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_0d2_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(0.2) 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=true $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] 0.2e0+/-0.50e-33 y[1] (closed_form) -0.70590821591235807372367440199793104e0+/-0.465e-32 y[1] (numeric) -0.70590821591235807372367440199793104e0+/-0.5e-32 $glob_prec 0.1e-15+/-0.50e-49% absolute error 0.0e0+/-0.965e-32 relative error 0.0e0+/-0.136703324631627382417509208076869464e-29% Desired digits 8 Estimated correct digits 14 Correct digits 34 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.21e0+/-0.550e-32 y[1] (closed_form) -0.69226489882698656237137583181895427e0+/-0.219e-31 y[1] (numeric) -0.69226489846308000675964772355391542e0+/-0.212e-31 absolute error 0.36390655561172810826503885e-9+/-0.431e-31 relative error 0.525675296015083668578511988131503136e-7+/-0.622e-29% Desired digits 8 Estimated correct digits 13 Correct digits 8 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.22e0+/-0.105e-31 y[1] (closed_form) -0.67872386347499341386158703780937217e0+/-0.407e-31 y[1] (numeric) -0.67872386272688630054769493832729061e0+/-0.362e-31 absolute error 0.74810711331389209948208156e-9+/-0.769e-31 relative error 0.110222603561286895843118709043084874e-6+/-0.113e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.23e0+/-0.155e-31 y[1] (closed_form) -0.66528534070374657702767351342021754e0+/-0.602e-31 y[1] (numeric) -0.66528533955075306633233985441030977e0+/-0.512e-31 absolute error 0.115299351069533365900990777e-8+/-0.111e-30 relative error 0.173308119111069500352241774571429328e-6+/-0.166e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.24e0+/-0.205e-31 y[1] (closed_form) -0.65194957377950374649235487672682493e0+/-0.805e-31 y[1] (numeric) -0.65194957220052004531639899501533491e0+/-0.68e-31 absolute error 0.157898370117595588171149002e-8+/-0.148e-30 relative error 0.242194145786800514020464609114029566e-6+/-0.227e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.25e0+/-0.255e-31 y[1] (closed_form) -0.63871681863864972985840028628408988e0+/-0.101e-30 y[1] (numeric) -0.63871681661212670084967300787345026e0+/-0.83e-31 absolute error 0.202652302900872727841063962e-8+/-0.184e-30 relative error 0.317280361166631611839942198606443637e-6+/-0.288e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.26e0+/-0.305e-31 y[1] (closed_form) -0.62558734415539366312490811112600672e0+/-0.124e-30 y[1] (numeric) -0.62558734165930805099966677091157259e0+/-0.98e-31 absolute error 0.249608561212524134021443413e-8+/-0.222e-30 relative error 0.398998738616621148342139289335730512e-6+/-0.354e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.27e0+/-0.355e-31 y[1] (closed_form) -0.61256143242675791293042491059531992e0+/-0.147e-30 y[1] (numeric) -0.61256142943858207119942226992752813e0+/-0.1e-30 absolute error 0.298817584173100264066779179e-8+/-0.247e-30 relative error 0.487816516605179781458005159278572747e-6+/-0.403e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.28e0+/-0.405e-31 y[1] (closed_form) -0.59963937907576074339042683191829942e0+/-0.171e-30 y[1] (numeric) -0.59963937557243073486705528761696591e0+/-0.1e-30 absolute error 0.350333000852337154430133351e-8+/-0.271e-30 relative error 0.584239483057824220839962389484625702e-6+/-0.451e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.29e0+/-0.455e-31 y[1] (closed_form) -0.58682149357377100921895384586814547e0+/-0.197e-30 y[1] (numeric) -0.58682148953165294273436923843307976e0+/-0.1e-30 absolute error 0.404211806648458460743506571e-8+/-0.297e-30 