##############ECHO OF PROBLEM################# ##############temp/lin_arctan_2_3postode.ode################# diff ( y , x , 1 ) = arctan ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(2.0); x_end=c(3.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=0; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(c(x)*arctan(c(x))-c(0.5)*ln(c(x)*c(x)+c(1.0))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 1.409578479371131 y[1] (numeric) = 1.409578479371131 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.009999999999999 y[1] (closed_form) = 1.420659939955546 y[1] (numeric) = 1.420659940486077 absolute error = 5.305313965919822e-10 relative error = 3.734401046098218e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999998 y[1] (closed_form) = 1.431761241560894 y[1] (numeric) = 1.431761242616166 absolute error = 1.055272313976729e-09 relative error = 7.37044895017748e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999997 y[1] (closed_form) = 1.442882226798611 y[1] (numeric) = 1.442882228372907 absolute error = 1.574296026873867e-09 relative error = 1.091077287968839e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999996 y[1] (closed_form) = 1.454022739994729 y[1] (numeric) = 1.454022742082406 absolute error = 2.08767714227065e-09 relative error = 1.435794011225862e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999994 y[1] (closed_form) = 1.46518262716761 y[1] (numeric) = 1.4651826297631 absolute error = 2.595489601020518e-09 relative error = 1.771444428083302e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999993 y[1] (closed_form) = 1.476361736005993 y[1] (numeric) = 1.476361739103798 absolute error = 3.097805123530861e-09 relative error = 2.098269718037644e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999992 y[1] (closed_form) = 1.487559915847327 y[1] (numeric) = 1.487559919442023 absolute error = 3.594695430209072e-09 relative error = 2.416504634142082e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999991 y[1] (closed_form) = 1.498777017656421 y[1] (numeric) = 1.498777021742651 absolute error = 4.086229798971885e-09 relative error = 2.726376072513684e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.08999999999999 y[1] (closed_form) = 1.510012894004366 y[1] (numeric) = 1.510012898576844 absolute error = 4.572478173869854e-09 relative error = 3.028105383752196e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.099999999999989 y[1] (closed_form) = 1.521267399047768 y[1] (numeric) = 1.521267404101276 absolute error = 5.053508056462874e-09 relative error = 3.321906496928877e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999988 y[1] (closed_form) = 1.532540388508257 y[1] (numeric) = 1.532540394037645 absolute error = 5.529388280578473e-09 relative error = 3.607988619445564e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999987 y[1] (closed_form) = 1.543831719652281 y[1] (numeric) = 1.543831725652466 absolute error = 6.000184127330499e-09 relative error = 3.886553211046814e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999986 y[1] (closed_form) = 1.555141251271187 y[1] (numeric) = 1.555141257737149 absolute error = 6.465961321922009e-09 relative error = 4.157796802468374e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999985 y[1] (closed_form) = 1.566468843661568 y[1] (numeric) = 1.566468850588353 absolute error = 6.926785145466852e-09 relative error = 4.421910575173475e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999983 y[1] (closed_form) = 1.577814358605892 y[1] (numeric) = 1.57781436598861 absolute error = 7.382717992499011e-09 relative error = 4.67907897543926e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999982 y[1] (closed_form) = 1.5891776593534 y[1] (numeric) = 1.589177667187224 absolute error = 7.833823367775494e-09 relative error = 4.92948244122869e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999981 y[1] (closed_form) = 1.600558610601267 y[1] (numeric) = 1.60055861888143 absolute error = 8.280163221741077e-09 relative error = 5.173295852396524e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.17999999999998 y[1] (closed_form) = 1.611957078476028 y[1] (numeric) = 1.611957087197826 absolute error = 8.721798616662113e-09 relative error = 5.410689113948278e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.189999999999979 y[1] (closed_form) = 1.623372930515266 y[1] (numeric) = 1.623372939674055 absolute error = 9.158789504581932e-09 relative error = 5.641827168865562e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999978 y[1] (closed_form) = 1.634806035649552 y[1] (numeric) = 1.634806045240748 absolute error = 9.591195837543864e-09 relative error = 5.866870826503296e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999977 y[1] (closed_form) = 1.646256264184643 y[1] (numeric) = 1.646256274203718 absolute error = 1.001907512510058e-08 relative error = 6.085975399500046e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999976 y[1] (closed_form) = 1.657723487783923 y[1] (numeric) = 1.657723498226409 absolute error = 1.0442486431117e-08 relative error = 6.299293282667259e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999975 y[1] (closed_form) = 1.669207579451099 y[1] (numeric) = 1.669207590312585 absolute error = 1.086148571083356e-08 relative error = 6.506971238655198e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999974 y[1] (closed_form) = 1.680708413513134 