##############ECHO OF PROBLEM################# ##############temp/sinpostode.ode################# diff ( y , x , 1 ) = sin ( x ) ; ! #BEGIN FIRST INPUT BLOCK # ELIMINATED in preodein.rb # Digits:=16; ELIMINATED in preodein.rb max_terms=40 # ELIMINATED in preodein.rb ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK # ELIMINATED in preodein.rb x_start=c(0.0) x_end=c(1.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=false # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=3 # ELIMINATED in preodein.rb #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 def exact_soln_y (x) x = c(x) return(c(2.0) - cos(c(x))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (closed_form) 1.0 y[1] (numeric) 1.0 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.010000000000000002 y[1] (closed_form) 1.0000499995833347 y[1] (numeric) 1.0000499995833345 absolute error 2.220446049250313e-16 relative error 2.2203350334237783e-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) 1.0001999933334222 y[1] (numeric) 1.0001999933334222 absolute error 0.0 relative error 0.0% 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) 1.0004499662510125 y[1] (numeric) 1.0004499662510125 absolute error 0.0 relative error 0.0% 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 0.0 relative error 0.0% 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) 1.0012497396050337 y[1] (numeric) 1.0012497396050337 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.060000000000000046 y[1] (closed_form) 1.0017994600647957 y[1] (numeric) 1.001799460064796 absolute error 2.220446049250313e-16 relative error 2.2164576222737196e-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) 1.0024489997467203 y[1] (numeric) 1.0024489997467205 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) 1.0031982936973807 y[1] (numeric) 1.003198293697381 absolute error 2.220446049250313e-16 relative error 2.2133670513599585e-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) 1.0040472669880058 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] 0.10000000000000007 y[1] (closed_form) 1.0049958347219743 y[1] (numeric) 1.0049958347219747 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] 0.11000000000000008 y[1] (closed_form) 1.0060439020433032 y[1] (numeric) 1.0060439020433034 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] 0.12000000000000009 y[1] (closed_form) 1.0071913641461339 y[1] (numeric) 1.007191364146134 absolute error 2.220446049250313e-16 relative error 2.2045920252034127e-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) 1.0084381062852121 y[1] (numeric) 1.0084381062852121 absolute error 0.0 relative error 0.0% 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) 1.0097840037873629 y[1] (numeric) 1.0097840037873633 absolute error 4.440892098500626e-16 relative error 4.3978633864710884e-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) 1.0112289220639576 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] 0.16000000000000011 y[1] (closed_form) 1.0127727166243732 y[1] (numeric) 1.0127727166243738 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] 0.17000000000000012 y[1] (closed_form) 1.0144152330904395 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] 0.18000000000000013 y[1] (closed_form) 1.0161563072118787 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] 0.19000000000000014 y[1] (closed_form) 1.0179957648827296 y[1] (numeric) 1.0179957648827305 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] 0.20000000000000015 y[1] (closed_form) 1.0199334221587584 y[1] (numeric) 1.0199334221587595 absolute error 1.1102230246251565e-15 relative error 1.0885249963426966e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.21000000000000016 y[1] (closed_form) 1.0219690852758518 y[1] (numeric) 1.021969085275853 absolute error 1.1102230246251565e-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] 0.22000000000000017 y[1] (closed_form) 1.0241025506693946 y[1] (numeric) 1.0241025506693961 absolute error 1.5543122344752192e-15 relative error 1.5177310450591673e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.23000000000000018 y[1] (closed_form) 1.0263336049946252 y[1] (numeric) 1.026333604994627 absolute error 1.7763568394002505e-15 relative error 1.7307791840349543e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.24000000000000019 y[1] (closed_form) 1.0286620251479706 y[1] (numeric) 1.0286620251479726 absolute error 1.9984014443252818e-15 relative error 1.9427191783791343e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.25000000000000017 y[1] (closed_form) 1.0310875782893554 y[1] (numeric) 1.0310875782893572 absolute error 1.7763568394002505e-15 relative error 1.7227991848639545e-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) 1.0336100218654867 y[1] (numeric) 1.0336100218654887 absolute error 1.9984014443252818e-15 relative error 1.9334191832994364e-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) 1.0362291036341096 y[1] (numeric) 1.0362291036341111 absolute error 1.5543122344752192e-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) 1.0389445616892292 y[1] (numeric) 1.038944561689231 absolute error 1.7763568394002505e-15 