 y1[1] (numeric) = 0.6674628258413091 absolute error = 1.443289932012704e-15 relative error = 2.162352532807351e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y2[1] (closed_form) = 0.7512804051402932 y2[1] (numeric) = 0.7512804051402917 absolute error = 1.443289932012704e-15 relative error = 1.921106849237184e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6599831458849816 y1[1] (numeric) = 0.6599831458849831 absolute error = 1.443289932012704e-15 relative error = 2.186858772093905e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y2[1] (closed_form) = 0.7578425628952774 y2[1] (numeric) = 0.757842562895276 absolute error = 1.443289932012704e-15 relative error = 1.904471987557322e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6524374681640513 y1[1] (numeric) = 0.6524374681640527 absolute error = 1.332267629550188e-15 relative error = 2.041985162653469e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y2[1] (closed_form) = 0.7643289370255055 y2[1] (numeric) = 0.7643289370255041 absolute error = 1.443289932012704e-15 relative error = 1.888309943660476e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6448265472400007 y1[1] (numeric) = 0.644826547240002 absolute error = 1.332267629550188e-15 relative error = 2.066086818622134e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y2[1] (closed_form) = 0.7707388788989697 y2[1] (numeric) = 0.7707388788989683 absolute error = 1.443289932012704e-15 relative error = 1.872605588645663e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6371511441985797 y1[1] (numeric) = 0.637151144198581 absolute error = 1.332267629550188e-15 relative error = 2.090975809556049e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y2[1] (closed_form) = 0.7770717475268243 y2[1] (numeric) = 0.7770717475268228 absolute error = 1.443289932012704e-15 relative error = 1.857344494387092e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6294120265736963 y1[1] (numeric) = 0.6294120265736975 absolute error = 1.221245327087672e-15 relative error = 1.940295506801346e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y2[1] (closed_form) = 0.7833269096274839 y2[1] (numeric) = 0.7833269096274823 absolute error = 1.554312234475219e-15 relative error = 1.984244656186243e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6216099682706639 y1[1] (numeric) = 0.6216099682706653 absolute error = 1.332267629550188e-15 relative error = 2.14325332210581e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y2[1] (closed_form) = 0.7895037396899508 y2[1] (numeric) = 0.7895037396899494 absolute error = 1.443289932012704e-15 relative error = 1.828097651037731e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.613745749488811 y1[1] (numeric) = 0.6137457494888126 absolute error = 1.554312234475219e-15 relative error = 2.532501831205848e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y2[1] (closed_form) = 0.7956016200363665 y2[1] (numeric) = 0.7956016200363649 absolute error = 1.554312234475219e-15 relative error = 1.953631309101875e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6058201566434622 y1[1] (numeric) = 0.6058201566434638 absolute error = 1.554312234475219e-15 relative error = 2.565633080098991e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y2[1] (closed_form) = 0.8016199408837775 y2[1] (numeric) = 0.8016199408837762 absolute error = 1.332267629550188e-15 relative error = 1.661969172175753e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.5978339822872977 y1[1] (numeric) = 0.5978339822872991 absolute error = 1.443289932012704e-15 relative error = 2.414198548049599e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y2[1] (closed_form) = 0.8075581004051147 y2[1] (numeric) = 0.8075581004051134 absolute error = 1.221245327087672e-15 relative error = 1.512269304802998e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.5897880250310976 y1[1] (numeric) = 0.589788025031099 absolute error = 1.332267629550188e-15 relative error = 2.258892301992638e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y2[1] (closed_form) = 0.8134155047893742 y2[1] (numeric) = 0.813415504789373 absolute error = 1.221245327087672e-15 relative error = 1.501379454776807e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.5816830894638829 y1[1] (numeric) = 0.5816830894638843 absolute error = 1.332267629550188e-15 relative error = 2.290366788517254e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y2[1] (closed_form) = 0.8191915683009987 y2[1] (numeric) = 0.8191915683009974 absolute error = 1.332267629550188e-15 relative error = 1.626319997791613e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.573519986072456 y1[1] (numeric) = 0.5735199860724575 absolute error = 1.443289932012704e-15 relative error = 2.5165468807749e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y2[1] (closed_form) = 0.8248857133384505 y2[1] (numeric) = 0.8248857133384494 absolute error = 1.110223024625157e-15 relative error = 1.345911326469576e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.5652995311603537 y1[1] (numeric) = 0.565299531160355 absolute error = 1.332267629550188e-15 relative error = 2.356746390387992e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y2[1] (closed_form) = 0.8304973704919709 y2[1] (numeric) = 0.8304973704919697 absolute error = 1.221245327087672e-15 relative error = 1.470498728206965e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.5570225467662167 y1[1] (numeric) = 0.5570225467662182 absolute error = 1.554312234475219e-15 relative error = 2.790393752458941e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y2[1] (closed_form) = 0.836025978600521 y2[1] (numeric) = 0.8360259786005197 absolute error = 1.221245327087672e-15 relative error = 1.460774375853721e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.548689860581587 y1[1] (numeric) = 0.5486898605815885 absolute error = 1.554312234475219e-15 relative error = 2.832770105916878e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y2[1] (closed_form) = 0.8414709848078968 y2[1] (numeric) = 0.8414709848078956 absolute error = 1.221245327087672e-15 relative error = 1.45132196966539e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.5403023058681392 y1[1] (numeric) = 0.5403023058681409 absolute error = 1.665334536937735e-15 relative error = 3.082227336161248e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y2[1] (closed_form) = 0.846831844618015 y2[1] (numeric) = 0.8468318446180143 absolute error = 6.661338147750939e-16 relative error = 7.866187590944582e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.5318607213743558 y1[1] (numeric) = 0.5318607213743567 absolute error = 8.881784197001252e-16 relative error = 1.669945502659091e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y2[1] (closed_form) = 0.8521080219493621 y2[1] (numeric) = 0.8521080219493622 absolute error = 1.110223024625157e-16 relative error = 1.302913475788324e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.5233659512516509 y1[1] (numeric) = 0.5233659512516508 absolute error = 1.110223024625157e-16 relative error = 2.121313054412526e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y2[1] (closed_form) = 0.857298989188602 y2[1] (numeric) = 0.8572989891886026 absolute error = 5.551115123125783e-16 relative error = 6.475121507351458e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.5148188449699576 y1[1] (numeric) = 0.5148188449699566 absolute error = 9.992007221626409e-16 relative error = 1.940878295201004e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y2[1] (closed_form) = 0.8624042272433365 y2[1] (numeric) = 0.8624042272433377 absolute error = 1.110223024625157e-15 relative error = 1.287358050381976e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.5062202572327816 y1[1] (numeric) = 0.5062202572327795 absolute error = 2.109423746787797e-15 relative error = 4.167007773096276e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y2[1] (closed_form) = 0.8674232255940145 y2[1] (numeric) = 0.8674232255940163 absolute error = 1.77635683940025e-15 relative error = 2.04785482678746e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4975710478917312 y1[1] (numeric) = 0.4975710478917282 absolute error = 2.997602166487923e-15 relative error = 6.024470634272485e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y2[1] (closed_form) = 0.8723554823449834 y2[1] (numeric) = 0.8723554823449857 absolute error = 2.331468351712829e-15 relative error = 2.672612712246155e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4888720818605328 y1[1] (numeric) = 0.4888720818605288 absolute error = 3.996802888650564e-15 relative error = 8.175559695369936e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y2[1] (closed_form) = 0.8772005042746782 y2[1] (numeric) = 0.8772005042746809 absolute error = 2.664535259100376e-15 relative error = 3.037544148818716e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4801242290285403 y1[1] (numeric) = 0.4801242290285352 absolute error = 5.051514762044462e-15 relative error = 1.052126607371065e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y2[1] (closed_form) = 0.8819578068849436 y2[1] (numeric) = 0.8819578068849467 absolute error = 3.108624468950438e-15 relative error = 3.524686152424949e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4713283641737472 y1[1] (numeric) = 0.4713283641737411 absolute error = 6.106226635438361e-15 relative error = 1.295535575530821e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y2[1] (closed_form) = 0.8866269144494829 y2[1] (numeric) = 0.8866269144494865 absolute error = 3.552713678800501e-15 relative error = 4.006999585622124e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4624853668753091 y1[1] (numeric) = 0.462485366875302 absolute error = 7.049916206369744e-15 relative error = 1.524354436120024e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y2[1] (closed_form) = 0.8912073600614306 y2[1] (numeric) = 0.8912073600614349 absolute error = 4.218847493575595e-15 relative error = 4.733856207476553e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4535961214255866 y1[1] (numeric) = 0.4535961214255785 absolute error = 8.049116928532385e-15 relative error = 1.774511850594133e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y2[1] (closed_form) = 0.8956986856800425 y2[1] (numeric) = 0.8956986856800473 absolute error = 4.773959005888173e-15 relative error = 5.32987162112852e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4446615167417171 y1[1] (numeric) = 0.444661516741708 absolute error = 9.159339953157541e-15 relative error = 2.059845434854164e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y2[1] (closed_form) = 0.9001004421764995 y2[1] (numeric) = 0.9001004421765045 absolute error = 4.996003610813204e-15 relative error = 5.550495674385575e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4356824462767235 y1[1] (numeric) = 0.4356824462767133 absolute error = 1.015854067532018e-14 relative error = 2.331638734159143e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y2[1] (closed_form) = 0.9044121893788201 y2[1] (numeric) = 0.9044121893788255 absolute error = 5.440092820663267e-15 relative error = 6.015059156157218e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4266598079301697 y1[1] (numeric) = 0.4266598079301584 absolute error = 1.126876369994534e-14 relative error = 2.641158949237063e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y2[1] (closed_form) = 0.9086334961158771 y2[1] (numeric) = 0.9086334961158827 absolute error = 5.662137425588298e-15 relative error = 6.23148656723768e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4175945039583715 y1[1] (numeric) = 0.4175945039583592 absolute error = 1.226796442210798e-14 relative error = 2.937769608033665e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y2[1] (closed_form) = 0.9127639402605146 y2[1] (numeric) = 0.9127639402605204 absolute error = 5.88418203051333e-15 relative error = 6.446554000406621e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4084874408841718 y1[1] (numeric) = 0.4084874408841584 absolute error = 1.337818744673314e-14 relative error = 3.27505477714958e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y2[1] (closed_form) = 0.9168031087717602 y2[1] (numeric) = 0.9168031087717663 absolute error = 6.106226635438361e-15 relative error = 6.660346782221173e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3993395294062887 y1[1] (numeric) = 0.3993395294062743 absolute error = 1.443289932012704e-14 relative error = 3.614192499696913e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y2[1] (closed_form) = 0.9207505977361286 y2[1] (numeric) = 0.9207505977361351 absolute error = 6.550315845288424e-15 relative error = 7.114104363759135e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3901516843082468 y1[1] (numeric) = 0.3901516843082313 absolute error = 1.548761119352093e-14 relative error = 3.96963842946905e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y2[1] (closed_form) = 0.9246060124080131 y2[1] (numeric) = 0.9246060124080199 absolute error = 6.772360450213455e-15 relative error = 7.324590538380499e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3809248243668995 y1[1] (numeric) = 0.3809248243668829 absolute error = 1.665334536937735e-14 relative error = 4.371819399550911e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y2[1] (closed_form) = 0.9283689672491592 y2[1] (numeric) = 0.9283689672491664 absolute error = 7.216449660063518e-15 relative error = 7.773256016351459e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3716598722605517 y1[1] (numeric) = 0.371659872260534 absolute error = 1.770805724277125e-14 relative error = 4.764586807573628e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y2[1] (closed_form) = 0.9320390859672186 y2[1] (numeric) = 0.9320390859672261 absolute error = 7.438494264988549e-15 relative error = 7.980882322407424e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3623577544766935 y1[1] (numeric) = 0.3623577544766747 absolute error = 1.88182802673964e-14 relative error = 5.193287582481356e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y2[1] (closed_form) = 0.935616001553378 y2[1] (numeric) = 0.9356160015533855 absolute error = 7.549516567451064e-15 relative error = 8.069033187671871e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3530194012193514 y1[1] (numeric) = 0.3530194012193315 absolute error = 1.98729921407903e-14 relative error = 5.629433417015532e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y2[1] (closed_form) = 0.9390993563190595 y2[1] (numeric) = 0.9390993563190673 absolute error = 7.771561172376096e-15 relative error = 8.275547331687984e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3436457463160691 y1[1] (numeric) = 0.3436457463160482 absolute error = 2.09277040141842e-14 relative error = 6.08990631734341e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y2[1] (closed_form) = 0.9424888019316893 y2[1] (numeric) = 0.9424888019316972 absolute error = 7.882583474838611e-15 relative error = 8.363583162667575e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3342377271245258 y1[1] (numeric) = 0.3342377271245038 absolute error = 2.19824158875781e-14 relative error = 6.576880496613773e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y2[1] (closed_form) = 0.9457839994495306 y2[1] (numeric) = 0.9457839994495387 absolute error = 8.104628079763643e-15 relative error = 8.569216739213958e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3247962844388006 y1[1] (numeric) = 0.3247962844387774 absolute error = 2.314815006343451e-14 relative error = 7.126975021722017e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y2[1] (closed_form) = 0.9489846193555778 y2[1] (numeric) = 0.9489846193555859 absolute error = 8.104628079763643e-15 relative error = 8.540315527207608e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3153223623952942 y1[1] (numeric) = 0.3153223623952698 absolute error = 2.436939539052219e-14 relative error = 7.728406956425198e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y2[1] (closed_form) = 0.9520903415905072 y2[1] (numeric) = 0.9520903415905153 absolute error = 8.104628079763643e-15 relative error = 8.512456986197884e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3058169083783159 y1[1] (numeric) = 0.3058169083782904 absolute error = 2.55351295663786e-14 relative error = 8.349809597443822e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y2[1] (closed_form) = 0.9551008555846836 y2[1] (numeric) = 0.9551008555846918 absolute error = 8.215650382226158e-15 relative error = 8.601866843891359e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2962808729253465 y1[1] (numeric) = 0.2962808729253198 absolute error = 2.664535259100376e-14 relative error = 8.993274634275009e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y2[1] (closed_form) = 0.9580158602892163 y2[1] (numeric) = 0.9580158602892246 absolute error = 8.326672684688674e-15 relative error = 8.691581246029609e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2867152096319844 y1[1] (numeric) = 0.2867152096319566 absolute error = 2.781108676686017e-14 relative error = 9.699899353981713e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y2[1] (closed_form) = 0.960835064206064 y2[1] (numeric) = 0.9608350642060723 absolute error = 8.326672684688674e-15 relative error = 8.666079116886711e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2771208750565877 y1[1] (numeric) = 0.2771208750565588 absolute error = 2.886579864025407e-14 relative error = 1.0416320544008e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y2[1] (closed_form) = 0.9635581854171843 y2[1] (numeric) = 0.9635581854171926 absolute error = 8.326672684688674e-15 relative error = 8.641587825942799e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2674988286246186 y1[1] (numeric) = 0.2674988286245886 absolute error = 2.997602166487923e-14 relative error = 1.120603847837577e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y2[1] (closed_form) = 0.9661849516127254 y2[1] (numeric) = 0.9661849516127338 absolute error = 8.326672684688674e-15 relative error = 8.618093948565494e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.257850032532702 y1[1] (numeric) = 0.257850032532671 absolute error = 3.103073353827313e-14 relative error = 1.203441133339304e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y2[1] (closed_form) = 0.9687151001182567 y2[1] (numeric) = 0.9687151001182649 absolute error = 8.215650382226158e-15 relative error = 8.480976895294836e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2481754516524065 y1[1] (numeric) = 0.2481754516523743 absolute error = 3.219646771412954e-14 relative error = 1.29732685081294e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y2[1] (closed_form) = 0.971148377921036 y2[1] (numeric) = 0.9711483779210444 absolute error = 8.326672684688674e-15 relative error = 8.57404787362546e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2384760534337579 y1[1] (numeric) = 0.2384760534337245 absolute error = 3.333444631437033e-14 relative error = 1.397811052069835e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y2[1] (closed_form) = 0.973484541695311 y2[1] (numeric) = 0.9734845416953191 absolute error = 8.104628079763643e-15 relative error = 8.325379328211557e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2287528078084953 y1[1] (numeric) = 0.2287528078084608 absolute error = 3.447242491461111e-14 relative error = 1.506972755651172e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y2[1] (closed_form) = 0.9757233578266508 y2[1] (numeric) = 0.9757233578266589 absolute error = 8.104628079763643e-15 relative error = 8.306276584190916e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2190066870930786 y1[1] (numeric) = 0.219006687093043 absolute error = 3.558264793923627e-14 relative error = 1.624728834152609e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y2[1] (closed_form) = 0.977864602435308 y2[1] (numeric) = 0.977864602435316 absolute error = 7.993605777301127e-15 relative error = 8.1745527523888e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2092386658914575 y1[1] (numeric) = 0.2092386658914207 absolute error = 3.674838211509268e-14 relative error = 1.756290213308658e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y2[1] (closed_form) = 0.9799080613986062 y2[1] (numeric) = 0.9799080613986141 absolute error = 7.882583474838611e-15 relative error = 8.044207191833827e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1994497209976122 y1[1] (numeric) = 0.1994497209975744 absolute error = 3.785860513971784e-14 relative error = 1.898152825201048e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y2[1] (closed_form) = 