##############ECHO OF PROBLEM################# ##############temp/arcsin_sin_m0d5_0d5postode.ode################# diff ( y , x , 1 ) = arcsin ( sin ( x ) ) ; ! #BEGIN FIRST INPUT BLOCK max_terms=30 # Digits:=32; ELIMINATED in preodein.rb ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(-0.5) x_end=c(0.5) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_display_interval=0.001 # 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=0 #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(x)*c(x)/c(2.0)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] -0.5 y[1] (closed_form) 0.125 y[1] (numeric) 0.125 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] -0.49 y[1] (closed_form) 0.12004999999999999 y[1] (numeric) 0.12005000090038248 absolute error 9.00382490787166e-10 relative error 7.500062397227539e-07% Desired digits 8 Estimated correct digits 13 Correct digits 9 h 0.001 TOP MAIN SOLVE Loop x[1] -0.48 y[1] (closed_form) 0.1152 y[1] (numeric) 0.11520000177934449 absolute error 1.7793444911928802e-09 relative error 1.544569870827153e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 TOP MAIN SOLVE Loop x[1] -0.47 y[1] (closed_form) 0.11044999999999999 y[1] (numeric) 0.11045000263711087 absolute error 2.6371108768907803e-09 relative error 2.3876060451704667e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 TOP MAIN SOLVE Loop x[1] -0.45999999999999996 y[1] (closed_form) 0.10579999999999998 y[1] (numeric) 0.10580000347389884 absolute error 3.4738988630156342e-09 relative error 3.2834582826234735e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 TOP MAIN SOLVE Loop x[1] -0.44999999999999996 y[1] (closed_form) 0.10124999999999998 y[1] (numeric) 0.1012500042899181 absolute error 4.2899181151856425e-09 relative error 4.2369561631463145e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 TOP MAIN SOLVE Loop x[1] -0.43999999999999995 y[1] (closed_form) 0.09679999999999998 y[1] (numeric) 0.09680000508537114 absolute error 5.0853711519582845e-09 relative error 5.253482594998228e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 TOP MAIN SOLVE Loop x[1] -0.42999999999999994 y[1] (closed_form) 0.09244999999999998 y[1] (numeric) 0.09245000586045347 absolute error 5.8604534974859845e-09 relative error 6.339051917237411e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 TOP MAIN SOLVE Loop x[1] -0.41999999999999993 y[1] (closed_form) 0.08819999999999997 y[1] (numeric) 0.08820000661535378 absolute error 6.615353806416202e-09 relative error 7.500401141061456e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 TOP MAIN SOLVE Loop x[1] -0.4099999999999999 y[1] (closed_form) 0.08404999999999997 y[1] (numeric) 0.08405000735025416 absolute error 7.350254183080551e-09 relative error 8.745097183914995e-06% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.001 TOP MAIN SOLVE Loop x[1] -0.3999999999999999 y[1] (closed_form) 0.07999999999999996 y[1] (numeric) 0.08000000806533032 absolute error 8.065330361906042e-09 relative error 1.0081662952382558e-05% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.3899999999999999 y[1] (closed_form) 0.07604999999999996 y[1] (numeric) 0.0760500087607518 absolute error 8.760751832315172e-09 relative error 1.1519726275233631e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.3799999999999999 y[1] (closed_form) 0.07219999999999996 y[1] (numeric) 0.07220000943668198 absolute error 9.436682019137166e-09 relative error 1.3070196702406054e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.3699999999999999 y[1] (closed_form) 0.06844999999999996 y[1] (numeric) 0.06845001009327846 absolute error 1.009327850465258e-08 relative error 1.4745476266840887e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.3599999999999999 y[1] (closed_form) 0.06479999999999995 y[1] (numeric) 0.0648000107306931 absolute error 1.073069313961561e-08 relative error 1.6559711635209286e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.34999999999999987 y[1] (closed_form) 0.06124999999999995 y[1] (numeric) 0.06125001134907211 absolute error 1.1349072161215279e-08 relative error 1.8529097406065776e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.33999999999999986 y[1] (closed_form) 0.05779999999999995 y[1] (numeric) 0.05780001194855637 absolute error 1.1948556422058942e-08 relative error 2.0672242944738672e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.32999999999999985 y[1] (closed_form) 0.05444999999999995 y[1] (numeric) 0.05445001252928138 absolute error 1.252928143180565e-08 relative error 2.3010617872921326e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.31999999999999984 y[1] (closed_form) 0.05119999999999995 y[1] (numeric) 0.05120001309137755 absolute error 1.3091377600027432e-08 relative error 