relative error 1.7097705738139253e-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 1.9984014443252818e-15 relative error 1.9183006438371443e-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) 1.0446635108743962 absolute error 2.220446049250313e-15 relative error 2.1255131687252838e-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) 1.0476664301142866 y[1] (numeric) 1.0476664301142886 absolute error 1.9984014443252818e-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] 0.32000000000000023 y[1] (closed_form) 1.050764581917559 y[1] (numeric) 1.0507645819175608 absolute error 1.7763568394002505e-15 relative error 1.6905374143450335e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.33000000000000024 y[1] (closed_form) 1.053957656471613 y[1] (numeric) 1.0539576564716147 absolute error 1.5543122344752192e-15 relative error 1.4747387856915128e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.34000000000000025 y[1] (closed_form) 1.057245334471654 y[1] (numeric) 1.0572453344716557 absolute error 1.7763568394002505e-15 relative error 1.6801746779880228e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.35000000000000026 y[1] (closed_form) 1.060627287152621 y[1] (numeric) 1.0606272871526228 absolute error 1.7763568394002505e-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] 0.36000000000000026 y[1] (closed_form) 1.0641031763220652 y[1] (numeric) 1.0641031763220667 absolute error 1.5543122344752192e-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) 1.0676726543939656 y[1] (numeric) 1.0676726543939667 absolute error 1.1102230246251565e-15 relative error 1.0398533858257739e-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 1.1102230246251565e-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) 1.0750909401426871 y[1] (numeric) 1.0750909401426885 absolute error 1.3322676295501878e-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 1.1102230246251565e-15 relative error 1.0289951688224768e-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) 1.0828791771833959 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) 1.0869110596876919 y[1] (numeric) 1.0869110596876927 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) 1.0910342503251158 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] 0.44000000000000034 y[1] (closed_form) 1.0952483367800367 y[1] (numeric) 1.0952483367800376 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] 0.45000000000000034 y[1] (closed_form) 1.0995528976473232 y[1] (numeric) 1.0995528976473241 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] 0.46000000000000035 y[1] (closed_form) 1.103947502474475 y[1] (numeric) 1.1039475024744763 absolute error 1.3322676295501878e-15 relative error 1.2068215441077934e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.47000000000000036 y[1] (closed_form) 1.1084317118046711 y[1] (numeric) 1.1084317118046725 absolute error 1.3322676295501878e-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] 0.48000000000000037 y[1] (closed_form) 1.1130050772207158 y[1] (numeric) 1.1130050772207172 absolute error 1.3322676295501878e-15 relative error 1.1970004960597237e-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) 1.1176671413898787 y[1] (numeric) 1.11766714138988 absolute error 1.3322676295501878e-15 relative error 1.1920075129823017e-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) 1.1224174381096275 y[1] (numeric) 1.1224174381096288 absolute error 1.3322676295501878e-15 relative error 1.1869626970461094e-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) 1.1272554923542488 y[1] (numeric) 1.1272554923542504 absolute error 1.5543122344752192e-15 relative error 1.3788464505318768e-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) 1.1321808203223502 y[1] (numeric) 1.1321808203223516 absolute error 1.3322676295501878e-15 relative error 1.1767269023077688e-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) 1.1371929294852392 y[1] (numeric) 1.137192929485241 absolute error 1.7763568394002505e-15 relative error 1.5620540660627697e-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) 1.1422913186361776 absolute error 1.5543122344752192e-15 relative error 1.3606968810119036e-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) 1.1474754779404943 y[1] (numeric) 1.1474754779404959 absolute error 1.5543122344752192e-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) 1.1527448889865841 y[1] (numeric) 1.1527448889865852 absolute error 1.1102230246251565e-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) 1.1580990248377314 y[1] (numeric) 1.1580990248377327 absolute error 1.3322676295501878e-15 relative error 1.1503918067255608e-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) 1.1635373500848134 y[1] (numeric) 1.1635373500848145 absolute error 1.1102230246251565e-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) 1.1690593208998368 y[1] (numeric) 1.169059320899838 absolute error 1.3322676295501878e-15 relative error 1.1396065244360124e-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) 1.1746643850903218 y[1] (numeric) 1.1746643850903233 absolute error 1.5543122344752192e-15 relative error 