y[1] (numeric) = 1.680708424789263 absolute error = 1.12761286974461e-08 relative error = 6.709152287680849e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999972 y[1] (closed_form) = 1.692225865603419 y[1] (numeric) = 1.692225877289891 absolute error = 1.168647156823965e-08 relative error = 6.905976209075644e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999971 y[1] (closed_form) = 1.703759812645186 y[1] (numeric) = 1.703759824737755 absolute error = 1.209256872414244e-08 relative error = 7.097578329053333e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.26999999999997 y[1] (closed_form) = 1.715310132835151 y[1] (numeric) = 1.715310145329625 absolute error = 1.249447367790424e-08 relative error = 7.284090170477067e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.279999999999969 y[1] (closed_form) = 1.726876705627391 y[1] (numeric) = 1.72687671851963 absolute error = 1.289223883205182e-08 relative error = 7.465639434500298e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999968 y[1] (closed_form) = 1.738459411717441 y[1] (numeric) = 1.738459425003358 absolute error = 1.328591769933496e-08 relative error = 7.642351388698614e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999967 y[1] (closed_form) = 1.75005813302662 y[1] (numeric) = 1.750058146702181 absolute error = 1.367556179410201e-08 relative error = 7.814347155686167e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999966 y[1] (closed_form) = 1.76167275268658 y[1] (numeric) = 1.761672766747801 absolute error = 1.406122041025526e-08 relative error = 7.981743708535916e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999965 y[1] (closed_form) = 1.773303155024067 y[1] (numeric) = 1.773303169467012 absolute error = 1.444294484009845e-08 relative error = 8.144656371460879e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999964 y[1] (closed_form) = 1.784949225545897 y[1] (numeric) = 1.784949240366681 absolute error = 1.482078437753387e-08 relative error = 8.303196620621621e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999963 y[1] (closed_form) = 1.796610850924146 y[1] (numeric) = 1.796610866118934 absolute error = 1.519478765033e-08 relative error = 8.457472937177274e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999961 y[1] (closed_form) = 1.808287918981553 y[1] (numeric) = 1.808287934546555 absolute error = 1.55650023980769e-08 relative error = 8.607590768423246e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.35999999999996 y[1] (closed_form) = 1.819980318677117 y[1] (numeric) = 1.819980334608593 absolute error = 1.59314752501416e-08 relative error = 8.753652490990484e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.369999999999959 y[1] (closed_form) = 1.831687940091906 y[1] (numeric) = 1.83168795638616 absolute error = 1.629425416815877e-08 relative error = 8.895758830699733e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999958 y[1] (closed_form) = 1.843410674415062 y[1] (numeric) = 1.843410691068447 absolute error = 1.665338533740623e-08 relative error = 9.034007217458787e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999957 y[1] (closed_form) = 1.855148413930007 y[1] (numeric) = 1.85514843093892 absolute error = 1.700891338884958e-08 relative error = 9.168491998339553e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999956 y[1] (closed_form) = 1.866901052000836 y[1] (numeric) = 1.866901069361719 absolute error = 1.736088250936518e-08 relative error = 9.299305118907507e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999955 y[1] (closed_form) = 1.878668483058908 y[1] (numeric) = 1.878668500768246 absolute error = 1.770933821809706e-08 relative error = 9.426537134035566e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999954 y[1] (closed_form) = 1.890450602589622 y[1] (numeric) = 1.890450620643944 absolute error = 1.805432203738633e-08 relative error = 9.550274422751235e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999953 y[1] (closed_form) = 1.902247307119378 y[1] (numeric) = 1.902247325515257 absolute error = 1.839587859819858e-08 relative error = 9.670603043752458e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999952 y[1] (closed_form) = 1.914058494202726 y[1] (numeric) = 1.914058512936776 absolute error = 1.873404986696414e-08 relative error = 9.787605720360988e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.44999999999995 y[1] (closed_form) = 1.925884062409692 y[1] (numeric) = 1.925884081478568 absolute error = 1.906887647784572e-08 relative error = 9.901362626152319e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.459999999999949 y[1] (closed_form) = 1.937723911313276 y[1] (numeric) = 1.937723930713676 absolute error = 1.940040017522904e-08 relative error = 1.001195271522484e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999948 y[1] (closed_form) = 1.94957794147714 y[1] (numeric) = 1.949577961205801 absolute error = 1.972866092714298e-08 relative error = 1.011945227088235e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999947 y[1] (closed_form) = 1.961446054443456 y[1] (numeric) = 1.961446074497155 absolute error = 2.005369958979486e-08 relative error = 1.02239363373595e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999946 y[1] (closed_form) = 1.973328152720925 y[1] (numeric) = 1.97332817309648 absolute error = 2.037555568712435e-08 relative error = 1.032547762470702e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999945 