##############ECHO OF PROBLEM################# ##############temp/arccos_sqrtpostode.ode################# diff ( y , x , 1 ) = arccos(sqrt(0.1 * x + 0.2)); ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.0 x_end=0.5 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=1000000 $glob_display_interval=0.1 $glob_max_minutes=10 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.01 $glob_look_poles=true $glob_max_iter=10000000 $glob_max_minutes=3 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(10.0 * (0.1 * x + 0.2) * arccos(sqrt ( 0.1 * x + 0.2)) - 5.0 * sqrt( 0.1 * x + 0.2) * sqrt( 0.8 - 0.1 * x) + 5.0 * arcsin(sqrt( 0.1 * x + 0.2))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 desired_abs_gbl_error 1.0e-10 range 0.5 estimated_steps 500000.0 step_error 2.0e-16 est_needed_step_err 2.0e-16 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.172096533994529e-168 estimated_step_error 1.172096533994529e-168 best_h 2.0e-06 opt_iter 2 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.865804904946755e-161 estimated_step_error 7.865804904946755e-161 best_h 4.0e-06 opt_iter 3 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.278649921019754e-153 estimated_step_error 5.278649921019754e-153 best_h 8.0e-06 opt_iter 4 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.5424387818267094e-145 estimated_step_error 3.5424387818267094e-145 best_h 1.6e-05 opt_iter 5 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.377286109685046e-137 estimated_step_error 2.377286109685046e-137 best_h 3.2e-05 opt_iter 6 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.59536391118642e-129 estimated_step_error 1.59536391118642e-129 best_h 6.4e-05 opt_iter 7 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.070622824928351e-121 estimated_step_error 1.070622824928351e-121 best_h 0.000128 opt_iter 8 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.184723836425154e-114 estimated_step_error 7.184723836425154e-114 best_h 0.000256 opt_iter 9 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.821446539804459e-106 estimated_step_error 4.821446539804459e-106 best_h 0.000512 opt_iter 10 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.235430101625355e-98 estimated_step_error 3.235430101625355e-98 best_h 0.001024 opt_iter 11 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.171008236243644e-90 estimated_step_error 2.171008236243644e-90 best_h 0.002048 opt_iter 12 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.4566006524607436e-82 estimated_step_error 1.4566006524607436e-82 best_h 0.004096 opt_iter 13 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.770543937362864e-75 estimated_step_error 9.770543937362864e-75 best_h 0.008192 opt_iter 14 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.550819349617228e-67 estimated_step_error 6.550819349617228e-67 best_h 0.016384 opt_iter 15 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.388040640368087e-59 estimated_step_error 4.388040640368087e-59 best_h 0.032768 opt_iter 16 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.9339006397091225e-51 estimated_step_error 2.9339006397091225e-51 best_h 0.065536 opt_iter 17 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.9544915641618e-43 estimated_step_error 1.9544915641618e-43 best_h 0.131072 opt_iter 18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.292731496281798e-35 estimated_step_error 1.292731496281798e-35 best_h 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (analytic) 2.532535480592211 y[1] (numeric) 2.532535480592211 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.243627707756313 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.01 y[1] (analytic) 2.543600721667676 y[1] (numeric) 2.543600721667675 absolute error 8.881784197001252e-16 relative error 3.49181541007664e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.2548444947098796 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.02 y[1] (analytic) 2.5546534860587964 y[1] (numeric) 2.5546534860587964 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.2660612684944903 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.03 y[1] (analytic) 2.5656937968912934 y[1] (numeric) 2.565693796891293 absolute error 4.440892098500626e-16 relative error 1.7308737714069408e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.2772780291141683 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.04 y[1] (analytic) 2.5767216770859345 y[1] (numeric) 2.576721677085934 absolute error 4.440892098500626e-16 relative error 1.7234659598637438e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.288494776572927 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.05 y[1] (analytic) 2.587737149360984 y[1] (numeric) 2.5877371493609838 absolute error 4.440892098500626e-16 relative error 1.7161295147759734e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.2997115108747788 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.060000000000000005 y[1] (analytic) 2.598740236234604 y[1] (numeric) 2.598740236234604 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.3109282320237368 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.07 y[1] (analytic) 2.6097309600272145 y[1] (numeric) 2.6097309600272145 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.322144940023807 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.08 y[1] (analytic) 