2.5569096875053605e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.30999999999999983 y[1] (closed_form) 0.04804999999999995 y[1] (numeric) 0.04805001363497018 absolute error 1.3634970236209298e-08 relative error 2.8376629003557364e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.2999999999999998 y[1] (closed_form) 0.04499999999999995 y[1] (numeric) 0.045000014160179694 absolute error 1.416017974403827e-08 relative error 3.1467066097862855e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.2899999999999998 y[1] (closed_form) 0.04204999999999995 y[1] (numeric) 0.04205001466712169 absolute error 1.4667121739364575e-08 relative error 3.4880194386122695e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.2799999999999998 y[1] (closed_form) 0.03919999999999994 y[1] (numeric) 0.03920001515590703 absolute error 1.5155907084896114e-08 relative error 3.866302827779627e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.2699999999999998 y[1] (closed_form) 0.03644999999999995 y[1] (numeric) 0.03645001562664202 absolute error 1.562664207060971e-08 relative error 4.287144600990324e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.2599999999999998 y[1] (closed_form) 0.03379999999999994 y[1] (numeric) 0.033800016079428424 absolute error 1.6079428483140035e-08 relative error 4.757227361875758e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.24999999999999978 y[1] (closed_form) 0.031249999999999944 y[1] (numeric) 0.03125001651436359 absolute error 1.651436364741299e-08 relative error 5.284596367172166e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.23999999999999977 y[1] (closed_form) 0.028799999999999944 y[1] (numeric) 0.028800016931540554 absolute error 1.6931540610526374e-08 relative error 5.8790071564327806e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.22999999999999976 y[1] (closed_form) 0.026449999999999946 y[1] (numeric) 0.026450017331048077 absolute error 1.7331048131341564e-08 relative error 6.552381146064877e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.21999999999999975 y[1] (closed_form) 0.024199999999999944 y[1] (numeric) 0.02420001771297075 absolute error 1.7712970805383588e-08 relative error 7.319409423712244e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.20999999999999974 y[1] (closed_form) 0.022049999999999945 y[1] (numeric) 0.022050018077389075 absolute error 1.8077389130760624e-08 relative error 8.198362417578535e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.19999999999999973 y[1] (closed_form) 0.01999999999999995 y[1] (numeric) 0.02000001842437952 absolute error 1.8424379570614047e-08 relative error 9.212189785307048e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] -0.18999999999999972 y[1] (closed_form) 0.018049999999999948 y[1] (numeric) 0.018050018754014602 absolute error 1.8754014653732387e-08 relative error 0.0001039003581924235% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] -0.17999999999999972 y[1] (closed_form) 0.01619999999999995 y[1] (numeric) 0.016200019066362918 absolute error 1.9066362967612438e-08 relative error 0.00011769359856550924% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] -0.1699999999999997 y[1] (closed_form) 0.01444999999999995 y[1] (numeric) 0.014450019361489241 absolute error 1.936148929029824e-08 relative error 0.00013398954526157997% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] -0.1599999999999997 y[1] (closed_form) 0.012799999999999952 y[1] (numeric) 0.012800019639454539 absolute error 1.963945458691163e-08 relative error 0.0001534332389602477% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] -0.1499999999999997 y[1] (closed_form) 0.011249999999999953 y[1] (numeric) 0.011250019900316046 absolute error 1.990031609291898e-08 relative error 0.000176891698603725% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] -0.13999999999999968 y[1] (closed_form) 0.009799999999999955 y[1] (numeric) 0.009800020144127305 absolute error 2.014412735056037e-08 relative error 0.0002055523199036782% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] -0.12999999999999967 y[1] (closed_form) 0.008449999999999958 y[1] (numeric) 0.00845002037093822 absolute error 2.0370938262626037e-08 relative error 0.00024107619245711408% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] -0.11999999999999966 y[1] (closed_form) 0.00719999999999996 y[1] (numeric) 0.007200020580795079 absolute error 2.0580795119344575e-08 relative error 0.0002858443766575651% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] -0.10999999999999965 y[1] (closed_form) 0.006049999999999962 y[1] (numeric) 0.006050020773740614 absolute error 2.0773740652159367e-08 relative error 0.00034336761408528096% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] -0.09999999999999964 