Initializing... Initialized Initializing(2)... PI = 0.3141592653589793238462643383279486e1+/-0.313e-31 E = 0.2718281828459045235360287471352649e1+/-0.256e-30 LOG_E_10 = 0.2302585092994045684017991454684277e1+/-0.5e-30 Initialized(2) ##############ECHO OF PROBLEM################# ##############temp/subpostode.ode################# diff ( y , x , 1 ) = sin ( x ) - cos ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.0) x_end=c(10.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true # 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=(20.0) $glob_subiter_method=3 $glob_max_iter=1000 $glob_upper_ratio_limit=c(1.11) $glob_lower_ratio_limit=c(0.99) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(c(2.0) - cos(c(x)) - sin(c(x))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.0e0+/-0.50e-31 y[1] (closed_form) 0.1e1+/-0.55e-31 y[1] (numeric) 0.1e1+/-0.155e-30 absolute error 0.0e0+/-0.210e-30 relative error 0.0e0+/-0.2100000000000000000000000000000231e-28% Desired digits 8 Estimated correct digits 14 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.1e0+/-0.2e-100 y[1] (closed_form) 0.905162418075146081597623813785508e0+/-0.558e-31 y[1] (numeric) 0.9051624180751460815935638722188184e0+/-0.407e-30 absolute error 0.40599415666896e-20+/-0.462e-30 relative error 0.4485318309307607493197374926087136e-18+/-0.51e-28% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.2e0+/-0.4e-100 y[1] (closed_form) 0.8212640913636971534163908561334423e0+/-0.718e-31 y[1] (numeric) 0.8212640913636971534087173632522063e0+/-0.679e-30 absolute error 0.7673492881236e-20+/-0.75e-30 relative error 0.9343514421158090549121312471029723e-18+/-0.913e-28% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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+/-0.6e-100 y[1] (closed_form) 0.7491433042130544052523690267469237e0+/-0.824e-31 y[1] (numeric) 0.7491433042130544052415644782135388e0+/-0.964e-30 absolute error 0.108045485333849e-19+/-0.104e-29 relative error 0.1442253901572897797371859686532314e-17+/-0.138e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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+/-0.8e-100 y[1] (closed_form) 0.6895206636884644255351615111524947e0+/-0.943e-31 y[1] (numeric) 0.6895206636884644255217396871024443e0+/-0.106e-29 absolute error 0.134218240500504e-19+/-0.115e-29 relative error 0.1946544136654703282154116938492666e-17+/-0.166e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.5e0+/-0.10e-99 y[1] (closed_form) 0.6429918995054242836104304821805996e0+/-0.107e-30 y[1] (numeric) 0.6429918995054242835949313137011754e0+/-0.112e-29 absolute error 0.154991684794242e-19+/-0.122e-29 relative error 0.2410476475884973247565040144332831e-17+/-0.189e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.6e0+/-0.12e-99 y[1] (closed_form) 0.6100219116952863455581020553859673e0+/-0.116e-30 y[1] (numeric) 0.6100219116952863455410862297033174e0+/-0.118e-29 absolute error 0.170158256826499e-19+/-0.129e-29 relative error 0.2789379423332832669966093504777905e-17+/-0.211e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.7e0+/-0.14e-99 y[1] (closed_form) 0.5909401254778205200715256584094161e0+/-0.136e-30 y[1] (numeric) 0.5909401254778205200535690166871252e0+/-0.122e-29 absolute error 0.179566417222909e-19+/-0.135e-29 relative error 0.3038656701094983988037651462943344e-17+/-0.228e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.8e0+/-0.16e-99 y[1] (closed_form) 0.5859371997533118174520754077762907e0+/-0.153e-30 y[1] (numeric) 0.5859371997533118174337631915008186e0+/-0.126e-29 absolute error 0.183122162754721e-19+/-0.141e-29 relative error 0.3125286512476390387407289382757511e-17+/-0.24e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.9e0+/-0.18e-99 y[1] (closed_form) 0.5950631221018521550539015328793182e0+/-0.17e-30 y[1] (numeric) 0.5950631221018521550358225363205233e0+/-0.13e-29 absolute error 0.180789965587949e-19+/-0.147e-29 relative error 0.3038164505126308932558276000940529e-17+/-0.247e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.1e1+/-0.20e-99 y[1] (closed_form) 0.618226709323963775946561070926724e0+/-0.19e-30 