##############ECHO OF PROBLEM################# ##############temp/lin_arctan_m2_2postode.ode################# diff ( y , x , 1 ) = arctan ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-2.0); x_end=c(2.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(x)*arctan(c(x))-c(0.5)*ln(c(x)*c(x)+c(1.0))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (closed_form) = 1.409578479371131 y[1] (numeric) = 1.409578479371131 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.990000000000001 y[1] (closed_form) = 1.398517018933384 y[1] (numeric) = 1.398517018397222 absolute error = 5.361615595944613e-10 relative error = 3.833786449044284e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.980000000000002 y[1] (closed_form) = 1.38747571952809 y[1] (numeric) = 1.387475718449824 absolute error = 1.078265698950531e-09 relative error = 7.77142031225795e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.970000000000003 y[1] (closed_form) = 1.376454743824288 y[1] (numeric) = 1.376454742197897 absolute error = 1.626391021858353e-09 relative error = 1.181579728033522e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.960000000000004 y[1] (closed_form) = 1.365454256297782 y[1] (numeric) = 1.365454254117165 absolute error = 2.180616798241886e-09 relative error = 1.596990004011039e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.950000000000006 y[1] (closed_form) = 1.354474423254985 y[1] (numeric) = 1.354474420513961 absolute error = 2.741023852337321e-09 relative error = 2.023680776304562e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.940000000000007 y[1] (closed_form) = 1.343515412857075 y[1] (numeric) = 1.343515409549382 absolute error = 3.307693674514667e-09 relative error = 2.461969280635669e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.930000000000008 y[1] (closed_form) = 1.332577395144496 y[1] (numeric) = 1.332577391263787 absolute error = 3.880709309456165e-09 relative error = 2.912183054880175e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.920000000000009 y[1] (closed_form) = 1.321660542061773 y[1] (numeric) = 1.321660537601619 absolute error = 4.460154245933268e-09 relative error = 3.374659456032095e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.91000000000001 y[1] (closed_form) = 1.310765027482672 y[1] (numeric) = 1.310765022436558 absolute error = 5.046113527029661e-09 relative error = 3.849746843429853e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.900000000000011 y[1] (closed_form) = 1.299891027235693 y[1] (numeric) = 1.29989102159702 absolute error = 5.638673084007451e-09 relative error = 4.337804451191939e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.890000000000012 y[1] (closed_form) = 1.28903871912991 y[1] (numeric) = 1.289038712891989 absolute error = 6.237920846530187e-09 relative error = 4.839203628220518e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.880000000000013 y[1] (closed_form) = 1.278208282981142 y[1] (numeric) = 1.278208276137198 absolute error = 6.843943634038396e-09 relative error = 5.354325836534551e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.870000000000014 y[1] (closed_form) = 1.267399900638489 y[1] (numeric) = 1.267399893181657 absolute error = 7.456832040730887e-09 relative error = 5.883566849716727e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.860000000000015 y[1] (closed_form) = 1.256613756011198 y[1] (numeric) = 1.25661374793452 absolute error = 8.07667754898489e-09 relative error = 6.427334978905736e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.850000000000017 y[1] (closed_form) = 1.245850035095892 y[1] (numeric) = 1.245850026392321 absolute error = 8.703570975043817e-09 relative error = 6.986050270788739e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.840000000000018 y[1] (closed_form) = 1.235108926004155 y[1] (numeric) = 1.235108916666548 absolute error = 9.337606465820159e-09 relative error = 7.560148153110141e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.830000000000019 y[1] (closed_form) = 1.224390618990463 y[1] (numeric) = 1.224390609011586 absolute error = 9.978876835958772e-09 relative error = 8.150076193973598e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.82000000000002 y[1] (closed_form) = 1.213695306480492 y[1] (numeric) = 1.213695295853013 absolute error = 1.062747911895201e-08 relative error = 8.756299099293604e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.810000000000021 y[1] (closed_form) = 1.203023183099769 y[1] (numeric) = 1.203023171816259 absolute error = 1.128350968215841e-08 relative error = 9.379295295943313e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.800000000000022 y[1] (closed_form) = 1.192374445702698 y[1] (numeric) = 1.192374433755632 absolute error = 1.194706555907032e-08 relative error = 1.001955853895343e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.790000000000023 y[1] (closed_form) = 1.181749293401951 y[1] (numeric) = 1.181749280783705 absolute error = 1.261824644771536e-08 relative error = 1.067760016288285e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.780000000000024 y[1] (closed_form) = 1.171147927598227 y[1] (numeric) = 1.171147914301073 absolute error = 1.329715382247798e-08 relative error = 1.13539489838381e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.770000000000025 y[1] (closed_form) = 1.160570552010371 y[1] (numeric) = 1.160570538026483 absolute error = 1.39838880475196e-08 relative error = 1.204914946643816e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.760000000000026 y[1] (closed_form) = 1.150017372705876 y[1] (numeric) = 1.150017358027324 absolute error = 1.467855237358151e-08 relative error = 1.276376576733301e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.750000000000028 y[1] (closed_form) = 1.139488598131755 y[1] (numeric) = 1.139488582750504 absolute error = 1.538125116162803e-08 relative error = 1.349838092881869e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.740000000000029 y[1] (closed_form) = 1.128984439145776 y[1] (numeric) = 1.128984423053687 absolute error = 1.609208966080189e-08 relative error = 1.425359739499833e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.73000000000003 y[1] (closed_form) = 1.118505109048084 y[1] (numeric) = 1.11850509223691 absolute error = 1.681117467455806e-08 relative error = 1.503003834185915e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.720000000000031 y[1] (closed_form) = 1.108050823613187 y[1] (numeric) = 1.108050806074574 absolute error = 1.753861322839612e-08 relative error = 1.582834726949196e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.710000000000032 y[1] (closed_form) = 1.097621801122326 y[1] (numeric) = 1.097621782847811 absolute error = 1.827451523439549e-08 relative error = 1.664919120202393e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.700000000000033 y[1] (closed_form) = 1.087218262396212 y[1] (numeric) = 1.08721824337722 absolute error = 1.901899127076945e-08 relative error = 1.749325956763447e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.690000000000034 y[1] (closed_form) = 1.07684043082814 y[1] (numeric) = 1.076840411055987 absolute error = 1.977215280390965e-08 relative error = 1.836126527001215e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.680000000000035 y[1] (closed_form) = 1.066488532417482 y[1] (numeric) = 1.06648851188337 absolute error = 2.053411218838619e-08 relative error = 1.925394560205924e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.670000000000036 y[1] (closed_form) = 1.056162795803549 y[1] (numeric) = 1.056162774498564 absolute error = 2.130498466534902e-08 relative error = 2.017206509261651e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.660000000000037 y[1] (closed_form) = 1.04586345229982 y[1] (numeric) = 1.045863430214937 absolute error = 2.208488369959127e-08 relative error = 2.111641213872358e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.650000000000039 y[1] (closed_form) = 1.035590735928558 y[1] (numeric) = 1.03559071305463 absolute error = 2.287392764088736e-08 relative error = 2.208780635757382e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.64000000000004 y[1] (closed_form) = 1.025344883455773 y[1] (numeric) = 1.02534485978354 absolute error = 2.367223395083329e-08 relative error = 2.308709423803776e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.630000000000041 y[1] (closed_form) = 1.015126134426571 y[1] (numeric) = 1.01512610994665 absolute error = 2.447992097920348e-08 relative error = 2.411515194910415e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.620000000000042 y[1] (closed_form) = 1.004934731200853 y[1] (numeric) = 1.004934705903744 absolute error = 2.529710951826303e-08 relative error = 2.517288808202906e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.610000000000043 y[1] (closed_form) = 0.9947709189893836 y[1] (numeric) = 0.9947708928654627 absolute error = 2.612392091538851e-08 relative error = 2.626124308290853e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.600000000000044 y[1] (closed_form) = 0.9846349458902097 y[1] (numeric) = 0.9846349189297323 absolute error = 2.696047740613494e-08 relative error = 2.738119088568397e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.590000000000045 y[1] (closed_form) = 0.9745270629254377 y[1] (numeric) = 0.9745270351185346 absolute error = 2.780690311343648e-08 relative error = 2.853374131033652e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.580000000000046 y[1] (closed_form) = 0.9644475240783532 y[1] (numeric) = 0.9644474954150304 absolute error = 2.866332282636108e-08 relative error = 2.971994028783719e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.570000000000047 y[1] (closed_form) = 0.9543965863308871 y[1] (numeric) = 0.9543965568010245 absolute error = 2.952986255522205e-08 relative error = 3.094087193746952e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.560000000000048 y[1] (closed_form) = 0.944374509701418 y[1] (numeric) = 0.944374479294768 absolute error = 3.040664997566722e-08 relative error = 3.219766063495388e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.55000000000005 y[1] (closed_form) = 0.9343815572829026 y[1] (numeric) = 0.9343815259890901 absolute error = 3.129381254129981e-08 relative error = 3.349147069244325e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.540000000000051 y[1] (closed_form) = 0.9244179952813324 y[1] (numeric) = 0.9244179630898528 absolute error = 3.21914795931022e-08 relative error = 3.482351031397352e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.530000000000052 y[1] (closed_form) = 0.9144840930545044 y[1] (numeric) = 0.9144840599547228 absolute error = 3.309978158227977e-08 relative error = 3.619503262404695e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.520000000000053 y[1] (closed_form) = 0.9045801231510984 y[1] (numeric) = 0.9045800891322481 absolute error = 3.401885029230556e-08 relative error = 3.760733783736164e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.510000000000054 y[1] (closed_form) = 0.894706361350052 y[1] (numeric) = 0.894706326401235 absolute error = 3.494881695154106e-08 relative error = 