##############ECHO OF PROBLEM################# ##############temp/addpostode.ode################# diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ; ! // BEGIN FIRST INPUT BLOCK max_terms=40; Digits=32; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(-5.0); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(c(2.0) - c(cos(x)) - c(cos(x))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (closed_form) = 1.432675629073548 y[1] (numeric) = 1.432675629073548 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] = -4.989999999999997 y[1] (closed_form) = 1.451882160909152 y[1] (numeric) = 1.451882160909145 absolute error = 6.661338147750939e-15 relative error = 4.588070800167201e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.979999999999993 y[1] (closed_form) = 1.471143504071902 y[1] (numeric) = 1.471143504071889 absolute error = 1.287858708565182e-14 relative error = 8.754133808160686e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.96999999999999 y[1] (closed_form) = 1.490457732443533 y[1] (numeric) = 1.490457732443514 absolute error = 1.953992523340276e-14 relative error = 1.311001634468896e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.959999999999987 y[1] (closed_form) = 1.509822914617303 y[1] (numeric) = 1.509822914617276 absolute error = 2.664535259100376e-14 relative error = 1.764799853879393e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.949999999999983 y[1] (closed_form) = 1.529237114091131 y[1] (numeric) = 1.529237114091098 absolute error = 3.286260152890463e-14 relative error = 2.148953960513561e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.93999999999998 y[1] (closed_form) = 1.548698389461248 y[1] (numeric) = 1.548698389461209 absolute error = 3.952393967665557e-14 relative error = 2.552074693536997e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.929999999999977 y[1] (closed_form) = 1.568204794616337 y[1] (numeric) = 1.568204794616291 absolute error = 4.618527782440651e-14 relative error = 2.945105000505103e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.919999999999973 y[1] (closed_form) = 1.587754378932135 y[1] (numeric) = 1.587754378932083 absolute error = 5.218048215738236e-14 relative error = 3.286432892251068e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.90999999999997 y[1] (closed_form) = 1.607345187466504 y[1] (numeric) = 1.607345187466445 absolute error = 5.88418203051333e-14 relative error = 3.660807943680083e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.899999999999967 y[1] (closed_form) = 1.626975261154915 y[1] (numeric) = 1.626975261154849 absolute error = 6.572520305780927e-14 relative error = 4.039717420850884e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.889999999999963 y[1] (closed_form) = 1.646642637006357 y[1] (numeric) = 1.646642637006285 absolute error = 7.216449660063518e-14 relative error = 4.382523261503314e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.87999999999996 y[1] (closed_form) = 1.666345348299636 y[1] (numeric) = 1.666345348299557 absolute error = 7.882583474838611e-14 relative error = 4.73046207551281e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.869999999999957 y[1] (closed_form) = 1.686081424780039 y[1] (numeric) = 1.686081424779954 absolute error = 8.526512829121202e-14 relative error = 5.056999444871734e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.859999999999953 y[1] (closed_form) = 1.705848892856367 y[1] (numeric) = 1.705848892856275 absolute error = 9.192646643896296e-14 relative error = 5.388898560940895e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.84999999999995 y[1] (closed_form) = 1.725645775798284 y[1] (numeric) = 1.725645775798186 absolute error = 9.836575998178887e-14 relative error = 5.700228943931721e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.839999999999947 y[1] (closed_form) = 1.745470093933994 y[1] (numeric) = 1.745470093933888 absolute error = 1.052491427344648e-13 relative error = 6.029845088737735e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.829999999999943 y[1] (closed_form) = 1.765319864848202 y[1] (numeric) = 1.76531986484809 absolute error = 1.114663916723657e-13 relative error = 6.314231992282634e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.81999999999994 y[1] (closed_form) = 1.785193103580359 y[1] (numeric) = 1.785193103580241 absolute error = 1.181277298201167e-13 relative error = 6.617084145306256e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.809999999999937 y[1] (closed_form) = 1.805087822823154 y[1] (numeric) = 1.805087822823028 absolute error = 1.254552017826427e-13 relative error = 6.950088532890937e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.799999999999933 y[1] (closed_form) = 1.82500203312124 y[1] (numeric) = 1.825002033121108 absolute error = 1.323385845353187e-13 relative error = 7.251421211240209e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.78999999999993 y[1] (closed_form) = 1.844933743070182 y[1] (numeric) = 1.844933743070044 absolute error = 1.387778780781446e-13 relative error = 7.522106341185033e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.779999999999927 y[1] (closed_form) = 1.864880959515597 y[1] (numeric) = 1.864880959515451 absolute error = 1.454392162258955e-13 relative error = 7.798847185595878e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.769999999999923 y[1] (closed_form) = 1.884841687752461 y[1] (numeric) = 1.884841687752308 absolute error = 1.521005543736464e-13 relative error = 8.069672660679292e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.75999999999992 y[1] (closed_form) = 1.904813931724584 y[1] (numeric) = 1.904813931724425 absolute error = 1.585398479164724e-13 relative error = 8.323114676767051e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.749999999999917 y[1] (closed_form) = 1.924795694224214 y[1] (numeric) = 1.924795694224049 absolute error = 1.652011860642233e-13 relative error = 8.582790711759535e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.739999999999913 y[1] (closed_form) = 1.944784977091751 y[1] (numeric) = 1.944784977091579 absolute error = 1.720845688168993e-13 relative error = 8.848513889398513e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.72999999999991 y[1] (closed_form) = 1.964779781415567 y[1] (numeric) = 1.964779781415388 absolute error = 1.785238623597252e-13 relative error = 9.086202130556531e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.719999999999906 y[1] (closed_form) = 1.984778107731891 y[1] (numeric) = 1.984778107731705 absolute error = 1.858513343222512e-13 relative error = 9.36383435499665e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.709999999999903 y[1] (closed_form) = 2.004777956224757 y[1] (numeric) = 2.004777956224565 absolute error = 1.918465386552271e-13 relative error = 9.569465688683929e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.6999999999999 y[1] (closed_form) = 2.024777326925982 y[1] (numeric) = 2.024777326925784 absolute error = 1.980637875931279e-13 relative error = 9.782003431154007e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.689999999999896 y[1] (closed_form) = 2.044774219915162 y[1] (numeric) = 2.044774219914957 absolute error = 2.051692149507289e-13 relative error = 1.00338322418424e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.679999999999893 y[1] (closed_form) = 2.064766635519662 y[1] (numeric) = 2.06476663551945 absolute error = 2.122746423083299e-13 relative error = 1.028080552332755e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.66999999999989 y[1] (closed_form) = 2.084752574514583 y[1] (numeric) = 2.084752574514364 absolute error = 2.193800696659309e-13 relative error = 1.052307464913488e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.659999999999886 y[1] (closed_form) = 2.104730038322679 y[1] (numeric) = 2.104730038322454 absolute error = 2.251532293939817e-13 relative error = 1.069748734015375e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.649999999999883 y[1] (closed_form) = 2.124697029214217 y[1] (numeric) = 2.124697029213985 absolute error = 2.318145675417327e-13 relative error = 1.091047638107092e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.63999999999988 y[1] (closed_form) = 2.144651550506748 y[1] (numeric) = 2.144651550506509 absolute error = 2.389199948993337e-13 relative error = 1.114027100779521e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.629999999999876 y[1] (closed_form) = 2.164591606764771 y[1] (numeric) = 2.164591606764525 absolute error = 2.451372438372346e-13 relative error = 1.132487269520647e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.619999999999873 y[1] (closed_form) = 2.184515203999276 y[1] (numeric) = 2.184515203999025 absolute error = 2.517985819849855e-13 relative error = 1.152652000425578e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.60999999999987 y[1] (closed_form) = 2.204420349867144 y[1] (numeric) = 2.204420349866886 absolute error = 2.580158309228864e-13 relative error = 1.170447509879123e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.599999999999866 y[1] (closed_form) = 2.224305053870374 y[1] (numeric) = 2.22430505387011 absolute error = 2.637889906509372e-13 relative error = 1.185938907938614e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.589999999999863 y[1] (closed_form) = 2.244167327555139 y[1] (numeric) = 2.244167327554867 absolute error = 2.713385072183883e-13 relative error = 1.209083226044434e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.57999999999986 y[1] (closed_form) = 2.264005184710618 y[1] (numeric) = 2.264005184710341 absolute error = 2.775557561562891e-13 relative error = 1.225950179048578e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.569999999999856 y[1] (closed_form) = 2.283816641567632 y[1] (numeric) = 2.283816641567347 absolute error = 2.851052727237402e-13 relative error = 1.248371990704304e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.559999999999853 y[1] (closed_form) = 2.303599716997001 y[1] (numeric) = 2.303599716996709 absolute error = 2.913225216616411e-13 relative error = 1.264640377892616e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.54999999999985 y[1] (closed_form) = 2.32335243270767 y[1] (numeric) = 2.323352432707371 absolute error = 2.984279490192421e-13 relative error = 1.284471287343391e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.539999999999846 y[1] (closed_form) = 2.343072813444526 y[1] (numeric) = 2.343072813444222 absolute error = 3.042011087472929e-13 relative error = 1.298299852235877e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.529999999999843 y[1] (closed_form) = 2.362758887185932 y[1] (numeric) = 2.362758887185622 absolute error = 3.104183576851938e-13 relative error = 1.313796170098867e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.51999999999984 y[1] (closed_form) = 2.382408685340917 y[1] (numeric) = 2.382408685340601 absolute error = 3.166356066230946e-13 relative error = 1.329056633193833e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.509999999999836 y[1] (closed_form) = 2.40202024294604 y[1] (numeric) = 2.402020242945718 absolute error = 3.228528555609955e-13 relative error = 1.344088820687962e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.499999999999833 y[1] (closed_form) = 2.421591598861886 y[1] (numeric) = 2.421591598861556 absolute error = 3.295141937087465e-13 relative error = 1.360733964652064e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.48999999999983 y[1] (closed_form) = 2.441120795969169 y[1] (numeric) = 2.441120795968833 absolute error = 3.366196210663475e-13 relative error = 1.378955198047475e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.479999999999826 y[1] (closed_form) = 2.460605881364456 y[1] (numeric) = 2.460605881364113 absolute error = 3.437250484239485e-13 relative error = 1.396912244367009e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.469999999999823 y[1] (closed_form) = 2.480044906555443 y[1] (numeric) = 2.480044906555092 absolute error = 3.503863865716994e-13 relative error = 1.412822750287834e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.45999999999982 y[1] (closed_form) = 2.49943592765581 y[1] (numeric) = 2.499435927655453 absolute error = 3.566036355096003e-13 relative error = 1.426736455069102e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.449999999999816 y[1] (closed_form) = 2.518777005579607 y[1] (numeric) = 2.518777005579244 absolute error = 3.632649736573512e-13 relative error = 1.442227608290233e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.439999999999813 y[1] (closed_form) = 2.538066206235159 y[1] (numeric) = 2.538066206234789 absolute error = 3.703704010149522e-13 relative error = 1.459262174111451e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.42999999999981 y[1] (closed_form) = 2.557301600718474 y[1] (numeric) = 2.557301600718098 absolute error = 3.75699471533153e-13 relative error = 1.469124609422683e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.419999999999806 y[1] (closed_form) = 2.576481265506134 y[1] (numeric) = 2.576481265505751 absolute error = 3.82804898890754e-13 relative error = 1.485766281384368e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.409999999999803 y[1] (closed_form) = 2.595603282647643 y[1] (numeric) = 2.595603282647253 absolute error = 3.894662370385049e-13 relative error = 1.500484452466982e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.3999999999998 y[1] (closed_form) = 2.61466573995722 y[1] (numeric) = 2.614665739956825 absolute error = 3.952393967665557e-13 relative error = 1.511624949707806e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.389999999999796 y[1] (closed_form) = 2.633666731205023 y[1] (numeric) = 2.63366673120462 absolute error = 4.023448241241567e-13 relative error = 1.527698320204947e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.379999999999793 y[1] (closed_form) = 2.652604356307759 y[1] (numeric) = 2.65260435630735 absolute error = 4.081179838522075e-13 relative error = 1.538555807924102e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.36999999999979 y[1] (closed_form) = 2.671476721518698 y[1] (numeric) = 2.671476721518285 absolute error = 4.134470543704083e-13 relative error = 1.547634875647987e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.359999999999786 y[1] (closed_form) = 2.690281939617048 y[1] (numeric) = 2.690281939616629 absolute error = 4.192202140984591e-13 relative error = 1.558276134278081e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.349999999999783 y[1] (closed_form) = 2.709018130096669 y[1] (numeric) = 2.709018130096243 absolute error = 4.2543746303636e-13 relative error = 1.570448932437298e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.33999999999978 y[1] (closed_form) = 2.727683419354127 y[1] (numeric) = 2.727683419353694 absolute error = 4.329869796038111e-13 relative error = 1.587379886285834e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.329999999999776 y[1] (closed_form) = 2.746275940876051 y[1] (numeric) = 2.746275940875612 absolute error = 4.387601393318619e-13 relative error = 1.597654965407078e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.319999999999773 y[1] (closed_form) = 2.764793835425781 y[1] (numeric) = 2.764793835425337 absolute error = 4.445332990599127e-13 relative error = 1.607835251091892e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.30999999999977 y[1] (closed_form) = 2.783235251229295 y[1] (numeric) = 2.783235251228843 absolute error = 4.511946372076636e-13 relative error = 1.621115703418821e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.299999999999766 y[1] (closed_form) = 2.801598344160379 y[1] (numeric) = 2.801598344159922 absolute error = 4.565237077258644e-13 relative error = 1.629511627451656e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.289999999999763 y[1] (closed_form) = 2.819881277925044 y[1] (numeric) = 2.819881277924581 absolute error = 4.622968674539152e-13 relative error = 1.639419613417511e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.27999999999976 y[1] (closed_form) = 2.838082224245149 y[1] (numeric) = 2.83808222424468 absolute error = 4.685141163918161e-13 relative error = 1.650812342184441e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.269999999999756 y[1] (closed_form) = 2.856199363041227 y[1] (numeric) = 2.856199363040753 absolute error = 4.742872761198669e-13 relative error = 1.660553819376441e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.259999999999753 y[1] (closed_form) = 2.8742308826145 y[1] (numeric) = 2.874230882614019 absolute error = 4.805045250577678e-13 relative error = 1.671767316829761e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.24999999999975 y[1] (closed_form) = 2.892174979828034 y[1] (numeric) = 2.892174979827547 absolute error = 4.862776847858186e-13 relative error = 1.68135637773456e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.239999999999746 y[1] (closed_form) = 2.910029860287062 y[1] (numeric) = 2.910029860286569 absolute error = 4.929390229335695e-13 relative error = 1.693931150537896e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.229999999999743 y[1] (closed_form) = 2.927793738518417 y[1] (numeric) = 2.927793738517918 absolute error = 4.987121826616203e-13 relative error = 1.70337198314383e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.21999999999974 y[1] (closed_form) = 2.945464838149078 y[1] (numeric) = 2.945464838148573 absolute error = 5.053735208093713e-13 relative error = 1.715768303406217e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.209999999999736 y[1] (closed_form) = 2.963041392083809 y[1] (numeric) = 2.963041392083299 absolute error = 5.10702591327572e-13 relative error = 1.723575622979778e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.199999999999733 y[1] (closed_form) = 2.980521642681865 y[1] (numeric) = 2.980521642681348 absolute error = 5.164757510556228e-13 relative error = 1.732836774809994e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.189999999999729 y[1] (closed_form) = 2.99790384193275 y[1] (numeric) = 2.997903841932228 absolute error = 5.222489107836736e-13 relative error = 1.742046904503046e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.179999999999726 y[1] (closed_form) = 3.015186251631026 y[1] (numeric) = 3.015186251630498 absolute error = 5.280220705117245e-13 relative error = 1.751208802527863e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.169999999999723 y[1] (closed_form) = 3.032367143550124 y[1] (numeric) = 3.032367143549591 absolute error = 5.337952302397753e-13 relative error = 1.760325201304081e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.159999999999719 y[1] (closed_form) = 3.049444799615171 y[1] (numeric) = 3.049444799614631 absolute error = 5.395683899678261e-13 relative error = 1.769398777232884e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.149999999999716 y[1] (closed_form) = 3.066417512074789 y[1] (numeric) = 3.066417512074244 absolute error = 5.448974604860268e-13 relative error = 1.776983918009717e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.139999999999713 y[1] (closed_form) = 3.083283583671879 y[1] (numeric) = 3.083283583671328 absolute error = 5.511147094239277e-13 relative error = 1.787427897785534e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.129999999999709 y[1] (closed_form) = 3.100041327813336 y[1] (numeric) = 3.100041327812778 absolute error = 5.577760475716786e-13 relative error = 1.799253585967885e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.119999999999706 y[1] (closed_form) = 3.116689068738708 y[1] (numeric) = 3.116689068738145 absolute error = 5.626610288800293e-13 relative error = 1.805316528118515e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.109999999999703 y[1] (closed_form) = 3.133225141687777 y[1] (numeric) = 3.13322514168721 absolute error = 5.6754601018838e-13 relative error = 1.811379599369165e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.099999999999699 y[1] (closed_form) = 3.14964789306703 y[1] (numeric) = 3.149647893066456 absolute error = 5.737632591262809e-13 relative error = 1.821674290606395e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.089999999999696 y[1] (closed_form) = 3.165955680615012 y[1] (numeric) = 3.165955680614433 absolute error = 5.790923296444817e-13 relative error = 1.829123298188395e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.079999999999693 y[1] (closed_form) = 3.182146873566559 y[1] (numeric) = 3.182146873565974 absolute error = 5.848654893725325e-13 relative error = 1.837958814003496e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.069999999999689 y[1] (closed_form) = 3.198219852815868 y[1] (numeric) = 3.198219852815278 absolute error = 5.893063814710331e-13 relative error = 1.84260747725701e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.059999999999686 y[1] (closed_form) = 3.214173011078408 y[1] (numeric) = 3.214173011077813 absolute error = 5.950795411990839e-13 relative error = 1.851423489488591e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.049999999999683 y[1] (closed_form) = 3.230004753051649 y[1] (numeric) = 3.230004753051048 absolute error = 6.008527009271347e-13 relative error = 1.860222342891168e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.039999999999679 y[1] (closed_form) = 3.245713495574584 y[1] (numeric) = 3.245713495573978 absolute error = 6.066258606551855e-13 relative error = 1.869006187645023e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.029999999999676 y[1] (closed_form) = 3.261297667786054 y[1] (numeric) = 3.261297667785442 absolute error = 6.119549311733863e-13 relative error = 1.876415444128455e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.019999999999673 y[1] (closed_form) = 3.276755711281822 y[1] (numeric) = 3.276755711281205 absolute error = 6.17284001691587e-13 relative error = 1.883826736202174e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -4.009999999999669 y[1] (closed_form) = 3.292086080270422 y[1] (numeric) = 3.2920860802698 absolute error = 6.217248937900877e-13 relative error = 1.88854385526583e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.999999999999666 y[1] (closed_form) = 3.307287241727728 y[1] (numeric) = 3.307287241727102 absolute error = 6.257216966787382e-13 relative error = 1.891948448819525e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.989999999999668 y[1] (closed_form) = 3.322357675550259 y[1] (numeric) = 3.322357675549634 absolute error = 6.24389429049188e-13 relative error = 1.879356439085911e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.979999999999669 y[1] (closed_form) = 3.337295874707195 y[1] (numeric) = 3.337295874706573 absolute error = 6.221689829999377e-13 relative error = 1.864290750230604e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.96999999999967 y[1] (closed_form) = 3.35210034539107 y[1] (numeric) = 3.352100345390448 absolute error = 6.221689829999377e-13 relative error = 1.856057154898067e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.959999999999671 y[1] (closed_form) = 3.366769607167153 y[1] (numeric) = 3.366769607166533 absolute error = 6.199485369506874e-13 relative error = 1.841374995280181e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.949999999999672 y[1] (closed_form) = 3.38130219312149 y[1] (numeric) = 3.381302193120872 absolute error = 6.181721801112872e-13 relative error = 1.828207432535375e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.939999999999673 y[1] (closed_form) = 3.395696650007595 y[1] (numeric) = 3.39569665000698 absolute error = 6.155076448521868e-13 relative error = 1.812610808008454e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.929999999999674 y[1] (closed_form) = 3.409951538391778 y[1] (numeric) = 3.409951538391163 absolute error = 6.146194664324867e-13 relative error = 1.80242874279192e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.919999999999675 y[1] (closed_form) = 3.424065432797076 y[1] (numeric) = 3.424065432796463 absolute error = 6.132871988029365e-13 relative error = 1.791108291706768e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.909999999999676 y[1] (closed_form) = 3.438036921845812 y[1] (numeric) = 3.4380369218452 absolute error = 6.119549311733863e-13 relative error = 1.779954506261789e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.899999999999678 y[1] (closed_form) = 3.451864608400724 y[1] (numeric) = 3.451864608400113 absolute error = 6.106226635438361e-13 relative error = 1.768964698261275e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.889999999999679 y[1] (closed_form) = 3.465547109704678 y[1] (numeric) = 3.46554710970407 absolute error = 6.079581282847357e-13 relative error = 1.754291917089373e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.87999999999968 y[1] (closed_form) = 3.479083057518948 y[1] (numeric) = 3.47908305751834 absolute error = 6.075140390748857e-13 relative error = 1.74619009960666e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.869999999999681 y[1] (closed_form) = 3.49247109826003 y[1] (numeric) = 3.492471098259425 absolute error = 6.052935930256353e-13 relative error = 1.733138445518407e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.859999999999682 y[1] (closed_form) = 3.505709893135009 y[1] (numeric) = 3.505709893134405 absolute error = 6.039613253960852e-13 relative error = 1.722793225357241e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.849999999999683 y[1] (closed_form) = 3.518798118275429 y[1] (numeric) = 3.518798118274825 absolute error = 6.035172361862351e-13 relative error = 1.715123220771814e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.839999999999684 y[1] (closed_form) = 3.531734464869681 y[1] (numeric) = 3.531734464869078 absolute error = 6.021849685566849e-13 relative error = 1.705068641333729e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.829999999999685 y[1] (closed_form) = 3.544517639293888 y[1] (numeric) = 3.544517639293287 absolute error = 6.012967901369848e-13 relative error = 1.696413592278724e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.819999999999686 y[1] (closed_form) = 3.557146363241259 y[1] (numeric) = 3.557146363240659 absolute error = 5.999645225074346e-13 relative error = 1.686645589586449e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.809999999999687 y[1] (closed_form) = 3.569619373849923 y[1] (numeric) = 3.569619373849324 absolute error = 5.986322548778844e-13 relative error = 1.677019850528895e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.799999999999689 y[1] (closed_form) = 3.581935423829215 y[1] (numeric) = 3.581935423828617 absolute error = 5.977440764581843e-13 relative error = 1.668774016643703e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.78999999999969 y[1] (closed_form) = 3.594093281584398 y[1] (numeric) = 3.594093281583802 absolute error = 5.95967719618784e-13 relative error = 1.658186565920351e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.779999999999691 y[1] (closed_form) = 3.606091731339831 y[1] (numeric) = 3.606091731339236 absolute error = 5.941913627793838e-13 relative error = 1.647743338349893e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.769999999999692 y[1] (closed_form) = 3.617929573260533 y[1] (numeric) = 3.617929573259941 absolute error = 5.924150059399835e-13 relative error = 1.637442061665369e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.759999999999693 y[1] (closed_form) = 3.62960562357218 y[1] (numeric) = 3.62960562357159 absolute error = 5.906386491005833e-13 relative error = 1.627280510215017e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.749999999999694 y[1] (closed_form) = 3.641118714679472 y[1] (numeric) = 3.641118714678881 absolute error = 5.906386491005833e-13 relative error = 1.62213510567336e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.739999999999695 y[1] (closed_form) = 3.652467695282888 y[1] (numeric) = 3.652467695282299 absolute error = 5.88862292261183e-13 relative error = 1.6122313498397e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.729999999999696 y[1] (closed_form) = 3.663651430493829 y[1] (numeric) = 3.663651430493241 absolute error = 5.879741138414829e-13 relative error = 1.604885521989271e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.719999999999697 y[1] (closed_form) = 3.674668801948091 y[1] (numeric) = 3.674668801947505 absolute error = 5.853095785823825e-13 relative error = 1.592822673630032e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.709999999999698 y[1] (closed_form) = 3.685518707917712 y[1] (numeric) = 3.685518707917127 absolute error = 5.853095785823825e-13 relative error = 1.588133516524944e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.6999999999997 y[1] (closed_form) = 3.696200063421134 y[1] (numeric) = 3.696200063420551 absolute error = 5.830891325331322e-13 relative error = 1.57753672022135e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.689999999999701 y[1] (closed_form) = 3.706711800331711 y[1] (numeric) = 3.706711800331129 absolute error = 5.81756864903582e-13 relative error = 1.569468834484302e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.679999999999702 y[1] (closed_form) = 3.71705286748451 y[1] (numeric) = 3.717052867483928 absolute error = 5.81756864903582e-13 relative error = 1.565102476729856e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.669999999999703 y[1] (closed_form) = 3.727222230781432 y[1] (numeric) = 3.727222230780852 absolute error = 5.799805080641818e-13 relative error = 1.556066346874589e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.659999999999704 y[1] (closed_form) = 3.737218873294623 y[1] (numeric) = 3.737218873294045 absolute error = 5.777600620149315e-13 relative error = 1.545962603751905e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.649999999999705 y[1] (closed_form) = 3.747041795368163 y[1] (numeric) = 3.747041795367586 absolute error = 5.768718835952313e-13 relative error = 1.539539495685159e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.639999999999706 y[1] (closed_form) = 3.756690014718028 y[1] (numeric) = 3.756690014717453 absolute error = 5.755396159656812e-13 relative error = 1.532039145393476e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.629999999999707 y[1] (closed_form) = 3.766162566530327 y[1] (numeric) = 3.766162566529752 absolute error = 5.755396159656812e-13 relative error = 1.528185801325915e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.619999999999708 y[1] (closed_form) = 3.775458503557768 y[1] (numeric) = 3.775458503557195 absolute error = 5.737632591262809e-13 relative error = 1.519718091420156e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.609999999999709 y[1] (closed_form) = 3.784576896214399 y[1] (numeric) = 3.784576896213826 absolute error = 5.733191699164308e-13 relative error = 1.514883131295086e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.599999999999711 y[1] (closed_form) = 3.79351683266855 y[1] (numeric) = 3.793516832667978 absolute error = 5.728750807065808e-13 relative error = 1.510142450860279e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.589999999999712 y[1] (closed_form) = 3.802277418934027 y[1] (numeric) = 3.802277418933455 absolute error = 5.719869022868806e-13 relative error = 1.504327115740118e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.579999999999713 y[1] (closed_form) = 3.810857778959504 y[1] (numeric) = 3.810857778958932 absolute error = 5.710987238671805e-13 relative error = 1.498609386632923e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.569999999999714 y[1] (closed_form) = 3.819257054716127 y[1] (numeric) = 3.819257054715557 absolute error = 5.702105454474804e-13 relative error = 1.492988131666519e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.559999999999715 y[1] (closed_form) = 3.827474406283321 y[1] (numeric) = 3.827474406282752 absolute error = 5.693223670277803e-13 relative error = 1.487462244275651e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.549999999999716 y[1] (closed_form) = 3.835509011932777 y[1] (numeric) = 3.835509011932209 absolute error = 5.679900993982301e-13 relative error = 1.480872806271964e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.539999999999717 y[1] (closed_form) = 3.843360068210626 y[1] (numeric) = 3.843360068210059 absolute error = 5.6710192097853e-13 relative error = 1.475536798306172e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.529999999999718 y[1] (closed_form) = 3.851026790017782 y[1] (numeric) = 3.851026790017216 absolute error = 5.662137425588298e-13 relative error = 1.470292920388163e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.519999999999719 y[1] (closed_form) = 3.858508410688454 y[1] (numeric) = 3.858508410687888 absolute error = 5.666578317686799e-13 relative error = 1.468592967684043e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.50999999999972 y[1] (closed_form) = 3.865804182066809 y[1] (numeric) = 3.865804182066243 absolute error = 5.653255641391297e-13 relative error = 1.4623750648355e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.499999999999722 y[1] (closed_form) = 3.872913374581788 y[1] (numeric) = 3.872913374581223 absolute error = 5.648814749292796e-13 relative error = 1.458544047580919e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.489999999999723 y[1] (closed_form) = 3.879835277320066 y[1] (numeric) = 3.879835277319502 absolute error = 5.639932965095795e-13 relative error = 1.453652684191142e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.479999999999724 y[1] (closed_form) = 3.886569198097135 y[1] (numeric) = 3.886569198096572 absolute error = 5.631051180898794e-13 relative error = 1.448848815982939e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.469999999999725 y[1] (closed_form) = 3.893114463526531 y[1] (numeric) = 3.893114463525968 absolute error = 5.626610288800293e-13 relative error = 1.445272247069637e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.459999999999726 y[1] (closed_form) = 3.899470419087164 y[1] (numeric) = 3.899470419086602 absolute error = 5.622169396701793e-13 relative error = 1.441777675548543e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.449999999999727 y[1] (closed_form) = 3.905636429188775 y[1] (numeric) = 3.905636429188214 absolute error = 5.608846720406291e-13 relative error = 1.436090333060336e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.439999999999728 y[1] (closed_form) = 3.911611877235493 y[1] (numeric) = 3.911611877234932 absolute error = 5.608846720406291e-13 relative error = 1.433896535862425e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.429999999999729 y[1] (closed_form) = 3.917396165687491 y[1] (numeric) = 3.917396165686931 absolute error = 5.59996493620929e-13 relative error = 1.429512027723781e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.41999999999973 y[1] (closed_form) = 3.922988716120746 y[1] (numeric) = 3.922988716120186 absolute error = 5.595524044110789e-13 relative error = 1.42634212051569e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.409999999999731 y[1] (closed_form) = 3.928388969284874 y[1] (numeric) = 3.928388969284315 absolute error = 5.591083152012288e-13 relative error = 1.423250904054466e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.399999999999733 y[1] (closed_form) = 3.933596385159059 y[1] (numeric) = 3.9335963851585 absolute error = 5.586642259913788e-13 relative error = 1.420237795873378e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.389999999999734 y[1] (closed_form) = 3.938610443006053 y[1] (numeric) = 3.938610443005495 absolute error = 5.577760475716786e-13 relative error = 1.416174703345297e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.379999999999735 y[1] (closed_form) = 3.94343064142425 y[1] (numeric) = 3.943430641423692 absolute error = 5.577760475716786e-13 relative error = 1.414443661598741e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.369999999999736 y[1] (closed_form) = 3.948056498397824 y[1] (numeric) = 3.948056498397267 absolute error = 5.564437799421285e-13 relative error = 1.409411897139621e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.359999999999737 y[1] (closed_form) = 3.952487551344934 y[1] (numeric) = 3.952487551344377 absolute error = 5.568878691519785e-13 relative error = 1.408955403192815e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.349999999999738 y[1] (closed_form) = 3.956723357163977 y[1] (numeric) = 3.956723357163421 absolute error = 5.559996907322784e-13 relative error = 1.405202336740563e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.339999999999739 y[1] (closed_form) = 3.9607634922779 y[1] (numeric) = 3.960763492277345 absolute error = 5.551115123125783e-13 relative error = 1.401526532434595e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.32999999999974 y[1] (closed_form) = 3.964607552676561 y[1] (numeric) = 3.964607552676005 absolute error = 5.551115123125783e-13 relative error = 1.400167620469307e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.319999999999741 y[1] (closed_form) = 3.968255153957121 y[1] (numeric) = 3.968255153956566 absolute error = 5.551115123125783e-13 relative error = 1.398880593046101e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.309999999999742 y[1] (closed_form) = 3.971705931362493 y[1] (numeric) = 3.971705931361938 absolute error = 5.551115123125783e-13 relative error = 1.397665189482312e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.299999999999744 y[1] (closed_form) = 3.97495953981781 y[1] (numeric) = 3.974959539817256 absolute error = 5.537792446830281e-13 relative error = 1.393169513137762e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.289999999999745 y[1] (closed_form) = 3.978015653964942 y[1] (numeric) = 3.978015653964387 absolute error = 5.546674231027282e-13 relative error = 1.394331926647608e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.279999999999746 y[1] (closed_form) = 3.980873968195016 y[1] (numeric) = 3.980873968194463 absolute error = 5.53335155473178e-13 relative error = 1.389984108751044e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.269999999999747 y[1] (closed_form) = 3.983534196678995 y[1] (numeric) = 3.983534196678442 absolute error = 5.52891066263328e-13 relative error = 1.387941056773816e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.259999999999748 y[1] (closed_form) = 3.985996073396245 y[1] (numeric) = 3.985996073395692 absolute error = 5.524469770534779e-13 relative error = 1.385969697112041e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.249999999999749 y[1] (closed_form) = 3.988259352161147 y[1] (numeric) = 3.988259352160595 absolute error = 5.520028878436278e-13 relative error = 1.384069688307783e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.23999999999975 y[1] (closed_form) = 3.99032380664771 y[1] (numeric) = 3.990323806647158 absolute error = 5.515587986337778e-13 relative error = 1.382240703661453e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.229999999999751 y[1] (closed_form) = 3.992189230412206 y[1] (numeric) = 3.992189230411654 absolute error = 5.515587986337778e-13 relative error = 1.381594826297419e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.219999999999752 y[1] (closed_form) = 3.993855436913813 y[1] (numeric) = 3.993855436913261 absolute error = 5.515587986337778e-13 relative error = 1.381018435309181e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.209999999999753 y[1] (closed_form) = 3.995322259533269 y[1] (numeric) = 3.995322259532717 absolute error = 5.520028878436278e-13 relative error = 1.38162293799077e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.199999999999755 y[1] (closed_form) = 3.996589551589535 y[1] (numeric) = 3.996589551588984 absolute error = 5.515587986337778e-13 relative error = 1.380073664092952e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.189999999999756 y[1] (closed_form) = 3.997657186354461 y[1] (numeric) = 3.99765718635391 absolute error = 5.506706202140776e-13 relative error = 1.377483347230793e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.179999999999757 y[1] (closed_form) = 3.998525057065461 y[1] (numeric) = 3.99852505706491 absolute error = 5.506706202140776e-13 relative error = 1.37718436762334e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.169999999999758 y[1] (closed_form) = 3.999193076936185 y[1] (numeric) = 3.999193076935635 absolute error = 5.502265310042276e-13 relative error = 1.37584387754982e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.159999999999759 y[1] (closed_form) = 3.999661179165205 y[1] (numeric) = 3.999661179164655 absolute error = 5.497824417943775e-13 relative error = 1.374572537939642e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.14999999999976 y[1] (closed_form) = 3.999929316942688 y[1] (numeric) = 3.999929316942138 absolute error = 5.502265310042276e-13 relative error = 1.375590635248496e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.139999999999761 y[1] (closed_form) = 3.999997463455078 y[1] (numeric) = 3.999997463454527 absolute error = 5.511147094239277e-13 relative error = 1.377787647264884e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.129999999999762 y[1] (closed_form) = 3.999865611887782 y[1] (numeric) = 3.99986561188723 absolute error = 5.515587986337778e-13 relative error = 1.378943324982019e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.119999999999763 y[1] (closed_form) = 3.999533775425847 y[1] (numeric) = 3.999533775425295 absolute error = 5.520028878436278e-13 relative error = 1.380168086678688e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.109999999999765 y[1] (closed_form) = 3.99900198725264 y[1] (numeric) = 3.999001987252089 absolute error = 5.511147094239277e-13 relative error = 1.378130621541776e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.099999999999766 y[1] (closed_form) = 3.998270300546539 y[1] (numeric) = 3.998270300545987 absolute error = 5.520028878436278e-13 relative error = 1.380604227203379e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.089999999999767 y[1] (closed_form) = 3.997338788475603 y[1] (numeric) = 3.99733878847505 absolute error = 5.52891066263328e-13 relative error = 1.383147877926491e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.079999999999768 y[1] (closed_form) = 3.996207544190263 y[1] (numeric) = 3.99620754418971 absolute error = 5.52891066263328e-13 relative error = 1.383539418684918e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.069999999999769 y[1] (closed_form) = 3.994876680814004 y[1] (numeric) = 3.994876680813451 absolute error = 5.52891066263328e-13 relative error = 1.384000334525144e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.05999999999977 y[1] (closed_form) = 3.993346331432056 y[1] (numeric) = 3.993346331431503 absolute error = 5.53335155473178e-13 relative error = 1.385642790653588e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.049999999999771 y[1] (closed_form) = 3.991616649078081 y[1] (numeric) = 3.991616649077527 absolute error = 5.53335155473178e-13 relative error = 1.386243229547052e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.039999999999772 y[1] (closed_form) = 3.989687806718873 y[1] (numeric) = 3.989687806718319 absolute error = 5.537792446830281e-13 relative error = 1.388026511123078e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.029999999999773 y[1] (closed_form) = 3.987559997237061 y[1] (numeric) = 3.987559997236508 absolute error = 5.53335155473178e-13 relative error = 1.38765349200157e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.019999999999774 y[1] (closed_form) = 3.985233433411819 y[1] (numeric) = 3.985233433411266 absolute error = 5.52891066263328e-13 relative error = 1.387349261972816e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -3.009999999999776 y[1] (closed_form) = 3.982708347897593 y[1] (numeric) = 3.98270834789704 absolute error = 5.53335155473178e-13 relative error = 1.389343901531918e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.999999999999777 y[1] (closed_form) = 3.979984993200828 y[1] (numeric) = 3.979984993200274 absolute error = 5.542233338928781e-13 relative error = 1.392526190022527e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.989999999999778 y[1] (closed_form) = 3.977063641654725 y[1] (numeric) = 3.977063641654171 absolute error = 5.542233338928781e-13 relative error = 1.393549069942175e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.979999999999779 y[1] (closed_form) = 3.973944585392004 y[1] (numeric) = 3.97394458539145 absolute error = 5.537792446830281e-13 relative error = 1.393525331779133e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.96999999999978 y[1] (closed_form) = 3.970628136315693 y[1] (numeric) = 3.970628136315138 absolute error = 5.546674231027282e-13 relative error = 1.396926138788204e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.959999999999781 y[1] (closed_form) = 3.967114626067934 y[1] (numeric) = 3.967114626067379 absolute error = 5.551115123125783e-13 relative error = 1.399282765022561e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.949999999999782 y[1] (closed_form) = 3.963404405996825 y[1] (numeric) = 3.96340440599627 absolute error = 5.551115123125783e-13 relative error = 1.400592660876764e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.939999999999783 y[1] (closed_form) = 3.959497847121282 y[1] (numeric) = 3.959497847120727 absolute error = 5.555556015224283e-13 relative error = 1.403096107064031e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.929999999999784 y[1] (closed_form) = 3.955395340093935 y[1] (numeric) = 3.955395340093381 absolute error = 5.546674231027282e-13 relative error = 1.402305902220018e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.919999999999785 y[1] (closed_form) = 3.951097295162072 y[1] (numeric) = 3.951097295161516 absolute error = 5.559996907322784e-13 relative error = 1.407203237979164e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.909999999999787 y[1] (closed_form) = 3.946604142126599 y[1] (numeric) = 3.946604142126044 absolute error = 5.551115123125783e-13 relative error = 1.406554831246542e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.899999999999788 y[1] (closed_form) = 3.94191633029908 y[1] (numeric) = 3.941916330298524 absolute error = 5.559996907322784e-13 relative error = 1.410480700614195e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.889999999999789 y[1] (closed_form) = 3.937034328456788 y[1] (numeric) = 3.937034328456232 absolute error = 5.559996907322784e-13 relative error = 1.412229725083996e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.87999999999979 y[1] (closed_form) = 3.931958624795841 y[1] (numeric) = 3.931958624795284 absolute error = 5.564437799421285e-13 relative error = 1.415182185369564e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.869999999999791 y[1] (closed_form) = 3.926689726882374 y[1] (numeric) = 3.926689726881817 absolute error = 5.573319583618286e-13 relative error = 1.419343001679755e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.859999999999792 y[1] (closed_form) = 3.921228161601789 y[1] (numeric) = 3.921228161601231 absolute error = 5.577760475716786e-13 relative error = 1.422452416907645e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.849999999999793 y[1] (closed_form) = 3.915574475106061 y[1] (numeric) = 3.915574475105503 absolute error = 5.582201367815287e-13 relative error = 1.425640452839064e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.839999999999794 y[1] (closed_form) = 3.909729232759131 y[1] (numeric) = 3.909729232758571 absolute error = 5.595524044110789e-13 relative error = 1.431179427267391e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.829999999999795 y[1] (closed_form) = 3.903693019080359 y[1] (numeric) = 3.903693019079799 absolute error = 5.60440582830779e-13 relative error = 1.435667661600115e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.819999999999796 y[1] (closed_form) = 3.897466437686085 y[1] (numeric) = 3.897466437685524 absolute error = 5.608846720406291e-13 relative error = 1.439100710700731e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.809999999999798 y[1] (closed_form) = 3.89105011122926 y[1] (numeric) = 3.891050111228698 absolute error = 5.622169396701793e-13 relative error = 1.444897710383287e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.799999999999799 y[1] (closed_form) = 3.884444681337182 y[1] (numeric) = 3.884444681336619 absolute error = 5.622169396701793e-13 relative error = 1.447354733538493e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.7899999999998 y[1] (closed_form) = 3.877650808547335 y[1] (numeric) = 3.877650808546771 absolute error = 5.635492072997295e-13 relative error = 1.453326344026447e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.779999999999801 y[1] (closed_form) = 3.870669172241337 y[1] (numeric) = 3.870669172240773 absolute error = 5.639932965095795e-13 relative error = 1.457095069127273e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.769999999999802 y[1] (closed_form) = 3.863500470577001 y[1] (numeric) = 3.863500470576436 absolute error = 5.648814749292796e-13 relative error = 1.462097595771527e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.759999999999803 y[1] (closed_form) = 3.856145420418518 y[1] (numeric) = 3.856145420417953 absolute error = 5.648814749292796e-13 relative error = 1.464886339447156e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.749999999999804 y[1] (closed_form) = 3.848604757264778 y[1] (numeric) = 3.848604757264211 absolute error = 5.666578317686799e-13 relative error = 1.472372112774205e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.739999999999805 y[1] (closed_form) = 3.840879235175809 y[1] (numeric) = 3.840879235175242 absolute error = 5.666578317686799e-13 relative error = 1.475333633453181e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.729999999999806 y[1] (closed_form) = 3.832969626697384 y[1] (numeric) = 3.832969626696816 absolute error = 5.679900993982301e-13 relative error = 1.48185390106425e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.719999999999807 y[1] (closed_form) = 3.824876722783758 y[1] (numeric) = 3.824876722783189 absolute error = 5.684341886080801e-13 relative error = 1.486150351518707e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.709999999999809 y[1] (closed_form) = 3.81660133271858 y[1] (numeric) = 3.81660133271801 absolute error = 5.697664562376303e-13 relative error = 1.492863431538403e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.69999999999981 y[1] (closed_form) = 3.808144284033959 y[1] (numeric) = 3.808144284033389 absolute error = 5.706546346573305e-13 relative error = 1.498511064955861e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.689999999999811 y[1] (closed_form) = 3.799506422427718 y[1] (numeric) = 3.799506422427145 absolute error = 5.724309914967307e-13 relative error = 1.506593035657964e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.679999999999812 y[1] (closed_form) = 3.790688611678816 y[1] (numeric) = 3.790688611678243 absolute error = 5.728750807065808e-13 relative error = 1.511269163448555e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.669999999999813 y[1] (closed_form) = 3.781691733560983 y[1] (numeric) = 3.781691733560409 absolute error = 5.74207348336131e-13 relative error = 1.518387506946357e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.659999999999814 y[1] (closed_form) = 3.772516687754532 y[1] (numeric) = 3.772516687753956 absolute error = 5.755396159656812e-13 relative error = 1.52561184907111e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.649999999999815 y[1] (closed_form) = 3.763164391756398 y[1] (numeric) = 3.763164391755821 absolute error = 5.764277943853813e-13 relative error = 1.531763522338025e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.639999999999816 y[1] (closed_form) = 3.753635780788386 y[1] (numeric) = 3.753635780787809 absolute error = 5.768718835952313e-13 relative error = 1.536834997544885e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.629999999999817 y[1] (closed_form) = 3.743931807703654 y[1] (numeric) = 3.743931807703076 absolute error = 5.777600620149315e-13 relative error = 1.543190666096297e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.619999999999818 y[1] (closed_form) = 3.734053442891424 y[1] (numeric) = 3.734053442890845 absolute error = 5.790923296444817e-13 relative error = 1.550841032409187e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.60999999999982 y[1] (closed_form) = 3.724001674179944 y[1] (numeric) = 3.724001674179364 absolute error = 5.799805080641818e-13 relative error = 1.557412049745918e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.599999999999821 y[1] (closed_form) = 3.71377750673771 y[1] (numeric) = 3.713777506737128 absolute error = 5.81756864903582e-13 relative error = 1.566482816614973e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.589999999999822 y[1] (closed_form) = 3.703381962972944 y[1] (numeric) = 3.703381962972362 absolute error = 5.822009541134321e-13 relative error = 1.572079142617149e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.579999999999823 y[1] (closed_form) = 3.692816082431363 y[1] (numeric) = 3.692816082430779 absolute error = 5.839773109528323e-13 relative error = 1.581387477516453e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.569999999999824 y[1] (closed_form) = 3.682080921692212 y[1] (numeric) = 3.682080921691628 absolute error = 5.839773109528323e-13 relative error = 1.585998035818419e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.559999999999825 y[1] (closed_form) = 3.671177554262623 y[1] (numeric) = 3.671177554262037 absolute error = 5.861977570020827e-13 relative error = 1.596756758118237e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.549999999999826 y[1] (closed_form) = 3.66010707047025 y[1] (numeric) = 3.660107070469663 absolute error = 5.866418462119327e-13 relative error = 1.602799685683952e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.539999999999827 y[1] (closed_form) = 3.648870577354249 y[1] (numeric) = 3.648870577353661 absolute error = 5.88418203051333e-13 relative error = 1.612603655232923e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.529999999999828 y[1] (closed_form) = 3.637469198554566 y[1] (numeric) = 3.637469198553977 absolute error = 5.88862292261183e-13 relative error = 1.618879116543946e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.519999999999829 y[1] (closed_form) = 3.625904074199582 y[1] (numeric) = 3.625904074198991 absolute error = 5.906386491005833e-13 relative error = 1.628941739808621e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.509999999999831 y[1] (closed_form) = 3.614176360792092 y[1] (numeric) = 3.614176360791501 absolute error = 5.906386491005833e-13 relative error = 1.634227525552011e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.499999999999832 y[1] (closed_form) = 3.602287231093666 y[1] (numeric) = 3.602287231093074 absolute error = 5.919709167301335e-13 relative error = 1.643319587678769e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.489999999999833 y[1] (closed_form) = 3.590237874007365 y[1] (numeric) = 3.590237874006772 absolute error = 5.937472735695337e-13 relative error = 1.653782547023277e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.479999999999834 y[1] (closed_form) = 3.578029494458859 y[1] (numeric) = 3.578029494458262 absolute error = 5.964118088286341e-13 relative error = 1.666872253994193e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.469999999999835 y[1] (closed_form) = 3.565663313275925 y[1] (numeric) = 3.565663313275328 absolute error = 5.968558980384842e-13 relative error = 1.673898642690769e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.459999999999836 y[1] (closed_form) = 3.55314056706638 y[1] (numeric) = 3.553140567065781 absolute error = 5.981881656680343e-13 relative error = 1.683547707660559e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.449999999999837 y[1] (closed_form) = 3.540462508094407 y[1] (numeric) = 3.540462508093807 absolute error = 6.004086117172847e-13 relative error = 1.695847958690697e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.439999999999838 y[1] (closed_form) = 3.52763040415534 y[1] (numeric) = 3.527630404154739 absolute error = 6.008527009271347e-13 relative error = 1.703275661246614e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.429999999999839 y[1] (closed_form) = 3.514645538448877 y[1] (numeric) = 3.514645538448276 absolute error = 6.012967901369848e-13 relative error = 1.710831956050839e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.419999999999841 y[1] (closed_form) = 3.501509209450771 y[1] (numeric) = 3.501509209450168 absolute error = 6.03073146976385e-13 relative error = 1.722323463690047e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.409999999999842 y[1] (closed_form) = 3.488222730782973 y[1] (numeric) = 3.488222730782368 absolute error = 6.048495038157853e-13 relative error = 1.733976154900004e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.399999999999843 y[1] (closed_form) = 3.474787431082278 y[1] (numeric) = 3.474787431081672 absolute error = 6.061817714453355e-13 relative error = 1.744514688936038e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.389999999999844 y[1] (closed_form) = 3.461204653867461 y[1] (numeric) = 3.461204653866853 absolute error = 6.079581282847357e-13 relative error = 1.756492866162707e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.379999999999845 y[1] (closed_form) = 3.447475757404924 y[1] (numeric) = 3.447475757404314 absolute error = 6.092903959142859e-13 relative error = 1.767352227511898e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.369999999999846 y[1] (closed_form) = 3.433602114572871 y[1] (numeric) = 3.433602114572261 absolute error = 6.10178574333986e-13 relative error = 1.777080028417592e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.359999999999847 y[1] (closed_form) = 3.419585112724025 y[1] (numeric) = 3.419585112723414 absolute error = 6.115108419635362e-13 relative error = 1.78826033511536e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.349999999999848 y[1] (closed_form) = 3.405426153546892 y[1] (numeric) = 3.405426153546278 absolute error = 6.137312880127865e-13 relative error = 1.802215817757669e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.339999999999849 y[1] (closed_form) = 3.391126652925587 y[1] (numeric) = 3.391126652924973 absolute error = 6.141753772226366e-13 relative error = 1.811124856374138e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.32999999999985 y[1] (closed_form) = 3.37668804079826 y[1] (numeric) = 3.376688040797644 absolute error = 6.159517340620368e-13 relative error = 1.824129817797512e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.319999999999852 y[1] (closed_form) = 3.362111761014088 y[1] (numeric) = 3.36211176101347 absolute error = 6.177280909014371e-13 relative error = 1.837321703770837e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.309999999999853 y[1] (closed_form) = 3.347399271188904 y[1] (numeric) = 3.347399271188285 absolute error = 6.186162693211372e-13 relative error = 1.848050439173998e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.299999999999854 y[1] (closed_form) = 3.33255204255943 y[1] (numeric) = 3.33255204255881 absolute error = 6.208367153703875e-13 relative error = 1.862946797054606e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.289999999999855 y[1] (closed_form) = 3.317571559836157 y[1] (numeric) = 3.317571559835534 absolute error = 6.226130722097878e-13 relative error = 1.876713315689674e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.279999999999856 y[1] (closed_form) = 3.302459321054872 y[1] (numeric) = 3.302459321054248 absolute error = 6.23945339839338e-13 relative error = 1.889335429088759e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.269999999999857 y[1] (closed_form) = 3.287216837426862 y[1] (numeric) = 3.287216837426236 absolute error = 6.261657858885883e-13 relative error = 1.904850871896643e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.259999999999858 y[1] (closed_form) = 3.271845633187786 y[1] (numeric) = 3.271845633187158 absolute error = 6.279421427279885e-13 relative error = 1.919229123643524e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.249999999999859 y[1] (closed_form) = 3.256347245445259 y[1] (numeric) = 3.256347245444629 absolute error = 6.297184995673888e-13 relative error = 1.933818638194047e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.23999999999986 y[1] (closed_form) = 3.240723224025141 y[1] (numeric) = 3.240723224024508 absolute error = 6.328271240363392e-13 relative error = 1.952734251863497e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.229999999999861 y[1] (closed_form) = 3.224975131316551 y[1] (numeric) = 3.224975131315917 absolute error = 6.337153024560394e-13 relative error = 1.965023842516683e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.219999999999863 y[1] (closed_form) = 3.20910454211564 y[1] (numeric) = 3.209104542115004 absolute error = 6.363798377151397e-13 relative error = 1.983044894185961e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.209999999999864 y[1] (closed_form) = 3.193113043468101 y[1] (numeric) = 3.193113043467464 absolute error = 6.368239269249898e-13 relative error = 1.994366996269331e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.199999999999865 y[1] (closed_form) = 3.177002234510473 y[1] (numeric) = 3.177002234509833 absolute error = 6.399325513939402e-13 relative error = 2.01426534877003e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.189999999999866 y[1] (closed_form) = 3.160773726310225 y[1] (numeric) = 3.160773726309585 absolute error = 6.403766406037903e-13 relative error = 2.02601228703373e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.179999999999867 y[1] (closed_form) = 3.144429141704655 y[1] (numeric) = 3.144429141704013 absolute error = 6.417089082333405e-13 relative error = 2.040780311193331e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.169999999999868 y[1] (closed_form) = 3.127970115138602 y[1] (numeric) = 3.127970115137957 absolute error = 6.448175327022909e-13 relative error = 2.061456820132435e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.159999999999869 y[1] (closed_form) = 3.111398292501008 y[1] (numeric) = 3.111398292500361 absolute error = 6.465938895416912e-13 relative error = 2.078145671996064e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.14999999999987 y[1] (closed_form) = 3.094715330960325 y[1] (numeric) = 3.094715330959676 absolute error = 6.483702463810914e-13 relative error = 2.095088488090098e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.139999999999871 y[1] (closed_form) = 3.077922898798806 y[1] (numeric) = 3.077922898798155 absolute error = 6.514788708500419e-13 relative error = 2.116618551765182e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.129999999999872 y[1] (closed_form) = 3.061022675245674 y[1] (numeric) = 3.06102267524502 absolute error = 6.541434061091422e-13 relative error = 2.13700934461925e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.119999999999874 y[1] (closed_form) = 3.044016350309199 y[1] (numeric) = 3.044016350308543 absolute error = 6.554756737386924e-13 relative error = 2.153325075511214e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.109999999999875 y[1] (closed_form) = 3.026905624607704 y[1] (numeric) = 3.026905624607046 absolute error = 6.572520305780927e-13 relative error = 2.171366114737306e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.099999999999876 y[1] (closed_form) = 3.009692209199501 y[1] (numeric) = 3.009692209198841 absolute error = 6.59916565837193e-13 relative error = 2.192638050562365e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.089999999999877 y[1] (closed_form) = 2.992377825411785 y[1] (numeric) = 2.992377825411123 absolute error = 6.616929226765933e-13 relative error = 2.211261282106102e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.079999999999878 y[1] (closed_form) = 2.974964204668505 y[1] (numeric) = 2.974964204667842 absolute error = 6.634692795159935e-13 relative error = 2.230175672281485e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.069999999999879 y[1] (closed_form) = 2.957453088317227 y[1] (numeric) = 2.957453088316562 absolute error = 6.656897255652439e-13 relative error = 2.25088853715011e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.05999999999988 y[1] (closed_form) = 2.939846227454993 y[1] (numeric) = 2.939846227454325 absolute error = 6.679101716144942e-13 relative error = 2.271922134487626e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.049999999999881 y[1] (closed_form) = 2.922145382753215 y[1] (numeric) = 2.922145382752545 absolute error = 6.701306176637445e-13 relative error = 2.293282947586798e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.039999999999882 y[1] (closed_form) = 2.904352324281614 y[1] (numeric) = 2.904352324280941 absolute error = 6.727951529228449e-13 relative error = 2.316506669311408e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.029999999999883 y[1] (closed_form) = 2.886468831331209 y[1] (numeric) = 2.886468831330535 absolute error = 6.741274205523951e-13 relative error = 2.335474449732736e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.019999999999885 y[1] (closed_form) = 2.868496692236393 y[1] (numeric) = 2.868496692235716 absolute error = 6.767919558114954e-13 relative error = 2.359395977841765e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -2.009999999999886 y[1] (closed_form) = 2.850437704196098 y[1] (numeric) = 2.850437704195419 absolute error = 6.794564910705958e-13 relative error = 2.383691775022395e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.999999999999887 y[1] (closed_form) = 2.832293673094079 y[1] (numeric) = 2.832293673093398 absolute error = 6.812328479099961e-13 relative error = 2.405233801782277e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.989999999999888 y[1] (closed_form) = 2.814066413318326 y[1] (numeric) = 2.814066413317643 absolute error = 6.825651155395462e-13 relative error = 2.425547287402754e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.979999999999889 y[1] (closed_form) = 2.795757747579628 y[1] (numeric) = 2.795757747578944 absolute error = 6.847855615887966e-13 relative error = 2.449373741990471e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.96999999999989 y[1] (closed_form) = 2.777369506729301 y[1] (numeric) = 2.777369506728615 absolute error = 6.865619184281968e-13 relative error = 2.471986232889512e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.959999999999891 y[1] (closed_form) = 2.758903529576108 y[1] (numeric) = 2.758903529575419 absolute error = 6.883382752675971e-13 relative error = 2.494970439844836e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.949999999999892 y[1] (closed_form) = 2.740361662702374 y[1] (numeric) = 2.740361662701683 absolute error = 6.905587213168474e-13 relative error = 2.519954685966017e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.939999999999893 y[1] (closed_form) = 2.721745760279336 y[1] (numeric) = 2.721745760278644 absolute error = 6.918909889463976e-13 relative error = 2.542085300705632e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.929999999999894 y[1] (closed_form) = 2.703057683881722 y[1] (numeric) = 2.703057683881029 absolute error = 6.936673457857978e-13 relative error = 2.566232122688768e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.919999999999896 y[1] (closed_form) = 2.6842993023016 y[1] (numeric) = 2.684299302300905 absolute error = 6.954437026251981e-13 relative error = 2.590783010035071e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.909999999999897 y[1] (closed_form) = 2.665472491361496 y[1] (numeric) = 2.665472491360798 absolute error = 6.981082378842984e-13 relative error = 2.619078756756225e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.899999999999898 y[1] (closed_form) = 2.646579133726814 y[1] (numeric) = 2.646579133726113 absolute error = 7.003286839335487e-13 relative error = 2.646165667252776e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.889999999999899 y[1] (closed_form) = 2.627621118717572 y[1] (numeric) = 2.627621118716871 absolute error = 7.016609515630989e-13 relative error = 2.670327721774246e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.8799999999999 y[1] (closed_form) = 2.608600342119476 y[1] (numeric) = 2.608600342118772 absolute error = 7.034373084024992e-13 relative error = 2.696608204194896e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.869999999999901 y[1] (closed_form) = 2.589518705994333 y[1] (numeric) = 2.589518705993628 absolute error = 7.056577544517495e-13 relative error = 2.725053705224301e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.859999999999902 y[1] (closed_form) = 2.570378118489854 y[1] (numeric) = 2.570378118489146 absolute error = 7.078782005009998e-13 relative error = 2.753984697461133e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.849999999999903 y[1] (closed_form) = 2.55118049364884 y[1] (numeric) = 2.55118049364813 absolute error = 7.096545573404001e-13 relative error = 2.781671305135345e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.839999999999904 y[1] (closed_form) = 2.531927751217776 y[1] (numeric) = 2.531927751217063 absolute error = 7.132072710192006e-13 relative error = 2.81685474901948e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.829999999999905 y[1] (closed_form) = 2.512621816454862 y[1] (numeric) = 2.512621816454147 absolute error = 7.149836278586008e-13 relative error = 2.845568016548523e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.819999999999907 y[1] (closed_form) = 2.493264619937487 y[1] (numeric) = 2.493264619936769 absolute error = 7.176481631177012e-13 relative error = 2.878347357833581e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.809999999999908 y[1] (closed_form) = 2.47385809736917 y[1] (numeric) = 2.47385809736845 absolute error = 7.198686091669515e-13 relative error = 2.909902592765921e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.799999999999909 y[1] (closed_form) = 2.454404189385997 y[1] (numeric) = 2.454404189385273 absolute error = 7.23421322845752e-13 relative error = 2.947441688594598e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.78999999999991 y[1] (closed_form) = 2.434904841362553 y[1] (numeric) = 2.434904841361829 absolute error = 7.247535904753022e-13 relative error = 2.976517103106731e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.779999999999911 y[1] (closed_form) = 2.415362003217393 y[1] (numeric) = 2.415362003216666 absolute error = 7.274181257344026e-13 relative error = 3.011631899340315e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.769999999999912 y[1] (closed_form) = 2.395777629218045 y[1] (numeric) = 2.395777629217317 absolute error = 7.287503933639528e-13 relative error = 3.041811495676285e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.759999999999913 y[1] (closed_form) = 2.37615367778559 y[1] (numeric) = 2.376153677784859 absolute error = 7.309708394132031e-13 relative error = 3.076277625672836e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.749999999999914 y[1] (closed_form) = 2.356492111298816 y[1] (numeric) = 2.356492111298082 absolute error = 7.340794638821535e-13 relative error = 3.115136521622195e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.739999999999915 y[1] (closed_form) = 2.336794895897987 y[1] (numeric) = 2.33679489589725 absolute error = 7.367439991412539e-13 relative error = 3.152797023112877e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.729999999999916 y[1] (closed_form) = 2.31706400128823 y[1] (numeric) = 2.317064001287492 absolute error = 7.380762667708041e-13 relative error = 3.185394388590267e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.719999999999918 y[1] (closed_form) = 2.297301400542564 y[1] (numeric) = 2.297301400541824 absolute error = 7.402967128200544e-13 relative error = 3.222462288340638e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.709999999999919 y[1] (closed_form) = 2.277509069904594 y[1] (numeric) = 2.277509069903852 absolute error = 7.425171588693047e-13 relative error = 3.260216034618949e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.69999999999992 y[1] (closed_form) = 2.25768898859089 y[1] (numeric) = 2.257688988590147 absolute error = 7.434053372890048e-13 relative error = 3.292771241060057e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.689999999999921 y[1] (closed_form) = 2.237843138593067 y[1] (numeric) = 2.237843138592321 absolute error = 7.465139617579553e-13 relative error = 3.335863666598584e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.679999999999922 y[1] (closed_form) = 2.217973504479588 y[1] (numeric) = 2.217973504478838 absolute error = 7.496225862269057e-13 relative error = 3.379763485510134e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.669999999999923 y[1] (closed_form) = 2.198082073197303 y[1] (numeric) = 2.198082073196552 absolute error = 7.509548538564559e-13 relative error = 3.416409528167101e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.659999999999924 y[1] (closed_form) = 2.178170833872767 y[1] (numeric) = 2.178170833872013 absolute error = 7.536193891155563e-13 relative error = 3.459872739989031e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.649999999999925 y[1] (closed_form) = 2.158241777613319 y[1] (numeric) = 2.158241777612563 absolute error = 7.558398351648066e-13 relative error = 3.502109184452209e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.639999999999926 y[1] (closed_form) = 2.138296897307978 y[1] (numeric) = 2.13829689730722 absolute error = 7.576161920042068e-13 relative error = 3.543082314518683e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.629999999999928 y[1] (closed_form) = 2.118338187428152 y[1] (numeric) = 2.118338187427392 absolute error = 7.593925488436071e-13 relative error = 3.584850395231633e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.619999999999929 y[1] (closed_form) = 2.098367643828198 y[1] (numeric) = 2.098367643827437 absolute error = 7.616129948928574e-13 relative error = 3.62954984143481e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.60999999999993 y[1] (closed_form) = 2.078387263545835 y[1] (numeric) = 2.078387263545071 absolute error = 7.638334409421077e-13 relative error = 3.675125682010622e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.599999999999931 y[1] (closed_form) = 2.058399044602439 y[1] (numeric) = 2.058399044601673 absolute error = 7.65609797781508e-13 relative error = 3.719443029227496e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.589999999999932 y[1] (closed_form) = 2.038404985803249 y[1] (numeric) = 2.038404985802481 absolute error = 7.678302438307583e-13 relative error = 3.766818905852455e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.579999999999933 y[1] (closed_form) = 2.018407086537483 y[1] (numeric) = 2.018407086536712 absolute error = 7.704947790898586e-13 relative error = 3.817340833912843e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.569999999999934 y[1] (closed_form) = 1.998407346578402 y[1] (numeric) = 1.99840734657763 absolute error = 7.722711359292589e-13 relative error = 3.864433030890887e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.559999999999935 y[1] (closed_form) = 1.978407765883336 y[1] (numeric) = 1.978407765882561 absolute error = 7.742695373735842e-13 relative error = 3.913599363718035e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.549999999999936 y[1] (closed_form) = 1.958410344393688 y[1] (numeric) = 1.958410344392911 absolute error = 7.762679388179095e-13 relative error = 3.963765515435109e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.539999999999937 y[1] (closed_form) = 1.938417081834943 y[1] (numeric) = 1.938417081834164 absolute error = 7.787104294720848e-13 relative error = 4.017249108922124e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.529999999999939 y[1] (closed_form) = 1.918429977516695 y[1] (numeric) = 1.918429977515914 absolute error = 7.807088309164101e-13 relative error = 4.069519555397044e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.51999999999994 y[1] (closed_form) = 1.898451030132721 y[1] (numeric) = 1.898451030131938 absolute error = 7.829292769656604e-13 relative error = 4.124042519605711e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.509999999999941 y[1] (closed_form) = 1.87848223756111 y[1] (numeric) = 1.878482237560325 absolute error = 7.849276784099857e-13 relative error = 4.178520630725159e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.499999999999942 y[1] (closed_form) = 1.858525596664478 y[1] (numeric) = 1.858525596663691 absolute error = 7.86926079854311e-13 relative error = 4.234141737227715e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.489999999999943 y[1] (closed_form) = 1.838583103090285 y[1] (numeric) = 1.838583103089496 absolute error = 7.893685705084863e-13 relative error = 4.293352686542795e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.479999999999944 y[1] (closed_form) = 1.818656751071269 y[1] (numeric) = 1.818656751070477 absolute error = 7.915890165577366e-13 relative error = 4.352602634287398e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.469999999999945 y[1] (closed_form) = 1.798748533226028 y[1] (numeric) = 1.798748533225234 absolute error = 7.938094626069869e-13 relative error = 4.413120833423569e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.459999999999946 y[1] (closed_form) = 1.778860440359754 y[1] (numeric) = 1.778860440358958 absolute error = 7.955858194463872e-13 relative error = 4.472446524728433e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.449999999999947 y[1] (closed_form) = 1.758994461265162 y[1] (numeric) = 1.758994461264364 absolute error = 7.980283101005625e-13 relative error = 4.536843791574978e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.439999999999948 y[1] (closed_form) = 1.739152582523607 y[1] (numeric) = 1.739152582522807 absolute error = 8.000267115448878e-13 relative error = 4.600095009398225e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.42999999999995 y[1] (closed_form) = 1.719336788306427 y[1] (numeric) = 1.719336788305625 absolute error = 8.018030683842881e-13 relative error = 4.663443915337126e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.419999999999951 y[1] (closed_form) = 1.699549060176531 y[1] (numeric) = 1.699549060175726 absolute error = 8.042455590384634e-13 relative error = 4.732111463466239e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.409999999999952 y[1] (closed_form) = 1.679791376890242 y[1] (numeric) = 1.679791376889436 absolute error = 8.064660050877137e-13 relative error = 4.800989076278657e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.399999999999953 y[1] (closed_form) = 1.660065714199425 y[1] (numeric) = 1.660065714198617 absolute error = 8.08242361927114e-13 relative error = 4.868737153076453e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.389999999999954 y[1] (closed_form) = 1.64037404465391 y[1] (numeric) = 1.640374044653101 absolute error = 8.097966741615892e-13 relative error = 4.936658665142692e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.379999999999955 y[1] (closed_form) = 1.620718337404243 y[1] (numeric) = 1.620718337403431 absolute error = 8.120171202108395e-13 relative error = 5.010229732523255e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.369999999999956 y[1] (closed_form) = 1.601100558004768 y[1] (numeric) = 1.601100558003954 absolute error = 8.144596108650148e-13 relative error = 5.086873568265843e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.359999999999957 y[1] (closed_form) = 1.581522668217078 y[1] (numeric) = 1.581522668216261 absolute error = 8.166800569142652e-13 relative error = 5.163884611498775e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.349999999999958 y[1] (closed_form) = 1.561986625813836 y[1] (numeric) = 1.561986625813016 absolute error = 8.191225475684405e-13 relative error = 5.24410730560293e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.339999999999959 y[1] (closed_form) = 1.542494384383002 y[1] (numeric) = 1.542494384382181 absolute error = 8.213429936176908e-13 relative error = 5.324771369888831e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.329999999999961 y[1] (closed_form) = 1.523047893132477 y[1] (numeric) = 1.523047893131654 absolute error = 8.22897305852166e-13 relative error = 5.402964079873417e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.319999999999962 y[1] (closed_form) = 1.50364909669518 y[1] (numeric) = 1.503649096694355 absolute error = 8.251177519014163e-13 relative error = 5.487435557371166e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.309999999999963 y[1] (closed_form) = 1.484299934934588 y[1] (numeric) = 1.484299934933762 absolute error = 8.268941087408166e-13 relative error = 5.570936771463626e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.299999999999964 y[1] (closed_form) = 1.465002342750755 y[1] (numeric) = 1.465002342749926 absolute error = 8.293365993949919e-13 relative error = 5.660991625704786e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.289999999999965 y[1] (closed_form) = 1.445758249886818 y[1] (numeric) = 1.445758249885986 absolute error = 8.317790900491673e-13 relative error = 5.753237722242179e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.279999999999966 y[1] (closed_form) = 1.426569580736024 y[1] (numeric) = 1.42656958073519 absolute error = 8.342215807033426e-13 relative error = 5.84774547255476e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.269999999999967 y[1] (closed_form) = 1.4074382541493 y[1] (numeric) = 1.407438254148463 absolute error = 8.364420267525929e-13 relative error = 5.943010460932546e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.259999999999968 y[1] (closed_form) = 1.388366183243361 y[1] (numeric) = 1.388366183242522 absolute error = 8.388845174067683e-13 relative error = 6.042242511604907e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.249999999999969 y[1] (closed_form) = 1.369355275209404 y[1] (numeric) = 1.369355275208564 absolute error = 8.406608742461685e-13 relative error = 6.139099833807652e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.23999999999997 y[1] (closed_form) = 1.350407431122392 y[1] (numeric) = 1.350407431121549 absolute error = 8.428813202954188e-13 relative error = 6.241681590828167e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.229999999999972 y[1] (closed_form) = 1.331524545750941 y[1] (numeric) = 1.331524545750096 absolute error = 8.448797217397441e-13 relative error = 6.345205760088008e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.219999999999973 y[1] (closed_form) = 1.312708507367855 y[1] (numeric) = 1.312708507367008 absolute error = 8.466560785791444e-13 relative error = 6.449688364378746e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.209999999999974 y[1] (closed_form) = 1.29396119756129 y[1] (numeric) = 1.293961197560442 absolute error = 8.486544800234697e-13 relative error = 6.55857750311923e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.199999999999975 y[1] (closed_form) = 1.275284491046606 y[1] (numeric) = 1.275284491045755 absolute error = 8.5087492607272e-13 relative error = 6.672040098083684e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.189999999999976 y[1] (closed_form) = 1.256680255478889 y[1] (numeric) = 1.256680255478037 absolute error = 8.526512829121202e-13 relative error = 6.784950103216162e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.179999999999977 y[1] (closed_form) = 1.238150351266194 y[1] (numeric) = 1.23815035126534 absolute error = 8.544276397515205e-13 relative error = 6.900839133775154e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.169999999999978 y[1] (closed_form) = 1.219696631383499 y[1] (numeric) = 1.219696631382643 absolute error = 8.562039965909207e-13 relative error = 7.019811111716612e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.159999999999979 y[1] (closed_form) = 1.201320941187416 y[1] (numeric) = 1.201320941186557 absolute error = 8.590905764549461e-13 relative error = 7.151216190452813e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.14999999999998 y[1] (closed_form) = 1.18302511823165 y[1] (numeric) = 1.183025118230789 absolute error = 8.608669332943464e-13 relative error = 7.276827178286328e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.139999999999981 y[1] (closed_form) = 1.16481099208325 y[1] (numeric) = 1.164810992082387 absolute error = 8.633094239485217e-13 relative error = 7.411583766088122e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.129999999999983 y[1] (closed_form) = 1.146680384139654 y[1] (numeric) = 1.146680384138789 absolute error = 8.65085780787922e-13 relative error = 7.544262488077615e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.119999999999984 y[1] (closed_form) = 1.128635107446546 y[1] (numeric) = 1.128635107445679 absolute error = 8.673062268371723e-13 relative error = 7.684558287393598e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.109999999999985 y[1] (closed_form) = 1.110676966516559 y[1] (numeric) = 1.11067696651569 absolute error = 8.693046282814976e-13 relative error = 7.826799821084947e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.099999999999986 y[1] (closed_form) = 1.09280775714882 y[1] (numeric) = 1.092807757147949 absolute error = 8.713030297258229e-13 relative error = 7.973067760784274e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.089999999999987 y[1] (closed_form) = 1.075029266249375 y[1] (numeric) = 1.075029266248502 absolute error = 8.728573419602981e-13 relative error = 8.119382135572677e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.079999999999988 y[1] (closed_form) = 1.057343271652499 y[1] (numeric) = 1.057343271651624 absolute error = 8.748557434046234e-13 relative error = 8.274093824206496e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.069999999999989 y[1] (closed_form) = 1.039751541942913 y[1] (numeric) = 1.039751541942036 absolute error = 8.761880110341735e-13 relative error = 8.426897924064637e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.05999999999999 y[1] (closed_form) = 1.022255836278928 y[1] (numeric) = 1.02225583627805 absolute error = 8.779643678735738e-13 relative error = 8.588499441288753e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.049999999999991 y[1] (closed_form) = 1.004857904216531 y[1] (numeric) = 1.004857904215651 absolute error = 8.801848139228241e-13 relative error = 8.759296316717412e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.039999999999992 y[1] (closed_form) = 0.9875594855344304 y[1] (numeric) = 0.9875594855335483 absolute error = 8.820721930646869e-13 relative error = 8.931838597928531e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.029999999999994 y[1] (closed_form) = 0.9703623100600782 y[1] (numeric) = 0.9703623100591946 absolute error = 8.836265052991621e-13 relative error = 9.106150312499812e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.019999999999995 y[1] (closed_form) = 0.9532680974966919 y[1] (numeric) = 0.9532680974958061 absolute error = 8.858469513484124e-13 relative error = 9.292736782807174e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.009999999999996 y[1] (closed_form) = 0.9362785572512821 y[1] (numeric) = 0.9362785572503944 absolute error = 8.876233081878127e-13 relative error = 9.480333617739671e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9999999999999968 y[1] (closed_form) = 0.9193953882637151 y[1] (numeric) = 0.919395388262826 absolute error = 8.891776204222879e-13 relative error = 9.671330004183578e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9899999999999968 y[1] (closed_form) = 0.9026202788368193 y[1] (numeric) = 0.9026202788359303 absolute error = 8.889555758173628e-13 relative error = 9.84861072435614e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9799999999999968 y[1] (closed_form) = 0.88595490646756 y[1] (numeric) = 0.8859549064666709 absolute error = 8.891776204222879e-13 relative error = 1.003637559802651e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9699999999999968 y[1] (closed_form) = 0.8694009376792859 y[1] (numeric) = 0.8694009376783969 absolute error = 8.890665981198254e-13 relative error = 1.022619782873749e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9599999999999967 y[1] (closed_form) = 0.8529600278550813 y[1] (numeric) = 0.8529600278541921 absolute error = 8.891776204222879e-13 relative error = 1.042461066620299e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9499999999999967 y[1] (closed_form) = 0.8366338210722278 y[1] (numeric) = 0.8366338210713385 absolute error = 8.892886427247504e-13 relative error = 1.062936520525838e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9399999999999967 y[1] (closed_form) = 0.8204239499377984 y[1] (numeric) = 0.8204239499369091 absolute error = 8.892886427247504e-13 relative error = 1.083937935736972e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9299999999999967 y[1] (closed_form) = 0.8043320354253982 y[1] (numeric) = 0.8043320354245092 absolute error = 8.890665981198254e-13 relative error = 1.105347740687231e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9199999999999967 y[1] (closed_form) = 0.7883596867130692 y[1] (numeric) = 0.78835968671218 absolute error = 8.891776204222879e-13 relative error = 1.127883167300908e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9099999999999967 y[1] (closed_form) = 0.7725085010223718 y[1] (numeric) = 0.7725085010214827 absolute error = 8.890665981198254e-13 relative error = 1.150882607690654e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8999999999999967 y[1] (closed_form) = 0.7567800634586659 y[1] (numeric) = 0.7567800634577769 absolute error = 8.889555758173628e-13 relative error = 1.174655119420857e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8899999999999967 y[1] (closed_form) = 0.741175946852601 y[1] (numeric) = 0.7411759468517122 absolute error = 8.888445535149003e-13 relative error = 1.199235562472545e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8799999999999967 y[1] (closed_form) = 0.7256977116028346 y[1] (numeric) = 0.7256977116019455 absolute error = 8.890665981198254e-13 relative error = 1.22511974876724e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8699999999999967 y[1] (closed_form) = 0.7103469055199926 y[1] (numeric) = 0.7103469055191036 absolute error = 8.889555758173628e-13 relative error = 1.251438654704386e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8599999999999967 y[1] (closed_form) = 0.6951250636718913 y[1] (numeric) = 0.6951250636710022 absolute error = 8.890665981198254e-13 relative error = 1.279002361709514e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8499999999999966 y[1] (closed_form) = 0.6800337082300308 y[1] (numeric) = 0.6800337082291416 absolute error = 8.892886427247504e-13 relative error = 1.307712591246927e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8399999999999966 y[1] (closed_form) = 0.6650743483173787 y[1] (numeric) = 0.6650743483164898 absolute error = 8.888445535149003e-13 relative error = 1.336458932394032e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8299999999999966 y[1] (closed_form) = 0.6502484798574608 y[1] (numeric) = 0.6502484798565719 absolute error = 8.889555758173628e-13 relative error = 1.367101351797437e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8199999999999966 y[1] (closed_form) = 0.6355575854247678 y[1] (numeric) = 0.6355575854238789 absolute error = 8.889555758173628e-13 relative error = 1.398701858342607e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8099999999999966 y[1] (closed_form) = 0.621003134096501 y[1] (numeric) = 0.6210031340956118 absolute error = 8.891776204222879e-13 relative error = 1.431840793711862e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7999999999999966 y[1] (closed_form) = 0.6065865813056642 y[1] (numeric) = 0.6065865813047749 absolute error = 8.892886427247504e-13 relative error = 1.46605393217004e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7899999999999966 y[1] (closed_form) = 0.5923093686955231 y[1] (numeric) = 0.5923093686946338 absolute error = 8.892886427247504e-13 relative error = 1.501392160457097e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7799999999999966 y[1] (closed_form) = 0.5781729239754405 y[1] (numeric) = 0.5781729239745514 absolute error = 8.890665981198254e-13 relative error = 1.537717456581538e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7699999999999966 y[1] (closed_form) = 0.5641786607781086 y[1] (numeric) = 0.5641786607772195 absolute error = 8.891776204222879e-13 relative error = 1.576056810082013e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7599999999999966 y[1] (closed_form) = 0.5503279785181849 y[1] (numeric) = 0.5503279785172959 absolute error = 8.890665981198254e-13 relative error = 1.615521348766838e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7499999999999966 y[1] (closed_form) = 0.5366222622523535 y[1] (numeric) = 0.5366222622514644 absolute error = 8.891776204222879e-13 relative error = 1.656989810095021e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7399999999999965 y[1] (closed_form) = 0.5230628825408195 y[1] (numeric) = 0.5230628825399304 absolute error = 8.890665981198254e-13 relative error = 1.699731768006772e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7299999999999965 y[1] (closed_form) = 0.5096511953102548 y[1] (numeric) = 0.5096511953093655 absolute error = 8.892886427247504e-13 relative error = 1.744896609500519e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7199999999999965 y[1] (closed_form) = 0.4963885417182055 y[1] (numeric) = 0.4963885417173164 absolute error = 8.890110869685941e-13 relative error = 1.790958114970503e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7099999999999965 y[1] (closed_form) = 0.4832762480189792 y[1] (numeric) = 0.4832762480180901 absolute error = 8.890665981198254e-13 relative error = 1.839665412410067e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6999999999999965 y[1] (closed_form) = 0.4703156254310185 y[1] (numeric) = 0.4703156254301296 absolute error = 8.888445535149003e-13 relative error = 1.889889481558949e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6899999999999965 y[1] (closed_form) = 0.4575079700057821 y[1] (numeric) = 0.4575079700048933 absolute error = 8.888445535149003e-13 relative error = 1.942795780155845e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6799999999999965 y[1] (closed_form) = 0.4448545624981398 y[1] (numeric) = 0.4448545624972507 absolute error = 8.890665981198254e-13 relative error = 1.998555647326969e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6699999999999965 y[1] (closed_form) = 0.4323566682382971 y[1] (numeric) = 0.432356668237408 absolute error = 8.890665981198254e-13 relative error = 2.056326786267602e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6599999999999965 y[1] (closed_form) = 0.4200155370052654 y[1] (numeric) = 0.4200155370043764 absolute error = 8.889555758173628e-13 relative error = 2.116482600038243e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6499999999999965 y[1] (closed_form) = 0.4078324029018842 y[1] (numeric) = 0.4078324029009949 absolute error = 8.892331315735191e-13 relative error = 2.180388623479361e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6399999999999965 y[1] (closed_form) = 0.3958084842314104 y[1] (numeric) = 0.3958084842305213 absolute error = 8.890110869685941e-13 relative error = 2.246063746447718e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6299999999999965 y[1] (closed_form) = 0.3839449833756921 y[1] (numeric) = 0.3839449833748029 absolute error = 8.891776204222879e-13 relative error = 2.315898524326396e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6199999999999964 y[1] (closed_form) = 0.3722430866749279 y[1] (numeric) = 0.3722430866740389 absolute error = 8.890110869685941e-13 relative error = 2.388254124232934e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6099999999999964 y[1] (closed_form) = 0.360703964309037 y[1] (numeric) = 0.3607039643081478 absolute error = 8.891776204222879e-13 relative error = 2.465117404865769e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5999999999999964 y[1] (closed_form) = 0.3493287701806392 y[1] (numeric) = 0.3493287701797503 absolute error = 8.889555758173628e-13 relative error = 2.544753400522037e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5899999999999964 y[1] (closed_form) = 0.3381186417996691 y[1] (numeric) = 0.33811864179878 absolute error = 8.891221092710566e-13 relative error = 2.629615760132652e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5799999999999964 y[1] (closed_form) = 0.3270747001696223 y[1] (numeric) = 0.3270747001687331 absolute error = 8.891221092710566e-13 relative error = 2.718406861826837e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5699999999999964 y[1] (closed_form) = 0.3161980496754585 y[1] (numeric) = 0.3161980496745695 absolute error = 8.889555758173628e-13 relative error = 2.81138854818926e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5599999999999964 y[1] (closed_form) = 0.3054897779731639 y[1] (numeric) = 0.3054897779722748 absolute error = 8.891221092710566e-13 relative error = 2.910480721057588e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5499999999999964 y[1] (closed_form) = 0.2949509558809846 y[1] (numeric) = 0.2949509558800957 absolute error = 8.889555758173628e-13 relative error = 3.013909797858273e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5399999999999964 y[1] (closed_form) = 0.284582637272348 y[1] (numeric) = 0.2845826372714589 absolute error = 8.890665981198254e-13 relative error = 3.12410696113193e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5299999999999964 y[1] (closed_form) = 0.2743858589704744 y[1] (numeric) = 0.2743858589695852 absolute error = 8.892331315735191e-13 relative error = 3.240812536440539e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5199999999999964 y[1] (closed_form) = 0.2643616406446965 y[1] (numeric) = 0.2643616406438075 absolute error = 8.890110869685941e-13 relative error = 3.362859622147034e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5099999999999963 y[1] (closed_form) = 0.254510984708494 y[1] (numeric) = 0.2545109847076049 absolute error = 8.891221092710566e-13 relative error = 3.493452788646506e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4999999999999963 y[1] (closed_form) = 0.244834876219251 y[1] (numeric) = 0.244834876218362 absolute error = 8.890110869685941e-13 relative error = 3.631063926417409e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4899999999999963 y[1] (closed_form) = 0.2353342827797534 y[1] (numeric) = 0.2353342827788645 absolute error = 8.889000646661316e-13 relative error = 3.777180503267527e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4799999999999963 y[1] (closed_form) = 0.2260101544414281 y[1] (numeric) = 0.2260101544405392 absolute error = 8.889555758173628e-13 relative error = 3.933255025706117e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4699999999999963 y[1] (closed_form) = 0.2168634236093387 y[1] (numeric) = 0.2168634236084497 absolute error = 8.890110869685941e-13 relative error = 4.099405386913346e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4599999999999963 y[1] (closed_form) = 0.2078950049489463 y[1] (numeric) = 0.2078950049480572 absolute error = 8.89094353695441e-13 relative error = 4.27665086957611e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4499999999999963 y[1] (closed_form) = 0.1991057952946429 y[1] (numeric) = 0.199105795293754 absolute error = 8.889278202417472e-13 relative error = 4.464600434790381e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4399999999999963 y[1] (closed_form) = 0.1904966735600699 y[1] (numeric) = 0.1904966735591811 absolute error = 8.88872309090516e-13 relative error = 4.666077850489211e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4299999999999963 y[1] (closed_form) = 0.1820685006502267 y[1] (numeric) = 0.1820685006493377 absolute error = 8.889833313929785e-13 relative error = 4.882686067156732e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4199999999999963 y[1] (closed_form) = 0.1738221193753803 y[1] (numeric) = 0.1738221193744915 absolute error = 8.887612867880534e-13 relative error = 5.113050571364368e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4099999999999963 y[1] (closed_form) = 0.1657583543667869 y[1] (numeric) = 0.1657583543658979 absolute error = 8.889555758173628e-13 relative error = 5.362960915081838e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3999999999999962 y[1] (closed_form) = 0.157878011994227 y[1] (numeric) = 0.157878011993338 absolute error = 8.890110869685941e-13 relative error = 5.631000009051936e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3899999999999962 y[1] (closed_form) = 0.1501818802853712 y[1] (numeric) = 0.1501818802844821 absolute error = 8.890110869685941e-13 relative error = 5.919562901192351e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3799999999999962 y[1] (closed_form) = 0.1426707288469765 y[1] (numeric) = 0.1426707288460878 absolute error = 8.887335312124378e-13 relative error = 6.229263272115624e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3699999999999962 y[1] (closed_form) = 0.1353453087879285 y[1] (numeric) = 0.1353453087870395 absolute error = 8.890388425442097e-13 relative error = 6.568671278715967e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3599999999999962 y[1] (closed_form) = 0.1282063526441277 y[1] (numeric) = 0.1282063526432387 absolute error = 8.890388425442097e-13 relative error = 6.934436743645484e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3499999999999962 y[1] (closed_form) = 0.1212545743052394 y[1] (numeric) = 0.1212545743043506 absolute error = 8.888306757270925e-13 relative error = 7.330285730001411e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3399999999999962 y[1] (closed_form) = 0.1144906689433051 y[1] (numeric) = 0.1144906689424161 absolute error = 8.889972091807863e-13 relative error = 7.764800549999504e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3299999999999962 y[1] (closed_form) = 0.1079153129432235 y[1] (numeric) = 0.1079153129423347 absolute error = 8.88872309090516e-13 relative error = 8.236757924782833e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3199999999999962 y[1] (closed_form) = 0.1015291638351159 y[1] (numeric) = 0.1015291638342269 absolute error = 8.889555758173628e-13 relative error = 8.75566726089691e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3099999999999962 y[1] (closed_form) = 0.0953328602285709 y[1] (numeric) = 0.09533286022768198 absolute error = 8.889278202417472e-13 relative error = 9.324463968776832e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2999999999999962 y[1] (closed_form) = 0.08932702174878571 y[1] (numeric) = 0.08932702174789682 absolute error = 8.888861868783238e-13 relative error = 9.950921562997337e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2899999999999961 y[1] (closed_form) = 0.08351224897460341 y[1] (numeric) = 0.08351224897371459 absolute error = 8.888167979392847e-13 relative error = 1.064295128981114e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2799999999999961 y[1] (closed_form) = 0.07788912337845588 y[1] (numeric) = 0.07788912337756711 absolute error = 8.887751645758613e-13 relative error = 1.141077375152095e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2699999999999961 y[1] (closed_form) = 0.07245820726821695 y[1] (numeric) = 0.07245820726732805 absolute error = 8.889000646661316e-13 relative error = 1.226776231677538e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2599999999999961 y[1] (closed_form) = 0.06722004373097157 y[1] (numeric) = 0.06722004373008268 absolute error = 8.888861868783238e-13 relative error = 1.322352883963939e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2499999999999961 y[1] (closed_form) = 0.06217515657870853 y[1] (numeric) = 0.06217515657781966 absolute error = 8.88872309090516e-13 relative error = 1.429626169039523e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2399999999999961 y[1] (closed_form) = 0.0573240502959389 y[1] (numeric) = 0.0573240502950501 absolute error = 8.88795981257573e-13 relative error = 1.550476591708209e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2299999999999961 y[1] (closed_form) = 0.05266720998924856 y[1] (numeric) = 0.05266720998835971 absolute error = 8.888514924088042e-13 relative error = 1.687675296622421e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2199999999999961 y[1] (closed_form) = 0.04820510133878741 y[1] (numeric) = 0.04820510133789849 absolute error = 8.889208813478433e-13 relative error = 1.844039026285768e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2099999999999961 y[1] (closed_form) = 0.0439381705517019 y[1] (numeric) = 0.04393817055081306 absolute error = 8.888445535149003e-13 relative error = 2.022943928603035e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1999999999999961 y[1] (closed_form) = 0.0398668443175153 y[1] (numeric) = 0.03986684431662637 absolute error = 8.889347591356511e-13 relative error = 2.229759526627749e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1899999999999961 y[1] (closed_form) = 0.03599152976545783 y[1] (numeric) = 0.03599152976456908 absolute error = 8.887543478941495e-13 relative error = 2.469343075122954e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1799999999999961 y[1] (closed_form) = 0.03231261442375566 y[1] (numeric) = 0.03231261442286697 absolute error = 8.886918978490144e-13 relative error = 2.750294006527877e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.169999999999996 y[1] (closed_form) = 0.02883046618087715 y[1] (numeric) = 0.02883046617998846 absolute error = 8.886849589551105e-13 relative error = 3.082450881576667e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.159999999999996 y[1] (closed_form) = 0.0255454332487447 y[1] (numeric) = 0.02554543324785606 absolute error = 8.886398561447351e-13 relative error = 3.478664258663152e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.149999999999996 y[1] (closed_form) = 0.02245784412791429 y[1] (numeric) = 0.02245784412702546 absolute error = 8.888376146209964e-13 relative error = 3.957804718736128e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.139999999999996 y[1] (closed_form) = 0.01956800757472454 y[1] (numeric) = 0.01956800757383576 absolute error = 8.887821034697652e-13 relative error = 4.542016350288931e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.129999999999996 y[1] (closed_form) = 0.01687621257042293 y[1] (numeric) = 0.01687621256953411 absolute error = 8.888202673862367e-13 relative error = 5.26670462153323e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.119999999999996 y[1] (closed_form) = 0.01438272829226672 y[1] (numeric) = 0.01438272829137776 absolute error = 8.889573105408388e-13 relative error = 6.18072797091503e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.109999999999996 y[1] (closed_form) = 0.01208780408660548 y[1] (numeric) = 0.01208780408571665 absolute error = 8.888306757270925e-13 relative error = 7.353119469499076e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.09999999999999598 y[1] (closed_form) = 0.009991669443947693 y[1] (numeric) = 0.009991669443058895 absolute error = 8.88797715981049e-13 relative error = 8.895387512238259e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.08999999999999597 y[1] (closed_form) = 0.008094533976010787 y[1] (numeric) = 0.008094533975122001 absolute error = 8.887855729167171e-13 relative error = 1.098007094109123e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.07999999999999596 y[1] (closed_form) = 0.006396587394760789 y[1] (numeric) = 0.006396587393871816 absolute error = 8.889729230521226e-13 relative error = 1.389761240157913e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.06999999999999595 y[1] (closed_form) = 0.004897999493440497 y[1] (numeric) = 0.004897999492551515 absolute error = 8.889815966695025e-13 relative error = 1.814989156001435e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.05999999999999595 y[1] (closed_form) = 0.003598920129591288 y[1] (numeric) = 0.003598920128702414 absolute error = 8.888740438139919e-13 relative error = 2.46983542787024e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.04999999999999594 y[1] (closed_form) = 0.00249947921006699 y[1] (numeric) = 0.002499479209178333 absolute error = 8.886572033794948e-13 relative error = 3.55536945376584e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.03999999999999593 y[1] (closed_form) = 0.001599786678043724 y[1] (numeric) = 0.001599786677155027 absolute error = 8.886975357003113e-13 relative error = 5.555100238658332e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.02999999999999592 y[1] (closed_form) = 0.0008999325020245807 y[1] (numeric) = 0.0008999325011359562 absolute error = 8.88624568894103e-13 relative error = 9.874346874848522e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.01999999999999591 y[1] (closed_form) = 0.0003999866668441543 y[1] (numeric) = 0.0003999866659555136 absolute error = 8.886407235064731e-13 relative error = 2.221675863642504e-07 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.009999999999995901 y[1] (closed_form) = 9.999916666947328e-05 y[1] (numeric) = 9.999916578059669e-05 absolute error = 8.888765916890973e-13 relative error = 8.888839990308083e-07 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.100886297209172e-15 y[1] (closed_form) = 0 y[1] (numeric) = -8.887657356168507e-13 absolute error = 8.887657356168507e-13 relative error = -1 % Desired digits = 8 Estimated correct digits = 0 Correct digits = -16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.0100000000000041 y[1] (closed_form) = 9.999916666947328e-05 y[1] (numeric) = 9.999916578076072e-05 absolute error = 8.887125654529274e-13 relative error = 8.887199714277463e-07 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.02000000000000411 y[1] (closed_form) = 0.0003999866668448204 y[1] (numeric) = 0.0003999866659558415 absolute error = 8.889788861640713e-13 relative error = 2.222521298463584e-07 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.03000000000000412 y[1] (closed_form) = 0.0008999325020252469 y[1] (numeric) = 0.0008999325011364481 absolute error = 8.887988001832214e-13 relative error = 9.876282923252914e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.04000000000000413 y[1] (closed_form) = 0.001599786678044279 y[1] (numeric) = 0.001599786677155683 absolute error = 8.885967048982701e-13 relative error = 5.554469962111257e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.05000000000000414 y[1] (closed_form) = 0.002499479210067879 y[1] (numeric) = 0.002499479209179152 absolute error = 8.887261586376649e-13 relative error = 3.555645332267155e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.06000000000000415 y[1] (closed_form) = 0.003598920129592176 y[1] (numeric) = 0.003598920128703397 absolute error = 8.887786340228132e-13 relative error = 2.46957032114944e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.07000000000000416 y[1] (closed_form) = 0.004897999493441496 y[1] (numeric) = 0.004897999492552661 absolute error = 8.888350125357825e-13 relative error = 1.814689882524381e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.08000000000000417 y[1] (closed_form) = 0.006396587394761788 y[1] (numeric) = 0.006396587393873122 absolute error = 8.886658769968747e-13 relative error = 1.389281224742758e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.09000000000000417 y[1] (closed_form) = 0.008094533976012452 y[1] (numeric) = 0.008094533975123469 absolute error = 8.889833313929785e-13 relative error = 1.098251405241382e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1000000000000042 y[1] (closed_form) = 0.009991669443949358 y[1] (numeric) = 0.009991669443060524 absolute error = 8.888341451740445e-13 relative error = 8.895752107895189e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1100000000000042 y[1] (closed_form) = 0.01208780408660726 y[1] (numeric) = 0.01208780408571844 absolute error = 8.888185326627607e-13 relative error = 7.353019012340973e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1200000000000042 y[1] (closed_form) = 0.01438272829226861 y[1] (numeric) = 0.01438272829137972 absolute error = 8.888931257722277e-13 relative error = 6.180281708096018e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1300000000000042 y[1] (closed_form) = 0.01687621257042504 y[1] (numeric) = 0.01687621256953622 absolute error = 8.888202673862367e-13 relative error = 5.266704621532573e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1400000000000042 y[1] (closed_form) = 0.01956800757472699 y[1] (numeric) = 0.01956800757383804 absolute error = 8.88945167476507e-13 relative error = 4.542849669705882e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1500000000000042 y[1] (closed_form) = 0.02245784412791663 y[1] (numeric) = 0.02245784412702789 absolute error = 8.887335312124378e-13 relative error = 3.957341257470398e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000042 y[1] (closed_form) = 0.02554543324874736 y[1] (numeric) = 0.02554543324785865 absolute error = 8.88716183977678e-13 relative error = 3.478963051140488e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000042 y[1] (closed_form) = 0.02883046618087992 y[1] (numeric) = 0.02883046617999121 absolute error = 8.887127145307261e-13 relative error = 3.082547153261474e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000042 y[1] (closed_form) = 0.03231261442375866 y[1] (numeric) = 0.03231261442286988 absolute error = 8.887751645758613e-13 relative error = 2.750551697613076e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000042 y[1] (closed_form) = 0.03599152976546094 y[1] (numeric) = 0.03599152976457216 absolute error = 8.887821034697652e-13 relative error = 2.469420192088305e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000043 y[1] (closed_form) = 0.03986684431751852 y[1] (numeric) = 0.0398668443166296 absolute error = 8.889208813478433e-13 relative error = 2.229724716278154e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000043 y[1] (closed_form) = 0.04393817055170512 y[1] (numeric) = 0.04393817055081646 absolute error = 8.886641422733987e-13 relative error = 2.02253332606929e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000043 y[1] (closed_form) = 0.04820510133879097 y[1] (numeric) = 0.04820510133790205 absolute error = 8.889139424539394e-13 relative error = 1.84402463176366e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000043 y[1] (closed_form) = 0.05266720998925223 y[1] (numeric) = 0.05266720998836343 absolute error = 8.88795981257573e-13 relative error = 1.687569896789576e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000043 y[1] (closed_form) = 0.0573240502959429 y[1] (numeric) = 0.05732405029505398 absolute error = 8.889139424539394e-13 relative error = 1.550682371299315e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000043 y[1] (closed_form) = 0.06217515657871253 y[1] (numeric) = 0.06217515657782371 absolute error = 8.888237368331886e-13 relative error = 1.42954804739085e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000043 y[1] (closed_form) = 0.0672200437309759 y[1] (numeric) = 0.06722004373008691 absolute error = 8.889833313929785e-13 relative error = 1.322497401148406e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000043 y[1] (closed_form) = 0.07245820726822128 y[1] (numeric) = 0.07245820726733242 absolute error = 8.888584313027081e-13 relative error = 1.226718773226596e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000043 y[1] (closed_form) = 0.07788912337846032 y[1] (numeric) = 0.07788912337757163 absolute error = 8.886918978490144e-13 relative error = 1.140970470974354e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000043 y[1] (closed_form) = 0.08351224897460796 y[1] (numeric) = 0.08351224897371927 absolute error = 8.886918978490144e-13 relative error = 1.06414556997408e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000043 y[1] (closed_form) = 0.08932702174879037 y[1] (numeric) = 0.08932702174790164 absolute error = 8.887335312124378e-13 relative error = 9.949212610174958e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000043 y[1] (closed_form) = 0.0953328602285759 y[1] (numeric) = 0.09533286022768694 absolute error = 8.889555758173628e-13 relative error = 9.324755112622746e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000043 y[1] (closed_form) = 0.1015291638351209 y[1] (numeric) = 0.1015291638342321 absolute error = 8.888306757270925e-13 relative error = 8.754437071603547e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000043 y[1] (closed_form) = 0.1079153129432289 y[1] (numeric) = 0.1079153129423399 absolute error = 8.889278202417472e-13 relative error = 8.237272320281242e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000044 y[1] (closed_form) = 0.1144906689433105 y[1] (numeric) = 0.1144906689424215 absolute error = 8.889833313929785e-13 relative error = 7.76467933673402e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000044 y[1] (closed_form) = 0.1212545743052451 y[1] (numeric) = 0.1212545743043562 absolute error = 8.889000646661316e-13 relative error = 7.330857988321521e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000044 y[1] (closed_form) = 0.1282063526441332 y[1] (numeric) = 0.1282063526432444 absolute error = 8.887335312124378e-13 relative error = 6.93205533800128e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000044 y[1] (closed_form) = 0.1353453087879344 y[1] (numeric) = 0.1353453087870454 absolute error = 8.889833313929785e-13 relative error = 6.56826113408837e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000044 y[1] (closed_form) = 0.1426707288469827 y[1] (numeric) = 0.1426707288460938 absolute error = 8.889000646661316e-13 relative error = 6.230430529443044e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000044 y[1] (closed_form) = 0.150181880285377 y[1] (numeric) = 0.1501818802844883 absolute error = 8.887612867880534e-13 relative error = 5.917899583486509e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000044 y[1] (closed_form) = 0.1578780119942333 y[1] (numeric) = 0.1578780119933443 absolute error = 8.890665981198254e-13 relative error = 5.6313516169199e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000044 y[1] (closed_form) = 0.1657583543667932 y[1] (numeric) = 0.1657583543659043 absolute error = 8.889000646661316e-13 relative error = 5.362626023054964e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000044 y[1] (closed_form) = 0.1738221193753872 y[1] (numeric) = 0.1738221193744981 absolute error = 8.89094353695441e-13 relative error = 5.114966707863849e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000044 y[1] (closed_form) = 0.1820685006502334 y[1] (numeric) = 0.1820685006493445 absolute error = 8.889278202417472e-13 relative error = 4.882381175585343e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000044 y[1] (closed_form) = 0.190496673560077 y[1] (numeric) = 0.190496673559188 absolute error = 8.890665981198254e-13 relative error = 4.667097758215919e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000045 y[1] (closed_form) = 0.19910579529465 y[1] (numeric) = 0.1991057952937611 absolute error = 8.889278202417472e-13 relative error = 4.464600434790221e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000045 y[1] (closed_form) = 0.2078950049489534 y[1] (numeric) = 0.2078950049480645 absolute error = 8.889000646661316e-13 relative error = 4.275716315956664e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000045 y[1] (closed_form) = 0.216863423609346 y[1] (numeric) = 0.2168634236084572 absolute error = 8.887612867880534e-13 relative error = 4.098253509033652e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000045 y[1] (closed_form) = 0.2260101544414357 y[1] (numeric) = 0.2260101544405468 absolute error = 8.88872309090516e-13 relative error = 3.93288660541508e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000045 y[1] (closed_form) = 0.2353342827797613 y[1] (numeric) = 0.2353342827788723 absolute error = 8.890388425442097e-13 relative error = 3.777770208585465e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000044 y[1] (closed_form) = 0.2448348762192589 y[1] (numeric) = 0.2448348762183699 absolute error = 8.890388425442097e-13 relative error = 3.631177290885804e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000044 y[1] (closed_form) = 0.254510984708502 y[1] (numeric) = 0.2545109847076129 absolute error = 8.890665981198254e-13 relative error = 3.493234679587981e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000045 y[1] (closed_form) = 0.2643616406447046 y[1] (numeric) = 0.2643616406438157 absolute error = 8.888445535149003e-13 relative error = 3.362229676541784e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000045 y[1] (closed_form) = 0.2743858589704824 y[1] (numeric) = 0.2743858589695936 absolute error = 8.888445535149003e-13 relative error = 3.239396362662114e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000045 y[1] (closed_form) = 0.2845826372723562 y[1] (numeric) = 0.2845826372714674 absolute error = 8.887890423636691e-13 relative error = 3.123131653014603e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000045 y[1] (closed_form) = 0.2949509558809932 y[1] (numeric) = 0.2949509558801043 absolute error = 8.889000646661316e-13 relative error = 3.013721593174917e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000045 y[1] (closed_form) = 0.3054897779731726 y[1] (numeric) = 0.3054897779722836 absolute error = 8.889555758173628e-13 relative error = 2.909935585129231e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000045 y[1] (closed_form) = 0.3161980496754673 y[1] (numeric) = 0.3161980496745784 absolute error = 8.888445535149003e-13 relative error = 2.811037431847458e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000045 y[1] (closed_form) = 0.3270747001696311 y[1] (numeric) = 0.3270747001687421 absolute error = 8.890110869685941e-13 relative error = 2.71806742162425e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000045 y[1] (closed_form) = 0.338118641799678 y[1] (numeric) = 0.3381186417987891 absolute error = 8.889000646661316e-13 relative error = 2.628959053942876e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000045 y[1] (closed_form) = 0.3493287701806485 y[1] (numeric) = 0.3493287701797596 absolute error = 8.889000646661316e-13 relative error = 2.544594492478975e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000045 y[1] (closed_form) = 0.3607039643090461 y[1] (numeric) = 0.3607039643081571 absolute error = 8.889555758173628e-13 relative error = 2.464501818049658e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000045 y[1] (closed_form) = 0.3722430866749374 y[1] (numeric) = 0.3722430866740484 absolute error = 8.890110869685941e-13 relative error = 2.388254124232873e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000046 y[1] (closed_form) = 0.3839449833757015 y[1] (numeric) = 0.3839449833748126 absolute error = 8.888445535149003e-13 relative error = 2.315031038301495e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000046 y[1] (closed_form) = 0.3958084842314201 y[1] (numeric) = 0.3958084842305312 absolute error = 8.889555758173628e-13 relative error = 2.245923498945543e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000046 y[1] (closed_form) = 0.4078324029018939 y[1] (numeric) = 0.4078324029010049 absolute error = 8.890665981198254e-13 relative error = 2.17998028551374e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000046 y[1] (closed_form) = 0.4200155370052753 y[1] (numeric) = 0.4200155370043864 absolute error = 8.888445535149003e-13 relative error = 2.116218271001095e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000046 y[1] (closed_form) = 0.432356668238307 y[1] (numeric) = 0.4323566682374181 absolute error = 8.889000646661316e-13 relative error = 2.055941610171226e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000046 y[1] (closed_form) = 0.4448545624981498 y[1] (numeric) = 0.4448545624972609 absolute error = 8.889555758173628e-13 relative error = 1.998306077440894e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000046 y[1] (closed_form) = 0.4575079700057927 y[1] (numeric) = 0.4575079700049036 absolute error = 8.890665981198254e-13 relative error = 1.943281115099631e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000046 y[1] (closed_form) = 0.470315625431029 y[1] (numeric) = 0.47031562543014 absolute error = 8.889555758173628e-13 relative error = 1.890125540699746e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000046 y[1] (closed_form) = 0.4832762480189895 y[1] (numeric) = 0.4832762480181007 absolute error = 8.888445535149003e-13 relative error = 1.839205955513822e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000046 y[1] (closed_form) = 0.4963885417182161 y[1] (numeric) = 0.496388541717327 absolute error = 8.890665981198254e-13 relative error = 1.791069945011986e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000046 y[1] (closed_form) = 0.5096511953102655 y[1] (numeric) = 0.5096511953093763 absolute error = 8.891776204222879e-13 relative error = 1.744678769724015e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000047 y[1] (closed_form) = 0.5230628825408306 y[1] (numeric) = 0.5230628825399413 absolute error = 8.892886427247504e-13 relative error = 1.700156276440304e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000047 y[1] (closed_form) = 0.5366222622523646 y[1] (numeric) = 0.5366222622514755 absolute error = 8.891776204222879e-13 relative error = 1.656989810094987e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000047 y[1] (closed_form) = 0.550327978518196 y[1] (numeric) = 0.5503279785173072 absolute error = 8.888445535149003e-13 relative error = 1.615117871906474e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000047 y[1] (closed_form) = 0.5641786607781198 y[1] (numeric) = 0.5641786607772308 absolute error = 8.890665981198254e-13 relative error = 1.575860024364653e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000047 y[1] (closed_form) = 0.5781729239754519 y[1] (numeric) = 0.5781729239745629 absolute error = 8.890665981198254e-13 relative error = 1.537717456581508e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000047 y[1] (closed_form) = 0.5923093686955346 y[1] (numeric) = 0.5923093686946456 absolute error = 8.890665981198254e-13 relative error = 1.501017281016254e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000047 y[1] (closed_form) = 0.6065865813056758 y[1] (numeric) = 0.6065865813047869 absolute error = 8.888445535149003e-13 relative error = 1.465321820343709e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000047 y[1] (closed_form) = 0.6210031340965126 y[1] (numeric) = 0.6210031340956238 absolute error = 8.888445535149003e-13 relative error = 1.431304456793227e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000047 y[1] (closed_form) = 0.63555758542478 y[1] (numeric) = 0.6355575854238908 absolute error = 8.891776204222879e-13 relative error = 1.39905122810862e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000047 y[1] (closed_form) = 0.6502484798574728 y[1] (numeric) = 0.6502484798565838 absolute error = 8.889555758173628e-13 relative error = 1.367101351797411e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000047 y[1] (closed_form) = 0.6650743483173908 y[1] (numeric) = 0.6650743483165019 absolute error = 8.888445535149003e-13 relative error = 1.336458932394008e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000048 y[1] (closed_form) = 0.6800337082300426 y[1] (numeric) = 0.6800337082291539 absolute error = 8.887335312124378e-13 relative error = 1.306896291252368e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000048 y[1] (closed_form) = 0.6951250636719034 y[1] (numeric) = 0.6951250636710146 absolute error = 8.888445535149003e-13 relative error = 1.278682930550224e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000048 y[1] (closed_form) = 0.710346905520005 y[1] (numeric) = 0.7103469055191159 absolute error = 8.890665981198254e-13 relative error = 1.251594947779761e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000048 y[1] (closed_form) = 0.725697711602847 y[1] (numeric) = 0.7256977116019581 absolute error = 8.889555758173628e-13 relative error = 1.224966761785604e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000048 y[1] (closed_form) = 0.7411759468526138 y[1] (numeric) = 0.7411759468517247 absolute error = 8.890665981198254e-13 relative error = 1.199535146674991e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000048 y[1] (closed_form) = 0.7567800634586784 y[1] (numeric) = 0.7567800634577896 absolute error = 8.888445535149003e-13 relative error = 1.174508415896494e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000048 y[1] (closed_form) = 0.7725085010223846 y[1] (numeric) = 0.7725085010214954 absolute error = 8.891776204222879e-13 relative error = 1.151026324299987e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000048 y[1] (closed_form) = 0.7883596867130819 y[1] (numeric) = 0.7883596867121927 absolute error = 8.891776204222879e-13 relative error = 1.12788316730089e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000048 y[1] (closed_form) = 0.8043320354254114 y[1] (numeric) = 0.8043320354245219 absolute error = 8.895106873296754e-13 relative error = 1.105899862435807e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000048 y[1] (closed_form) = 0.8204239499378114 y[1] (numeric) = 0.8204239499369219 absolute error = 8.895106873296754e-13 relative error = 1.084208581913169e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000048 y[1] (closed_form) = 0.8366338210722408 y[1] (numeric) = 0.8366338210713515 absolute error = 8.892886427247504e-13 relative error = 1.062936520525822e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000048 y[1] (closed_form) = 0.8529600278550946 y[1] (numeric) = 0.8529600278542053 absolute error = 8.892886427247504e-13 relative error = 1.042591227822258e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000049 y[1] (closed_form) = 0.8694009376792994 y[1] (numeric) = 0.8694009376784101 absolute error = 8.892886427247504e-13 relative error = 1.022875182419906e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000049 y[1] (closed_form) = 0.8859549064675737 y[1] (numeric) = 0.8859549064666841 absolute error = 8.896217096321379e-13 relative error = 1.00413881467081e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000049 y[1] (closed_form) = 0.9026202788368329 y[1] (numeric) = 0.9026202788359435 absolute error = 8.893996650272129e-13 relative error = 9.853530724717853e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.000000000000005 y[1] (closed_form) = 0.9193953882637286 y[1] (numeric) = 0.9193953882628393 absolute error = 8.892886427247504e-13 relative error = 9.672537561931493e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.010000000000004 y[1] (closed_form) = 0.9362785572512955 y[1] (numeric) = 0.9362785572504079 absolute error = 8.876233081878127e-13 relative error = 9.480333617739536e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.020000000000003 y[1] (closed_form) = 0.9532680974967054 y[1] (numeric) = 0.9532680974958198 absolute error = 8.856249067434874e-13 relative error = 9.290407484202504e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.030000000000002 y[1] (closed_form) = 0.970362310060092 y[1] (numeric) = 0.9703623100592083 absolute error = 8.837375276016246e-13 relative error = 9.107294444967643e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (closed_form) = 0.9875594855344439 y[1] (numeric) = 0.9875594855335622 absolute error = 8.817391261572993e-13 relative error = 8.928465971648511e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999999 y[1] (closed_form) = 1.004857904216545 y[1] (numeric) = 1.004857904215665 absolute error = 8.799627693178991e-13 relative error = 8.757086605234771e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999998 y[1] (closed_form) = 1.022255836278942 y[1] (numeric) = 1.022255836278064 absolute error = 8.779643678735738e-13 relative error = 8.588499441288633e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999997 y[1] (closed_form) = 1.039751541942927 y[1] (numeric) = 1.039751541942051 absolute error = 8.761880110341735e-13 relative error = 8.426897924064521e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999996 y[1] (closed_form) = 1.057343271652513 y[1] (numeric) = 1.057343271651639 absolute error = 8.746336987996983e-13 relative error = 8.271993800393133e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999995 y[1] (closed_form) = 1.075029266249389 y[1] (numeric) = 1.075029266248517 absolute error = 8.72635297355373e-13 relative error = 8.117316660595319e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.099999999999994 y[1] (closed_form) = 1.092807757148834 y[1] (numeric) = 1.092807757147964 absolute error = 8.708589405159728e-13 relative error = 7.969004015748093e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999993 y[1] (closed_form) = 1.110676966516573 y[1] (numeric) = 1.110676966515704 absolute error = 8.688605390716475e-13 relative error = 7.822801455914433e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999992 y[1] (closed_form) = 1.128635107446561 y[1] (numeric) = 1.128635107445694 absolute error = 8.668621376273222e-13 relative error = 7.680623541726634e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999991 y[1] (closed_form) = 1.146680384139668 y[1] (numeric) = 1.146680384138803 absolute error = 8.65085780787922e-13 relative error = 7.544262488077519e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999989 y[1] (closed_form) = 1.164810992083265 y[1] (numeric) = 1.164810992082402 absolute error = 8.626432901337466e-13 relative error = 7.405864951453704e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999988 y[1] (closed_form) = 1.183025118231664 y[1] (numeric) = 1.183025118230804 absolute error = 8.606448886894214e-13 relative error = 7.274950256135532e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999987 y[1] (closed_form) = 1.20132094118743 y[1] (numeric) = 1.201320941186572 absolute error = 8.58424442640171e-13 relative error = 7.14567117919107e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999986 y[1] (closed_form) = 1.219696631383514 y[1] (numeric) = 1.219696631382658 absolute error = 8.564260411958458e-13 relative error = 7.021631602150061e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999985 y[1] (closed_form) = 1.238150351266209 y[1] (numeric) = 1.238150351265354 absolute error = 8.546496843564455e-13 relative error = 6.902632491138317e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.189999999999984 y[1] (closed_form) = 1.256680255478904 y[1] (numeric) = 1.256680255478052 absolute error = 8.528733275170453e-13 relative error = 6.786717017305459e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999983 y[1] (closed_form) = 1.275284491046621 y[1] (numeric) = 1.27528449104577 absolute error = 8.506528814677949e-13 relative error = 6.670298960270955e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999982 y[1] (closed_form) = 1.293961197561305 y[1] (numeric) = 1.293961197560457 absolute error = 8.488765246283947e-13 relative error = 6.560293509791869e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999981 y[1] (closed_form) = 1.31270850736787 y[1] (numeric) = 1.312708507367023 absolute error = 8.466560785791444e-13 relative error = 6.449688364378672e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.22999999999998 y[1] (closed_form) = 1.331524545750956 y[1] (numeric) = 1.331524545750111 absolute error = 8.448797217397441e-13 relative error = 6.345205760087937e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999978 y[1] (closed_form) = 1.350407431122407 y[1] (numeric) = 1.350407431121564 absolute error = 8.424372310855688e-13 relative error = 6.238393033614806e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999977 y[1] (closed_form) = 1.36935527520942 y[1] (numeric) = 1.369355275208579 absolute error = 8.406608742461685e-13 relative error = 6.139099833807583e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999976 y[1] (closed_form) = 1.388366183243376 y[1] (numeric) = 1.388366183242538 absolute error = 8.382183835919932e-13 relative error = 6.037444542432047e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999975 y[1] (closed_form) = 1.407438254149315 y[1] (numeric) = 1.407438254148479 absolute error = 8.357758929378178e-13 relative error = 5.938277508614247e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.279999999999974 y[1] (closed_form) = 1.426569580736039 y[1] (numeric) = 1.426569580735205 absolute error = 8.339995360984176e-13 relative error = 5.846188979216247e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999973 y[1] (closed_form) = 1.445758249886833 y[1] (numeric) = 1.445758249886002 absolute error = 8.311129562343922e-13 relative error = 5.748630217392485e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999972 y[1] (closed_form) = 1.465002342750771 y[1] (numeric) = 1.465002342749942 absolute error = 8.291145547900669e-13 relative error = 5.659475965296237e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999971 y[1] (closed_form) = 1.484299934934604 y[1] (numeric) = 1.484299934933778 absolute error = 8.264500195309665e-13 relative error = 5.567944861274811e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.31999999999997 y[1] (closed_form) = 1.503649096695195 y[1] (numeric) = 1.503649096694371 absolute error = 8.246736626915663e-13 relative error = 5.484482147490931e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999969 y[1] (closed_form) = 1.523047893132492 y[1] (numeric) = 1.52304789313167 absolute error = 8.222311720373909e-13 relative error = 5.39859039065598e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999967 y[1] (closed_form) = 1.542494384383017 y[1] (numeric) = 1.542494384382197 absolute error = 8.200107259881406e-13 relative error = 5.316134271154166e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999966 y[1] (closed_form) = 1.561986625813851 y[1] (numeric) = 1.561986625813033 absolute error = 8.182343691487404e-13 relative error = 5.238421095458553e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999965 y[1] (closed_form) = 1.581522668217093 y[1] (numeric) = 1.581522668216278 absolute error = 8.15791878494565e-13 relative error = 5.158268641285023e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.369999999999964 y[1] (closed_form) = 1.601100558004784 y[1] (numeric) = 1.60110055800397 absolute error = 8.135714324453147e-13 relative error = 5.081326268845656e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999963 y[1] (closed_form) = 1.620718337404259 y[1] (numeric) = 1.620718337403447 absolute error = 8.115730310009894e-13 relative error = 5.007489656103997e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999962 y[1] (closed_form) = 1.640374044653926 y[1] (numeric) = 1.640374044653117 absolute error = 8.093525849517391e-13 relative error = 4.933951421564282e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999961 y[1] (closed_form) = 1.660065714199441 y[1] (numeric) = 1.660065714198633 absolute error = 8.073541835074138e-13 relative error = 4.863386892468632e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.40999999999996 y[1] (closed_form) = 1.679791376890258 y[1] (numeric) = 1.679791376889452 absolute error = 8.055778266680136e-13 relative error = 4.795701643375221e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999959 y[1] (closed_form) = 1.699549060176547 y[1] (numeric) = 1.699549060175743 absolute error = 8.038014698286133e-13 relative error = 4.729498480880073e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999958 y[1] (closed_form) = 1.719336788306443 y[1] (numeric) = 1.719336788305641 absolute error = 8.01136934569513e-13 relative error = 4.659569550411574e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999956 y[1] (closed_form) = 1.739152582523622 y[1] (numeric) = 1.739152582522824 absolute error = 7.989164885202626e-13 relative error = 4.59371130830271e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999955 y[1] (closed_form) = 1.758994461265178 y[1] (numeric) = 1.758994461264381 absolute error = 7.969180870759374e-13 relative error = 4.530532100156498e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.459999999999954 y[1] (closed_form) = 1.77886044035977 y[1] (numeric) = 1.778860440358975 absolute error = 7.949196856316121e-13 relative error = 4.468701802547488e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999953 y[1] (closed_form) = 1.798748533226043 y[1] (numeric) = 1.79874853322525 absolute error = 7.926992395823618e-13 relative error = 4.406948636453708e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999952 y[1] (closed_form) = 1.818656751071285 y[1] (numeric) = 1.818656751070494 absolute error = 7.909228827429615e-13 relative error = 4.348939855071971e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999951 y[1] (closed_form) = 1.838583103090301 y[1] (numeric) = 1.838583103089512 absolute error = 7.887024366937112e-13 relative error = 4.289729604106856e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.49999999999995 y[1] (closed_form) = 1.858525596664494 y[1] (numeric) = 1.858525596663708 absolute error = 7.862599460395359e-13 relative error = 4.230557531468175e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999949 y[1] (closed_form) = 1.878482237561126 y[1] (numeric) = 1.878482237560342 absolute error = 7.842615445952106e-13 relative error = 4.17497450289141e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999948 y[1] (closed_form) = 1.898451030132737 y[1] (numeric) = 1.898451030131955 absolute error = 7.820410985459603e-13 relative error = 4.119364082260689e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999947 y[1] (closed_form) = 1.918429977516711 y[1] (numeric) = 1.918429977515931 absolute error = 7.7982065249671e-13 relative error = 4.064889840316922e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999945 y[1] (closed_form) = 1.938417081834959 y[1] (numeric) = 1.938417081834181 absolute error = 7.778222510523847e-13 relative error = 4.012667131039089e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.549999999999944 y[1] (closed_form) = 1.958410344393704 y[1] (numeric) = 1.958410344392928 absolute error = 7.753797603982093e-13 relative error = 3.959230314616501e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999943 y[1] (closed_form) = 1.978407765883352 y[1] (numeric) = 1.978407765882578 absolute error = 7.73381358953884e-13 relative error = 3.909110003966104e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999942 y[1] (closed_form) = 1.998407346578418 y[1] (numeric) = 1.998407346577646 absolute error = 7.713829575095588e-13 relative error = 3.859988599572983e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999941 y[1] (closed_form) = 2.018407086537499 y[1] (numeric) = 2.018407086536729 absolute error = 7.696066006701585e-13 relative error = 3.812940441020694e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.58999999999994 y[1] (closed_form) = 2.038404985803265 y[1] (numeric) = 2.038404985802498 absolute error = 7.669420654110581e-13 relative error = 3.762461683289265e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999939 y[1] (closed_form) = 2.058399044602455 y[1] (numeric) = 2.05839904460169 absolute error = 7.647216193618078e-13 relative error = 3.715128130121635e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999938 y[1] (closed_form) = 2.078387263545851 y[1] (numeric) = 2.078387263545088 absolute error = 7.629452625224076e-13 relative error = 3.670852280054767e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999937 y[1] (closed_form) = 2.098367643828214 y[1] (numeric) = 2.098367643827454 absolute error = 7.607248164731573e-13 relative error = 3.625317130249436e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999936 y[1] (closed_form) = 2.118338187428168 y[1] (numeric) = 2.118338187427409 absolute error = 7.585043704239069e-13 relative error = 3.580657587751803e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.639999999999934 y[1] (closed_form) = 2.138296897307993 y[1] (numeric) = 2.138296897307237 absolute error = 7.558398351648066e-13 relative error = 3.534774970287665e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999933 y[1] (closed_form) = 2.158241777613335 y[1] (numeric) = 2.15824177761258 absolute error = 7.549516567451064e-13 relative error = 3.497993897513931e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999932 y[1] (closed_form) = 2.178170833872783 y[1] (numeric) = 2.17817083387203 absolute error = 7.527312106958561e-13 relative error = 3.45579510564606e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999931 y[1] (closed_form) = 2.198082073197319 y[1] (numeric) = 2.198082073196569 absolute error = 7.500666754367558e-13 relative error = 3.412368830913182e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.67999999999993 y[1] (closed_form) = 2.217973504479604 y[1] (numeric) = 2.217973504478855 absolute error = 7.487344078072056e-13 relative error = 3.375759026404054e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999929 y[1] (closed_form) = 2.237843138593083 y[1] (numeric) = 2.237843138592338 absolute error = 7.456257833382551e-13 relative error = 3.331894762771554e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999928 y[1] (closed_form) = 2.257688988590906 y[1] (numeric) = 2.257688988590163 absolute error = 7.425171588693047e-13 relative error = 3.288837225240368e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999927 y[1] (closed_form) = 2.27750906990461 y[1] (numeric) = 2.277509069903869 absolute error = 7.416289804496046e-13 relative error = 3.256316254673209e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999926 y[1] (closed_form) = 2.29730140054258 y[1] (numeric) = 2.297301400541841 absolute error = 7.394085344003543e-13 relative error = 3.218596106830908e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.729999999999924 y[1] (closed_form) = 2.317064001288246 y[1] (numeric) = 2.317064001287509 absolute error = 7.371880883511039e-13 relative error = 3.181561182346455e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999923 y[1] (closed_form) = 2.336794895898003 y[1] (numeric) = 2.336794895897267 absolute error = 7.358558207215538e-13 relative error = 3.148996182819772e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999922 y[1] (closed_form) = 2.356492111298831 y[1] (numeric) = 2.356492111298098 absolute error = 7.327471962526033e-13 relative error = 3.109482916319775e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999921 y[1] (closed_form) = 2.376153677785606 y[1] (numeric) = 2.376153677784875 absolute error = 7.30526750203353e-13 relative error = 3.074408684223439e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.76999999999992 y[1] (closed_form) = 2.395777629218061 y[1] (numeric) = 2.395777629217333 absolute error = 7.283063041541027e-13 relative error = 3.039957862833074e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999919 y[1] (closed_form) = 2.415362003217409 y[1] (numeric) = 2.415362003216682 absolute error = 7.269740365245525e-13 relative error = 3.009793296227144e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999918 y[1] (closed_form) = 2.434904841362568 y[1] (numeric) = 2.434904841361845 absolute error = 7.23421322845752e-13 relative error = 2.971045564314237e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999917 y[1] (closed_form) = 2.454404189386012 y[1] (numeric) = 2.45440418938529 absolute error = 7.220890552162018e-13 relative error = 2.942013619186487e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999916 y[1] (closed_form) = 2.473858097369185 y[1] (numeric) = 2.473858097368466 absolute error = 7.194245199571014e-13 relative error = 2.908107464701272e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.819999999999915 y[1] (closed_form) = 2.493264619937502 y[1] (numeric) = 2.493264619936785 absolute error = 7.167599846980011e-13 relative error = 2.874785046747135e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.829999999999913 y[1] (closed_form) = 2.512621816454878 y[1] (numeric) = 2.512621816454163 absolute error = 7.149836278586008e-13 relative error = 2.845568016548504e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999912 y[1] (closed_form) = 2.531927751217792 y[1] (numeric) = 2.531927751217079 absolute error = 7.123190925995004e-13 relative error = 2.813346835259787e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.849999999999911 y[1] (closed_form) = 2.551180493648856 y[1] (numeric) = 2.551180493648145 absolute error = 7.100986465502501e-13 relative error = 2.78341202560162e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.85999999999991 y[1] (closed_form) = 2.570378118489869 y[1] (numeric) = 2.570378118489162 absolute error = 7.074341112911497e-13 relative error = 2.752256978077516e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999909 y[1] (closed_form) = 2.589518705994348 y[1] (numeric) = 2.589518705993643 absolute error = 7.052136652418994e-13 relative error = 2.723338756385251e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999908 y[1] (closed_form) = 2.608600342119491 y[1] (numeric) = 2.608600342118788 absolute error = 7.029932191926491e-13 relative error = 2.694905800025566e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999907 y[1] (closed_form) = 2.627621118717588 y[1] (numeric) = 2.627621118716886 absolute error = 7.02105040772949e-13 relative error = 2.672017802610795e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999906 y[1] (closed_form) = 2.646579133726829 y[1] (numeric) = 2.646579133726129 absolute error = 6.998845947236987e-13 relative error = 2.644487692828377e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.909999999999905 y[1] (closed_form) = 2.665472491361511 y[1] (numeric) = 2.665472491360813 absolute error = 6.981082378842984e-13 relative error = 2.61907875675621e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.919999999999904 y[1] (closed_form) = 2.684299302301615 y[1] (numeric) = 2.68429930230092 absolute error = 6.954437026251981e-13 relative error = 2.590783010035056e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999902 y[1] (closed_form) = 2.703057683881737 y[1] (numeric) = 2.703057683881044 absolute error = 6.936673457857978e-13 relative error = 2.566232122688754e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999901 y[1] (closed_form) = 2.721745760279351 y[1] (numeric) = 2.721745760278659 absolute error = 6.918909889463976e-13 relative error = 2.542085300705618e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9499999999999 y[1] (closed_form) = 2.740361662702389 y[1] (numeric) = 2.740361662701698 absolute error = 6.905587213168474e-13 relative error = 2.519954685966003e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999899 y[1] (closed_form) = 2.758903529576123 y[1] (numeric) = 2.758903529575434 absolute error = 6.887823644774471e-13 relative error = 2.496580098193109e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999898 y[1] (closed_form) = 2.777369506729316 y[1] (numeric) = 2.777369506728629 absolute error = 6.874500968478969e-13 relative error = 2.475184145221827e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999897 y[1] (closed_form) = 2.795757747579643 y[1] (numeric) = 2.795757747578958 absolute error = 6.847855615887966e-13 relative error = 2.449373741990459e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999896 y[1] (closed_form) = 2.814066413318341 y[1] (numeric) = 2.814066413317657 absolute error = 6.834532939592464e-13 relative error = 2.428703497275744e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.999999999999895 y[1] (closed_form) = 2.832293673094093 y[1] (numeric) = 2.832293673093412 absolute error = 6.812328479099961e-13 relative error = 2.405233801782265e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.009999999999894 y[1] (closed_form) = 2.850437704196112 y[1] (numeric) = 2.850437704195433 absolute error = 6.794564910705958e-13 relative error = 2.383691775022383e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999893 y[1] (closed_form) = 2.868496692236407 y[1] (numeric) = 2.86849669223573 absolute error = 6.767919558114954e-13 relative error = 2.359395977841754e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999891 y[1] (closed_form) = 2.886468831331223 y[1] (numeric) = 2.886468831330549 absolute error = 6.741274205523951e-13 relative error = 2.335474449732725e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.03999999999989 y[1] (closed_form) = 2.904352324281628 y[1] (numeric) = 2.904352324280956 absolute error = 6.727951529228449e-13 relative error = 2.316506669311397e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999889 y[1] (closed_form) = 2.92214538275323 y[1] (numeric) = 2.922145382752559 absolute error = 6.705747068735946e-13 relative error = 2.294802684463915e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999888 y[1] (closed_form) = 2.939846227455007 y[1] (numeric) = 2.939846227454339 absolute error = 6.683542608243442e-13 relative error = 2.273432721013205e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999887 y[1] (closed_form) = 2.957453088317242 y[1] (numeric) = 2.957453088316575 absolute error = 6.661338147750939e-13 relative error = 2.252390130570479e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999886 y[1] (closed_form) = 2.974964204668519 y[1] (numeric) = 2.974964204667855 absolute error = 6.639133687258436e-13 relative error = 2.231668427082198e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.089999999999885 y[1] (closed_form) = 2.992377825411798 y[1] (numeric) = 2.992377825411137 absolute error = 6.612488334667432e-13 relative error = 2.209777214131524e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.099999999999884 y[1] (closed_form) = 3.009692209199514 y[1] (numeric) = 3.009692209198854 absolute error = 6.59472476627343e-13 relative error = 2.191162520245691e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999883 y[1] (closed_form) = 3.026905624607718 y[1] (numeric) = 3.02690562460706 absolute error = 6.576961197879427e-13 relative error = 2.17283325400401e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999882 y[1] (closed_form) = 3.044016350309212 y[1] (numeric) = 3.044016350308557 absolute error = 6.550315845288424e-13 relative error = 2.151866183183622e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.12999999999988 y[1] (closed_form) = 3.061022675245687 y[1] (numeric) = 3.061022675245034 absolute error = 6.536993168992922e-13 relative error = 2.135558557555684e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999879 y[1] (closed_form) = 3.077922898798819 y[1] (numeric) = 3.077922898798168 absolute error = 6.514788708500419e-13 relative error = 2.116618551765173e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999878 y[1] (closed_form) = 3.094715330960338 y[1] (numeric) = 3.09471533095969 absolute error = 6.483702463810914e-13 relative error = 2.095088488090089e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999877 y[1] (closed_form) = 3.111398292501021 y[1] (numeric) = 3.111398292500374 absolute error = 6.465938895416912e-13 relative error = 2.078145671996055e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999876 y[1] (closed_form) = 3.127970115138615 y[1] (numeric) = 3.127970115137971 absolute error = 6.448175327022909e-13 relative error = 2.061456820132426e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.179999999999875 y[1] (closed_form) = 3.144429141704668 y[1] (numeric) = 3.144429141704026 absolute error = 6.421529974431905e-13 relative error = 2.042192615906951e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.189999999999874 y[1] (closed_form) = 3.160773726310238 y[1] (numeric) = 3.160773726309598 absolute error = 6.408207298136404e-13 relative error = 2.027417288619736e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999873 y[1] (closed_form) = 3.177002234510486 y[1] (numeric) = 3.177002234509846 absolute error = 6.394884621840902e-13 relative error = 2.012867524100508e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999872 y[1] (closed_form) = 3.193113043468114 y[1] (numeric) = 3.193113043467477 absolute error = 6.372680161348399e-13 relative error = 1.995757768233248e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999871 y[1] (closed_form) = 3.209104542115653 y[1] (numeric) = 3.209104542115017 absolute error = 6.359357485052897e-13 relative error = 1.981661052668727e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999869 y[1] (closed_form) = 3.224975131316564 y[1] (numeric) = 3.22497513131593 absolute error = 6.337153024560394e-13 relative error = 1.965023842516675e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999868 y[1] (closed_form) = 3.240723224025153 y[1] (numeric) = 3.24072322402452 absolute error = 6.328271240363392e-13 relative error = 1.952734251863489e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999867 y[1] (closed_form) = 3.256347245445271 y[1] (numeric) = 3.256347245444641 absolute error = 6.297184995673888e-13 relative error = 1.93381863819404e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999866 y[1] (closed_form) = 3.271845633187798 y[1] (numeric) = 3.27184563318717 absolute error = 6.279421427279885e-13 relative error = 1.919229123643517e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.269999999999865 y[1] (closed_form) = 3.287216837426874 y[1] (numeric) = 3.287216837426248 absolute error = 6.266098750984384e-13 relative error = 1.906201829961811e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.279999999999864 y[1] (closed_form) = 3.302459321054885 y[1] (numeric) = 3.30245932105426 absolute error = 6.24389429049188e-13 relative error = 1.890680151814082e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999863 y[1] (closed_form) = 3.317571559836169 y[1] (numeric) = 3.317571559835546 absolute error = 6.230571614196379e-13 relative error = 1.878051912919118e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999862 y[1] (closed_form) = 3.332552042559442 y[1] (numeric) = 3.332552042558821 absolute error = 6.208367153703875e-13 relative error = 1.862946797054599e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999861 y[1] (closed_form) = 3.347399271188916 y[1] (numeric) = 3.347399271188296 absolute error = 6.195044477408373e-13 relative error = 1.850703777923702e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.31999999999986 y[1] (closed_form) = 3.362111761014099 y[1] (numeric) = 3.362111761013482 absolute error = 6.177280909014371e-13 relative error = 1.83732170377083e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999858 y[1] (closed_form) = 3.376688040798271 y[1] (numeric) = 3.376688040797655 absolute error = 6.159517340620368e-13 relative error = 1.824129817797506e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999857 y[1] (closed_form) = 3.3911266529256 y[1] (numeric) = 3.391126652924985 absolute error = 6.150635556423367e-13 relative error = 1.813743981256813e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999856 y[1] (closed_form) = 3.405426153546903 y[1] (numeric) = 3.40542615354629 absolute error = 6.137312880127865e-13 relative error = 1.802215817757663e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.359999999999855 y[1] (closed_form) = 3.419585112724037 y[1] (numeric) = 3.419585112723425 absolute error = 6.119549311733863e-13 relative error = 1.789558999120521e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.369999999999854 y[1] (closed_form) = 3.433602114572882 y[1] (numeric) = 3.433602114572272 absolute error = 6.106226635438361e-13 relative error = 1.778373390883683e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999853 y[1] (closed_form) = 3.447475757404934 y[1] (numeric) = 3.447475757404325 absolute error = 6.088463067044358e-13 relative error = 1.766064069911665e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999852 y[1] (closed_form) = 3.461204653867472 y[1] (numeric) = 3.461204653866864 absolute error = 6.075140390748857e-13 relative error = 1.755209818050092e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999851 y[1] (closed_form) = 3.474787431082289 y[1] (numeric) = 3.474787431081683 absolute error = 6.057376822354854e-13 relative error = 1.743236656196885e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.40999999999985 y[1] (closed_form) = 3.488222730782984 y[1] (numeric) = 3.488222730782379 absolute error = 6.044054146059352e-13 relative error = 1.732703044654111e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999848 y[1] (closed_form) = 3.501509209450782 y[1] (numeric) = 3.501509209450179 absolute error = 6.02629057766535e-13 relative error = 1.721055184261699e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999847 y[1] (closed_form) = 3.514645538448888 y[1] (numeric) = 3.514645538448287 absolute error = 6.008527009271347e-13 relative error = 1.709568416940014e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999846 y[1] (closed_form) = 3.527630404155349 y[1] (numeric) = 3.52763040415475 absolute error = 5.995204332975845e-13 relative error = 1.699498996809256e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.449999999999845 y[1] (closed_form) = 3.540462508094417 y[1] (numeric) = 3.540462508093818 absolute error = 5.990763440877345e-13 relative error = 1.692084982450994e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.459999999999844 y[1] (closed_form) = 3.553140567066389 y[1] (numeric) = 3.553140567065793 absolute error = 5.968558980384842e-13 relative error = 1.679798158200286e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999843 y[1] (closed_form) = 3.565663313275935 y[1] (numeric) = 3.565663313275339 absolute error = 5.95523630408934e-13 relative error = 1.670162261791901e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999842 y[1] (closed_form) = 3.578029494458868 y[1] (numeric) = 3.578029494458273 absolute error = 5.941913627793838e-13 relative error = 1.660666474939855e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999841 y[1] (closed_form) = 3.590237874007375 y[1] (numeric) = 3.590237874006782 absolute error = 5.928590951498336e-13 relative error = 1.651308676347098e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.49999999999984 y[1] (closed_form) = 3.602287231093675 y[1] (numeric) = 3.602287231093084 absolute error = 5.910827383104333e-13 relative error = 1.640853991898301e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999839 y[1] (closed_form) = 3.614176360792102 y[1] (numeric) = 3.614176360791511 absolute error = 5.901945598907332e-13 relative error = 1.632998783051592e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999837 y[1] (closed_form) = 3.625904074199591 y[1] (numeric) = 3.625904074199001 absolute error = 5.893063814710331e-13 relative error = 1.625267435132357e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999836 y[1] (closed_form) = 3.637469198554576 y[1] (numeric) = 3.637469198553987 absolute error = 5.88418203051333e-13 relative error = 1.617658242398735e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999835 y[1] (closed_form) = 3.648870577354258 y[1] (numeric) = 3.648870577353671 absolute error = 5.870859354217828e-13 relative error = 1.6089524771456e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.549999999999834 y[1] (closed_form) = 3.660107070470259 y[1] (numeric) = 3.660107070469674 absolute error = 5.853095785823825e-13 relative error = 1.599159716677853e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999833 y[1] (closed_form) = 3.671177554262632 y[1] (numeric) = 3.671177554262048 absolute error = 5.848654893725325e-13 relative error = 1.593127765486147e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999832 y[1] (closed_form) = 3.682080921692221 y[1] (numeric) = 3.682080921691639 absolute error = 5.826450433232822e-13 relative error = 1.582379789348868e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999831 y[1] (closed_form) = 3.692816082431371 y[1] (numeric) = 3.692816082430789 absolute error = 5.81756864903582e-13 relative error = 1.575374597373802e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.58999999999983 y[1] (closed_form) = 3.703381962972953 y[1] (numeric) = 3.703381962972372 absolute error = 5.808686864838819e-13 relative error = 1.568481707508182e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999829 y[1] (closed_form) = 3.713777506737718 y[1] (numeric) = 3.713777506737138 absolute error = 5.795364188543317e-13 relative error = 1.560503874566821e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999828 y[1] (closed_form) = 3.724001674179952 y[1] (numeric) = 3.724001674179374 absolute error = 5.777600620149315e-13 relative error = 1.551449522756076e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999826 y[1] (closed_form) = 3.734053442891431 y[1] (numeric) = 3.734053442890855 absolute error = 5.759837051755312e-13 relative error = 1.542515965517417e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999825 y[1] (closed_form) = 3.743931807703662 y[1] (numeric) = 3.743931807703087 absolute error = 5.755396159656812e-13 relative error = 1.537259879524056e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.639999999999824 y[1] (closed_form) = 3.753635780788394 y[1] (numeric) = 3.753635780787819 absolute error = 5.74651437545981e-13 relative error = 1.530919543358797e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999823 y[1] (closed_form) = 3.763164391756405 y[1] (numeric) = 3.763164391755832 absolute error = 5.733191699164308e-13 relative error = 1.523502856192902e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999822 y[1] (closed_form) = 3.772516687754539 y[1] (numeric) = 3.772516687753967 absolute error = 5.724309914967307e-13 relative error = 1.517371661614705e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999821 y[1] (closed_form) = 3.78169173356099 y[1] (numeric) = 3.781691733560419 absolute error = 5.710987238671805e-13 relative error = 1.51016731162646e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.67999999999982 y[1] (closed_form) = 3.790688611678823 y[1] (numeric) = 3.790688611678253 absolute error = 5.702105454474804e-13 relative error = 1.504240004548791e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999819 y[1] (closed_form) = 3.799506422427725 y[1] (numeric) = 3.799506422427155 absolute error = 5.697664562376303e-13 relative error = 1.499580189875225e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999818 y[1] (closed_form) = 3.808144284033967 y[1] (numeric) = 3.808144284033398 absolute error = 5.688782778179302e-13 relative error = 1.493846439072727e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999817 y[1] (closed_form) = 3.816601332718587 y[1] (numeric) = 3.816601332718019 absolute error = 5.684341886080801e-13 relative error = 1.489372714239402e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999815 y[1] (closed_form) = 3.824876722783765 y[1] (numeric) = 3.824876722783198 absolute error = 5.6710192097853e-13 relative error = 1.482667186632332e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.729999999999814 y[1] (closed_form) = 3.83296962669739 y[1] (numeric) = 3.832969626696824 absolute error = 5.662137425588298e-13 relative error = 1.477219486987425e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999813 y[1] (closed_form) = 3.840879235175815 y[1] (numeric) = 3.84087923517525 absolute error = 5.648814749292796e-13 relative error = 1.470708763128874e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999812 y[1] (closed_form) = 3.848604757264784 y[1] (numeric) = 3.848604757264219 absolute error = 5.648814749292796e-13 relative error = 1.467756526213782e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999811 y[1] (closed_form) = 3.856145420418525 y[1] (numeric) = 3.856145420417961 absolute error = 5.631051180898794e-13 relative error = 1.460279778631282e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.76999999999981 y[1] (closed_form) = 3.863500470577007 y[1] (numeric) = 3.863500470576444 absolute error = 5.631051180898794e-13 relative error = 1.457499804589853e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999809 y[1] (closed_form) = 3.870669172241342 y[1] (numeric) = 3.870669172240781 absolute error = 5.617728504603292e-13 relative error = 1.451358474366927e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999808 y[1] (closed_form) = 3.87765080854734 y[1] (numeric) = 3.877650808546779 absolute error = 5.613287612504791e-13 relative error = 1.447600077895529e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999807 y[1] (closed_form) = 3.884444681337187 y[1] (numeric) = 3.884444681336627 absolute error = 5.59996493620929e-13 relative error = 1.441638482616143e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999806 y[1] (closed_form) = 3.891050111229266 y[1] (numeric) = 3.891050111228706 absolute error = 5.59996493620929e-13 relative error = 1.439191163343857e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.819999999999804 y[1] (closed_form) = 3.897466437686091 y[1] (numeric) = 3.897466437685532 absolute error = 5.586642259913788e-13 relative error = 1.433403558243481e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999803 y[1] (closed_form) = 3.903693019080364 y[1] (numeric) = 3.903693019079806 absolute error = 5.582201367815287e-13 relative error = 1.429979596379827e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999802 y[1] (closed_form) = 3.909729232759135 y[1] (numeric) = 3.909729232758579 absolute error = 5.564437799421285e-13 relative error = 1.423228430449237e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999801 y[1] (closed_form) = 3.915574475106066 y[1] (numeric) = 3.915574475105511 absolute error = 5.551115123125783e-13 relative error = 1.417701325416729e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8599999999998 y[1] (closed_form) = 3.921228161601793 y[1] (numeric) = 3.921228161601239 absolute error = 5.546674231027282e-13 relative error = 1.414524736240164e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999799 y[1] (closed_form) = 3.926689726882379 y[1] (numeric) = 3.926689726881825 absolute error = 5.542233338928781e-13 relative error = 1.411426347487117e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999798 y[1] (closed_form) = 3.931958624795845 y[1] (numeric) = 3.931958624795292 absolute error = 5.53335155473178e-13 relative error = 1.407276139641241e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999797 y[1] (closed_form) = 3.937034328456792 y[1] (numeric) = 3.937034328456239 absolute error = 5.52891066263328e-13 relative error = 1.404333871988477e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999796 y[1] (closed_form) = 3.941916330299083 y[1] (numeric) = 3.941916330298531 absolute error = 5.520028878436278e-13 relative error = 1.400341462350993e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.909999999999795 y[1] (closed_form) = 3.946604142126603 y[1] (numeric) = 3.946604142126051 absolute error = 5.515587986337778e-13 relative error = 1.397552880326563e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999793 y[1] (closed_form) = 3.951097295162075 y[1] (numeric) = 3.951097295161523 absolute error = 5.524469770534779e-13 relative error = 1.398211523998465e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999792 y[1] (closed_form) = 3.955395340093939 y[1] (numeric) = 3.955395340093388 absolute error = 5.511147094239277e-13 relative error = 1.393323958891146e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999791 y[1] (closed_form) = 3.959497847121285 y[1] (numeric) = 3.959497847120734 absolute error = 5.511147094239277e-13 relative error = 1.391880310844494e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.94999999999979 y[1] (closed_form) = 3.963404405996828 y[1] (numeric) = 3.963404405996277 absolute error = 5.506706202140776e-13 relative error = 1.389387919589749e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999789 y[1] (closed_form) = 3.967114626067937 y[1] (numeric) = 3.967114626067386 absolute error = 5.506706202140776e-13 relative error = 1.38808850290238e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999788 y[1] (closed_form) = 3.970628136315695 y[1] (numeric) = 3.970628136315145 absolute error = 5.502265310042276e-13 relative error = 1.385741782192621e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999787 y[1] (closed_form) = 3.973944585392006 y[1] (numeric) = 3.973944585391457 absolute error = 5.493383525845275e-13 relative error = 1.382350309070398e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999786 y[1] (closed_form) = 3.977063641654727 y[1] (numeric) = 3.977063641654178 absolute error = 5.488942633746774e-13 relative error = 1.380149559654269e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.999999999999785 y[1] (closed_form) = 3.97998499320083 y[1] (numeric) = 3.979984993200281 absolute error = 5.488942633746774e-13 relative error = 1.379136515118463e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.009999999999784 y[1] (closed_form) = 3.982708347897595 y[1] (numeric) = 3.982708347897046 absolute error = 5.484501741648273e-13 relative error = 1.377078425675696e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999782 y[1] (closed_form) = 3.985233433411821 y[1] (numeric) = 3.985233433411273 absolute error = 5.480060849549773e-13 relative error = 1.375091557650164e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999781 y[1] (closed_form) = 3.987559997237063 y[1] (numeric) = 3.987559997236514 absolute error = 5.484501741648273e-13 relative error = 1.375402939503964e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.03999999999978 y[1] (closed_form) = 3.989687806718875 y[1] (numeric) = 3.989687806718326 absolute error = 5.488942633746774e-13 relative error = 1.37578249217973e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999779 y[1] (closed_form) = 3.991616649078082 y[1] (numeric) = 3.991616649077534 absolute error = 5.488942633746774e-13 relative error = 1.375117681958391e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999778 y[1] (closed_form) = 3.993346331432057 y[1] (numeric) = 3.993346331431509 absolute error = 5.480060849549773e-13 relative error = 1.37229791626527e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999777 y[1] (closed_form) = 3.994876680814005 y[1] (numeric) = 3.994876680813457 absolute error = 5.475619957451272e-13 relative error = 1.370660572264661e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999776 y[1] (closed_form) = 3.996207544190264 y[1] (numeric) = 3.996207544189716 absolute error = 5.475619957451272e-13 relative error = 1.37020409898675e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.089999999999775 y[1] (closed_form) = 3.997338788475604 y[1] (numeric) = 3.997338788475056 absolute error = 5.480060849549773e-13 relative error = 1.370927294266096e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.099999999999774 y[1] (closed_form) = 3.99827030054654 y[1] (numeric) = 3.998270300545993 absolute error = 5.475619957451272e-13 relative error = 1.369497193999812e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.109999999999773 y[1] (closed_form) = 3.999001987252641 y[1] (numeric) = 3.999001987252094 absolute error = 5.471179065352771e-13 relative error = 1.368136120660328e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999771 y[1] (closed_form) = 3.999533775425847 y[1] (numeric) = 3.9995337754253 absolute error = 5.471179065352771e-13 relative error = 1.367954209805425e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.12999999999977 y[1] (closed_form) = 3.999865611887783 y[1] (numeric) = 3.999865611887235 absolute error = 5.480060849549773e-13 relative error = 1.370061242373439e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999769 y[1] (closed_form) = 3.999997463455078 y[1] (numeric) = 3.999997463454532 absolute error = 5.466738173254271e-13 relative error = 1.366685409978302e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999768 y[1] (closed_form) = 3.999929316942688 y[1] (numeric) = 3.999929316942142 absolute error = 5.45785638905727e-13 relative error = 1.364488208813884e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.159999999999767 y[1] (closed_form) = 3.999661179165205 y[1] (numeric) = 3.99966117916466 absolute error = 5.453415496958769e-13 relative error = 1.363469367196995e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.169999999999766 y[1] (closed_form) = 3.999193076936185 y[1] (numeric) = 3.99919307693564 absolute error = 5.45785638905727e-13 relative error = 1.364739407190257e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.179999999999765 y[1] (closed_form) = 3.99852505706546 y[1] (numeric) = 3.998525057064914 absolute error = 5.453415496958769e-13 relative error = 1.363856776968921e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.189999999999764 y[1] (closed_form) = 3.99765718635446 y[1] (numeric) = 3.997657186353915 absolute error = 5.453415496958769e-13 relative error = 1.364152863225334e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999763 y[1] (closed_form) = 3.996589551589534 y[1] (numeric) = 3.996589551588988 absolute error = 5.46229728115577e-13 relative error = 1.366739619029252e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999761 y[1] (closed_form) = 3.995322259533268 y[1] (numeric) = 3.995322259532721 absolute error = 5.46229728115577e-13 relative error = 1.367173140570111e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.21999999999976 y[1] (closed_form) = 3.993855436913812 y[1] (numeric) = 3.993855436913265 absolute error = 5.466738173254271e-13 relative error = 1.368787193128504e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999759 y[1] (closed_form) = 3.992189230412205 y[1] (numeric) = 3.992189230411657 absolute error = 5.475619957451272e-13 relative error = 1.371583269585119e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999758 y[1] (closed_form) = 3.990323806647709 y[1] (numeric) = 3.990323806647161 absolute error = 5.475619957451272e-13 relative error = 1.372224466678399e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999757 y[1] (closed_form) = 3.988259352161145 y[1] (numeric) = 3.988259352160597 absolute error = 5.475619957451272e-13 relative error = 1.372934775288413e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999756 y[1] (closed_form) = 3.985996073396243 y[1] (numeric) = 3.985996073395695 absolute error = 5.480060849549773e-13 relative error = 1.37482846160471e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.269999999999755 y[1] (closed_form) = 3.983534196678993 y[1] (numeric) = 3.983534196678444 absolute error = 5.484501741648273e-13 relative error = 1.376792935835875e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.279999999999754 y[1] (closed_form) = 3.980873968195014 y[1] (numeric) = 3.980873968194466 absolute error = 5.480060849549773e-13 relative error = 1.376597423915561e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999753 y[1] (closed_form) = 3.978015653964939 y[1] (numeric) = 3.97801565396439 absolute error = 5.493383525845275e-13 relative error = 1.380935623108961e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999752 y[1] (closed_form) = 3.974959539817808 y[1] (numeric) = 3.974959539817259 absolute error = 5.497824417943775e-13 relative error = 1.383114560757458e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.30999999999975 y[1] (closed_form) = 3.971705931362489 y[1] (numeric) = 3.97170593136194 absolute error = 5.493383525845275e-13 relative error = 1.383129471511698e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999749 y[1] (closed_form) = 3.968255153957118 y[1] (numeric) = 3.968255153956568 absolute error = 5.502265310042276e-13 relative error = 1.386570443827296e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999748 y[1] (closed_form) = 3.964607552676558 y[1] (numeric) = 3.964607552676008 absolute error = 5.502265310042276e-13 relative error = 1.387846145409178e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999747 y[1] (closed_form) = 3.960763492277898 y[1] (numeric) = 3.960763492277347 absolute error = 5.502265310042276e-13 relative error = 1.389193098949172e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999746 y[1] (closed_form) = 3.956723357163973 y[1] (numeric) = 3.956723357163423 absolute error = 5.502265310042276e-13 relative error = 1.390611577653002e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.359999999999745 y[1] (closed_form) = 3.95248755134493 y[1] (numeric) = 3.952487551344379 absolute error = 5.511147094239277e-13 relative error = 1.394349007465937e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.369999999999744 y[1] (closed_form) = 3.94805649839782 y[1] (numeric) = 3.948056498397269 absolute error = 5.515587986337778e-13 relative error = 1.397038767954837e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999743 y[1] (closed_form) = 3.943430641424245 y[1] (numeric) = 3.943430641423693 absolute error = 5.520028878436278e-13 relative error = 1.39980371924143e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999742 y[1] (closed_form) = 3.938610443006048 y[1] (numeric) = 3.938610443005496 absolute error = 5.520028878436278e-13 relative error = 1.401516844154623e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999741 y[1] (closed_form) = 3.933596385159055 y[1] (numeric) = 3.933596385158501 absolute error = 5.53335155473178e-13 relative error = 1.406690217534364e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999739 y[1] (closed_form) = 3.928388969284869 y[1] (numeric) = 3.928388969284315 absolute error = 5.537792446830281e-13 relative error = 1.409685367240604e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999738 y[1] (closed_form) = 3.922988716120742 y[1] (numeric) = 3.922988716120187 absolute error = 5.546674231027282e-13 relative error = 1.413889927400078e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999737 y[1] (closed_form) = 3.917396165687487 y[1] (numeric) = 3.917396165686932 absolute error = 5.551115123125783e-13 relative error = 1.417042057616755e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999736 y[1] (closed_form) = 3.911611877235488 y[1] (numeric) = 3.911611877234932 absolute error = 5.564437799421285e-13 relative error = 1.42254343581601e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.449999999999735 y[1] (closed_form) = 3.90563642918877 y[1] (numeric) = 3.905636429188214 absolute error = 5.564437799421285e-13 relative error = 1.424719863281555e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.459999999999734 y[1] (closed_form) = 3.899470419087159 y[1] (numeric) = 3.899470419086602 absolute error = 5.568878691519785e-13 relative error = 1.428111536443819e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999733 y[1] (closed_form) = 3.893114463526525 y[1] (numeric) = 3.893114463525968 absolute error = 5.573319583618286e-13 relative error = 1.431583796426517e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999732 y[1] (closed_form) = 3.88656919809713 y[1] (numeric) = 3.886569198096572 absolute error = 5.577760475716786e-13 relative error = 1.435137312992566e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999731 y[1] (closed_form) = 3.87983527732006 y[1] (numeric) = 3.879835277319502 absolute error = 5.586642259913788e-13 relative error = 1.439917383238156e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.49999999999973 y[1] (closed_form) = 3.872913374581782 y[1] (numeric) = 3.872913374581223 absolute error = 5.586642259913788e-13 relative error = 1.442490889824527e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999728 y[1] (closed_form) = 3.865804182066803 y[1] (numeric) = 3.865804182066243 absolute error = 5.59996493620929e-13 relative error = 1.448589911042866e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999727 y[1] (closed_form) = 3.858508410688448 y[1] (numeric) = 3.858508410687888 absolute error = 5.60440582830779e-13 relative error = 1.452479878696917e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999726 y[1] (closed_form) = 3.851026790017777 y[1] (numeric) = 3.851026790017216 absolute error = 5.608846720406291e-13 relative error = 1.456454869372747e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.539999999999725 y[1] (closed_form) = 3.84336006821062 y[1] (numeric) = 3.843360068210059 absolute error = 5.608846720406291e-13 relative error = 1.459360200674001e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.549999999999724 y[1] (closed_form) = 3.835509011932771 y[1] (numeric) = 3.835509011932209 absolute error = 5.617728504603292e-13 relative error = 1.464663096117309e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999723 y[1] (closed_form) = 3.827474406283315 y[1] (numeric) = 3.827474406282752 absolute error = 5.631051180898794e-13 relative error = 1.471218506818665e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999722 y[1] (closed_form) = 3.81925705471612 y[1] (numeric) = 3.819257054715557 absolute error = 5.631051180898794e-13 relative error = 1.474383918187812e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999721 y[1] (closed_form) = 3.810857778959496 y[1] (numeric) = 3.810857778958932 absolute error = 5.639932965095795e-13 relative error = 1.479964168758799e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.58999999999972 y[1] (closed_form) = 3.80227741893402 y[1] (numeric) = 3.802277418933455 absolute error = 5.648814749292796e-13 relative error = 1.48563982237689e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999719 y[1] (closed_form) = 3.793516832668543 y[1] (numeric) = 3.793516832667978 absolute error = 5.657696533489798e-13 relative error = 1.491412001857364e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999717 y[1] (closed_form) = 3.784576896214392 y[1] (numeric) = 3.784576896213826 absolute error = 5.662137425588298e-13 relative error = 1.49610843718144e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999716 y[1] (closed_form) = 3.775458503557761 y[1] (numeric) = 3.775458503557195 absolute error = 5.666578317686799e-13 relative error = 1.500898053136318e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.629999999999715 y[1] (closed_form) = 3.766162566530319 y[1] (numeric) = 3.766162566529751 absolute error = 5.684341886080801e-13 relative error = 1.509319309951524e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.639999999999714 y[1] (closed_form) = 3.756690014718021 y[1] (numeric) = 3.756690014717452 absolute error = 5.697664562376303e-13 relative error = 1.516671468780735e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999713 y[1] (closed_form) = 3.747041795368155 y[1] (numeric) = 3.747041795367585 absolute error = 5.702105454474804e-13 relative error = 1.521761903356234e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999712 y[1] (closed_form) = 3.737218873294616 y[1] (numeric) = 3.737218873294044 absolute error = 5.719869022868806e-13 relative error = 1.530514860593741e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999711 y[1] (closed_form) = 3.727222230781424 y[1] (numeric) = 3.72722223078085 absolute error = 5.733191699164308e-13 relative error = 1.538194221910489e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.67999999999971 y[1] (closed_form) = 3.717052867484501 y[1] (numeric) = 3.717052867483927 absolute error = 5.74207348336131e-13 relative error = 1.544791986573824e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999709 y[1] (closed_form) = 3.706711800331703 y[1] (numeric) = 3.706711800331127 absolute error = 5.755396159656812e-13 relative error = 1.552695885108138e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999708 y[1] (closed_form) = 3.696200063421126 y[1] (numeric) = 3.696200063420549 absolute error = 5.768718835952313e-13 relative error = 1.560716069739176e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999706 y[1] (closed_form) = 3.685518707917703 y[1] (numeric) = 3.685518707917125 absolute error = 5.782041512247815e-13 relative error = 1.56885420221205e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.719999999999705 y[1] (closed_form) = 3.674668801948083 y[1] (numeric) = 3.674668801947504 absolute error = 5.790923296444817e-13 relative error = 1.575903464653692e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.729999999999704 y[1] (closed_form) = 3.66365143049382 y[1] (numeric) = 3.663651430493239 absolute error = 5.808686864838819e-13 relative error = 1.585491135016595e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999703 y[1] (closed_form) = 3.652467695282879 y[1] (numeric) = 3.652467695282297 absolute error = 5.81756864903582e-13 relative error = 1.592777577895937e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999702 y[1] (closed_form) = 3.641118714679462 y[1] (numeric) = 3.641118714678879 absolute error = 5.826450433232822e-13 relative error = 1.600181397476281e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999701 y[1] (closed_form) = 3.629605623572171 y[1] (numeric) = 3.629605623571588 absolute error = 5.835332217429823e-13 relative error = 1.607704203325216e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7699999999997 y[1] (closed_form) = 3.617929573260524 y[1] (numeric) = 3.617929573259939 absolute error = 5.848654893725325e-13 relative error = 1.616575108855545e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999699 y[1] (closed_form) = 3.606091731339821 y[1] (numeric) = 3.606091731339234 absolute error = 5.866418462119327e-13 relative error = 1.626807884873105e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999698 y[1] (closed_form) = 3.594093281584389 y[1] (numeric) = 3.5940932815838 absolute error = 5.88418203051333e-13 relative error = 1.637181221940739e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999697 y[1] (closed_form) = 3.581935423829204 y[1] (numeric) = 3.581935423828615 absolute error = 5.893063814710331e-13 relative error = 1.64521777123789e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999695 y[1] (closed_form) = 3.569619373849913 y[1] (numeric) = 3.569619373849322 absolute error = 5.910827383104333e-13 relative error = 1.655870490396116e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.819999999999694 y[1] (closed_form) = 3.557146363241248 y[1] (numeric) = 3.557146363240657 absolute error = 5.915268275202834e-13 relative error = 1.662925185291752e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999693 y[1] (closed_form) = 3.544517639293877 y[1] (numeric) = 3.544517639293284 absolute error = 5.933031843596837e-13 relative error = 1.673861565202646e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999692 y[1] (closed_form) = 3.53173446486967 y[1] (numeric) = 3.531734464869075 absolute error = 5.946354519892338e-13 relative error = 1.683692412054476e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999691 y[1] (closed_form) = 3.518798118275418 y[1] (numeric) = 3.518798118274822 absolute error = 5.964118088286341e-13 relative error = 1.694930452904012e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.85999999999969 y[1] (closed_form) = 3.505709893134998 y[1] (numeric) = 3.505709893134401 absolute error = 5.972999872483342e-13 relative error = 1.703791829489336e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999689 y[1] (closed_form) = 3.49247109826002 y[1] (numeric) = 3.492471098259421 absolute error = 5.986322548778844e-13 relative error = 1.714065021686589e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999688 y[1] (closed_form) = 3.479083057518937 y[1] (numeric) = 3.479083057518336 absolute error = 6.008527009271347e-13 relative error = 1.727043278339049e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999687 y[1] (closed_form) = 3.465547109704668 y[1] (numeric) = 3.465547109704066 absolute error = 6.012967901369848e-13 relative error = 1.735070310985405e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999685 y[1] (closed_form) = 3.451864608400713 y[1] (numeric) = 3.451864608400109 absolute error = 6.039613253960852e-13 relative error = 1.749666901552975e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.909999999999684 y[1] (closed_form) = 3.438036921845801 y[1] (numeric) = 3.438036921845196 absolute error = 6.044054146059352e-13 relative error = 1.757995706111976e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999683 y[1] (closed_form) = 3.424065432797065 y[1] (numeric) = 3.424065432796459 absolute error = 6.057376822354854e-13 relative error = 1.769059891301983e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999682 y[1] (closed_form) = 3.409951538391766 y[1] (numeric) = 3.409951538391159 absolute error = 6.070699498650356e-13 relative error = 1.78028908337902e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999681 y[1] (closed_form) = 3.395696650007585 y[1] (numeric) = 3.395696650006976 absolute error = 6.088463067044358e-13 relative error = 1.792993807921788e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.94999999999968 y[1] (closed_form) = 3.381302193121478 y[1] (numeric) = 3.381302193120868 absolute error = 6.10178574333986e-13 relative error = 1.804566819183631e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999679 y[1] (closed_form) = 3.366769607167141 y[1] (numeric) = 3.366769607166528 absolute error = 6.128431095930864e-13 relative error = 1.820270410807062e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999678 y[1] (closed_form) = 3.352100345391058 y[1] (numeric) = 3.352100345390444 absolute error = 6.141753772226366e-13 relative error = 1.832210596162767e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999677 y[1] (closed_form) = 3.337295874707183 y[1] (numeric) = 3.337295874706568 absolute error = 6.150635556423367e-13 relative error = 1.842999778065236e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999676 y[1] (closed_form) = 3.322357675550247 y[1] (numeric) = 3.322357675549629 absolute error = 6.177280909014371e-13 relative error = 1.859306405952e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.999999999999674 y[1] (closed_form) = 3.307287241727717 y[1] (numeric) = 3.307287241727098 absolute error = 6.190603585309873e-13 relative error = 1.87180705298398e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999677 y[1] (closed_form) = 3.29208608027041 y[1] (numeric) = 3.292086080269795 absolute error = 6.150635556423367e-13 relative error = 1.86830945681656e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999681 y[1] (closed_form) = 3.27675571128181 y[1] (numeric) = 3.2767557112812 absolute error = 6.09734485124136e-13 relative error = 1.860787128637119e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.029999999999684 y[1] (closed_form) = 3.261297667786041 y[1] (numeric) = 3.261297667785437 absolute error = 6.044054146059352e-13 relative error = 1.853266632408445e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999687 y[1] (closed_form) = 3.245713495574572 y[1] (numeric) = 3.245713495573972 absolute error = 5.995204332975845e-13 relative error = 1.847114460703361e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999691 y[1] (closed_form) = 3.230004753051636 y[1] (numeric) = 3.230004753051042 absolute error = 5.941913627793838e-13 relative error = 1.83959903532032e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.059999999999694 y[1] (closed_form) = 3.214173011078396 y[1] (numeric) = 3.214173011077807 absolute error = 5.88418203051333e-13 relative error = 1.83069859968089e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999697 y[1] (closed_form) = 3.198219852815855 y[1] (numeric) = 3.198219852815272 absolute error = 5.830891325331322e-13 relative error = 1.823167760089272e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999701 y[1] (closed_form) = 3.182146873566546 y[1] (numeric) = 3.182146873565967 absolute error = 5.782041512247815e-13 relative error = 1.817025342317814e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.089999999999704 y[1] (closed_form) = 3.165955680614998 y[1] (numeric) = 3.165955680614426 absolute error = 5.724309914967307e-13 relative error = 1.808082769451573e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.099999999999707 y[1] (closed_form) = 3.149647893067017 y[1] (numeric) = 3.14964789306645 absolute error = 5.6710192097853e-13 relative error = 1.800524821288217e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.109999999999711 y[1] (closed_form) = 3.133225141687765 y[1] (numeric) = 3.133225141687203 absolute error = 5.617728504603292e-13 relative error = 1.792953985291082e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.119999999999714 y[1] (closed_form) = 3.116689068738695 y[1] (numeric) = 3.116689068738139 absolute error = 5.559996907322784e-13 relative error = 1.783943404265502e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.129999999999717 y[1] (closed_form) = 3.100041327813322 y[1] (numeric) = 3.100041327812771 absolute error = 5.511147094239277e-13 relative error = 1.777765684861588e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.139999999999721 y[1] (closed_form) = 3.083283583671866 y[1] (numeric) = 3.083283583671322 absolute error = 5.444533712761768e-13 relative error = 1.765823209254694e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.149999999999724 y[1] (closed_form) = 3.066417512074776 y[1] (numeric) = 3.066417512074237 absolute error = 5.38680211548126e-13 relative error = 1.75670863288166e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.159999999999727 y[1] (closed_form) = 3.049444799615157 y[1] (numeric) = 3.049444799614624 absolute error = 5.324629626102251e-13 relative error = 1.746098052594435e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.169999999999731 y[1] (closed_form) = 3.03236714355011 y[1] (numeric) = 3.032367143549583 absolute error = 5.271338920920243e-13 relative error = 1.73835774870878e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.179999999999734 y[1] (closed_form) = 3.015186251631012 y[1] (numeric) = 3.01518625163049 absolute error = 5.218048215738236e-13 relative error = 1.730589018477921e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999737 y[1] (closed_form) = 2.997903841932736 y[1] (numeric) = 2.99790384193222 absolute error = 5.160316618457728e-13 relative error = 1.721308250878018e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999741 y[1] (closed_form) = 2.980521642681851 y[1] (numeric) = 2.98052164268134 absolute error = 5.111466805374221e-13 relative error = 1.714957117632255e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.209999999999744 y[1] (closed_form) = 2.963041392083796 y[1] (numeric) = 2.963041392083291 absolute error = 5.053735208093713e-13 relative error = 1.705590486044344e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999748 y[1] (closed_form) = 2.945464838149064 y[1] (numeric) = 2.945464838148565 absolute error = 4.991562718714704e-13 relative error = 1.694660433241298e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999751 y[1] (closed_form) = 2.927793738518402 y[1] (numeric) = 2.92779373851791 absolute error = 4.924949337237194e-13 relative error = 1.682136713540976e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.239999999999754 y[1] (closed_form) = 2.910029860287048 y[1] (numeric) = 2.910029860286561 absolute error = 4.867217739956686e-13 relative error = 1.672566253143732e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999758 y[1] (closed_form) = 2.892174979828019 y[1] (numeric) = 2.892174979827539 absolute error = 4.800604358479177e-13 relative error = 1.659859583863989e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999761 y[1] (closed_form) = 2.874230882614485 y[1] (numeric) = 2.874230882614011 absolute error = 4.742872761198669e-13 relative error = 1.650136316427166e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.269999999999764 y[1] (closed_form) = 2.856199363041213 y[1] (numeric) = 2.856199363040745 absolute error = 4.68070027181966e-13 relative error = 1.638786259946421e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999768 y[1] (closed_form) = 2.838082224245134 y[1] (numeric) = 2.838082224244672 absolute error = 4.618527782440651e-13 relative error = 1.627341076655761e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999771 y[1] (closed_form) = 2.819881277925029 y[1] (numeric) = 2.819881277924573 absolute error = 4.565237077258644e-13 relative error = 1.618946553883967e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.299999999999774 y[1] (closed_form) = 2.801598344160364 y[1] (numeric) = 2.801598344159914 absolute error = 4.507505479978136e-13 relative error = 1.608904962902178e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999778 y[1] (closed_form) = 2.78323525122928 y[1] (numeric) = 2.783235251228835 absolute error = 4.445332990599127e-13 relative error = 1.59718190858489e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999781 y[1] (closed_form) = 2.764793835425766 y[1] (numeric) = 2.764793835425328 absolute error = 4.378719609121617e-13 relative error = 1.583741815760854e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.329999999999784 y[1] (closed_form) = 2.746275940876036 y[1] (numeric) = 2.746275940875603 absolute error = 4.320988011841109e-13 relative error = 1.573399070183295e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999788 y[1] (closed_form) = 2.727683419354112 y[1] (numeric) = 2.727683419353686 absolute error = 4.263256414560601e-13 relative error = 1.562958657266061e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999791 y[1] (closed_form) = 2.709018130096654 y[1] (numeric) = 2.709018130096235 absolute error = 4.18776124888609e-13 relative error = 1.545859439758226e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.359999999999794 y[1] (closed_form) = 2.690281939617033 y[1] (numeric) = 2.69028193961662 absolute error = 4.125588759507082e-13 relative error = 1.53351539061901e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999798 y[1] (closed_form) = 2.671476721518683 y[1] (numeric) = 2.671476721518276 absolute error = 4.067857162226574e-13 relative error = 1.522699834686965e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999801 y[1] (closed_form) = 2.652604356307743 y[1] (numeric) = 2.652604356307342 absolute error = 4.014566457044566e-13 relative error = 1.513443362745806e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999804 y[1] (closed_form) = 2.633666731205007 y[1] (numeric) = 2.633666731204612 absolute error = 3.956834859764058e-13 relative error = 1.502405301658516e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999808 y[1] (closed_form) = 2.614665739957205 y[1] (numeric) = 2.614665739956817 absolute error = 3.885780586188048e-13 relative error = 1.486148124712739e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999811 y[1] (closed_form) = 2.595603282647628 y[1] (numeric) = 2.595603282647245 absolute error = 3.82804898890754e-13 relative error = 1.474820522265161e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.419999999999814 y[1] (closed_form) = 2.576481265506119 y[1] (numeric) = 2.576481265505743 absolute error = 3.76143560743003e-13 relative error = 1.459911879736157e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999818 y[1] (closed_form) = 2.557301600718459 y[1] (numeric) = 2.55730160071809 absolute error = 3.69038133385402e-13 relative error = 1.443076300744984e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999821 y[1] (closed_form) = 2.538066206235143 y[1] (numeric) = 2.538066206234781 absolute error = 3.628208844475012e-13 relative error = 1.429517021881371e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.449999999999824 y[1] (closed_form) = 2.518777005579592 y[1] (numeric) = 2.518777005579235 absolute error = 3.570477247194503e-13 relative error = 1.417544006192365e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999828 y[1] (closed_form) = 2.499435927655795 y[1] (numeric) = 2.499435927655445 absolute error = 3.503863865716994e-13 relative error = 1.401861846886088e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999831 y[1] (closed_form) = 2.480044906555428 y[1] (numeric) = 2.480044906555083 absolute error = 3.441691376337985e-13 relative error = 1.387753652057133e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.479999999999834 y[1] (closed_form) = 2.46060588136444 y[1] (numeric) = 2.460605881364104 absolute error = 3.366196210663475e-13 relative error = 1.368035505465374e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999838 y[1] (closed_form) = 2.441120795969154 y[1] (numeric) = 2.441120795968824 absolute error = 3.304023721284466e-13 relative error = 1.353486368532094e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999841 y[1] (closed_form) = 2.421591598861871 y[1] (numeric) = 2.421591598861547 absolute error = 3.232969447708456e-13 relative error = 1.33505973890392e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.509999999999844 y[1] (closed_form) = 2.402020242946025 y[1] (numeric) = 2.402020242945709 absolute error = 3.166356066230946e-13 relative error = 1.318205404608697e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999848 y[1] (closed_form) = 2.382408685340901 y[1] (numeric) = 2.382408685340592 absolute error = 3.095301792654936e-13 relative error = 1.299232080415299e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999851 y[1] (closed_form) = 2.362758887185916 y[1] (numeric) = 2.362758887185613 absolute error = 3.033129303275928e-13 relative error = 1.283723582514352e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.539999999999854 y[1] (closed_form) = 2.34307281344451 y[1] (numeric) = 2.343072813444213 absolute error = 2.970956813896919e-13 relative error = 1.267974600212858e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999858 y[1] (closed_form) = 2.323352432707654 y[1] (numeric) = 2.323352432707362 absolute error = 2.913225216616411e-13 relative error = 1.253888637644748e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999861 y[1] (closed_form) = 2.303599716996985 y[1] (numeric) = 2.3035997169967 absolute error = 2.842170943040401e-13 relative error = 1.233795490626951e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.569999999999864 y[1] (closed_form) = 2.283816641567616 y[1] (numeric) = 2.283816641567338 absolute error = 2.779998453661392e-13 relative error = 1.217259916169626e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999868 y[1] (closed_form) = 2.264005184710603 y[1] (numeric) = 2.264005184710332 absolute error = 2.713385072183883e-13 relative error = 1.198488895037898e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999871 y[1] (closed_form) = 2.244167327555123 y[1] (numeric) = 2.244167327554858 absolute error = 2.642330798607873e-13 relative error = 1.177421472170938e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.599999999999874 y[1] (closed_form) = 2.224305053870359 y[1] (numeric) = 2.224305053870101 absolute error = 2.575717417130363e-13 relative error = 1.157987485865995e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999878 y[1] (closed_form) = 2.204420349867128 y[1] (numeric) = 2.204420349866877 absolute error = 2.509104035652854e-13 relative error = 1.138214876216367e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999881 y[1] (closed_form) = 2.18451520399926 y[1] (numeric) = 2.184515203999016 absolute error = 2.446931546273845e-13 relative error = 1.120125665316575e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.629999999999884 y[1] (closed_form) = 2.164591606764755 y[1] (numeric) = 2.164591606764517 absolute error = 2.380318164796336e-13 relative error = 1.099661551563535e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999888 y[1] (closed_form) = 2.144651550506732 y[1] (numeric) = 2.1446515505065 absolute error = 2.318145675417327e-13 relative error = 1.080896183284227e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999891 y[1] (closed_form) = 2.124697029214201 y[1] (numeric) = 2.124697029213976 absolute error = 2.247091401841317e-13 relative error = 1.057605564908415e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.659999999999894 y[1] (closed_form) = 2.104730038322663 y[1] (numeric) = 2.104730038322445 absolute error = 2.180478020363807e-13 relative error = 1.035989405131268e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999898 y[1] (closed_form) = 2.084752574514567 y[1] (numeric) = 2.084752574514355 absolute error = 2.122746423083299e-13 relative error = 1.018224632041804e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999901 y[1] (closed_form) = 2.064766635519646 y[1] (numeric) = 2.064766635519441 absolute error = 2.051692149507289e-13 relative error = 9.936678141793653e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.689999999999904 y[1] (closed_form) = 2.044774219915146 y[1] (numeric) = 2.044774219914948 absolute error = 1.980637875931279e-13 relative error = 9.686340216150963e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999908 y[1] (closed_form) = 2.024777326925966 y[1] (numeric) = 2.024777326925775 absolute error = 1.909583602355269e-13 relative error = 9.431079541247212e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999911 y[1] (closed_form) = 2.004777956224741 y[1] (numeric) = 2.004777956224556 absolute error = 1.84741111297626e-13 relative error = 9.215041033547562e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.719999999999914 y[1] (closed_form) = 1.984778107731875 y[1] (numeric) = 1.984778107731696 absolute error = 1.787459069646502e-13 relative error = 9.005838298413815e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999918 y[1] (closed_form) = 1.964779781415551 y[1] (numeric) = 1.964779781415379 absolute error = 1.716404796070492e-13 relative error = 8.735863491194348e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999921 y[1] (closed_form) = 1.944784977091735 y[1] (numeric) = 1.94478497709157 absolute error = 1.652011860642233e-13 relative error = 8.494573333822643e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.749999999999925 y[1] (closed_form) = 1.924795694224198 y[1] (numeric) = 1.924795694224039 absolute error = 1.583178033115473e-13 relative error = 8.225174432102957e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999928 y[1] (closed_form) = 1.904813931724568 y[1] (numeric) = 1.904813931724416 absolute error = 1.516564651637964e-13 relative error = 7.961746952705803e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999931 y[1] (closed_form) = 1.884841687752445 y[1] (numeric) = 1.884841687752299 absolute error = 1.452171716209705e-13 relative error = 7.704475795743505e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.779999999999935 y[1] (closed_form) = 1.864880959515581 y[1] (numeric) = 1.864880959515442 absolute error = 1.385558334732195e-13 relative error = 7.429741440934152e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999938 y[1] (closed_form) = 1.844933743070166 y[1] (numeric) = 1.844933743070035 absolute error = 1.318944953254686e-13 relative error = 7.149009866662317e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999941 y[1] (closed_form) = 1.825002033121224 y[1] (numeric) = 1.825002033121099 absolute error = 1.254552017826427e-13 relative error = 6.874249973742876e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.809999999999945 y[1] (closed_form) = 1.805087822823138 y[1] (numeric) = 1.805087822823019 absolute error = 1.185718190299667e-13 relative error = 6.568756241705828e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999948 y[1] (closed_form) = 1.785193103580344 y[1] (numeric) = 1.785193103580232 absolute error = 1.116884362772907e-13 relative error = 6.256378430618563e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999951 y[1] (closed_form) = 1.765319864848186 y[1] (numeric) = 1.765319864848081 absolute error = 1.050270981295398e-13 relative error = 5.949465602290263e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.839999999999955 y[1] (closed_form) = 1.745470093933978 y[1] (numeric) = 1.745470093933879 absolute error = 9.836575998178887e-14 relative error = 5.63548813145747e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999958 y[1] (closed_form) = 1.725645775798268 y[1] (numeric) = 1.725645775798176 absolute error = 9.14823772291129e-14 relative error = 5.301341591196142e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999961 y[1] (closed_form) = 1.705848892856351 y[1] (numeric) = 1.705848892856266 absolute error = 8.504308368628699e-14 relative error = 4.985382002029909e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.869999999999965 y[1] (closed_form) = 1.686081424780023 y[1] (numeric) = 1.686081424779945 absolute error = 7.838174553853605e-14 relative error = 4.648752093853487e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999968 y[1] (closed_form) = 1.66634534829962 y[1] (numeric) = 1.666345348299548 absolute error = 7.194245199571014e-14 relative error = 4.317379471735677e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999971 y[1] (closed_form) = 1.646642637006341 y[1] (numeric) = 1.646642637006276 absolute error = 6.572520305780927e-14 relative error = 3.991467339707671e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.899999999999975 y[1] (closed_form) = 1.626975261154899 y[1] (numeric) = 1.62697526115484 absolute error = 5.928590951498336e-14 relative error = 3.643934295159448e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999978 y[1] (closed_form) = 1.607345187466489 y[1] (numeric) = 1.607345187466436 absolute error = 5.240252676230739e-14 relative error = 3.260191225315124e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999981 y[1] (closed_form) = 1.58775437893212 y[1] (numeric) = 1.587754378932074 absolute error = 4.574118861455645e-14 relative error = 2.880873088526496e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.929999999999985 y[1] (closed_form) = 1.568204794616321 y[1] (numeric) = 1.568204794616282 absolute error = 3.97459842815806e-14 relative error = 2.534489399473166e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999988 y[1] (closed_form) = 1.548698389461233 y[1] (numeric) = 1.5486983894612 absolute error = 3.308464613382966e-14 relative error = 2.136287243466384e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999991 y[1] (closed_form) = 1.529237114091115 y[1] (numeric) = 1.529237114091089 absolute error = 2.642330798607873e-14 relative error = 1.727875143926462e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.959999999999995 y[1] (closed_form) = 1.509822914617287 y[1] (numeric) = 1.509822914617267 absolute error = 2.020605904817785e-14 relative error = 1.338306555858554e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999998 y[1] (closed_form) = 1.490457732443518 y[1] (numeric) = 1.490457732443504 absolute error = 1.310063169057685e-14 relative error = 8.789670049280186e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.980000000000001 y[1] (closed_form) = 1.471143504071887 y[1] (numeric) = 1.47114350407188 absolute error = 6.883382752675971e-15 relative error = 4.678933587120415e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.990000000000005 y[1] (closed_form) = 1.451882160909137 y[1] (numeric) = 1.451882160909137 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.001 Finished! diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ; Iterations = 10000 Total Elapsed Time = 1.0 Seconds Elapsed Time(since restart) = 1.0 Seconds Time to Timeout = 2 Minutes 59.0 Seconds Percent Done = 100 %