##############ECHO OF PROBLEM################# ##############temp/lin_arcsin_3postode.ode################# diff ( y , x , 1 ) = arcsin ( x + 0.001 ) ; ! /* BEGIN FIRST INPUT BLOCK */ max_terms=30; Digits=32; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-0.1); x_end=c(0.1); array_y_init[0 + 1] = exact_soln_y(x_start); glob_display_interval=c(0.001); glob_look_poles=true; glob_type_given_pole=0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(6.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.0000001); glob_lower_ratio_limit=c(0.9999999); glob_look_poles=false; glob_h=c(0.0001); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return((c(x) + c(0.001)) * arcsin(c(x) + c(0.001)) + sqrt((c(1.0) - (c(x) + c(0.001)) * (c(x) +c(0.001)) ))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -0.1 y[1] (closed_form) = 1.004904514303646 y[1] (numeric) = 1.004904514303646 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.09899999999999998 y[1] (closed_form) = 1.004805854321422 y[1] (numeric) = 1.004805854321588 absolute error = 1.665334536937735e-13 relative error = 1.657369460752585e-11 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.09799999999999995 y[1] (closed_form) = 1.004708199176153 y[1] (numeric) = 1.004708199176484 absolute error = 3.310685059432217e-13 relative error = 3.295170739272292e-11 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.09699999999999992 y[1] (closed_form) = 1.004611548768932 y[1] (numeric) = 1.004611548769426 absolute error = 4.944933351680447e-13 relative error = 4.92223422848369e-11 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.09599999999999989 y[1] (closed_form) = 1.004515903001894 y[1] (numeric) = 1.00451590300255 absolute error = 6.559197629485425e-13 relative error = 6.529710092079104e-11 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.09499999999999986 y[1] (closed_form) = 1.00442126177822 y[1] (numeric) = 1.004421261779035 absolute error = 8.15347789284715e-13 relative error = 8.117587911681893e-11 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.09399999999999983 y[1] (closed_form) = 1.004327625002127 y[1] (numeric) = 1.0043276250031 absolute error = 9.734435479913373e-13 relative error = 9.692490017779566e-11 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.09299999999999981 y[1] (closed_form) = 1.004234992578876 y[1] (numeric) = 1.004234992580006 absolute error = 1.129540905253634e-12 relative error = 1.124777480968844e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.09199999999999978 y[1] (closed_form) = 1.004143364414768 y[1] (numeric) = 1.004143364416052 absolute error = 1.284083950281456e-12 relative error = 1.278785476045886e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.09099999999999975 y[1] (closed_form) = 1.00405274041714 y[1] (numeric) = 1.004052740418577 absolute error = 1.436628593864953e-12 relative error = 1.430829812055585e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.08999999999999972 y[1] (closed_form) = 1.00396312049437 y[1] (numeric) = 1.003963120495958 absolute error = 1.588063014423824e-12 relative error = 1.581794173516883e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.08899999999999969 y[1] (closed_form) = 1.003874504555872 y[1] (numeric) = 1.003874504557609 absolute error = 1.737276988933445e-12 relative error = 1.730571880298963e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.08799999999999966 y[1] (closed_form) = 1.003786892512094 y[1] (numeric) = 1.003786892513979 absolute error = 1.884936651208591e-12 relative error = 1.877825527778428e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.08699999999999963 y[1] (closed_form) = 1.003700284274522 y[1] (numeric) = 1.003700284276553 absolute error = 2.031264045854186e-12 relative error = 2.023775501191963e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.0859999999999996 y[1] (closed_form) = 1.003614679755677 y[1] (numeric) = 1.003614679757852 absolute error = 2.175370994450532e-12 relative error = 2.167536045786129e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.08499999999999958 y[1] (closed_form) = 1.003530078869111 y[1] (numeric) = 1.003530078871429 absolute error = 2.317479541602552e-12 relative error = 2.309327433627246e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.08399999999999955 y[1] (closed_form) = 1.003446481529412 y[1] (numeric) = 1.00344648153187 absolute error = 2.458255821125022e-12 relative error = 2.449812587292397e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.08299999999999952 y[1] (closed_form) = 1.003363887652199 y[1] (numeric) = 1.003363887654796 absolute error = 2.597255743808091e-12 relative error = 2.588548158620187e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.08199999999999949 y[1] (closed_form) = 1.003282297154122 y[1] (numeric) = 1.003282297156856 absolute error = 2.734479309651761e-12 relative error = 2.72553329945948e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.08099999999999946 y[1] (closed_form) = 1.003201709952862 y[1] (numeric) = 1.003201709955732 absolute error = 2.87037060786588e-12 relative error = 2.861209843831658e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.07999999999999943 y[1] (closed_form) = 1.00312212596713 y[1] (numeric) = 1.003122125970134 absolute error = 3.004041460030749e-12 relative error = 2.994691655449722e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.0789999999999994 y[1] (closed_form) = 1.003043545116666 y[1] (numeric) = 1.003043545119803 absolute error = 3.136380044566067e-12 relative error = 3.126863295053923e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.07799999999999938 y[1] (closed_form) = 