3.906177318199195e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.500000000000055 y[1] (closed_form) = 0.8848630867002247 y[1] (numeric) = 0.8848630508104091 absolute error = 3.588981567492766e-08 relative error = 4.055973880520396e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.490000000000056 y[1] (closed_form) = 0.8750505815603358 y[1] (numeric) = 0.8750505447183559 absolute error = 3.684197991127292e-08 relative error = 4.210268604767805e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.480000000000057 y[1] (closed_form) = 0.8652691316391696 y[1] (numeric) = 0.8652690938337251 absolute error = 3.780544455267432e-08 relative error = 4.369212210431628e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.470000000000058 y[1] (closed_form) = 0.8555190260360321 y[1] (numeric) = 0.8555189872556864 absolute error = 3.878034571247468e-08 relative error = 4.532961223803497e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.460000000000059 y[1] (closed_form) = 0.8458005572814447 y[1] (numeric) = 0.8458005175146251 absolute error = 3.976681950401684e-08 relative error = 4.701678092035616e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.450000000000061 y[1] (closed_form) = 0.8361140213780633 y[1] (numeric) = 0.83611398061306 absolute error = 4.076500337291122e-08 relative error = 4.875531605811766e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.440000000000062 y[1] (closed_form) = 0.8264597178418055 y[1] (numeric) = 0.8264596760667707 absolute error = 4.177503476476829e-08 relative error = 5.054697024297626e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.430000000000063 y[1] (closed_form) = 0.8168379497431675 y[1] (numeric) = 0.8168379069461152 absolute error = 4.279705223542152e-08 relative error = 5.239356502581435e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.420000000000064 y[1] (closed_form) = 0.8072490237487152 y[1] (numeric) = 0.8072489799175206 absolute error = 4.383119456274898e-08 relative error = 5.429699296408562e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.410000000000065 y[1] (closed_form) = 0.7976932501627295 y[1] (numeric) = 0.7976932052851281 absolute error = 4.487760141280717e-08 relative error = 5.625922170414772e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.400000000000066 y[1] (closed_form) = 0.7881709429689836 y[1] (numeric) = 0.7881708970325717 absolute error = 4.593641189654107e-08 relative error = 5.828229561914817e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.390000000000067 y[1] (closed_form) = 0.7786824198726341 y[1] (numeric) = 0.7786823728648679 absolute error = 4.700776623511871e-08 relative error = 6.036834148998455e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.380000000000068 y[1] (closed_form) = 0.7692280023421991 y[1] (numeric) = 0.7692279542503943 absolute error = 4.809180487175269e-08 relative error = 6.251957121337159e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.370000000000069 y[1] (closed_form) = 0.7598080156515997 y[1] (numeric) = 0.7598079664629319 absolute error = 4.918866780556641e-08 relative error = 6.473828492501881e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.36000000000007 y[1] (closed_form) = 0.7504227889222415 y[1] (numeric) = 0.7504227386237454 absolute error = 5.029849603488401e-08 relative error = 6.702687708501337e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.350000000000072 y[1] (closed_form) = 0.741072655165102 y[1] (numeric) = 0.7410726037436729 absolute error = 5.142142911473968e-08 relative error = 6.938783769222143e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.340000000000073 y[1] (closed_form) = 0.7317579513228049 y[1] (numeric) = 0.731757898765197 absolute error = 5.255760782141294e-08 relative error = 7.182376047490037e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.330000000000074 y[1] (closed_form) = 0.7224790183116366 y[1] (numeric) = 0.722478964604465 absolute error = 5.370717159891569e-08 relative error = 7.433734439018609e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.320000000000075 y[1] (closed_form) = 0.7132362010634867 y[1] (numeric) = 0.7132361461932265 absolute error = 5.487026022432673e-08 relative error = 7.693140104570016e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.310000000000076 y[1] (closed_form) = 0.7040298485676646 y[1] (numeric) = 0.7040297925206519 absolute error = 5.604701269756873e-08 relative error = 7.96088586465408e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.300000000000077 y[1] (closed_form) = 0.6948603139125653 y[1] (numeric) = 0.6948602566749983 absolute error = 5.723756701936367e-08 relative error = 8.237276740856711e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.290000000000078 y[1] (closed_form) = 0.6857279543271415 y[1] (numeric) = 0.6857278958850804 absolute error = 5.844206107941119e-08 relative error = 8.522630689127502e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.280000000000079 y[1] (closed_form) = 0.6766331312221415 y[1] (numeric) = 0.67663307156151 absolute error = 5.966063154616563e-08 relative error = 8.817279082743998e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.27000000000008 y[1] (closed_form) = 0.6675762102310705 y[1] (numeric) = 0.6675761493376565 absolute error = 6.08934139778583e-08 relative error = 9.121567402286706e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.260000000000081 y[1] (closed_form) = 0.6585575612508301 y[1] (numeric) = 0.6585574991102873 absolute error = 6.214054282249748e-08 relative error = 9.435855949246252e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.250000000000083 y[1] (closed_form) = 0.6495775584819907 y[1] (numeric) = 0.6495774950798396 absolute error = 6.340215108480152e-08 relative error = 9.760520550150642e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.240000000000084 y[1] (closed_form) = 0.6406365804686427 y[1] (numeric) = 0.6406365157902727 absolute error = 6.467836999313192e-08 relative error = 1.009595330098353e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.230000000000085 y[1] (closed_form) = 0.6317350101377788 y[1] (numeric) = 0.631734944168449 absolute error = 6.596932977664949e-08 relative error = 1.04425635302786e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.220000000000086 y[1] (closed_form) = 0.6228732348381475 y[1] (numeric) = 0.6228731675629902 absolute error = 6.727515733384593e-08 relative error = 1.080077832391165e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.210000000000087 y[1] (closed_form) = 0.6140516463785275 y[1] (numeric) = 0.6140515777825486 absolute error = 6.859597889707914e-08 relative error = 1.117104388558119e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.200000000000088 y[1] (closed_form) = 0.6052706410653539 y[1] (numeric) = 0.6052705711334366 absolute error = 6.993191725701564e-08 relative error = 1.155382609239505e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.190000000000089 y[1] (closed_form) = 0.5965306197396412 y[1] (numeric) = 0.5965305484565473 absolute error = 7.128309387205434e-08 relative error = 1.194961189136715e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.18000000000009 y[1] (closed_form) = 0.5878319878131298 y[1] (numeric) = 0.5878319151635041 absolute error = 7.264962575970202e-08 relative error = 1.235890990382734e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.170000000000091 y[1] (closed_form) = 0.5791751553035941 y[1] (numeric) = 0.5791750812719657 absolute error = 7.403162838315325e-08 relative error = 1.278225208820414e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.160000000000093 y[1] (closed_form) = 0.5705605368692327 y[1] (numeric) = 0.5705604614400197 absolute error = 7.542921298675509e-08 relative error = 1.322019454774223e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.150000000000094 y[1] (closed_form) = 0.5619885518420706 y[1] (numeric) = 0.5619884749995832 absolute error = 7.684248748418554e-08 relative error = 1.367331900842345e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.140000000000095 y[1] (closed_form) = 0.5534596242602932 y[1] (numeric) = 0.5534595459887363 absolute error = 7.827155690254273e-08 relative error = 1.414223431513253e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.130000000000096 y[1] (closed_form) = 0.5449741828994253 y[1] (numeric) = 0.5449741031829053 absolute error = 7.971652005167584e-08 relative error = 1.462757733358306e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.120000000000097 y[1] (closed_form) = 0.5365326613022798 y[1] (numeric) = 0.5365325801248066 absolute error = 8.117747318792112e-08 relative error = 1.513001519625776e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.110000000000098 y[1] (closed_form) = 0.5281354978075732 y[1] (numeric) = 0.5281354151530657 absolute error = 8.265450746058889e-08 relative error = 1.565024653781257e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.100000000000099 y[1] (closed_form) = 0.5197831355771267 y[1] (numeric) = 0.5197830514294182 absolute error = 8.414770857889664e-08 relative error = 1.618900322448237e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.0900000000001 y[1] (closed_form) = 0.5114760226215487 y[1] (numeric) = 0.5114759369643918 absolute error = 8.565715692299136e-08 relative error = 1.674705228291235e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.080000000000101 y[1] (closed_form) = 0.5032146118243012 y[1] (numeric) = 0.5032145246413738 absolute error = 8.718292732190491e-08 relative error = 1.732519789237461e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.070000000000102 y[1] (closed_form) = 0.4949993609640445 y[1] (numeric) = 0.4949992722389557 absolute error = 8.872508883150942e-08 relative error = 1.792428350992441e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.060000000000104 y[1] (closed_form) = 0.486830732735151 y[1] (numeric) = 0.4868306424514477 absolute error = 9.028370329122737e-08 relative error = 1.854519388781976e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.050000000000105 y[1] (closed_form) = 0.478709194766277 y[1] (numeric) = 0.4787091029074507 absolute error = 9.185882632323228e-08 relative error = 1.918885772981258e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.040000000000106 y[1] (closed_form) = 0.4706352196368722 y[1] (numeric) = 0.4706351261863667 absolute error = 9.345050555609191e-08 relative error = 1.985624994835607e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.030000000000107 y[1] (closed_form) = 0.4626092848915115 y[1] (numeric) = 0.4626091898327294 absolute error = 9.505878217908048e-08 relative error = 2.054839478662282e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.020000000000108 y[1] (closed_form) = 0.4546318730519142 y[1] (numeric) = 0.4546317763682264 absolute error = 9.668368772253189e-08 relative error = 2.126636812186101e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.010000000000109 y[1] (closed_form) = 0.4467034716265322 y[1] (numeric) = 0.4467033733012855 absolute error = 9.832524672237497e-08 relative error = 2.201130122502833e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.00000000000011 y[1] (closed_form) = 