0.9818535303723519 y2[1] (numeric) = 0.9818535303723596 absolute error = 7.66053886991358e-15 relative error = 7.802119799893622e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1896408312978748 y1[1] (numeric) = 0.1896408312978358 absolute error = 3.899658373995862e-14 relative error = 2.056339000049281e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y2[1] (closed_form) = 0.9837008148112689 y2[1] (numeric) = 0.9837008148112765 absolute error = 7.549516567451064e-15 relative error = 7.674606398389028e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1798129776730411 y1[1] (numeric) = 0.1798129776730009 absolute error = 4.016231791581504e-14 relative error = 2.233560582531662e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y2[1] (closed_form) = 0.9854497299884528 y2[1] (numeric) = 0.9854497299884601 absolute error = 7.327471962526033e-15 relative error = 7.435662864925534e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1699671429002837 y1[1] (numeric) = 0.1699671429002424 absolute error = 4.130029651605582e-14 relative error = 2.429898850525826e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999956 y2[1] (closed_form) = 0.9871001010138433 y2[1] (numeric) = 0.9871001010138504 absolute error = 7.105427357601002e-15 relative error = 7.198284500531476e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1601043115548751 y1[1] (numeric) = 0.1601043115548327 absolute error = 4.246603069191224e-14 relative error = 2.652397694946346e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y2[1] (closed_form) = 0.988651762851713 y2[1] (numeric) = 0.9886517628517199 absolute error = 6.883382752675971e-15 relative error = 6.962393646900727e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1502254699117309 y1[1] (numeric) = 0.1502254699116873 absolute error = 4.360400929215302e-14 relative error = 2.902571003290838e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y2[1] (closed_form) = 0.9901045603371712 y2[1] (numeric) = 0.9901045603371776 absolute error = 6.439293542825908e-15 relative error = 6.503650019178847e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1403316058467829 y1[1] (numeric) = 0.1403316058467381 absolute error = 4.474198789239381e-14 relative error = 3.188304418125457e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y2[1] (closed_form) = 0.9914583481916802 y2[1] (numeric) = 0.9914583481916864 absolute error = 6.217248937900877e-15 relative error = 6.270812030823595e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1304237087381929 y1[1] (numeric) = 0.130423708738147 absolute error = 4.590772206825022e-14 relative error = 3.519890862818775e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y2[1] (closed_form) = 0.9927129910375826 y2[1] (numeric) = 0.9927129910375885 absolute error = 5.88418203051333e-15 relative error = 5.927374864272893e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1205027693674151 y1[1] (numeric) = 0.1205027693673681 absolute error = 4.704570066849101e-14 relative error = 3.904117798741025e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y2[1] (closed_form) = 0.9938683634116393 y2[1] (numeric) = 0.9938683634116448 absolute error = 5.440092820663267e-15 relative error = 5.473655285685048e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1105697798201192 y1[1] (numeric) = 0.110569779820071 absolute error = 4.819755705653961e-14 relative error = 4.359017186698747e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y2[1] (closed_form) = 0.9949243497775757 y2[1] (numeric) = 0.9949243497775808 absolute error = 5.10702591327572e-15 relative error = 5.133079630041663e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1006257333869825 y1[1] (numeric) = 0.1006257333869332 absolute error = 4.934941344458821e-14 relative error = 4.904253791105517e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y2[1] (closed_form) = 0.9958808445376354 y2[1] (numeric) = 0.9958808445376399 absolute error = 4.551914400963142e-15 relative error = 4.570741997830565e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.09067162446436164 y1[1] (numeric) = 0.09067162446431115 absolute error = 5.048739204482899e-14 relative error = 5.568157882146801e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999947 y2[1] (closed_form) = 0.9967377520431391 y2[1] (numeric) = 0.9967377520431431 absolute error = 3.996802888650564e-15 relative error = 4.009884124944413e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.08070844845485374 y1[1] (numeric) = 0.08070844845480209 absolute error = 5.165312622068541e-14 relative error = 6.399965209290185e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999946 y2[1] (closed_form) = 0.9974949866040506 y2[1] (numeric) = 0.9974949866040542 absolute error = 3.663735981263017e-15 relative error = 3.672936736991655e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.07073720166775717 y1[1] (numeric) = 0.07073720166770441 absolute error = 5.276334924531056e-14 relative error = 7.459066516814264e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y2[1] (closed_form) = 0.9981524724975448 y2[1] (numeric) = 0.998152472497548 absolute error = 3.219646771412954e-15 relative error = 3.225606167519536e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.06075888121944131 y1[1] (numeric) = 0.06075888121938738 absolute error = 5.392214452726307e-14 relative error = 8.874775743897231e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y2[1] (closed_form) = 0.9987101439755801 y2[1] (numeric) = 0.9987101439755828 absolute error = 2.664535259100376e-15 relative error = 2.667976564745424e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.05077448493363573 y1[1] (numeric) = 0.05077448493358068 absolute error = 5.504624533969604e-14 relative error = 1.08413202835329e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y2[1] (closed_form) = 0.9991679452714737 y2[1] (numeric) = 0.9991679452714759 absolute error = 2.220446049250313e-15 relative error = 2.222295120413434e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.04078501124164872 y1[1] (numeric) = 0.04078501124159254 absolute error = 5.617728504603292e-14 relative error = 1.377400258962439e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y2[1] (closed_form) = 0.9995258306054773 y2[1] (numeric) = 0.9995258306054788 absolute error = 1.554312234475219e-15 relative error = 1.555049591398425e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.03079145908252493 y1[1] (numeric) = 0.03079145908246765 absolute error = 5.728750807065808e-14 relative error = 1.860499949584086e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y2[1] (closed_form) = 0.9997837641893558 y2[1] (numeric) = 0.9997837641893567 absolute error = 8.881784197001252e-16 relative error = 8.883705172190686e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.02079482780315237 y1[1] (numeric) = 0.02079482780309397 absolute error = 5.840120054223519e-14 relative error = 2.808448384140114e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y2[1] (closed_form) = 0.9999417202299656 y2[1] (numeric) = 0.9999417202299661 absolute error = 4.440892098500626e-16 relative error = 4.441150927755383e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.01079611705832845 y1[1] (numeric) = 0.01079611705826894 absolute error = 5.950968884338437e-14 relative error = 5.512138162440245e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999938 y2[1] (closed_form) = 0.9999996829318346 y2[1] (numeric) = 0.9999996829318345 absolute error = 1.110223024625157e-16 relative error = 1.110223376641646e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.0007963267107954358 y1[1] (numeric) = 0.0007963267107348223 absolute error = 6.061351507519186e-14 relative error = 7.611639073948198e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999937 y2[1] (closed_form) = 0.9999576464987406 y2[1] (numeric) = 0.9999576464987397 absolute error = 8.881784197001252e-16 relative error = 8.882160387592414e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = -0.009203543268745056 y1[1] (numeric) = -0.009203543268806767 absolute error = 6.171105293439894e-14 relative error = 6.70514074117169e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999936 y2[1] (closed_form) = 0.9998156151342921 y2[1] (numeric) = 0.9998156151342905 absolute error = 1.554312234475219e-15 relative error = 1.55459887898075e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = -0.01920249290162827 y1[1] (numeric) = -0.01920249290169107 absolute error = 6.280392872426432e-14 relative error = 3.270613302449855e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999935 y2[1] (closed_form) = 0.9995736030415071 y2[1] (numeric) = 0.9995736030415046 absolute error = 2.55351295663786e-15 relative error = 2.554602231259428e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = -0.02919952230122334 y1[1] (numeric) = -0.02919952230128722 absolute error = 6.38829267263219e-14 relative error = 2.187807254766132e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999933 y2[1] (closed_form) = 0.9992316344213932 y2[1] (numeric) = 0.99923163442139 absolute error = 3.219646771412954e-15 relative error = 3.22212253946233e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = -0.03919363177292114 y1[1] (numeric) = -0.03919363177298611 absolute error = 6.496886362228338e-14 relative error = 1.657638261202687e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999932 y2[1] (closed_form) = 0.9987897434705273 y2[1] (numeric) = 0.9987897434705235 absolute error = 3.774758283725532e-15 relative error = 3.779332245252396e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = -0.04918382191410291 y1[1] (numeric) = -0.04918382191416893 absolute error = 6.602357549567728e-14 relative error = 1.342383997953314e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999931 y2[1] (closed_form) = 0.9982479743776366 y2[1] (numeric) = 0.9982479743776319 absolute error = 4.662936703425657e-15 relative error = 4.671120626448346e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = -0.05916909371407965 y1[1] (numeric) = -0.05916909371414673 absolute error = 6.707828736907118e-14 relative error = 1.133671029223648e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63999999999993 y2[1] (closed_form) = 0.9976063813191784 y2[1] (numeric) = 0.997606381319173 absolute error = 5.440092820663267e-15 relative error = 5.453145571773103e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = -0.06914844865399239 y1[1] (numeric) = -0.06914844865406052 absolute error = 6.812606034856117e-14 relative error = 9.852145879577562e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999929 y2[1] (closed_form) = 0.9968650284539244 y2[1] (numeric) = 0.9968650284539179 absolute error = 6.550315845288424e-15 relative error = 6.570915478344702e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = -0.07912088880666325 y1[1] (numeric) = -0.07912088880673242 absolute error = 6.916689443414725e-14 relative error = 8.741925865261803e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999928 y2[1] (closed_form) = 0.9960239899165432 y2[1] (numeric) = 0.9960239899165358 absolute error = 7.327471962526033e-15 relative error = 7.356722364829789e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = -0.0890854169363873 y1[1] (numeric) = -0.08908541693645751 absolute error = 7.020772851973334e-14 relative error = 7.880945157372519e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999927 y2[1] (closed_form) = 0.9950833498101874 y2[1] (numeric) = 0.9950833498101792 absolute error = 8.215650382226158e-15 relative error = 8.256243443117903e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = -0.09904103659865532 y1[1] (numeric) = -0.09904103659872657 absolute error = 7.124856260531942e-14 relative error = 7.193842578005364e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999926 y2[1] (closed_form) = 0.9940432021980841 y2[1] (numeric) = 0.994043202198075 absolute error = 9.103828801926284e-15 relative error = 9.158383440272401e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = -0.1089867522397974 y1[1] (numeric) = -0.1089867522398697 absolute error = 7.227551890309769e-14 relative error = 6.631587547821771e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999925 y2[1] (closed_form) = 0.9929036510941275 y2[1] (numeric) = 0.9929036510941175 absolute error = 9.992007221626409e-15 relative error = 1.006342076657261e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.1189215692965375 y1[1] (numeric) = -0.1189215692966107 absolute error = 7.326084183745252e-14 relative error = 6.160433491654704e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999924 y2[1] (closed_form) = 0.9916648104524785 y2[1] (numeric) = 0.9916648104524675 absolute error = 1.099120794378905e-14 relative error = 1.108359178216071e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.1288444942954489 y1[1] (numeric) = -0.1288444942955232 absolute error = 7.427392034742297e-14 relative error = 5.764617320559154e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999922 y2[1] (closed_form) = 0.9903268041561688 y2[1] (numeric) = 0.9903268041561569 absolute error = 1.187938636348917e-14 relative error = 1.199542041438663e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.1387545349523008 y1[1] (numeric) = -0.1387545349523761 absolute error = 7.527312106958561e-14 relative error = 5.424912497127536e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999921 y2[1] (closed_form) = 0.9888897660047131 y2[1] (numeric) = 0.9888897660047004 absolute error = 1.27675647831893e-14 relative error = 1.291100911557866e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.1486507002712859 y1[1] (numeric) = -0.1486507002713621 absolute error = 7.6216810640517e-14 relative error = 5.127241950520391e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72999999999992 y2[1] (closed_form) = 0.9873538397007291 y2[1] (numeric) = 0.9873538397007152 absolute error = 1.387778780781446e-14 relative error = 1.405553637389091e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.158532000644119 y1[1] (numeric) = -0.1585320006441962 absolute error = 7.718825578706401e-14 relative error = 4.868938477622588e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999919 y2[1] (closed_form) = 0.9857191788355671 y2[1] (numeric) = 0.9857191788355524 absolute error = 1.476596622751458e-14 relative error = 1.497989137733696e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.1683974479489973 y1[1] (numeric) = -0.1683974479490755 absolute error = 7.815970093361102e-14 relative error = 4.641382745733968e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999918 y2[1] (closed_form) = 0.9839859468739515 y2[1] (numeric) = 0.9839859468739356 absolute error = 1.587618925213974e-14 relative error = 1.61345690988547e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.1782460556494115 y1[1] (numeric) = -0.1782460556494906 absolute error = 7.91033905045424e-14 relative error = 4.437876070600365e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999917 y2[1] (closed_form) = 0.9821543171376341 y2[1] (numeric) = 0.9821543171376171 absolute error = 1.69864122767649e-14 relative error = 1.729505433145136e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.1880768388927986 y1[1] (numeric) = -0.1880768388928785 absolute error = 7.999156892424253e-14 relative error = 4.25313235777196e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999916 y2[1] (closed_form) = 0.9802244727880621 y2[1] (numeric) = 0.980224472788044 absolute error = 1.809663530139005e-14 relative error = 1.846172565954981e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.1978888146090265 y1[1] (numeric) = -0.1978888146091074 absolute error = 8.090750291955828e-14 relative error = 4.088533405963803e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999915 y2[1] (closed_form) = 0.9781966068080624 y2[1] (numeric) = 0.9781966068080431 absolute error = 1.931788062847772e-14 relative error = 1.974846415743926e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.2076810016087004 y1[1] (numeric) = -0.2076810016087822 absolute error = 8.176792576364278e-14 relative error = 3.937188530981029e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999914 y2[1] (closed_form) = 0.976070921982543 y2[1] (numeric) = 0.9760709219825224 absolute error = 2.05391259555654e-14 relative error = 2.104265734486529e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.2174524206812803 y1[1] (numeric) = -0.217452420681363 absolute error = 8.26561041833429e-14 relative error = 3.801112166255984e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999913 y2[1] (closed_form) = 0.973847630878215 y2[1] (numeric) = 0.9738476308781934 absolute error = 2.164934898019055e-14 relative error = 2.223073537763519e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.2272020946930019 y1[1] (numeric) = -0.2272020946930854 absolute error = 8.354428260304303e-14 relative error = 3.677091213262318e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999911 y2[1] (closed_form) = 0.9715269558223363 y2[1] (numeric) = 0.9715269558223134 absolute error = 2.287059430727822e-14 relative error = 2.354087467178892e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.2369290486845886 y1[1] (numeric) = -0.236929048684673 absolute error = 8.440470544712753e-14 relative error = 3.562446475674291e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81999999999991 y2[1] (closed_form) = 0.9691091288804785 y2[1] (numeric) = 0.9691091288804543 absolute error = 2.420286193682841e-14 relative error = 2.497434108869424e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.2466323099687471 y1[1] (numeric) = -0.2466323099688323 absolute error = 8.523737271559639e-14 relative error = 3.45605053637934e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.829999999999909 y2[1] (closed_form) = 0.9665943918333209 y2[1] (numeric) = 0.9665943918332954 absolute error = 2.542410726391608e-14 relative error = 2.630276719865369e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.2563109082274349 y1[1] (numeric) = -0.256310908227521 absolute error = 8.604228440844963e-14 relative error = 3.356949768680968e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999908 y2[1] (closed_form) = 0.9639829961524726 y2[1] (numeric) = 0.9639829961524461 absolute error = 2.653433028854124e-14 relative error = 2.75257244105417e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.2659638756088917 y1[1] (numeric) = -0.2659638756089786 absolute error = 8.68749516769185e-14 relative error = 3.26641922622119e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.849999999999907 y2[1] (closed_form) = 0.9612752029753255 y2[1] (numeric) = 0.9612752029752978 absolute error = 2.775557561562891e-14 relative error = 2.887370394005821e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.2755902468244235 y1[1] (numeric) = -0.2755902468245113 absolute error = 8.776313009661862e-14 relative error = 3.184551380460567e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.859999999999906 y2[1] (closed_form) = 0.958471283078941 y2[1] (numeric) = 0.9584712830789118 absolute error = 2.919886554764162e-14 relative error = 3.046399622307386e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.2851890592449306 y1[1] (numeric) = -0.2851890592450191 absolute error = 8.854028621385623e-14 relative error = 3.104617212465176e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999905 y2[1] (closed_form) = 0.955571516852972 y2[1] (numeric) = 0.9555715168529415 absolute error = 3.05311331771918e-14 relative error = 3.195065218953093e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.29475935299717 y1[1] (numeric) = -0.2947593529972592 absolute error = 8.926193117986259e-14 relative error = 3.0282985178326e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999904 y2[1] (closed_form) = 0.9525761942716247 y2[1] (numeric) = 0.9525761942715928 absolute error = 3.186340080674199e-14 relative error = 3.344971352250298e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.3043001710597416 y1[1] (numeric) = -0.3043001710598316 absolute error = 8.998357614586894e-14 relative error = 2.957066236029258e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999903 y2[1] (closed_form) = 0.949485614864661 y2[1] (numeric) = 0.9494856148646277 absolute error = 3.33066907387547e-14 relative error = 3.507866808861786e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.3138105593587899 y1[1] (numeric) = -0.3138105593588807 absolute error = 9.076073226310655e-14 relative error = 2.892214094024058e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999902 y2[1] (closed_form) = 0.9463000876874463 y2[1] (numeric) = 0.9463000876874116 absolute