1.00296596732224 y[1] (numeric) = 1.002965967325506 absolute error = 3.266720227657061e-12 relative error = 3.257059894443564e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.07699999999999935 y[1] (closed_form) = 1.002889392505647 y[1] (numeric) = 1.002889392509042 absolute error = 3.395284053908654e-12 relative error = 3.385502009773762e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.07599999999999932 y[1] (closed_form) = 1.00281382058971 y[1] (numeric) = 1.002813820593233 absolute error = 3.522293567925772e-12 relative error = 3.512410275572855e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.07499999999999929 y[1] (closed_form) = 1.002739251498281 y[1] (numeric) = 1.002739251501928 absolute error = 3.647082635893639e-12 relative error = 3.637119650441741e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.07399999999999926 y[1] (closed_form) = 1.002665685156233 y[1] (numeric) = 1.002665685160004 absolute error = 3.770761480836882e-12 relative error = 3.760736541262336e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.07299999999999923 y[1] (closed_form) = 1.002593121489467 y[1] (numeric) = 1.00259312149336 absolute error = 3.892441924335799e-12 relative error = 3.882374455704552e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.0719999999999992 y[1] (closed_form) = 1.002521560424908 y[1] (numeric) = 1.002521560428921 absolute error = 4.012568055600241e-12 relative error = 4.002475571597238e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.07099999999999917 y[1] (closed_form) = 1.002451001890505 y[1] (numeric) = 1.002451001894636 absolute error = 4.131139874630207e-12 relative error = 4.12103919976075e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.06999999999999915 y[1] (closed_form) = 1.002381445815227 y[1] (numeric) = 1.002381445819474 absolute error = 4.247713292215849e-12 relative error = 4.237621625928268e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.06899999999999912 y[1] (closed_form) = 1.002312892129068 y[1] (numeric) = 1.002312892133431 absolute error = 4.362732397567015e-12 relative error = 4.35266515259511e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.06799999999999909 y[1] (closed_form) = 1.002245340763043 y[1] (numeric) = 1.00224534076752 absolute error = 4.476641279893556e-12 relative error = 4.466612213418063e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.06699999999999906 y[1] (closed_form) = 1.002178791649188 y[1] (numeric) = 1.002178791653776 absolute error = 4.588107671565922e-12 relative error = 4.578132873891413e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.06599999999999903 y[1] (closed_form) = 1.00211324472056 y[1] (numeric) = 1.002113244725258 absolute error = 4.698241795608737e-12 relative error = 4.688334198116347e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.064999999999999 y[1] (closed_form) = 1.002048699911234 y[1] (numeric) = 1.002048699916041 absolute error = 4.806599562812153e-12 relative error = 4.796772415590122e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.06399999999999897 y[1] (closed_form) = 1.001985157156307 y[1] (numeric) = 1.001985157161219 absolute error = 4.912958928571243e-12 relative error = 4.903225255865578e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.06299999999999895 y[1] (closed_form) = 1.001922616391891 y[1] (numeric) = 1.001922616396908 absolute error = 5.017763982095858e-12 relative error = 5.008135259153803e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.06199999999999892 y[1] (closed_form) = 1.001861077555118 y[1] (numeric) = 1.001861077560239 absolute error = 5.121014723385997e-12 relative error = 5.111501822071993e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.06099999999999889 y[1] (closed_form) = 1.001800540584139 y[1] (numeric) = 1.001800540589361 absolute error = 5.222267063231811e-12 relative error = 5.212881059324208e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.05999999999999886 y[1] (closed_form) = 1.001741005418119 y[1] (numeric) = 1.001741005423441 absolute error = 5.32196509084315e-12 relative error = 5.312715624156567e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.05899999999999883 y[1] (closed_form) = 1.001682471997241 y[1] (numeric) = 1.001682472002661 absolute error = 5.420108806220014e-12 relative error = 5.411004941928286e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.0579999999999988 y[1] (closed_form) = 1.001624940262704 y[1] (numeric) = 1.00162494026822 absolute error = 5.516476164757478e-12 relative error = 5.507526762772731e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.05699999999999877 y[1] (closed_form) = 1.001568410156719 y[1] (numeric) = 1.001568410162331 absolute error = 5.611289211060466e-12 relative error = 5.602502189723061e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.05599999999999875 y[1] (closed_form) = 1.001512881622518 y[1] (numeric) = 1.001512881628222 absolute error = 5.704325900524054e-12 relative error = 5.695708967100519e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.05499999999999872 y[1] (closed_form) = 1.001458354604341 y[1] (numeric) = 1.001458354610136 absolute error = 5.795808277753167e-12 relative error = 5.787368242629514e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.05399999999999869 y[1] (closed_form) = 1.001404829047444 y[1] (numeric) = 1.00140482905333 absolute error = 5.88551429814288e-12 relative error = 5.877257755728318e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.05299999999999866 y[1] (closed_form) = 1.001352304898098 y[1] (numeric) = 1.001352304904071 absolute error = 5.973221917088267e-12 relative error = 5.965155208481922e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.05199999999999863 y[1] (closed_form) = 1.001300782103584 y[1] (numeric) = 1.001300782109644 absolute error = 6.059597268404104e-12 relative error = 6.05172529244788e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.0509999999999986 y[1] (closed_form) = 1.001250260612197 y[1] (numeric) = 1.001250260618341 absolute error = 6.143752173670691e-12 relative error = 6.13608047394085e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.04999999999999857 y[1] (closed_form) = 1.001200740373243 y[1] (numeric) = 1.00120074037947 absolute error = 6.226574811307728e-12 relative error = 6.219107278113365e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.04899999999999854 y[1] (closed_form) = 1.00115222133704 y[1] (numeric) = 1.001152221343348 absolute error = 6.307843136710289e-12 relative error = 6.300583470000354e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.04799999999999852 y[1] (closed_form) = 1.001104703454915 y[1] (numeric) = 1.001104703461302 absolute error = 6.387557149878376e-12 relative error = 6.38050858000593e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.04699999999999849 y[1] (closed_form) = 1.001058186679207 y[1] (numeric) = 1.001058186685673 absolute error = 6.465716850811987e-12 relative error = 6.458882147760657e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.04599999999999846 y[1] (closed_form) = 1.001012670963266 y[1] (numeric) = 1.001012670969807 absolute error = 6.541212016486497e-12 relative error = 6.534594622255824e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.04499999999999843 y[1] (closed_form) = 1.000968156261449 y[1] (numeric) = 1.000968156268065 absolute error = 6.615819003741308e-12 relative error = 6.609420052333095e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.0439999999999984 y[1] (closed_form) = 1.000924642529124 y[1] (numeric) = 1.000924642535812 absolute error = 6.688649634156718e-12 relative error = 6.682470737513188e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.04299999999999837 y[1] (closed_form) = 1.000882129722667 y[1] (numeric) = 1.000882129729427 absolute error = 6.759703907732728e-12 relative error = 6.753746227446149e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.04199999999999834 y[1] (closed_form) = 1.000840617799463 y[1] (numeric) = 1.000840617806291 absolute error = 6.828759779864413e-12 relative error = 6.823024224255339e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.04099999999999832 y[1] (closed_form) = 1.000800106717903 y[1] (numeric) = 1.0008001067248 absolute error = 6.896705428971472e-12 relative error = 6.891191740165806e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.03999999999999829 y[1] (closed_form) = 1.000760596437389 y[1] (numeric) = 1.000760596444352 absolute error = 6.962874721239132e-12 relative error = 6.957582808542115e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.03899999999999826 y[1] (closed_form) = 1.000722086918328 y[1] (numeric) = 1.000722086925355 absolute error = 7.027045612062466e-12 relative error = 7.021975135676173e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.03799999999999823 y[1] (closed_form) = 1.000684578122133 y[1] (numeric) = 1.000684578129222 absolute error = 7.0894401460464e-12 relative error = 7.084590190597639e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.0369999999999982 y[1] (closed_form) = 1.000648070011225 y[1] (numeric) = 1.000648070018376 absolute error = 7.150724457005708e-12 relative error = 7.146093288248175e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.03599999999999817 y[1] (closed_form) = 1.000612562549033 y[1] (numeric) = 1.000612562556242 absolute error = 7.209788321915767e-12 relative error = 7.205374579296739e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.03499999999999814 y[1] (closed_form) = 1.000578055699987 y[1] (numeric) = 1.000578055707254 absolute error = 7.26729787459135e-12 relative error = 7.263099398584429e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.03399999999999812 y[1] (closed_form) = 1.000544549429526 y[1] (numeric) = 1.000544549436849 absolute error = 7.323031070427533e-12 relative error = 7.319045488382158e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.03299999999999809 y[1] (closed_form) = 1.000512043704094 y[1] (numeric) = 1.000512043711472 absolute error = 7.37720995402924e-12 relative error = 7.37343443335009e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.03199999999999806 y[1] (closed_form) = 1.00048053849114 y[1] (numeric) = 1.00048053849857 absolute error = 7.430278614606323e-12 relative error = 7.426709794687448e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.03099999999999804 y[1] (closed_form) = 1.000450033759116 y[1] (numeric) = 1.000450033766597 absolute error = 7.48134887373908e-12 relative error = 7.477983528701051e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.02999999999999805 y[1] (closed_form) = 1.00042052947748 y[1] (numeric) = 1.00042052948501 absolute error = 7.530420731427512e-12 relative error = 7.527255298689897e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.02899999999999805 y[1] (closed_form) = 1.000392025616692 y[1] (numeric) = 1.00039202562427 absolute error = 7.578160321486394e-12 relative error = 7.575190652699208e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.02799999999999806 y[1] (closed_form) = 1.000364522148219 y[1] (numeric) = 1.000364522155843 absolute error = 7.62390151010095e-12 relative error = 7.621123441812096e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.02699999999999806 y[1] (closed_form) = 1.000338019044529 y[1] (numeric) = 1.000338019052197 absolute error = 7.668088386481031e-12 relative error = 7.66549730240703e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.02599999999999807 y[1] (closed_form) = 1.000312516279094 y[1] (numeric) = 1.000312516286805 absolute error = 7.710720950626637e-12 relative error = 7.708311977649285e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.02499999999999808 y[1] (closed_form) = 1.000288013826389 y[1] (numeric) = 1.000288013834141 absolute error = 7.752021247142693e-12 relative error = 7.749789200701289e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.02399999999999808 y[1] (closed_form) = 1.000264511661892 y[1] (numeric) = 1.000264511669684 absolute error = 7.791101097609499e-12 relative error = 7.789040805481493e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.02299999999999809 y[1] (closed_form) = 1.000242009762084 y[1] (numeric) = 1.000242009769913 absolute error = 7.828626635841829e-12 relative error = 7.826732490173986e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.02199999999999809 y[1] (closed_form) = 1.000220508104447 y[1] (numeric) = 1.000220508112311 absolute error = 7.864153772629834e-12 relative error = 7.862420045289279e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.0209999999999981 y[1] (closed_form) = 1.000200006667467 y[1] (numeric) = 1.000200006675365 absolute error = 7.898348641788289e-12 relative error = 7.896769235289785e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.01999999999999811 y[1] (closed_form) = 1.00018050543063 y[1] (numeric) = 1.00018050543856 absolute error = 7.930545109502418e-12 relative error = 7.929113861390354e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.01899999999999811 y[1] (closed_form) = 1.000162004374425 y[1] (numeric) = 1.000162004382387 absolute error = 7.961631354191923e-12 relative error = 7.960341744007473e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.01799999999999812 y[1] (closed_form) = 1.000144503480343 y[1] (numeric) = 1.000144503488334 absolute error = 7.990719197437102e-12 relative error = 7.98956467753477e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.01699999999999812 y[1] (closed_form) = 1.000128002730876 y[1] (numeric) = 1.000128002738895 absolute error = 8.018252728447806e-12 relative error = 8.017226501561552e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.01599999999999813 y[1] (closed_form) = 1.000112502109517 y[1] (numeric) = 1.000112502117562 absolute error = 8.044231947224034e-12 relative error = 8.043327055962699e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.01499999999999814 y[1] (closed_form) = 1.000098001600761 y[1] (numeric) = 1.000098001608829 absolute error = 8.068656853765788e-12 relative error = 8.067866189964447e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.01399999999999814 y[1] (closed_form) = 1.000084501190102 y[1] (numeric) = 1.000084501198194 absolute error = 8.091527448073066e-12 relative error = 8.090843762146234e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.01299999999999815 y[1] (closed_form) = 1.000072000864037 y[1] (numeric) = 1.00007200087215 absolute error = 8.112177596331094e-12 relative error = 8.111593554586444e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.01199999999999815 y[1] (closed_form) = 1.000060500610064 y[1] (numeric) = 1.000060500618195 absolute error = 8.131495476959572e-12 relative error = 8.131003546284591e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.01099999999999816 y[1] (closed_form) = 1.000050000416679 y[1] (numeric) = 1.000050000424828 absolute error = 8.149037000748649e-12 relative error = 8.14862956587499e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.009999999999998167 y[1] (closed_form) = 1.000040500273382 y[1] (numeric) = 1.000040500281547 absolute error = 8.165024212303251e-12 relative error = 8.164693539982804e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.008999999999998173 y[1] (closed_form) = 1.00003200017067 y[1] (numeric) = 1.000032000178849 absolute error = 8.179457111623378e-12 relative error = 8.179195375975404e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.007999999999998179 y[1] (closed_form) = 1.000024500100043 y[1] (numeric) = 1.000024500108235 absolute error = 8.19189160949918e-12 relative error = 8.191690912252307e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.006999999999998177 y[1] (closed_form) = 1.000018000054001 y[1] (numeric) = 1.000018000062204 absolute error = 8.202993839745432e-12 relative error = 8.202846188071088e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.005999999999998174 y[1] (closed_form) = 1.000012500026042 y[1] (numeric) = 1.000012500034254 absolute error = 8.212319713152283e-12 relative error = 8.21221706022517e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.004999999999998172 y[1] (closed_form) = 1.000008000010667 y[1] (numeric) = 1.000008000018886 absolute error = 8.219869229719734e-12 relative error = 8.219803471204287e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.003999999999998169 y[1] (closed_form) = 1.000004500003375 y[1] (numeric) = 1.0000045000116 absolute error = 8.22542034484286e-12 relative error = 8.225383330590111e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.002999999999998171 y[1] (closed_form) = 1.000002000000667 y[1] (numeric) = 1.000002000008896 absolute error = 8.229639192336435e-12 relative error = 8.229622733085483e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.001999999999998173 y[1] (closed_form) = 1.000000500000042 y[1] (numeric) = 1.000000500008274 absolute error = 8.232081682990611e-12 relative error = 8.232077566951485e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = -0.0009999999999981721 y[1] (closed_form) = 1 y[1] (numeric) = 1.000000000008233 absolute error = 8.232747816805386e-12 relative error = 8.232747816805386e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 1.828154598190745e-15 y[1] (closed_form) = 1.000000500000042 y[1] (numeric) = 1.000000500008274 absolute error = 8.232081682990611e-12 relative error = 8.232077566951485e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.001000000000001828 y[1] (closed_form) = 1.000002000000667 y[1] (numeric) = 1.000002000008896 absolute error = 8.229639192336435e-12 relative error = 8.229622733085483e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.002000000000001829 y[1] (closed_form) = 1.000004500003375 y[1] (numeric) = 1.0000045000116 absolute error = 8.22542034484286e-12 relative error = 8.225383330590111e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.003000000000001827 y[1] (closed_form) = 1.000008000010667 y[1] (numeric) = 1.000008000018886 absolute error = 8.219869229719734e-12 relative error = 8.219803471204287e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.004000000000001826 y[1] (closed_form) = 1.000012500026042 y[1] (numeric) = 1.000012500034254 absolute error = 8.212319713152283e-12 relative error = 8.21221706022517e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.005000000000001829 y[1] (closed_form) = 1.000018000054001 y[1] (numeric) = 1.000018000062204 absolute error = 8.202993839745432e-12 relative error = 8.202846188071088e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.006000000000001831 y[1] (closed_form) = 1.000024500100043 y[1] (numeric) = 1.000024500108235 absolute error = 8.192113654104105e-12 relative error = 8.19191295141725e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.007000000000001834 y[1] (closed_form) = 1.00003200017067 y[1] (numeric) = 1.00003200017885 absolute error = 8.179679156228303e-12 relative error = 8.179417413475091e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.008000000000001836 y[1] (closed_form) = 1.000040500273382 y[1] (numeric) = 1.000040500281547 absolute error = 8.165246256908176e-12 relative error = 8.164915575595227e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.009000000000001829 y[1] (closed_form) = 1.000050000416679 y[1] (numeric) = 1.000050000424829 absolute error = 8.149703134563424e-12 relative error = 8.149295666384463e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.01000000000000182 y[1] (closed_form) = 1.000060500610064 y[1] (numeric) = 1.000060500618196 absolute error = 8.132383655379272e-12 relative error = 8.131891670972206e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.01100000000000182 y[1] (closed_form) = 1.000072000864037 y[1] (numeric) = 1.00007200087215 absolute error = 8.113065774750794e-12 relative error = 8.112481669061134e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.01200000000000181 y[1] (closed_form) = 1.000084501190102 y[1] (numeric) = 1.000084501198195 absolute error = 8.092637671097691e-12 relative error = 8.09195389136362e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.01300000000000181 y[1] (closed_form) = 1.000098001600761 y[1] (numeric) = 1.000098001608831 absolute error = 8.069767076790413e-12 relative error = 8.068976304196101e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.0140000000000018 y[1] (closed_form) = 1.000112502109517 y[1] (numeric) = 1.000112502117563 absolute error = 8.045342170248659e-12 relative error = 8.044437154098943e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.01500000000000179 y[1] (closed_form) = 1.000128002730876 y[1] (numeric) = 1.000128002738896 absolute error = 8.019362951472431e-12 relative error = 8.018336582492786e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.01600000000000179 y[1] (closed_form) = 1.000144503480344 y[1] (numeric) = 1.000144503488335 absolute error = 7.991607375856802e-12 relative error = 7.990452727628139e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.01700000000000178 y[1] (closed_form) = 1.000162004374425 y[1] (numeric) = 1.000162004382388 absolute error = 7.962741577216548e-12 relative error = 7.961451787200246e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.01800000000000177 y[1] (closed_form) = 1.00018050543063 y[1] (numeric) = 1.000180505438562 absolute error = 7.931655332527043e-12 relative error = 7.930223884049862e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.01900000000000177 y[1] (closed_form) = 1.000200006667467 y[1] (numeric) = 1.000200006675366 absolute error = 7.899458864812914e-12 relative error = 7.897879236306803e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.02000000000000176 y[1] (closed_form) = 1.000220508104447 y[1] (numeric) = 1.000220508112313 absolute error = 7.865486040259384e-12 relative error = 7.863752019207785e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.02100000000000176 y[1] (closed_form) = 1.000242009762084 y[1] (numeric) = 1.000242009769914 absolute error = 7.829736858866454e-12 relative error = 7.827842444578808e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.02200000000000175 y[1] (closed_form) = 1.000264511661892 y[1] (numeric) = 1.000264511669685 absolute error = 7.792655409843974e-12 relative error = 7.790594706690976e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.02300000000000174 y[1] (closed_form) = 1.000288013826389 y[1] (numeric) = 1.000288013834143 absolute error = 7.753353514772243e-12 relative error = 7.751121084729822e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.02400000000000174 y[1] (closed_form) = 1.000312516279094 y[1] (numeric) = 1.000312516286807 absolute error = 7.712497307466037e-12 relative error = 7.710087779521692e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.02500000000000173 y[1] (closed_form) = 1.000338019044529 y[1] (numeric) = 1.000338019052199 absolute error = 7.669864743320431e-12 relative error = 7.667273059006879e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.02600000000000173 y[1] (closed_form) = 1.000364522148219 y[1] (numeric) = 1.000364522155845 absolute error = 7.625899911545275e-12 relative error = 7.623121115060277e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.02700000000000172 y[1] (closed_form) = 1.000392025616692 y[1] (numeric) = 1.000392025624272 absolute error = 7.579936678325794e-12 relative error = 7.576966313434112e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.02800000000000171 y[1] (closed_form) = 1.00042052947748 y[1] (numeric) = 1.000420529485012 absolute error = 7.532641177476762e-12 relative error = 7.52947481136864e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.02900000000000171 y[1] (closed_form) = 1.000450033759116 y[1] (numeric) = 1.0004500337666 absolute error = 7.483347275183405e-12 relative error = 7.479981031201815e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.0300000000000017 y[1] (closed_form) = 1.00048053849114 y[1] (numeric) = 1.000480538498573 absolute error = 7.432721105260498e-12 relative error = 7.429151112194592e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.0310000000000017 y[1] (closed_form) = 1.000512043704095 y[1] (numeric) = 1.000512043711474 absolute error = 7.379652444683416e-12 relative error = 7.375875673982368e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.03200000000000171 y[1] (closed_form) = 1.000544549429526 y[1] (numeric) = 1.000544549436852 absolute error = 7.325473561081708e-12 relative error = 7.321486649703327e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.03300000000000174 y[1] (closed_form) = 1.000578055699987 y[1] (numeric) = 1.000578055707257 absolute error = 7.26996240985045e-12 relative error = 7.265762394483569e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.03400000000000177 y[1] (closed_form) = 1.000612562549033 y[1] (numeric) = 1.000612562556245 absolute error = 7.212674901779792e-12 relative error = 7.208259392032521e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.0350000000000018 y[1] (closed_form) = 1.000648070011226 y[1] (numeric) = 1.000648070018379 absolute error = 7.153388992264809e-12 relative error = 7.148756097820245e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.03600000000000183 y[1] (closed_form) = 1.000684578122133 y[1] (numeric) = 1.000684578129225 absolute error = 7.092326725910425e-12 relative error = 7.087474795724104e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.03700000000000186 y[1] (closed_form) = 1.000722086918328 y[1] (numeric) = 1.000722086925357 absolute error = 7.029710147321566e-12 relative error = 7.024637748297529e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.03800000000000189 y[1] (closed_form) = 1.000760596437389 y[1] (numeric) = 1.000760596444355 absolute error = 6.965539256498232e-12 relative error = 6.960245318705469e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.03900000000000192 y[1] (closed_form) = 1.000800106717903 y[1] (numeric) = 1.000800106724803 absolute error = 6.899814053440423e-12 relative error = 6.894297879391895e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.04000000000000194 y[1] (closed_form) = 1.000840617799463 y[1] (numeric) = 1.000840617806295 absolute error = 6.832090448938288e-12 relative error = 6.826352095861109e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.04100000000000197 y[1] (closed_form) = 1.000882129722667 y[1] (numeric) = 1.00088212972943 absolute error = 6.762812532201679e-12 relative error = 6.756852112121909e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.042000000000002 y[1] (closed_form) = 1.000924642529124 y[1] (numeric) = 1.000924642535816 absolute error = 6.691758258625669e-12 relative error = 6.685576490271052e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.04300000000000203 y[1] (closed_form) = 1.000968156261449 y[1] (numeric) = 1.000968156268069 absolute error = 6.619371717420108e-12 relative error = 6.612969329756733e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.04400000000000206 y[1] (closed_form) = 1.001012670963266 y[1] (numeric) = 1.001012670969811 absolute error = 6.544986774770223e-12 relative error = 6.53836556181855e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.04500000000000209 y[1] (closed_form) = 1.001058186679207 y[1] (numeric) = 1.001058186685677 absolute error = 6.469269564490787e-12 relative error = 6.462431105979144e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.04600000000000212 y[1] (closed_form) = 1.001104703454915 y[1] (numeric) = 1.001104703461307 absolute error = 6.391553952767026e-12 relative error = 6.384500972484814e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.04700000000000214 y[1] (closed_form) = 1.00115222133704 y[1] (numeric) = 1.001152221343352 absolute error = 6.31183993959894e-12 relative error = 6.30457567298754e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.04800000000000217 y[1] (closed_form) = 1.001200740373243 y[1] (numeric) = 1.001200740379474 absolute error = 6.230793658801304e-12 relative error = 6.22332106594177e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.0490000000000022 y[1] (closed_form) = 1.001250260612198 y[1] (numeric) = 1.001250260618345 absolute error = 6.147748976559342e-12 relative error = 6.14007228602408e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.05000000000000223 y[1] (closed_form) = 1.001300782103584 y[1] (numeric) = 1.001300782109648 absolute error = 6.063594071292755e-12 relative error = 6.055716903120801e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.05100000000000226 y[1] (closed_form) = 1.001352304898098 y[1] (numeric) = 1.001352304904076 absolute error = 5.977440764581843e-12 relative error = 5.969368358512075e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.05200000000000229 y[1] (closed_form) = 1.001404829047444 y[1] (numeric) = 1.001404829053334 absolute error = 5.88951110103153e-12 relative error = 5.881248951668975e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.05300000000000232 y[1] (closed_form) = 1.001458354604341 y[1] (numeric) = 1.001458354610141 absolute error = 5.800249169851668e-12 relative error = 5.791802667763703e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.05400000000000234 y[1] (closed_form) = 1.001512881622518 y[1] (numeric) = 1.001512881628227 absolute error = 5.708766792622555e-12 relative error = 5.700143150803983e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.05500000000000237 y[1] (closed_form) = 1.00156841015672 y[1] (numeric) = 1.001568410162335 absolute error = 5.615730103158967e-12 relative error = 5.606936127588378e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.0560000000000024 y[1] (closed_form) = 1.001624940262704 y[1] (numeric) = 1.001624940268225 absolute error = 5.521139101460903e-12 relative error = 5.512182134774752e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.05700000000000243 y[1] (closed_form) = 1.001682471997241 y[1] (numeric) = 1.001682472002666 absolute error = 5.424549698318515e-12 relative error = 5.415438374899959e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.05800000000000246 y[1] (closed_form) = 1.00174100541812 y[1] (numeric) = 1.001741005423446 absolute error = 5.326405982941651e-12 relative error = 5.317148798075255e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.05900000000000249 y[1] (closed_form) = 1.001800540584139 y[1] (numeric) = 1.001800540589366 absolute error = 5.226707955330312e-12 relative error = 5.217313969787513e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.06000000000000252 y[1] (closed_form) = 1.001861077555118 y[1] (numeric) = 1.001861077560244 absolute error = 5.125677660089423e-12 relative error = 5.116156096809169e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.06100000000000255 y[1] (closed_form) = 1.001922616391891 y[1] (numeric) = 1.001922616396913 absolute error = 5.022426918799283e-12 relative error = 5.012789248021943e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.06200000000000257 y[1] (closed_form) = 1.001985157156307 y[1] (numeric) = 1.001985157161224 absolute error = 4.917621865274668e-12 relative error = 4.907878954246359e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.0630000000000026 y[1] (closed_form) = 1.002048699911235 y[1] (numeric) = 1.002048699916046 absolute error = 4.811484544120503e-12 relative error = 4.801647409498884e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.06400000000000262 y[1] (closed_form) = 1.00211324472056 y[1] (numeric) = 1.002113244725263 absolute error = 4.703126776917088e-12 relative error = 4.693208878033098e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.06500000000000265 y[1] (closed_form) = 1.002178791649188 y[1] (numeric) = 1.002178791653782 absolute error = 4.593214697479198e-12 relative error = 4.5832287968503e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.06600000000000268 y[1] (closed_form) = 1.002245340763043 y[1] (numeric) = 1.002245340767525 absolute error = 4.481748305806832e-12 relative error = 4.471707798007548e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.06700000000000271 y[1] (closed_form) = 1.002312892129068 y[1] (numeric) = 1.002312892133436 absolute error = 4.368283512690141e-12 relative error = 4.35820345821476e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.06800000000000274 y[1] (closed_form) = 1.002381445815227 y[1] (numeric) = 1.00238144581948 absolute error = 4.25304236273405e-12 relative error = 4.242938035704654e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.06900000000000277 y[1] (closed_form) = 1.002451001890505 y[1] (numeric) = 1.002451001894641 absolute error = 4.136468945148408e-12 relative error = 4.126355240652674e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.0700000000000028 y[1] (closed_form) = 1.002521560424909 y[1] (numeric) = 1.002521560428927 absolute error = 4.017897126118442e-12 relative error = 4.007791238340545e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.07100000000000282 y[1] (closed_form) = 1.002593121489468 y[1] (numeric) = 1.002593121493366 absolute error = 3.898437128668775e-12 relative error = 3.888354153953497e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.07200000000000285 y[1] (closed_form) = 1.002665685156233 y[1] (numeric) = 1.00266568516001 absolute error = 3.776756685169858e-12 relative error = 3.766715806756039e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.07300000000000288 y[1] (closed_form) = 1.002739251498281 y[1] (numeric) = 1.002739251501934 absolute error = 3.65374397404139e-12 relative error = 3.64376279135579e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.07400000000000291 y[1] (closed_form) = 1.002813820589711 y[1] (numeric) = 1.002813820593239 absolute error = 3.528732861468598e-12 relative error = 3.518831500939532e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.07500000000000294 y[1] (closed_form) = 1.002889392505647 y[1] (numeric) = 1.002889392509049 absolute error = 3.40172334745148e-12 relative error = 3.391922751274215e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.07600000000000297 y[1] (closed_form) = 1.00296596732224 y[1] (numeric) = 1.002965967325513 absolute error = 3.272937476594961e-12 relative error = 3.263258757755446e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.077000000000003 y[1] (closed_form) = 1.003043545116666 y[1] (numeric) = 1.003043545119809 absolute error = 3.142819338108893e-12 relative error = 3.133283049783591e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.07800000000000303 y[1] (closed_form) = 1.00312212596713 y[1] (numeric) = 1.003122125970141 absolute error = 3.0107027981785e-12 relative error = 3.001332260791099e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.07900000000000305 y[1] (closed_form) = 1.003201709952862 y[1] (numeric) = 1.003201709955739 absolute error = 2.876809901408706e-12 relative error = 2.867628586422445e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.08000000000000308 y[1] (closed_form) = 1.003282297154122 y[1] (numeric) = 1.003282297156863 absolute error = 2.741362692404437e-12 relative error = 2.732394162819873e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.08100000000000311 y[1] (closed_form) = 1.003363887652199 y[1] (numeric) = 1.003363887654804 absolute error = 2.604361171165692e-12 relative error = 2.595629764252044e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.08200000000000314 y[1] (closed_form) = 1.003446481529413 y[1] (numeric) = 1.003446481531878 absolute error = 2.465583293087548e-12 relative error = 2.457114891996637e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.08300000000000317 y[1] (closed_form) = 1.003530078869111 y[1] (numeric) = 1.003530078871436 absolute error = 2.325029058170003e-12 relative error = 2.31685039355283e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.0840000000000032 y[1] (closed_form) = 1.003614679755677 y[1] (numeric) = 1.00361467975786 absolute error = 2.182920511017983e-12 relative error = 2.175058371554908e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.08500000000000323 y[1] (closed_form) = 1.003700284274522 y[1] (numeric) = 1.003700284276561 absolute error = 2.038813562421637e-12 relative error = 2.031297185389658e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.08600000000000325 y[1] (closed_form) = 1.003786892512094 y[1] (numeric) = 1.003786892513987 absolute error = 1.892486167776042e-12 relative error = 1.885346562993938e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.08700000000000328 y[1] (closed_form) = 1.003874504555872 y[1] (numeric) = 1.003874504557617 absolute error = 1.745048550105821e-12 relative error = 1.738313446736906e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.08800000000000331 y[1] (closed_form) = 1.003963120494371 y[1] (numeric) = 1.003963120495967 absolute error = 1.5958345755962e-12 relative error = 1.589535056636722e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.08900000000000334 y[1] (closed_form) = 1.004052740417141 y[1] (numeric) = 1.004052740418585 absolute error = 1.444400155037329e-12 relative error = 1.438570004238266e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.09000000000000337 y[1] (closed_form) = 1.004143364414768 y[1] (numeric) = 1.00414336441606 absolute error = 1.292299600663682e-12 relative error = 1.286967226454617e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.0910000000000034 y[1] (closed_form) = 1.004234992578877 y[1] (numeric) = 1.004234992580014 absolute error = 1.137534511030935e-12 relative error = 1.132737376647019e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.09200000000000343 y[1] (closed_form) = 1.004327625002127 y[1] (numeric) = 1.004327625003109 absolute error = 9.816591983735634e-13 relative error = 9.774292511086552e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.09300000000000345 y[1] (closed_form) = 1.00442126177822 y[1] (numeric) = 1.004421261779044 absolute error = 8.235634396669411e-13 relative error = 8.199382778983695e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.09400000000000348 y[1] (closed_form) = 1.004515903001895 y[1] (numeric) = 1.004515903002559 absolute error = 6.641354133307686e-13 relative error = 6.611497253015773e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.09500000000000351 y[1] (closed_form) = 1.004611548768932 y[1] (numeric) = 1.004611548769435 absolute error = 5.027089855502709e-13 relative error = 5.004013602733305e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.09600000000000354 y[1] (closed_form) = 1.004708199176153 y[1] (numeric) = 1.004708199176493 absolute error = 3.397282455352979e-13 relative error = 3.381362328025893e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.09700000000000357 y[1] (closed_form) = 1.004805854321422 y[1] (numeric) = 1.004805854321597 absolute error = 1.749711486809247e-13 relative error = 1.741342846764048e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.0980000000000036 y[1] (closed_form) = 1.004904514303646 y[1] (numeric) = 1.004904514303655 absolute error = 8.43769498715119e-15 relative error = 8.396514163336339e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001 TOP MAIN SOLVE Loop x[1] = 0.09900000000000363 y[1] (closed_form) = 1.005004179222776 y[1] (numeric) = 1.005004179222616 absolute error = 1.600941601509476e-13 relative error = 1.592970093664257e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.0001 Finished! diff ( y , x , 1 ) = arcsin ( x + 0.001 ) ; Iterations = 2000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 6 Minutes 0.0 Seconds Percent Done = 100.1 %