0.4388245731175621 y[1] (numeric) = 0.4388244731340887 absolute error = 9.99834734449756e-08 relative error = 2.278438345753026e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9900000000001101 y[1] (closed_form) = 0.4309956750252496 y[1] (numeric) = 0.4309955733668772 absolute error = 1.016583724422482e-07 relative error = 2.358686602511559e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9800000000001101 y[1] (closed_form) = 0.4232172798493415 y[1] (numeric) = 0.4232171764994017 absolute error = 1.033499398839233e-07 relative error = 2.442006619406329e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9700000000001101 y[1] (closed_form) = 0.4154898950875336 y[1] (numeric) = 0.4154897900293733 absolute error = 1.05058160393412e-07 relative error = 2.528537074801272e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9600000000001101 y[1] (closed_form) = 0.4078140332307671 y[1] (numeric) = 0.4078139264477591 absolute error = 1.067830079914955e-07 relative error = 2.618424068086713e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9500000000001101 y[1] (closed_form) = 0.400190211755214 y[1] (numeric) = 0.4001901032307695 absolute error = 1.085244444865019e-07 relative error = 2.711821561315035e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9400000000001101 y[1] (closed_form) = 0.3926189531107932 y[1] (numeric) = 0.3926188428283729 absolute error = 1.102824202514618e-07 relative error = 2.808891913588829e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9300000000001101 y[1] (closed_form) = 0.3851007847060467 y[1] (numeric) = 0.3851006726491742 absolute error = 1.120568725032633e-07 relative error = 2.909806392339555e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9200000000001101 y[1] (closed_form) = 0.3776362388892113 y[1] (numeric) = 0.3776361250414857 absolute error = 1.138477255246961e-07 relative error = 3.014745773858216e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9100000000001101 y[1] (closed_form) = 0.3702258529253075 y[1] (numeric) = 0.3702257372704179 absolute error = 1.156548896652509e-07 relative error = 3.123900958061515e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.90000000000011 y[1] (closed_form) = 0.3628701689690694 y[1] (numeric) = 0.3628700514908089 absolute error = 1.174782605084523e-07 relative error = 3.237473635328399e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.89000000000011 y[1] (closed_form) = 0.3555697340335314 y[1] (numeric) = 0.3555696147158123 absolute error = 1.193177190939032e-07 relative error = 3.355677035285888e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.88000000000011 y[1] (closed_form) = 0.3483250999540866 y[1] (numeric) = 0.3483249787809561 absolute error = 1.211731304739949e-07 relative error = 3.478736688512169e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.87000000000011 y[1] (closed_form) = 0.3411368233478243 y[1] (numeric) = 0.3411367003034811 absolute error = 1.230443432143069e-07 relative error = 3.606891276256344e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.86000000000011 y[1] (closed_form) = 0.3340054655679551 y[1] (numeric) = 0.3340053406367663 absolute error = 1.24931188782984e-07 relative error = 3.74039354627166e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.85000000000011 y[1] (closed_form) = 0.3269315926531242 y[1] (numeric) = 0.3269314658196427 absolute error = 1.268334814397143e-07 relative error = 3.879511319491389e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.84000000000011 y[1] (closed_form) = 0.3199157752714118 y[1] (numeric) = 0.319915646520395 absolute error = 1.287510167924388e-07 relative error = 4.024528539838599e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.83000000000011 y[1] (closed_form) = 0.3129585886588183 y[1] (numeric) = 0.3129584579752473 absolute error = 1.306835710201959e-07 relative error = 4.175746432786502e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.82000000000011 y[1] (closed_form) = 0.3060606125520282 y[1] (numeric) = 0.3060604799211271 absolute error = 1.326309010951654e-07 relative error = 4.333484795356314e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.81000000000011 y[1] (closed_form) = 0.2992224311152412 y[1] (numeric) = 0.2992222965224978 absolute error = 1.34592743339379e-07 relative error = 4.498083343475762e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.80000000000011 y[1] (closed_form) = 0.2924446328608628 y[1] (numeric) = 0.29244449629205 absolute error = 1.365688127030751e-07 relative error = 4.669903200721445e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7900000000001099 y[1] (closed_form) = 0.2857278105638419 y[1] (numeric) = 0.2857276720050391 absolute error = 1.3855880282021e-07 relative error = 4.849328546170727e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7800000000001099 y[1] (closed_form) = 0.2790725611694397 y[1] (numeric) = 0.2790724206070556 absolute error = 1.40562384121079e-07 relative error = 5.03676834197025e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7700000000001099 y[1] (closed_form) = 0.2724794856942184 y[1] (numeric) = 0.2724793431150144 absolute error = 1.425792040543605e-07 relative error = 5.232658293195899e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7600000000001099 y[1] (closed_form) = 0.2659491891200346 y[1] (numeric) = 0.2659490445111488 absolute error = 1.446088858658712e-07 relative error = 5.437462935846847e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7500000000001099 y[1] (closed_form) = 0.2594822802808243 y[1] (numeric) = 0.2594821336297959 absolute error = 1.46651028376521e-07 relative error = 5.651677957269689e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7400000000001099 y[1] (closed_form) = 0.2530793717419654 y[1] (numeric) = 0.253079223036761 absolute error = 1.487052044280013e-07 relative error = 5.875832684602129e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7300000000001099 y[1] (closed_form) = 0.2467410796720094 y[1] (numeric) = 0.246740928901048 absolute error = 1.507709613546293e-07 relative error = 6.11049289218673e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7200000000001099 y[1] (closed_form) = 0.2404680237065703 y[1] (numeric) = 0.240467870858751 absolute error = 1.52847819373525e-07 relative error = 6.356263798301791e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7100000000001099 y[1] (closed_form) = 0.2342608268041691 y[1] (numeric) = 0.234260671868898 absolute error = 1.549352711682772e-07 relative error = 6.613793406346837e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7000000000001099 y[1] (closed_form) = 0.2281201150938293 y[1] (numeric) = 0.2281199580610478 absolute error = 1.570327814448547e-07 relative error = 6.883776179942075e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6900000000001099 y[1] (closed_form) = 0.2220465177142279 y[1] (numeric) = 0.2220463585744419 absolute error = 1.591397859601607e-07 relative error = 7.166957068201912e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6800000000001098 y[1] (closed_form) = 0.2160406666442121 y[1] (numeric) = 0.2160405053885209 absolute error = 1.612556912444774e-07 relative error = 7.464135977234429e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6700000000001098 y[1] (closed_form) = 0.2101031965244943 y[1] (numeric) = 0.2101030331446208 absolute error = 1.633798735745096e-07 relative error = 7.776172675005558e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6600000000001098 y[1] (closed_form) = 0.2042347444703514 y[1] (numeric) = 0.2042345789586725 absolute error = 1.655116788623623e-07 relative error = 8.103992261042024e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6500000000001098 y[1] (closed_form) = 0.1984359498751582 y[1] (numeric) = 0.1984357822247361 absolute error = 1.676504221004294e-07 relative error = 8.448591205671306e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6400000000001098 y[1] (closed_form) = 0.1927074542045971 y[1] (numeric) = 0.1927072844092107 absolute error = 1.697953864454593e-07 relative error = 8.811044032847214e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6300000000001098 y[1] (closed_form) = 0.187049900781396 y[1] (numeric) = 0.187049728835573 absolute error = 1.719458230242665e-07 relative error = 9.192510784874378e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6200000000001098 y[1] (closed_form) = 0.1814639345604586 y[1] (numeric) = 0.1814637604595079 absolute error = 1.74100950739442e-07 relative error = 9.594245333715967e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6100000000001098 y[1] (closed_form) = 0.1759502018942644 y[1] (numeric) = 0.1759500256343089 absolute error = 1.762599554366862e-07 relative error = 0.0001001760461420828 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6000000000001098 y[1] (closed_form) = 0.1705093502884295 y[1] (numeric) = 0.1705091718664395 absolute error = 1.784219900158313e-07 relative error = 0.0001046405899230845 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5900000000001098 y[1] (closed_form) = 0.1651420281473369 y[1] (numeric) = 0.165141847561163 absolute error = 1.805861739034853e-07 relative error = 0.0001093520383208382 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5800000000001098 y[1] (closed_form) = 0.1598488845097595 y[1] (numeric) = 0.1598487017581663 absolute error = 1.827515931640544e-07 relative error = 0.0001143277250413948 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5700000000001098 y[1] (closed_form) = 0.1546305687744175 y[1] (numeric) = 0.1546303838571179 absolute error = 1.849172996670756e-07 relative error = 0.0001195865094028347 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5600000000001097 y[1] (closed_form) = 0.1494877304154371 y[1] (numeric) = 0.1494875433331248 absolute error = 1.870823122807064e-07 relative error = 0.0001251489414955938 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5500000000001097 y[1] (closed_form) = 0.1444210186876861 y[1] (numeric) = 0.1444208294420707 absolute error = 1.89245615428435e-07 relative error = 0.0001310374467290548 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5400000000001097 y[1] (closed_form) = 0.139431082322001 y[1] (numeric) = 0.1394308909158405 absolute error = 1.914061605878814e-07 relative error = 0.0001372765364797567 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5300000000001097 y[1] (closed_form) = 0.1345185692103276 y[1] (numeric) = 0.1345183756474626 absolute error = 1.93562865069552e-07 relative error = 0.0001438930448084867 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5200000000001097 y[1] (closed_form) = 0.1296841260808355 y[1] (numeric) = 0.129683930366222 absolute error = 1.957146134878851e-07 relative error = 0.0001509163992560594 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5100000000001097 y[1] (closed_form) = 0.1249283981630836 y[1] (numeric) = 0.1249282003028261 absolute error = 1.97860257497573e-07 relative error = 0.0001583789277753188 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5000000000001097 y[1] (closed_form) = 0.120252028843349 y[1] (numeric) = 0.1202518288447327 absolute error = 1.999986163209178e-07 relative error = 0.0001663162095846663 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4900000000001097 y[1] (closed_form) = 0.1156556593102552 y[1] (numeric) = 0.1156554571817777 absolute error = 2.021284774833543e-07 relative error = 0.0001747674767398361 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4800000000001097 y[1] (closed_form) = 0.1111399281908694 y[1] (numeric) = 0.1111397239422721 absolute error = 2.042485972852948e-07 relative error = 0.0001837760745485839 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4700000000001097 y[1] (closed_form) = 0.1067054711774698 y[1] (numeric) = 0.1067052648197682 absolute error = 2.063577015515294e-07 relative error = 0.0001933899914169543 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4600000000001097 y[1] (closed_form) = 0.1023529206452145 y[1] (numeric) = 0.1023527121907275 absolute error = 2.084544870328831e-07 relative error = 0.0002036624707129247 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4500000000001096 y[1] (closed_form) = 0.09808290526098008 y[1] (numeric) = 0.09808269472335857 absolute error = 2.105376215172372e-07 relative error = 0.0002146527174710378 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4400000000001096 y[1] (closed_form) = 0.09389604958367162 y[1] (numeric) = 0.09389583697792582 absolute error = 2.126057458001762e-07 relative error = 0.000226426720551988 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4300000000001096 y[1] (closed_form) = 0.08979297365634066 y[1] (numeric) = 0.08979275899886634 absolute error = 2.146574743233653e-07 relative error = 0.0002390582086577411 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4200000000001096 y[1] (closed_form) = 0.08577429259048647 y[1] (numeric) = 0.08577407589908953 absolute error = 2.166913969370299e-07 relative error = 0.0002526297686552578 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4100000000001096 y[1] (closed_form) = 0.08184061614295011 y[1] (numeric) = 0.08184039743686997 absolute error = 2.18706080148956e-07 relative error = 0.0002672341564082857 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4000000000001096 y[1] (closed_form) = 0.07799254828585105 y[1] (numeric) = 0.07799232758578209 absolute error = 2.207000689563587e-07 relative error = 0.0002829758403937122 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3900000000001096 y[1] (closed_form) = 0.07423068677005205 y[1] (numeric) = 0.07423046409816371 absolute error = 2.226718883446832e-07 relative error = 0.0002999728253012997 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3800000000001096 y[1] (closed_form) = 0.07055562268267768 y[1] (numeric) = 0.07055539806263236 absolute error = 2.246200453137615e-07 relative error = 0.0003183588164532047 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3700000000001096 y[1] (closed_form) = 0.06696793999924891 y[1] (numeric) = 0.06696771345621789 absolute error = 2.265430310149918e-07 relative error = 0.0003382857991712642 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3600000000001096 y[1] (closed_form) = 0.0634682151310339 y[1] (numeric) = 0.06346798669171147 absolute error = 2.284393224305514e-07 relative error = 0.0003599271256627036 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3500000000001096 y[1] (closed_form) = 0.06005701646825527 y[1] (numeric) = 0.06005678616087001 absolute error = 2.303073852599757e-07 relative error = 0.0003834812296773198 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3400000000001095 y[1] (closed_form) = 0.05673490391982632 y[1] (numeric) = 0.05673467177415077 absolute error = 2.3214567554386e-07 relative error = 0.0004091761147104639 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3300000000001095 y[1] (closed_form) = 0.05350242845033099 y[1] (numeric) = 0.0535021944976881 absolute error = 2.339526428904448e-07 relative error = 0.0004372748110071955 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3200000000001095 y[1] (closed_form) = 0.05036013161499141 y[1] (numeric) = 0.05035989588825873 absolute error = 2.357267326821844e-07 relative error = 0.0004680820425259021 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3100000000001095 y[1] (closed_form) = 0.04730854509340522 y[1] (numeric) = 0.04730830762701665 absolute error = 2.374663885737482e-07 relative error = 0.000501952423404479 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3000000000001095 y[1] (closed_form) = 0.04434819022286584 y[1] (numeric) = 0.04434795105281009 absolute error = 2.391700557533016e-07 relative error = 0.0005393005995315363 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2900000000001095 y[1] (closed_form) = 0.04147957753210881 y[1] (numeric) = 0.04147933669592494 absolute error = 2.408361838707185e-07 relative error = 0.0005806138784424462 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2800000000001095 y[1] (closed_form) = 0.03870320627635609 y[1] (numeric) = 0.03870296381312658 absolute error = 2.424632295078277e-07 relative error = 0.0006264680703106225 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2700000000001095 y[1] (closed_form) = 0.03601956397455903 y[1] (numeric) = 0.03601931992489928 absolute error = 2.440496597519437e-07 relative error = 0.0006775475125804365 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2600000000001095 y[1] (closed_form) = 0.03342912594976098 y[1] (numeric) = 0.033428880355806 absolute error = 2.455939549714237e-07 relative error = 0.000734670584389538 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2500000000001095 y[1] (closed_form) = 0.03093235487352549 y[1] (numeric) = 0.03093210777891291 absolute error = 2.470946125765483e-07 relative error = 0.0007988225066822593 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2400000000001095 y[1] (closed_form) = 0.02852970031539061 y[1] (numeric) = 0.02852945176524109 absolute error = 2.48550149520993e-07 relative error = 0.0008711978982369832 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2300000000001095 y[1] (closed_form) = 0.02622159829832974 y[1] (numeric) = 0.02622134833922344 absolute error = 2.499591062951612e-07 relative error = 0.0009532565614472213 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2200000000001094 y[1] (closed_form) = 0.02400847086120621 y[1] (numeric) = 0.02400821954115634 absolute error = 2.513200498717449e-07 relative error = 0.001046797404652028 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2100000000001094 y[1] (closed_form) = 0.02189072562922125 y[1] (numeric) = 0.02189047299764411 absolute error = 2.526315771335386e-07 relative error = 0.001154057574027188 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2000000000001094 y[1] (closed_form) = 0.0198687553933571 y[1] (numeric) = 0.01986850150103885 absolute error = 2.538923182492103e-07 relative error = 0.001277847118366038 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1900000000001094 y[1] (closed_form) = 0.01794293769981879 y[1] (numeric) = 0.01794268259887881 absolute error = 2.551009399796855e-07 relative error = 0.001421734524454499 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1800000000001094 y[1] (closed_form) = 0.01611363445047422 y[1] (numeric) = 0.01611337819432522 absolute error = 2.562561489949378e-07 relative error = 0.001590306332085101 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1700000000001094 y[1] (closed_form) = 0.01438119151528474 y[1] (numeric) = 0.01438093415858971 absolute error = 2.573566950311856e-07 relative error = 0.001789536665009013 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1600000000001094 y[1] (closed_form) = 0.01274593835770734 y[1] (numeric) = 0.01274567995633279 absolute error = 2.58401374552894e-07 relative error = 0.002027323271939733 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1500000000001094 y[1] (closed_form) = 0.01120818767403099 y[1] (numeric) = 0.01120792828499784 absolute error = 2.593890331466925e-07 relative error = 0.002314281672385702 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1400000000001094 y[1] (closed_form) = 0.009768235047593497 y[1] (numeric) = 0.009767974729024173 absolute error = 2.603185693238891e-07 relative error = 0.002664949891720933 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1300000000001094 y[1] (closed_form) = 0.00842635861879543 y[1] (numeric) = 0.00842609742985824 absolute error = 2.611889371902099e-07 relative error = 0.003099665573307246 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1200000000001094 y[1] (closed_form) = 0.007182818771801497 y[1] (numeric) = 0.007182556772652536 absolute error = 2.619991489611478e-07 relative error = 0.003647581225210792 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1100000000001093 y[1] (closed_form) = 0.006037857838786667 y[1] (numeric) = 0.006037595090508312 absolute error = 2.627482783559495e-07 relative error = 0.00435168043652962 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1000000000001093 y[1] (closed_form) = 0.004991699822543107 y[1] (numeric) = 0.004991436387080366 absolute error = 2.634354627408658e-07 relative error = 0.005277470042392375 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.09000000000010933 y[1] (closed_form) = 0.004044550138225922 y[1] (numeric) = 0.004044286078320343 absolute error = 2.640599055794488e-07 relative error = 0.00652878309218524 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.08000000000010932 y[1] (closed_form) = 0.003196595374968193 y[1] (numeric) = 0.003196330754089053 absolute error = 2.646208791395877e-07 relative error = 0.008278210035958045 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.07000000000010931 y[1] (closed_form) = 0.002448003078044671 y[1] (numeric) = 0.002447737960318738 absolute error = 2.651177259333296e-07 relative error = 0.01082995884731856 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.0600000000001093 y[1] (closed_form) = 0.001798921552213922 y[1] (numeric) = 0.001798656002352967 absolute error = 2.655498609544556e-07 relative error = 0.01476161429205432 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.05000000000010929 y[1] (closed_form) = 0.00124947968680905 y[1] (numeric) = 0.001249213770035334 absolute error = 2.659167737161308e-07 relative error = 0.0212822006250646 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.04000000000010928 y[1] (closed_form) = 0.0007997868030874753 y[1] (numeric) = 0.0007995205850584916 absolute error = 2.66218028983716e-07 relative error = 0.0332861242466136 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.03000000000010927 y[1] (closed_form) = 0.0004499325242915648 y[1] (numeric) = 0.0004496660710227327 absolute error = 2.664532688320957e-07 relative error = 0.0592207174290492 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.02000000000010926 y[1] (closed_form) = 0.0001999866688017148 y[1] (numeric) = 0.0001997200465884491 absolute error = 2.666222132657067e-07 relative error = 0.1333199932091776 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 3 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.01000000000010925 y[1] (closed_form) = 4.999916670107855e-05 y[1] (numeric) = 4.973244203991585e-05 