##############ECHO OF PROBLEM################# ##############temp/mult2postode.ode################# diff ( y , x , 1 ) = sin ( x ) * cos ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.1); x_end=c(1.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=c(0.00000000001); 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) - expt(cos(c(x)),c(2))/c(2.0)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 1.504983355539689 y[1] (numeric) = 1.504983355539689 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) = 1.506025637667349 y[1] (numeric) = 1.506025637667348 absolute error = 2.220446049250313e-16 relative error = 1.474374667810778e-14 % 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) = 1.507165506286993 y[1] (numeric) = 1.507165506286992 absolute error = 6.661338147750939e-16 relative error = 4.419778796664217e-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) = 1.508402505466372 y[1] (numeric) = 1.508402505466371 absolute error = 6.661338147750939e-16 relative error = 4.416154258303469e-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) = 1.509736140422307 y[1] (numeric) = 1.509736140422306 absolute error = 8.881784197001252e-16 relative error = 5.883004294059501e-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) = 1.511165877718599 y[1] (numeric) = 1.511165877718598 absolute error = 6.661338147750939e-16 relative error = 4.408078719860679e-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) = 1.51269114547939 y[1] (numeric) = 1.512691145479389 absolute error = 4.440892098500626e-16 relative error = 2.935755994719764e-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) = 1.514311333617913 y[1] (numeric) = 1.514311333617913 absolute error = 4.440892098500626e-16 relative error = 2.932614978117267e-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) = 1.516025794080516 y[1] (numeric) = 1.516025794080516 absolute error = 2.220446049250313e-16 relative error = 1.464649254597303e-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) = 1.517833841105872 y[1] (numeric) = 1.517833841105872 absolute error = 4.440892098500626e-16 relative error = 2.925809122337827e-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) = 1.519734751499279 y[1] (numeric) = 1.519734751499278 absolute error = 4.440892098500626e-16 relative error = 2.922149469912108e-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) = 1.521727764921923 y[1] (numeric) = 1.521727764921922 absolute error = 6.661338147750939e-16 relative error = 4.37748347720574e-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) = 1.523812084195009 y[1] (numeric) = 1.523812084195008 absolute error = 8.881784197001252e-16 relative error = 5.828661085656944e-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) = 1.525986875618619 y[1] (numeric) = 1.525986875618618 absolute error = 6.661338147750939e-16 relative error = 4.365265687524674e-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) = 1.528251269305179 y[1] (numeric) = 1.528251269305178 absolute error = 6.661338147750939e-16 relative error = 4.358797719683572e-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) = 1.530604359527407 y[1] (numeric) = 1.530604359527406 absolute error = 6.661338147750939e-16 relative error = 4.352096677555336e-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) = 1.533045205080588 y[1] (numeric) = 1.533045205080587 absolute error = 8.881784197001252e-16 relative error = 5.79355662022658e-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) = 1.535572829659044 y[1] (numeric) = 1.535572829659043 absolute error = 6.661338147750939e-16 relative error = 4.338015116632411e-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) = 1.538186222246646 y[1] (numeric) = 1.538186222246646 absolute error = 4.440892098500626e-16 relative error = 2.887096525942315e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = 1.540884337521203 y[1] (numeric) = 1.540884337521203 absolute error = 4.440892098500626e-16 relative error = 2.882041169712076e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 1.543666096272581 y[1] (numeric) = 1.54366609627258 absolute error = 6.661338147750939e-16 relative error = 4.315271394400489e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 1.546530385834366 y[1] (numeric) = 1.546530385834366 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] = 0.3200000000000002 y[1] (closed_form) = 1.549476060528927 y[1] (numeric) = 1.549476060528927 absolute error = 2.220446049250313e-16 relative error = 1.433030238939184e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 1.552501942125659 y[1] (numeric) = 1.552501942125659 absolute error = 2.220446049250313e-16 relative error = 1.430237211948422e-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) = 1.555606820312268 y[1] (numeric) = 1.555606820312268 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] = 0.3500000000000002 y[1] (closed_form) = 1.558789453178878 y[1] (numeric) = 1.558789453178878 absolute error = 2.220446049250313e-16 relative error = 1.424468227394086e-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) = 1.562048567714776 y[1] (numeric) = 1.562048567714776 absolute error = 4.440892098500626e-16 relative error = 2.842992330896279e-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) = 1.565382860317603 y[1] (numeric) = 1.565382860317603 absolute error = 2.220446049250313e-16 relative error = 1.418468353997311e-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) = 1.568790997314774 y[1] (numeric) = 1.568790997314774 absolute error = 2.220446049250313e-16 relative error = 1.415386787055093e-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) = 1.572271615496931 