##############ECHO OF PROBLEM################# ##############temp/sinpostode.ode################# diff ( y , x , 1 ) = sin ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=16; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.0); x_end=c(1.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=false; 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) - cos(c(x))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 1 y[1] (numeric) = 1 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] = 0.01 y[1] (closed_form) = 1.000049999583335 y[1] (numeric) = 1.000049999583335 absolute error = 2.220446049250313e-16 relative error = 2.220335033423778e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.02000000000000001 y[1] (closed_form) = 1.000199993333422 y[1] (numeric) = 1.000199993333422 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] = 0.03000000000000002 y[1] (closed_form) = 1.000449966251012 y[1] (numeric) = 1.000449966251012 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] = 0.04000000000000003 y[1] (closed_form) = 1.000799893339022 y[1] (numeric) = 1.000799893339022 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] = 0.05000000000000004 y[1] (closed_form) = 1.001249739605034 y[1] (numeric) = 1.001249739605034 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] = 0.06000000000000005 y[1] (closed_form) = 1.001799460064796 y[1] (numeric) = 1.001799460064796 absolute error = 2.220446049250313e-16 relative error = 2.21645762227372e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.07000000000000005 y[1] (closed_form) = 1.00244899974672 y[1] (numeric) = 1.002448999746721 absolute error = 2.220446049250313e-16 relative error = 2.215021462250282e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.08000000000000006 y[1] (closed_form) = 1.003198293697381 y[1] (numeric) = 1.003198293697381 absolute error = 2.220446049250313e-16 relative error = 2.213367051359958e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.09000000000000007 y[1] (closed_form) = 1.004047266988006 y[1] (numeric) = 1.004047266988006 absolute error = 2.220446049250313e-16 relative error = 2.211495536371833e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1000000000000001 y[1] (closed_form) = 1.004995834721974 y[1] (numeric) = 1.004995834721975 absolute error = 4.440892098500626e-16 relative error = 4.41881642198962e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1100000000000001 y[1] (closed_form) = 1.006043902043303 y[1] (numeric) = 1.006043902043303 absolute error = 2.220446049250313e-16 relative error = 2.20710651368248e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1200000000000001 y[1] (closed_form) = 1.007191364146134 y[1] (numeric) = 1.007191364146134 absolute error = 2.220446049250313e-16 relative error = 2.204592025203413e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1300000000000001 y[1] (closed_form) = 1.008438106285212 y[1] (numeric) = 1.008438106285212 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] = 0.1400000000000001 y[1] (closed_form) = 1.009784003787363 y[1] (numeric) = 1.009784003787363 absolute error = 4.440892098500626e-16 relative error = 4.397863386471088e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1500000000000001 y[1] (closed_form) = 1.011228922063958 y[1] (numeric) = 1.011228922063958 absolute error = 4.440892098500626e-16 relative error = 4.391579395728311e-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) = 1.012772716624373 y[1] (numeric) = 1.012772716624374 absolute error = 6.661338147750939e-16 relative error = 6.577327803570325e-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) = 1.014415233090439 y[1] (numeric) = 1.01441523309044 absolute error = 4.440892098500626e-16 relative error = 4.377785302938862e-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) = 1.016156307211879 y[1] (numeric) = 1.016156307211879 absolute error = 4.440892098500626e-16 relative error = 4.370284440476987e-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) = 1.01799576488273 y[1] (numeric) = 1.01799576488273 absolute error = 8.881784197001252e-16 relative error = 8.724775193956146e-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) = 1.019933422158758 y[1] (numeric) = 1.019933422158759 absolute error = 1.110223024625157e-15 relative error = 1.088524996342697e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000002 y[1] (closed_form) = 1.021969085275852 y[1] (numeric) = 1.021969085275853 absolute error = 1.110223024625157e-15 relative error = 1.086356760317738e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000002 y[1] (closed_form) = 1.024102550669395 y[1] (numeric) = 1.024102550669396 absolute error = 1.554312234475219e-15 relative error = 1.517731045059167e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000002 y[1] (closed_form) = 1.026333604994625 y[1] (numeric) = 1.026333604994627 absolute error = 1.77635683940025e-15 