Initializing... Initialized Initializing(2)... PI = 0.314159265358979323846264338327950271e1+/-0.313e-33 E = 0.271828182845904523536028747135266232e1+/-0.256e-32 LOG_E_10 = 0.230258509299404568401799145468436324e1+/-0.5e-32 Initialized(2) ##############ECHO OF PROBLEM################# ##############temp/lin_arccos_m0d5_0d5postode.ode################# diff ( y , x , 1 ) = arccos ( 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=0.0001 # 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) $glob_display_interval=c(0.01) #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return ( c(x) *arccos(c(x)) - sqrt($glob__1 - c(x) * c(x))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] -0.5e0+/-0.50e-32 y[1] (closed_form) -0.19132229549810363929179376318461037e1+/-0.428e-31 y[1] (numeric) -0.19132229549810363929179376318461037e1+/-0.446e-31 $glob_prec 0.1e-15+/-0.50e-49% absolute error 0.0e0+/-0.874e-31 relative error 0.0e0+/-0.456820778636676439914964182890842487e-29% Desired digits 8 Estimated correct digits 14 Correct digits 34 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.49e0+/-0.100e-31 y[1] (closed_form) -0.18923366119551321416935202930286368e1+/-0.803e-31 y[1] (numeric) -0.18923366132141187500299004352865436e1+/-0.888e-31 absolute error 0.12589866083363801422579068e-8+/-0.169e-30 relative error 0.665307958627728059555077173365324431e-7+/-0.893e-29% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.48e0+/-0.150e-31 y[1] (closed_form) -0.18715649867942050477053047165394972e1+/-0.116e-30 y[1] (numeric) -0.18715649892631000218595681827009262e1+/-0.107e-30 absolute error 0.2468894974154263466161429e-8+/-0.223e-30 relative error 0.131916069790513776001509145654625485e-6+/-0.119e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.47e0+/-0.200e-31 y[1] (closed_form) -0.18509073541645302039093815971244711e1+/-0.149e-30 y[1] (numeric) -0.18509073577964121937534728460345044e1+/-0.117e-30 absolute error 0.36318819898440912489100333e-8+/-0.266e-30 relative error 0.196221706163324654208762069107233513e-6+/-0.143e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.46e0+/-0.250e-31 y[1] (closed_form) -0.18303630168612950627098600269437395e1+/-0.182e-30 y[1] (numeric) -0.18303630216112535943278909658697296e1+/-0.127e-30 absolute error 0.47499585316180309389259901e-8+/-0.309e-30 relative error 0.259509096712588509909965837504697909e-6+/-0.168e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.45e0+/-0.300e-31 y[1] (closed_form) -0.18099313046035744262025321386476886e1+/-0.214e-30 y[1] (numeric) -0.18099313104285757897117922339552623e1+/-0.137e-30 absolute error 0.58250013635092600953075737e-8+/-0.351e-30 relative error 0.32183549445734893794182078653901921e-6+/-0.193e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.44e0+/-0.350e-31 y[1] (closed_form) -0.17896115729096627247125064780150094e1+/-0.245e-30 y[1] (numeric) -0.17896115797684265830060030762754001e1+/-0.147e-30 absolute error 0.68587638582934965982603907e-8+/-0.392e-30 relative error 0.383254330834600504573161079286563426e-6+/-0.219e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.43e0+/-0.400e-31 y[1] (closed_form) -0.17694032020463409224562098319506526e1+/-0.274e-30 y[1] (numeric) -0.17694032098992265933402641243625061e1+/-0.157e-30 absolute error 0.78528856708840542924118535e-8+/-0.431e-30 relative error 0.443815500152937221577229915853925615e-6+/-0.243e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.42e0+/-0.450e-31 y[1] (closed_form) -0.17493055960462828944590230689258457e1+/-0.3e-30 y[1] (numeric) -0.17493056048551843765636181820367172e1+/-0.167e-30 absolute error 0.88089014821045951131108715e-8+/-0.467e-30 relative error 0.50356561495110716898496219509883793e-6+/-0.266e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.41e0+/-0.500e-31 y[1] (closed_form) -0.17293181817883629982125392166798551e1+/-0.327e-30 y[1] (numeric) -0.17293181915166119138653609810138247e1+/-0.174e-30 absolute error 0.97282489156528217643339696e-8+/-0.501e-30 relative error 0.562548235374037256452546216449188645e-6+/-0.289e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.4e0+/-0.550e-31 y[1] (closed_form) -0.17094404081361218567640332744484365e1+/-0.350e-30 y[1] (numeric) -0.17094404187483975748906504423325076e1+/-0.174e-30 absolute error 0.106122757181266171678840711e-7+/-0.524e-30 relative error 0.620804075276168804227269868874597509e-6+/-0.306e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.39e0+/-0.600e-31 y[1] (closed_form) -0.16896717451300888293085563113972441e1+/-0.373e-30 y[1] (numeric) -0.16896717565923351101635737429352615e1+/-0.174e-30 absolute error 0.114622462808550174315380174e-7+/-0.547e-30 relative error 0.678371187415016654342129024045548298e-6+/-0.323e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.38e0+/-0.650e-31 y[1] (closed_form) -0.16700116832300539373709771444848681e1+/-0.396e-30 y[1] (numeric) -0.16700116955094015100516026788426269e1+/-0.174e-30 absolute error 0.122793475726806255343577588e-7+/-0.570e-30 relative error 0.735285129798045439323675398469670082e-6+/-0.341e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.37e0+/-0.700e-31 y[1] (closed_form) -0.1650459732603734887264681796598388e1+/-0.417e-30 y[1] (numeric) -0.16504597456684294318098178477782703e1+/-0.174e-30 absolute error 0.130646945445451360511798823e-7+/-0.591e-30 relative error 0.791579114986011471724189878771082343e-6+/-0.358e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.36e0+/-0.750e-31 y[1] (closed_form) -0.16310154224586012513987691598604972e1+/-0.436e-30 y[1] (numeric) -0.16310154362779363109401520223165472e1+/-0.174e-30 absolute error 0.1381933505954138286245605e-7+/-0.610e-30 relative error 0.847284143929800755464017636447247027e-6+/-0.374e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.35e0+/-0.800e-31 y[1] (closed_form) -0.16116783004139021479581900325271071e1+/-0.454e-30 y[1] (numeric) -0.16116783149581565438092851845910357e1+/-0.174e-30 absolute error 0.145442543958510951520639286e-7+/-0.628e-30 relative error 0.902429125720432025231508378354198182e-6+/-0.389e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.34e0+/-0.850e-31 y[1] (closed_form) -0.15924479319101996307967841599132241e1+/-0.471e-30 y[1] (numeric) -0.15924479471505789953474881784096217e1+/-0.174e-30 absolute error 0.152403793645507040184963976e-7+/-0.645e-30 relative error 0.957040984459021568559937726045510863e-6+/-0.405e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.33e0+/-0.900e-31 y[1] (closed_form) -0.15733238996539407257294727899087612e1+/-0.488e-30 y[1] (numeric) -0.15733239155625228052524218580419119e1+/-0.174e-30 absolute error 0.159085820795229490681331507e-7+/-0.662e-30 relative error 0.101114475430152108327430226068083006e-5+/-0.42e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.32e0+/-0.950e-31 y[1] (closed_form) -0.15543058030948094677967445091691407e1+/-0.502e-30 y[1] (numeric) -0.15543058196444928803591605356064928e1+/-0.174e-30 absolute error 0.165496834125624160264373521e-7+/-0.676e-30 relative error 0.106476366359888828541458691789498958e-5+/-0.434e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.31e0+/-0.1e-30 y[1] (closed_form) -0.15353932579337888921244271497546613e1+/-0.516e-30 y[1] (numeric) -0.15353932750982450552505118756877099e1+/-0.174e-30 absolute error 0.171644561631260847259330486e-7+/-0.690e-30 relative error 0.111791920893443648424059831201466492e-5+/-0.449e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.3e0+/-0.1e-30 y[1] (closed_form) -0.15165858956600338873136189818834107e1+/-0.504e-30 y[1] (numeric) -0.15165859134136618562991058843740653e1+/-0.174e-30 absolute error 0.177536279689854869024906546e-7+/-0.678e-30 relative error 0.117063121975421801985307636295185098e-5+/-0.447e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.29e0+/-0.1e-30 y[1] (closed_form) -0.14978833631148110483731204270192012e1+/-0.491e-30 y[1] (numeric) -0.14978833814326950295986832646857461e1+/-0.174e-30 absolute error 0.183178839812255628376665449e-7+/-0.665e-30 relative error 0.122291791419152827319576511103834859e-5+/-0.443e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.28e0+/-0.1e-30 