y[1] (numeric) = 1.572271615496931 absolute error = 2.220446049250313e-16 relative error = 1.412253472850822e-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) = 1.575823322663209 y[1] (numeric) = 1.575823322663209 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] = 0.4100000000000003 y[1] (closed_form) = 1.579444698178097 y[1] (numeric) = 1.579444698178097 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] = 0.4200000000000003 y[1] (closed_form) = 1.583134293539673 y[1] (numeric) = 1.583134293539673 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] = 0.4300000000000003 y[1] (closed_form) = 1.586890632958987 y[1] (numeric) = 1.586890632958987 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] = 0.4400000000000003 y[1] (closed_form) = 1.590712213950355 y[1] (numeric) = 1.590712213950355 absolute error = 2.220446049250313e-16 relative error = 1.395881687320477e-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) = 1.594597507932334 y[1] (numeric) = 1.594597507932334 absolute error = 2.220446049250313e-16 relative error = 1.392480571557833e-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) = 1.598544960839134 y[1] (numeric) = 1.598544960839134 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] = 0.4700000000000003 y[1] (closed_form) = 1.602552993742226 y[1] (numeric) = 1.602552993742226 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] = 0.4800000000000003 y[1] (closed_form) = 1.606620003481886 y[1] (numeric) = 1.606620003481886 absolute error = 2.220446049250313e-16 relative error = 1.382060502444969e-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) = 1.610744363308446 y[1] (numeric) = 1.610744363308446 absolute error = 4.440892098500626e-16 relative error = 2.757043389168904e-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) = 1.614924423532965 y[1] (numeric) = 1.614924423532965 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] = 0.5100000000000003 y[1] (closed_form) = 1.619158512187088 y[1] (numeric) = 1.619158512187088 absolute error = 2.220446049250313e-16 relative error = 1.371358043414189e-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) = 1.623444935691805 y[1] (numeric) = 1.623444935691805 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] = 0.5300000000000004 y[1] (closed_form) = 1.627781979534868 y[1] (numeric) = 1.627781979534868 absolute error = 2.220446049250313e-16 relative error = 1.364093027915689e-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) = 1.632167908956565 y[1] (numeric) = 1.632167908956565 absolute error = 2.220446049250313e-16 relative error = 1.360427464028398e-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) = 1.636600969643606 y[1] (numeric) = 1.636600969643606 absolute error = 2.220446049250313e-16 relative error = 1.356742474455364e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (closed_form) = 1.641079388430822 y[1] (numeric) = 1.641079388430822 absolute error = 2.220446049250313e-16 relative error = 1.353039996056177e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (closed_form) = 1.645601374010411 y[1] (numeric) = 1.64560137401041 absolute error = 4.440892098500626e-16 relative error = 2.698643893130665e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (closed_form) = 1.650165117648432 y[1] (numeric) = 1.650165117648432 absolute error = 2.220446049250313e-16 relative error = 1.345590223367805e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (closed_form) = 1.65476879390828 y[1] (numeric) = 1.654768793908279 absolute error = 6.661338147750939e-16 relative error = 4.025540107036949e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (closed_form) = 1.659410561380832 y[1] (numeric) = 1.659410561380831 absolute error = 4.440892098500626e-16 relative error = 2.676186473590516e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (closed_form) = 1.664088563420989 y[1] (numeric) = 1.664088563420988 absolute error = 4.440892098500626e-16 relative error = 2.668663312829432e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (closed_form) = 1.668800928890306 y[1] (numeric) = 1.668800928890306 absolute error = 2.220446049250313e-16 relative error = 1.330563766360576e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (closed_form) = 1.673545772905428 y[1] (numeric) = 1.673545772905427 absolute error = 4.440892098500626e-16 relative error = 2.653582692746332e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (closed_form) = 1.678321197592011 y[1] (numeric) = 1.678321197592011 absolute error = 6.661338147750939e-16 relative error = 3.969048449908374e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (closed_form) = 1.683125292843853 y[1] (numeric) = 1.683125292843853 absolute error = 6.661338147750939e-16 relative error = 3.957719711107047e-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) = 1.687956137086907 y[1] (numeric) = 1.687956137086906 absolute error = 8.881784197001252e-16 relative error = 5.261857225940439e-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) = 1.692811798047885 y[1] (numeric) = 1.692811798047885 absolute error = 8.881784197001252e-16 relative error = 5.246764115918578e-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) = 1.697690333527145 y[1] (numeric) = 1.697690333527144 absolute error = 8.881784197001252e-16 relative error = 5.231686852188368e-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) = 1.702589792175542 y[1] (numeric) = 1.702589792175541 absolute error = 1.110223024625157e-15 relative error = 6.520789856296105e-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) = 1.70750821427494 y[1] (numeric) = 1.707508214274939 absolute error = 1.110223024625157e-15 relative error = 6.502006932344926e-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) = 1.712443632522079 y[1] (numeric) = 1.712443632522078 absolute error = 8.881784197001252e-16 relative error = 5.186614045754139e-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) = 1.717394072815464 y[1] (numeric) = 1.717394072815463 absolute error = 1.110223024625157e-15 relative error = 6.464579342614578e-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) = 1.722357555044983 y[1] (numeric) = 1.722357555044982 absolute error = 1.110223024625157e-15 relative error = 6.445949747038214e-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) = 1.727332093883923 y[1] (numeric) = 1.727332093883922 absolute error = 1.110223024625157e-15 relative error = 6.427386074491382e-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) = 1.732315699583075 y[1] (numeric) = 1.732315699583074 absolute error = 1.110223024625157e-15 relative error = 6.40889547380053e-14 % 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) = 1.737306378766605 y[1] (numeric) = 1.737306378766604 absolute error = 1.110223024625157e-15 relative error = 6.390484938030076e-14 % 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) = 1.742302135229384 y[1] (numeric) = 1.742302135229382 absolute error = 1.332267629550188e-15 relative error = 7.64659356498342e-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) = 1.747300970735433 y[1] (numeric) = 1.747300970735432 absolute error = 1.110223024625157e-15 relative error = 6.353931252941885e-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) = 1.752300885817202 y[1] (numeric) = 1.752300885817201 absolute error = 1.110223024625157e-15 relative error = 6.33580130907366e-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) = 1.757299880575323 y[1] (numeric) = 1.757299880575321 absolute error = 1.110223024625157e-15 relative error = 6.317777841432962e-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) = 1.762295955478543 y[1] (numeric) = 1.762295955478542 absolute error = 8.881784197001252e-16 relative error = 5.039893650887627e-14 % 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) = 1.767287112163516 y[1] (numeric) = 1.767287112163515 absolute error = 8.881784197001252e-16 relative error = 5.025660027661356e-14 % 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) = 1.772271354234115 y[1] (numeric) = 1.772271354234114 absolute error = 6.661338147750939e-16 relative error = 3.75864459572537e-14 % 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) = 1.777246688059968 y[1] (numeric) = 1.777246688059968 absolute error = 4.440892098500626e-16 relative error = 2.498748276384905e-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) = 1.782211123573882 y[1] (numeric) = 1.782211123573881 absolute error = 6.661338147750939e-16 relative error = 3.737681837824526e-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) = 1.787162675067841 y[1] (numeric) = 1.787162675067841 absolute error = 6.661338147750939e-16 relative error = 3.727326135824805e-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) = 1.79209936198727 y[1] (numeric) = 1.792099361987269 absolute error = 6.661338147750939e-16 relative error = 3.717058489638734e-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) = 1.79701920972322 y[1] (numeric) = 1.79701920972322 absolute error = 4.440892098500626e-16 relative error = 2.471254661314733e-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) = 1.801920250402196 y[1] (numeric) = 1.801920250402196 absolute error = 6.661338147750939e-16 relative error = 3.696799648188703e-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) = 1.806800523673272 y[1] (numeric) = 1.806800523673272 absolute error = 4.440892098500626e-16 relative error = 2.457876251592056e-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) = 1.811658077492209 y[1] (numeric) = 1.811658077492208 absolute error = 6.661338147750939e-16 relative error = 3.676929013543168e-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) = 1.816490968902245 y[1] (numeric) = 1.816490968902245 absolute error = 8.881784197001252e-16 relative error = 4.889528408923912e-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) = 1.821297264811256 y[1] (numeric) = 1.821297264811255 absolute error = 8.881784197001252e-16 relative error = 4.87662523224713e-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) = 1.826075042764959 y[1] (numeric) = 1.826075042764958 absolute error = 6.661338147750939e-16 relative error = 3.647899451965922e-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) = 1.830822391715876 y[1] (numeric) = 1.830822391715875 absolute error = 8.881784197001252e-16 relative error = 4.851253861209935e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (closed_form) = 1.835537412787725 y[1] (numeric) = 1.835537412787724 absolute error = 1.110223024625157e-15 relative error = 6.048490305294316e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (closed_form) = 1.840218220034942 y[1] (numeric) = 1.840218220034941 absolute error = 1.110223024625157e-15 relative error = 6.033105272721816e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = 1.844862941197039 y[1] (numeric) = 1.844862941197038 absolute error = 1.110223024625157e-15 relative error = 6.017916018762827e-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) = 1.849469718447479 y[1] (numeric) = 1.849469718447479 absolute error = 6.661338147750939e-16 relative error = 3.601755725604818e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 Finished! diff ( y , x , 1 ) = sin ( x ) * cos ( x ) ; Iterations = 900 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.1 %