y[1] (closed_form) 0.0049999999999999645 y[1] (numeric) 0.00500002094981402 absolute error 2.094981405541263e-08 relative error 0.0004189962811082556% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] -0.08999999999999964 y[1] (closed_form) 0.004049999999999967 y[1] (numeric) 0.0040500211090509965 absolute error 2.11090510297135e-08 relative error 0.0005212111365361401% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] -0.07999999999999963 y[1] (closed_form) 0.0031999999999999702 y[1] (numeric) 0.003200021251483768 absolute error 2.1251483797984222e-08 relative error 0.0006641088686870131% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] -0.06999999999999962 y[1] (closed_form) 0.0024499999999999735 y[1] (numeric) 0.002450021377141119 absolute error 2.1377141145358797e-08 relative error 0.0008725363732799604% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] -0.05999999999999961 y[1] (closed_form) 0.0017999999999999765 y[1] (numeric) 0.001800021486048408 absolute error 2.148604843154288e-08 relative error 0.0011936693573079533% Desired digits 8 Estimated correct digits 11 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] -0.0499999999999996 y[1] (closed_form) 0.00124999999999998 y[1] (numeric) 0.0012500215782275989 absolute error 2.1578227618786194e-08 relative error 0.001726258209502923% Desired digits 8 Estimated correct digits 10 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] -0.03999999999999959 y[1] (closed_form) 0.0007999999999999837 y[1] (numeric) 0.0008000216536972678 absolute error 2.1653697284134028e-08 relative error 0.0027067121605168086% Desired digits 8 Estimated correct digits 10 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] -0.029999999999999583 y[1] (closed_form) 0.00044999999999998747 y[1] (numeric) 0.00045002171247262543 absolute error 2.171247263796708e-08 relative error 0.004824993919548374% Desired digits 8 Estimated correct digits 10 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] -0.019999999999999574 y[1] (closed_form) 0.00019999999999999147 y[1] (numeric) 0.000200021754565526 absolute error 2.1754565534518218e-08 relative error 0.010877282767259572% Desired digits 8 Estimated correct digits 10 Correct digits 4 h 0.001 TOP MAIN SOLVE Loop x[1] -0.009999999999999565 y[1] (closed_form) 4.9999999999995645e-05 y[1] (numeric) 5.00217799844779e-05 absolute error 2.177998448225373e-08 relative error 0.04355996896451125% Desired digits 8 Estimated correct digits 9 Correct digits 4 h 0.001 TOP MAIN SOLVE Loop x[1] 4.371503159461554e-16 y[1] (closed_form) 9.555019936591174e-32 y[1] (numeric) 2.1788734649880786e-08 absolute error 2.1788734649880786e-08 relative error -1% Desired digits 8 Estimated correct digits 6 Correct digits -16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.010000000000000439 y[1] (closed_form) 5.0000000000004393e-05 y[1] (numeric) 5.0021780817875486e-05 absolute error 2.1780817871092626e-08 relative error 0.04356163574218142% Desired digits 8 Estimated correct digits 9 Correct digits 4 h 0.001 TOP MAIN SOLVE Loop x[1] 0.020000000000000448 y[1] (closed_form) 0.00020000000000000895 y[1] (numeric) 0.00020002175623265458 absolute error 2.1756232645628835e-08 relative error 0.01087811632281393% Desired digits 8 Estimated correct digits 10 Correct digits 4 h 0.001 TOP MAIN SOLVE Loop x[1] 0.030000000000000457 y[1] (closed_form) 0.0004500000000000137 y[1] (numeric) 0.000450021714974152 absolute error 2.1714974138276055e-08 relative error 0.004825549808505643% Desired digits 8 Estimated correct digits 10 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 0.040000000000000466 y[1] (closed_form) 0.0008000000000000186 y[1] (numeric) 0.0008000216570341938 absolute error 2.165703417522733e-08 relative error 0.0027071292719033535% Desired digits 8 Estimated correct digits 10 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 0.050000000000000475 y[1] (closed_form) 0.0012500000000000237 y[1] (numeric) 0.0012500215824012605 absolute error 2.158240123683458e-08 relative error 0.0017265920989467337% Desired digits 8 Estimated correct digits 10 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 0.060000000000000484 y[1] (closed_form) 0.001800000000000029 y[1] (numeric) 0.001800021491060478 absolute error 2.149106044903662e-08 relative error 0.0011939478027242374% Desired digits 8 Estimated correct digits 11 Correct digits 5 h 0.001 TOP MAIN SOLVE Loop x[1] 0.07000000000000049 y[1] (closed_form) 0.0024500000000000346 y[1] (numeric) 0.002450021382993606 absolute error 2.138299357154136e-08 relative error 0.0008727752478180023% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.0800000000000005 y[1] (closed_form) 0.00320000000000004 y[1] (numeric) 0.0032000212581790224 