error = 3.47499806707674e-14 relative error = 3.672194594812822e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.3232895668634103 y1[1] (numeric) = -0.3232895668635018 absolute error = 9.153788838034416e-14 relative error = 2.831451978746313e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9099999999999 y2[1] (closed_form) = 0.9430199312900437 y2[1] (numeric) = 0.9430199312900076 absolute error = 3.608224830031759e-14 relative error = 3.826244504817344e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.3327362456807513 y1[1] (numeric) = -0.3327362456808436 absolute error = 9.225953334635051e-14 relative error = 2.772752729646119e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.919999999999899 y2[1] (closed_form) = 0.9396454736853593 y2[1] (numeric) = 0.9396454736853219 absolute error = 3.741451592986778e-14 relative error = 3.981769398954827e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.3421496511508036 y1[1] (numeric) = -0.3421496511508965 absolute error = 9.287015600989434e-14 relative error = 2.714313917828942e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999898 y2[1] (closed_form) = 0.9361770523163419 y2[1] (numeric) = 0.936177052316303 absolute error = 3.885780586188048e-14 relative error = 4.150689847154052e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.3515288419408646 y1[1] (numeric) = -0.3515288419409582 absolute error = 9.353628982466944e-14 relative error = 2.660842544476178e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999897 y2[1] (closed_form) = 0.9326150140222376 y2[1] (numeric) = 0.9326150140221975 absolute error = 4.007905118896815e-14 relative error = 4.297491525051997e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.3608728801396713 y1[1] (numeric) = -0.3608728801397655 absolute error = 9.420242363944453e-14 relative error = 2.610404627884054e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.949999999999896 y2[1] (closed_form) = 0.9289597150039077 y2[1] (numeric) = 0.9289597150038662 absolute error = 4.152234112098085e-14 relative error = 4.469767682100853e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.3701808313511903 y1[1] (numeric) = -0.3701808313512853 absolute error = 9.492406860545088e-14 relative error = 2.564262127214158e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999895 y2[1] (closed_form) = 0.9252115207882081 y2[1] (numeric) = 0.925211520788165 absolute error = 4.307665335545607e-14 relative error = 4.655870834677688e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.3794517647880573 y1[1] (numeric) = -0.3794517647881527 absolute error = 9.54236689665322e-14 relative error = 2.514777313523132e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999894 y2[1] (closed_form) = 0.9213708061914366 y2[1] (numeric) = 0.9213708061913921 absolute error = 4.451994328746878e-14 relative error = 4.831924670100596e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.3886847533646542 y1[1] (numeric) = -0.3886847533647503 absolute error = 9.603429163007604e-14 relative error = 2.470750159319449e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999893 y2[1] (closed_form) = 0.9174379552818526 y2[1] (numeric) = 0.9174379552818065 absolute error = 4.6074255521944e-14 relative error = 5.02205683301921e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.3978788737898176 y1[1] (numeric) = -0.3978788737899142 absolute error = 9.664491429361988e-14 relative error = 2.429003414357538e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999892 y2[1] (closed_form) = 0.9134133613412693 y2[1] (numeric) = 0.9134133613412218 absolute error = 4.75175454539567e-14 relative error = 5.202195135856263e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.4070332066591665 y1[1] (numeric) = -0.4070332066592637 absolute error = 9.71445146547012e-14 relative error = 2.386648388028109e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.999999999999891 y2[1] (closed_form) = 0.9092974268257272 y2[1] (numeric) = 0.909297426825678 absolute error = 4.918287999089443e-14 relative error = 5.408888064556313e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.4161468365470429 y1[1] (numeric) = -0.4161468365471406 absolute error = 9.769962616701378e-14 relative error = 2.347720025404288e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.00999999999989 y2[1] (closed_form) = 0.9050905633252478 y2[1] (numeric) = 0.9050905633251973 absolute error = 5.051514762044462e-14 relative error = 5.581225754343857e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.4252188520980525 y1[1] (numeric) = -0.4252188520981505 absolute error = 9.803269307440132e-14 relative error = 2.305464411812947e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999889 y2[1] (closed_form) = 0.9007931915226757 y2[1] (numeric) = 0.9007931915226237 absolute error = 5.195843755245733e-14 relative error = 5.768076184571093e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.4342483461182001 y1[1] (numeric) = -0.4342483461182985 absolute error = 9.842127113302013e-14 relative error = 2.266474288568284e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999887 y2[1] (closed_form) = 0.8964057411516098 y2[1] (numeric) = 0.8964057411515561 absolute error = 5.362377208939506e-14 relative error = 5.982087087093481e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.4432344156656082 y1[1] (numeric) = -0.4432344156657071 absolute error = 9.892087149410145e-14 relative error = 2.231795817243823e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999886 y2[1] (closed_form) = 0.891928650953431 y2[1] (numeric) = 0.8919286509533757 absolute error = 5.52891066263328e-14 relative error = 6.198826169249218e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.4521761621408106 y1[1] (numeric) = -0.4521761621409099 absolute error = 9.936496070395151e-14 relative error = 2.197483393054422e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999885 y2[1] (closed_form) = 0.8873623686334283 y2[1] (numeric) = 0.8873623686333714 absolute error = 5.695444116327053e-14 relative error = 6.418397170817885e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.4610726913766111 y1[1] (numeric) = -0.4610726913767109 absolute error = 9.980904991380157e-14 relative error = 2.164713976353808e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999884 y2[1] (closed_form) = 0.8827073508160285 y2[1] (numeric) = 0.8827073508159697 absolute error = 5.873079800267078e-14 relative error = 6.653484639997215e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.4699231137274999 y1[1] (numeric) = -0.4699231137276 absolute error = 1.001421168211891e-13 relative error = 2.131031947478535e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999883 y2[1] (closed_form) = 0.8779640629991341 y2[1] (numeric) = 0.8779640629990737 absolute error = 6.039613253960852e-14 relative error = 6.879112151048041e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.4787265441586173 y1[1] (numeric) = -0.4787265441587178 absolute error = 1.005862060310392e-13 relative error = 2.10112030048018e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999882 y2[1] (closed_form) = 0.8731329795075741 y2[1] (numeric) = 0.873132979507512 absolute error = 6.206146707654625e-14 relative error = 7.107905500436763e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.4874821023342563 y1[1] (numeric) = -0.4874821023343572 absolute error = 1.009192729384267e-13 relative error = 2.070214936203514e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.089999999999881 y2[1] (closed_form) = 0.8682145834456717 y2[1] (numeric) = 0.8682145834456078 absolute error = 6.394884621840902e-14 relative error = 7.365557713234449e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.4961889127058955 y1[1] (numeric) = -0.4961889127059967 absolute error = 1.01196828694583e-13 relative error = 2.039481860703427e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09999999999988 y2[1] (closed_form) = 0.8632093666489344 y2[1] (numeric) = 0.8632093666488689 absolute error = 6.550315845288424e-14 relative error = 7.588328044582519e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.5048461045997537 y1[1] (numeric) = -0.5048461045998551 absolute error = 1.014743844507393e-13 relative error = 2.010006287583205e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999879 y2[1] (closed_form) = 0.8581178296348712 y2[1] (numeric) = 0.8581178296348038 absolute error = 6.7390537594747e-14 relative error = 7.853296513303034e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.5134528123038554 y1[1] (numeric) = -0.5134528123039571 absolute error = 1.016964290556643e-13 relative error = 1.980638271301971e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999878 y2[1] (closed_form) = 0.8529404815529402 y2[1] (numeric) = 0.8529404815528708 absolute error = 6.938893903907228e-14 relative error = 8.135261549872335e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.5220081751546028 y1[1] (numeric) = -0.522008175154705 absolute error = 1.021405182655144e-13 relative error = 1.956684265246679e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999876 y2[1] (closed_form) = 0.8476778401336353 y2[1] (numeric) = 0.847677840133564 absolute error = 7.138734048339757e-14 relative error = 8.421517834197888e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.5305113376228401 y1[1] (numeric) = -0.5305113376229424 absolute error = 1.023625628704394e-13 relative error = 1.929507545100058e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999875 y2[1] (closed_form) = 0.842330431636713 y2[1] (numeric) = 0.8423304316366397 absolute error = 7.327471962526033e-14 relative error = 8.699046938489674e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.5389614493994064 y1[1] (numeric) = -0.538961449399509 absolute error = 1.025846074753645e-13 relative error = 1.903375604872667e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999874 y2[1] (closed_form) = 0.8368987907985665 y2[1] (numeric) = 0.8368987907984915 absolute error = 7.505107646466058e-14 relative error = 8.967760174805253e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.5473576654801658 y1[1] (numeric) = -0.5473576654802687 absolute error = 1.028066520802895e-13 relative error = 1.878235358046974e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999873 y2[1] (closed_form) = 0.8313834607787537 y2[1] (numeric) = 0.8313834607786768 absolute error = 7.693845560652335e-14 relative error = 9.254268245179594e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.5556991462505071 y1[1] (numeric) = -0.5556991462506102 absolute error = 1.03139718987677e-13 relative error = 1.856035224880156e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999872 y2[1] (closed_form) = 0.8257849931056802 y2[1] (numeric) = 0.8257849931056014 absolute error = 7.882583474838611e-14 relative error = 9.545563967193376e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.5639850575693045 y1[1] (numeric) = -0.5639850575694078 absolute error = 1.032507412901396e-13 relative error = 1.830735405209769e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.179999999999871 y2[1] (closed_form) = 0.8201039476214481 y2[1] (numeric) = 0.8201039476213672 absolute error = 8.093525849517391e-14 relative error = 9.868902439734728e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y1[1] (closed_form) = -0.5722145708523309 y1[1] (numeric) = -0.5722145708524342 absolute error = 1.033617635926021e-13 relative error = 1.806346235445239e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.18999999999987 y2[1] (closed_form) = 0.8143408924258715 y2[1] (numeric) = 0.8143408924257888 absolute error = 8.271161533457416e-14 relative error = 1.015687853868929e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.5803868631551159 y1[1] (numeric) = -0.5803868631552194 absolute error = 1.034727858950646e-13 relative error = 1.782824396344239e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999869 y2[1] (closed_form) = 0.8084964038196675 y2[1] (numeric) = 0.8084964038195825 absolute error = 8.493206138382448e-14 relative error = 1.050493990852287e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.5885011172552396 y1[1] (numeric) = -0.588501117255343 absolute error = 1.034727858950646e-13 relative error = 1.758242811460752e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999868 y2[1] (closed_form) = 0.8025710662468262 y2[1] (numeric) = 0.8025710662467395 absolute error = 8.670841822322473e-14 relative error = 1.080383057275056e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.5965565217340537 y1[1] (numeric) = -0.5965565217341572 absolute error = 1.034727858950646e-13 relative error = 1.73450095884113e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999867 y2[1] (closed_form) = 0.7965654722361674 y2[1] (numeric) = 0.7965654722360787 absolute error = 8.870681966755001e-14 relative error = 1.113616177946137e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6045522710578232 y1[1] (numeric) = -0.6045522710579269 absolute error = 1.036948304999896e-13 relative error = 1.715233495336115e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999865 y2[1] (closed_form) = 0.7904802223420871 y2[1] (numeric) = 0.7904802223419964 absolute error = 9.070522111187529e-14 relative error = 1.147469836033694e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6124875656582788 y1[1] (numeric) = -0.6124875656583822 absolute error = 1.034727858950646e-13 relative error = 1.689385902615932e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999864 y2[1] (closed_form) = 0.7843159250845042 y2[1] (numeric) = 0.7843159250844115 absolute error = 9.270362255620057e-14 relative error = 1.181967872783055e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6203616120125732 y1[1] (numeric) = -0.6203616120126767 absolute error = 1.034727858950646e-13 relative error = 1.667943081767726e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999863 y2[1] (closed_form) = 0.7780731968880071 y2[1] (numeric) = 0.7780731968879124 absolute error = 9.470202400052585e-14 relative error = 1.217135153598626e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6281736227226327 y1[1] (numeric) = -0.6281736227227361 absolute error = 1.034727858950646e-13 relative error = 1.64720042599994e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999862 y2[1] (closed_form) = 0.7717526620202135 y2[1] (numeric) = 0.7717526620201167 absolute error = 9.681144774731365e-14 relative error = 1.25443620102185e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6359228165938962 y1[1] (numeric) = -0.6359228165939993 absolute error = 1.03139718987677e-13 relative error = 1.621890523446065e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.269999999999861 y2[1] (closed_form) = 0.7653549525293429 y2[1] (numeric) = 0.765354952529244 absolute error = 9.892087149410145e-14 relative error = 1.292483587741714e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6436084187134341 y1[1] (numeric) = -0.6436084187135371 absolute error = 1.030286966852145e-13 relative error = 1.600797840574673e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.27999999999986 y2[1] (closed_form) = 0.7588807081810132 y2[1] (numeric) = 0.758880708180912 absolute error = 1.011413175433518e-13 relative error = 1.33276964947206e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6512296605274394 y1[1] (numeric) = -0.6512296605275421 absolute error = 1.02695629777827e-13 relative error = 1.576949515700075e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999859 y2[1] (closed_form) = 0.7523305763942637 y2[1] (numeric) = 0.7523305763941606 absolute error = 1.03139718987677e-13 relative error = 1.370936157905484e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6587857799180815 y1[1] (numeric) = -0.6587857799181842 absolute error = 1.02695629777827e-13 relative error = 1.558862272203218e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999858 y2[1] (closed_form) = 0.745705212176815 y2[1] (numeric) = 0.7457052121767097 absolute error = 1.052491427344648e-13 relative error = 1.41140414490638e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6662760212797181 y1[1] (numeric) = -0.6662760212798206 absolute error = 1.024735851729019e-13 relative error = 1.538004999430726e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999857 y2[1] (closed_form) = 0.7390052780595675 y2[1] (numeric) = 0.7390052780594601 absolute error = 1.073585664812526e-13 relative error = 1.452744245117543e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6736996355944549 y1[1] (numeric) = -0.6736996355945571 absolute error = 1.022515405679769e-13 relative error = 1.517761553748695e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999856 y2[1] (closed_form) = 0.7322314440303498 y2[1] (numeric) = 0.7322314440302401 absolute error = 1.096900348329655e-13 relative error = 1.498024097807236e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6810558805070468 y1[1] (numeric) = -0.6810558805071487 absolute error = 1.019184736605894e-13 relative error = 1.496477404830731e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999854 y2[1] (closed_form) = 0.7253843874669198 y2[1] (numeric) = 0.7253843874668082 absolute error = 1.115774139748282e-13 relative error = 1.53818328465081e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6883440203991327 y1[1] (numeric) = -0.6883440203992341 absolute error = 1.014743844507393e-13 relative error = 1.474181244312981e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999853 y2[1] (closed_form) = 0.7184647930692282 y2[1] (numeric) = 0.7184647930691144 absolute error = 1.137978600240785e-13 relative error = 1.583903082264373e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6955633264627967 y1[1] (numeric) = -0.695563326462898 absolute error = 1.012523398458143e-13 relative error = 1.455688303187588e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999852 y2[1] (closed_form) = 0.7114733527909483 y2[1] (numeric) = 0.7114733527908322 absolute error = 1.160183060733289e-13 relative error = 1.630676758563275e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7027130767734487 y1[1] (numeric) = -0.7027130767735498 absolute error = 1.010302952408892e-13 relative error = 1.437717591720026e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.359999999999851 y2[1] (closed_form) = 0.7044107657702818 y2[1] (numeric) = 0.7044107657701635 absolute error = 1.183497744250417e-13 relative error = 1.680124441250195e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7097925563620157 y1[1] (numeric) = -0.7097925563621164 absolute error = 1.006972283335017e-13 relative error = 1.418685324760479e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36999999999985 y2[1] (closed_form) = 0.6972777382600454 y2[1] (numeric) = 0.6972777382599249 absolute error = 1.204591981718295e-13 relative error = 1.727564090493091e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7168010572864383 y1[1] (numeric) = -0.7168010572865385 absolute error = 1.002531391236516e-13 relative error = 1.398618739531098e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999849 y2[1] (closed_form) = 0.6900749835570457 y2[1] (numeric) = 0.6900749835569231 absolute error = 1.225686219186173e-13 relative error = 1.776163820442058e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7237378787024644 y1[1] (numeric) = -0.7237378787025643 absolute error = 9.992007221626409e-14 relative error = 1.380611339500474e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999848 y2[1] (closed_form) = 0.6828032219307509 y2[1] (numeric) = 0.6828032219306261 absolute error = 1.247890679678676e-13 relative error = 1.827599284241859e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7306023269337333 y1[1] (numeric) = -0.7306023269338325 absolute error = 9.925393840148899e-14 relative error = 1.358522067922341e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999847 y2[1] (closed_form) = 0.675463180551264 y2[1] (numeric) = 0.675463180551137 absolute error = 1.270095140171179e-13 relative error = 1.880332158348912e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.737393715541142 y1[1] (numeric) = -0.7373937155412408 absolute error = 9.880984919163893e-14 relative error = 1.339987676991885e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999846 y2[1] (closed_form) = 0.6680555934166059 y2[1] (numeric) = 0.6680555934164766 absolute error = 1.293409823688307e-13 relative error = 1.936081123239282e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7441113653914893 y1[1] (numeric) = -0.7441113653915876 absolute error = 9.836575998178887e-14 relative error = 1.321922558326159e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999844 y2[1] (closed_form) = 0.6605812012793174 y2[1] (numeric) = 