absolute error = 2.667246611627014e-07 relative error = 0.5334582129284722 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 3 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.092528845170193e-13 y[1] (closed_form) = 1.193619277528916e-26 y[1] (numeric) = -2.667604908743086e-07 absolute error = 2.667604908743086e-07 relative error = -1 % Desired digits = 8 Estimated correct digits = 5 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.009999999999890749 y[1] (closed_form) = 4.999916669892897e-05 y[1] (numeric) = 4.973243703834096e-05 absolute error = 2.667296605880068e-07 relative error = 0.5334682119686616 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 3 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.01999999999989076 y[1] (closed_form) = 0.000199986668797305 y[1] (numeric) = 0.0001997200365889644 absolute error = 2.666322083406513e-07 relative error = 0.1333249910827278 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 3 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.02999999999989077 y[1] (closed_form) = 0.0004499325242850067 y[1] (numeric) = 0.0004496660560326604 absolute error = 2.664682523462539e-07 relative error = 0.05922404759907096 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.03999999999989078 y[1] (closed_form) = 0.0007997868030787702 y[1] (numeric) = 0.0007995205650887951 absolute error = 2.662379899751261e-07 relative error = 0.03328862003602034 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.04999999999989078 y[1] (closed_form) = 0.001249479686798088 y[1] (numeric) = 0.001249213745100594 absolute error = 2.659416974946666e-07 relative error = 0.02128419535784273 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.05999999999989079 y[1] (closed_form) = 0.001798921552200818 y[1] (numeric) = 0.00179865597247135 absolute error = 2.655797294675005e-07 relative error = 0.01476327464877986 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.0699999999998908 y[1] (closed_form) = 0.002448003078029316 y[1] (numeric) = 0.002447737925511956 absolute error = 2.651525173595799e-07 relative error = 0.01083138006399209 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 4 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.07999999999989081 y[1] (closed_form) = 0.00319659537495081 y[1] (numeric) = 0.00319633071438232 absolute error = 2.646605684907856e-07 relative error = 0.008279451649236595 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.08999999999989082 y[1] (closed_form) = 0.004044550138206295 y[1] (numeric) = 0.004044286033742315 absolute error = 2.641044639806883e-07 relative error = 0.006529884782138346 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.09999999999989083 y[1] (closed_form) = 0.004991699822521241 y[1] (numeric) = 0.004991436337663085 absolute error = 2.634848581557075e-07 relative error = 0.005278459593402091 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1099999999998908 y[1] (closed_form) = 0.006037857838762674 y[1] (numeric) = 0.006037595036287135 absolute error = 2.628024755382818e-07 relative error = 0.004352578059243234 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1199999999998908 y[1] (closed_form) = 0.007182818771775384 y[1] (numeric) = 0.007182556713666063 absolute error = 2.620581093203123e-07 relative error = 0.003648402077887023 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1299999999998908 y[1] (closed_form) = 0.008426358618767086 y[1] (numeric) = 0.008426097366148229 absolute error = 2.612526188577879e-07 relative error = 0.003100421316936704 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1399999999998909 y[1] (closed_form) = 0.009768235047563151 y[1] (numeric) = 0.009767974660635451 absolute error = 2.603869277001403e-07 relative error = 0.002665649694466536 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1499999999998909 y[1] (closed_form) = 0.01120818767399842 y[1] (numeric) = 0.01120792821197822 absolute error = 2.594620202075321e-07 relative error = 0.002314932866528021 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1599999999998909 y[1] (closed_form) = 0.01274593835767268 y[1] (numeric) = 0.01274567987873295 absolute error = 2.584789397346021e-07 relative error = 0.002027931820170818 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1699999999998909 y[1] (closed_form) = 0.01438119151524798 y[1] (numeric) = 0.01438093407646312 absolute error = 2.5743878486785e-07 relative error = 0.001790107478889316 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1799999999998909 y[1] (closed_form) = 0.01611363445043527 y[1] (numeric) = 0.01611337810772802 absolute error = 2.563427072520275e-07 relative error = 0.001590843506103634 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1899999999998909 y[1] (closed_form) = 0.01794293769977776 y[1] (numeric) = 0.01794268250786968 absolute error = 2.55191908080793e-07 relative error = 0.001422241510006211 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1999999999998909 y[1] (closed_form) = 0.019868755393314 y[1] (numeric) = 0.01986850140567894 absolute error = 2.539876350592107e-07 relative error = 0.001278326850531763 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2099999999998909 y[1] (closed_form) = 0.02189072562917598 y[1] (numeric) = 0.02189047289799689 absolute error = 2.527311790921638e-07 relative error = 0.001154512570178685 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2199999999998909 y[1] (closed_form) = 0.02400847086115889 y[1] (numeric) = 0.02400821943728744 absolute error = 2.51423871448081e-07 relative error = 0.001047229841925654 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 5 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2299999999998909 y[1] (closed_form) = 0.02622159829828037 y[1] (numeric) = 0.0262213482312006 absolute error = 2.500670797690729e-07 relative error = 0.000953668334494593 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2399999999998909 y[1] (closed_form) = 0.0285297003153391 y[1] (numeric) = 0.02852945165313396 absolute error = 2.486622051357801e-07 relative error = 0.0008715906665240571 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2499999999998909 y[1] (closed_form) = 0.03093235487347195 y[1] (numeric) = 0.03093210766279299 absolute error = 2.47210678958748e-07 relative error = 0.0007991977331501508 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2599999999998909 y[1] (closed_form) = 0.03342912594970539 y[1] (numeric) = 0.03342888023574647 absolute error = 2.457139589157054e-07 relative error = 0.0007350295645940179 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2699999999998909 y[1] (closed_form) = 0.03601956397450135 y[1] (numeric) = 0.03601931980097488 absolute error = 2.441735264605005e-07 relative error = 0.0006778913998885541 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2799999999998909 y[1] (closed_form) = 0.03870320627629641 y[1] (numeric) = 0.03870296368541347 absolute error = 2.425908829442602e-07 relative error = 0.000626797896826532 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.289999999999891 y[1] (closed_form) = 0.04147957753204712 y[1] (numeric) = 0.04147933656450054 absolute error = 2.40967546576154e-07 relative error = 0.0005809305709297125 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.299999999999891 y[1] (closed_form) = 0.04434819022280219 y[1] (numeric) = 0.04434795091775302 absolute error = 2.393050491655835e-07 relative error = 0.0005396049939430036 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.309999999999891 y[1] (closed_form) = 0.0473085450933395 y[1] (numeric) = 0.04730830748840655 absolute error = 2.376049329441687e-07 relative error = 0.0005022452761448815 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.319999999999891 y[1] (closed_form) = 0.05036013161492365 y[1] (numeric) = 0.05035989574617615 absolute error = 2.358687474987575e-07 relative error = 0.0004683640410281623 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.329999999999891 y[1] (closed_form) = 0.05350242845026136 y[1] (numeric) = 0.05350219435221432 absolute error = 2.340980470375009e-07 relative error = 0.0004375465821240818 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.339999999999891 y[1] (closed_form) = 0.05673490391975466 y[1] (numeric) = 0.05673467162536775 absolute error = 2.322943869065286e-07 relative error = 0.0004094382308906061 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.349999999999891 y[1] (closed_form) = 0.06005701646818168 y[1] (numeric) = 0.06005678600886021 absolute error = 2.304593214666473e-07 relative error = 0.0003837342162821976 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.359999999999891 y[1] (closed_form) = 0.06346821513095843 y[1] (numeric) = 0.06346798653655777 absolute error = 2.285944006585883e-07 relative error = 0.000360171465649244 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.369999999999891 y[1] (closed_form) = 0.06696793999917143 y[1] (numeric) = 0.06696771329800343 absolute error = 2.26701168004606e-07 relative error = 0.000338521937523255 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.379999999999891 y[1] (closed_form) = 0.07055562268259831 y[1] (numeric) = 0.07055539790144043 absolute error = 2.247811578814929e-07 relative error = 0.0003185871647575048 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.389999999999891 y[1] (closed_form) = 0.07423068676997073 y[1] (numeric) = 0.07423046393407763 absolute error = 2.228358930989049e-07 relative error = 0.0003001937645942014 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3999999999998911 y[1] (closed_form) = 0.07799254828576786 y[1] (numeric) = 0.07799232741888518 absolute error = 2.208668826858551e-07 relative error = 0.0002831897245831613 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4099999999998911 y[1] (closed_form) = 0.08184061614286509 y[1] (numeric) = 0.08184039726724536 absolute error = 2.18875619725778e-07 relative error = 0.0002674413146446719 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4199999999998911 y[1] (closed_form) = 0.08577429259039959 y[1] (numeric) = 0.08577407572682007 absolute error = 2.168635795246621e-07 relative error = 0.0002528305078075745 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4299999999998911 y[1] (closed_form) = 0.08979297365625187 y[1] (numeric) = 0.08979275882403447 absolute error = 2.148322174044814e-07 relative error = 0.0002392528152892102 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4399999999998911 y[1] (closed_form) = 0.09389604958358103 y[1] (numeric) = 0.09389583680061359 absolute error = 2.12782967440317e-07 relative error = 0.0002266154629337302 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4499999999998911 y[1] (closed_form) = 0.09808290526088768 y[1] (numeric) = 0.09808269454364744 absolute error = 2.107172402399105e-07 relative error = 0.0002148358469597023 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4599999999998911 y[1] (closed_form) = 0.1023529206451202 y[1] (numeric) = 0.1023527120086983 absolute error = 2.08636421986097e-07 relative error = 0.0002038402232892647 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4699999999998911 