absolute error 2.1258178982321713e-08 relative error 0.0006643180931975452% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.09000000000000051 y[1] (closed_form) 0.004050000000000046 y[1] (numeric) 0.004050021116591706 absolute error 2.1116591660159945e-08 relative error 0.000521397324942215% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.10000000000000052 y[1] (closed_form) 0.005000000000000052 y[1] (numeric) 0.005000020958203218 absolute error 2.095820316599939e-08 relative error 0.0004191640633199834% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.11000000000000053 y[1] (closed_form) 0.006050000000000058 y[1] (numeric) 0.006050020782981678 absolute error 2.078298162039305e-08 relative error 0.0003435203573618653% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.12000000000000054 y[1] (closed_form) 0.007200000000000064 y[1] (numeric) 0.007200020590891738 absolute error 2.059089167401329e-08 relative error 0.0002859846065835154% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.13000000000000053 y[1] (closed_form) 0.008450000000000069 y[1] (numeric) 0.008450020381894551 absolute error 2.038189448293204e-08 relative error 0.00024120585186901625% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.14000000000000054 y[1] (closed_form) 0.009800000000000076 y[1] (numeric) 0.009800020155947744 absolute error 2.015594766785478e-08 relative error 0.00020567293538627165% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.15000000000000055 y[1] (closed_form) 0.011250000000000083 y[1] (numeric) 0.01125001991300538 absolute error 1.9913005296773312e-08 relative error 0.0001770044915268726% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.16000000000000056 y[1] (closed_form) 0.012800000000000089 y[1] (numeric) 0.012800019653017922 absolute error 1.9653017832924058e-08 relative error 0.00015353920181971815% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.17000000000000057 y[1] (closed_form) 0.014450000000000096 y[1] (numeric) 0.014450019375932195 absolute error 1.937593209835886e-08 relative error 0.00013408949549037185% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.18000000000000058 y[1] (closed_form) 0.016200000000000103 y[1] (numeric) 0.01620001908169133 absolute error 1.9081691227107456e-08 relative error 0.00011778821745127985% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.19000000000000059 y[1] (closed_form) 0.01805000000000011 y[1] (numeric) 0.018050018770234735 absolute error 1.8770234623544102e-08 relative error 0.00010399021952101932% Desired digits 8 Estimated correct digits 11 Correct digits 6 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2000000000000006 y[1] (closed_form) 0.02000000000000012 y[1] (numeric) 0.020000018441498027 absolute error 1.844149790861116e-08 relative error 9.220748954305526e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2100000000000006 y[1] (closed_form) 0.022050000000000125 y[1] (numeric) 0.022050018095412984 absolute error 1.8095412859103766e-08 relative error 8.206536444037943e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2200000000000006 y[1] (closed_form) 0.024200000000000135 y[1] (numeric) 0.024200017731907497 absolute error 1.7731907362567023e-08 relative error 7.327234447341705e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.23000000000000062 y[1] (closed_form) 0.026450000000000144 y[1] (numeric) 0.026450017350905495 absolute error 1.735090535137651e-08 relative error 6.5598886016546e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.24000000000000063 y[1] (closed_form) 0.028800000000000152 y[1] (numeric) 0.028800016952326875 absolute error 1.6952326722941002e-08 relative error 5.886224556576706e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2500000000000006 y[1] (closed_form) 0.03125000000000015 y[1] (numeric) 0.03125001653608746 absolute error 1.6536087305007996e-08 relative error 5.291547937602533e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2600000000000006 y[1] (closed_form) 0.03380000000000016 y[1] (numeric) 0.03380001610209889 absolute error 1.610209872382473e-08 relative error 4.7639345336759334e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.27000000000000063 y[1] (closed_form) 0.03645000000000017 y[1] (numeric) 0.03645001565026858 absolute error 1.5650268407607637e-08 relative error 4.293626449275052e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.28000000000000064 y[1] (closed_form) 0.03920000000000018 y[1] (numeric) 0.03920001518049962 absolute error 1.5180499440825557e-08 relative error 3.8725763879656855e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.29000000000000065 y[1] (closed_form) 0.042050000000000184 y[1] (numeric) 0.042050014692690686 absolute error 1.4692690501749706e-08 