0.6605812012791858 absolute error = 1.315614284180811e-13 relative error = 1.9916011561227e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7507546047253882 y1[1] (numeric) = -0.7507546047254859 absolute error = 9.769962616701378e-14 relative error = 1.301352340059911e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999843 y2[1] (closed_form) = 0.6530407515723835 y2[1] (numeric) = 0.6530407515722495 absolute error = 1.340039190722564e-13 relative error = 2.051999339238836e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7573227692244414 y1[1] (numeric) = -0.7573227692245385 absolute error = 9.703349235223868e-14 relative error = 1.281269972268346e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999842 y2[1] (closed_form) = 0.6454349983344911 y2[1] (numeric) = 0.6454349983343548 absolute error = 1.363353874239692e-13 relative error = 2.112302366245634e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7638152020776723 y1[1] (numeric) = -0.7638152020777687 absolute error = 9.636735853746359e-14 relative error = 1.26165803292907e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.449999999999841 y2[1] (closed_form) = 0.6377647021346261 y2[1] (numeric) = 0.6377647021344873 absolute error = 1.387778780781446e-13 relative error = 2.176004372986604e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.770231254047206 y1[1] (numeric) = -0.7702312540473016 absolute error = 9.559020242022598e-14 relative error = 1.241058473256493e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45999999999984 y2[1] (closed_form) = 0.6300306299960163 y2[1] (numeric) = 0.6300306299958752 absolute error = 1.411093464298574e-13 relative error = 2.239722002575488e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7765702835331924 y1[1] (numeric) = -0.7765702835332871 absolute error = 9.470202400052585e-14 relative error = 1.219490701725752e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999839 y2[1] (closed_form) = 0.6222335553194308 y2[1] (numeric) = 0.6222335553192873 absolute error = 1.435518370840327e-13 relative error = 2.307041075763565e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7828316566379651 y1[1] (numeric) = -0.7828316566380591 absolute error = 9.403589018575076e-14 relative error = 1.201227484713733e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999838 y2[1] (closed_form) = 0.6143742578058397 y2[1] (numeric) = 0.6143742578056937 absolute error = 1.459943277382081e-13 relative error = 2.376309324215641e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7890147472294315 y1[1] (numeric) = -0.7890147472295247 absolute error = 9.314771176605063e-14 relative error = 1.18055729747932e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999837 y2[1] (closed_form) = 0.6064535233784447 y2[1] (numeric) = 0.6064535233782964 absolute error = 1.483257960899209e-13 relative error = 2.445789996628666e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7951189370036852 y1[1] (numeric) = -0.7951189370037776 absolute error = 9.237055564881302e-14 relative error = 1.161719981125099e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999836 y2[1] (closed_form) = 0.5984721441040881 y2[1] (numeric) = 0.5984721441039377 absolute error = 1.504352198367087e-13 relative error = 2.513654500359578e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8011436155468353 y1[1] (numeric) = -0.801143615546927 absolute error = 9.170442183403793e-14 relative error = 1.14466894642159e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999835 y2[1] (closed_form) = 0.5904309181140464 y2[1] (numeric) = 0.5904309181138935 absolute error = 1.528777104908841e-13 relative error = 2.589256520969563e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8070881803960483 y1[1] (numeric) = -0.8070881803961392 absolute error = 9.081624341433781e-14 relative error = 1.125233222592519e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999833 y2[1] (closed_form) = 0.5823306495242173 y2[1] (numeric) = 0.5823306495240618 absolute error = 1.555422457499844e-13 relative error = 2.671029695535816e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.812952037099793 y1[1] (numeric) = -0.8129520370998828 absolute error = 8.981704269217516e-14 relative error = 1.104825851874331e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999832 y2[1] (closed_form) = 0.5741721483547098 y2[1] (numeric) = 0.5741721483545517 absolute error = 1.580957587066223e-13 relative error = 2.753455721592308e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8187345992772854 y1[1] (numeric) = -0.8187345992773744 absolute error = 8.892886427247504e-14 relative error = 1.086174498439109e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999831 y2[1] (closed_form) = 0.5659562304488419 y2[1] (numeric) = 0.5659562304486814 absolute error = 1.605382493607976e-13 relative error = 2.836584186615984e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8244352886771268 y1[1] (numeric) = -0.8244352886772146 absolute error = 8.781864124784988e-14 relative error = 1.065197504934099e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54999999999983 y2[1] (closed_form) = 0.5576837173915579 y2[1] (numeric) = 0.5576837173913948 absolute error = 1.630917623174355e-13 relative error = 2.924449060127864e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8300535352351275 y1[1] (numeric) = -0.8300535352352144 absolute error = 8.693046282814976e-14 relative error = 1.047287423497632e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999829 y2[1] (closed_form) = 0.5493554364272695 y2[1] (numeric) = 0.549355436427104 absolute error = 1.654232306691483e-13 relative error = 3.011224058234092e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8355887771313137 y1[1] (numeric) = -0.8355887771313998 absolute error = 8.604228440844963e-14 relative error = 1.02972044100262e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999828 y2[1] (closed_form) = 0.5409722203771331 y2[1] (numeric) = 0.5409722203769651 absolute error = 1.679767436257862e-13 relative error = 3.105090008294381e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8410404608461085 y1[1] (numeric) = -0.8410404608461935 absolute error = 8.504308368628699e-14 relative error = 1.01116518937426e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999827 y2[1] (closed_form) = 0.5325349075557677 y2[1] (numeric) = 0.5325349075555972 absolute error = 1.70530256582424e-13 relative error = 3.202236213305245e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8464080412156834 y1[1] (numeric) = -0.8464080412157673 absolute error = 8.393286066166183e-14 relative error = 9.916359081502854e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999826 y2[1] (closed_form) = 0.5240443416874244 y2[1] (numeric) = 0.5240443416872514 absolute error = 1.729727472365994e-13 relative error = 3.300727314021302e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8516909814864744 y1[1] (numeric) = -0.8516909814865573 absolute error = 8.293365993949919e-14 relative error = 9.737529425843317e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999825 y2[1] (closed_form) = 0.5155013718216145 y2[1] (numeric) = 0.5155013718214391 absolute error = 1.754152378907747e-13 relative error = 3.402808362486296e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8568887533688568 y1[1] (numeric) = -0.8568887533689387 absolute error = 8.182343691487404e-14 relative error = 9.54889845305885e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999824 y2[1] (closed_form) = 0.5069068522482054 y2[1] (numeric) = 0.5069068522480276 absolute error = 1.778577285449501e-13 relative error = 3.508686610885713e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8620008370899741 y1[1] (numeric) = -0.8620008370900547 absolute error = 8.060219158778636e-14 relative error = 9.350593191984714e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999822 y2[1] (closed_form) = 0.4982616424119926 y2[1] (numeric) = 0.4982616424118123 absolute error = 1.803557303503567e-13 relative error = 3.619699270393119e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8670267214457139 y1[1] (numeric) = -0.8670267214457935 absolute error = 7.960299086562372e-14 relative error = 9.181146197304117e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999821 y2[1] (closed_form) = 0.4895666068267552 y2[1] (numeric) = 0.4895666068265723 absolute error = 1.829092433069945e-13 relative error = 3.736146231307834e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8719659038518291 y1[1] (numeric) = -0.8719659038519074 absolute error = 7.827072323607354e-14 relative error = 8.97635135620783e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999982 y2[1] (closed_form) = 0.480822614988806 y2[1] (numeric) = 0.4808226149886206 absolute error = 1.854072451124011e-13 relative error = 3.856042526550412e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.876817890394195 y1[1] (numeric) = -0.8768178903942722 absolute error = 7.716050021144838e-14 relative error = 8.800059973315438e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999819 y2[1] (closed_form) = 0.472030541290042 y2[1] (numeric) = 0.4720305412898542 absolute error = 1.878497357665765e-13 relative error = 3.979609778070506e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8815821958782005 y1[1] (numeric) = -0.8815821958782765 absolute error = 7.593925488436071e-14 relative error = 8.613973290228798e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999818 y2[1] (closed_form) = 0.4631912649305066 y2[1] (numeric) = 0.4631912649303162 absolute error = 1.903477375719831e-13 relative error = 4.109484612162134e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8862583438772678 y1[1] (numeric) = -0.8862583438773424 absolute error = 7.460698725481052e-14 relative error = 8.418198572711251e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999817 y2[1] (closed_form) = 0.4543056698304694 y2[1] (numeric) = 0.4543056698302766 absolute error = 1.928457393773897e-13 relative error = 4.244845534271074e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8908458667804934 y1[1] (numeric) = -0.8908458667805668 absolute error = 7.338574192772285e-14 relative error = 8.23775971402753e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999816 y2[1] (closed_form) = 0.4453746445420361 y2[1] (numeric) = 0.4453746445418408 absolute error = 1.95288230031565e-13 relative error = 4.384807990862915e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.89534430583941 y1[1] (numeric) = -0.895344305839482 absolute error = 7.194245199571014e-14 relative error = 8.035171668206691e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999815 y2[1] (closed_form) = 0.4363990821602929 y2[1] (numeric) = 0.436399082160095 absolute error = 1.979527652906654e-13 relative error = 4.536049074868488e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8997532112138605 y1[1] (numeric) = -0.8997532112139309 absolute error = 7.038813976123492e-14 relative error = 7.823049574479875e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999814 y2[1] (closed_form) = 0.4273798802339984 y2[1] (numeric) = 0.4273798802337978 absolute error = 2.006173005497658e-13 relative error = 4.694121315208477e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9040721420169815 y1[1] (numeric) = -0.9040721420170504 absolute error = 6.894484982922222e-14 relative error = 7.626034098938888e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999813 y2[1] (closed_form) = 0.4183179406758292 y2[1] (numeric) = 0.4183179406756261 absolute error = 2.031153023551724e-13 relative error = 4.855524533014813e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9083006663592917 y1[1] (numeric) = -0.9083006663593591 absolute error = 6.7390537594747e-14 relative error = 7.41940858249791e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999811 y2[1] (closed_form) = 0.4092141696721895 y2[1] (numeric) = 0.4092141696719839 absolute error = 2.056688153118102e-13 relative error = 5.025945594126567e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9124383613918808 y1[1] (numeric) = -0.9124383613919467 absolute error = 6.583622536027178e-14 relative error = 7.215416201905605e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999981 y2[1] (closed_form) = 0.4000694775925933 y2[1] (numeric) = 0.4000694775923851 absolute error = 2.082223282684481e-13 relative error = 5.204654189602767e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9164848133486935 y1[1] (numeric) = -0.9164848133487578 absolute error = 6.428191312579656e-14 relative error = 7.013963809276928e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999809 y2[1] (closed_form) = 0.390884778898628 y2[1] (numeric) = 0.3908847788984172 absolute error = 2.108313523763172e-13 relative error = 5.39369562995939e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.920439617587906 y1[1] (numeric) = -0.9204396175879687 absolute error = 6.261657858885883e-14 relative error = 6.802899113898546e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999808 y2[1] (closed_form) = 0.381660992052509 y2[1] (numeric) = 0.3816609920522956 absolute error = 2.134403764841863e-13 relative error = 5.592407422522791e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9243023786323903 y1[1] (numeric) = -0.9243023786324512 absolute error = 6.095124405192109e-14 relative error = 6.594297002903459e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999807 y2[1] (closed_form) = 0.3723990394252346 y2[1] (numeric) = 0.3723990394250185 absolute error = 2.161049117432867e-13 relative error = 5.803046970175481e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9280727102092609 y1[1] (numeric) = -0.9280727102093198 absolute error = 5.895284260759581e-14 relative error = 6.35217930223411e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999806 y2[1] (closed_form) = 0.3630998472043491 y2[1] (numeric) = 0.3630998472041305 absolute error = 2.186584246999246e-13 relative error = 6.021991647296555e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9317502352885018 y1[1] (numeric) = -0.9317502352885589 absolute error = 5.717648576819556e-14 relative error = 6.136460566655158e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999805 y2[1] (closed_form) = 0.3537643453013254 y2[1] (numeric) = 0.3537643453011042 absolute error = 2.212674488077937e-13 relative error = 6.254656574260613e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9353345861206698 y1[1] (numeric) = -0.9353345861207251 absolute error = 5.52891066263328e-14 relative error = 5.911158150972064e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999804 y2[1] (closed_form) = 0.3443934672585743 y2[1] (numeric) = 0.3443934672583504 absolute error = 2.238764729156628e-13 relative error = 6.500601614129167e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9388254042736687 y1[1] (numeric) = -0.9388254042737221 absolute error = 5.340172748447003e-14 relative error = 5.688142570639617e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999803 y2[1] (closed_form) = 0.3349881501560908 y2[1] (numeric) = 0.3349881501558644 absolute error = 2.264854970235319e-13 relative error = 6.761000259800202e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.942222340668592 y1[1] (numeric) = -0.9422223406686435 absolute error = 5.151434834260726e-14 relative error = 5.467324018877877e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999802 y2[1] (closed_form) = 0.3255493345177477 y2[1] (numeric) = 0.3255493345175186 absolute error = 2.290945211314011e-13 relative error = 7.037167545458818e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9455250556146313 y1[1] (numeric) = -0.9455250556146809 absolute error = 4.96269692007445e-14 relative error = 5.248614926283986e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8199999999998 y2[1] (closed_form) = 0.316077964217243 y2[1] (numeric) = 0.3160779642170113 absolute error = 2.316480340880389e-13 relative error = 7.328825806054145e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9487332188430441 y1[1] (numeric) = -0.9487332188430916 absolute error = 4.75175454539567e-14 relative error = 5.008525527534825e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999799 y2[1] (closed_form) = 0.306574986383714 y2[1] (numeric) = 0.3065749863834797 absolute error = 2.34257058195908e-13 relative error = 7.641101479254679e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9518465095401808 y1[1] (numeric) = -0.9518465095402265 absolute error = 4.574118861455645e-14 relative error = 4.805521494915515e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999798 y2[1] (closed_form) = 0.2970413513070249 y2[1] (numeric) = 0.2970413513067882 absolute error = 2.367550600013146e-13 relative error = 7.970441117358177e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9548646163795664 y1[1] (numeric) = -0.95486461637961 absolute error = 4.352074256530614e-14 relative error = 4.557791944403382e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999797 y2[1] (closed_form) = 0.2874780123427388 y2[1] (numeric) = 0.2874780123424995 absolute error = 2.392530618067212e-13 relative error = 8.322482121571005e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.957787237553032 y1[1] (numeric) = -0.9577872375530733 absolute error = 4.130029651605582e-14 relative error = 4.312053334681133e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999796 y2[1] (closed_form) = 0.2778859258167826 y2[1] (numeric) = 0.2778859258165408 absolute error = 2.418620859145904e-13 relative error = 8.703646476650145e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9606140808008956 y1[1] (numeric) = -0.9606140808009346 absolute error = 3.896882816434299e-14 relative error = 4.056658021486985e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999795 y2[1] (closed_form) = 0.2682660509298156 y2[1] (numeric) = 0.2682660509295711 absolute error = 2.445266211736907e-13 relative error = 9.115078867644881e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9633448634411882 y1[1] (numeric) = -0.9633448634412252 absolute error = 3.697042672001771e-14 relative error = 3.837714625679814e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999794 y2[1] (closed_form) = 0.2586193496613098 y2[1] (numeric) = 0.2586193496610628 absolute error = 2.470801341303286e-13 relative error = 9.553814687644482e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9659793123979215 y1[1] (numeric) = -0.9659793123979562 absolute error = 3.47499806707674e-14 relative error = 3.597383528277119e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999793 y2[1] (closed_form) = 0.2489467866733534 y2[1] (numeric) = 0.2489467866731037 absolute error = 2.49744669389429e-13 relative error = 1.003205033199012e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.968517164228395 y1[1] (numeric) = -0.9685171642284276 absolute error = 3.26405569239796e-14 relative error = 3.370157817490401e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999792 y2[1] (closed_form) = 0.2392493292141847 y2[1] (numeric) = 0.2392493292139323 absolute error = 2.523536934972981e-13 relative error = 1.054772836045789e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9709581651495407 y1[1] (numeric) = -0.9709581651495709 absolute error = 3.019806626980426e-14 relative error = 3.110130524022458e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.909999999999791 y2[1] (closed_form) = 0.2295279470214682 y2[1] (numeric) = 0.2295279470212132 absolute error = 2.549904731807828e-13 relative error = 1.11093431754057e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9733020710633005 y1[1] (numeric) = -0.9733020710633286 absolute error = 2.808864252301646e-14 relative error = 2.88591212924581e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999789 y2[1] (closed_form) = 0.2197836122253223 y2[1] (numeric) = 0.2197836122250647 absolute error = 2.575994972886519e-13 relative error = 1.172059621190322e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9755486475810364 y1[1] (numeric) = -0.9755486475810621 absolute error = 2.564615186884112e-14 relative error = 2.628895230641049e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999788 y2[1] (closed_form) = 0.2100172992511063 y2[1] (numeric) = 0.210017299250846 absolute error = 2.602362769721367e-13 relative error = 1.239118291207937e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9776976700469687 y1[1] (numeric) = -0.9776976700469918 absolute error = 2.309263891220326e-14 relative error = 2.36194067140345e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999787 y2[1] (closed_form) = 0.2002299847219789 y2[1] (numeric) = 0.2002299847217161 absolute error = 2.628175455043902e-13 relative error = 