##############ECHO OF PROBLEM################# ##############temp/mult2postode.ode################# diff ( y , x , 1 ) = sin ( x ) * cos ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb 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) # 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 # 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) - expt(cos(c(x)),c(2))/c(2.0)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 1.5049833555396894 y[1] (numeric) 1.5049833555396894 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] 0.11000000000000001 y[1] (closed_form) 1.5060256376673486 y[1] (numeric) 1.5060256376673484 absolute error 2.220446049250313e-16 relative error 1.4743746678107784e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.12000000000000002 y[1] (closed_form) 1.5071655062869926 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] 0.13000000000000003 y[1] (closed_form) 1.5084025054663717 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] 0.14000000000000004 y[1] (closed_form) 1.5097361404223073 y[1] (numeric) 1.5097361404223064 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] 0.15000000000000005 y[1] (closed_form) 1.5111658777185986 y[1] (numeric) 1.511165877718598 absolute error 6.661338147750939e-16 relative error 4.4080787198606787e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.16000000000000006 y[1] (closed_form) 1.5126911454793899 y[1] (numeric) 1.5126911454793894 absolute error 4.440892098500626e-16 relative error 2.9357559947197644e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.17000000000000007 y[1] (closed_form) 1.5143113336179135 y[1] (numeric) 1.514311333617913 absolute error 4.440892098500626e-16 relative error 2.9326149781172666e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.18000000000000008 y[1] (closed_form) 1.5160257940805162 y[1] (numeric) 1.516025794080516 absolute error 2.220446049250313e-16 relative error 1.4646492545973034e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.19000000000000009 y[1] (closed_form) 1.5178338411058725 y[1] (numeric) 1.517833841105872 absolute error 4.440892098500626e-16 relative error 2.9258091223378274e-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) 1.5197347514992787 y[1] (numeric) 1.5197347514992783 absolute error 4.440892098500626e-16 relative error 2.9221494699121076e-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) 1.5217277649219223 absolute error 6.661338147750939e-16 relative error 4.3774834772057404e-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) 1.5238120841950091 y[1] (numeric) 1.5238120841950082 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] 0.23000000000000012 y[1] (closed_form) 1.5259868756186188 y[1] (numeric) 1.5259868756186181 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] 0.24000000000000013 y[1] (closed_form) 1.528251269305179 y[1] (numeric) 1.5282512693051784 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) 1.5306043595274068 y[1] (numeric) 1.5306043595274061 absolute error 6.661338147750939e-16 relative error 4.3520966775553355e-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) 1.5330452050805876 y[1] (numeric) 1.5330452050805867 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] 0.27000000000000013 y[1] (closed_form) 1.5355728296590438 y[1] (numeric) 1.5355728296590432 absolute error 6.661338147750939e-16 relative error 4.3380151166324113e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y[1] (closed_form) 1.538186222246646 y[1] (numeric) 1.5381862222466456 absolute error 4.440892098500626e-16 relative error 2.8870965259423154e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y[1] (closed_form) 1.5408843375212034 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] 0.30000000000000016 y[1] (closed_form) 1.5436660962725806 y[1] (numeric) 1.54366609627258 absolute error 6.661338147750939e-16 relative error 4.3152713944004894e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y[1] (closed_form) 1.5465303858343664 y[1] (numeric) 1.5465303858343664 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] 0.3200000000000002 y[1] (closed_form) 1.5494760605289268 y[1] (numeric) 1.5494760605289266 absolute error 2.220446049250313e-16 relative error 1.4330302389391837e-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) 1.5525019421256587 y[1] (numeric) 1.5525019421256585 absolute error 2.220446049250313e-16 relative error 1.4302372119484222e-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 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y[1] (closed_form) 1.558789453178878 y[1] (numeric) 1.5587894531788777 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) 1.5620485677147764 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) 1.5653828603176028 absolute error 2.220446049250313e-16 relative error 1.4184683539973111e-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) 1.5687909973147738 y[1] (numeric) 1.5687909973147736 absolute error 2.220446049250313e-16 relative error 1.4153867870550932e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y[1] (closed_form) 1.5722716154969307 y[1] (numeric) 1.572271615496931 absolute error 2.220446049250313e-16 relative error 1.4122534728508222e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y[1] (closed_form) 1.5758233226632088 y[1] (numeric) 1.5758233226632088 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] 0.41000000000000025 y[1] (closed_form) 1.5794446981780967 y[1] (numeric) 1.5794446981780967 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] 0.42000000000000026 y[1] (closed_form) 1.583134293539673 y[1] (numeric) 1.583134293539673 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] 0.43000000000000027 y[1] (closed_form) 1.5868906329589871 y[1] (numeric) 1.5868906329589871 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] 0.4400000000000003 y[1] (closed_form) 1.5907122139503551 y[1] (numeric) 1.590712213950355 absolute error 2.220446049250313e-16 relative error 1.3958816873204769e-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) 1.5945975079323338 absolute error 2.220446049250313e-16 relative error 1.3924805715578334e-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) 1.5985449608391344 y[1] (numeric) 1.5985449608391344 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] 0.4700000000000003 y[1] (closed_form) 1.6025529937422256 y[1] (numeric) 1.6025529937422256 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] 0.4800000000000003 y[1] (closed_form) 1.606620003481886 y[1] (numeric) 1.6066200034818858 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) 1.6107443633084455 absolute error 4.440892098500626e-16 relative error 2.7570433891689038e-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) 1.6149244235329652 y[1] (numeric) 1.6149244235329652 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] 0.5100000000000003 y[1] (closed_form) 1.6191585121870877 y[1] (numeric) 1.6191585121870875 absolute error 2.220446049250313e-16 relative error 1.3713580434141886e-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) 1.6234449356918055 y[1] (numeric) 1.6234449356918055 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] 0.5300000000000004 y[1] (closed_form) 1.6277819795348683 y[1] (numeric) 1.627781979534868 absolute error 2.220446049250313e-16 relative error 1.3640930279156893e-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) 1.6321679089565648 absolute error 2.220446049250313e-16 relative error 1.3604274640283981e-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) 1.6366009696436057 absolute error 2.220446049250313e-16 relative error 1.3567424744553635e-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) 1.6410793884308221 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) 1.6456013740104107 y[1] (numeric) 1.6456013740104103 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) 1.6501651176484318 y[1] (numeric) 1.6501651176484315 absolute error 2.220446049250313e-16 relative error 1.3455902233678048e-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) 1.6547687939082798 y[1] (numeric) 1.6547687939082791 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) 1.6594105613808319 y[1] (numeric) 1.6594105613808314 absolute error 4.440892098500626e-16 relative error 2.6761864735905155e-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) 1.6640885634209885 y[1] (numeric) 1.664088563420988 absolute error 4.440892098500626e-16 relative error 2.6686633128294325e-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) 1.6688009288903058 absolute error 2.220446049250313e-16 relative error 1.3305637663605759e-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) 1.6735457729054275 absolute error 4.440892098500626e-16 relative error 2.6535826927463315e-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) 1.6783211975920114 y[1] (numeric) 1.6783211975920107 absolute error 6.661338147750939e-16 relative error 3.9690484499083745e-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) 1.6831252928438534 y[1] (numeric) 1.6831252928438527 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 5.2618572259404393e-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) 1.6928117980478854 y[1] (numeric) 1.6928117980478845 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) 1.6976903335271454 y[1] (numeric) 1.6976903335271445 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) 1.7025897921755417 y[1] (numeric) 1.7025897921755406 absolute error 1.1102230246251565e-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 1.1102230246251565e-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) 1.7124436325220787 y[1] (numeric) 1.7124436325220778 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) 1.7173940728154629 absolute error 1.1102230246251565e-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 1.1102230246251565e-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) 1.7273320938839218 absolute error 1.1102230246251565e-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) 1.7323156995830746 y[1] (numeric) 1.7323156995830735 absolute error 1.1102230246251565e-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) 1.7373063787666054 y[1] (numeric) 1.7373063787666043 absolute error 1.1102230246251565e-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) 1.7423021352293837 y[1] (numeric) 1.7423021352293824 absolute error 1.3322676295501878e-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) 1.7473009707354334 y[1] (numeric) 1.7473009707354323 absolute error 1.1102230246251565e-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) 1.7523008858172024 y[1] (numeric) 1.7523008858172013 absolute error 1.1102230246251565e-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) 1.7572998805753226 y[1] (numeric) 1.7572998805753215 absolute error 1.1102230246251565e-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 5.0398936508876267e-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) 1.7672871121635159 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) 1.7722713542341144 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) 1.7772466880599675 absolute error 4.440892098500626e-16 relative error 2.4987482763849053e-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) 1.7822111235738816 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) 1.7871626750678413 y[1] (numeric) 1.7871626750678407 absolute error 6.661338147750939e-16 relative error 3.7273261358248055e-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) 1.7920993619872696 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) 1.7970192097232203 y[1] (numeric) 1.7970192097232198 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) 1.8019202504021963 y[1] (numeric) 1.8019202504021956 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) 1.8068005236732716 absolute error 4.440892098500626e-16 relative error 2.4578762515920563e-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) 1.8116580774922089 y[1] (numeric) 1.8116580774922082 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) 1.8164909689022455 y[1] (numeric) 1.8164909689022446 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) 1.8212972648112555 y[1] (numeric) 1.8212972648112546 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) 1.8260750427649586 y[1] (numeric) 1.826075042764958 absolute error 6.661338147750939e-16 relative error 3.6478994519659216e-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) 1.8308223917158761 y[1] (numeric) 1.8308223917158752 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) 1.8355374127877249 y[1] (numeric) 1.8355374127877238 absolute error 1.1102230246251565e-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) 1.8402182200349422 y[1] (numeric) 1.840218220034941 absolute error 1.1102230246251565e-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) 1.8448629411970379 absolute error 1.1102230246251565e-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) 1.8494697184474793 y[1] (numeric) 1.8494697184474786 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 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.11111111111117%