relative error 0.68881561271177917041988266558896112e-6+/-0.506e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3e0+/-0.505e-31 y[1] (closed_form) -0.57410809958309591577482596689955998e0+/-0.225e-30 y[1] (numeric) -0.57410809497795036936488858376854893e0+/-0.1e-30 absolute error 0.460514554640993738313101105e-8+/-0.325e-30 relative error 0.802139100589956500292822337364382909e-6+/-0.566e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.31e0+/-0.555e-31 y[1] (closed_form) -0.56149953532095298820100770093801554e0+/-0.253e-30 y[1] (numeric) -0.56149953012789735551614732287086112e0+/-0.1e-30 absolute error 0.519305563268486037806715442e-8+/-0.353e-30 relative error 0.924854840657439036072476095145390443e-6+/-0.628e-28% Desired digits 8 Estimated correct digits 13 Correct digits 7 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.32e0+/-0.605e-31 y[1] (closed_form) -0.54899615394607563148869862651969993e0+/-0.281e-30 y[1] (numeric) -0.54899614813954421314394822340203154e0+/-0.1e-30 absolute error 0.580653141834475040311766839e-8+/-0.381e-30 relative error 0.105766340558281738264296235848089769e-5+/-0.693e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.33e0+/-0.655e-31 y[1] (closed_form) -0.53659832396930895703680047342652538e0+/-0.311e-30 y[1] (numeric) -0.53659831752301060187505839509973507e0+/-0.1e-30 absolute error 0.644629835516174207832679031e-8+/-0.411e-30 relative error 0.120132659145809067764429569366293518e-5+/-0.765e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.34e0+/-0.705e-31 y[1] (closed_form) -0.52430642968966992971948540959819332e0+/-0.342e-30 y[1] (numeric) -0.52430642257654301228891818698687378e0+/-0.1e-30 absolute error 0.711312691743056722261131954e-8+/-0.442e-30 relative error 0.135667360052035473999113918218625248e-5+/-0.843e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.35e0+/-0.755e-31 y[1] (closed_form) -0.51212087165747451449626484837928125e0+/-0.375e-30 y[1] (numeric) -0.51212086384963901419315463481254676e0+/-0.1e-30 absolute error 0.780783550030311021356673449e-8+/-0.475e-30 relative error 0.152460794558775198313333033166290195e-5+/-0.927e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.36e0+/-0.805e-31 y[1] (closed_form) -0.50004206716627568555221754187987636e0+/-0.409e-30 y[1] (numeric) -0.50004205863498210956693764087363602e0+/-0.1e-30 absolute error 0.853129357598527990100624034e-8+/-0.509e-30 relative error 0.170611517233577574222261013456759501e-5+/-0.101e-27% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.37e0+/-0.855e-31 y[1] (closed_form) -0.48807045077551138903350374478497214e0+/-0.444e-30 y[1] (numeric) -0.48807044149108625512992140490742047e0+/-0.1e-30 absolute error 0.928442513390358233987755167e-8+/-0.544e-30 relative error 0.190227151001484521944994195215281882e-5+/-0.111e-27% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.38e0+/-0.905e-31 y[1] (closed_form) -0.47620647486593250675517265883865715e0+/-0.480e-30 y[1] (numeric) -0.47620646479772007263239937510826423e0+/-0.1e-30 absolute error 0.1006821243412277328373039292e-7+/-0.580e-30 relative error 0.211425357812644190878832144773952759e-5+/-0.121e-27% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.39e0+/-0.955e-31 y[1] (closed_form) -0.46445061023006946630812539191823821e0+/-0.517e-30 y[1] (numeric) -0.46445059934636935939880134725031206e0+/-0.1e-30 absolute error 0.1088370010690932404466792615e-7+/-0.617e-30 relative error 0.234334929639084612779952963941039337e-5+/-0.132e-27% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4e0+/-0.1e-30 y[1] (closed_form) -0.45280334670020456137897592113663556e0+/-0.554e-30 y[1] (numeric) -0.45280333496820492592139642366296529e0+/-0.1e-30 absolute error 0.1173199963545757949747367027e-7+/-0.654e-30 relative error 0.259097016860725410649176911705728756e-5+/-0.144e-27% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.41e0+/-0.1e-30 y[1] (closed_form) -0.44126519381654777044285542953525916e0+/-0.565e-30 y[1] (numeric) -0.44126518120225350693469973631255378e0+/-0.1e-30 absolute error 0.1261429426350815569322270538e-7+/-0.665e-30 relative error 0.285866513839576493431352951892664563e-5+/-0.15e-27% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.42e0+/-0.1e-30 y[1] (closed_form) -0.42983668153856973430471284794845469e0+/-0.576e-30 y[1] (numeric) -0.4298366680067253593169301700135311e0+/-0.1e-30 absolute error 0.1353184437498778267793492359e-7+/-0.676e-30 relative error 0.314813624713263446592691699658122715e-5+/-0.157e-27% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.43e0+/-0.1e-30 y[1] (closed_form) -0.41851836100272982991727317714046652e0+/-0.591e-30 y[1] (numeric) -0.41851834651673643091666746456738638e0+/-0.1e-30 absolute error 0.1448599339900060571257308014e-7+/-0.691e-30 relative error 0.346125636263449844220152678821329498e-5+/-0.165e-27% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.44e0+/-0.1e-30 y[1] (closed_form) -0.40731080533015369978894338937202837e0+/-0.600e-30 y[1] (numeric) -0.40731078985197939915055474409284214e0+/-0.1e-30 absolute error 0.1547817430063838864527918623e-7+/-0.700e-30 relative error 0.380008929252251318271132662093883743e-5+/-0.171e-27% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.45e0+/-0.1e-30 y[1] (closed_form) -0.39621461048816746889434261617191252e0+/-0.615e-30 y[1] (numeric) -0.39621459397825074258200059773795444e0+/-0.1e-30 absolute error 0.1650991672631234201843395808e-7+/-0.715e-30 relative error 0.416691265018491620058838308269443579e-5+/-0.18e-27% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.46e0+/-0.1e-30 y[1] (closed_form) -0.38523039620999017301704407063516837e0+/-0.627e-30 y[1] (numeric) -0.38523037862713529118218003176538386e0+/-0.1e-30 absolute error 0.1758285488183486403886978451e-7+/-0.727e-30 relative error 0.45642439056783048771717438204732006e-5+/-0.188e-27% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.47e0+/-0.1e-30 y[1] (closed_form) -0.37435880697732738183193920698310496e0+/-0.641e-30 y[1] (numeric) -0.37435878827859114930620931589116314e0+/-0.1e-30 absolute error 0.1869873623252572989109194182e-7+/-0.741e-30 relative error 0.499487013101262440017524471766210254e-5+/-0.197e-27% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.48e0+/-0.1e-30 y[1] (closed_form) -0.36360051307110429324323589256533606e0+/-0.654e-30 y[1] (numeric) -0.36360049321167316578233293925247138e0+/-0.1e-30 absolute error 0.1985943112746090295331286468e-7+/-0.754e-30 relative error 0.546188204183784260218710003743366049e-5+/-0.207e-27% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.49e0+/-0.1e-30 y[1] (closed_form) -0.35295621169613345484682503522168072e0+/-0.667e-30 y[1] (numeric) -0.35295619062918998989023605351743208e0+/-0.1e-30 absolute error 0.2106694346495658898170424864e-7+/-0.767e-30 relative error 0.596871304905479638193017202744822328e-5+/-0.217e-27% Desired digits 8 Estimated correct digits 12 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arccos ( x ) ; Iterations 300 Total Elapsed Time 2 Minutes 54 Seconds Elapsed Time(since restart) 2 Minutes 54 Seconds Time to Timeout 6 Seconds Percent Done 0.100333333333333333333333333333333333e3+/-0.336e-28%