y[1] (closed_form) = 0.1067054711773737 y[1] (numeric) = 0.106705264635501 absolute error = 2.065418727020818e-07 relative error = 0.0001935625890810722 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4799999999998911 y[1] (closed_form) = 0.1111399281907716 y[1] (numeric) = 0.1111397237558462 absolute error = 2.044349253216282e-07 relative error = 0.0001839437263003409 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4899999999998911 y[1] (closed_form) = 0.1156556593101556 y[1] (numeric) = 0.1156554569932715 absolute error = 2.023168840931122e-07 relative error = 0.0001749303798014379 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4999999999998911 y[1] (closed_form) = 0.1202520288432477 y[1] (numeric) = 0.1202518286542237 absolute error = 2.001890240244109e-07 relative error = 0.0001664745501178725 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5099999999998911 y[1] (closed_form) = 0.1249283981629805 y[1] (numeric) = 0.1249282001103907 absolute error = 1.980525897726793e-07 relative error = 0.0001585328817826524 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5199999999998911 y[1] (closed_form) = 0.1296841260807307 y[1] (numeric) = 0.1296839301719357 absolute error = 1.95908794964339e-07 relative error = 0.0001510661334467276 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5299999999998911 y[1] (closed_form) = 0.1345185692102211 y[1] (numeric) = 0.1345183754513996 absolute error = 1.937588215150665e-07 relative error = 0.0001440387172214616 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5399999999998911 y[1] (closed_form) = 0.1394310823218927 y[1] (numeric) = 0.1394308907180739 absolute error = 1.916038188387592e-07 relative error = 0.0001374182970167438 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5499999999998911 y[1] (closed_form) = 0.1444210186875762 y[1] (numeric) = 0.1444208292426725 absolute error = 1.894449037642687e-07 relative error = 0.0001311754379562243 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5599999999998911 y[1] (closed_form) = 0.1494877304153256 y[1] (numeric) = 0.1494875431321656 absolute error = 1.872831599247782e-07 relative error = 0.0001252832987727117 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5699999999998911 y[1] (closed_form) = 0.1546305687743043 y[1] (numeric) = 0.154630383654667 absolute error = 1.851196373414687e-07 relative error = 0.0001197173617149825 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5799999999998912 y[1] (closed_form) = 0.1598488845096445 y[1] (numeric) = 0.1598487015542917 absolute error = 1.829553527565864e-07 relative error = 0.0001144551951787613 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5899999999998912 y[1] (closed_form) = 0.1651420281472205 y[1] (numeric) = 0.1651418473559313 absolute error = 1.80791289161597e-07 relative error = 0.0001094762436854812 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5999999999998912 y[1] (closed_form) = 0.1705093502883114 y[1] (numeric) = 0.1705091716599159 absolute error = 1.786283954641199e-07 relative error = 0.000104761642198554 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6099999999998912 y[1] (closed_form) = 0.1759502018941447 y[1] (numeric) = 0.1759500254265573 absolute error = 1.764675873483501e-07 relative error = 0.0001002940522083156 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 6 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6199999999998912 y[1] (closed_form) = 0.1814639345603374 y[1] (numeric) = 0.1814637602505907 absolute error = 1.743097466921917e-07 relative error = 9.605751529333952e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6299999999998912 y[1] (closed_form) = 0.1870499007812732 y[1] (numeric) = 0.187049728625551 absolute error = 1.721557221501246e-07 relative error = 9.203732342602788e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6399999999998912 y[1] (closed_form) = 0.1927074542044727 y[1] (numeric) = 0.1927072841981435 absolute error = 1.700063291809606e-07 relative error = 8.821990300415415e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6499999999998912 y[1] (closed_form) = 0.1984359498750322 y[1] (numeric) = 0.1984357820126817 absolute error = 1.678623504641763e-07 relative error = 8.45927114365567e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6599999999998912 y[1] (closed_form) = 0.2042347444702238 y[1] (numeric) = 0.2042345787456875 absolute error = 1.657245363162474e-07 relative error = 8.114414457056743e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6699999999998912 y[1] (closed_form) = 0.2101031965243653 y[1] (numeric) = 0.2101030329307602 absolute error = 1.635936051624931e-07 relative error = 7.786345370691275e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6799999999998912 y[1] (closed_form) = 0.2160406666440816 y[1] (numeric) = 0.2160405051738383 absolute error = 1.614702432872761e-07 relative error = 7.474067072441132e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6899999999998913 y[1] (closed_form) = 0.2220465177140959 y[1] (numeric) = 0.2220463583589894 absolute error = 1.593551064715815e-07 relative error = 7.176654158421208e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6999999999998913 y[1] (closed_form) = 0.2281201150936957 y[1] (numeric) = 0.228119957844876 absolute error = 1.572488196877053e-07 relative error = 6.893246552287534e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7099999999998913 y[1] (closed_form) = 0.2342608268040342 y[1] (numeric) = 0.2342606716520561 absolute error = 1.551519781262112e-07 relative error = 6.623044076250964e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7199999999998913 y[1] (closed_form) = 0.2404680237064339 y[1] (numeric) = 0.2404678706412866 absolute error = 1.530651473347078e-07 relative error = 6.365301505599407e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7299999999998913 y[1] (closed_form) = 0.2467410796718715 y[1] (numeric) = 0.2467409286830075 absolute error = 1.509888640505164e-07 relative error = 6.119324121111443e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7399999999998913 y[1] (closed_form) = 0.2530793717418262 y[1] (numeric) = 0.2530792228181892 absolute error = 1.48923637033338e-07 relative error = 5.884463676686357e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7499999999998913 y[1] (closed_form) = 0.2594822802806837 y[1] (numeric) = 0.2594821334107363 absolute error = 1.468699473705648e-07 relative error = 5.660114718110795e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7599999999998913 y[1] (closed_form) = 0.2659491891198926 y[1] (numeric) = 0.2659490442916431 absolute error = 1.448282494487252e-07 relative error = 5.445711262666612e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7699999999998913 y[1] (closed_form) = 0.2724794856940749 y[1] (numeric) = 0.2724793428951034 absolute error = 1.427989714808398e-07 relative error = 5.240723760069286e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7799999999998913 y[1] (closed_form) = 0.279072561169295 y[1] (numeric) = 0.2790724203867786 absolute error = 1.407825163668441e-07 relative error = 5.044656335147211e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7899999999998913 y[1] (closed_form) = 0.2857278105636958 y[1] (numeric) = 0.2857276717844339 absolute error = 1.387792618601225e-07 relative error = 4.857044247332205e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7999999999998914 y[1] (closed_form) = 0.2924446328607153 y[1] (numeric) = 0.2924444960711532 absolute error = 1.367895621218196e-07 relative error = 4.677451618233983e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8099999999998914 y[1] (closed_form) = 0.2992224311150922 y[1] (numeric) = 0.2992222963013446 absolute error = 1.348137476098188e-07 relative error = 4.50546929611585e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8199999999998914 y[1] (closed_form) = 0.3060606125518781 y[1] (numeric) = 0.3060604796997516 absolute error = 1.328521264665206e-07 relative error = 4.34071295090288e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8299999999998914 y[1] (closed_form) = 0.312958588658667 y[1] (numeric) = 0.3129584577536823 absolute error = 1.309049847408872e-07 relative error = 4.182821289613518e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8399999999998914 y[1] (closed_form) = 0.3199157752712591 y[1] (numeric) = 0.3199156462986718 absolute error = 1.289725873321323e-07 relative error = 4.031454442119195e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8499999999998914 y[1] (closed_form) = 0.3269315926529703 y[1] (numeric) = 0.3269314655977915 absolute error = 1.270551787668772e-07 relative error = 3.886292472864288e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8599999999998914 y[1] (closed_form) = 0.3340054655677998 y[1] (numeric) = 0.3340053404148163 absolute error = 1.251529834767062e-07 relative error = 3.747033997301502e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8699999999998914 y[1] (closed_form) = 0.3411368233476677 y[1] (numeric) = 0.3411367000814604 absolute error = 1.232662073524793e-07 relative error = 3.613394946427498e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8799999999998914 y[1] (closed_form) = 0.3483250999539287 y[1] (numeric) = 0.3483249785588914 absolute error = 1.213950373002426e-07 relative error = 3.485107369991394e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8899999999998914 y[1] (closed_form) = 0.3555697340333725 y[1] (numeric) = 0.3555696144937294 absolute error = 1.195396430730966e-07 relative error = 3.361918398315562e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8999999999998914 y[1] (closed_form) = 0.3628701689689092 y[1] (numeric) = 0.3628700512687325 absolute error = 1.177001766605734e-07 relative error = 3.243589215256159e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9099999999998915 y[1] (closed_form) = 0.3702258529251461 y[1] (numeric) = 0.3702257370483718 absolute error = 1.158767743980604e-07 relative error = 3.129894184388276e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9199999999998915 y[1] (closed_form) = 0.3776362388890487 y[1] (numeric) = 0.3776361248194923 absolute error = 1.140695563561778e-07 relative error = 3.020619967293233e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9299999999998915 y[1] (closed_form) = 0.3851007847058829 y[1] (numeric) = 0.3851006724272551 absolute error = 1.122786277840682e-07 relative error = 2.915564762347081e-05 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9399999999998915 y[1] (closed_form) = 0.3926189531106281 y[1] (numeric) = 0.3926188426065488 absolute error = 1.105040792759304e-07 relative error = 2.814537566269597e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9499999999998915 y[1] (closed_form) = 0.4001902117550479 y[1] (numeric) = 0.40019010300906 absolute error = 1.087459879367536e-07 relative error = 2.717357515063758e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9599999999998915 y[1] (closed_form) = 0.4078140332305997 y[1] (numeric) = 0.407813926226183 absolute error = 1.070044167716944e-07 relative error = 2.623853228493203e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9699999999998915 