relative error = 1.730779184034954e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000002 y[1] (closed_form) = 1.028662025147971 y[1] (numeric) = 1.028662025147973 absolute error = 1.998401444325282e-15 relative error = 1.942719178379134e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000002 y[1] (closed_form) = 1.031087578289355 y[1] (numeric) = 1.031087578289357 absolute error = 1.77635683940025e-15 relative error = 1.722799184863955e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000002 y[1] (closed_form) = 1.033610021865487 y[1] (numeric) = 1.033610021865489 absolute error = 1.998401444325282e-15 relative error = 1.933419183299436e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000002 y[1] (closed_form) = 1.03622910363411 y[1] (numeric) = 1.036229103634111 absolute error = 1.554312234475219e-15 relative error = 1.499969677578216e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000002 y[1] (closed_form) = 1.038944561689229 y[1] (numeric) = 1.038944561689231 absolute error = 1.77635683940025e-15 relative error = 1.709770573813925e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000002 y[1] (closed_form) = 1.041756124487303 y[1] (numeric) = 1.041756124487305 absolute error = 1.998401444325282e-15 relative error = 1.918300643837144e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 1.044663510874394 y[1] (numeric) = 1.044663510874396 absolute error = 2.220446049250313e-15 relative error = 2.125513168725284e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 1.047666430114287 y[1] (numeric) = 1.047666430114289 absolute error = 1.998401444325282e-15 relative error = 1.907478742167278e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 1.050764581917559 y[1] (numeric) = 1.050764581917561 absolute error = 1.77635683940025e-15 relative error = 1.690537414345033e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 1.053957656471613 y[1] (numeric) = 1.053957656471615 absolute error = 1.554312234475219e-15 relative error = 1.474738785691513e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (closed_form) = 1.057245334471654 y[1] (numeric) = 1.057245334471656 absolute error = 1.77635683940025e-15 relative error = 1.680174677988023e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000003 y[1] (closed_form) = 1.060627287152621 y[1] (numeric) = 1.060627287152623 absolute error = 1.77635683940025e-15 relative error = 1.674817215168101e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000003 y[1] (closed_form) = 1.064103176322065 y[1] (numeric) = 1.064103176322067 absolute error = 1.554312234475219e-15 relative error = 1.460678126953345e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000003 y[1] (closed_form) = 1.067672654393966 y[1] (numeric) = 1.067672654393967 absolute error = 1.110223024625157e-15 relative error = 1.039853385825774e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000003 y[1] (closed_form) = 1.07133536442349 y[1] (numeric) = 1.071335364423491 absolute error = 1.110223024625157e-15 relative error = 1.036298307227628e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000003 y[1] (closed_form) = 1.075090940142687 y[1] (numeric) = 1.075090940142688 absolute error = 1.332267629550188e-15 relative error = 1.239213893266897e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000003 y[1] (closed_form) = 1.078939005997115 y[1] (numeric) = 1.078939005997116 absolute error = 1.110223024625157e-15 relative error = 1.028995168822477e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = 1.082879177183395 y[1] (numeric) = 1.082879177183396 absolute error = 8.881784197001252e-16 relative error = 8.202008482703556e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 1.086911059687692 y[1] (numeric) = 1.086911059687693 absolute error = 8.881784197001252e-16 relative error = 8.17158323842367e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = 1.091034250325115 y[1] (numeric) = 1.091034250325116 absolute error = 8.881784197001252e-16 relative error = 8.140701535588447e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = 1.095248336780037 y[1] (numeric) = 1.095248336780038 absolute error = 8.881784197001252e-16 relative error = 8.109379305804888e-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) = 1.099552897647323 y[1] (numeric) = 1.099552897647324 absolute error = 8.881784197001252e-16 relative error = 8.077632477714634e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000004 y[1] (closed_form) = 1.103947502474475 y[1] (numeric) = 1.103947502474476 absolute error = 1.332267629550188e-15 relative error = 1.206821544107793e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000004 y[1] (closed_form) = 1.108431711804671 y[1] (numeric) = 1.108431711804672 absolute error = 1.332267629550188e-15 relative error = 1.201939294375729e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000004 y[1] (closed_form) = 1.113005077220716 y[1] (numeric) = 1.113005077220717 absolute error = 1.332267629550188e-15 relative error = 1.197000496059724e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000004 y[1] (closed_form) = 1.117667141389879 y[1] (numeric) = 1.11766714138988 absolute error = 1.332267629550188e-15 relative error = 1.192007512982302e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (closed_form) = 1.122417438109627 y[1] (numeric) = 1.122417438109629 absolute error = 1.332267629550188e-15 relative error = 1.186962697046109e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (closed_form) = 1.127255492354249 y[1] (numeric) = 1.12725549235425 absolute error = 1.554312234475219e-15 relative error = 1.378846450531877e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (closed_form) = 1.13218082032235 y[1] (numeric) = 1.132180820322352 absolute error = 1.332267629550188e-15 relative error = 1.176726902307769e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (closed_form) = 1.137192929485239 y[1] (numeric) = 1.137192929485241 absolute error = 1.77635683940025e-15 relative error = 1.56205406606277e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (closed_form) = 1.142291318636176 y[1] (numeric) = 1.142291318636178 absolute error = 1.554312234475219e-15 relative error = 1.360696881011904e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (closed_form) = 1.147475477940494 y[1] (numeric) = 1.147475477940496 absolute error = 1.554312234475219e-15 relative error = 1.354549412476266e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (closed_form) = 1.152744888986584 y[1] (numeric) = 1.152744888986585 absolute error = 1.110223024625157e-15 relative error = 9.631125110441305e-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) = 1.158099024837731 y[1] (numeric) = 1.158099024837733 absolute error = 1.332267629550188e-15 relative error = 1.150391806725561e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (closed_form) = 1.163537350084813 y[1] (numeric) = 1.163537350084815 absolute error = 1.110223024625157e-15 relative error = 9.541791026684527e-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) = 1.169059320899837 y[1] (numeric) = 1.169059320899838 absolute error = 1.332267629550188e-15 relative error = 1.139606524436012e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (closed_form) = 1.174664385090322 y[1] (numeric) = 1.174664385090323 absolute error = 1.554312234475219e-15 relative error = 1.323196867295594e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (closed_form) = 1.180351982154521 y[1] (numeric) = 1.180351982154522 absolute error = 1.332267629550188e-15 relative error = 1.128703683047469e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (closed_form) = 1.186121543337466 y[1] (numeric) = 1.186121543337468 absolute error = 1.332267629550188e-15 relative error = 1.123213415213335e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (closed_form) = 1.191972491687848 y[1] (numeric) = 1.19197249168785 absolute error = 1.110223024625157e-15 relative error = 9.314166496015913e-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) = 1.197904242115708 y[1] (numeric) = 1.197904242115709 absolute error = 8.881784197001252e-16 relative error = 7.414435882883654e-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) = 1.203916201450944 y[1] (numeric) = 1.203916201450945 absolute error = 8.881784197001252e-16 relative error = 7.377410642283109e-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) = 1.210007768502635 y[1] (numeric) = 1.210007768502636 absolute error = 6.661338147750939e-16 relative error = 5.505202793858287e-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) = 1.216178334119151 y[1] (numeric) = 1.216178334119152 absolute error = 8.881784197001252e-16 relative error = 7.303027810830158e-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) = 1.222427281249072 y[1] (numeric) = 1.222427281249073 absolute error = 4.440892098500626e-16 relative error = 3.632847668421582e-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) = 1.228753985002894 y[1] (numeric) = 1.228753985002894 absolute error = 2.220446049250313e-16 relative error = 1.807071290389414e-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) = 1.235157812715512 y[1] (numeric) = 1.235157812715512 absolute error = 2.220446049250313e-16 relative error = 1.797702306856345e-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) = 1.241638124009492 y[1] (numeric) = 1.241638124009492 absolute error = 2.220446049250313e-16 relative error = 1.788319806160638e-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) = 1.248194270859105 y[1] (numeric) = 1.248194270859105 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] = 0.7300000000000005 y[1] (closed_form) = 1.25482559765513 y[1] (numeric) = 1.25482559765513 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] = 0.7400000000000005 y[1] (closed_form) = 1.261531441270412 y[1] (numeric) = 1.261531441270413 absolute error = 6.661338147750939e-16 relative error = 5.280358403943311e-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) = 1.268311131126179 y[1] (numeric) = 1.26831113112618 absolute error = 6.661338147750939e-16 relative error = 5.252132528267016e-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) = 1.275163989259095 y[1] (numeric) = 1.275163989259096 absolute error = 6.661338147750939e-16 relative error = 5.223907045572513e-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) = 1.282089330389057 y[1] (numeric) = 1.282089330389057 absolute error = 4.440892098500626e-16 relative error = 3.463793039407803e-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) = 1.289086461987723 y[1] (numeric) = 1.289086461987724 absolute error = 6.661338147750939e-16 relative error = 5.167487475959841e-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) = 1.296154684347764 y[1] (numeric) = 1.296154684347765 absolute error = 4.440892098500626e-16 relative error = 3.426205338088424e-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) = 1.303293290652835 y[1] (numeric) = 1.303293290652836 absolute error = 4.440892098500626e-16 relative error = 3.407438778631424e-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) = 1.310501567048253 y[1] (numeric) = 1.310501567048254 absolute error = 4.440892098500626e-16 relative error = 3.388696519076432e-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) = 1.317778792712387 y[1] (numeric) = 1.317778792712387 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (closed_form) = 1.325124239928734 y[1] (numeric) = 1.325124239928733 absolute error = 4.440892098500626e-16 relative error = 3.351302439942886e-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) = 1.332537174158692 y[1] (numeric) = 1.332537174158692 absolute error = 2.220446049250313e-16 relative error = 1.666329534597944e-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) = 1.340016854115018 y[1] (numeric) = 1.340016854115017 absolute error = 8.881784197001252e-16 relative error = 6.628113795529095e-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) = 1.347562531835949 y[1] (numeric) = 1.347562531835948 absolute error = 8.881784197001252e-16 relative error = 6.59099966581923e-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) = 1.355173452759999 y[1] (numeric) = 1.355173452759998 absolute error = 1.110223024625157e-15 relative error = 8.19247914253362e-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) = 1.36284885580142 y[1] (numeric) = 1.362848855801419 absolute error = 1.554312234475219e-15 relative error = 1.140487610096139e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (closed_form) = 1.370587973426304 y[1] (numeric) = 1.370587973426302 absolute error = 1.554312234475219e-15 relative error = 1.134047769724425e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (closed_form) = 1.378390031729336 y[1] (numeric) = 1.378390031729335 absolute error = 1.332267629550188e-15 relative error = 9.665389322924203e-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) = 1.386254250511189 y[1] (numeric) = 1.386254250511188 absolute error = 1.332267629550188e-15 relative error = 9.610557580320541e-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) = 1.394179843356538 y[1] (numeric) = 1.394179843356536 absolute error = 1.77635683940025e-15 relative error = 1.274123168445477e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (closed_form) = 1.402166017712702 y[1] (numeric) = 1.402166017712701 absolute error = 1.332267629550188e-15 relative error = 9.501497060408461e-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) = 1.410211974968902 y[1] (numeric) = 1.410211974968901 absolute error = 1.77635683940025e-15 relative error = 1.25963817562918e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (closed_form) = 1.418316910536117 y[1] (numeric) = 1.418316910536116 absolute error = 1.554312234475219e-15 relative error = 1.09588500491593e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (closed_form) = 1.426480013927544 y[1] (numeric) = 1.426480013927543 absolute error = 1.332267629550188e-15 relative error = 9.339546411744248e-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) = 1.434700468839646 y[1] (numeric) = 1.434700468839645 absolute error = 1.77635683940025e-15 relative error = 1.238137770204347e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = 1.442977453233783 y[1] (numeric) = 1.442977453233782 absolute error = 1.77635683940025e-15 relative error = 1.231035755561771e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (closed_form) = 1.451310139418413 y[1] (numeric) = 1.451310139418411 absolute error = 1.998401444325282e-15 relative error = 1.376963744721101e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 Finished! diff ( y , x , 1 ) = sin ( x ) ; Iterations = 1000 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 %