y[1] (closed_form) = 1.985224139772972 y[1] (numeric) = 1.985224160467239 absolute error = 2.069426718875889e-08 relative error = 1.042414645991835e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999944 y[1] (closed_form) = 1.997133920006099 y[1] (numeric) = 1.997133941015971 absolute error = 2.100987250841513e-08 relative error = 1.052001185195982e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999943 y[1] (closed_form) = 2.0090573987584 y[1] (numeric) = 2.009057420080809 absolute error = 2.132240917163131e-08 relative error = 1.061314086138534e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999942 y[1] (closed_form) = 2.020994482288244 y[1] (numeric) = 2.02099450392016 absolute error = 2.163191625825789e-08 relative error = 1.070359986028534e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999941 y[1] (closed_form) = 2.032945077763105 y[1] (numeric) = 2.032945099701533 absolute error = 2.193842751907482e-08 relative error = 1.079145116070433e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.549999999999939 y[1] (closed_form) = 2.04490909324856 y[1] (numeric) = 2.044909115490541 absolute error = 2.224198114575415e-08 relative error = 1.087675790536994e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999938 y[1] (closed_form) = 2.056886437697428 y[1] (numeric) = 2.05688646024004 absolute error = 2.254261177725425e-08 relative error = 1.095958015187726e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999937 y[1] (closed_form) = 2.06887702093907 y[1] (numeric) = 2.068877043779425 absolute error = 2.284035582889032e-08 relative error = 1.103997753260511e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999936 y[1] (closed_form) = 2.080880753668831 y[1] (numeric) = 2.080880776804078 absolute error = 2.313524705144232e-08 relative error = 1.111800712782423e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999935 y[1] (closed_form) = 2.092897547437636 y[1] (numeric) = 2.092897570864956 absolute error = 2.342732008386861e-08 relative error = 1.119372523158193e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999934 y[1] (closed_form) = 2.104927314641718 y[1] (numeric) = 2.104927338358327 absolute error = 2.371660867694914e-08 relative error = 1.126718652562403e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999933 y[1] (closed_form) = 2.116969968512505 y[1] (numeric) = 2.11696999251565 absolute error = 2.400314524919622e-08 relative error = 1.133844391097438e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999932 y[1] (closed_form) = 2.12902542310663 y[1] (numeric) = 2.129025447393593 absolute error = 2.428696310730061e-08 relative error = 1.140754959697079e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999931 y[1] (closed_form) = 2.141093593296095 y[1] (numeric) = 2.141093617864191 absolute error = 2.456809644613145e-08 relative error = 1.147455511662628e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999993 y[1] (closed_form) = 2.153174394758557 y[1] (numeric) = 2.153174419605132 absolute error = 2.48465745755766e-08 relative error = 1.15395086603576e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999928 y[1] (closed_form) = 2.165267743967761 y[1] (numeric) = 2.165267769090191 absolute error = 2.512242947005916e-08 relative error = 1.160245865207569e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999927 y[1] (closed_form) = 2.177373558184091 y[1] (numeric) = 2.177373583579783 absolute error = 2.539569221582383e-08 relative error = 1.166345210741128e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999926 y[1] (closed_form) = 2.189491755445263 y[1] (numeric) = 2.189491781111657 absolute error = 2.566639389911529e-08 relative error = 1.172253507476473e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999925 y[1] (closed_form) = 2.20162225455714 y[1] (numeric) = 2.201622280491706 absolute error = 2.593456605026745e-08 relative error = 1.177975286023089e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999924 y[1] (closed_form) = 2.213764975084678 y[1] (numeric) = 2.213765001284915 absolute error = 2.620023709098973e-08 relative error = 1.183514843981465e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999923 y[1] (closed_form) = 2.225919837342987 y[1] (numeric) = 2.225919863806423 absolute error = 2.646343544299157e-08 relative error = 1.18887639163952e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999922 y[1] (closed_form) = 2.238086762388525 y[1] (numeric) = 2.238086789112718 absolute error = 2.672419308069607e-08 relative error = 1.194064212782151e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999921 y[1] (closed_form) = 2.250265672010407 y[1] (numeric) = 2.250265698992942 absolute error = 2.698253531718819e-08 relative error = 1.199082208505708e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999992 y[1] (closed_form) = 2.262456488721836 y[1] (numeric) = 2.262456515960326 absolute error = 2.723849013008817e-08 relative error = 1.203934319438622e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999919 y[1] (closed_form) = 2.274659135751641 y[1] (numeric) = 2.274659163243729 absolute error = 2.749208727337304e-08 relative error = 1.208624485368817e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999917 y[1] (closed_form) = 2.286873537035948 y[1] (numeric) = 2.286873564779303 absolute error = 2.774335516875226e-08 relative error = 