1.312578362672877e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9797489235606417 y1[1] (numeric) = -0.9797489235606622 absolute error = 2.05391259555654e-14 relative error = 2.096366269117327e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999786 y2[1] (closed_form) = 0.1904226473612372 y2[1] (numeric) = 0.1904226473609718 absolute error = 2.65371058461028e-13 relative error = 1.393589796898536e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9817022029984133 y1[1] (numeric) = -0.9817022029984313 absolute error = 1.798561299892754e-14 relative error = 1.832084408489059e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999785 y2[1] (closed_form) = 0.1805962678944443 y2[1] (numeric) = 0.1805962678941764 absolute error = 2.679523269932815e-13 relative error = 1.483709104940615e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9835573130339675 y1[1] (numeric) = -0.983557313033983 absolute error = 1.543210004228968e-14 relative error = 1.569008723516727e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999784 y2[1] (closed_form) = 0.1707518289513584 y2[1] (numeric) = 0.1707518289510879 absolute error = 2.705613511011506e-13 relative error = 1.584529739814527e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9853140681578468 y1[1] (numeric) = -0.9853140681578598 absolute error = 1.298960938811433e-14 relative error = 1.318321721763279e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999783 y2[1] (closed_form) = 0.1608903149676701 y2[1] (numeric) = 0.1608903149673969 absolute error = 2.731426196334041e-13 relative error = 1.697694604478153e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9869722926960026 y1[1] (numeric) = -0.9869722926960131 absolute error = 1.043609643147647e-14 relative error = 1.057384944715048e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999782 y2[1] (closed_form) = 0.1510127120865598 y2[1] (numeric) = 0.1510127120862841 absolute error = 2.757238881656576e-13 relative error = 1.825832304816921e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.988531820827363 y1[1] (numeric) = -0.9885318208273709 absolute error = 7.882583474838611e-15 relative error = 7.974031092131352e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.999999999999781 y2[1] (closed_form) = 0.1411200080600844 y2[1] (numeric) = 0.1411200080598061 absolute error = 2.783051566979111e-13 relative error = 1.972116927455231e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9899924966004146 y1[1] (numeric) = -0.9899924966004197 absolute error = 5.10702591327572e-15 relative error = 5.158651132016653e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.00999999999978 y2[1] (closed_form) = 0.1312131921504026 y2[1] (numeric) = 0.1312131921501218 absolute error = 2.808309140789333e-13 relative error = 2.140264324619372e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9913541739487969 y1[1] (numeric) = -0.9913541739487995 absolute error = 2.664535259100376e-15 relative error = 2.687773279338609e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999778 y2[1] (closed_form) = 0.1212932550308497 y2[1] (numeric) = 0.1212932550305663 absolute error = 2.83398304823379e-13 relative error = 2.336472087844452e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9926167167059102 y1[1] (numeric) = -0.99261671670591 absolute error = 2.220446049250313e-16 relative error = 2.236962174704318e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999777 y2[1] (closed_form) = 0.1113611886868711 y2[1] (numeric) = 0.1113611886865852 absolute error = 2.859379399922091e-13 relative error = 2.567662426774361e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9937799986185308 y1[1] (numeric) = -0.9937799986185278 absolute error = 2.997602166487923e-15 relative error = 3.016363954451626e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999776 y2[1] (closed_form) = 0.1014179863168245 y2[1] (numeric) = 0.101417986316536 absolute error = 2.884775751610391e-13 relative error = 2.844441953913876e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9948439033594367 y1[1] (numeric) = -0.994843903359431 absolute error = 5.773159728050814e-15 relative error = 5.803080974367668e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999775 y2[1] (closed_form) = 0.09146464223266096 y2[1] (numeric) = 0.09146464223236994 absolute error = 2.910172103298692e-13 relative error = 3.18174546170094e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9958083245390407 y1[1] (numeric) = -0.995808324539032 absolute error = 8.659739592076221e-15 relative error = 8.696191203347101e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999774 y2[1] (closed_form) = 0.08150215176049441 y2[1] (numeric) = 0.08150215176020086 absolute error = 2.935568454986992e-13 relative error = 3.601829389257813e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9966731657160282 y1[1] (numeric) = -0.9966731657160167 absolute error = 1.143529715363911e-14 relative error = 1.147346747860297e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999773 y2[1] (closed_form) = 0.07153151114107005 y2[1] (numeric) = 0.07153151114077397 absolute error = 2.960826028797214e-13 relative error = 4.139191220157582e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9974383404070023 y1[1] (numeric) = -0.997438340406988 absolute error = 1.432187701766452e-14 relative error = 1.435865901427101e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999772 y2[1] (closed_form) = 0.06155371743014097 y2[1] (numeric) = 0.06155371742984239 absolute error = 2.98580604685128e-13 relative error = 4.850732289629712e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9981037720951316 y1[1] (numeric) = -0.9981037720951145 absolute error = 1.709743457922741e-14 relative error = 1.712991680548204e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.089999999999771 y2[1] (closed_form) = 0.05156976839876348 y2[1] (numeric) = 0.0515697683984624 absolute error = 3.010855453844385e-13 relative error = 5.838411820202354e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9986693942378018 y1[1] (numeric) = -0.9986693942377816 absolute error = 2.020605904817785e-14 relative error = 2.023298116950845e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09999999999977 y2[1] (closed_form) = 0.04158066243352077 y2[1] (numeric) = 0.0415806624332172 absolute error = 3.035766082959412e-13 relative error = 7.300908415812278e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9991351502732699 y1[1] (numeric) = -0.9991351502732467 absolute error = 2.320366121466577e-14 relative error = 2.322374626527695e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.109999999999769 y2[1] (closed_form) = 0.03158739843668516 y2[1] (numeric) = 0.03158739843637907 absolute error = 3.060815489952518e-13 relative error = 9.689989177449098e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9995009936263206 y1[1] (numeric) = -0.9995009936262944 absolute error = 2.620126338115369e-14 relative error = 2.621434450614409e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999767 y2[1] (closed_form) = 0.02159097572632861 y2[1] (numeric) = 0.02159097572602005 absolute error = 3.085552646719947e-13 relative error = 1.429093657382673e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 y1[1] (closed_form) = -0.9997668877129233 y1[1] (numeric) = -0.9997668877128943 absolute error = 2.897682094271659e-14 relative error = 2.898357737072514e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.129999999999766 y2[1] (closed_form) = 0.01159239393639185 y2[1] (numeric) = 0.01159239393608082 absolute error = 3.110341845191655e-13 relative error = 2.683088464952351e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 y1[1] (closed_form) = -0.9999328059438911 y1[1] (numeric) = -0.9999328059438591 absolute error = 3.197442310920451e-14 relative error = 3.19765717447605e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999765 y2[1] (closed_form) = 0.001592652916721751 y2[1] (numeric) = 0.00159265291640825 absolute error = 3.135005276211356e-13 relative error = 1.968417125474091e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.001 y1[1] (closed_form) = -0.9999987317275392 y1[1] (numeric) = -0.9999987317275041 absolute error = 3.508304757815495e-14 relative error = 3.508309207307446e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999764 y2[1] (closed_form) = -0.008407247366912814 y2[1] (numeric) = -0.008407247367228773 absolute error = 3.159590644674637e-13 relative error = 3.758174949281712e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 y1[1] (closed_form) = -0.999964658471344 y1[1] (numeric) = -0.9999646584713056 absolute error = 3.841371665203042e-14 relative error = 3.841507429947959e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.159999999999763 y2[1] (closed_form) = -0.01840630693281671 y2[1] (numeric) = -0.01840630693313511 absolute error = 3.18405024568591e-13 relative error = 1.729869146107223e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 y1[1] (closed_form) = -0.9998305895826027 y1[1] (numeric) = -0.9998305895825612 absolute error = 4.152234112098085e-14 relative error = 4.152937663000999e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.169999999999762 y2[1] (closed_form) = -0.02840352588336585 y2[1] (numeric) = -0.0284035258836867 absolute error = 3.208440457758144e-13 relative error = 1.129592315733282e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 y1[1] (closed_form) = -0.9995965384680926 y1[1] (numeric) = -0.9995965384680479 absolute error = 4.474198789239381e-14 relative error = 4.476004684946394e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.179999999999761 y2[1] (closed_form) = -0.03839790450499619 y2[1] (numeric) = -0.03839790450531946 absolute error = 3.232761280891339e-13 relative error = 8.419108601279802e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9992625285327301 y1[1] (numeric) = -0.9992625285326822 absolute error = 4.796163466380676e-14 relative error = 4.799703110476019e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18999999999976 y2[1] (closed_form) = -0.04838844336817417 y2[1] (numeric) = -0.04838844336849988 absolute error = 3.257047409555014e-13 relative error = 6.731043990758389e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9988285931772303 y1[1] (numeric) = -0.998828593177179 absolute error = 5.129230373768223e-14 relative error = 5.135245835776852e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999759 y2[1] (closed_form) = -0.05837414342733891 y2[1] (numeric) = -0.05837414342766702 absolute error = 3.281055982462533e-13 relative error = 5.620735123157088e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9982947757947672 y1[1] (numeric) = -0.9982947757947127 absolute error = 5.451195050909519e-14 relative error = 5.460506438661554e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999757 y2[1] (closed_form) = -0.06835400612080587 y2[1] (numeric) = -0.06835400612113636 absolute error = 3.304856388552935e-13 relative error = 4.834912503463332e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9976611297666341 y1[1] (numeric) = -0.9976611297665765 absolute error = 5.762057497804562e-14 relative error = 5.775565796727374e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999756 y2[1] (closed_form) = -0.07832703347062224 y2[1] (numeric) = -0.07832703347095513 absolute error = 3.328864961460454e-13 relative error = 4.249956641992571e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.996927718456906 y1[1] (numeric) = -0.9969277184568449 absolute error = 6.106226635438361e-14 relative error = 6.125044496595882e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999755 y2[1] (closed_form) = -0.08829222818236386 y2[1] (numeric) = -0.08829222818269913 absolute error = 3.352734756489895e-13 relative error = 3.797315828936793e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9960946152061025 y1[1] (numeric) = -0.996094615206038 absolute error = 6.450395773072159e-14 relative error = 6.475685817995818e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999754 y2[1] (closed_form) = -0.09824859374486385 y2[1] (numeric) = -0.09824859374520151 absolute error = 3.376604551519335e-13 relative error = 3.436796826108114e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9951619033238545 y1[1] (numeric) = -0.9951619033237867 absolute error = 6.772360450213455e-14 relative error = 6.80528507732629e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999753 y2[1] (closed_form) = -0.1081951345298629 y2[1] (numeric) = -0.1081951345302029 absolute error = 3.399919235036464e-13 relative error = 3.142395681478683e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9941296760805729 y1[1] (numeric) = -0.9941296760805016 absolute error = 7.127631818093505e-14 relative error = 7.16972039924882e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999752 y2[1] (closed_form) = -0.1181308558915713 y2[1] (numeric) = -0.1181308558919136 absolute error = 3.423233918553592e-13 relative error = 2.8978321478477e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.992998036698122 y1[1] (numeric) = -0.9929980366980473 absolute error = 7.471800955727304e-14 relative error = 7.524487138536791e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.269999999999751 y2[1] (closed_form) = -0.1280547642661326 y2[1] (numeric) = -0.1280547642664772 absolute error = 3.446409824192642e-13 relative error = 2.691356189629982e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9917670983394968 y1[1] (numeric) = -0.9917670983394187 absolute error = 7.815970093361102e-14 relative error = 7.880852375973435e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27999999999975 y2[1] (closed_form) = -0.1379658672709792 y2[1] (numeric) = -0.1379658672713262 absolute error = 3.469446951953614e-13 relative error = 2.514713980044979e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9904369840975076 y1[1] (numeric) = -0.9904369840974259 absolute error = 8.171241461241152e-14 relative error = 8.250137658870684e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999749 y2[1] (closed_form) = -0.1478631738040699 y2[1] (numeric) = -0.1478631738044192 absolute error = 3.492761635470742e-13 relative error = 2.362157896122885e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.98900782698247 y1[1] (numeric) = -0.9890078269823847 absolute error = 8.537615059367454e-14 relative error = 8.632505048434548e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999748 y2[1] (closed_form) = -0.1577456941429991 y2[1] (numeric) = -0.1577456941433507 absolute error = 3.515521207475558e-13 relative error = 2.228600423342573e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9874797699089047 y1[1] (numeric) = -0.9874797699088155 absolute error = 8.926193117986259e-14 relative error = 9.039368086304899e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999746 y2[1] (closed_form) = -0.1676124400439683 y2[1] (numeric) = -0.1676124400443222 absolute error = 3.538280779480374e-13 relative error = 2.110989362455559e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9858529656812456 y1[1] (numeric) = -0.9858529656811525 absolute error = 9.303668946358812e-14 relative error = 9.437177013440109e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999745 y2[1] (closed_form) = -0.1774624248406097 y2[1] (numeric) = -0.1774624248409658 absolute error = 3.560762795729033e-13 relative error = 2.006488302482726e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9841275769785597 y1[1] (numeric) = -0.9841275769784628 absolute error = 9.692247004977617e-14 relative error = 9.848567636661983e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999744 y2[1] (closed_form) = -0.1872946635426519 y2[1] (numeric) = -0.1872946635430103 absolute error = 3.583799923490005e-13 relative error = 1.913455437385636e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9823037763382796 y1[1] (numeric) = -0.9823037763381789 absolute error = 1.006972283335017e-13 relative error = 1.025112910680944e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999743 y2[1] (closed_form) = -0.1971081729344182 y2[1] (numeric) = -0.1971081729347788 absolute error = 3.606004383982508e-13 relative error = 1.829454522508459e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9803817461389495 y1[1] (numeric) = -0.980381746138845 absolute error = 1.044719866172272e-13 relative error = 1.065625579307965e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999742 y2[1] (closed_form) = -0.2069019716731473 y2[1] (numeric) = -0.2069019716735101 absolute error = 3.627653732962699e-13 relative error = 1.753320040223431e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9783616785819874 y1[1] (numeric) = -0.9783616785818793 absolute error = 1.081357225984902e-13 relative error = 1.105273488994575e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.359999999999741 y2[1] (closed_form) = -0.2166750803871269 y2[1] (numeric) = -0.2166750803874918 absolute error = 3.649580637699046e-13 relative error = 1.684356424919031e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.976243775672466 y1[1] (numeric) = -0.9762437756723539 absolute error = 1.121325254871408e-13 relative error = 1.148611937729391e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36999999999974 y2[1] (closed_form) = -0.2264265217736297 y2[1] (numeric) = -0.2264265217739969 absolute error = 3.671785098191549e-13 relative error = 1.621623239817473e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9740282491989111 y1[1] (numeric) = -0.974028249198795 absolute error = 1.160183060733289e-13 relative error = 1.191118493418934e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999739 y2[1] (closed_form) = -0.2361553206966432 y2[1] (numeric) = -0.2361553206970126 absolute error = 3.693712002927896e-13 relative error = 1.564102808283836e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9717153207121237 y1[1] (numeric) = -0.9717153207120038 absolute error = 1.199040866595169e-13 relative error = 1.233942535470625e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999738 y2[1] (closed_form) = -0.2458605042843826 y2[1] (numeric) = -0.2458605042847541 absolute error = 3.714806240395774e-13 relative error = 1.510940625135512e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9693052215030253 y1[1] (numeric) = -0.9693052215029013 absolute error = 1.2401191185063e-13 relative error = 1.27938970202115e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999737 y2[1] (closed_form) = -0.2555411020265766 y2[1] (numeric) = -0.2555411020269502 absolute error = 3.735900477863652e-13 relative error = 1.461956784343488e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9667981925795284 y1[1] (numeric) = -0.9667981925794 absolute error = 1.283417816466681e-13 relative error = 1.327492982834789e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y2[1] (closed_form) = -0.2651961458715182 y2[1] (numeric) = -0.2651961458718939 absolute error = 3.75699471533153e-13 relative error = 1.416685262519506e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9641944846424358 y1[1] (numeric) = -0.9641944846423035 absolute error = 1.323385845353187e-13 relative error = 1.3725299889513e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999734 y2[1] (closed_form) = -0.2748246703228687 y2[1] (numeric) = -0.2748246703232465 absolute error = 3.778088952799408e-13 relative error = 1.374727002623471e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9614943580603719 y1[1] (numeric) = -0.9614943580602355 absolute error = 1.363353874239692e-13 relative error = 1.417953067337799e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999733 y2[1] (closed_form) = -0.2844257125362066 y2[1] (numeric) = -0.2844257125365866 absolute error = 3.799183190267286e-13 relative error = 1.335738304526058e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9586980828437445 y1[1] (numeric) = -0.9586980828436041 absolute error = 1.403321903126198e-13 relative error = 1.463778772732689e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999732 y2[1] (closed_form) = -0.2939983124153117 y2[1] (numeric) = -0.2939983124156937 absolute error = 3.820277427735164e-13 relative error = 1.299421549855196e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9558059386177451 y1[1] (numeric) = -0.9558059386176008 absolute error = 1.443289932012704e-13 relative error = 1.510024026529843e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.449999999999731 y2[1] (closed_form) = -0.3035415127081729 y2[1] (numeric) = -0.3035415127085569 absolute error = 3.839706330666104e-13 relative error = 1.26496909645358e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9528182145943863 y1[1] (numeric) = -0.9528182145942377 absolute error = 1.486588629973085e-13 