y[1] (closed_form) -0.14792853220809028501599669792365601e1+/-0.478e-30 y[1] (numeric) -0.14792853409387721747158543658783834e1+/-0.174e-30 absolute error 0.188578693245558873866418233e-7+/-0.652e-30 relative error 0.127479594660133734039156583251089345e-5+/-0.44e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.27e0+/-0.1e-30 y[1] (closed_form) -0.14607914488960020873153386240807856e1+/-0.465e-30 y[1] (numeric) -0.14607914682701934490244136089730302e1+/-0.174e-30 absolute error 0.193741913617090749848922446e-7+/-0.639e-30 relative error 0.132628044724325183028710472846172383e-5+/-0.437e-28% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.26e0+/-0.1e-30 y[1] (closed_form) -0.14424014340887399051251953907786773e1+/-0.454e-30 y[1] (numeric) -0.14424014539561616838867271601240017e1+/-0.174e-30 absolute error 0.198674217787615317693453244e-7+/-0.628e-30 relative error 0.137738505448125071531161842084911226e-5+/-0.435e-28% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.25e0+/-0.1e-30 y[1] (closed_form) -0.14241149820360980394740611321039655e1+/-0.441e-30 y[1] (numeric) -0.14241150023741965459652652351139532e1+/-0.174e-30 absolute error 0.203380985064912041030099877e-7+/-0.615e-30 relative error 0.142812193980385216405523817364472764e-5+/-0.431e-28% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.24e0+/-0.1e-30 y[1] (closed_form) -0.14059318106410541237233892887139055e1+/-0.429e-30 y[1] (numeric) -0.14059318314277816150813127290682413e1+/-0.174e-30 absolute error 0.207867274913579234403543358e-7+/-0.603e-30 relative error 0.147850182590860694133107386969717846e-5+/-0.428e-28% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.23e0+/-0.1e-30 y[1] (closed_form) -0.13878516510293990218740814915745031e1+/-0.417e-30 y[1] (numeric) -0.13878516722431833502045722391248331e1+/-0.174e-30 absolute error 0.2121378432833049074755033e-7+/-0.591e-30 relative error 0.152853399803903945516969813606492966e-5+/-0.425e-28% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.22e0+/-0.1e-30 y[1] (closed_form) -0.13698742472647479263233685821308627e1+/-0.405e-30 y[1] (numeric) -0.1369874268884463692893487369545778e1+/-0.174e-30 absolute error 0.216197157665701187874149153e-7+/-0.579e-30 relative error 0.157822630870961963287542202566736455e-5+/-0.422e-28% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.21e0+/-0.1e-30 y[1] (closed_form) -0.13519993560808431424485309423076498e1+/-0.395e-30 y[1] (numeric) -0.13519993780857842403428723873219625e1+/-0.174e-30 absolute error 0.220049410978943414450143127e-7+/-0.569e-30 relative error 0.162758517590437006412204015121682035e-5+/-0.42e-28% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.2e0+/-0.1e-30 y[1] (closed_form) -0.13342267466303167214162030786538315e1+/-0.382e-30 y[1] (numeric) -0.13342267690001701583896402254362228e1+/-0.174e-30 absolute error 0.223698534369734371467823913e-7+/-0.556e-30 relative error 0.167661557478667488989413451239847633e-5+/-0.416e-28% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.19e0+/-0.1e-30 y[1] (closed_form) -0.1316556200249145979347414577678216e1+/-0.370e-30 y[1] (numeric) -0.1316556222963966880686655404950037e1+/-0.174e-30 absolute error 0.22714820901339240827271821e-7+/-0.544e-30 relative error 0.172532102291118851347575662415511752e-5+/-0.413e-28% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] -0.18e0+/-0.1e-30 y[1] (closed_form) -0.1298987510236094977755795148597866e1+/-0.359e-30 y[1] (numeric) -0.12989875332762826762579000279503874e1+/-0.174e-30 absolute error 0.230401876985021048793525214e-7+/-0.533e-30 relative error 0.177370355888290872454610215161400351e-5+/-0.41e-28% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 Finished! Maximum Time Reached before Solution Completed! diff ( y , x , 1 ) = arccos ( x ) ; Iterations 324 Total Elapsed Time 3 Minutes 0 Seconds Elapsed Time(since restart) 3 Minutes 0 Seconds Expected Time Remaining 6 Minutes 13 Seconds Optimized Time Remaining 6 Minutes 13 Seconds Expected Total Time 9 Minutes 13 Seconds Time to Timeout 0 Seconds Percent Done 0.325e2+/-0.106e-28%