2.6207093428638126 y[1] (numeric) 2.620709342863812 absolute error 4.440892098500626e-16 relative error 1.6945382022593113e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.333361634879001 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.09 y[1] (analytic) 2.631675406676253 y[1] (numeric) 2.631675406676252 absolute error 8.881784197001252e-16 relative error 3.374954287473753e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.3445783165933207 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.09999999999999999 y[1] (analytic) 2.6426291732054885 y[1] (numeric) 2.6426291732054885 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.3557949851707742 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.10999999999999999 y[1] (analytic) 2.6535706640037775 y[1] (numeric) 2.6535706640037775 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.3670116406153574 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11999999999999998 y[1] (analytic) 2.6644999004368435 y[1] (numeric) 2.664499900436844 absolute error 4.440892098500626e-16 relative error 1.666688783802373e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.378228282931078 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.12999999999999998 y[1] (analytic) 2.675416903686012 y[1] (numeric) 2.6754169036860107 absolute error 1.3322676295501878e-15 relative error 4.9796636468681865e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.389444912121931 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.13999999999999999 y[1] (analytic) 2.686321694750294 y[1] (numeric) 2.6863216947502937 absolute error 4.440892098500626e-16 relative error 1.6531497724859893e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.4006615281919172 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.15 y[1] (analytic) 2.6972142944484596 y[1] (numeric) 2.697214294448459 absolute error 4.440892098500626e-16 relative error 1.6464735885617582e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.4118781311450337 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.16 y[1] (analytic) 2.708094723421051 y[1] (numeric) 2.708094723421051 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.423094720985276 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.17 y[1] (analytic) 2.7189630021323805 y[1] (numeric) 2.7189630021323805 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.434311297716641 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18000000000000002 y[1] (analytic) 2.7298191508724856 y[1] (numeric) 2.729819150872486 absolute error 4.440892098500626e-16 relative error 1.6268081704538043e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.445527861343124 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19000000000000003 y[1] (analytic) 2.7406631897590596 y[1] (numeric) 2.7406631897590596 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.4567444118687223 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.20000000000000004 y[1] (analytic) 2.751495138739343 y[1] (numeric) 2.751495138739343 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.467960949297429 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.21000000000000005 y[1] (analytic) 2.7623150175919906 y[1] (numeric) 2.762315017591991 absolute error 4.440892098500626e-16 relative error 1.6076704033459267e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.4791774736332437 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.22000000000000006 y[1] (analytic) 2.773122845928907 y[1] (numeric) 2.7731228459289072 absolute error 4.440892098500626e-16 relative error 1.6014047502511815e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.4903939848801655 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.23000000000000007 y[1] (analytic) 2.7839186431970475 y[1] (numeric) 2.7839186431970475 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.5016104830421892 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.24000000000000007 y[1] (analytic) 2.794702428680198 y[1] (numeric) 2.7947024286801976 absolute error 4.440892098500626e-16 relative error 1.589039338473629e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.5128269681233184 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.25000000000000006 y[1] (analytic) 2.8054742215007202 y[1] (numeric) 2.80547422150072 absolute error 4.440892098500626e-16 relative error 1.5829381230689332e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.524043440127557 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.26000000000000006 y[1] (analytic) 2.816234040621273 y[1] (numeric) 2.816234040621273 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.5352598990589095 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2700000000000001 y[1] (analytic) 2.8269819048465052 y[1] (numeric) 2.8269819048465052 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.5464763449213876 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2800000000000001 y[1] (analytic) 2.8377178328247203 y[1] (numeric) 2.83771783282472 absolute error 4.440892098500626e-16 relative error 1.5649519649668885e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.5576927777190077 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2900000000000001 y[1] (analytic) 2.848441843049515 y[1] (numeric) 2.848441843049515 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.5689091974557874 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3000000000000001 y[1] (analytic) 2.8591539538613966 y[1] (numeric) 2.859153953861397 absolute error 4.440892098500626e-16 relative error 1.5532189487393752e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.580125604135755 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3100000000000001 y[1] (analytic) 2.8698541834493714 y[1] (numeric) 2.869854183449372 absolute error 4.440892098500626e-16 relative error 1.547427783652399e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.591341997762941 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3200000000000001 y[1] (analytic) 2.880542549852506 y[1] (numeric) 2.880542549852506 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.6025583783413917 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3300000000000001 y[1] (analytic) 2.8912190709614696 y[1] (numeric) 2.8912190709614696 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.613774745875156 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.34000000000000014 y[1] (analytic) 2.90188376452005 y[1] (numeric) 2.9018837645200506 absolute error 4.440892098500626e-16 relative error 1.5303480286830567e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.624991100368294 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.35000000000000014 y[1] (analytic) 2.9125366481266495 y[1] (numeric) 2.912536648126649 absolute error 4.440892098500626e-16 relative error 1.5247506332176174e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.6362074418248866 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.36000000000000015 y[1] (analytic) 2.9231777392357476 y[1] (numeric) 2.923177739235747 absolute error 4.440892098500626e-16 relative error 1.5192001631969455e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.647423770249018 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.37000000000000016 y[1] (analytic) 2.9338070551593582 y[1] (numeric) 2.9338070551593574 absolute error 8.881784197001252e-16 relative error 3.027392064308337e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.6586400856447967 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.38000000000000017 y[1] (analytic) 2.944424613068448 y[1] (numeric) 2.944424613068448 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.6698563880163455 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3900000000000002 y[1] (analytic) 2.9550304299943475 y[1] (numeric) 2.9550304299943475 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.6810726773678093 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4000000000000002 y[1] (analytic) 2.965624522830128 y[1] (numeric) 2.965624522830128 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.6922889537033576 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4100000000000002 y[1] (analytic) 2.9762069083319687 y[1] (numeric) 2.976206908331968 absolute error 4.440892098500626e-16 relative error 1.4921315067404196e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.703505217027185 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4200000000000002 y[1] (analytic) 2.9867776031204936 y[1] (numeric) 2.9867776031204945 absolute error 8.881784197001252e-16 relative error 2.973701218236616e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.714721467343514 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4300000000000002 y[1] (analytic) 2.997336623682104 y[1] (numeric) 2.997336623682104 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.7259377046566042 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4400000000000002 y[1] (analytic) 3.0078839863702678 y[1] (numeric) 3.0078839863702673 absolute error 4.440892098500626e-16 relative error 1.4764173480838355e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.7371539289707516 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.45000000000000023 y[1] (analytic) 3.018419707406812 y[1] (numeric) 3.0184197074068115 absolute error 4.440892098500626e-16 relative error 1.4712639490138667e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.748370140290292 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.46000000000000024 y[1] (analytic) 3.028943802883184 y[1] (numeric) 3.0289438028831834 absolute error 4.440892098500626e-16 relative error 1.466152027737669e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.7595863386196084 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.47000000000000025 y[1] (analytic) 3.0394562887616985 y[1] (numeric) 3.0394562887616976 absolute error 8.881784197001252e-16 relative error 2.922162174149828e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.770802523963137 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.48000000000000026 y[1] (analytic) 3.049957180876763 y[1] (numeric) 3.049957180876763 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.7820186963253746 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.49000000000000027 y[1] (analytic) 3.060446494936092 y[1] (numeric) 3.0604464949360914 absolute error 4.440892098500626e-16 relative error 1.4510601985196153e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 2.7932348557108804 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arccos(sqrt(0.1 * x + 0.2)); Iterations 50 Total Elapsed Time 0.0 Seconds Elapsed Time(since restart) 0.0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 102.00000000000004%