1.3231968672955942e-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) 1.1803519821545208 y[1] (numeric) 1.180351982154522 absolute error 1.3322676295501878e-15 relative error 1.1287036830474689e-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) 1.1861215433374663 y[1] (numeric) 1.1861215433374677 absolute error 1.3322676295501878e-15 relative error 1.1232134152133355e-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) 1.1919724916878485 y[1] (numeric) 1.1919724916878496 absolute error 1.1102230246251565e-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) 1.1979042421157078 y[1] (numeric) 1.1979042421157087 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) 1.2039162014509444 y[1] (numeric) 1.2039162014509452 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) 1.2100077685026354 y[1] (numeric) 1.210007768502636 absolute error 6.661338147750939e-16 relative error 5.5052027938582866e-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) 1.2161783341191519 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) 1.2224272812490724 y[1] (numeric) 1.2224272812490729 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) 1.2287539850028937 y[1] (numeric) 1.228753985002894 absolute error 2.220446049250313e-16 relative error 1.8070712903894136e-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) 1.2351578127155118 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) 1.2416381240094923 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) 1.2481942708591054 y[1] (numeric) 1.2481942708591054 absolute error 0.0 relative error 0.0% 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) 1.2548255976551301 y[1] (numeric) 1.2548255976551301 absolute error 0.0 relative error 0.0% 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) 1.2615314412704124 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) 1.2683111311261794 y[1] (numeric) 1.26831113112618 absolute error 6.661338147750939e-16 relative error 5.2521325282670156e-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) 1.2751639892590951 y[1] (numeric) 1.2751639892590958 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) 1.2820893303890575 absolute error 4.440892098500626e-16 relative error 3.4637930394078026e-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) 1.2890864619877236 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) 1.2961546843477643 y[1] (numeric) 1.2961546843477647 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) 1.3032932906528352 y[1] (numeric) 1.3032932906528356 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) 1.3105015670482534 y[1] (numeric) 1.3105015670482538 absolute error 4.440892098500626e-16 relative error 3.3886965190764324e-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 0.0 relative error 0.0% 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) 1.3251242399287335 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) 1.3325371741586922 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) 1.3400168541150184 y[1] (numeric) 1.3400168541150175 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) 1.3475625318359485 y[1] (numeric) 1.3475625318359477 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) 1.3551734527599995 y[1] (numeric) 1.3551734527599983 absolute error 1.1102230246251565e-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) 1.3628488558014205 y[1] (numeric) 1.362848855801419 absolute error 1.5543122344752192e-15 relative error 1.1404876100961387e-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) 1.3705879734263036 y[1] (numeric) 1.370587973426302 absolute error 1.5543122344752192e-15 relative error 1.1340477697244251e-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) 1.3783900317293347 absolute error 1.3322676295501878e-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) 1.3862542505111877 absolute error 1.3322676295501878e-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) 1.3941798433565378 y[1] (numeric) 1.394179843356536 absolute error 1.7763568394002505e-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) 1.4021660177127022 y[1] (numeric) 1.4021660177127009 absolute error 1.3322676295501878e-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) 1.4102119749689024 y[1] (numeric) 1.4102119749689006 absolute error 1.7763568394002505e-15 relative error 1.2596381756291795e-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) 1.4183169105361155 absolute error 1.5543122344752192e-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) 1.4264800139275426 absolute error 1.3322676295501878e-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) 1.4347004688396463 y[1] (numeric) 1.4347004688396445 absolute error 1.7763568394002505e-15 relative error 1.2381377702043468e-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) 1.4429774532337833 y[1] (numeric) 1.4429774532337816 absolute error 1.7763568394002505e-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) 1.4513101394184131 y[1] (numeric) 1.4513101394184111 absolute error 1.9984014443252818e-15 relative error 1.3769637447211012e-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 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.10000000000005%