relative error = 1.560201733345246e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45999999999973 y2[1] (closed_form) = -0.3130543591027138 y2[1] (numeric) = -0.3130543591030998 absolute error = 3.860245456621669e-13 relative error = 1.233091105227228e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9497352095435807 y1[1] (numeric) = -0.9497352095434276 absolute error = 1.530997550958091e-13 relative error = 1.612025684183964e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999729 y2[1] (closed_form) = -0.3225359003222221 y2[1] (numeric) = -0.3225359003226101 absolute error = 3.880229471064922e-13 relative error = 1.203038008230546e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.946557231763264 y1[1] (numeric) = -0.9465572317631068 absolute error = 1.572075802869222e-13 relative error = 1.660835446728066e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999728 y2[1] (closed_form) = -0.3319851882204773 y2[1] (numeric) = -0.3319851882208674 absolute error = 3.900768597020488e-13 relative error = 1.174982720744131e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9432845990485662 y1[1] (numeric) = -0.9432845990484047 absolute error = 1.615374500829603e-13 relative error = 1.712499602409424e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999727 y2[1] (closed_form) = -0.3414012778765638 y2[1] (numeric) = -0.3414012778769558 absolute error = 3.920197499951428e-13 relative error = 1.148266791599065e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9399176386600313 y1[1] (numeric) = -0.9399176386598656 absolute error = 1.657562975765359e-13 relative error = 1.76351938466483e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999726 y2[1] (closed_form) = -0.3507832276893628 y2[1] (numeric) = -0.3507832276897568 absolute error = 3.940181514394681e-13 relative error = 1.12325253985174e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9364566872908926 y1[1] (numeric) = -0.9364566872907225 absolute error = 1.70086167372574e-13 relative error = 1.816273722862955e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y2[1] (closed_form) = -0.3601300994717113 y2[1] (numeric) = -0.3601300994721073 absolute error = 3.959610417325621e-13 relative error = 1.099494439130227e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9329020910334028 y1[1] (numeric) = -0.9329020910332283 absolute error = 1.745270594710746e-13 relative error = 1.870797173128274e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999723 y2[1] (closed_form) = -0.36944095854422 y2[1] (numeric) = -0.3694409585446178 absolute error = 3.978484208744248e-13 relative error = 1.076893104766034e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9292542053442254 y1[1] (numeric) = -0.9292542053440467 absolute error = 1.787459069646502e-13 relative error = 1.923541544785767e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999722 y2[1] (closed_form) = -0.3787148738287408 y2[1] (numeric) = -0.3787148738291404 absolute error = 3.996247777138251e-13 relative error = 1.055212787587899e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9255133950088896 y1[1] (numeric) = -0.9255133950087066 absolute error = 1.830757767606883e-13 relative error = 1.978099698480646e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.539999999999721 y2[1] (closed_form) = -0.3879509179414732 y2[1] (numeric) = -0.3879509179418748 absolute error = 4.015676680069191e-13 relative error = 1.035099156712139e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9216800341053115 y1[1] (numeric) = -0.9216800341051241 absolute error = 1.874056465567264e-13 relative error = 2.033304830549399e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54999999999972 y2[1] (closed_form) = -0.397148167285703 y2[1] (numeric) = -0.3971481672861064 absolute error = 4.033440248463194e-13 relative error = 1.015600871591481e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y1[1] (closed_form) = -0.9177545059663871 y1[1] (numeric) = -0.9177545059661951 absolute error = 1.919575609576896e-13 relative error = 2.091600310428986e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999719 y2[1] (closed_form) = -0.4063057021441599 y2[1] (numeric) = -0.4063057021445651 absolute error = 4.052314039881821e-13 relative error = 9.973559363053276e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9137372031416588 y1[1] (numeric) = -0.9137372031414625 absolute error = 1.963984530561902e-13 relative error = 2.14939757712527e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999718 y2[1] (closed_form) = -0.4154226067709894 y2[1] (numeric) = -0.4154226067713963 absolute error = 4.069522496763511e-13 relative error = 9.796102644473856e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9096285273580617 y1[1] (numeric) = -0.9096285273578608 absolute error = 2.008393451546908e-13 relative error = 2.207927072582162e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999717 y2[1] (closed_form) = -0.4244979694833261 y2[1] (numeric) = -0.4244979694837348 absolute error = 4.087286065157514e-13 relative error = 9.628517352232138e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9054288894797499 y1[1] (numeric) = -0.9054288894795446 absolute error = 2.052802372531914e-13 relative error = 2.267215455993936e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999716 y2[1] (closed_form) = -0.4335308827524616 y2[1] (numeric) = -0.433530882752872 absolute error = 4.103939410526891e-13 relative error = 9.466313874737655e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.9011387094670118 y1[1] (numeric) = -0.901138709466802 absolute error = 2.098321516541546e-13 relative error = 2.328522229150072e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999715 y2[1] (closed_form) = -0.4425204432945964 y2[1] (numeric) = -0.4425204432950086 absolute error = 4.121702978920894e-13 relative error = 9.314152693680138e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8967584163342733 y1[1] (numeric) = -0.8967584163340591 absolute error = 2.142730437526552e-13 relative error = 2.389417705479146e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y2[1] (closed_form) = -0.4514657521611676 y2[1] (numeric) = -0.4514657521615815 absolute error = 4.138911435802584e-13 relative error = 9.167719624333862e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8922884481071977 y1[1] (numeric) = -0.8922884481069786 absolute error = 2.190470027585434e-13 relative error = 2.454890043944932e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999712 y2[1] (closed_form) = -0.4603659148287428 y2[1] (numeric) = -0.4603659148291585 absolute error = 4.156675004196586e-13 relative error = 9.02906768356836e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8877292517788826 y1[1] (numeric) = -0.8877292517786588 absolute error = 2.238209617644316e-13 relative error = 2.52127505448228e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.629999999999711 y2[1] (closed_form) = -0.4692200412884722 y2[1] (numeric) = -0.4692200412888896 absolute error = 4.173328349565963e-13 relative error = 8.894181796041911e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8830812832651616 y1[1] (numeric) = -0.8830812832649331 absolute error = 2.284838984678572e-13 relative error = 2.587348444562727e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63999999999971 y2[1] (closed_form) = -0.4780272461350882 y2[1] (numeric) = -0.4780272461355072 absolute error = 4.189981694935341e-13 relative error = 8.765152465287036e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8783450073590126 y1[1] (numeric) = -0.8783450073587793 absolute error = 2.332578574737454e-13 relative error = 2.65565188530074e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999709 y2[1] (closed_form) = -0.4867866486554453 y2[1] (numeric) = -0.4867866486558659 absolute error = 4.206079928792406e-13 relative error = 8.640499776257278e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8735208976840795 y1[1] (numeric) = -0.8735208976838414 absolute error = 2.380318164796336e-13 relative error = 2.724969913263838e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999708 y2[1] (closed_form) = -0.4954973729165911 y2[1] (numeric) = -0.4954973729170133 absolute error = 4.22217816264947e-13 relative error = 8.52109091476496e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8686094366473096 y1[1] (numeric) = -0.868609436647067 absolute error = 2.425837308805967e-13 relative error = 2.792782586117533e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999707 y2[1] (closed_form) = -0.5041585478533583 y2[1] (numeric) = -0.5041585478537822 absolute error = 4.238831508018848e-13 relative error = 8.407735078711334e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8636111153907139 y1[1] (numeric) = -0.8636111153904664 absolute error = 2.474687121889474e-13 relative error = 2.865510966437572e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999706 y2[1] (closed_form) = -0.5127693073554711 y2[1] (numeric) = -0.5127693073558965 absolute error = 4.2543746303636e-13 relative error = 8.296858976027413e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8585264337422526 y1[1] (numeric) = -0.8585264337420002 absolute error = 2.523536934972981e-13 relative error = 2.93938175435446e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999705 y2[1] (closed_form) = -0.5213287903541545 y2[1] (numeric) = -0.5213287903545815 absolute error = 4.269917752708352e-13 relative error = 8.190450693904066e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8533559001658534 y1[1] (numeric) = -0.8533559001655961 absolute error = 2.572386748056488e-13 relative error = 3.014436002090726e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999704 y2[1] (closed_form) = -0.5298361409082418 y2[1] (numeric) = -0.5298361409086702 absolute error = 4.283240429003854e-13 relative error = 8.084085056299765e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8481000317105652 y1[1] (numeric) = -0.848100031710303 absolute error = 2.62234678416462e-13 relative error = 3.092025334411919e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999702 y2[1] (closed_form) = -0.5382905082897669 y2[1] (numeric) = -0.5382905082901968 absolute error = 4.298783551348606e-13 relative error = 7.985991737076163e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8427593539588537 y1[1] (numeric) = -0.8427593539585866 absolute error = 2.671196597248127e-13 relative error = 3.169584039263649e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.719999999999701 y2[1] (closed_form) = -0.5466910470690369 y2[1] (numeric) = -0.5466910470694684 absolute error = 4.314326673693358e-13 relative error = 7.89170903168008e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8373344009740433 y1[1] (numeric) = -0.8373344009737715 absolute error = 2.717825964282383e-13 relative error = 3.245807124514204e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7299999999997 y2[1] (closed_form) = -0.5550369171991745 y2[1] (numeric) = -0.5550369171996072 absolute error = 4.32764934998886e-13 relative error = 7.797047756439393e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8318257152469121 y1[1] (numeric) = -0.8318257152466352 absolute error = 2.76889622341514e-13 relative error = 3.32869755366152e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999699 y2[1] (closed_form) = -0.5633272841001213 y2[1] (numeric) = -0.5633272841005554 absolute error = 4.340972026284362e-13 relative error = 7.70595025096074e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8262338476414418 y1[1] (numeric) = -0.82623384764116 absolute error = 2.817746036498647e-13 relative error = 3.41034931519951e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999698 y2[1] (closed_form) = -0.5715613187420959 y2[1] (numeric) = -0.5715613187425316 absolute error = 4.356515148629114e-13 relative error = 7.622130829666751e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8205593573397333 y1[1] (numeric) = -0.8205593573394465 absolute error = 2.867706072606779e-13 relative error = 3.494818561211621e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999697 y2[1] (closed_form) = -0.579738197728496 y2[1] (numeric) = -0.5797381977289329 absolute error = 4.368727601899991e-13 relative error = 7.535690453065439e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.814802811786088 y1[1] (numeric) = -0.8148028117857963 absolute error = 2.917666108714911e-13 relative error = 3.580824791607239e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999696 y2[1] (closed_form) = -0.5878571033782367 y2[1] (numeric) = -0.5878571033786747 absolute error = 4.379829832146243e-13 relative error = 7.450500822354084e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8089647866302644 y1[1] (numeric) = -0.8089647866299674 absolute error = 2.969846590872294e-13 relative error = 3.671169178133406e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999695 y2[1] (closed_form) = -0.5959172238075189 y2[1] (numeric) = -0.5959172238079581 absolute error = 4.392042285417119e-13 relative error = 7.370222087817599e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.8030458656699127 y1[1] (numeric) = -0.8030458656696107 absolute error = 3.019806626980426e-13 relative error = 3.760441035906783e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999694 y2[1] (closed_form) = -0.6039177530110164 y2[1] (numeric) = -0.6039177530114568 absolute error = 4.404254738687996e-13 relative error = 7.292805546333485e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7970466407921967 y1[1] (numeric) = -0.7970466407918896 absolute error = 3.070876886113183e-13 relative error = 3.852819557787725e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999693 y2[1] (closed_form) = -0.6118578909424759 y2[1] (numeric) = -0.6118578909429175 absolute error = 4.416467191958873e-13 relative error = 7.218125740204091e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7909677119146048 y1[1] (numeric) = -0.7909677119142926 absolute error = 3.12194714524594e-13 relative error = 3.946996948445596e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999691 y2[1] (closed_form) = -0.619736843594721 y2[1] (numeric) = -0.6197368435951638 absolute error = 4.427569422205124e-13 relative error = 7.144273360485484e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7848096869249591 y1[1] (numeric) = -0.7848096869246418 absolute error = 3.173017404378697e-13 relative error = 4.043040570525081e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81999999999969 y2[1] (closed_form) = -0.6275538230790524 y2[1] (numeric) = -0.6275538230794963 absolute error = 4.438671652451376e-13 relative error = 7.072973646584319e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7785731816206267 y1[1] (numeric) = -0.7785731816203044 absolute error = 3.222977440486829e-13 relative error = 4.139594731195456e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999689 y2[1] (closed_form) = -0.6353080477040356 y2[1] (numeric) = -0.6353080477044806 absolute error = 4.449773882697627e-13 relative error = 7.004120125313756e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7722588196469412 y1[1] (numeric) = -0.7722588196466137 absolute error = 3.275157922644212e-13 relative error = 4.241010706930531e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999688 y2[1] (closed_form) = -0.64299874205367 y2[1] (numeric) = -0.6429987420541161 absolute error = 4.460876112943879e-13 relative error = 6.937612504024987e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7658672324348378 y1[1] (numeric) = -0.7658672324345054 absolute error = 3.324007735727719e-13 relative error = 4.340187952891084e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999687 y2[1] (closed_form) = -0.6506251370649296 y2[1] (numeric) = -0.6506251370653766 absolute error = 4.46975789714088e-13 relative error = 6.869943447473683e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7593990591377116 y1[1] (numeric) = -0.7593990591373737 absolute error = 3.378408663934351e-13 relative error = 4.448792269732983e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999686 y2[1] (closed_form) = -0.6581864701046686 y2[1] (numeric) = -0.6581864701051167 absolute error = 4.480860127387132e-13 relative error = 6.807888540575074e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.752854946567502 y1[1] (numeric) = -0.7528549465671589 absolute error = 3.430589146091734e-13 relative error = 4.556773069942421e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999685 y2[1] (closed_form) = -0.6656819850458839 y2[1] (numeric) = -0.6656819850463331 absolute error = 4.491962357633383e-13 relative error = 6.747910351402649e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7462355491300127 y1[1] (numeric) = -0.7462355491296645 absolute error = 3.481659405224491e-13 relative error = 4.665630589809787e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999684 y2[1] (closed_form) = -0.6731109323433279 y2[1] (numeric) = -0.6731109323437779 absolute error = 4.500844141830385e-13 relative error = 6.68663057686705e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7395415287594713 y1[1] (numeric) = -0.7395415287591179 absolute error = 3.533839887381873e-13 relative error = 4.778419804645238e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999683 y2[1] (closed_form) = -0.6804725691084613 y2[1] (numeric) = -0.6804725691089124 absolute error = 4.510836149052011e-13 relative error = 6.628975735145355e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7327735548523365 y1[1] (numeric) = -0.7327735548519777 absolute error = 3.588240815588506e-13 relative error = 4.896793548058081e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999681 y2[1] (closed_form) = -0.6877661591837426 y2[1] (numeric) = -0.6877661591841945 absolute error = 4.518607710224387e-13 relative error = 6.569976800817271e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7259323042003591 y1[1] (numeric) = -0.7259323041999952 absolute error = 3.639311074721263e-13 relative error = 5.013292635778341e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.90999999999968 y2[1] (closed_form) = -0.694990973216242 y2[1] (numeric) = -0.6949909732166948 absolute error = 4.527489494421388e-13 relative error = 6.514457984208507e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7190184609229033 y1[1] (numeric) = -0.719018460922534 absolute error = 3.693712002927896e-13 relative error = 5.137158784750526e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999679 y2[1] (closed_form) = -0.7021462887305772 y2[1] (numeric) = -0.7021462887310307 absolute error = 4.535261055593764e-13 relative error = 6.45913982368709e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.7120327163985353 y1[1] (numeric) = -0.7120327163981606 absolute error = 3.747002708109903e-13 relative error = 5.262402445581798e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999678 y2[1] (closed_form) = -0.7092313902011591 y2[1] (numeric) = -0.7092313902016134 absolute error = 4.543032616766141e-13 relative error = 6.405571833865956e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.704975769195886 y1[1] (numeric) = -0.704975769195506 absolute error = 3.800293413291911e-13 relative error = 5.390672388111475e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999677 y2[1] (closed_form) = -0.7162455691237452 y2[1] (numeric) = -0.7162455691242003 absolute error = 4.551914400963142e-13 relative error = 6.355242667025436e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.697848325003795 y1[1] (numeric) = -0.6978483250034095 absolute error = 3.854694341498544e-13 relative error = 5.523685023500746e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999676 y2[1] (closed_form) = -0.7231881240862882 y2[1] (numeric) = -0.7231881240867439 absolute error = 4.557465516086268e-13 relative error = 6.301908679493867e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.690651096560742 y1[1] (numeric) = -0.6906510965603511 absolute error = 3.909095269705176e-13 relative error = 5.6600145705573e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999675 y2[1] (closed_form) = -0.7300583608390774 y2[1] (numeric) = -0.7300583608395338 absolute error = 4.564126854234019e-13 relative error = 6.251728764517311e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6833848035835736 y1[1] (numeric) = -0.6833848035831772 absolute error = 3.963496197911809e-13 relative error = 5.799801483919153e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999674 y2[1] (closed_form) = -0.7368555923641626 y2[1] (numeric) = -0.7368555923646198 absolute error = 4.571898415406395e-13 relative error = 6.204605709427675e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6760501726955322 