y[1] (numeric) 0.6182267093239637759293017581001474e0+/-0.136e-29 absolute error 0.172593128265766e-19+/-0.155e-29 relative error 0.2791744932122037726956356433605829e-17+/-0.25e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.11e1+/-0.22e-99 y[1] (closed_form) 0.6551965185129872722768273703435804e0+/-0.213e-30 y[1] (numeric) 0.655196518512987272260966015255861e0+/-0.152e-29 absolute error 0.158613550877194e-19+/-0.173e-29 relative error 0.2420854604618140537490070528396439e-17+/-0.264e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.12e1+/-0.24e-99 y[1] (closed_form) 0.7056031595561000726914922088820987e0+/-0.213e-30 y[1] (numeric) 0.7056031595561000726775931176082531e0+/-0.16e-29 absolute error 0.138990912738456e-19+/-0.181e-29 relative error 0.1969817040302032719072760793698815e-17+/-0.256e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.13e1+/-0.26e-99 y[1] (closed_form) 0.768942985958219628300667260667574e0+/-0.265e-30 y[1] (numeric) 0.7689429859582196282892751329912302e0+/-0.168e-29 absolute error 0.113921276763438e-19+/-0.194e-29 relative error 0.148153086566586994039055354207876e-17+/-0.252e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.14e1+/-0.28e-99 y[1] (closed_form) 0.8445831271112988807237773859902537e0+/-0.294e-30 y[1] (numeric) 0.8445831271112988807154118729434629e0+/-0.178e-29 absolute error 0.83655130467908e-20+/-0.207e-29 relative error 0.9904901931208478311665010671172815e-18+/-0.245e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.15e1+/-0.30e-99 y[1] (closed_form) 0.9317678117282426589700867774242378e0+/-0.341e-30 y[1] (numeric) 0.9317678117282426589652372891061474e0+/-0.201e-29 absolute error 0.48494883180904e-20+/-0.235e-29 relative error 0.5204610265614961001551008929782215e-18+/-0.252e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.16e1+/-0.32e-99 y[1] (closed_form) 0.1029625919259783561863656637400256e1+/-0.397e-30 y[1] (numeric) 0.1029625919259783561862777452953154e1+/-0.219e-29 absolute error 0.879184447102e-21+/-0.258e-29 relative error 0.8538872523081600164781936967867518e-19+/-0.25e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.17e1+/-0.34e-99 y[1] (closed_form) 0.1137179683843056068741509458686977e1+/-0.461e-30 y[1] (numeric) 0.1137179683843056068745015187289296e1+/-0.263e-29 absolute error 0.3505728602319e-20+/-0.309e-29 relative error 0.3082827324589128906485206390969205e-18+/-0.271e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.18e1+/-0.36e-99 y[1] (closed_form) 0.1253354463814891868784301127687202e1+/-0.533e-30 y[1] (numeric) 0.1253354463814891868792562565915622e1+/-0.294e-29 absolute error 0.826143822842e-20+/-0.347e-29 relative error 0.6591461926320735711011647219385854e-18+/-0.276e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.19e1+/-0.38e-99 y[1] (closed_form) 0.1376989479176088933789124083445331e1+/-0.624e-30 y[1] (numeric) 0.1376989479176088933802464510397989e1+/-0.318e-29 absolute error 0.13340426952658e-19+/-0.38e-29 relative error 0.9688111023651496511844117353289198e-18+/-0.275e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.2e1+/-0.40e-99 y[1] (closed_form) 0.1506849409721460691601548363588996e1+/-0.724e-30 y[1] (numeric) 0.1506849409721460691620240310787588e1+/-0.36e-29 absolute error 0.18691947198592e-19+/-0.432e-29 relative error 0.1240465508895622426490461330727669e-17+/-0.286e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.21e1+/-0.42e-99 y[1] (closed_form) 0.1641636737950983680940179210450117e1+/-0.847e-30 y[1] (numeric) 0.1641636737950983680964441738795022e1+/-0.39e-29 absolute error 0.24262528344905e-19+/-0.474e-29 relative error 0.1477947452320565418460191714059135e-17+/-0.288e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.22e1+/-0.44e-99 y[1] (closed_form) 0.1780004713435755524220105702238785e1+/-0.982e-30 y[1] (numeric) 0.1780004713435755524250102213224949e1+/-0.416e-29 absolute error 0.29996510986164e-19+/-0.514e-29 relative error 0.1685192784027234165522275897926844e-17+/-0.288e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.23e1+/-0.46e-99 y[1] (closed_form) 0.1920570809103104015932474359522491e1+/-0.111e-29 y[1] (numeric) 0.1920570809103104015968310962585719e1+/-0.445e-29 absolute error 0.35836603063228e-19+/-0.556e-29 relative error 0.1865935007101534368524728391457611e-17+/-0.289e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.24e1+/-0.48e-99 y[1] (closed_form) 0.2061930534990094573043050701993479e1+/-0.128e-29 y[1] (numeric) 0.2061930534990094573084775154300008e1+/-0.486e-29 absolute error 0.41724452306529e-19+/-0.614e-29 relative error 0.2023562462385739027897943418956417e-17+/-0.297e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.25e1+/-0.50e-99 y[1] (closed_form) 0.2202671471442977220781648088281156e1+/-0.146e-29 y[1] (numeric) 0.2202671471442977220829249317553876e1+/-0.582e-29 absolute error 0.4760122927272e-19+/-0.728e-29 relative error 0.2161068043503386385925927368279227e-17+/-0.33e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.26e1+/-0.52e-99 y[1] (closed_form) 0.2341387381547482998539975216435802e1+/-0.167e-29 y[1] (numeric) 0.2341387381547482998593383431584727e1+/-0.686e-29 absolute error 0.53408215148925e-19+/-0.853e-29 relative error 0.2281049926630515117800976615577315e-17+/-0.364e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.27e1+/-0.54e-99 y[1] (closed_form) 0.2476692261783231213426474196085413e1+/-0.16e-29 y[1] (numeric) 0.2476692261783231213485561584537239e1+/-0.798e-29 absolute error 0.59087388451826e-19+/-0.958e-29 relative error 0.2385738000783463315682689647231185e-17+/-0.386e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.28e1+/-0.56e-99 y[1] (closed_form) 0.2607234190512753233042934364653699e1+/-0.216e-29 y[1] (numeric) 0.2607234190512753233107516369412747e1+/-0.866e-29 absolute error 0.64582004759048e-19+/-0.108e-28 relative error 0.2477031215456212714028024310115169e-17+/-0.414e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.29e1+/-0.58e-99 y[1] (closed_form) 0.2731708835935608193596849750605929e1+/-0.246e-29 y[1] (numeric) 0.2731708835935608193666686914286665e1+/-0.992e-29 absolute error 0.69837163680736e-19+/-0.123e-28 relative error 0.2556537606132420210320120656516051e-17+/-0.45e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.3e1+/-0.60e-99 y[1] (closed_form) 0.2848872488540578235170827991923107e1+/-0.277e-29 y[1] (numeric) 0.2848872488540578235245628349329199e1+/-0.104e-28 absolute error 0.74800357406092e-19+/-0.131e-28 relative error 0.262561268385903656110471058915504e-17+/-0.459e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.31e1+/-0.62e-99 y[1] (closed_form) 0.2957554487839988885297677782944752e1+/-0.315e-29 y[1] (numeric) 0.2957554487839988885377099778288737e1+/-0.108e-28 absolute error 0.79421995343985e-19+/-0.139e-28 relative error 0.2685394154884693678765522156497916e-17+/-0.469e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.32e1+/-0.64e-99 y[1] (closed_form) 0.3056668919222332993798878136902636e1+/-0.358e-29 y[1] (numeric) 0.305666891922233299388253403651851e1+/-0.112e-28 absolute error 0.83655899615874e-19+/-0.147e-28 relative error 0.2736832212667554493700275910174242e-17+/-0.48e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.33e1+/-0.66e-99 y[1] (closed_form) 0.314522546405211326594824532870527e1+/-0.41e-29 y[1] (numeric) 0.3145225464052113266035705095155105e1+/-0.117e-28 absolute error 0.87459766449835e-19+/-0.158e-28 relative error 0.2780715323891510959355402364180217e-17+/-0.502e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.34e1+/-0.68e-99 y[1] (closed_form) 0.3222339294606292333532103969129384e1+/-0.39e-29 y[1] (numeric) 0.3222339294606292333622899557995177e1+/-0.123e-28 absolute error 0.90795588865793e-19+/-0.162e-28 relative error 0.28176917625580601215560532187419e-17+/-0.502e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.35e1+/-0.70e-99 y[1] (closed_form) 0.3287239914980416185819026426715347e1+/-0.447e-29 y[1] (numeric) 0.3287239914980416185912656463144246e1+/-0.128e-28 absolute error 0.93630036428899e-19+/-0.172e-28 relative error 0.2848287282051234258289821732515322e-17+/-0.523e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.36e1+/-0.72e-99 y[1] (closed_form) 0.3339278859628999390137019072758614e1+/-0.598e-29 y[1] (numeric) 0.3339278859628999390232953861034615e1+/-0.137e-28 absolute error 0.95934788276001e-19+/-0.196e-28 relative error 0.2872919343030235824135805176422416e-17+/-0.586e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.37e1+/-0.74e-99 y[1] (closed_form) 0.3377936172618901372046447732055564e1+/-0.576e-29 y[1] (numeric) 0.3377936172618901372144134548144144e1+/-0.145e-28 absolute error 0.9768681608858e-19+/-0.202e-28 relative error 0.2891908286498017936395124118012471e-17+/-0.597e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.38e1+/-0.76e-99 y[1] (closed_form) 0.3402825602857135775730154260469559e1+/-0.649e-29 y[1] (numeric) 0.3402825602857135775829022874653351e1+/-0.152e-28 absolute error 0.98868614183792e-19+/-0.216e-28 relative error 0.2905485785130402397768640110278567e-17+/-0.634e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.39e1+/-0.78e-99 y[1] (closed_form) 0.3413698463384113947463218609992999e1+/-0.877e-29 y[1] (numeric) 0.3413698463384113947562686984418735e1+/-0.161e-28 absolute error 0.99468374425736e-19+/-0.248e-28 relative error 0.2913800837790742051863109895457136e-17+/-0.726e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.4e1+/-0.80e-99 y[1] (closed_form) 0.3410446116171540166011807277609526e1+/-0.993e-29 y[1] (numeric) 0.3410446116171540166111287381817886e1+/-0.171e-28 absolute error 0.9948010420836e-19+/-0.27e-28 relative error 0.2916923499733613870301053011969519e-17+/-0.791e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.41e1+/-0.82e-99 y[1] (closed_form) 0.3393101057597679415800065704018208e1+/-0.11e-28 y[1] (numeric) 0.3393101057597679415898969390349716e1+/-0.183e-28 absolute error 0.98903686331508e-19+/-0.293e-28 relative error 0.2914846467954360212822318262539207e-17+/-0.863e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.42e1+/-0.84e-99 y[1] (closed_form) 0.3361836593754287637674121979285935e1+/-0.125e-28 y[1] (numeric) 0.3361836593754287637771866859458017e1+/-0.197e-28 absolute error 0.97744880172082e-19+/-0.322e-28 relative error 0.290748456821712046057960903781953e-17+/-0.957e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.43e1+/-0.86e-99 y[1] (closed_form) 0.3316965108829430280938471756620631e1+/-0.141e-28 y[1] (numeric) 0.3316965108829430281034487020758857e1+/-0.21e-28 absolute error 0.96015264138226e-19+/-0.351e-28 relative error 0.2894672117069997015088851989705117e-17+/-0.105e-26% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.44e1+/-0.88e-99 y[1] (closed_form) 0.3258934943867935637154532075598042e1+/-0.16e-28 y[1] (numeric) 0.3258934943867935637248264195579617e1+/-0.226e-28 absolute error 0.93732119981575e-19+/-0.386e-28 relative error 0.2876158057648338862123105479038983e-17+/-0.118e-26% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.45e1+/-0.90e-99 y[1] (closed_form) 0.3188325917095876761369616839292502e1+/-0.182e-28 y[1] (numeric) 0.3188325917095876761460535099416213e1+/-0.244e-28 absolute error 0.90918260123711e-19+/-0.426e-28 relative error 0.285159869121927598494004833026603e-17+/-0.133e-26% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.46e1+/-0.92e-99 y[1] (closed_form) 0.3105843530568518973568012481138039e1+/-0.205e-28 y[1] (numeric) 0.3105843530568518973655614280860477e1+/-0.264e-28 absolute error 0.87601799722438e-19+/-0.469e-28 relative error 0.282054774685969614510997443861183e-17+/-0.151e-26% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.47e1+/-0.94e-99 y[1] (closed_form) 0.3012311921026991621330044837902078e1+/-0.232e-28 y[1] (numeric) 0.3012311921026991621413860713655766e1+/-0.285e-28 absolute error 0.83815875753688e-19+/-0.517e-28 relative error 0.2782443450448270273937954817490297e-17+/-0.171e-26% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.48e1+/-0.96e-99 y[1] (closed_form) 0.2908665625396394102461381208854171e1+/-0.262e-28 y[1] (numeric) 0.2908665625396394102540979524772427e1+/-0.31e-28 absolute error 0.79598315918256e-19+/-0.572e-28 relative error 0.2736592175575640806343924569668192e-17+/-0.196e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.49e1+/-0.98e-99 y[1] (closed_form) 0.2795940243201757107782048105796403e1+/-0.295e-28 y[1] (numeric) 0.2795940243201757107857039366476378e1+/-0.339e-28 absolute error 0.74991260679975e-19+/-0.634e-28 relative error 0.2682148191911967675825964242576209e-17+/-0.226e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.5e1+/-0.100e-98 y[1] (closed_form) 0.2675262089199912204426515234642437e1+/-0.332e-28 y[1] (numeric) 0.2675262089199912204496555976854242e1+/-0.371e-28 absolute error 0.70040742211805e-19+/-0.703e-28 relative error 0.2618088990030580909793693750887352e-17+/-0.262e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.51e1+/-0.102e-98 y[1] (closed_form) 0.2547836939614751733625570694615934e1+/-0.375e-28 y[1] (numeric) 0.2547836939614751733690366919073779e1+/-0.407e-28 absolute error 0.64796224457845e-19+/-0.782e-28 relative error 0.2543185690197371060259764367089737e-17+/-0.306e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.52e1+/-0.104e-98 y[1] (closed_form) 0.2414937984419776306033990513813168e1+/-0.423e-28 y[1] (numeric) 0.2414937984419776306093300622719195e1+/-0.448e-28 absolute error 0.59310108906027e-19+/-0.871e-28 relative error 0.245596819830042589697429353025256e-17+/-0.36e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.53e1+/-0.106e-98 y[1] (closed_form) 0.2277893106044740234119613034293706e1+/-0.475e-28 y[1] (numeric) 0.2277893106044740234173250245303098e1+/-0.493e-28 absolute error 0.53637211009392e-19+/-0.968e-28 relative error 0.2354685163542459412713605648763926e-17+/-0.424e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.54e1+/-0.108e-98 y[1] (closed_form) 0.2138071611613352999951717943753407e1+/-0.536e-28 y[1] (numeric) 0.2138071611613352999999552156241888e1+/-0.544e-28 absolute error 0.47834212488481e-19+/-0.108e-27 relative error 0.2237259604807441648277215134297842e-17+/-0.505e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.55e1+/-0.110e-98 y[1] (closed_form) 0.1996870551279131906204497994196095e1+/-0.605e-28 y[1] (numeric) 0.1996870551279131906246457089182428e1+/-0.601e-28 absolute error 0.41959094986333e-19+/-0.12e-27 relative error 0.2101242614823246068055346654198814e-17+/-0.6e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.56e1+/-0.112e-98 y[1] (closed_form) 0.185570075936207151380785949155933e1+/-0.677e-28 y[1] (numeric) 0.1855700759362071513843930052294165e1+/-0.663e-28 absolute error 0.36070560734835e-19+/-0.134e-27 relative error 0.194377032788599303196573144399658e-17+/-0.722e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.57e1+/-0.114e-98 y[1] (closed_form) 0.1715972757758478078478116576874746e1+/-0.763e-28 y[1] (numeric) 0.1715972757758478078508344022896925e1+/-0.733e-28 absolute error 0.30227446022179e-19+/-0.149e-27 relative error 0.1761534143564387000122804982346043e-17+/-0.868e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.58e1+/-0.116e-98 y[1] (closed_form) 0.1579082662472438207253568424940991e1+/-0.86e-28 y[1] (numeric) 0.1579082662472438207278056558259344e1+/-0.813e-28 absolute error 0.24488133318353e-19+/-0.167e-27 relative error 0.1550782229475616409285765323679201e-17+/-0.105e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.59e1+/-0.118e-98 y[1] (closed_form) 0.1446398234086200618908741788950802e1+/-0.969e-28 y[1] (numeric) 0.1446398234086200618927651756890135e1+/-0.903e-28 absolute error 0.18909967939333e-19+/-0.187e-27 relative error 0.1307383229161632643762864183437636e-17+/-0.129e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.6e1+/-0.120e-98 y[1] (closed_form) 0.1319245211548559852265903148688644e1+/-0.927e-28 y[1] (numeric) 0.1319245211548559852279451833758367e1+/-0.1e-27 absolute error 0.13548685069723e-19+/-0.192e-27 relative error 0.1027002785465428916177747101374733e-17+/-0.145e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.61e1+/-0.122e-98 y[1] (closed_form) 0.1198894065829510943439107088576558e1+/-0.12e-27 y[1] (numeric) 0.1198894065829510943447564941451676e1+/-0.109e-27 absolute error 0.8457852875118e-20+/-0.229e-27 relative error 0.7054712435552876668793028272924459e-18+/-0.191e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.62e1+/-0.124e-98 y[1] (closed_form) 0.1086547305794279102861176665228845e1+/-0.134e-27 y[1] (numeric) 0.1086547305794279102864865002497654e1+/-0.121e-27 absolute error 0.3688337268809e-20+/-0.255e-27 relative error 0.3394548262316826833036988289309227e-18+/-0.234e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.63e1+/-0.126e-98 y[1] (closed_form) 0.9833274631322349674023599703661892e0+/-0.5e-30 y[1] (numeric) 0.9833274631322349674016477640395574e0+/-0.134e-27 absolute error 0.7122063266318e-21+/-0.134e-27 relative error 0.7242819440465730191234204437243294e-19+/-0.136e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.64e1+/-0.128e-98 y[1] (closed_form) 0.8902658763913140519248404125288715e0+/-0.553e-30 y[1] (numeric) 0.8902658763913140519201406033952954e0+/-0.134e-27 absolute error 0.46998091335761e-20+/-0.134e-27 relative error 0.5279107352318995445151531143943686e-18+/-0.15e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.65e1+/-0.130e-98 y[1] (closed_form) 0.8082923861841609758167409969811788e0+/-0.602e-30 y[1] (numeric) 0.8082923861841609758085063686380097e0+/-0.134e-27 absolute error 0.82346283431691e-20+/-0.134e-27 relative error 0.1018768515443237883060549751736109e-17+/-0.165e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.66e1+/-0.132e-98 y[1] (closed_form) 0.7382260445280923594252771727391906e0+/-0.652e-30 y[1] (numeric) 0.7382260445280923594139958275288771e0+/-0.134e-27 absolute error 0.112813452103135e-19+/-0.134e-27 relative error 0.1528169494145258530373791759768443e-17+/-0.181e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.67e1+/-0.134e-98 y[1] (closed_form) 0.6807669311480823972299053081364875e0+/-0.698e-30 y[1] (numeric) 0.6807669311480823972160957901892961e0+/-0.134e-27 absolute error 0.138095179471914e-19+/-0.134e-27 relative error 0.2028523612905561889820226761920045e-17+/-0.196e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.68e1+/-0.136e-98 y[1] (closed_form) 0.6364891585115665053362959825333757e0+/-0.748e-30 y[1] (numeric) 0.6364891585115665053205020966458628e0+/-0.134e-27 absolute error 0.157938858875129e-19+/-0.134e-27 relative error 0.2481406898500359600181585696540071e-17+/-0.21e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.69e1+/-0.138e-98 y[1] (closed_form) 0.6058351354864430571694609306530757e0+/-0.795e-30 y[1] (numeric) 0.6058351354864430571522463087703073e0+/-0.134e-27 absolute error 0.172146218827684e-19+/-0.134e-27 relative error 0.2841469712539248464316911303973312e-17+/-0.221e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.7e1+/-0.140e-98 y[1] (closed_form) 0.589111146937906271461803386687181e0+/-0.846e-30 y[1] (numeric) 0.5891111469379062714437458562786579e0+/-0.134e-27 absolute error 0.180575304085231e-19+/-0.134e-27 relative error 0.3065216216393611549929852274979236e-17+/-0.227e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.71e1+/-0.142e-98 y[1] (closed_form) 0.5864842934313175073022142900574969e0+/-0.896e-30 y[1] (numeric) 0.5864842934313175072839001006560794e0+/-0.134e-27 absolute error 0.183141894014175e-19+/-0.134e-27 relative error 0.3122707565494633897752293999424554e-17+/-0.228e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.72e1+/-0.144e-98 y[1] (closed_form) 0.5979808216185922765307037732626989e0+/-0.952e-30 y[1] (numeric) 0.5979808216185922765127217388530662e0+/-0.134e-27 absolute error 0.179820344096327e-19+/-0.134e-27 relative error 0.3007125606630593467111560739897024e-17+/-0.224e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.73e1+/-0.146e-98 y[1] (closed_form) 0.6234858619903302935672271952954205e0+/-0.990e-30 y[1] (numeric) 0.6234858619903302935501628110793659e0+/-0.134e-27 absolute error 0.170643842160546e-19+/-0.134e-27 relative error 0.2736932023058327711029041742284182e-17+/-0.214e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.74e1+/-0.148e-98 y[1] (closed_form) 0.6627445766139825915964026347651185e0+/-0.104e-29 y[1] (numeric) 0.6627445766139825915808322270870407e0+/-0.134e-27 absolute error 0.155704076780778e-19+/-0.135e-27 relative error 0.2349382888597642488147012709469675e-17+/-0.203e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.75e1+/-0.150e-98 y[1] (closed_form) 0.7153647053902353310799168656790779e0+/-0.111e-29 y[1] (numeric) 0.7153647053902353310664018335636458e0+/-0.134e-27 absolute error 0.135150321154321e-19+/-0.135e-27 relative error 0.1889250617705492836282382081830457e-17+/-0.188e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.76e1+/-0.152e-98 y[1] (closed_form) 0.7808204853862581940383842326194093e0+/-0.121e-29 y[1] (numeric) 0.7808204853862581940274654384580935e0+/-0.134e-27 absolute error 0.109187941613158e-19+/-0.135e-27 relative error 0.1398374449143001685828726420962044e-17+/-0.172e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.77e1+/-0.154e-98 y[1] (closed_form) 0.858457904085135105470222141704309e0+/-0.129e-29 y[1] (numeric) 0.858457904085135105462414507137139e0+/-0.134e-27 absolute error 0.780763456717e-20+/-0.135e-27 relative error 0.9094953322714936747351465407252089e-18+/-0.157e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.78e1+/-0.156e-98 y[1] (closed_form) 0.947501234062745463528658766451461e0+/-0.141e-29 y[1] (numeric) 0.9475012340627454635244461274402177e0+/-0.134e-27 absolute error 0.42126390112433e-20+/-0.135e-27 relative error 0.4446051213231802984389163175963287e-18+/-0.142e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.79e1+/-0.158e-98 y[1] (closed_form) 0.1047060783799764558192842447914615e1+/-0.156e-29 y[1] (numeric) 0.104706078379976455819267272041383e1+/-0.134e-27 absolute error 0.169727500785e-21+/-0.135e-27 relative error 0.1620989950259257956179098826219197e-19+/-0.128e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.8e1+/-0.160e-98 y[1] (closed_form) 0.1156141787185231748060717783585921e1+/-0.183e-29 y[1] (numeric) 0.1156141787185231748064998488114734e1+/-0.134e-27 absolute error 0.4280704528813e-20+/-0.135e-27 relative error 0.3702577466069189923354773582159358e-18+/-0.116e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.81e1+/-0.162e-98 y[1] (closed_form) 0.1273654342890705221240731832002325e1+/-0.212e-29 y[1] (numeric) 0.1273654342890705221249826021834119e1+/-0.134e-27 absolute error 0.9094189831794e-20+/-0.136e-27 relative error 0.7140233833893808877127084847490369e-18+/-0.106e-25% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.82e1+/-0.164e-98 y[1] (closed_form) 0.1398424304304062306246839374574014e1+/-0.245e-29 y[1] (numeric) 0.139842430430406230626106200822819e1+/-0.134e-27 absolute error 0.14222633654176e-19+/-0.136e-27 relative error 0.1017047087239663933280923114487726e-17+/-0.972e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.83e1+/-0.166e-98 y[1] (closed_form) 0.152920501121432653370882206019357e1+/-0.28e-29 y[1] (numeric) 0.152920501121432653372843685447407e1+/-0.134e-27 absolute error 0.196147942805e-19+/-0.136e-27 relative error 0.1282679178831887713282207664999543e-17+/-0.889e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.84e1+/-0.168e-98 y[1] (closed_form) 0.1664689746028404636311565559163074e1+/-0.319e-29 y[1] (numeric) 0.1664689746028404636336782354187279e1+/-0.134e-27 absolute error 0.25216795024205e-19+/-0.137e-27 relative error 0.1514804490408312114014082174174837e-17+/-0.822e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.85e1+/-0.170e-98 y[1] (closed_form) 0.1803524790061333328681513362617916e1+/-0.362e-29 y[1] (numeric) 0.1803524790061333328712486025163548e1+/-0.134e-27 absolute error 0.30972662545632e-19+/-0.137e-27 relative error 0.1717340549811832521359631549519216e-17+/-0.759e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.86e1+/-0.172e-98 y[1] (closed_form) 0.1944322949445899557147305597597045e1+/-0.409e-29 y[1] (numeric) 0.194432294944589955718413048371621e1+/-0.134e-27 absolute error 0.36824886119165e-19+/-0.138e-27 relative error 0.1893969627301858165711366096133094e-17+/-0.709e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.87e1+/-0.174e-98 y[1] (closed_form) 0.2085677415515216365116445594273707e1+/-0.456e-29 y[1] (numeric) 0.2085677415515216365159160586535029e1+/-0.134e-27 absolute error 0.42714992261322e-19+/-0.138e-27 relative error 0.204801528479754334841070693484113e-17+/-0.661e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.88e1+/-0.176e-98 y[1] (closed_form) 0.222617582116989330935815419240697e1+/-0.511e-29 y[1] (numeric) 0.2226175821169893309406738321385516e1+/-0.134e-27 absolute error 0.48584128978546e-19+/-0.139e-27 relative error 0.218240304815700553051478101453621e-17+/-0.624e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.89e1+/-0.178e-98 y[1] (closed_form) 0.2364414352783227077623653031114074e1+/-0.573e-29 y[1] (numeric) 0.2364414352783227077678026684910913e1+/-0.134e-27 absolute error 0.54373653796839e-19+/-0.139e-27 relative error 0.2299666880842355261346316075005017e-17+/-0.587e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.9e1+/-0.180e-98 y[1] (closed_form) 0.2499011776642920418612022144828731e1+/-0.64e-29 y[1] (numeric) 0.2499011776642920418672047864526732e1+/-0.134e-27 absolute error 0.60025719698001e-19+/-0.14e-27 relative error 0.2401978264329643210452885600238863e-17+/-0.56e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.91e1+/-0.182e-98 y[1] (closed_form) 0.2628623239781760253925068905589973e1+/-0.711e-29 y[1] (numeric) 0.2628623239781760253990552758697791e1+/-0.134e-27 absolute error 0.65483853107818e-19+/-0.141e-27 relative error 0.2491184438940544198863662200387767e-17+/-0.536e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.92e1+/-0.184e-98 y[1] (closed_form) 0.2751953707303916784413376280717529e1+/-0.799e-29 y[1] (numeric) 0.2751953707303916784484069798879059e1+/-0.134e-27 absolute error 0.7069351816153e-19+/-0.141e-27 relative error 0.2568848377569123062811635222395576e-17+/-0.512e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.93e1+/-0.186e-98 y[1] (closed_form) 0.2867770901945540999767502956048812e1+/-0.889e-29 y[1] (numeric) 0.2867770901945540999843105617656791e1+/-0.134e-27 absolute error 0.75602661607979e-19+/-0.142e-27 relative error 0.2636286655837429769556668527181552e-17+/-0.495e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.94e1+/-0.188e-98 y[1] (closed_form) 0.2974917616581848351098174343305312e1+/-0.991e-29 y[1] (numeric) 0.2974917616581848351178336576213912e1+/-0.134e-27 absolute error 0.801622329086e-19+/-0.143e-27 relative error 0.2694603455967484318490746808939521e-17+/-0.48e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.95e1+/-0.190e-98 y[1] (closed_form) 0.3072323276658187780175084144711983e1+/-0.108e-28 y[1] (numeric) 0.3072323276658187780259410819046151e1+/-0.134e-27 absolute error 0.84326674334168e-19+/-0.144e-27 relative error 0.2744720094230819079331894308254005e-17+/-0.468e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.96e1+/-0.192e-98 y[1] (closed_form) 0.3159014637017106895144443806404109e1+/-0.12e-28 y[1] (numeric) 0.3159014637017106895232498182566655e1+/-0.134e-27 absolute error 0.88054376162546e-19+/-0.146e-27 relative error 0.2787400068702789058745056370395789e-17+/-0.462e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.97e1+/-0.194e-98 y[1] (closed_form) 0.3234125506242253158408097267716228e1+/-0.126e-28 y[1] (numeric) 0.3234125506242253158499405360145464e1+/-0.134e-27 absolute error 0.91308092429236e-19+/-0.146e-27 relative error 0.2823269914943014566505971148576154e-17+/-0.451e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.98e1+/-0.196e-98 y[1] (closed_form) 0.3296905401356681266718630700818033e1+/-0.149e-28 y[1] (numeric) 0.3296905401356681266812686013894883e1+/-0.134e-27 absolute error 0.9405531307685e-19+/-0.148e-27 relative error 0.2852836269980512778893196146843279e-17+/-0.448e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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] 0.99e1+/-0.198e-98 y[1] (closed_form) 0.3346727046400682099048256806194455e1+/-0.166e-28 y[1] (numeric) 0.334672704640068209914452539497923e1+/-0.134e-27 absolute error 0.96268588784775e-19+/-0.15e-27 relative error 0.287649956061727124134893770525582e-17+/-0.448e-26% Desired digits 8 Estimated correct digits 12 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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 ) = sin ( x ) - cos ( x ) ; Iterations 200 Total Elapsed Time 6 Minutes 6 Seconds Elapsed Time(since restart) 6 Minutes 6 Seconds Time to Timeout 13 Minutes 54 Seconds Percent Done 0.1005e3+/-0.1e-28%