y[1] (closed_form) = 0.4154898950873653 y[1] (numeric) = 0.4154897898079483 absolute error = 1.052794170175453e-07 relative error = 2.533862273483405e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9799999999998915 y[1] (closed_form) = 0.4232172798491722 y[1] (numeric) = 0.4232171762781451 absolute error = 1.03571027088023e-07 relative error = 2.447230583896151e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9899999999998915 y[1] (closed_form) = 0.430995675025079 y[1] (numeric) = 0.430995573145805 absolute error = 1.018792739615471e-07 relative error = 2.363811979218095e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9999999999998915 y[1] (closed_form) = 0.4388245731173905 y[1] (numeric) = 0.4388244729132165 absolute error = 1.002041740694182e-07 relative error = 2.28346770459029e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.009999999999891 y[1] (closed_form) = 0.4467034716263594 y[1] (numeric) = 0.4467033730806276 absolute error = 9.854573179701731e-08 relative error = 2.206065948810106e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999889 y[1] (closed_form) = 0.4546318730517405 y[1] (numeric) = 0.4546317761477968 absolute error = 9.690394364714194e-08 relative error = 2.131481521448751e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999888 y[1] (closed_form) = 0.4626092848913366 y[1] (numeric) = 0.4626091896125412 absolute error = 9.52787953534262e-08 relative error = 2.059595396486832e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999887 y[1] (closed_form) = 0.4706352196366965 y[1] (numeric) = 0.4706351259664323 absolute error = 9.367026415629809e-08 relative error = 1.99029439888936e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999886 y[1] (closed_form) = 0.4787091947660999 y[1] (numeric) = 0.4787091026877818 absolute error = 9.207831808133449e-08 relative error = 1.923470848023391e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999885 y[1] (closed_form) = 0.486830732734973 y[1] (numeric) = 0.4868306422320554 absolute error = 9.050291766010687e-08 relative error = 1.859022275600172e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999884 y[1] (closed_form) = 0.4949993609638655 y[1] (numeric) = 0.4949992720198502 absolute error = 8.89440153750698e-08 relative error = 1.796851115158563e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999883 y[1] (closed_form) = 0.5032146118241212 y[1] (numeric) = 0.503214524422565 absolute error = 8.740155621467238e-08 relative error = 1.736864434398025e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999882 y[1] (closed_form) = 0.5114760226213677 y[1] (numeric) = 0.5114759367458889 absolute error = 8.587547883909252e-08 relative error = 1.678973696537558e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.099999999999881 y[1] (closed_form) = 0.5197831355769449 y[1] (numeric) = 0.5197830512112297 absolute error = 8.436571519165881e-08 relative error = 1.623094506481346e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.10999999999988 y[1] (closed_form) = 0.5281354978073902 y[1] (numeric) = 0.5281354149351999 absolute error = 8.287219033231707e-08 relative error = 1.569146377707419e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999878 y[1] (closed_form) = 0.5365326613020959 y[1] (numeric) = 0.536532579907271 absolute error = 8.139482488012106e-08 relative error = 1.517052562701146e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999877 y[1] (closed_form) = 0.5449741828992405 y[1] (numeric) = 0.5449741029657071 absolute error = 7.993353334789788e-08 relative error = 1.466739817336937e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999876 y[1] (closed_form) = 0.5534596242601073 y[1] (numeric) = 0.5534595457718816 absolute error = 7.848822569656022e-08 relative error = 1.418138239107997e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999875 y[1] (closed_form) = 0.5619885518418839 y[1] (numeric) = 0.561988474783078 absolute error = 7.705880589181646e-08 relative error = 1.371181061238006e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999874 y[1] (closed_form) = 0.570560536869045 y[1] (numeric) = 0.5705604612238699 absolute error = 7.564517501279511e-08 relative error = 1.32580454000374e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999873 y[1] (closed_form) = 0.5791751553034055 y[1] (numeric) = 0.5791750810561764 absolute error = 7.424722903159875e-08 relative error = 1.281947755385049e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999872 y[1] (closed_form) = 0.5878319878129403 y[1] (numeric) = 0.58783191494808 absolute error = 7.28648603676163e-08 relative error = 1.239552489117066e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.189999999999871 y[1] (closed_form) = 0.5965306197394508 y[1] (numeric) = 0.596530548241493 absolute error = 7.14979577765007e-08 relative error = 1.198563081434599e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.19999999999987 y[1] (closed_form) = 0.6052706410651627 y[1] (numeric) = 0.6052705709187556 absolute error = 7.014640712732501e-08 relative error = 1.158926311110688e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999869 y[1] (closed_form) = 0.6140516463783352 y[1] (numeric) = 0.6140515775682448 absolute error = 6.881009040338171e-08 relative error = 1.120591253345257e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999867 y[1] (closed_form) = 0.6228732348379544 y[1] (numeric) = 0.6228731673490667 absolute error = 6.748888770058414e-08 relative error = 1.083509194581815e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999866 y[1] (closed_form) = 0.6317350101375847 y[1] (numeric) = 0.6317349439549089 absolute error = 6.618267578417658e-08 relative error = 1.047633496990498e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999865 y[1] (closed_form) = 0.640636580468448 y[1] (numeric) = 0.6406365155771181 absolute error = 6.489132986509105e-08 relative error = 1.012919521667668e-05 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 7 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999864 y[1] (closed_form) = 0.6495775584817949 y[1] (numeric) = 0.6495774948670728 absolute error = 6.361472204563512e-08 relative error = 9.793245042873197e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999863 y[1] (closed_form) = 0.6585575612506334 y[1] (numeric) = 0.6585574988979104 absolute error = 6.235272298482641e-08 relative error = 9.468074873579086e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999862 y[1] (closed_form) = 0.6675762102308729 y[1] (numeric) = 0.6675761491256711 absolute error = 6.110520178737033e-08 relative error = 9.153292290963733e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.279999999999861 y[1] (closed_form) = 0.6766331312219434 y[1] (numeric) = 0.6766330713499178 absolute error = 5.987202555957083e-08 relative error = 8.848521125686961e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.28999999999986 y[1] (closed_form) = 0.6857279543269424 y[1] (numeric) = 0.6857278956738825 absolute error = 5.865305996444192e-08 relative error = 8.553400746511965e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999859 y[1] (closed_form) = 0.6948603139123651 y[1] (numeric) = 0.6948602564641955 absolute error = 5.744816966579691e-08 relative error = 8.267585371560332e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999858 y[1] (closed_form) = 0.7040298485674636 y[1] (numeric) = 0.7040297923102449 absolute error = 5.625721877233758e-08 relative error = 7.990743416178716e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999856 y[1] (closed_form) = 0.7132362010632853 y[1] (numeric) = 0.7132361459832153 absolute error = 5.508007006049809e-08 relative error = 7.722556703990246e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999855 y[1] (closed_form) = 0.7224790183114342 y[1] (numeric) = 0.7224789643948502 absolute error = 5.391658408626654e-08 relative error = 7.462719708079478e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999854 y[1] (closed_form) = 0.7317579513226015 y[1] (numeric) = 0.7317578985559784 absolute error = 5.276662307096558e-08 relative error = 7.210939488336763e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999853 y[1] (closed_form) = 0.7410726551648981 y[1] (numeric) = 0.7410726035348503 absolute error = 5.163004779262792e-08 relative error = 6.966934676754411e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999852 y[1] (closed_form) = 0.7504227889220366 y[1] (numeric) = 0.7504227384153184 absolute error = 5.050671825213016e-08 relative error = 6.730435029122953e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.369999999999851 y[1] (closed_form) = 0.7598080156513944 y[1] (numeric) = 0.7598079662549 absolute error = 4.939649445034888e-08 relative error = 6.501181013206415e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.37999999999985 y[1] (closed_form) = 0.7692280023419931 y[1] (numeric) = 0.7692279540427567 absolute error = 4.829923638816069e-08 relative error = 6.278923315468072e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999849 y[1] (closed_form) = 0.7786824198724273 y[1] (numeric) = 0.7786823726576239 absolute error = 4.721480340030837e-08 relative error = 6.063422288131745e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999848 y[1] (closed_form) = 0.7881709429687758 y[1] (numeric) = 0.7881708968257203 absolute error = 4.614305548766851e-08 relative error = 5.854447680329737e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999846 y[1] (closed_form) = 0.7976932501625209 y[1] (numeric) = 0.7976932050786678 absolute error = 4.50838530952069e-08 relative error = 5.651778184912757e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999845 y[1] (closed_form) = 0.8072490237485062 y[1] (numeric) = 0.8072489797114503 absolute error = 4.403705589073326e-08 relative error = 5.455200885377936e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999844 y[1] (closed_form) = 0.8168379497429578 y[1] (numeric) = 0.8168379067404334 absolute error = 4.300252431921336e-08 relative error = 5.264511073799324e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999843 y[1] (closed_form) = 0.826459717841595 y[1] (numeric) = 0.826459675861476 absolute error = 4.198011904765764e-08 relative error = 5.07951181907499e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999842 y[1] (closed_form) = 0.8361140213778518 y[1] (numeric) = 0.8361139804081504 absolute error = 4.09697014092103e-08 relative error = 4.900013677763156e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.459999999999841 y[1] (closed_form) = 0.8458005572812326 y[1] (numeric) = 0.8458005173100992 absolute error = 3.997113340314939e-08 relative error = 4.725834365921186e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.46999999999984 y[1] (closed_form) = 0.8555190260358193 y[1] (numeric) = 0.8555189870515425 absolute error = 3.898427680670835e-08 relative error = 4.556798343497756e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999839 y[1] (closed_form) = 0.8652691316389564 y[1] (numeric) = 0.8652690936299611 absolute error = 3.800899528449975e-08 relative error = 4.39273676763491e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999838 