1.213156509070058e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999916 y[1] (closed_form) = 2.299099617209952 y[1] (numeric) = 2.299099645202269 absolute error = 2.799231735295393e-08 relative error = 1.217533905160826e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999915 y[1] (closed_form) = 2.311337301599797 y[1] (numeric) = 2.311337329838799 absolute error = 2.82390026917767e-08 relative error = 1.221760349397339e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999914 y[1] (closed_form) = 2.323586516214581 y[1] (numeric) = 2.323586544698019 absolute error = 2.848343827466238e-08 relative error = 1.225839368403012e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999913 y[1] (closed_form) = 2.33584718773846 y[1] (numeric) = 2.33584721646411 absolute error = 2.872564941469591e-08 relative error = 1.229774343351105e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999912 y[1] (closed_form) = 2.348119243522857 y[1] (numeric) = 2.348119272488518 absolute error = 2.896566098087305e-08 relative error = 1.233568570283347e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999911 y[1] (closed_form) = 2.360402611578781 y[1] (numeric) = 2.360402640782279 absolute error = 2.920349784218956e-08 relative error = 1.237225280930209e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.81999999999991 y[1] (closed_form) = 2.37269722056925 y[1] (numeric) = 2.372697250008437 absolute error = 2.943918664399803e-08 relative error = 1.240747719042511e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999909 y[1] (closed_form) = 2.385002999801815 y[1] (numeric) = 2.385003029474566 absolute error = 2.967275092302657e-08 relative error = 1.244138935066005e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999907 y[1] (closed_form) = 2.397319879221179 y[1] (numeric) = 2.397319909125394 absolute error = 2.990421554827094e-08 relative error = 1.247401976159559e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999906 y[1] (closed_form) = 2.40964778940193 y[1] (numeric) = 2.409647819535534 absolute error = 3.013360405645926e-08 relative error = 1.250539775522064e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999905 y[1] (closed_form) = 2.421986661541353 y[1] (numeric) = 2.421986691902292 absolute error = 3.036093954023045e-08 relative error = 1.253555191790724e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999904 y[1] (closed_form) = 2.434336427452354 y[1] (numeric) = 2.4343364580386 absolute error = 3.058624598040183e-08 relative error = 1.256451065492692e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999903 y[1] (closed_form) = 2.446697019556467 y[1] (numeric) = 2.446697050366014 absolute error = 3.080954646961231e-08 relative error = 1.2592301467387e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999902 y[1] (closed_form) = 2.459068370876969 y[1] (numeric) = 2.459068401907832 absolute error = 3.103086365641161e-08 relative error = 1.261895115398731e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999901 y[1] (closed_form) = 2.471450415032065 y[1] (numeric) = 2.471450446282284 absolute error = 3.125021885708179e-08 relative error = 1.26444854677274e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.9099999999999 y[1] (closed_form) = 2.483843086228189 y[1] (numeric) = 2.483843117695824 absolute error = 3.146763472017255e-08 relative error = 1.266893021328387e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999899 y[1] (closed_form) = 2.496246319253372 y[1] (numeric) = 2.496246350936507 absolute error = 3.168313433832282e-08 relative error = 1.269231088853413e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999898 y[1] (closed_form) = 2.508660049470717 y[1] (numeric) = 2.508660081367454 absolute error = 3.189673725145781e-08 relative error = 1.271465109757995e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999896 y[1] (closed_form) = 2.521084212811942 y[1] (numeric) = 2.521084244920408 absolute error = 3.210846566403802e-08 relative error = 1.273597506218374e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999895 y[1] (closed_form) = 2.533518745771028 y[1] (numeric) = 2.533518778089368 absolute error = 3.231834089234553e-08 relative error = 1.275630620309859e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999894 y[1] (closed_form) = 2.545963585397932 y[1] (numeric) = 2.545963617924315 absolute error = 3.252638247630557e-08 relative error = 1.277566680955561e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999893 y[1] (closed_form) = 2.558418669292401 y[1] (numeric) = 2.558418702025013 absolute error = 3.273261173220021e-08 relative error = 1.279407945426434e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999892 y[1] (closed_form) = 2.57088393559785 y[1] (numeric) = 2.570883968534898 absolute error = 3.293704819995469e-08 relative error = 1.281156560352278e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999891 y[1] (closed_form) = 2.583359322995336 y[1] (numeric) = 2.583359356135049 absolute error = 3.313971275176186e-08 relative error = 1.282814684615273e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.99999999999989 y[1] (closed_form) = 2.595844770697602 y[1] (numeric) = 2.595844804038227 absolute error = 3.334062448345776e-08 relative error = 1.284384369197002e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 Finished! diff ( y , x , 1 ) = arctan ( x ) ; Iterations = 1001 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.2 %