y1[1] (numeric) = -0.6760501726951303 absolute error = 4.019007349143067e-13 relative error = 5.944835918196085e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999673 y2[1] (closed_form) = -0.7435791389440558 y2[1] (numeric) = -0.7435791389445137 absolute error = 4.578559753554146e-13 relative error = 6.15746127581804e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6686479373535946 y1[1] (numeric) = -0.6686479373531874 absolute error = 4.072298054325074e-13 relative error = 6.090347142088857e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999672 y2[1] (closed_form) = -0.7502283282297016 y2[1] (numeric) = -0.7502283282301603 absolute error = 4.586331314726522e-13 relative error = 6.113247317051854e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6611788377751264 y1[1] (numeric) = -0.6611788377747139 absolute error = 4.125588759507082e-13 relative error = 6.239747136175336e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99999999999967 y2[1] (closed_form) = -0.7568024953077128 y2[1] (numeric) = -0.756802495308172 absolute error = 4.591882429849647e-13 relative error = 6.067477919695028e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6536436208638613 y1[1] (numeric) = -0.6536436208634433 absolute error = 4.179989687713714e-13 relative error = 6.394906267408229e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999674 y2[1] (closed_form) = -0.7633009827668628 y2[1] (numeric) = -0.7633009827673194 absolute error = 4.566347300283269e-13 relative error = 5.982367903852131e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6460430401352075 y1[1] (numeric) = -0.6460430401347875 absolute error = 4.199973702156967e-13 relative error = 6.501074140939546e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999677 y2[1] (closed_form) = -0.769723140763818 y2[1] (numeric) = -0.7697231407642724 absolute error = 4.544142839790766e-13 relative error = 5.903606893358415e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6383778556409077 y1[1] (numeric) = -0.6383778556404857 absolute error = 4.21995771660022e-13 relative error = 6.610438753962635e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.029999999999681 y2[1] (closed_form) = -0.7760683270881307 y2[1] (numeric) = -0.7760683270885826 absolute error = 4.519717933249012e-13 relative error = 5.82386598639755e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6306488338930235 y1[1] (numeric) = -0.6306488338925994 absolute error = 4.241051954068098e-13 relative error = 6.724902554545125e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999684 y2[1] (closed_form) = -0.7823359072264559 y2[1] (numeric) = -0.7823359072269057 absolute error = 4.498623695781134e-13 relative error = 5.750245711883141e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6228567477872888 y1[1] (numeric) = -0.6228567477868628 absolute error = 4.259925745486726e-13 relative error = 6.839334663420117e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999687 y2[1] (closed_form) = -0.7885252544260027 y2[1] (numeric) = -0.7885252544264504 absolute error = 4.476419235288631e-13 relative error = 5.676951004628489e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.615002376525821 y1[1] (numeric) = -0.6150023765253931 absolute error = 4.278799536905353e-13 relative error = 6.957370735827891e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.059999999999691 y2[1] (closed_form) = -0.7946357497572092 y2[1] (numeric) = -0.7946357497576546 absolute error = 4.454214774796128e-13 relative error = 5.605354121252481e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.6070865055392007 y1[1] (numeric) = -0.6070865055387711 absolute error = 4.296563105299356e-13 relative error = 7.077349053382835e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999694 y2[1] (closed_form) = -0.8006667821756341 y2[1] (numeric) = -0.8006667821760773 absolute error = 4.432010314303625e-13 relative error = 5.535399260926776e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.5991099264079304 y1[1] (numeric) = -0.5991099264074987 absolute error = 4.316547119742609e-13 relative error = 7.204933401159335e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999697 y2[1] (closed_form) = -0.8066177485830615 y2[1] (numeric) = -0.8066177485835024 absolute error = 4.409805853811122e-13 relative error = 5.467033004862057e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.5910734367832757 y1[1] (numeric) = -0.5910734367828424 absolute error = 4.333200465111986e-13 relative error = 7.33106953459796e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.089999999999701 y2[1] (closed_form) = -0.8124880538878098 y2[1] (numeric) = -0.8124880538882486 absolute error = 4.388711616343244e-13 relative error = 5.4015706389072e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.5829778403075022 y1[1] (numeric) = -0.5829778403070672 absolute error = 4.349853810481363e-13 relative error = 7.461439371669691e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.099999999999704 y2[1] (closed_form) = -0.8182771110642403 y2[1] (numeric) = -0.8182771110646772 absolute error = 4.368727601899991e-13 relative error = 5.338934137138557e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.5748239465335112 y1[1] (numeric) = -0.5748239465330746 absolute error = 4.366507155850741e-13 relative error = 7.596251308218909e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.109999999999707 y2[1] (closed_form) = -0.8239843412114597 y2[1] (numeric) = -0.8239843412118947 absolute error = 4.349853810481363e-13 relative error = 5.279049118926226e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.5666125708438852 y1[1] (numeric) = -0.5666125708434467 absolute error = 4.384270724244743e-13 relative error = 7.737687001393251e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.119999999999711 y2[1] (closed_form) = -0.8296091736112092 y2[1] (numeric) = -0.8296091736116422 absolute error = 4.329869796038111e-13 relative error = 5.2191681743231e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.5583445343693503 y1[1] (numeric) = -0.5583445343689101 absolute error = 4.402034292638746e-13 relative error = 7.884082357161139e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.129999999999714 y2[1] (closed_form) = -0.8351510457849362 y2[1] (numeric) = -0.8351510457853673 absolute error = 4.310996004619483e-13 relative error = 5.161935707770914e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.5500206639066639 y1[1] (numeric) = -0.5500206639062223 absolute error = 4.416467191958873e-13 relative error = 8.029638669554291e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.139999999999717 y2[1] (closed_form) = -0.8406094035500415 y2[1] (numeric) = -0.8406094035504709 absolute error = 4.29323243622548e-13 relative error = 5.107285759705285e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.541641791835936 y1[1] (numeric) = -0.5416417918354928 absolute error = 4.432010314303625e-13 relative error = 8.182548653199358e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.149999999999721 y2[1] (closed_form) = -0.8459837010752973 y2[1] (numeric) = -0.8459837010757248 absolute error = 4.275468867831478e-13 relative error = 5.053843073332375e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.533208756037391 y1[1] (numeric) = -0.5332087560369464 absolute error = 4.446443213623752e-13 relative error = 8.339028876172369e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.159999999999724 y2[1] (closed_form) = -0.8512734009354296 y2[1] (numeric) = -0.8512734009358552 absolute error = 4.25659507641285e-13 relative error = 5.00026791831561e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.5247223998075815 y1[1] (numeric) = -0.5247223998071354 absolute error = 4.460876112943879e-13 relative error = 8.501402102482581e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.169999999999727 y2[1] (closed_form) = -0.8564779741648604 y2[1] (numeric) = -0.8564779741652844 absolute error = 4.239941731043473e-13 relative error = 4.950438725733467e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.5161835717750582 y1[1] (numeric) = -0.5161835717746108 absolute error = 4.474198789239381e-13 relative error = 8.667844220329315e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.179999999999731 y2[1] (closed_form) = -0.8615969003106039 y2[1] (numeric) = -0.8615969003110261 absolute error = 4.22217816264947e-13 relative error = 4.900410111883392e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.5075931258155091 y1[1] (numeric) = -0.5075931258150602 absolute error = 4.488631688559508e-13 relative error = 8.842971782464516e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999734 y2[1] (closed_form) = -0.8666296674843114 y2[1] (numeric) = -0.8666296674847319 absolute error = 4.205524817280093e-13 relative error = 4.852735805235085e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.4989519209663713 y1[1] (numeric) = -0.498951920965921 absolute error = 4.502509476367322e-13 relative error = 9.023934545931502e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999737 y2[1] (closed_form) = -0.8715757724134593 y2[1] (numeric) = -0.8715757724138783 absolute error = 4.189981694935341e-13 relative error = 4.807363659654013e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.4902608213409286 y1[1] (numeric) = -0.490260821340477 absolute error = 4.515277041150512e-13 relative error = 9.209948755033348e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.209999999999741 y2[1] (closed_form) = -0.8764347204916765 y2[1] (numeric) = -0.8764347204920939 absolute error = 4.174438572590589e-13 relative error = 4.762977179006264e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.4815206960419011 y1[1] (numeric) = -0.4815206960414483 absolute error = 4.528044605933701e-13 relative error = 9.403634450511093e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999744 y2[1] (closed_form) = -0.8812060258282044 y2[1] (numeric) = -0.8812060258286204 absolute error = 4.160005673270462e-13 relative error = 4.720809380939794e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.4727324190745353 y1[1] (numeric) = -0.4727324190740813 absolute error = 4.540257059204578e-13 relative error = 9.604285375843283e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999747 y2[1] (closed_form) = -0.8858892112964852 y2[1] (numeric) = -0.8858892112968997 absolute error = 4.144462550925709e-13 relative error = 4.678307962301914e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.4638968692592044 y1[1] (numeric) = -0.4638968692587492 absolute error = 4.551359289450829e-13 relative error = 9.811144655317209e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.239999999999751 y2[1] (closed_form) = -0.8904838085818749 y2[1] (numeric) = -0.8904838085822878 absolute error = 4.128919428580957e-13 relative error = 4.636714770992185e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.455014930143527 y1[1] (numeric) = -0.4550149301430707 absolute error = 4.563016631209393e-13 relative error = 1.002827891772708e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999754 y2[1] (closed_form) = -0.8949893582284738 y2[1] (numeric) = -0.8949893582288854 absolute error = 4.115596752285455e-13 relative error = 4.598486802604888e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.446087489914013 y1[1] (numeric) = -0.4460874899135555 absolute error = 4.574673972967958e-13 relative error = 1.025510483122888e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999757 y2[1] (closed_form) = -0.8994054096850717 y2[1] (numeric) = -0.8994054096854819 absolute error = 4.102274075989953e-13 relative error = 4.561095621413231e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.4371154413072459 y1[1] (numeric) = -0.4371154413067873 absolute error = 4.586331314726522e-13 relative error = 1.049226561525841e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.269999999999761 y2[1] (closed_form) = -0.9037315213502031 y2[1] (numeric) = -0.9037315213506121 absolute error = 4.090061622719077e-13 relative error = 4.525748550419484e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.4280996815206098 y1[1] (numeric) = -0.4280996815201502 absolute error = 4.596323321948148e-13 relative error = 1.073657262631453e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999764 y2[1] (closed_form) = -0.9079672606163064 y2[1] (numeric) = -0.9079672606167143 absolute error = 4.078959392472825e-13 relative error = 4.492408007865972e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.4190411121225701 y1[1] (numeric) = -0.4190411121221094 absolute error = 4.606870440682087e-13 relative error = 1.099383880819449e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999767 y2[1] (closed_form) = -0.912112203912985 y2[1] (numeric) = -0.9121122039133918 absolute error = 4.067857162226574e-13 relative error = 4.459821000941947e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.4099406389625179 y1[1] (numeric) = -0.4099406389620561 absolute error = 4.617417559416026e-13 relative error = 1.126362482895532e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.299999999999771 y2[1] (closed_form) = -0.9161659367493631 y2[1] (numeric) = -0.9161659367497687 absolute error = 4.055644708955697e-13 relative error = 4.426757802571747e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.4007991720801854 y1[1] (numeric) = -0.4007991720797227 absolute error = 4.62685445512534e-13 relative error = 1.154407188795209e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999774 y2[1] (closed_form) = -0.9201280537555353 y2[1] (numeric) = -0.9201280537559398 absolute error = 4.044542478709445e-13 relative error = 4.395630001934515e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.3916176256146431 y1[1] (numeric) = -0.3916176256141794 absolute error = 4.636846462346966e-13 relative error = 1.184023945569213e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999777 y2[1] (closed_form) = -0.9239981587231028 y2[1] (numeric) = -0.9239981587235061 absolute error = 4.033440248463194e-13 relative error = 4.365203772740317e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.3823969177128863 y1[1] (numeric) = -0.3823969177124215 absolute error = 4.647393581080905e-13 relative error = 1.215332385228662e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.329999999999781 y2[1] (closed_form) = -0.9277758646447937 y2[1] (numeric) = -0.9277758646451959 absolute error = 4.022338018216942e-13 relative error = 4.335463091354425e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.3731379704380211 y1[1] (numeric) = -0.3731379704375555 absolute error = 4.656275365277907e-13 relative error = 1.247869617721288e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999784 y2[1] (closed_form) = -0.931460793753164 y2[1] (numeric) = -0.9314607937535652 absolute error = 4.011235787970691e-13 relative error = 4.306392512569523e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.3638417096770594 y1[1] (numeric) = -0.3638417096765929 absolute error = 4.665157149474908e-13 relative error = 1.282194158997228e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999787 y2[1] (closed_form) = -0.9350525775583738 y2[1] (numeric) = -0.9350525775587741 absolute error = 4.003464226798314e-13 relative error = 4.28153915927619e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.3545090650483305 y1[1] (numeric) = -0.354509065047863 absolute error = 4.674594045184222e-13 relative error = 1.318610581804708e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.359999999999791 y2[1] (closed_form) = -0.9385508568850355 y2[1] (numeric) = -0.938550856885435 absolute error = 3.995692665625938e-13 relative error = 4.257300109327349e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.3451409698085198 y1[1] (numeric) = -0.3451409698080515 absolute error = 4.68292071786891e-13 relative error = 1.35681391880742e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999794 y2[1] (closed_form) = -0.9419552819081318 y2[1] (numeric) = -0.9419552819085305 absolute error = 3.986810881428937e-13 relative error = 4.232484235719555e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.3357383607593448 y1[1] (numeric) = -0.3357383607588756 absolute error = 4.692357613578224e-13 relative error = 1.397623316848704e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y2[1] (closed_form) = -0.9452655121879973 y2[1] (numeric) = -0.9452655121883952 absolute error = 3.979039320256561e-13 relative error = 4.209440912581604e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.326302178153875 y1[1] (numeric) = -0.3263021781534048 absolute error = 4.701239397775225e-13 relative error = 1.440762493334707e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999801 y2[1] (closed_form) = -0.9484812167043626 y2[1] (numeric) = -0.9484812167047598 absolute error = 3.97237798210881e-13 relative error = 4.188146177434511e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.3168333656025072 y1[1] (numeric) = -0.3168333656020362 absolute error = 4.710121181972227e-13 relative error = 1.486624103814069e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999804 y2[1] (closed_form) = -0.9516020738894557 y2[1] (numeric) = -0.9516020738898523 absolute error = 3.965716643961059e-13 relative error = 4.167410678028579e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.3073328699786061 y1[1] (numeric) = -0.3073328699781343 absolute error = 4.718447854656915e-13 relative error = 1.535289035300836e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y2[1] (closed_form) = -0.954627771660159 y2[1] (numeric) = -0.954627771660555 absolute error = 3.960165528837933e-13 relative error = 4.148387095371164e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.297801641323817 y1[1] (numeric) = -0.2978016413233445 absolute error = 4.725109192804666e-13 relative error = 1.58666324732132e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.419999999999811 y2[1] (closed_form) = -0.9575580074492166 y2[1] (numeric) = -0.9575580074496122 absolute error = 3.955724636739433e-13 relative error = 4.131054835285497e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.2882406327530628 y1[1] (numeric) = -0.2882406327525894 absolute error = 4.733435865489355e-13 relative error = 1.642182026967903e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999814 y2[1] (closed_form) = -0.9603924882354916 y2[1] (numeric) = -0.9603924882358869 absolute error = 3.952393967665557e-13 relative error = 4.115394503894137e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.2786508003592329 y1[1] (numeric) = -0.2786508003587588 absolute error = 4.740652315149418e-13 relative error = 1.70128788757751e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y2[1] (closed_form) = -0.9631309305732675 y2[1] (numeric) = -0.9631309305736623 absolute error = 3.947953075567057e-13 relative error = 4.099082430274756e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.2690331031175753 y1[1] (numeric) = -0.2690331031171005 absolute error = 4.747868764809482e-13 relative error = 1.764789800879829e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.449999999999821 y2[1] (closed_form) = -0.9657730606205923 y2[1] (numeric) = -0.9657730606209869 absolute error = 3.945732629517806e-13 relative error = 4.085569157398461e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.2593885027897994 y1[1] (numeric) = -0.2593885027893239 absolute error = 4.755085214469545e-13 relative error = 1.833190431853073e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999824 y2[1] (closed_form) = -0.9683186141666632 y2[1] (numeric) = -0.9683186141670577 absolute error = 3.944622406493181e-13 relative error = 4.073682307437548e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.2497179638279009 y1[1] (numeric) = -0.2497179638274247 absolute error = 4.762301664129609e-13 relative error = 1.907072118933207e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y2[1] (closed_form) = -0.9707673366582469 y2[1] (numeric) = -0.9707673366586411 absolute error = 3.942401960443931e-13 relative error = 4.061119293542765e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.2400224532777172 y1[1] (numeric) = -0.2400224532772403 absolute error = 4.769240558033516e-13 relative error = 1.986997671636695e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.479999999999831 y2[1] (closed_form) = -0.9731189832251348 y2[1] (numeric) = -0.9731189832255289 absolute error = 3.941291737419306e-13 relative error = 4.050164271132581e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.2303029406822238 y1[1] (numeric) = -0.2303029406817461 absolute error = 4.776179451937423e-13 relative error = 2.07386820063565e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999834 y2[1] (closed_form) = -0.9753733187046298 y2[1] (numeric) = -0.9753733187050239 absolute error = 3.940181514394681e-13 relative error = 4.039665058326121e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.2205603979845805 y1[1] (numeric) = -0.2205603979841022 absolute error = 4.783395901597487e-13 relative error = 2.168746495430198e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y2[1] (closed_form) = -0.9775301176650628 y2[1] (numeric) = -0.9775301176654569 absolute error = 3.941291737419306e-13 relative error = 4.031887781456299e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.2107957994309386 y1[1] (numeric) = -0.2107957994304596 absolute error = 4.790334795501394e-13 relative error = 2.272500120226928e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.509999999999841 y2[1] (closed_form) = -0.9795891644283349 y2[1] (numeric) = -0.9795891644287291 absolute error = 3.942401960443931e-13 relative error = 4.024546313499316e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.2010101214730161 y1[1] (numeric) = -0.2010101214725364 absolute error = 4.796996133649145e-13 relative error = 2.386445069778788e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999844 y2[1] (closed_form) = -0.9815502530914857 y2[1] (numeric) = -0.98155025309188 absolute error = 3.943512183468556e-13 relative error = 4.01763656119296e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.1912043426704542 y1[1] (numeric) = -0.1912043426699738 absolute error = 4.803935027553052e-13 relative error = 2.51246125504208e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y2[1] (closed_form) = -0.983413187547283 y2[1] (numeric) = -0.9834131875476776 absolute error = 3.945732629517806e-13 relative error = 4.012283625521438e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.1813794435929616 y1[1] (numeric) = -0.1813794435924806 absolute error = 4.810596365700803e-13 relative error = 2.652227987034953e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.539999999999851 y2[1] (closed_form) = -0.9851777815038338 y2[1] (numeric) = -0.9851777815042285 absolute error = 3.946842852542432e-13 relative error = 4.006223979714338e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.1715364067222588 y1[1] (numeric) = -0.1715364067217771 absolute error = 4.816980148092398e-13 relative error = 2.808138657055908e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999854 y2[1] (closed_form) = -0.986843858503213 y2[1] (numeric) = -0.9868438585036079 absolute error = 3.949063298591682e-13 relative error = 4.001710366401216e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.1616762163538302 y1[1] (numeric) = -0.1616762163533479 absolute error = 4.823086374727836e-13 relative error = 2.983176179836159e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999858 y2[1] (closed_form) = -0.9884112519391088 y2[1] (numeric) = -0.9884112519395041 absolute error = 3.952393967665557e-13 relative error = 3.998734291937264e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.151799858498496 y1[1] (numeric) = -0.151799858498013 absolute error = 4.830025268631744e-13 relative error = 3.181837793794516e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.569999999999861 y2[1] (closed_form) = -0.9898798050734841 y2[1] (numeric) = -0.9898798050738796 absolute error = 3.955724636739433e-13 relative error = 3.996166621912019e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.1419083207838114 y1[1] (numeric) = -0.1419083207833277 absolute error = 4.837241718291807e-13 relative error = 3.408709011264425e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999864 y2[1] (closed_form) = -0.991249371052249 y2[1] (numeric) = -0.991249371052645 absolute error = 3.960165528837933e-13 relative error = 3.995125388714312e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.132002592355305 y1[1] (numeric) = -0.1320025923548206 absolute error = 4.843347944927245e-13 relative error = 3.669130930315855e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999868 y2[1] (closed_form) = -0.992519812919947 y2[1] (numeric) = -0.9925198129203434 absolute error = 3.964606420936434e-13 relative error = 3.994485922928578e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.1220836637775648 y1[1] (numeric) = -0.1220836637770798 absolute error = 4.84973172731884e-13 relative error = 3.972465747878442e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.599999999999871 y2[1] (closed_form) = -0.99369100363345 y2[1] (numeric) = -0.993691003633847 absolute error = 3.97015753605956e-13 relative error = 3.995364274752014e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.1121525269351829 y1[1] (numeric) = -0.1121525269346972 absolute error = 4.856531843344669e-13 relative error = 4.330291947992791e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999874 y2[1] (closed_form) = -0.9947628260746626 y2[1] (numeric) = -0.9947628260750602 absolute error = 3.975708651182686e-13 relative error = 3.996639748663352e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.1022101749335675 y1[1] (numeric) = -0.1022101749330812 absolute error = 4.862915625736264e-13 relative error = 4.757760789370492e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999878 y2[1] (closed_form) = -0.995735173062234 y2[1] (numeric) = -0.9957351730626322 absolute error = 3.981259766305811e-13 relative error = 3.998311874493742e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.0922576019996337 y1[1] (numeric) = -0.09225760199914675 absolute error = 4.869576963884015e-13 relative error = 5.278239254368815e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.629999999999881 y2[1] (closed_form) = -0.9966079473622756 y2[1] (numeric) = -0.9966079473626744 absolute error = 3.987921104453562e-13 relative error = 4.001494384033763e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.08229580338238099 y1[1] (numeric) = -0.08229580338189338 absolute error = 4.876099524153688e-13 relative error = 5.92508891552741e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999884 y2[1] (closed_form) = -0.9973810616980849 y2[1] (numeric) = -0.9973810616984844 absolute error = 3.994582442601313e-13 relative error = 4.005071477696159e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.07232577525336964 y1[1] (numeric) = -0.07232577525288136 absolute error = 4.882760862301438e-13 relative error = 6.751066055215152e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999888 y2[1] (closed_form) = -0.9980544387588723 y2[1] (numeric) = -0.9980544387592727 absolute error = 4.003464226798314e-13 relative error = 4.011268395115612e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.06234851460710424 y1[1] (numeric) = -0.0623485146066153 absolute error = 4.88935281151015e-13 relative error = 7.841971604810354e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.659999999999891 y2[1] (closed_form) = -0.9986280112074931 y2[1] (numeric) = -0.9986280112078944 absolute error = 4.012346010995316e-13 relative error = 4.017858467782993e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.05236501916133503 y1[1] (numeric) = -0.05236501916084543 absolute error = 4.89608353859694e-13 relative error = 9.349912626809618e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999894 y2[1] (closed_form) = -0.9991017216871803 y2[1] (numeric) = -0.9991017216875826 absolute error = 4.023448241241567e-13 relative error = 4.027065666994529e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.04237628725728707 y1[1] (numeric) = -0.04237628725679676 absolute error = 4.903022432500848e-13 relative error = 1.157020293621339e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999898 y2[1] (closed_form) = -0.9994755228272807 y2[1] (numeric) = -0.9994755228276841 absolute error = 4.034550471487819e-13 relative error = 4.036667611503908e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.03238331775982681 y1[1] (numeric) = -0.03238331775933583 absolute error = 4.909891937465716e-13 relative error = 1.516179402580143e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.689999999999901 y2[1] (closed_form) = -0.9997493772479917 y2[1] (numeric) = -0.9997493772483962 absolute error = 4.044542478709445e-13 relative error = 4.045556387184606e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.02238710995757659 y1[1] (numeric) = -0.0223871099570849 absolute error = 4.916934914778182e-13 relative error = 2.196324100831119e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999904 y2[1] (closed_form) = -0.9999232575640997 y2[1] (numeric) = -0.9999232575645052 absolute error = 4.054534485931072e-13 relative error = 4.054845664664578e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.01238866346298647 y1[1] (numeric) = -0.01238866346249407 absolute error = 4.924064628264446e-13 relative error = 3.974653636347489e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999908 y2[1] (closed_form) = -0.9999971463877178 y2[1] (numeric) = -0.9999971463881244 absolute error = 4.066746939201948e-13 relative error = 4.066758544154079e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = -0.002388978112373909 y1[1] (numeric) = -0.002388978111880781 absolute error = 4.93127674111582e-13 relative error = 2.06417828425211e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.719999999999911 y2[1] (closed_form) = -0.9999710363300252 y2[1] (numeric) = -0.999971036330433 absolute error = 4.078959392472825e-13 relative error = 4.079077537528424e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.007610946134059087 y1[1] (numeric) = 0.007610946134552949 absolute error = 4.938618958227892e-13 relative error = 6.488837092313011e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999914 y2[1] (closed_form) = -0.9998449300020059 y2[1] (numeric) = -0.9998449300024151 absolute error = 4.092282068768327e-13 relative error = 4.092916757361681e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.01761010929222111 y1[1] (numeric) = 0.01761010929271572 absolute error = 4.946078269174592e-13 relative error = 2.808658474004711e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999918 y2[1] (closed_form) = -0.9996188400141877 y2[1] (numeric) = -0.9996188400145983 absolute error = 4.106714968088454e-13 relative error = 4.108280880370529e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.02760751145412895 y1[1] (numeric) = 0.02760751145462432 absolute error = 4.95367635799937e-13 relative error = 1.794321942501088e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.749999999999921 y2[1] (closed_form) = -0.9992927889753809 y2[1] (numeric) = -0.999292788975793 absolute error = 4.121147867408581e-13 relative error = 4.124064451254748e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.03760215288789756 y1[1] (numeric) = 0.03760215288839371 absolute error = 4.961447919171746e-13 relative error = 1.319458471955901e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999924 y2[1] (closed_form) = -0.9988668094904177 y2[1] (numeric) = -0.9988668094908313 absolute error = 4.135580766728708e-13 relative error = 4.140272484214905e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.0475930341377124 y1[1] (numeric) = 0.04759303413820935 absolute error = 4.96942764716124e-13 relative error = 1.044150207524487e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999928 y2[1] (closed_form) = -0.9983409441568918 y2[1] (numeric) = -0.998340944157307 absolute error = 4.152234112098085e-13 relative error = 4.159134348240806e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.0575791561237742 y1[1] (numeric) = 0.05757915612427195 absolute error = 4.977546153028811e-13 relative error = 8.64470146510814e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.779999999999931 y2[1] (closed_form) = -0.997715245560898 y2[1] (numeric) = -0.9977152455613146 absolute error = 4.166667011418212e-13 relative error = 4.176208622607331e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.06755952024220609 y1[1] (numeric) = 0.06755952024270466 absolute error = 4.985734047835422e-13 relative error = 7.379765323911687e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999934 y2[1] (closed_form) = -0.9969897762717747 y2[1] (numeric) = -0.9969897762721928 absolute error = 4.18109991073834e-13 relative error = 4.193723958106659e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.07753312846491316 y1[1] (numeric) = 0.07753312846541258 absolute error = 4.994199498398189e-13 relative error = 6.441374928729032e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999938 y2[1] (closed_form) = -0.9961646088358461 y2[1] (numeric) = -0.9961646088362659 absolute error = 4.197753256107717e-13 relative error = 4.213915269498846e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.08749898343938446 y1[1] (numeric) = 0.08749898343988474 absolute error = 5.002803726839034e-13 relative error = 5.717556399160638e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.809999999999941 y2[1] (closed_form) = -0.9952398257691684 y2[1] (numeric) = -0.9952398257695899 absolute error = 4.215516824501719e-13 relative error = 4.235679396414597e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.09745608858842739 y1[1] (numeric) = 0.09745608858892855 absolute error = 5.011685511036035e-13 relative error = 5.142506316050896e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999944 y2[1] (closed_form) = -0.9942155195492773 y2[1] (numeric) = -0.9942155195497006 absolute error = 4.232170169871097e-13 relative error = 4.256793508704964e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.1074034482098246 y1[1] (numeric) = 0.1074034482103267 absolute error = 5.020428517354958e-13 relative error = 4.674364371939894e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999948 y2[1] (closed_form) = -0.9930917926059415 y2[1] (numeric) = -0.9930917926063666 absolute error = 4.251043961289724e-13 relative error = 4.280615339831469e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.1173400675759034 y1[1] (numeric) = 0.1173400675764064 absolute error = 5.029726635186194e-13 relative error = 4.286452819649716e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.839999999999951 y2[1] (closed_form) = -0.9918687573109188 y2[1] (numeric) = -0.9918687573113457 absolute error = 4.268807529683727e-13 relative error = 4.303802794693324e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.1272649530330077 y1[1] (numeric) = 0.1272649530335116 absolute error = 5.039302308773586e-13 relative error = 3.959693685241515e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999954 y2[1] (closed_form) = -0.9905465359667195 y2[1] (numeric) = -0.9905465359671483 absolute error = 4.287681321102355e-13 relative error = 4.328601600648486e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.1371771121008624 y1[1] (numeric) = 0.1371771121013673 absolute error = 5.049016760239056e-13 relative error = 3.680655382602498e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999958 y2[1] (closed_form) = -0.989125260794376 y2[1] (numeric) = -0.9891252607948067 absolute error = 4.306555112520982e-13 relative error = 4.353902668568333e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.1470755535718209 y1[1] (numeric) = 0.1470755535723269 absolute error = 5.059008767460682e-13 relative error = 3.439734642909389e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.869999999999961 y2[1] (closed_form) = -0.9876050739202215 y2[1] (numeric) = -0.987605073920654 absolute error = 4.32542890393961e-13 relative error = 4.379715149467749e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.1569592876099848 y1[1] (numeric) = 0.1569592876104917 absolute error = 5.069000774682308e-13 relative error = 3.229500370362186e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999964 y2[1] (closed_form) = -0.9859861273616762 y2[1] (numeric) = -0.985986127362111 absolute error = 4.347633364432113e-13 relative error = 4.409426505893757e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.1668273258501867 y1[1] (numeric) = 0.1668273258506946 absolute error = 5.079547893416247e-13 relative error = 3.044793691638835e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999968 y2[1] (closed_form) = -0.9842685830120471 y2[1] (numeric) = -0.984268583012484 absolute error = 4.368727601899991e-13 relative error = 4.438552319257069e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.1766786814968258 y1[1] (numeric) = 0.1766786814973348 absolute error = 5.08981745639403e-13 relative error = 2.880832827861846e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.899999999999971 y2[1] (closed_form) = -0.9824526126243379 y2[1] (numeric) = -0.9824526126247767 absolute error = 4.387601393318619e-13 relative error = 4.465967454245362e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.186512369422547 y1[1] (numeric) = 0.186512369423057 absolute error = 5.100642130884125e-13 relative error = 2.734747377171824e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999974 y2[1] (closed_form) = -0.9805383977940739 y2[1] (numeric) = -0.980538397794515 absolute error = 4.410916076835747e-13 relative error = 4.498463381708482e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.1963274062667523 y1[1] (numeric) = 0.1963274062672635 absolute error = 5.112021916886533e-13 relative error = 2.603824913746769e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999978 y2[1] (closed_form) = -0.9785261299411431 y2[1] (numeric) = -0.9785261299415865 absolute error = 4.434230760352875e-13 relative error = 4.531540471606607e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.2061228105339366 y1[1] (numeric) = 0.2061228105344489 absolute error = 5.123401702888941e-13 relative error = 2.485606367202824e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.929999999999981 y2[1] (closed_form) = -0.9764160102906538 y2[1] (numeric) = -0.9764160102910996 absolute error = 4.457545443870004e-13 relative error = 4.565211341160934e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.2158976026918359 y1[1] (numeric) = 0.2158976026923494 absolute error = 5.134781488891349e-13 relative error = 2.378341132495362e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y2[1] (closed_form) = -0.9742082498528126 y2[1] (numeric) = -0.9742082498532607 absolute error = 4.480860127387132e-13 relative error = 4.599488998439624e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.2256508052693801 y1[1] (numeric) = 0.2256508052698948 absolute error = 5.146993942162226e-13 relative error = 2.280955273356009e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999988 y2[1] (closed_form) = -0.9719030694018237 y2[1] (numeric) = -0.9719030694022741 absolute error = 4.50417481090426e-13 relative error = 4.634386856784433e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.2353814429544391 y1[1] (numeric) = 0.2353814429549551 absolute error = 5.159761506945415e-13 relative error = 2.192085086309947e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.959999999999991 y2[1] (closed_form) = -0.969500699453811 y2[1] (numeric) = -0.9695006994542639 absolute error = 4.528599717446014e-13 relative error = 4.671063899177481e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.2450885426913531 y1[1] (numeric) = 0.2450885426918704 absolute error = 5.172251515972448e-13 relative error = 2.110360386158895e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y2[1] (closed_form) = -0.9670013802437675 y2[1] (numeric) = -0.9670013802442228 absolute error = 4.553024623987767e-13 relative error = 4.708395165723563e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.2547711337782378 y1[1] (numeric) = 0.2547711337787564 absolute error = 5.185851748024106e-13 relative error = 2.035494237953215e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999998 y2[1] (closed_form) = -0.9644053617015312 y2[1] (numeric) = -0.9644053617019891 absolute error = 4.578559753554146e-13 relative error = 4.7475469707842e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.2644282479640532 y1[1] (numeric) = 0.264428247964573 absolute error = 5.198619312807296e-13 relative error = 1.965984857076996e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.990000000000001 y2[1] (closed_form) = -0.9617129034267932 y2[1] (numeric) = -0.9617129034272539 absolute error = 4.6074255521944e-13 relative error = 4.790853419744225e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y1[1] (closed_form) = 0.2740589195454283 y1[1] (numeric) = 0.2740589195459495 absolute error = 5.211941989102797e-13 relative error = 1.901759664581491e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 Finished! diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ; diff ( y1 , x , 1 ) = neg ( y2 ) ; Iterations = 4900 Total Elapsed Time = 1.0 Seconds Elapsed Time(since restart) = 1.0 Seconds Time to Timeout = 2 Minutes 59.0 Seconds Percent Done = 100 %