y[1] (closed_form) = 0.8750505815601216 y[1] (numeric) = 0.8750505445149699 absolute error = 3.704515172398004e-08 relative error = 4.233486898315352e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999837 y[1] (closed_form) = 0.8848630867000099 y[1] (numeric) = 0.8848630506073986 absolute error = 3.609261134407404e-08 relative error = 4.078892190957709e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999835 y[1] (closed_form) = 0.8947063613498366 y[1] (numeric) = 0.894706326198598 absolute error = 3.515123858655045e-08 relative error = 3.928801683439251e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999834 y[1] (closed_form) = 0.9045801231508822 y[1] (numeric) = 0.9045800889299827 absolute error = 3.422089955851249e-08 relative error = 3.783070032460188e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999833 y[1] (closed_form) = 0.9144840930542877 y[1] (numeric) = 0.9144840597528261 absolute error = 3.330146158830871e-08 relative error = 3.641557227866597e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999832 y[1] (closed_form) = 0.9244179952811152 y[1] (numeric) = 0.9244179628883227 absolute error = 3.23927925593992e-08 relative error = 3.504128297453638e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.549999999999831 y[1] (closed_form) = 0.9343815572826846 y[1] (numeric) = 0.9343815257879241 absolute error = 3.149476046626631e-08 relative error = 3.370653050757721e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.55999999999983 y[1] (closed_form) = 0.9443745097011993 y[1] (numeric) = 0.9443744790939638 absolute error = 3.060723552383848e-08 relative error = 3.241006106096895e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999829 y[1] (closed_form) = 0.9543965863306679 y[1] (numeric) = 0.9543965566005791 absolute error = 2.973008883522255e-08 relative error = 3.115066552105418e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999828 y[1] (closed_form) = 0.9644475240781331 y[1] (numeric) = 0.9644474952149412 absolute error = 2.886319183659225e-08 relative error = 2.992717707910664e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999827 y[1] (closed_form) = 0.9745270629252171 y[1] (numeric) = 0.9745270349187992 absolute error = 2.800641785150049e-08 relative error = 2.873847111791254e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999826 y[1] (closed_form) = 0.9846349458899888 y[1] (numeric) = 0.9846349187303481 absolute error = 2.715964064758936e-08 relative error = 2.758346203428762e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999824 y[1] (closed_form) = 0.9947709189891618 y[1] (numeric) = 0.9947708926664269 absolute error = 2.632273488067938e-08 relative error = 2.64611021273393e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999823 y[1] (closed_form) = 1.004934731200631 y[1] (numeric) = 1.004934705705053 absolute error = 2.549557720499251e-08 relative error = 2.537038119334582e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999822 y[1] (closed_form) = 1.015126134426348 y[1] (numeric) = 1.015126109748303 absolute error = 2.467804494088455e-08 relative error = 2.431032371640221e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.639999999999821 y[1] (closed_form) = 1.02534488345555 y[1] (numeric) = 1.025344859585533 absolute error = 2.38700172960904e-08 relative error = 2.327998869575009e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.64999999999982 y[1] (closed_form) = 1.035590735928334 y[1] (numeric) = 1.03559071285696 absolute error = 2.30713741444788e-08 relative error = 2.227846710486159e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999819 y[1] (closed_form) = 1.045863452299596 y[1] (numeric) = 1.0458634300176 absolute error = 2.228199558196309e-08 relative error = 2.130488022405839e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999818 y[1] (closed_form) = 1.056162795803323 y[1] (numeric) = 1.056162774301559 absolute error = 2.150176414694727e-08 relative error = 2.035838057578321e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999817 y[1] (closed_form) = 1.066488532417256 y[1] (numeric) = 1.066488511686693 absolute error = 2.073056326601375e-08 relative error = 1.943814924950647e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999816 y[1] (closed_form) = 1.076840430827913 y[1] (numeric) = 1.076840410859636 absolute error = 1.996827725392336e-08 relative error = 1.854339480787422e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999815 y[1] (closed_form) = 1.087218262395985 y[1] (numeric) = 1.087218243181192 absolute error = 1.921479264588299e-08 relative error = 1.767335346587898e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999813 y[1] (closed_form) = 1.097621801122099 y[1] (numeric) = 1.097621782652102 absolute error = 1.846999642118874e-08 relative error = 1.682728641350496e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999812 y[1] (closed_form) = 1.108050823612959 y[1] (numeric) = 1.108050805879183 absolute error = 1.77337762252705e-08 relative error = 1.600447907926008e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.729999999999811 y[1] (closed_form) = 1.118505109047855 y[1] (numeric) = 1.118505092041833 absolute error = 1.700602236809345e-08 relative error = 1.520424201063337e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.73999999999981 y[1] (closed_form) = 1.128984439145547 y[1] (numeric) = 1.128984422858921 absolute error = 1.628662604780118e-08 relative error = 1.442590835009864e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999809 y[1] (closed_form) = 1.139488598131525 y[1] (numeric) = 1.139488582556047 absolute error = 1.557547868458187e-08 relative error = 1.366883241317354e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999808 y[1] (closed_form) = 1.150017372705646 y[1] (numeric) = 1.150017357833171 absolute error = 1.487247458520358e-08 relative error = 1.293239123006734e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999807 y[1] (closed_form) = 1.16057055201014 y[1] (numeric) = 1.160570537832632 absolute error = 1.417750739030055e-08 relative error = 1.221598063620063e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999806 y[1] (closed_form) = 1.171147927597996 y[1] (numeric) = 1.171147914107523 absolute error = 1.349047296095307e-08 relative error = 1.151901706270514e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999805 y[1] (closed_form) = 1.18174929340172 y[1] (numeric) = 1.181749280590451 absolute error = 1.281126871255367e-08 relative error = 1.084093621556214e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999804 y[1] (closed_form) = 1.192374445702465 y[1] (numeric) = 1.192374433562672 absolute error = 1.21397933927625e-08 relative error = 1.018119218884347e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999802 y[1] (closed_form) = 1.203023183099536 y[1] (numeric) = 1.20302317162359 absolute error = 1.147594597128432e-08 relative error = 9.539255878442052e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.819999999999801 y[1] (closed_form) = 1.213695306480258 y[1] (numeric) = 1.213695295660632 absolute error = 1.081962675009152e-08 relative error = 8.914615301157139e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.8299999999998 y[1] (closed_form) = 1.224390618990229 y[1] (numeric) = 1.22439060881949 absolute error = 1.017073958387016e-08 relative error = 8.306776796655056e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999799 y[1] (closed_form) = 1.23510892600392 y[1] (numeric) = 1.235108916474734 absolute error = 9.529185884815661e-09 relative error = 7.715259508039066e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.849999999999798 y[1] (closed_form) = 1.245850035095657 y[1] (numeric) = 1.245850026200786 absolute error = 8.894871061926324e-09 relative error = 7.139600121489238e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.859999999999797 y[1] (closed_form) = 1.256613756010962 y[1] (numeric) = 1.256613747743261 absolute error = 8.267701190334265e-09 relative error = 6.579349581990521e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999796 y[1] (closed_form) = 1.267399900638253 y[1] (numeric) = 1.267399892990671 absolute error = 7.647581679037785e-09 relative error = 6.034071546941515e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999795 y[1] (closed_form) = 1.278208282980905 y[1] (numeric) = 1.278208275946483 absolute error = 7.03442171179347e-09 relative error = 5.503345429266441e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999794 y[1] (closed_form) = 1.289038719129672 y[1] (numeric) = 1.289038712701542 absolute error = 6.428129806224092e-09 relative error = 4.986762391873079e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999793 y[1] (closed_form) = 1.299891027235455 y[1] (numeric) = 1.299891021406838 absolute error = 5.828616922443075e-09 relative error = 4.483927344924514e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.909999999999791 y[1] (closed_form) = 1.310765027482434 y[1] (numeric) = 1.310765022246639 absolute error = 5.235794686697659e-09 relative error = 3.994457112388762e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.91999999999979 y[1] (closed_form) = 1.321660542061535 y[1] (numeric) = 1.321660537411959 absolute error = 4.649576057502713e-09 relative error = 3.51798053246734e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999789 y[1] (closed_form) = 1.332577395144258 y[1] (numeric) = 1.332577391074384 absolute error = 4.069873993373108e-09 relative error = 3.054137049152424e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999788 y[1] (closed_form) = 1.343515412856836 y[1] (numeric) = 1.343515409360232 absolute error = 3.496603451225155e-09 relative error = 2.602577847462143e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.949999999999787 y[1] (closed_form) = 1.354474423254745 y[1] (numeric) = 1.354474420325063 absolute error = 2.929681830465825e-09 relative error = 2.16296578227437e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999786 y[1] (closed_form) = 1.365454256297542 y[1] (numeric) = 1.365454253928516 absolute error = 2.369025420279058e-09 relative error = 1.734972379596751e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999785 y[1] (closed_form) = 1.376454743824047 y[1] (numeric) = 1.376454742009494 absolute error = 1.814553174384059e-09 relative error = 1.318280301278118e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999784 y[1] (closed_form) = 1.387475719527849 y[1] (numeric) = 1.387475718261665 absolute error = 1.26618404650003e-09 relative error = 9.125810482153199e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999783 y[1] (closed_form) = 1.398517018933142 y[1] (numeric) = 1.398517018209303 absolute error = 7.238392107922209e-10 relative error = 5.175762618494276e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.999999999999782 y[1] (closed_form) = 1.409578479370889 y[1] (numeric) = 1.40957847918345 absolute error = 1.874391752920701e-10 relative error = 1.329753383974239e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 Finished! diff ( y , x , 1 ) = arctan ( x ) ; Iterations = 4001 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %