##############ECHO OF PROBLEM################# ##############temp/h2sinpostode.ode################# diff ( y , x , 2 ) = sin ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.1); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); array_y_init[1 + 1] = exact_soln_yp(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) - sin(c(x))); } double exact_soln_yp (double x) { return(neg( cos(c(x)))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 1.900166583353172 y[1] (numeric) = 1.900166583353172 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 1.890221699162825 y[1] (numeric) = 1.890221699162825 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 1.880287792711081 y[1] (numeric) = 1.880287792711081 absolute error = 2.220446049250313e-16 relative error = 1.180907549289983e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 1.870365857380305 y[1] (numeric) = 1.870365857380306 absolute error = 6.661338147750939e-16 relative error = 3.561516118071694e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 1.860456885355763 y[1] (numeric) = 1.860456885355764 absolute error = 6.661338147750939e-16 relative error = 3.580485094916421e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 1.850561867526401 y[1] (numeric) = 1.850561867526402 absolute error = 6.661338147750939e-16 relative error = 3.599630071625209e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 1.840681793385754 y[1] (numeric) = 1.840681793385755 absolute error = 8.881784197001252e-16 relative error = 4.825268674312294e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 1.830817650933004 y[1] (numeric) = 1.830817650933005 absolute error = 1.110223024625157e-15 relative error = 6.064083029019167e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 1.820970426574176 y[1] (numeric) = 1.820970426574177 absolute error = 8.881784197001252e-16 relative error = 4.877500516969247e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 1.811141105023499 y[1] (numeric) = 1.8111411050235 absolute error = 1.110223024625157e-15 relative error = 6.12996426145798e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (closed_form) = 1.801330669204939 y[1] (numeric) = 1.80133066920494 absolute error = 1.110223024625157e-15 relative error = 6.163349370580475e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y[1] (closed_form) = 1.7915401001539 y[1] (numeric) = 1.791540100153902 absolute error = 1.110223024625157e-15 relative error = 6.197031395109626e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (closed_form) = 1.781770376919131 y[1] (numeric) = 1.781770376919132 absolute error = 1.110223024625157e-15 relative error = 6.231010679080036e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (closed_form) = 1.772022476464811 y[1] (numeric) = 1.772022476464813 absolute error = 1.332267629550188e-15 relative error = 7.518344982892456e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (closed_form) = 1.762297373572865 y[1] (numeric) = 1.762297373572866 absolute error = 8.881784197001252e-16 relative error = 5.039889595360632e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (closed_form) = 1.752596040745477 y[1] (numeric) = 1.752596040745478 absolute error = 8.881784197001252e-16 relative error = 5.067787436757721e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = 1.742919448107845 y[1] (numeric) = 1.742919448107846 absolute error = 8.881784197001252e-16 relative error = 5.09592351307086e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = 1.733268563311169 y[1] (numeric) = 1.73326856331117 absolute error = 1.110223024625157e-15 relative error = 6.405372185971168e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = 1.723644351435886 y[1] (numeric) = 1.723644351435887 absolute error = 1.110223024625157e-15 relative error = 6.441137486977998e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = 1.714047774895164 y[1] (numeric) = 1.714047774895165 absolute error = 8.881784197001252e-16 relative error = 5.181759999393532e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 1.70447979333866 y[1] (numeric) = 1.704479793338661 absolute error = 1.110223024625157e-15 relative error = 6.513559321524724e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 1.694941363556556 y[1] (numeric) = 1.694941363556557 absolute error = 8.881784197001252e-16 relative error = 5.240171954010424e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 1.685433439383882 y[1] (numeric) = 1.685433439383883 absolute error = 6.661338147750939e-16 relative error = 3.952299742068735e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 1.675956971605131 y[1] (numeric) = 1.675956971605132 absolute error = 8.881784197001252e-16 relative error = 5.299529968537802e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (closed_form) = 1.666512907859185 y[1] (numeric) = 1.666512907859186 absolute error = 1.110223024625157e-15 relative error = 6.661952748096966e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (closed_form) = 1.657102192544548 y[1] (numeric) = 1.657102192544549 absolute error = 1.110223024625157e-15 relative error = 6.69978610625313e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (closed_form) = 1.64772576672491 y[1] (numeric) = 1.647725766724911 absolute error = 8.881784197001252e-16 relative error = 5.390329129012205e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (closed_form) = 1.638384568035038 y[1] (numeric) = 1.638384568035039 absolute error = 1.110223024625157e-15 relative error = 6.776327403746724e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (closed_form) = 1.629079530587017 y[1] (numeric) = 1.629079530587018 absolute error = 8.881784197001252e-16 relative error = 5.452026147428677e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (closed_form) = 1.619811584876838 y[1] (numeric) = 1.619811584876839 absolute error = 8.881784197001252e-16 relative error = 5.483220567086248e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (closed_form) = 1.610581657691349 y[1] (numeric) = 1.610581657691351 absolute error = 1.332267629550188e-15 relative error = 8.271965740997547e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = 1.601390672015577 y[1] (numeric) = 1.601390672015578 absolute error = 1.332267629550188e-15 relative error = 8.319441675486597e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 1.59223954694043 y[1] (numeric) = 1.592239546940431 absolute error = 1.110223024625157e-15 relative error = 6.972713538980409e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = 1.583129197570789 y[1] (numeric) = 1.58312919757079 absolute error = 1.110223024625157e-15 relative error = 7.012839042629768e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = 1.574060534934 y[1] (numeric) = 1.574060534934001 absolute error = 1.110223024625157e-15 relative error = 7.053242235513565e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (closed_form) = 1.56503446588877 y[1] (numeric) = 1.565034465888771 absolute error = 1.332267629550188e-15 relative error = 8.512704726880277e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y[1] (closed_form) = 1.55605189303448 y[1] (numeric) = 1.556051893034481 absolute error = 1.110223024625157e-15 relative error = 7.134871462802529e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (closed_form) = 1.547113714620932 y[1] (numeric) = 1.547113714620933 absolute error = 1.110223024625157e-15 relative error = 7.176091932564761e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (closed_form) = 1.538220824458517 y[1] (numeric) = 1.538220824458518 absolute error = 6.661338147750939e-16 relative error = 4.330547371243565e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (closed_form) = 1.529374111828842 y[1] (numeric) = 1.529374111828842 absolute error = 6.661338147750939e-16 relative error = 4.355597558654397e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (closed_form) = 1.520574461395797 y[1] (numeric) = 1.520574461395798 absolute error = 1.332267629550188e-15 relative error = 8.761607296279628e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (closed_form) = 1.511822753117092 y[1] (numeric) = 1.511822753117094 absolute error = 1.332267629550188e-15 relative error = 8.812326886887397e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (closed_form) = 1.503119862156263 y[1] (numeric) = 1.503119862156264 absolute error = 1.332267629550188e-15 relative error = 8.863349245076282e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (closed_form) = 1.494466658795153 y[1] (numeric) = 1.494466658795154 absolute error = 1.332267629550188e-15 relative error = 8.914669468934618e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (closed_form) = 1.485864008346887 y[1] (numeric) = 1.485864008346888 absolute error = 1.332267629550188e-15 relative error = 8.966282392373283e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (closed_form) = 1.477312771069341 y[1] (numeric) = 1.477312771069342 absolute error = 1.554312234475219e-15 relative error = 1.052121300860442e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (closed_form) = 1.468813802079116 y[1] (numeric) = 1.468813802079118 absolute error = 1.554312234475219e-15 relative error = 1.058209170062999e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (closed_form) = 1.460367951266031 y[1] (numeric) = 1.460367951266032 absolute error = 1.554312234475219e-15 relative error = 1.064329187125577e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (closed_form) = 1.451976063208126 y[1] (numeric) = 1.451976063208128 absolute error = 1.998401444325282e-15 relative error = 1.37633222403807e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (closed_form) = 1.443638977087216 y[1] (numeric) = 1.443638977087218 absolute error = 1.77635683940025e-15 relative error = 1.230471653643176e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (closed_form) = 1.435357526604964 y[1] (numeric) = 1.435357526604966 absolute error = 1.998401444325282e-15 relative error = 1.392267367038566e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (closed_form) = 1.427132539899518 y[1] (numeric) = 1.42713253989952 absolute error = 1.998401444325282e-15 relative error = 1.400291415446238e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (closed_form) = 1.418964839462695 y[1] (numeric) = 1.418964839462696 absolute error = 1.77635683940025e-15 relative error = 1.251868115402272e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (closed_form) = 1.41085524205773 y[1] (numeric) = 1.410855242057732 absolute error = 2.220446049250313e-15 relative error = 1.573829818296451e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (closed_form) = 1.402804558637607 y[1] (numeric) = 1.402804558637609 absolute error = 1.77635683940025e-15 relative error = 1.266289611380672e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (closed_form) = 1.39481359426396 y[1] (numeric) = 1.394813594263961 absolute error = 1.332267629550188e-15 relative error = 9.551581910507708e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (closed_form) = 1.386883148026566 y[1] (numeric) = 1.386883148026567 absolute error = 1.332267629550188e-15 relative error = 9.606199566603056e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (closed_form) = 1.37901401296344 y[1] (numeric) = 1.379014012963441 absolute error = 1.110223024625157e-15 relative error = 8.050846577253676e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (closed_form) = 1.371206975981531 y[1] (numeric) = 1.371206975981532 absolute error = 8.881784197001252e-16 relative error = 6.477347586890399e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (closed_form) = 1.363462817778032 y[1] (numeric) = 1.363462817778032 absolute error = 4.440892098500626e-16 relative error = 3.257068722811033e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (closed_form) = 1.355782312762309 y[1] (numeric) = 1.355782312762309 absolute error = 4.440892098500626e-16 relative error = 3.275520012834973e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (closed_form) = 1.348166228978463 y[1] (numeric) = 1.348166228978463 absolute error = 6.661338147750939e-16 relative error = 4.941036205007443e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (closed_form) = 1.340615328028526 y[1] (numeric) = 1.340615328028527 absolute error = 4.440892098500626e-16 relative error = 3.312577445337198e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (closed_form) = 1.333130364996302 y[1] (numeric) = 1.333130364996302 absolute error = 4.440892098500626e-16 relative error = 3.331176166340601e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (closed_form) = 1.325712088371855 y[1] (numeric) = 1.325712088371855 absolute error = 4.440892098500626e-16 relative error = 3.349816402409527e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y[1] (closed_form) = 1.318361239976666 y[1] (numeric) = 1.318361239976666 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (closed_form) = 1.311078554889448 y[1] (numeric) = 1.311078554889448 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (closed_form) = 1.303864761372643 y[1] (numeric) = 1.303864761372643 absolute error = 2.220446049250313e-16 relative error = 1.702972666362069e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (closed_form) = 1.296720580799589 y[1] (numeric) = 1.29672058079959 absolute error = 4.440892098500626e-16 relative error = 3.424710122023562e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (closed_form) = 1.289646727582392 y[1] (numeric) = 1.289646727582392 absolute error = 2.220446049250313e-16 relative error = 1.7217475156261e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (closed_form) = 1.282643909100477 y[1] (numeric) = 1.282643909100477 absolute error = 2.220446049250313e-16 relative error = 1.731147696953179e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (closed_form) = 1.275712825629857 y[1] (numeric) = 1.275712825629857 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y[1] (closed_form) = 1.268854170273104 y[1] (numeric) = 1.268854170273104 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (closed_form) = 1.262068628890037 y[1] (numeric) = 1.262068628890037 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (closed_form) = 1.25535688002914 y[1] (numeric) = 1.255356880029141 absolute error = 4.440892098500626e-16 relative error = 3.537553479132994e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (closed_form) = 1.248719594859707 y[1] (numeric) = 1.248719594859707 absolute error = 4.440892098500626e-16 relative error = 3.556356540556696e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (closed_form) = 1.242157437104723 y[1] (numeric) = 1.242157437104723 absolute error = 2.220446049250313e-16 relative error = 1.787572157057507e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (closed_form) = 1.235671062974494 y[1] (numeric) = 1.235671062974495 absolute error = 4.440892098500626e-16 relative error = 3.593911220847527e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (closed_form) = 1.22926112110103 y[1] (numeric) = 1.229261121101031 absolute error = 4.440892098500626e-16 relative error = 3.612651553254192e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (closed_form) = 1.222928252473176 y[1] (numeric) = 1.222928252473176 absolute error = 4.440892098500626e-16 relative error = 3.631359476338563e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (closed_form) = 1.216673090372516 y[1] (numeric) = 1.216673090372517 absolute error = 4.440892098500626e-16 relative error = 3.650029028866687e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (closed_form) = 1.210496260310049 y[1] (numeric) = 1.21049626031005 absolute error = 6.661338147750939e-16 relative error = 5.502981187273346e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (closed_form) = 1.204398379963634 y[1] (numeric) = 1.204398379963634 absolute error = 4.440892098500626e-16 relative error = 3.687228555251559e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (closed_form) = 1.198380059116222 y[1] (numeric) = 1.198380059116223 absolute error = 6.661338147750939e-16 relative error = 5.558618984918293e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (closed_form) = 1.192441899594885 y[1] (numeric) = 1.192441899594886 absolute error = 8.881784197001252e-16 relative error = 7.4483999597957e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (closed_form) = 1.186584495210626 y[1] (numeric) = 1.186584495210627 absolute error = 1.332267629550188e-15 relative error = 1.122775187883862e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (closed_form) = 1.180808431699001 y[1] (numeric) = 1.180808431699003 absolute error = 1.554312234475219e-15 relative error = 1.316311937440016e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (closed_form) = 1.175114286661549 y[1] (numeric) = 1.175114286661551 absolute error = 1.332267629550188e-15 relative error = 1.13373451814215e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = 1.169502629508029 y[1] (numeric) = 1.16950262950803 absolute error = 8.881784197001252e-16 relative error = 7.594496987781484e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (closed_form) = 1.163974021399479 y[1] (numeric) = 1.16397402139948 absolute error = 6.661338147750939e-16 relative error = 5.722926822491985e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y[1] (closed_form) = 1.158529015192103 y[1] (numeric) = 1.158529015192104 absolute error = 6.661338147750939e-16 relative error = 5.749824182561694e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 1.153168155381985 y[1] (numeric) = 1.153168155381985 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = 1.147891978050638 y[1] (numeric) = 1.147891978050637 absolute error = 4.440892098500626e-16 relative error = 3.868736939901084e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y[1] (closed_form) = 1.142701010811398 y[1] (numeric) = 1.142701010811397 absolute error = 1.110223024625157e-15 relative error = 9.715778791836547e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = 1.137595772756663 y[1] (numeric) = 1.137595772756662 absolute error = 1.554312234475219e-15 relative error = 1.366313300117803e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y[1] (closed_form) = 1.132576774405985 y[1] (numeric) = 1.132576774405983 absolute error = 1.998401444325282e-15 relative error = 1.764473269702537e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y[1] (closed_form) = 1.127644517655017 y[1] (numeric) = 1.127644517655014 absolute error = 2.664535259100376e-15 relative error = 2.362921308429173e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y[1] (closed_form) = 1.122799495725322 y[1] (numeric) = 1.122799495725318 absolute error = 3.33066907387547e-15 relative error = 2.966397016168837e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y[1] (closed_form) = 1.118042193115056 y[1] (numeric) = 1.118042193115053 absolute error = 3.552713678800501e-15 relative error = 3.177620398119354e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y[1] (closed_form) = 1.113373085550517 y[1] (numeric) = 1.113373085550513 absolute error = 3.996802888650564e-15 relative error = 3.5898145379312e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y[1] (closed_form) = 1.108792639938569 y[1] (numeric) = 1.108792639938565 absolute error = 4.440892098500626e-15 relative error = 4.005160152169359e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y[1] (closed_form) = 1.104301314319958 y[1] (numeric) = 1.104301314319952 absolute error = 5.329070518200751e-15 relative error = 4.82573954146062e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = 1.0998995578235 y[1] (numeric) = 1.099899557823495 absolute error = 5.773159728050814e-15 relative error = 5.248806299617793e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = 1.09558781062118 y[1] (numeric) = 1.095587810621174 absolute error = 5.995204332975845e-15 relative error = 5.472134935105443e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = 1.091366503884123 y[1] (numeric) = 1.091366503884116 absolute error = 6.439293542825908e-15 relative error = 5.900211816936621e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = 1.087236059739485 y[1] (numeric) = 1.087236059739479 absolute error = 6.661338147750939e-15 relative error = 6.12685542213075e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = 1.08319689122824 y[1] (numeric) = 1.083196891228233 absolute error = 6.661338147750939e-15 relative error = 6.149702054810766e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = 1.079249402263871 y[1] (numeric) = 1.079249402263865 absolute error = 6.883382752675971e-15 relative error = 6.377935200369021e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y[1] (closed_form) = 1.075393987591987 y[1] (numeric) = 1.07539398759198 absolute error = 7.105427357601002e-15 relative error = 6.607278299473679e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y[1] (closed_form) = 1.071631032750841 y[1] (numeric) = 1.071631032750834 absolute error = 7.105427357601002e-15 relative error = 6.630479279198932e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y[1] (closed_form) = 1.067960914032781 y[1] (numeric) = 1.067960914032774 absolute error = 7.327471962526033e-15 relative error = 6.861179904849135e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y[1] (closed_form) = 1.064383998446622 y[1] (numeric) = 1.064383998446615 absolute error = 7.327471962526033e-15 relative error = 6.884237242592763e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y[1] (closed_form) = 1.060900643680941 y[1] (numeric) = 1.060900643680933 absolute error = 7.327471962526033e-15 relative error = 6.906840905574684e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y[1] (closed_form) = 1.057511198068311 y[1] (numeric) = 1.057511198068303 absolute error = 7.771561172376096e-15 relative error = 7.348916197362182e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y[1] (closed_form) = 1.054216000550469 y[1] (numeric) = 1.054216000550461 absolute error = 8.215650382226158e-15 relative error = 7.793137628281372e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y[1] (closed_form) = 1.051015380644422 y[1] (numeric) = 1.051015380644414 absolute error = 8.43769498715119e-15 relative error = 8.028136545421133e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y[1] (closed_form) = 1.047909658409493 y[1] (numeric) = 1.047909658409484 absolute error = 8.881784197001252e-15 relative error = 8.475715559757258e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y[1] (closed_form) = 1.044899144415316 y[1] (numeric) = 1.044899144415308 absolute error = 8.881784197001252e-15 relative error = 8.500135390551155e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y[1] (closed_form) = 1.041984139710784 y[1] (numeric) = 1.041984139710775 absolute error = 8.881784197001252e-15 relative error = 8.523914960420135e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y[1] (closed_form) = 1.039164935793936 y[1] (numeric) = 1.039164935793927 absolute error = 9.103828801926284e-15 relative error = 8.760715925206651e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y[1] (closed_form) = 1.036441814582816 y[1] (numeric) = 1.036441814582807 absolute error = 9.103828801926284e-15 relative error = 8.783733610352954e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y[1] (closed_form) = 1.033815048387275 y[1] (numeric) = 1.033815048387265 absolute error = 9.103828801926284e-15 relative error = 8.806051736360413e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y[1] (closed_form) = 1.031284899881743 y[1] (numeric) = 1.031284899881734 absolute error = 9.103828801926284e-15 relative error = 8.827656453585439e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y[1] (closed_form) = 1.028851622078964 y[1] (numeric) = 1.028851622078955 absolute error = 8.881784197001252e-15 relative error = 8.632716327991151e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y[1] (closed_form) = 1.026515458304689 y[1] (numeric) = 1.02651545830468 absolute error = 9.325873406851315e-15 relative error = 9.084980972671548e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y[1] (closed_form) = 1.024276642173349 y[1] (numeric) = 1.02427664217334 absolute error = 9.103828801926284e-15 relative error = 8.88805663146768e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y[1] (closed_form) = 1.022135397564692 y[1] (numeric) = 1.022135397564683 absolute error = 8.881784197001252e-15 relative error = 8.689439988246876e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y[1] (closed_form) = 1.020091938601394 y[1] (numeric) = 1.020091938601385 absolute error = 8.659739592076221e-15 relative error = 8.489175597200812e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y[1] (closed_form) = 1.018146469627648 y[1] (numeric) = 1.01814646962764 absolute error = 8.43769498715119e-15 relative error = 8.287309575641887e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y[1] (closed_form) = 1.016299185188731 y[1] (numeric) = 1.016299185188723 absolute error = 7.993605777301127e-15 relative error = 7.865406067226828e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y[1] (closed_form) = 1.014550270011547 y[1] (numeric) = 1.01455027001154 absolute error = 7.549516567451064e-15 relative error = 7.441244451460388e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999956 y[1] (closed_form) = 1.012899898986157 y[1] (numeric) = 1.01289989898615 absolute error = 7.105427357601002e-15 relative error = 7.014935399552362e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y[1] (closed_form) = 1.011348237148287 y[1] (numeric) = 1.01134823714828 absolute error = 7.105427357601002e-15 relative error = 7.025698069772955e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y[1] (closed_form) = 1.009895439662829 y[1] (numeric) = 1.009895439662822 absolute error = 6.661338147750939e-15 relative error = 6.596067163126257e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y[1] (closed_form) = 1.00854165180832 y[1] (numeric) = 1.008541651808313 absolute error = 6.439293542825908e-15 relative error = 6.384757170197408e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y[1] (closed_form) = 1.007287008962417 y[1] (numeric) = 1.007287008962411 absolute error = 5.995204332975845e-15 relative error = 5.951833270590241e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y[1] (closed_form) = 1.006131636588361 y[1] (numeric) = 1.006131636588355 absolute error = 5.995204332975845e-15 relative error = 5.958667946576724e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y[1] (closed_form) = 1.005075650222424 y[1] (numeric) = 1.005075650222419 absolute error = 5.551115123125783e-15 relative error = 5.52308189129576e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y[1] (closed_form) = 1.004119155462365 y[1] (numeric) = 1.004119155462359 absolute error = 5.10702591327572e-15 relative error = 5.08607557727957e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999947 y[1] (closed_form) = 1.003262247956861 y[1] (numeric) = 1.003262247956856 absolute error = 4.662936703425657e-15 relative error = 4.647774510524748e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999946 y[1] (closed_form) = 1.002505013395949 y[1] (numeric) = 1.002505013395945 absolute error = 4.218847493575595e-15 relative error = 4.208305631594202e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y[1] (closed_form) = 1.001847527502455 y[1] (numeric) = 1.001847527502452 absolute error = 3.552713678800501e-15 relative error = 3.546162046890707e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y[1] (closed_form) = 1.00128985602442 y[1] (numeric) = 1.001289856024417 absolute error = 3.33066907387547e-15 relative error = 3.326378524496147e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y[1] (closed_form) = 1.000832054728526 y[1] (numeric) = 1.000832054728524 absolute error = 2.664535259100376e-15 relative error = 2.662320063103021e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y[1] (closed_form) = 1.000474169394523 y[1] (numeric) = 1.00047416939452 absolute error = 2.220446049250313e-15 relative error = 2.219393680692532e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y[1] (closed_form) = 1.000216235810644 y[1] (numeric) = 1.000216235810642 absolute error = 1.998401444325282e-15 relative error = 1.997969411789881e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y[1] (closed_form) = 1.000058279770034 y[1] (numeric) = 1.000058279770033 absolute error = 1.110223024625157e-15 relative error = 1.110158324853282e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999938 y[1] (closed_form) = 1.000000317068166 y[1] (numeric) = 1.000000317068165 absolute error = 2.220446049250313e-16 relative error = 2.220445345217781e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999937 y[1] (closed_form) = 1.000042353501259 y[1] (numeric) = 1.00004235350126 absolute error = 2.220446049250313e-16 relative error = 2.220352009568679e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999936 y[1] (closed_form) = 1.000184384865708 y[1] (numeric) = 1.000184384865709 absolute error = 8.881784197001252e-16 relative error = 8.880146832320108e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999935 y[1] (closed_form) = 1.000426396958493 y[1] (numeric) = 1.000426396958494 absolute error = 1.554312234475219e-15 relative error = 1.553649762941738e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999933 y[1] (closed_form) = 1.000768365578607 y[1] (numeric) = 1.000768365578609 absolute error = 2.220446049250313e-15 relative error = 2.218741244849935e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999932 y[1] (closed_form) = 1.001210256529473 y[1] (numeric) = 1.001210256529476 absolute error = 2.886579864025407e-15 relative error = 2.883090584820067e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999931 y[1] (closed_form) = 1.001752025622364 y[1] (numeric) = 1.001752025622367 absolute error = 3.552713678800501e-15 relative error = 3.546500119721034e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63999999999993 y[1] (closed_form) = 1.002393618680822 y[1] (numeric) = 1.002393618680826 absolute error = 4.218847493575595e-15 relative error = 4.208773295192878e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999929 y[1] (closed_form) = 1.003134971546076 y[1] (numeric) = 1.00313497154608 absolute error = 4.884981308350689e-15 relative error = 4.869714890730747e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999928 y[1] (closed_form) = 1.003976010083457 y[1] (numeric) = 1.003976010083462 absolute error = 5.551115123125783e-15 relative error = 5.529131241556597e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999927 y[1] (closed_form) = 1.004916650189813 y[1] (numeric) = 1.004916650189819 absolute error = 6.217248937900877e-15 relative error = 6.186830456761303e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999926 y[1] (closed_form) = 1.005956797801916 y[1] (numeric) = 1.005956797801923 absolute error = 6.883382752675971e-15 relative error = 6.842622633215094e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999925 y[1] (closed_form) = 1.007096348905872 y[1] (numeric) = 1.00709634890588 absolute error = 7.993605777301127e-15 relative error = 7.937280068570921e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999924 y[1] (closed_form) = 1.008335189547521 y[1] (numeric) = 1.00833518954753 absolute error = 8.881784197001252e-15 relative error = 8.808364806733412e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999922 y[1] (closed_form) = 1.009673195843831 y[1] (numeric) = 1.009673195843841 absolute error = 9.769962616701378e-15 relative error = 9.676361278994004e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999921 y[1] (closed_form) = 1.011110233995287 y[1] (numeric) = 1.011110233995297 absolute error = 1.043609643147647e-14 relative error = 1.032142300670761e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72999999999992 y[1] (closed_form) = 1.012646160299271 y[1] (numeric) = 1.012646160299282 absolute error = 1.13242748511766e-14 relative error = 1.118285467831122e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999919 y[1] (closed_form) = 1.014280821164433 y[1] (numeric) = 1.014280821164445 absolute error = 1.265654248072678e-14 relative error = 1.247834151709247e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999918 y[1] (closed_form) = 1.016014053126049 y[1] (numeric) = 1.016014053126062 absolute error = 1.332267629550188e-14 relative error = 1.311268899727418e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999917 y[1] (closed_form) = 1.017845682862366 y[1] (numeric) = 1.017845682862381 absolute error = 1.465494392505207e-14 relative error = 1.439800175193524e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999916 y[1] (closed_form) = 1.019775527211938 y[1] (numeric) = 1.019775527211954 absolute error = 1.598721155460225e-14 relative error = 1.56771869180968e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999915 y[1] (closed_form) = 1.021803393191937 y[1] (numeric) = 1.021803393191955 absolute error = 1.754152378907747e-14 relative error = 1.716722013838766e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999914 y[1] (closed_form) = 1.023929078017457 y[1] (numeric) = 1.023929078017475 absolute error = 1.84297022087776e-14 relative error = 1.799900266965891e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999913 y[1] (closed_form) = 1.026152369121785 y[1] (numeric) = 1.026152369121805 absolute error = 1.976196983832779e-14 relative error = 1.925831916681217e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999911 y[1] (closed_form) = 1.028473044177664 y[1] (numeric) = 1.028473044177685 absolute error = 2.087219286295294e-14 relative error = 2.029435091285424e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81999999999991 y[1] (closed_form) = 1.030890871119521 y[1] (numeric) = 1.030890871119543 absolute error = 2.176037128265307e-14 relative error = 2.110831698317578e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.829999999999909 y[1] (closed_form) = 1.033405608166679 y[1] (numeric) = 1.033405608166702 absolute error = 2.242650509742816e-14 relative error = 2.170155156910177e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999908 y[1] (closed_form) = 1.036017003847527 y[1] (numeric) = 1.036017003847551 absolute error = 2.398081733190338e-14 relative error = 2.314712716378609e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.849999999999907 y[1] (closed_form) = 1.038724797024674 y[1] (numeric) = 1.0387247970247 absolute error = 2.509104035652854e-14 relative error = 2.415561891696373e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.859999999999906 y[1] (closed_form) = 1.041528716921059 y[1] (numeric) = 1.041528716921085 absolute error = 2.597921877622866e-14 relative error = 2.494335331725445e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999905 y[1] (closed_form) = 1.044428483147028 y[1] (numeric) = 1.044428483147055 absolute error = 2.708944180085382e-14 relative error = 2.593709596968196e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999904 y[1] (closed_form) = 1.047423805728375 y[1] (numeric) = 1.047423805728404 absolute error = 2.819966482547898e-14 relative error = 2.692287942211607e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999903 y[1] (closed_form) = 1.050514385135339 y[1] (numeric) = 1.050514385135368 absolute error = 2.90878432451791e-14 relative error = 2.76891432014343e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999902 y[1] (closed_form) = 1.053699912312554 y[1] (numeric) = 1.053699912312584 absolute error = 3.064215547965432e-14 relative error = 2.908053338678185e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9099999999999 y[1] (closed_form) = 1.056980068709956 y[1] (numeric) = 1.056980068709989 absolute error = 3.241851231905457e-14 relative error = 3.067088328223763e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.919999999999899 y[1] (closed_form) = 1.060354526314641 y[1] (numeric) = 1.060354526314674 absolute error = 3.352873534367973e-14 relative error = 3.162030671025843e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999898 y[1] (closed_form) = 1.063822947683658 y[1] (numeric) = 1.063822947683693 absolute error = 3.486100297322992e-14 relative error = 3.276955347610747e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999897 y[1] (closed_form) = 1.067384985977762 y[1] (numeric) = 1.067384985977799 absolute error = 3.641531520770513e-14 relative error = 3.411638320389847e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.949999999999896 y[1] (closed_form) = 1.071040284996092 y[1] (numeric) = 1.07104028499613 absolute error = 3.796962744218035e-14 relative error = 3.545116647252805e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999895 y[1] (closed_form) = 1.074788479211792 y[1] (numeric) = 1.074788479211831 absolute error = 3.952393967665557e-14 relative error = 3.677369123424257e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999894 y[1] (closed_form) = 1.078629193808563 y[1] (numeric) = 1.078629193808605 absolute error = 4.130029651605582e-14 relative error = 3.828961496047349e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999893 y[1] (closed_form) = 1.082562044718147 y[1] (numeric) = 1.08256204471819 absolute error = 4.241051954068098e-14 relative error = 3.917606362388481e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999892 y[1] (closed_form) = 1.086586638658731 y[1] (numeric) = 1.086586638658774 absolute error = 4.352074256530614e-14 relative error = 4.005271279520573e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.999999999999891 y[1] (closed_form) = 1.090702573174273 y[1] (numeric) = 1.090702573174318 absolute error = 4.551914400963142e-14 relative error = 4.173378254454559e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.00999999999989 y[1] (closed_form) = 1.094909436674752 y[1] (numeric) = 1.094909436674799 absolute error = 4.685141163918161e-14 relative error = 4.279021631366123e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999889 y[1] (closed_form) = 1.099206808477324 y[1] (numeric) = 1.099206808477373 absolute error = 4.862776847858186e-14 relative error = 4.423896222581031e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999887 y[1] (closed_form) = 1.10359425884839 y[1] (numeric) = 1.10359425884844 absolute error = 5.018208071305708e-14 relative error = 4.54714949001479e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999886 y[1] (closed_form) = 1.108071349046569 y[1] (numeric) = 1.108071349046621 absolute error = 5.218048215738236e-14 relative error = 4.709126556000264e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999885 y[1] (closed_form) = 1.112637631366572 y[1] (numeric) = 1.112637631366626 absolute error = 5.395683899678261e-14 relative error = 4.849453000300857e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999884 y[1] (closed_form) = 1.117292649183971 y[1] (numeric) = 1.117292649184027 absolute error = 5.573319583618286e-14 relative error = 4.988236150742448e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999883 y[1] (closed_form) = 1.122035937000866 y[1] (numeric) = 1.122035937000923 absolute error = 5.728750807065808e-14 relative error = 5.105674977201187e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999882 y[1] (closed_form) = 1.126867020492426 y[1] (numeric) = 1.126867020492485 absolute error = 5.906386491005833e-14 relative error = 5.241422797540761e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.089999999999881 y[1] (closed_form) = 1.131785416554328 y[1] (numeric) = 1.131785416554389 absolute error = 6.039613253960852e-14 relative error = 5.336358964889469e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09999999999988 y[1] (closed_form) = 1.136790633351066 y[1] (numeric) = 1.136790633351128 absolute error = 6.195044477408373e-14 relative error = 5.449591416096063e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999879 y[1] (closed_form) = 1.141882170365129 y[1] (numeric) = 1.141882170365192 absolute error = 6.350475700855895e-14 relative error = 5.561410682877431e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999878 y[1] (closed_form) = 1.14705951844706 y[1] (numeric) = 1.147059518447125 absolute error = 6.550315845288424e-14 relative error = 5.710528302974664e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999876 y[1] (closed_form) = 1.152322159866365 y[1] (numeric) = 1.152322159866432 absolute error = 6.705747068735946e-14 relative error = 5.819333605034215e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999875 y[1] (closed_form) = 1.157669568363287 y[1] (numeric) = 1.157669568363356 absolute error = 6.883382752675971e-14 relative error = 5.945895910875239e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999874 y[1] (closed_form) = 1.163101209201433 y[1] (numeric) = 1.163101209201504 absolute error = 7.061018436615996e-14 relative error = 6.07085469497876e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999873 y[1] (closed_form) = 1.168616539221246 y[1] (numeric) = 1.168616539221319 absolute error = 7.260858581048524e-14 relative error = 6.213208813463382e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999872 y[1] (closed_form) = 1.17421500689432 y[1] (numeric) = 1.174215006894394 absolute error = 7.460698725481052e-14 relative error = 6.353775655800761e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.179999999999871 y[1] (closed_form) = 1.179896052378552 y[1] (numeric) = 1.179896052378628 absolute error = 7.638334409421077e-14 relative error = 6.473735032864092e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.18999999999987 y[1] (closed_form) = 1.185659107574129 y[1] (numeric) = 1.185659107574207 absolute error = 7.838174553853605e-14 relative error = 6.610816299375118e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999869 y[1] (closed_form) = 1.191503596180333 y[1] (numeric) = 1.191503596180413 absolute error = 8.01581023779363e-14 relative error = 6.727474649250196e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999868 y[1] (closed_form) = 1.197428933753174 y[1] (numeric) = 1.197428933753256 absolute error = 8.215650382226158e-14 relative error = 6.861075551661633e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999867 y[1] (closed_form) = 1.203434527763833 y[1] (numeric) = 1.203434527763916 absolute error = 8.37108160567368e-14 relative error = 6.955992546788934e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999865 y[1] (closed_form) = 1.209519777657913 y[1] (numeric) = 1.209519777657998 absolute error = 8.548717289613705e-14 relative error = 7.067860689444244e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999864 y[1] (closed_form) = 1.215684074915496 y[1] (numeric) = 1.215684074915583 absolute error = 8.748557434046234e-14 relative error = 7.196407039102128e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999863 y[1] (closed_form) = 1.221926803111993 y[1] (numeric) = 1.221926803112082 absolute error = 8.948397578478762e-14 relative error = 7.323186262621509e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999862 y[1] (closed_form) = 1.228247337979786 y[1] (numeric) = 1.228247337979878 absolute error = 9.14823772291129e-14 relative error = 7.44820480373135e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.269999999999861 y[1] (closed_form) = 1.234645047470657 y[1] (numeric) = 1.23464504747075 absolute error = 9.325873406851315e-14 relative error = 7.553485453942142e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.27999999999986 y[1] (closed_form) = 1.241119291818987 y[1] (numeric) = 1.241119291819082 absolute error = 9.547918011776346e-14 relative error = 7.692989767150343e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999859 y[1] (closed_form) = 1.247669423605736 y[1] (numeric) = 1.247669423605834 absolute error = 9.769962616701378e-14 relative error = 7.830569886425851e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999858 y[1] (closed_form) = 1.254294787823185 y[1] (numeric) = 1.254294787823285 absolute error = 9.969802761133906e-14 relative error = 7.948532400773496e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999857 y[1] (closed_form) = 1.260994721940432 y[1] (numeric) = 1.260994721940535 absolute error = 1.021405182655144e-13 relative error = 8.099995700881242e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999856 y[1] (closed_form) = 1.26776855596965 y[1] (numeric) = 1.267768555969754 absolute error = 1.041389197098397e-13 relative error = 8.214347896504599e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999854 y[1] (closed_form) = 1.27461561253308 y[1] (numeric) = 1.274615612533186 absolute error = 1.06137321154165e-13 relative error = 8.327006205677587e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999853 y[1] (closed_form) = 1.281535206930772 y[1] (numeric) = 1.28153520693088 absolute error = 1.081357225984902e-13 relative error = 8.437982976485772e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999852 y[1] (closed_form) = 1.288526647209052 y[1] (numeric) = 1.288526647209162 absolute error = 1.105782132526656e-13 relative error = 8.581756030593388e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.359999999999851 y[1] (closed_form) = 1.295589234229718 y[1] (numeric) = 1.295589234229831 absolute error = 1.125766146969909e-13 relative error = 8.689221222490504e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36999999999985 y[1] (closed_form) = 1.302722261739955 y[1] (numeric) = 1.30272226174007 absolute error = 1.147970607462412e-13 relative error = 8.812090198943465e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999849 y[1] (closed_form) = 1.309925016442954 y[1] (numeric) = 1.309925016443071 absolute error = 1.167954621905665e-13 relative error = 8.916194493919932e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999848 y[1] (closed_form) = 1.317196778069249 y[1] (numeric) = 1.317196778069368 absolute error = 1.187938636348917e-13 relative error = 9.01868768681777e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999847 y[1] (closed_form) = 1.324536819448736 y[1] (numeric) = 1.324536819448857 absolute error = 1.20792265079217e-13 relative error = 9.119585299976032e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999846 y[1] (closed_form) = 1.331944406583394 y[1] (numeric) = 1.331944406583517 absolute error = 1.230127111284673e-13 relative error = 9.235573986455675e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999844 y[1] (closed_form) = 1.339418798720683 y[1] (numeric) = 1.339418798720807 absolute error = 1.247890679678676e-13 relative error = 9.316657947988875e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999843 y[1] (closed_form) = 1.346959248427616 y[1] (numeric) = 1.346959248427744 absolute error = 1.270095140171179e-13 relative error = 9.42935090021346e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999842 y[1] (closed_form) = 1.354565001665509 y[1] (numeric) = 1.354565001665638 absolute error = 1.292299600663682e-13 relative error = 9.540329176338765e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.449999999999841 y[1] (closed_form) = 1.362235297865374 y[1] (numeric) = 1.362235297865506 absolute error = 1.318944953254686e-13 relative error = 9.682210961068739e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45999999999984 y[1] (closed_form) = 1.369969370003984 y[1] (numeric) = 1.369969370004118 absolute error = 1.338928967697939e-13 relative error = 9.773422654654282e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999839 y[1] (closed_form) = 1.377766444680569 y[1] (numeric) = 1.377766444680705 absolute error = 1.363353874239692e-13 relative error = 9.895391773427765e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999838 y[1] (closed_form) = 1.38562574219416 y[1] (numeric) = 1.385625742194299 absolute error = 1.385558334732195e-13 relative error = 9.999513523313602e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999837 y[1] (closed_form) = 1.393546476621555 y[1] (numeric) = 1.393546476621696 absolute error = 1.409983241273949e-13 relative error = 1.011794916730902e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999836 y[1] (closed_form) = 1.401527855895912 y[1] (numeric) = 1.401527855896055 absolute error = 1.432187701766452e-13 relative error = 1.021876016050313e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999835 y[1] (closed_form) = 1.409569081885954 y[1] (numeric) = 1.4095690818861 absolute error = 1.458833054357456e-13 relative error = 1.034949668735348e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999833 y[1] (closed_form) = 1.417669350475783 y[1] (numeric) = 1.417669350475931 absolute error = 1.483257960899209e-13 relative error = 1.046265097289022e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999832 y[1] (closed_form) = 1.42582785164529 y[1] (numeric) = 1.425827851645441 absolute error = 1.503241975342462e-13 relative error = 1.054294158728799e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999831 y[1] (closed_form) = 1.434043769551158 y[1] (numeric) = 1.434043769551311 absolute error = 1.527666881884215e-13 relative error = 1.065286091206519e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54999999999983 y[1] (closed_form) = 1.442316282608442 y[1] (numeric) = 1.442316282608597 absolute error = 1.552091788425969e-13 relative error = 1.076110564056725e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999829 y[1] (closed_form) = 1.450644563572731 y[1] (numeric) = 1.450644563572888 absolute error = 1.574296248918472e-13 relative error = 1.085239133314094e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999828 y[1] (closed_form) = 1.459027779622867 y[1] (numeric) = 1.459027779623027 absolute error = 1.598721155460225e-13 relative error = 1.095744150857406e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999827 y[1] (closed_form) = 1.467465092444232 y[1] (numeric) = 1.467465092444395 absolute error = 1.623146062001979e-13 relative error = 1.106088363095876e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999826 y[1] (closed_form) = 1.475955658312575 y[1] (numeric) = 1.475955658312741 absolute error = 1.652011860642233e-13 relative error = 1.119282853341907e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999825 y[1] (closed_form) = 1.484498628178386 y[1] (numeric) = 1.484498628178553 absolute error = 1.671995875085486e-13 relative error = 1.126303415407784e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999824 y[1] (closed_form) = 1.493093147751795 y[1] (numeric) = 1.493093147751964 absolute error = 1.696420781627239e-13 relative error = 1.136178800486495e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999822 y[1] (closed_form) = 1.501738357588007 y[1] (numeric) = 1.50173835758818 absolute error = 1.723066134218243e-13 relative error = 1.147381050441914e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999821 y[1] (closed_form) = 1.510433393173245 y[1] (numeric) = 1.51043339317342 absolute error = 1.749711486809247e-13 relative error = 1.158416845600392e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999982 y[1] (closed_form) = 1.519177385011194 y[1] (numeric) = 1.519177385011371 absolute error = 1.774136393351e-13 relative error = 1.167827016683721e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999819 y[1] (closed_form) = 1.527969458709958 y[1] (numeric) = 1.527969458710138 absolute error = 1.798561299892754e-13 relative error = 1.17709244097801e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999818 y[1] (closed_form) = 1.536808735069493 y[1] (numeric) = 1.536808735069676 absolute error = 1.822986206434507e-13 relative error = 1.186215411738971e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999817 y[1] (closed_form) = 1.545694330169531 y[1] (numeric) = 1.545694330169715 absolute error = 1.849631559025511e-13 relative error = 1.196634756900897e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999816 y[1] (closed_form) = 1.554625355457964 y[1] (numeric) = 1.554625355458151 absolute error = 1.874056465567264e-13 relative error = 1.205471439783125e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999815 y[1] (closed_form) = 1.563600917839707 y[1] (numeric) = 1.563600917839897 absolute error = 1.900701818158268e-13 relative error = 1.215592672319676e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999814 y[1] (closed_form) = 1.572620119766002 y[1] (numeric) = 1.572620119766194 absolute error = 1.920685832601521e-13 relative error = 1.221328538571228e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999813 y[1] (closed_form) = 1.581682059324171 y[1] (numeric) = 1.581682059324366 absolute error = 1.949551631241775e-13 relative error = 1.232581238276667e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999811 y[1] (closed_form) = 1.59078583032781 y[1] (numeric) = 1.590785830328008 absolute error = 1.976196983832779e-13 relative error = 1.242277210518997e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999981 y[1] (closed_form) = 1.599930522407407 y[1] (numeric) = 1.599930522407607 absolute error = 2.000621890374532e-13 relative error = 1.25044298008904e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999809 y[1] (closed_form) = 1.609115221101372 y[1] (numeric) = 1.609115221101575 absolute error = 2.029487689014786e-13 relative error = 1.261244479202482e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999808 y[1] (closed_form) = 1.618339007947491 y[1] (numeric) = 1.618339007947697 absolute error = 2.05835348765504e-13 relative error = 1.271892648911436e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999807 y[1] (closed_form) = 1.627600960574765 y[1] (numeric) = 1.627600960574973 absolute error = 2.078337502098293e-13 relative error = 1.276933076621162e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999806 y[1] (closed_form) = 1.636900152795651 y[1] (numeric) = 1.636900152795861 absolute error = 2.104982854689297e-13 relative error = 1.285956783065974e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999805 y[1] (closed_form) = 1.646235654698674 y[1] (numeric) = 1.646235654698888 absolute error = 2.131628207280301e-13 relative error = 1.294849981651304e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999804 y[1] (closed_form) = 1.655606532741426 y[1] (numeric) = 1.655606532741642 absolute error = 2.160494005920555e-13 relative error = 1.304956197740483e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999803 y[1] (closed_form) = 1.665011849843909 y[1] (numeric) = 1.665011849844128 absolute error = 2.184918912462308e-13 relative error = 1.312254271744155e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999802 y[1] (closed_form) = 1.674450665482252 y[1] (numeric) = 1.674450665482474 absolute error = 2.213784711102562e-13 relative error = 1.32209610992927e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8199999999998 y[1] (closed_form) = 1.683922035782757 y[1] (numeric) = 1.683922035782981 absolute error = 2.240430063693566e-13 relative error = 1.330483250462436e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999799 y[1] (closed_form) = 1.693425013616286 y[1] (numeric) = 1.693425013616513 absolute error = 2.26707541628457e-13 relative error = 1.338751582181523e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999798 y[1] (closed_form) = 1.702958648692975 y[1] (numeric) = 1.702958648693204 absolute error = 2.293720768875573e-13 relative error = 1.346903385256013e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999797 y[1] (closed_form) = 1.712521987657261 y[1] (numeric) = 1.712521987657493 absolute error = 2.318145675417327e-13 relative error = 1.35364432814586e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999796 y[1] (closed_form) = 1.722114074183217 y[1] (numeric) = 1.722114074183452 absolute error = 2.344791028008331e-13 relative error = 1.361577065747194e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999795 y[1] (closed_form) = 1.731733949070184 y[1] (numeric) = 1.731733949070421 absolute error = 2.366995488500834e-13 relative error = 1.366835529078666e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999794 y[1] (closed_form) = 1.74138065033869 y[1] (numeric) = 1.741380650338929 absolute error = 2.391420395042587e-13 relative error = 1.373289863176938e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999793 y[1] (closed_form) = 1.751053213326647 y[1] (numeric) = 1.751053213326889 absolute error = 2.420286193682841e-13 relative error = 1.382188830849285e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999792 y[1] (closed_form) = 1.760750670785815 y[1] (numeric) = 1.76075067078606 absolute error = 2.446931546273845e-13 relative error = 1.389709279611854e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.909999999999791 y[1] (closed_form) = 1.770472052978532 y[1] (numeric) = 1.770472052978779 absolute error = 2.471356452815598e-13 relative error = 1.395874308582246e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999789 y[1] (closed_form) = 1.780216387774678 y[1] (numeric) = 1.780216387774927 absolute error = 2.495781359357352e-13 relative error = 1.401953929026095e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999788 y[1] (closed_form) = 1.789982700748894 y[1] (numeric) = 1.789982700749146 absolute error = 2.524647157997606e-13 relative error = 1.410431037652678e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999787 y[1] (closed_form) = 1.799770015278021 y[1] (numeric) = 1.799770015278277 absolute error = 2.55573340268711e-13 relative error = 1.420033327031682e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999786 y[1] (closed_form) = 1.809577352638763 y[1] (numeric) = 1.809577352639021 absolute error = 2.582378755278114e-13 relative error = 1.427061822757914e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999785 y[1] (closed_form) = 1.819403732105556 y[1] (numeric) = 1.819403732105817 absolute error = 2.611244553918368e-13 relative error = 1.43521996126524e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999784 y[1] (closed_form) = 1.829248171048642 y[1] (numeric) = 1.829248171048905 absolute error = 2.637889906509372e-13 relative error = 1.442062344661067e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999783 y[1] (closed_form) = 1.83910968503233 y[1] (numeric) = 1.839109685032597 absolute error = 2.666755705149626e-13 relative error = 1.450025371979239e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999782 y[1] (closed_form) = 1.84898728791344 y[1] (numeric) = 1.848987287913709 absolute error = 2.691180611691379e-13 relative error = 1.455488974577183e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.999999999999781 y[1] (closed_form) = 1.858879991939915 y[1] (numeric) = 1.858879991940187 absolute error = 2.717825964282383e-13 relative error = 1.462077151869324e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.00999999999978 y[1] (closed_form) = 1.868786807849597 y[1] (numeric) = 1.868786807849872 absolute error = 2.740030424774886e-13 relative error = 1.466208137421424e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999778 y[1] (closed_form) = 1.87870674496915 y[1] (numeric) = 1.878706744969427 absolute error = 2.76667577736589e-13 relative error = 1.472649089473153e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999777 y[1] (closed_form) = 1.888638811313129 y[1] (numeric) = 1.888638811313408 absolute error = 2.795541576006144e-13 relative error = 1.48018856716307e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999776 y[1] (closed_form) = 1.898582013683175 y[1] (numeric) = 1.898582013683458 absolute error = 2.824407374646398e-13 relative error = 1.487640436015275e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999775 y[1] (closed_form) = 1.908535357767339 y[1] (numeric) = 1.908535357767624 absolute error = 2.848832281188152e-13 relative error = 1.492679855049057e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999774 y[1] (closed_form) = 1.918497848239506 y[1] (numeric) = 1.918497848239793 absolute error = 2.877698079828406e-13 relative error = 1.499974619449849e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999773 y[1] (closed_form) = 1.92846848885893 y[1] (numeric) = 1.928468488859221 absolute error = 2.90878432451791e-13 relative error = 1.508339047966001e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999772 y[1] (closed_form) = 1.938446282569859 y[1] (numeric) = 1.938446282570153 absolute error = 2.937650123158164e-13 relative error = 1.515466355489423e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.089999999999771 y[1] (closed_form) = 1.948430231601237 y[1] (numeric) = 1.948430231601533 absolute error = 2.964295475749168e-13 relative error = 1.521376248259649e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09999999999977 y[1] (closed_form) = 1.958419337566479 y[1] (numeric) = 1.958419337566778 absolute error = 2.990940828340172e-13 relative error = 1.527221862533638e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.109999999999769 y[1] (closed_form) = 1.968412601563315 y[1] (numeric) = 1.968412601563617 absolute error = 3.019806626980426e-13 relative error = 1.534132947829176e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999767 y[1] (closed_form) = 1.978409024273671 y[1] (numeric) = 1.978409024273976 absolute error = 3.04645197957143e-13 relative error = 1.539849415461429e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.129999999999766 y[1] (closed_form) = 1.988407606063608 y[1] (numeric) = 1.988407606063915 absolute error = 3.070876886113183e-13 relative error = 1.544390031877069e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999765 y[1] (closed_form) = 1.998407347083278 y[1] (numeric) = 1.998407347083588 absolute error = 3.101963130802687e-13 relative error = 1.55221763737512e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999764 y[1] (closed_form) = 2.008407247366913 y[1] (numeric) = 2.008407247367226 absolute error = 3.135269821541442e-13 relative error = 1.561072748393974e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.159999999999763 y[1] (closed_form) = 2.018406306932817 y[1] (numeric) = 2.018406306933132 absolute error = 3.157474282033945e-13 relative error = 1.564340277370647e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.169999999999762 y[1] (closed_form) = 2.028403525883366 y[1] (numeric) = 2.028403525883684 absolute error = 3.179678742526448e-13 relative error = 1.567577014115919e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.179999999999761 y[1] (closed_form) = 2.038397904504996 y[1] (numeric) = 2.038397904505317 absolute error = 3.210764987215953e-13 relative error = 1.575141428530684e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18999999999976 y[1] (closed_form) = 2.048388443368174 y[1] (numeric) = 2.048388443368498 absolute error = 3.232969447708456e-13 relative error = 1.578299007776313e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999759 y[1] (closed_form) = 2.058374143427339 y[1] (numeric) = 2.058374143427665 absolute error = 3.25961480029946e-13 relative error = 1.583587129049323e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999757 y[1] (closed_form) = 2.068354006120806 y[1] (numeric) = 2.068354006121135 absolute error = 3.290701044988964e-13 relative error = 1.590975739767424e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999756 y[1] (closed_form) = 2.078327033470622 y[1] (numeric) = 2.078327033470954 absolute error = 3.321787289678468e-13 relative error = 1.598298648952941e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999755 y[1] (closed_form) = 2.088292228182364 y[1] (numeric) = 2.088292228182698 absolute error = 3.343991750170971e-13 relative error = 1.601304503767445e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999754 y[1] (closed_form) = 2.098248593744864 y[1] (numeric) = 2.098248593745201 absolute error = 3.370637102761975e-13 relative error = 1.606405033612441e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999753 y[1] (closed_form) = 2.108195134529863 y[1] (numeric) = 2.108195134530203 absolute error = 3.397282455352979e-13 relative error = 1.611464897015137e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999752 y[1] (closed_form) = 2.118130855891571 y[1] (numeric) = 2.118130855891914 absolute error = 3.423927807943983e-13 relative error = 1.616485496361258e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.269999999999751 y[1] (closed_form) = 2.128054764266133 y[1] (numeric) = 2.128054764266478 absolute error = 3.450573160534987e-13 relative error = 1.62146821523408e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27999999999975 y[1] (closed_form) = 2.137965867270979 y[1] (numeric) = 2.137965867271327 absolute error = 3.47277762102749e-13 relative error = 1.624337261034171e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999749 y[1] (closed_form) = 2.14786317380407 y[1] (numeric) = 2.14786317380442 absolute error = 3.499422973618493e-13 relative error = 1.629257867213526e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999748 y[1] (closed_form) = 2.157745694142999 y[1] (numeric) = 2.157745694143351 absolute error = 3.517186542012496e-13 relative error = 1.630028298311322e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999746 y[1] (closed_form) = 2.167612440043968 y[1] (numeric) = 2.167612440044323 absolute error = 3.548272786702e-13 relative error = 1.636949816836273e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999745 y[1] (closed_form) = 2.17746242484061 y[1] (numeric) = 2.177462424840967 absolute error = 3.574918139293004e-13 relative error = 1.641781781632667e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999744 y[1] (closed_form) = 2.187294663542652 y[1] (numeric) = 2.187294663543011 absolute error = 3.592681707687007e-13 relative error = 1.642522961157926e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999743 y[1] (closed_form) = 2.197108172934418 y[1] (numeric) = 2.19710817293478 absolute error = 3.61488616817951e-13 relative error = 1.645292759232484e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999742 y[1] (closed_form) = 2.206901971673148 y[1] (numeric) = 2.206901971673512 absolute error = 3.645972412869014e-13 relative error = 1.652077192221114e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.359999999999741 y[1] (closed_form) = 2.216675080387127 y[1] (numeric) = 2.216675080387495 absolute error = 3.681499549657019e-13 relative error = 1.660820560591168e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36999999999974 y[1] (closed_form) = 2.22642652177363 y[1] (numeric) = 2.226426521774 absolute error = 3.703704010149522e-13 relative error = 1.663519534073397e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999739 y[1] (closed_form) = 2.236155320696643 y[1] (numeric) = 2.236155320697017 absolute error = 3.734790254839027e-13 relative error = 1.670183739148989e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999738 y[1] (closed_form) = 2.245860504284383 y[1] (numeric) = 2.245860504284759 absolute error = 3.765876499528531e-13 relative error = 1.676807839286743e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999737 y[1] (closed_form) = 2.255541102026577 y[1] (numeric) = 2.255541102026956 absolute error = 3.796962744218035e-13 relative error = 1.68339328456773e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y[1] (closed_form) = 2.265196145871518 y[1] (numeric) = 2.265196145871901 absolute error = 3.82804898890754e-13 relative error = 1.689941507221983e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999734 y[1] (closed_form) = 2.274824670322869 y[1] (numeric) = 2.274824670323254 absolute error = 3.850253449400043e-13 relative error = 1.692549540028319e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999733 y[1] (closed_form) = 2.284425712536207 y[1] (numeric) = 2.284425712536594 absolute error = 3.876898801991047e-13 relative error = 1.697099967276612e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999732 y[1] (closed_form) = 2.293998312415312 y[1] (numeric) = 2.293998312415702 absolute error = 3.90354415458205e-13 relative error = 1.70163340289125e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.449999999999731 y[1] (closed_form) = 2.303541512708173 y[1] (numeric) = 2.303541512708566 absolute error = 3.930189507173054e-13 relative error = 1.706150935631502e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45999999999973 y[1] (closed_form) = 2.313054359102714 y[1] (numeric) = 2.31305435910311 absolute error = 3.956834859764058e-13 relative error = 1.71065364036624e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999729 y[1] (closed_form) = 2.322535900322222 y[1] (numeric) = 2.322535900322621 absolute error = 3.987921104453562e-13 relative error = 1.717054665936612e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999728 y[1] (closed_form) = 2.331985188220477 y[1] (numeric) = 2.331985188220879 absolute error = 4.014566457044566e-13 relative error = 1.721523137163687e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999727 y[1] (closed_form) = 2.341401277876564 y[1] (numeric) = 2.341401277876968 absolute error = 4.04121180963557e-13 relative error = 1.725980013686752e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999726 y[1] (closed_form) = 2.350783227689363 y[1] (numeric) = 2.35078322768977 absolute error = 4.067857162226574e-13 relative error = 1.73042631677484e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y[1] (closed_form) = 2.360130099471711 y[1] (numeric) = 2.360130099472121 absolute error = 4.094502514817577e-13 relative error = 1.734863055106193e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999723 y[1] (closed_form) = 2.36944095854422 y[1] (numeric) = 2.369440958544632 absolute error = 4.11670697531008e-13 relative error = 1.737416988790207e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999722 y[1] (closed_form) = 2.378714873828741 y[1] (numeric) = 2.378714873829156 absolute error = 4.147793219999585e-13 relative error = 1.743711810791078e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.539999999999721 y[1] (closed_form) = 2.387950917941473 y[1] (numeric) = 2.387950917941891 absolute error = 4.178879464689089e-13 relative error = 1.749985493123737e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54999999999972 y[1] (closed_form) = 2.397148167285703 y[1] (numeric) = 2.397148167286124 absolute error = 4.205524817280093e-13 relative error = 1.754386681087811e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999719 y[1] (closed_form) = 2.40630570214416 y[1] (numeric) = 2.406305702144584 absolute error = 4.236611061969597e-13 relative error = 1.760628775551888e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999718 y[1] (closed_form) = 2.415422606770989 y[1] (numeric) = 2.415422606771416 absolute error = 4.263256414560601e-13 relative error = 1.765014702855602e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999717 y[1] (closed_form) = 2.424497969483326 y[1] (numeric) = 2.424497969483755 absolute error = 4.285460875053104e-13 relative error = 1.767566287533893e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999716 y[1] (closed_form) = 2.433530882752462 y[1] (numeric) = 2.433530882752892 absolute error = 4.307665335545607e-13 relative error = 1.770129718129319e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999715 y[1] (closed_form) = 2.442520443294597 y[1] (numeric) = 2.44252044329503 absolute error = 4.334310688136611e-13 relative error = 1.774523812087432e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y[1] (closed_form) = 2.451465752161168 y[1] (numeric) = 2.451465752161604 absolute error = 4.360956040727615e-13 relative error = 1.778917791073799e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999712 y[1] (closed_form) = 2.460365914828743 y[1] (numeric) = 2.460365914829182 absolute error = 4.392042285417119e-13 relative error = 1.785117514003129e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.629999999999711 y[1] (closed_form) = 2.469220041288472 y[1] (numeric) = 2.469220041288914 absolute error = 4.418687638008123e-13 relative error = 1.789507441265701e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63999999999971 y[1] (closed_form) = 2.478027246135088 y[1] (numeric) = 2.478027246135533 absolute error = 4.445332990599127e-13 relative error = 1.79389996519707e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999709 y[1] (closed_form) = 2.486786648655445 y[1] (numeric) = 2.486786648655893 absolute error = 4.476419235288631e-13 relative error = 1.800081739102524e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999708 y[1] (closed_form) = 2.495497372916591 y[1] (numeric) = 2.495497372917042 absolute error = 4.503064587879635e-13 relative error = 1.804475787773207e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999707 y[1] (closed_form) = 2.504158547853359 y[1] (numeric) = 2.50415854785381 absolute error = 4.516387264175137e-13 relative error = 1.803554838030013e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999706 y[1] (closed_form) = 2.512769307355471 y[1] (numeric) = 2.512769307355925 absolute error = 4.53859172466764e-13 relative error = 1.806211064176129e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999705 y[1] (closed_form) = 2.521328790354155 y[1] (numeric) = 2.521328790354611 absolute error = 4.565237077258644e-13 relative error = 1.810647264539185e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999704 y[1] (closed_form) = 2.529836140908242 y[1] (numeric) = 2.529836140908701 absolute error = 4.591882429849647e-13 relative error = 1.815090849402249e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999702 y[1] (closed_form) = 2.538290508289767 y[1] (numeric) = 2.538290508290229 absolute error = 4.618527782440651e-13 relative error = 1.819542628141683e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.719999999999701 y[1] (closed_form) = 2.546691047069037 y[1] (numeric) = 2.5466910470695 absolute error = 4.636291350834654e-13 relative error = 1.820515824316624e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7299999999997 y[1] (closed_form) = 2.555036917199175 y[1] (numeric) = 2.555036917199641 absolute error = 4.658495811327157e-13 relative error = 1.823259687548385e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999699 y[1] (closed_form) = 2.563327284100121 y[1] (numeric) = 2.563327284100589 absolute error = 4.68070027181966e-13 relative error = 1.826025221536571e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999698 y[1] (closed_form) = 2.571561318742096 y[1] (numeric) = 2.571561318742567 absolute error = 4.707345624410664e-13 relative error = 1.830539909782633e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999697 y[1] (closed_form) = 2.579738197728496 y[1] (numeric) = 2.579738197728969 absolute error = 4.729550084903167e-13 relative error = 1.833344984024975e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999696 y[1] (closed_form) = 2.587857103378237 y[1] (numeric) = 2.587857103378712 absolute error = 4.75175454539567e-13 relative error = 1.836173465371268e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999695 y[1] (closed_form) = 2.595917223807519 y[1] (numeric) = 2.595917223807996 absolute error = 4.773959005888173e-13 relative error = 1.839025898863619e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999694 y[1] (closed_form) = 2.603917753011016 y[1] (numeric) = 2.603917753011496 absolute error = 4.796163466380676e-13 relative error = 1.841902825400179e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999693 y[1] (closed_form) = 2.611857890942476 y[1] (numeric) = 2.611857890942958 absolute error = 4.818367926873179e-13 relative error = 1.844804781907371e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999691 y[1] (closed_form) = 2.619736843594721 y[1] (numeric) = 2.619736843595206 absolute error = 4.849454171562684e-13 relative error = 1.851122636008132e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81999999999969 y[1] (closed_form) = 2.627553823079052 y[1] (numeric) = 2.627553823079539 absolute error = 4.871658632055187e-13 relative error = 1.854066161943134e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999689 y[1] (closed_form) = 2.635308047704036 y[1] (numeric) = 2.635308047704525 absolute error = 4.89386309254769e-13 relative error = 1.857036446578372e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999688 y[1] (closed_form) = 2.64299874205367 y[1] (numeric) = 2.642998742054162 absolute error = 4.920508445138694e-13 relative error = 1.861714259203675e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999687 y[1] (closed_form) = 2.65062513706493 y[1] (numeric) = 2.650625137065424 absolute error = 4.942712905631197e-13 relative error = 1.864734788980506e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999686 y[1] (closed_form) = 2.658186470104669 y[1] (numeric) = 2.658186470105165 absolute error = 4.9649173661237e-13 relative error = 1.867783702144944e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999685 y[1] (closed_form) = 2.665681985045884 y[1] (numeric) = 2.665681985046383 absolute error = 4.991562718714704e-13 relative error = 1.872527460783656e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999684 y[1] (closed_form) = 2.673110932343328 y[1] (numeric) = 2.673110932343829 absolute error = 5.013767179207207e-13 relative error = 1.875630045331486e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999683 y[1] (closed_form) = 2.680472569108461 y[1] (numeric) = 2.680472569108965 absolute error = 5.03597163969971e-13 relative error = 1.87876260989856e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999681 y[1] (closed_form) = 2.687766159183743 y[1] (numeric) = 2.687766159184248 absolute error = 5.053735208093713e-13 relative error = 1.88027339760409e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.90999999999968 y[1] (closed_form) = 2.694990973216242 y[1] (numeric) = 2.69499097321675 absolute error = 5.075939668586216e-13 relative error = 1.883471862812406e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999679 y[1] (closed_form) = 2.702146288730577 y[1] (numeric) = 2.702146288731087 absolute error = 5.102585021177219e-13 relative error = 1.88834521745095e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999678 y[1] (closed_form) = 2.709231390201159 y[1] (numeric) = 2.709231390201671 absolute error = 5.115907697472721e-13 relative error = 1.888324384538032e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999677 y[1] (closed_form) = 2.716245569123745 y[1] (numeric) = 2.716245569124259 absolute error = 5.133671265866724e-13 relative error = 1.889987902501332e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999676 y[1] (closed_form) = 2.723188124086288 y[1] (numeric) = 2.723188124086804 absolute error = 5.155875726359227e-13 relative error = 1.893323373716305e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999675 y[1] (closed_form) = 2.730058360839077 y[1] (numeric) = 2.730058360839595 absolute error = 5.17808018685173e-13 relative error = 1.89669212245714e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999674 y[1] (closed_form) = 2.736855592364162 y[1] (numeric) = 2.736855592364682 absolute error = 5.200284647344233e-13 relative error = 1.900094642133493e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999673 y[1] (closed_form) = 2.743579138944056 y[1] (numeric) = 2.743579138944578 absolute error = 5.218048215738236e-13 relative error = 1.901912775786212e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999672 y[1] (closed_form) = 2.750228328229702 y[1] (numeric) = 2.750228328230226 absolute error = 5.240252676230739e-13 relative error = 1.905388226294594e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99999999999967 y[1] (closed_form) = 2.756802495307713 y[1] (numeric) = 2.756802495308239 absolute error = 5.262457136723242e-13 relative error = 1.908898858616221e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999674 y[1] (closed_form) = 2.763300982766863 y[1] (numeric) = 2.763300982767388 absolute error = 5.24913446042774e-13 relative error = 1.899588388367249e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999677 y[1] (closed_form) = 2.769723140763818 y[1] (numeric) = 2.769723140764341 absolute error = 5.235811784132238e-13 relative error = 1.890373700921002e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.029999999999681 y[1] (closed_form) = 2.776068327088131 y[1] (numeric) = 2.776068327088653 absolute error = 5.226929999935237e-13 relative error = 1.882853512261299e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999684 y[1] (closed_form) = 2.782335907226456 y[1] (numeric) = 2.782335907226979 absolute error = 5.226929999935237e-13 relative error = 1.878612135349844e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999687 y[1] (closed_form) = 2.788525254426003 y[1] (numeric) = 2.788525254426525 absolute error = 5.222489107836736e-13 relative error = 1.872849851206295e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.059999999999691 y[1] (closed_form) = 2.794635749757209 y[1] (numeric) = 2.794635749757731 absolute error = 5.213607323639735e-13 relative error = 1.865576694240987e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999694 y[1] (closed_form) = 2.800666782175634 y[1] (numeric) = 2.800666782176155 absolute error = 5.209166431541234e-13 relative error = 1.859973655093168e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999697 y[1] (closed_form) = 2.806617748583061 y[1] (numeric) = 2.806617748583581 absolute error = 5.200284647344233e-13 relative error = 1.852865303787675e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.089999999999701 y[1] (closed_form) = 2.81248805388781 y[1] (numeric) = 2.812488053888329 absolute error = 5.195843755245733e-13 relative error = 1.847418959900405e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.099999999999704 y[1] (closed_form) = 2.81827711106424 y[1] (numeric) = 2.81827711106476 absolute error = 5.195843755245733e-13 relative error = 1.843624154220829e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.109999999999707 y[1] (closed_form) = 2.82398434121146 y[1] (numeric) = 2.823984341211979 absolute error = 5.191402863147232e-13 relative error = 1.838325654780428e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.119999999999711 y[1] (closed_form) = 2.829609173611209 y[1] (numeric) = 2.829609173611729 absolute error = 5.195843755245733e-13 relative error = 1.836240779716827e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.129999999999714 y[1] (closed_form) = 2.835151045784936 y[1] (numeric) = 2.835151045785456 absolute error = 5.200284647344233e-13 relative error = 1.834217847079287e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.139999999999717 y[1] (closed_form) = 2.840609403550042 y[1] (numeric) = 2.840609403550561 absolute error = 5.191402863147232e-13 relative error = 1.827566597737547e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.149999999999721 y[1] (closed_form) = 2.845983701075297 y[1] (numeric) = 2.845983701075816 absolute error = 5.191402863147232e-13 relative error = 1.824115458281003e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.159999999999724 y[1] (closed_form) = 2.85127340093543 y[1] (numeric) = 2.851273400935948 absolute error = 5.186961971048731e-13 relative error = 1.819173836275056e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.169999999999727 y[1] (closed_form) = 2.85647797416486 y[1] (numeric) = 2.856477974165379 absolute error = 5.182521078950231e-13 relative error = 1.814304582714463e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.179999999999731 y[1] (closed_form) = 2.861596900310604 y[1] (numeric) = 2.861596900311122 absolute error = 5.17808018685173e-13 relative error = 1.80950719728893e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999734 y[1] (closed_form) = 2.866629667484311 y[1] (numeric) = 2.866629667484828 absolute error = 5.169198402654729e-13 relative error = 1.80323201887152e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999737 y[1] (closed_form) = 2.871575772413459 y[1] (numeric) = 2.871575772413976 absolute error = 5.169198402654729e-13 relative error = 1.800126067476255e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.209999999999741 y[1] (closed_form) = 2.876434720491677 y[1] (numeric) = 2.876434720492194 absolute error = 5.169198402654729e-13 relative error = 1.797085247869329e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999744 y[1] (closed_form) = 2.881206025828204 y[1] (numeric) = 2.881206025828722 absolute error = 5.17808018685173e-13 relative error = 1.797191919089954e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999747 y[1] (closed_form) = 2.885889211296485 y[1] (numeric) = 2.885889211297003 absolute error = 5.17808018685173e-13 relative error = 1.794275458178617e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.239999999999751 y[1] (closed_form) = 2.890483808581875 y[1] (numeric) = 2.890483808582394 absolute error = 5.191402863147232e-13 relative error = 1.796032500764718e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999754 y[1] (closed_form) = 2.894989358228474 y[1] (numeric) = 2.894989358228994 absolute error = 5.200284647344233e-13 relative error = 1.796305272267541e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999757 y[1] (closed_form) = 2.899405409685071 y[1] (numeric) = 2.899405409685591 absolute error = 5.200284647344233e-13 relative error = 1.793569340104487e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.269999999999761 y[1] (closed_form) = 2.903731521350203 y[1] (numeric) = 2.903731521350723 absolute error = 5.195843755245733e-13 relative error = 1.789367824484587e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999764 y[1] (closed_form) = 2.907967260616307 y[1] (numeric) = 2.907967260616827 absolute error = 5.204725539442734e-13 relative error = 1.789815727959626e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999767 y[1] (closed_form) = 2.912112203912985 y[1] (numeric) = 2.912112203913506 absolute error = 5.213607323639735e-13 relative error = 1.790318146613392e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.299999999999771 y[1] (closed_form) = 2.916165936749363 y[1] (numeric) = 2.916165936749885 absolute error = 5.222489107836736e-13 relative error = 1.790875149463621e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999774 y[1] (closed_form) = 2.920128053755535 y[1] (numeric) = 2.920128053756058 absolute error = 5.231370892033738e-13 relative error = 1.791486810075245e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999777 y[1] (closed_form) = 2.923998158723103 y[1] (numeric) = 2.923998158723627 absolute error = 5.244693568329239e-13 relative error = 1.793671980497954e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.329999999999781 y[1] (closed_form) = 2.927775864644794 y[1] (numeric) = 2.927775864645319 absolute error = 5.253575352526241e-13 relative error = 1.794391236012057e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999784 y[1] (closed_form) = 2.931460793753164 y[1] (numeric) = 2.931460793753691 absolute error = 5.266898028821743e-13 relative error = 1.796680358149531e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999787 y[1] (closed_form) = 2.935052577558374 y[1] (numeric) = 2.935052577558901 absolute error = 5.275779813018744e-13 relative error = 1.797507769829318e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.359999999999791 y[1] (closed_form) = 2.938550856885036 y[1] (numeric) = 2.938550856885564 absolute error = 5.289102489314246e-13 relative error = 1.799901634141148e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999794 y[1] (closed_form) = 2.941955281908132 y[1] (numeric) = 2.941955281908663 absolute error = 5.311306949806749e-13 relative error = 1.805366309430058e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y[1] (closed_form) = 2.945265512187997 y[1] (numeric) = 2.94526551218853 absolute error = 5.324629626102251e-13 relative error = 1.807860650955932e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999801 y[1] (closed_form) = 2.948481216704363 y[1] (numeric) = 2.948481216704897 absolute error = 5.342393194496253e-13 relative error = 1.811913592743746e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999804 y[1] (closed_form) = 2.951602073889456 y[1] (numeric) = 2.951602073889991 absolute error = 5.355715870791755e-13 relative error = 1.814511487903345e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y[1] (closed_form) = 2.954627771660159 y[1] (numeric) = 2.954627771660696 absolute error = 5.369038547087257e-13 relative error = 1.817162418422161e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.419999999999811 y[1] (closed_form) = 2.957558007449216 y[1] (numeric) = 2.957558007449755 absolute error = 5.38680211548126e-13 relative error = 1.821368203738859e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999814 y[1] (closed_form) = 2.960392488235492 y[1] (numeric) = 2.960392488236032 absolute error = 5.400124791776761e-13 relative error = 1.824124609570079e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y[1] (closed_form) = 2.963130930573267 y[1] (numeric) = 2.96313093057381 absolute error = 5.422329252269265e-13 relative error = 1.829932385478567e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.449999999999821 y[1] (closed_form) = 2.965773060620593 y[1] (numeric) = 2.965773060621137 absolute error = 5.440092820663267e-13 relative error = 1.834291670153926e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999824 y[1] (closed_form) = 2.968318614166663 y[1] (numeric) = 2.96831861416721 absolute error = 5.46229728115577e-13 relative error = 1.840199113089238e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y[1] (closed_form) = 2.970767336658247 y[1] (numeric) = 2.970767336658795 absolute error = 5.475619957451272e-13 relative error = 1.843166878093752e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.479999999999831 y[1] (closed_form) = 2.973118983225135 y[1] (numeric) = 2.973118983225684 absolute error = 5.497824417943775e-13 relative error = 1.849177395510734e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999834 y[1] (closed_form) = 2.97537331870463 y[1] (numeric) = 2.975373318705182 absolute error = 5.515587986337778e-13 relative error = 1.853746537170356e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y[1] (closed_form) = 2.977530117665063 y[1] (numeric) = 2.977530117665617 absolute error = 5.537792446830281e-13 relative error = 1.859861102319576e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.509999999999841 y[1] (closed_form) = 2.979589164428335 y[1] (numeric) = 2.979589164428891 absolute error = 5.559996907322784e-13 relative error = 1.866028032891416e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999844 y[1] (closed_form) = 2.981550253091486 y[1] (numeric) = 2.981550253092043 absolute error = 5.573319583618286e-13 relative error = 1.869269041445626e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y[1] (closed_form) = 2.983413187547283 y[1] (numeric) = 2.983413187547843 absolute error = 5.595524044110789e-13 relative error = 1.875544449379795e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.539999999999851 y[1] (closed_form) = 2.985177781503834 y[1] (numeric) = 2.985177781504396 absolute error = 5.617728504603292e-13 relative error = 1.881874017490934e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999854 y[1] (closed_form) = 2.986843858503213 y[1] (numeric) = 2.986843858503776 absolute error = 5.631051180898794e-13 relative error = 1.885284751282802e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999858 y[1] (closed_form) = 2.988411251939109 y[1] (numeric) = 2.988411251939675 absolute error = 5.657696533489798e-13 relative error = 1.893212164095104e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.569999999999861 y[1] (closed_form) = 2.989879805073484 y[1] (numeric) = 2.989879805074052 absolute error = 5.679900993982301e-13 relative error = 1.899708805800206e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999864 y[1] (closed_form) = 2.991249371052249 y[1] (numeric) = 2.991249371052819 absolute error = 5.693223670277803e-13 relative error = 1.903292893388913e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999868 y[1] (closed_form) = 2.992519812919947 y[1] (numeric) = 2.992519812920519 absolute error = 5.724309914967307e-13 relative error = 1.912872853925007e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.599999999999871 y[1] (closed_form) = 2.99369100363345 y[1] (numeric) = 2.993691003634025 absolute error = 5.74651437545981e-13 relative error = 1.919541585449284e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999874 y[1] (closed_form) = 2.994762826074663 y[1] (numeric) = 2.99476282607524 absolute error = 5.777600620149315e-13 relative error = 1.929234786088958e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999878 y[1] (closed_form) = 2.995735173062234 y[1] (numeric) = 2.995735173062815 absolute error = 5.808686864838819e-13 relative error = 1.938985434049964e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.629999999999881 y[1] (closed_form) = 2.996607947362276 y[1] (numeric) = 2.996607947362859 absolute error = 5.835332217429823e-13 relative error = 1.947312534683189e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999884 y[1] (closed_form) = 2.997381061698085 y[1] (numeric) = 2.997381061698671 absolute error = 5.866418462119327e-13 relative error = 1.957181399817035e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999888 y[1] (closed_form) = 2.998054438758873 y[1] (numeric) = 2.998054438759461 absolute error = 5.88862292261183e-13 relative error = 1.964148097674166e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.659999999999891 y[1] (closed_form) = 2.998628011207493 y[1] (numeric) = 2.998628011208085 absolute error = 5.919709167301335e-13 relative error = 1.974139221395979e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999894 y[1] (closed_form) = 2.99910172168718 y[1] (numeric) = 2.999101721687776 absolute error = 5.95523630408934e-13 relative error = 1.985673330459479e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999898 y[1] (closed_form) = 2.99947552282728 y[1] (numeric) = 2.99947552282788 absolute error = 5.990763440877345e-13 relative error = 1.99727032118952e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.689999999999901 y[1] (closed_form) = 2.999749377247992 y[1] (numeric) = 2.999749377248594 absolute error = 6.021849685566849e-13 relative error = 2.007450932814718e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999904 y[1] (closed_form) = 2.9999232575641 y[1] (numeric) = 2.999923257564705 absolute error = 6.052935930256353e-13 relative error = 2.017696924411081e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999908 y[1] (closed_form) = 2.999997146387718 y[1] (numeric) = 2.999997146388327 absolute error = 6.092903959142859e-13 relative error = 2.030969918247854e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.719999999999911 y[1] (closed_form) = 2.999971036330025 y[1] (numeric) = 2.999971036330637 absolute error = 6.119549311733863e-13 relative error = 2.039869464613276e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999914 y[1] (closed_form) = 2.999844930002006 y[1] (numeric) = 2.999844930002622 absolute error = 6.155076448521868e-13 relative error = 2.051798206955235e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999918 y[1] (closed_form) = 2.999618840014188 y[1] (numeric) = 2.999618840014806 absolute error = 6.186162693211372e-13 relative error = 2.062316255215317e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.749999999999921 y[1] (closed_form) = 2.999292788975381 y[1] (numeric) = 2.999292788976004 absolute error = 6.230571614196379e-13 relative error = 2.077346912278234e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999924 y[1] (closed_form) = 2.998866809490418 y[1] (numeric) = 2.998866809491044 absolute error = 6.266098750984384e-13 relative error = 2.089488846638424e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999928 y[1] (closed_form) = 2.998340944156892 y[1] (numeric) = 2.998340944157522 absolute error = 6.297184995673888e-13 relative error = 2.100223127708581e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.779999999999931 y[1] (closed_form) = 2.997715245560898 y[1] (numeric) = 2.997715245561531 absolute error = 6.328271240363392e-13 relative error = 2.111031476299984e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999934 y[1] (closed_form) = 2.996989776271775 y[1] (numeric) = 2.996989776272411 absolute error = 6.368239269249898e-13 relative error = 2.124878543019898e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999938 y[1] (closed_form) = 2.996164608835846 y[1] (numeric) = 2.996164608836487 absolute error = 6.408207298136404e-13 relative error = 2.138803482037758e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.809999999999941 y[1] (closed_form) = 2.995239825769168 y[1] (numeric) = 2.995239825769813 absolute error = 6.448175327022909e-13 relative error = 2.15280768890252e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999944 y[1] (closed_form) = 2.994215519549277 y[1] (numeric) = 2.994215519549927 absolute error = 6.492584248007915e-13 relative error = 2.168375724999666e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999948 y[1] (closed_form) = 2.993091792605941 y[1] (numeric) = 2.993091792606595 absolute error = 6.532552276894421e-13 relative error = 2.182543246094982e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.839999999999951 y[1] (closed_form) = 2.991868757310919 y[1] (numeric) = 2.991868757311576 absolute error = 6.572520305780927e-13 relative error = 2.196794324523875e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999954 y[1] (closed_form) = 2.99054653596672 y[1] (numeric) = 2.990546535967381 absolute error = 6.616929226765933e-13 relative error = 2.212615368858306e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999958 y[1] (closed_form) = 2.989125260794376 y[1] (numeric) = 2.989125260795042 absolute error = 6.66577903984944e-13 relative error = 2.230009938786564e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.869999999999961 y[1] (closed_form) = 2.987605073920221 y[1] (numeric) = 2.987605073920892 absolute error = 6.705747068735946e-13 relative error = 2.244522586761081e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999964 y[1] (closed_form) = 2.985986127361676 y[1] (numeric) = 2.985986127362351 absolute error = 6.745715097622451e-13 relative error = 2.259124727944652e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999968 y[1] (closed_form) = 2.984268583012047 y[1] (numeric) = 2.984268583012727 absolute error = 6.799005802804459e-13 relative error = 2.278282136369296e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.899999999999971 y[1] (closed_form) = 2.982452612624338 y[1] (numeric) = 2.982452612625023 absolute error = 6.847855615887966e-13 relative error = 2.296048422329285e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999974 y[1] (closed_form) = 2.980538397794074 y[1] (numeric) = 2.980538397794763 absolute error = 6.896705428971472e-13 relative error = 2.313912625341714e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999978 y[1] (closed_form) = 2.978526129941143 y[1] (numeric) = 2.978526129941837 absolute error = 6.941114349956479e-13 relative error = 2.330385582379846e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.929999999999981 y[1] (closed_form) = 2.976416010290654 y[1] (numeric) = 2.976416010291353 absolute error = 6.985523270941485e-13 relative error = 2.346957967834386e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y[1] (closed_form) = 2.974208249852813 y[1] (numeric) = 2.974208249853517 absolute error = 7.043254868221993e-13 relative error = 2.368110863982221e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999988 y[1] (closed_form) = 2.971903069401824 y[1] (numeric) = 2.971903069402533 absolute error = 7.096545573404001e-13 relative error = 2.38787921667727e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.959999999999991 y[1] (closed_form) = 2.969500699453811 y[1] (numeric) = 2.969500699454525 absolute error = 7.145395386487507e-13 relative error = 2.406261560336315e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y[1] (closed_form) = 2.967001380243767 y[1] (numeric) = 2.967001380244488 absolute error = 7.203126983768016e-13 relative error = 2.427746421599646e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999998 y[1] (closed_form) = 2.964405361701531 y[1] (numeric) = 2.964405361702257 absolute error = 7.260858581048524e-13 relative error = 2.449347405336254e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.990000000000001 y[1] (closed_form) = 2.961712903426793 y[1] (numeric) = 2.961712903427524 absolute error = 7.309708394132031e-13 relative error = 2.468067848735261e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 Finished! diff ( y , x , 2 ) = sin ( x ) ; Iterations = 4900 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %