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/arccos_cos_1d3_1d1postode.ode################# diff ( y , x , 1 ) = arccos ( cos ( 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(1.3) x_end=c(1.1) $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=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)*c(x)/c(2.0)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1299e1+/-0.100e-32 y[1] (closed_form) 0.8437005e0+/-0.15e-32 y[1] (numeric) 0.843700499953689061761493177678278266e0+/-0.403e-32 absolute error 0.46310938238506822321721734e-10+/-0.553e-32 relative error 0.548902581407819745534365974655698319e-8+/-0.655e-30% Desired digits 8 Estimated correct digits 14 Correct digits 9 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] 0.1298e1+/-0.150e-32 y[1] (closed_form) 0.842402e0+/-0.215e-32 y[1] (numeric) 0.842401999907198561888052894943325429e0+/-0.636e-32 absolute error 0.92801438111947105056674571e-10+/-0.851e-32 relative error 0.110162889109887090791183509773243653e-7+/-0.101e-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] 0.1297e1+/-0.200e-32 y[1] (closed_form) 0.8411045e0+/-0.28e-32 y[1] (numeric) 0.841104499860528400266646231911176671e0+/-0.869e-32 absolute error 0.139471599733353768088823329e-9+/-0.114e-31 relative error 0.165819585715394184775879012655383486e-7+/-0.135e-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] 0.1296e1+/-0.250e-32 y[1] (closed_form) 0.839808e0+/-0.344e-32 y[1] (numeric) 0.839807999813678476340866637807747953e0+/-0.105e-31 absolute error 0.186321523659133362192252047e-9+/-0.139e-31 relative error 0.221862049014933606481781606033760097e-7+/-0.165e-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] 0.1295e1+/-0.300e-32 y[1] (closed_form) 0.8385125e0+/-0.409e-32 y[1] (numeric) 0.83851249976664868911003502938569834e0+/-0.119e-31 absolute error 0.23335131088996497061430166e-9+/-0.159e-31 relative error 0.278291988360298708265293194794353095e-7+/-0.189e-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] 0.1294e1+/-0.350e-32 y[1] (closed_form) 0.837218e0+/-0.473e-32 y[1] (numeric) 0.837217999719438937128296184997301664e0+/-0.137e-31 absolute error 0.280561062871703815002698336e-9+/-0.184e-31 relative error 0.335111121442329017057323583582770556e-7+/-0.219e-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] 0.1293e1+/-0.400e-32 y[1] (closed_form) 0.8359245e0+/-0.535e-32 y[1] (numeric) 0.83592449967204911850371041653695557e0+/-0.147e-31 absolute error 0.32795088149628958346304443e-9+/-0.2e-31 relative error 0.392321174336066933632217299528845009e-7+/-0.239e-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] 0.1292e1+/-0.450e-32 y[1] (closed_form) 0.834632e0+/-0.6e-32 y[1] (numeric) 0.834631999624479130897340501355473202e0+/-0.157e-31 absolute error 0.375520869102659498644526798e-9+/-0.217e-31 relative error 0.449923881546189816163922301085987596e-7+/-0.259e-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] 0.1291e1+/-0.500e-32 y[1] (closed_form) 0.8333405e0+/-0.665e-32 y[1] (numeric) 0.833340499576728871522333856136195532e0+/-0.167e-31 absolute error 0.423271128477666143863804468e-9+/-0.233e-31 relative error 0.507920986052719319250419807989651288e-7+/-0.279e-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] 0.129e1+/-0.550e-32 y[1] (closed_form) 0.83205e0+/-0.725e-32 y[1] (numeric) 0.832049999528798237142999934610225925e0+/-0.177e-31 absolute error 0.471201762857000065389774075e-9+/-0.249e-31 relative error 0.56631423935700987367318559581755904e-7+/-0.299e-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] 0.1289e1+/-0.600e-32 y[1] (closed_form) 0.8307605e0+/-0.79e-32 y[1] (numeric) 0.830760499480687124073882830874718246e0+/-0.187e-31 absolute error 0.519312875926117169125281754e-9+/-0.266e-31 relative error 0.625105401528018206360655994116234462e-7+/-0.32e-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] 0.1288e1+/-0.650e-32 y[1] (closed_form) 0.829472e0+/-0.855e-32 y[1] (numeric) 0.829471999432395428178829069964140943e0+/-0.197e-31 absolute error 0.567604571821170930035859057e-9+/-0.282e-31 relative error 0.684296241248855814344376973544616334e-7+/-0.339e-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] 0.1287e1+/-0.700e-32 y[1] (closed_form) 0.8281845e0+/-0.92e-32 y[1] (numeric) 0.828184499383923044870050567209787265e0+/-0.207e-31 absolute error 0.616076955129949432790212735e-9+/-0.299e-31 relative error 0.743888535863626320934782931822558862e-7+/-0.361e-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] 0.1286e1+/-0.750e-32 y[1] (closed_form) 0.826898e0+/-0.98e-32 y[1] (numeric) 0.826897999335269869107182737807501315e0+/-0.217e-31 absolute error 0.664730130892817262192498685e-9+/-0.315e-31 relative error 0.803884071424549656901454212006801322e-7+/-0.38e-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] 0.1285e1+/-0.800e-32 y[1] (closed_form) 0.8256125e0+/-0.104e-31 y[1] (numeric) 0.825612499286435795396337737897636124e0+/-0.227e-31 absolute error 0.713564204603662262102363876e-9+/-0.331e-31 relative error 0.864284642739375024121320687368468864e-7+/-0.4e-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] 0.1284e1+/-0.850e-32 y[1] (closed_form) 0.824328e0+/-0.111e-31 y[1] (numeric) 0.824327999237420717789152818344648487e0+/-0.237e-31 absolute error 0.762579282210847181655351513e-9+/-0.348e-31 relative error 0.925092053419084613958705167117943342e-7+/-0.422e-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] 0.1283e1+/-0.900e-32 y[1] (closed_form) 0.8230445e0+/-0.117e-31 y[1] (numeric) 0.82304449918822452988183377228646102e0+/-0.251e-31 absolute error 0.81177547011816622771353898e-9+/-0.368e-31 relative error 0.986308115925890067564437864538308681e-7+/-0.447e-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] 0.1282e1+/-0.950e-32 y[1] (closed_form) 0.821762e0+/-0.123e-31 y[1] (numeric) 0.82176199913884712481419345740577976e0+/-0.273e-31 absolute error 0.86115287518580654259422024e-9+/-0.396e-31 relative error 0.104793465162152368032863559035341132e-6+/-0.481e-29% 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] 0.1281e1+/-0.1e-31 y[1] (closed_form) 0.8204805e0+/-0.13e-31 y[1] (numeric) 0.820480499089288395268685373756940758e0+/-0.291e-31 absolute error 0.910711604731314626243059242e-9+/-0.421e-31 relative error 0.110997349081582636789425128567954997e-6+/-0.513e-29% 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] 0.128e1+/-0.105e-31 y[1] (closed_form) 0.8192e0+/-0.136e-31 y[1] (numeric) 0.819199999039548233469432277862566318e0+/-0.301e-31 absolute error 0.960451766530567722137433682e-9+/-0.437e-31 relative error 0.117242647281563442643729697509765625e-6+/-0.533e-29% 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] 0.1279e1+/-0.110e-31 y[1] (closed_form) 0.8179205e0+/-0.142e-31 y[1] (numeric) 0.817920498989626531181249813674335901e0+/-0.315e-31 absolute error 0.1010373468818750186325664099e-8+/-0.457e-31 relative error 0.123529544597396713534587297787498907e-6+/-0.558e-29% 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] 0.1278e1+/-0.115e-31 y[1] (closed_form) 0.816642e0+/-0.148e-31 y[1] (numeric) 0.816641998939523179708665140871513028e0+/-0.333e-31 absolute error 0.1060476820291334859128486972e-8+/-0.481e-31 relative error 0.129858226773951726598495665420098402e-6+/-0.588e-29% 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] 0.1277e1+/-0.120e-31 y[1] (closed_form) 0.8153645e0+/-0.155e-31 y[1] (numeric) 0.815364498889238069894930540849512653e0+/-0.343e-31 absolute error 0.1110761930105069459150487347e-8+/-0.498e-31 relative error 0.136228880470644657591848473535455615e-6+/-0.61e-29% 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] 0.1276e1+/-0.125e-31 y[1] (closed_form) 0.814088e0+/-0.161e-31 y[1] (numeric) 0.814087998838771092121031980628738303e0+/-0.353e-31 absolute error 0.1161228907878968019371261697e-8+/-0.514e-31 relative error 0.14264169326644883837757855379271037e-6+/-0.631e-29% 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] 0.1275e1+/-0.130e-31 y[1] (closed_form) 0.8128125e0+/-0.167e-31 y[1] (numeric) 0.812812498788122136304692614791159497e0+/-0.363e-31 absolute error 0.1211877863695307385208840503e-8+/-0.530e-31 relative error 0.149096853664935933589707405213379469e-6+/-0.652e-29% 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] 0.1274e1+/-0.135e-31 y[1] (closed_form) 0.811538e0+/-0.173e-31 y[1] (numeric) 0.811537998737291091899371205428632363e0+/-0.373e-31 absolute error 0.1262708908100628794571367637e-8+/-0.546e-31 relative error 0.155594551099348249197371858988734969e-6+/-0.672e-29% 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] 0.1273e1+/-0.140e-31 y[1] (closed_form) 0.8102645e0+/-0.18e-31 y[1] (numeric) 0.810264498686277847893255439962784603e0+/-0.383e-31 absolute error 0.1313722152106744560037215397e-8+/-0.563e-31 relative error 0.162134975937702387311453901411205846e-6+/-0.694e-29% 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] 0.1272e1+/-0.145e-31 y[1] (closed_form) 0.808992e0+/-0.186e-31 y[1] (numeric) 0.808991998635082292808250126571384739e0+/-0.393e-31 absolute error 0.1364917707191749873428615261e-8+/-0.579e-31 relative error 0.168718319487924463212073204803014121e-6+/-0.715e-29% 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] 0.1271e1+/-0.150e-31 y[1] (closed_form) 0.8077205e0+/-0.192e-31 y[1] (numeric) 0.807720498583704314698960246830489466e0+/-0.403e-31 absolute error 0.1416295685301039753169510534e-8+/-0.595e-31 relative error 0.175344774003017102224037960408334318e-6+/-0.736e-29% 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] 0.127e1+/-0.155e-31 y[1] (closed_form) 0.80645e0+/-0.198e-31 y[1] (numeric) 0.806449998532143801151668845055306539e0+/-0.413e-31 absolute error 0.1467856198848331154944693461e-8+/-0.611e-31 relative error 0.182014532686258435730013449190898381e-6+/-0.757e-29% 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] 0.1269e1+/-0.160e-31 y[1] (closed_form) 0.8051805e0+/-0.205e-31 y[1] (numeric) 0.805180498480400639283309733695618464e0+/-0.423e-31 absolute error 0.1519599360716690266304381536e-8+/-0.628e-31 relative error 0.188727789696433317287785972958858293e-6+/-0.779e-29% 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] 0.1268e1+/-0.165e-31 y[1] (closed_form) 0.803912e0+/-0.211e-31 y[1] (numeric) 0.803911998428474715740434994013778847e0+/-0.433e-31 absolute error 0.1571525284259565005986221153e-8+/-0.644e-31 relative error 0.195484740153096981508700100632905094e-6+/-0.801e-29% 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] 0.1267e1+/-0.170e-31 y[1] (closed_form) 0.8026445e0+/-0.217e-31 y[1] (numeric) 0.802644498376365916698177251144713011e0+/-0.443e-31 absolute error 0.1623634083301822748855286989e-8+/-0.660e-31 relative error 0.20228558014187137005925873646427528e-6+/-0.822e-29% 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] 0.1266e1+/-0.175e-31 y[1] (closed_form) 0.801378e0+/-0.223e-31 y[1] (numeric) 0.801377998324074127859206702508021844e0+/-0.453e-31 absolute error 0.1675925872140793297491978156e-8+/-0.676e-31 relative error 0.20913050671977435086712864041688192e-6+/-0.843e-29% 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] 0.1265e1+/-0.180e-31 y[1] (closed_form) 0.8001125e0+/-0.229e-31 y[1] (numeric) 0.800112498271599234452682878412197161e0+/-0.467e-31 absolute error 0.1728400765547317121587802839e-8+/-0.696e-31 relative error 0.216019717920582058346520375447202737e-6+/-0.869e-29% 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] 0.1264e1+/-0.185e-31 y[1] (closed_form) 0.798848e0+/-0.235e-31 y[1] (numeric) 0.798847998218941121233201113560102444e0+/-0.484e-31 absolute error 0.1781058878766798886439897556e-8+/-0.719e-31 relative error 0.222953412760224584206244186128024355e-6+/-0.9e-29% 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] 0.1263e1+/-0.190e-31 y[1] (closed_form) 0.7975845e0+/-0.241e-31 y[1] (numeric) 0.797584498166099672479733708033248985e0+/-0.493e-31 absolute error 0.1833900327520266291966751015e-8+/-0.734e-31 relative error 0.229931791242215250166816307864558551e-6+/-0.92e-29% 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] 0.1262e1+/-0.195e-31 y[1] (closed_form) 0.796322e0+/-0.247e-31 y[1] (numeric) 0.796321998113074771994565756199998404e0+/-0.502e-31 absolute error 0.1886925228005434243800001596e-8+/-0.749e-31 relative error 0.236955054363113695690939292899103628e-6+/-0.94e-29% 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] 0.1261e1+/-0.200e-31 y[1] (closed_form) 0.7950605e0+/-0.253e-31 y[1] (numeric) 0.795060498059866303102225621859642452e0+/-0.511e-31 absolute error 0.1940133696897774378140357548e-8+/-0.764e-31 relative error 0.244023404118023015624642093023109562e-6+/-0.96e-29% 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] 0.126e1+/-0.205e-31 y[1] (closed_form) 0.7938e0+/-0.259e-31 y[1] (numeric) 0.793799998006474148648410037800344074e0+/-0.52e-31 absolute error 0.1993525851351589962199655926e-8+/-0.779e-31 relative error 0.251137043506121184454479204585537918e-6+/-0.981e-29% 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] 0.1259e1+/-0.210e-31 y[1] (closed_form) 0.7925405e0+/-0.265e-31 y[1] (numeric) 0.792540497952898190998903807814164022e0+/-0.529e-31 absolute error 0.2047101809001096192185835978e-8+/-0.794e-31 relative error 0.258296176536227005709592882382666879e-6+/-0.1e-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] 0.1258e1+/-0.215e-31 y[1] (closed_form) 0.791282e0+/-0.271e-31 y[1] (numeric) 0.791281997899138312038494089076838895e0+/-0.538e-31 absolute error 0.2100861687961505910923161105e-8+/-0.809e-31 relative error 0.265501008232400826876279392808126559e-6+/-0.102e-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] 0.1257e1+/-0.220e-31 y[1] (closed_form) 0.7900245e0+/-0.278e-31 y[1] (numeric) 0.790024497845194393169879232663613406e0+/-0.547e-31 absolute error 0.2154805606830120767336386594e-8+/-0.825e-31 relative error 0.272751744639580262047112031842050468e-6+/-0.104e-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] 0.1256e1+/-0.225e-31 y[1] (closed_form) 0.788768e0+/-0.284e-31 y[1] (numeric) 0.788767997791066315312572159835255816e0+/-0.556e-31 absolute error 0.2208933684687427840164744184e-8+/-0.840e-31 relative error 0.280048592829251166396804153312507606e-6+/-0.106e-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] 0.1255e1+/-0.230e-31 y[1] (closed_form) 0.7875125e0+/-0.29e-31 y[1] (numeric) 0.787512497736753958901798251590394867e0+/-0.565e-31 absolute error 0.2263246041098201748409605133e-8+/-0.855e-31 relative error 0.287391760905154108462990128156695925e-6+/-0.108e-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] 0.1254e1+/-0.235e-31 y[1] (closed_form) 0.786258e0+/-0.296e-31 y[1] (numeric) 0.786257997682257203887387728841502926e0+/-0.574e-31 absolute error 0.2317742796112612271158497074e-8+/-0.870e-31 relative error 0.294781458009026588112107867137758852e-6+/-0.11e-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] 0.1253e1+/-0.240e-31 y[1] (closed_form) 0.7850045e0+/-0.302e-31 y[1] (numeric) 0.78500449762757592973266250043220737e0+/-0.583e-31 absolute error 0.237242407026733749956779263e-8+/-0.885e-31 relative error 0.302217894326381249988731609818797217e-6+/-0.112e-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] 0.1252e1+/-0.245e-31 y[1] (closed_form) 0.783752e0+/-0.308e-31 y[1] (numeric) 0.783751997572710015413317456073134177e0+/-0.592e-31 absolute error 0.2427289984586682543926865823e-8+/-0.900e-31 relative error 0.309701281092320344181177952081780971e-6+/-0.114e-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] 0.1251e1+/-0.250e-31 y[1] (closed_form) 0.7825005e0+/-0.314e-31 y[1] (numeric) 0.782500497517659339416296181132168021e0+/-0.604e-31 absolute error 0.2482340660583703818867831979e-8+/-0.918e-31 relative error 0.317231830597386687787142880931066497e-6+/-0.117e-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] 0.125e1+/-0.255e-31 y[1] (closed_form) 0.78125e0+/-0.32e-31 y[1] (numeric) 0.781249997462423779738661070072845579e0+/-0.619e-31 absolute error 0.2537576220261338929927154421e-8+/-0.939e-31 relative error 0.324809756193451383030675765888e-6+/-0.12e-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] 0.1249e1+/-0.260e-31 y[1] (closed_form) 0.7800005e0+/-0.326e-31 y[1] (numeric) 0.780000497407003213886457815191576816e0+/-0.628e-31 absolute error 0.2592996786113542184808423184e-8+/-0.954e-31 relative error 0.332435272299638549566112224799855897e-6+/-0.122e-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] 0.1248e1+/-0.265e-31 y[1] (closed_form) 0.778752e0+/-0.332e-31 y[1] (numeric) 0.7787519973513975188735742471605064e0+/-0.64e-31 absolute error 0.26486024811264257528394936e-8+/-0.972e-31 relative error 0.340108594408287330605827477810650887e-6+/-0.124e-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] 0.1247e1+/-0.270e-31 y[1] (closed_form) 0.7775045e0+/-0.338e-31 y[1] (numeric) 0.777504497295606571220593503738077537e0+/-0.655e-31 absolute error 0.2704393428779406496261922463e-8+/-0.993e-31 relative error 0.347829939090951434526992765057951433e-6+/-0.127e-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] 0.1246e1+/-0.275e-31 y[1] (closed_form) 0.776258e0+/-0.344e-31 y[1] (numeric) 0.776257997239630246953641502863736961e0+/-0.667e-31 absolute error 0.2760369753046358497136263039e-8+/-0.101e-30 relative error 0.355599524004436475648078736579848452e-6+/-0.13e-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] 0.1245e1+/-0.280e-31 y[1] (closed_form) 0.7750125e0+/-0.35e-31 y[1] (numeric) 0.775012497183468421603228696206715963e0+/-0.679e-31 absolute error 0.2816531578396771303793284037e-8+/-0.102e-30 relative error 0.363417567896875379918812152965274753e-6+/-0.131e-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] 0.1244e1+/-0.285e-31 y[1] (closed_form) 0.773768e0+/-0.356e-31 y[1] (numeric) 0.773767997127120970203086079091431574e0+/-0.688e-31 absolute error 0.2872879029796913920908568426e-8+/-0.104e-30 relative error 0.371284290613842123337818109045605401e-6+/-0.134e-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] 0.1243e1+/-0.290e-31 y[1] (closed_form) 0.7725245e0+/-0.361e-31 y[1] (numeric) 0.772524497070587767288995432573767654e0+/-0.697e-31 absolute error 0.2929412232711004567426232346e-8+/-0.105e-30 relative error 0.379199913104504073000433299655868519e-6+/-0.135e-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] 0.1242e1+/-0.295e-31 y[1] (closed_form) 0.771282e0+/-0.367e-31 y[1] (numeric) 0.771281997013868686897613773293310984e0+/-0.706e-31 absolute error 0.2986131313102386226706689016e-8+/-0.107e-30 relative error 0.387164657427813202785322231816637753e-6+/-0.138e-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] 0.1241e1+/-0.300e-31 y[1] (closed_form) 0.7700405e0+/-0.373e-31 y[1] (numeric) 0.770040496956963602565291986576525661e0+/-0.718e-31 absolute error 0.3043036397434708013423474339e-8+/-0.109e-30 relative error 0.395178746758736457812735088479112462e-6+/-0.141e-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] 0.124e1+/-0.305e-31 y[1] (closed_form) 0.7688e0+/-0.379e-31 y[1] (numeric) 0.768799996899872387326887618114843425e0+/-0.733e-31 absolute error 0.3100127612673112381885156575e-8+/-0.111e-30 relative error 0.403242405394525543949682176768990634e-6+/-0.144e-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] 0.1239e1+/-0.310e-31 y[1] (closed_form) 0.7675605e0+/-0.385e-31 y[1] (numeric) 0.767560496842594913714571799389721011e0+/-0.742e-31 absolute error 0.3157405086285428200610278989e-8+/-0.112e-30 relative error 0.411355858761026420798136301828976347e-6+/-0.145e-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] 0.1238e1+/-0.315e-31 y[1] (closed_form) 0.766322e0+/-0.391e-31 y[1] (numeric) 0.766321996785131053756630281863861353e0+/-0.751e-31 absolute error 0.3214868946243369718136138647e-8+/-0.114e-30 relative error 0.419519333419028778781783460085969083e-6+/-0.148e-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] 0.1237e1+/-0.320e-31 y[1] (closed_form) 0.7650845e0+/-0.397e-31 y[1] (numeric) 0.765084496727480678976258554804006433e0+/-0.76e-31 absolute error 0.3272519321023741445195993567e-8+/-0.115e-30 relative error 0.427733057070655783144998175626352383e-6+/-0.15e-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] 0.1236e1+/-0.325e-31 y[1] (closed_form) 0.763848e0+/-0.403e-31 y[1] (numeric) 0.763847996669643660390351021445978742e0+/-0.769e-31 absolute error 0.3330356339609648978554021258e-8+/-0.117e-30 relative error 0.435997258565794369894798606267215466e-6+/-0.153e-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] 0.1235e1+/-0.330e-31 y[1] (closed_form) 0.7626125e0+/-0.409e-31 y[1] (numeric) 0.762612496611619868508284208056968557e0+/-0.778e-31 absolute error 0.3388380131491715791943031443e-8+/-0.118e-30 relative error 0.444312167908566380952716018030126702e-6+/-0.154e-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] 0.1234e1+/-0.335e-31 y[1] (closed_form) 0.761378e0+/-0.414e-31 y[1] (numeric) 0.761377996553409173330693980293428431e0+/-0.787e-31 absolute error 0.3446590826669306019706571569e-8+/-0.12e-30 relative error 0.452678016263840828038972963363795644e-6+/-0.157e-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] 0.1233e1+/-0.340e-31 y[1] (closed_form) 0.7601445e0+/-0.42e-31 y[1] (numeric) 0.76014449649501144434824674109533716e0+/-0.799e-31 absolute error 0.350498855565175325890466284e-8+/-0.121e-30 relative error 0.461095035963787577086285941686087316e-6+/-0.159e-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] 0.1232e1+/-0.345e-31 y[1] (closed_form) 0.758912e0+/-0.426e-31 y[1] (numeric) 0.758911996436426550540404584199025806e0+/-0.814e-31 absolute error 0.3563573449459595415800974194e-8+/-0.124e-30 relative error 0.469563460514472747275174749378057007e-6+/-0.163e-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] 0.1231e1+/-0.350e-31 y[1] (closed_form) 0.7576805e0+/-0.432e-31 y[1] (numeric) 0.757680496377654360374184377191210743e0+/-0.823e-31 absolute error 0.3622345639625815622808789257e-8+/-0.125e-30 relative error 0.478083524602496121097057302781317455e-6+/-0.164e-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] 0.123e1+/-0.355e-31 y[1] (closed_form) 0.75645e0+/-0.438e-31 y[1] (numeric) 0.756449996318694741802910747866345804e0+/-0.832e-31 absolute error 0.3681305258197089252133654196e-8+/-0.127e-30 relative error 0.486655464101670864185822486086324277e-6+/-0.167e-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] 0.1229e1+/-0.360e-31 y[1] (closed_form) 0.7552205e0+/-0.443e-31 y[1] (numeric) 0.755220496259547562264962947487879934e0+/-0.841e-31 absolute error 0.3740452437735037052512120066e-8+/-0.128e-30 relative error 0.495279516079745856013193506532198212e-6+/-0.169e-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] 0.1228e1+/-0.365e-31 y[1] (closed_form) 0.753992e0+/-0.449e-31 y[1] (numeric) 0.753991996200212688682515564391480829e0+/-0.85e-31 absolute error 0.3799787311317484435608519171e-8+/-0.129e-30 relative error 0.503955918805170934918211223859139089e-6+/-0.171e-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] 0.1227e1+/-0.370e-31 y[1] (closed_form) 0.7527645e0+/-0.455e-31 y[1] (numeric) 0.752764496140689987460273061204751301e0+/-0.862e-31 absolute error 0.3859310012539726938795248699e-8+/-0.131e-30 relative error 0.512684911753905363336773811597119683e-6+/-0.174e-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] 0.1226e1+/-0.375e-31 y[1] (closed_form) 0.751538e0+/-0.461e-31 y[1] (numeric) 0.751537996080979324484198108793415849e0+/-0.877e-31 absolute error 0.3919020675515801891206584151e-8+/-0.133e-30 relative error 0.521466735616269821513560744899126857e-6+/-0.176e-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] 0.1225e1+/-0.380e-31 y[1] (closed_form) 0.7503125e0+/-0.467e-31 y[1] (numeric) 0.750312496021080565120233689878382542e0+/-0.886e-31 absolute error 0.3978919434879766310121617458e-8+/-0.135e-30 relative error 0.530301632303842240416042310104123281e-6+/-0.179e-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] 0.1224e1+/-0.385e-31 y[1] (closed_form) 0.749088e0+/-0.472e-31 y[1] (numeric) 0.749087995960993574213018945101482006e0+/-0.895e-31 absolute error 0.4039006425786981054898517994e-8+/-0.136e-30 relative error 0.539189844956397787028829455818275022e-6+/-0.181e-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] 0.1223e1+/-0.390e-31 y[1] (closed_form) 0.7478645e0+/-0.478e-31 y[1] (numeric) 0.747864495900718216084598734150043259e0+/-0.904e-31 absolute error 0.4099281783915401265849956741e-8+/-0.138e-30 relative error 0.548131617948893317686553746166584989e-6+/-0.184e-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] 0.1222e1+/-0.395e-31 y[1] (closed_form) 0.746642e0+/-0.484e-31 y[1] (numeric) 0.746641995840254354533126884381777493e0+/-0.913e-31 absolute error 0.4159745645466873115618222507e-8+/-0.139e-30 relative error 0.557127196898496617604986393345137294e-6+/-0.186e-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] 0.1221e1+/-0.400e-31 y[1] (closed_form) 0.7454205e0+/-0.489e-31 y[1] (numeric) 0.745420495779601852831563099221697671e0+/-0.922e-31 absolute error 0.4220398147168436900778302329e-8+/-0.141e-30 relative error 0.566176828671660747293413895780971948e-6+/-0.189e-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] 0.122e1+/-0.405e-31 y[1] (closed_form) 0.7442e0+/-0.495e-31 y[1] (numeric) 0.744199995718760573726363498431996066e0+/-0.931e-31 absolute error 0.4281239426273636501568003934e-8+/-0.142e-30 relative error 0.575280761391243819076592842515452835e-6+/-0.19e-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] 0.1219e1+/-0.410e-31 y[1] (closed_form) 0.7429805e0+/-0.501e-31 y[1] (numeric) 0.742980495657730379436164762183925425e0+/-0.94e-31 absolute error 0.4342269620563835237816074575e-8+/-0.144e-30 relative error 0.584439244443674529522117279659425785e-6+/-0.193e-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] 0.1218e1+/-0.415e-31 y[1] (closed_form) 0.741762e0+/-0.506e-31 y[1] (numeric) 0.741761995596511131650461850687774309e0+/-0.949e-31 absolute error 0.4403488868349538149312225691e-8+/-0.145e-30 relative error 0.593652528486163776158960109981368686e-6+/-0.195e-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] 0.1217e1+/-0.420e-31 y[1] (closed_form) 0.7405445e0+/-0.511e-31 y[1] (numeric) 0.74054449553510269152827927096298498e0+/-0.961e-31 absolute error 0.446489730847172072903701502e-8+/-0.147e-30 relative error 0.602920865453962689485508976165510647e-6+/-0.198e-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] 0.1216e1+/-0.425e-31 y[1] (closed_form) 0.739328e0+/-0.516e-31 y[1] (numeric) 0.739327995473504919696835862155324854e0+/-0.976e-31 absolute error 0.4526495080303164137844675146e-8+/-0.149e-30 relative error 0.61224450856766741390082279394260734e-6+/-0.201e-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] 0.1215e1+/-0.430e-31 y[1] (closed_form) 0.7381125e0+/-0.521e-31 y[1] (numeric) 0.738112495411717676250203070631781574e0+/-0.985e-31 absolute error 0.4588282323749796929368218426e-8+/-0.15e-30 relative error 0.621623712340570973851305651374282375e-6+/-0.203e-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] 0.1214e1+/-0.435e-31 y[1] (closed_form) 0.736898e0+/-0.526e-31 y[1] (numeric) 0.736897995349740820747956685906498836e0+/-0.994e-31 absolute error 0.4650259179252043314093501164e-8+/-0.152e-30 relative error 0.631058732586062564166750508754264497e-6+/-0.206e-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] 0.1213e1+/-0.440e-31 y[1] (closed_form) 0.7356845e0+/-0.531e-31 y[1] (numeric) 0.735684495287574212213822008272596735e0+/-0.1e-30 absolute error 0.4712425787786177991727403265e-8+/-0.153e-30 relative error 0.640549826425074606264968646885995287e-6+/-0.207e-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] 0.1212e1+/-0.445e-31 y[1] (closed_form) 0.734472e0+/-0.536e-31 y[1] (numeric) 0.73447199522521770913431241883511805e0+/-0.1e-30 absolute error 0.477478229086568758116488195e-8+/-0.153e-30 relative error 0.650097252293577914633217052522083891e-6+/-0.208e-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] 0.1211e1+/-0.450e-31 y[1] (closed_form) 0.7332605e0+/-0.541e-31 y[1] (numeric) 0.733260495162671169457361322459601939e0+/-0.1e-30 absolute error 0.4837328830542638677540398061e-8+/-0.154e-30 relative error 0.659701269950125320747592166903849314e-6+/-0.21e-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] 0.121e1+/-0.455e-31 y[1] (closed_form) 0.73205e0+/-0.551e-31 y[1] (numeric) 0.73204999509993445059094743396890033e0+/-0.1e-30 absolute error 0.490006554940905256603109967e-8+/-0.155e-30 relative error 0.669362140483444104368704278396284406e-6+/-0.211e-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] 0.1209e1+/-0.460e-31 y[1] (closed_form) 0.7308405e0+/-0.556e-31 y[1] (numeric) 0.73084049503700740940171337773781105e0+/-0.1e-30 absolute error 0.496299259059828662226218895e-8+/-0.155e-30 relative error 0.679080126320077584953514337259634626e-6+/-0.212e-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] 0.1208e1+/-0.465e-31 y[1] (closed_form) 0.729632e0+/-0.561e-31 y[1] (numeric) 0.729631994973889902213577570650896703e0+/-0.1e-30 absolute error 0.5026110097786422429349103297e-8+/-0.156e-30 relative error 0.688855491232076228749438524763168282e-6+/-0.213e-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] 0.1207e1+/-0.470e-31 y[1] (closed_form) 0.7284245e0+/-0.566e-31 y[1] (numeric) 0.728424494910581784806339358203480506e0+/-0.1e-30 absolute error 0.5089418215193660641796519494e-8+/-0.156e-30 relative error 0.698688500344738629987942400893984208e-6+/-0.214e-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] 0.1206e1+/-0.475e-31 y[1] (closed_form) 0.727218e0+/-0.571e-31 y[1] (numeric) 0.727217994847082912414277373339250837e0+/-0.1e-30 absolute error 0.5152917087585722626660749163e-8+/-0.157e-30 relative error 0.708579420144402727471095209827039484e-6+/-0.215e-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] 0.1205e1+/-0.480e-31 y[1] (closed_form) 0.7260125e0+/-0.576e-31 y[1] (numeric) 0.726012494783393139724741087430156047e0+/-0.1e-30 absolute error 0.5216606860275258912569843953e-8+/-0.157e-30 relative error 0.718528518486287620746177779721423529e-6+/-0.216e-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] 0.1204e1+/-0.485e-31 y[1] (closed_form) 0.724808e0+/-0.581e-31 y[1] (numeric) 0.724807994719512320876735522615321051e0+/-0.1e-30 absolute error 0.5280487679123264477384678949e-8+/-0.158e-30 relative error 0.72853606460238635299067876582488052e-6+/-0.217e-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] 0.1203e1+/-0.490e-31 y[1] (closed_form) 0.7236045e0+/-0.586e-31 y[1] (numeric) 0.723604494655440309459499094525558167e0+/-0.1e-30 absolute error 0.5344559690540500905474441833e-8+/-0.158e-30 relative error 0.738602329109410030683120659559192901e-6+/-0.218e-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] 0.1202e1+/-0.495e-31 y[1] (closed_form) 0.722402e0+/-0.591e-31 y[1] (numeric) 0.722401994591176958511074554228667309e0+/-0.1e-30 absolute error 0.5408823041488925445771332691e-8+/-0.159e-30 relative error 0.748727584016783653114378516532346255e-6+/-0.22e-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] 0.1201e1+/-0.500e-31 y[1] (closed_form) 0.7212005e0+/-0.601e-31 y[1] (numeric) 0.721200494526722120516872998038115712e0+/-0.1e-30 absolute error 0.5473277879483127001961884288e-8+/-0.16e-30 relative error 0.758912102734694027799742829906523913e-6+/-0.221e-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] 0.12e1+/-0.505e-31 y[1] (closed_form) 0.72e0+/-0.606e-31 y[1] (numeric) 0.719999994462075647408230913633845336e0+/-0.1e-30 absolute error 0.5537924352591769086366154664e-8+/-0.16e-30 relative error 0.769156160082190150884188147777777777e-6+/-0.222e-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] 0.1199e1+/-0.510e-31 y[1] (closed_form) 0.7188005e0+/-0.611e-31 y[1] (numeric) 0.71880049439723739056096023074886761e0+/-0.1e-30 absolute error 0.560276260943903976925113239e-8+/-0.161e-30 relative error 0.779460032295336434692398292711259939e-6+/-0.223e-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] 0.1198e1+/-0.515e-31 y[1] (closed_form) 0.717602e0+/-0.616e-31 y[1] (numeric) 0.717601994332207200793891344478960546e0+/-0.1e-30 absolute error 0.5667792799206108655521039454e-8+/-0.161e-30 relative error 0.789823997035419167661327512186420885e-6+/-0.224e-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] 0.1197e1+/-0.520e-31 y[1] (closed_form) 0.7164045e0+/-0.621e-31 y[1] (numeric) 0.716404494266984928367409079075172912e0+/-0.1e-30 absolute error 0.5733015071632590920924827088e-8+/-0.162e-30 relative error 0.800248333397206595006707396170738737e-6+/-0.226e-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] 0.1196e1+/-0.525e-31 y[1] (closed_form) 0.715208e0+/-0.626e-31 y[1] (numeric) 0.71520799420157042298198155987995433e0+/-0.1e-30 absolute error 0.579842957701801844012004567e-8+/-0.162e-30 relative error 0.810733321917263011616207546615809666e-6+/-0.226e-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 Finished! Maximum Time Reached before Solution Completed! diff ( y , x , 1 ) = arccos ( cos ( x ) ) ; Iterations 105 Total Elapsed Time 3 Minutes 4 Seconds Elapsed Time(since restart) 3 Minutes 4 Seconds Expected Time Remaining 0 Seconds Optimized Time Remaining 0 Seconds Expected Total Time 3 Minutes 4 Seconds Time to Timeout 0.0 Seconds Percent Done 0.0%