relative error 3.494100000416086e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.30000000000000066 y[1] (closed_form) 0.0450000000000002 y[1] (numeric) 0.04500001418673594 absolute error 1.418673573755358e-08 relative error 3.152607941678559e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.31000000000000066 y[1] (closed_form) 0.048050000000000204 y[1] (numeric) 0.04805001366252497 absolute error 1.3662524764312955e-08 relative error 2.8433974535510714e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3200000000000007 y[1] (closed_form) 0.05120000000000022 y[1] (numeric) 0.051200013119942656 absolute error 1.3119942438022392e-08 relative error 2.5624887574262375e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3300000000000007 y[1] (closed_form) 0.05445000000000023 y[1] (numeric) 0.05445001255886908 absolute error 1.2558868854595229e-08 relative error 2.3064956574095824e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3400000000000007 y[1] (closed_form) 0.05780000000000023 y[1] (numeric) 0.05780001197917941 absolute error 1.1979179176391241e-08 relative error 2.072522348856608e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3500000000000007 y[1] (closed_form) 0.06125000000000024 y[1] (numeric) 0.06125001138074379 absolute error 1.1380743548949912e-08 relative error 1.8580805794203865e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3600000000000007 y[1] (closed_form) 0.06480000000000026 y[1] (numeric) 0.06480001076342716 absolute error 1.0763426899762507e-08 relative error 1.6610226697164298e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3700000000000007 y[1] (closed_form) 0.06845000000000026 y[1] (numeric) 0.06845001012708928 absolute error 1.012708901459991e-08 relative error 1.4794870729875635e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3800000000000007 y[1] (closed_form) 0.07220000000000028 y[1] (numeric) 0.07220000947158442 absolute error 9.47158414199567e-09 relative error 1.3118537592791737e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.39000000000000073 y[1] (closed_form) 0.07605000000000028 y[1] (numeric) 0.07605000879676127 absolute error 8.796760986307106e-09 relative error 1.1567075590147368e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.40000000000000074 y[1] (closed_form) 0.0800000000000003 y[1] (numeric) 0.08000000810246288 absolute error 8.102462589754111e-09 relative error 1.0128078237192602e-05% Desired digits 8 Estimated correct digits 12 Correct digits 7 h 0.001 TOP MAIN SOLVE Loop x[1] 0.41000000000000075 y[1] (closed_form) 0.0840500000000003 y[1] (numeric) 0.08405000738852637 absolute error 7.388526068741186e-09 relative error 8.790631848591503e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h 0.001 TOP MAIN SOLVE Loop x[1] 0.42000000000000076 y[1] (closed_form) 0.08820000000000032 y[1] (numeric) 0.08820000665478288 absolute error 6.654782558346284e-09 relative error 7.545104941435669e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h 0.001 TOP MAIN SOLVE Loop x[1] 0.43000000000000077 y[1] (closed_form) 0.09245000000000034 y[1] (numeric) 0.09245000590105733 absolute error 5.90105699027621e-09 relative error 6.382971325339306e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4400000000000008 y[1] (closed_form) 0.09680000000000034 y[1] (numeric) 0.09680000512716826 absolute error 5.127167912455377e-09 relative error 5.296661066586114e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4500000000000008 y[1] (closed_form) 0.10125000000000035 y[1] (numeric) 0.10125000433292765 absolute error 4.332927294736777e-09 relative error 4.27943436517211e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4600000000000008 y[1] (closed_form) 0.10580000000000037 y[1] (numeric) 0.10580000351814067 absolute error 3.5181403068573758e-09 relative error 3.3252743921147103e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4700000000000008 y[1] (closed_form) 0.11045000000000038 y[1] (numeric) 0.11045000268260555 absolute error 2.682605165782448e-09 relative error 2.42879598531683e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4800000000000008 y[1] (closed_form) 0.11520000000000039 y[1] (numeric) 0.11520000182611331 absolute error 1.8261129275387589e-09 relative error 1.585167471821834e-06% Desired digits 8 Estimated correct digits 12 Correct digits 8 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4900000000000008 y[1] (closed_form) 0.1200500000000004 y[1] (numeric) 0.12005000094844753 absolute error 9.484471263920824e-10 relative error 7.900434205681626e-07% Desired digits 8 Estimated correct digits 12 Correct digits 9 h 0.001 Finished! diff ( y , x , 1 ) = arcsin ( sin ( x ) ) ; Iterations 1000 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.10000000000008%