##############ECHO OF PROBLEM################# ##############temp/h3sinpostode.ode################# diff ( y , x , 3 ) = sin(x); ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=1.5 ## ## trouble about Pi/2 ## $array_y_init[0 + 1] = exact_soln_y(x_start) $array_y_init[1 + 1] = exact_soln_yp(x_start) $array_y_init[2 + 1] = exact_soln_ypp(x_start) $glob_look_poles=true $glob_max_iter=20 #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(1.0 + cos(x)) end def exact_soln_yp (x) return(-sin(x)) end def exact_soln_ypp (x) return(-cos(x)) 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 1.4 estimated_steps 1400000.0 step_error 7.142857142857143e-17 est_needed_step_err 7.142857142857143e-17 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.467208605532302e-183 estimated_step_error 2.467208605532302e-183 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 1.655715664606566e-175 estimated_step_error 1.655715664606566e-175 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 1.1111319694584357e-167 estimated_step_error 1.1111319694584357e-167 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 7.456680367024187e-160 estimated_step_error 7.456680367024187e-160 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 5.004093412037817e-152 estimated_step_error 5.004093412037817e-152 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 3.3581901424816246e-144 estimated_step_error 3.3581901424816246e-144 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 2.2536431215809203e-136 estimated_step_error 2.2536431215809203e-136 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 1.512394117654307e-128 estimated_step_error 1.512394117654307e-128 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 1.0149502701580557e-120 estimated_step_error 1.0149502701580557e-120 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 6.811212724408108e-113 estimated_step_error 6.811212724408108e-113 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 4.5709231343600255e-105 estimated_step_error 4.5709231343600255e-105 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 3.067488750234022e-97 estimated_step_error 3.067488750234022e-97 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 2.0585490116180908e-89 estimated_step_error 2.0585490116180908e-89 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 1.3814583197402446e-81 estimated_step_error 1.3814583197402446e-81 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 9.270668118428106e-74 estimated_step_error 9.270668118428106e-74 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 6.221249002016116e-66 estimated_step_error 6.221249002016116e-66 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 4.174750875079242e-58 estimated_step_error 4.174750875079242e-58 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 2.801274754399603e-50 estimated_step_error 2.801274754399603e-50 best_h 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (analytic) 1.9950041652780257 y[1] (numeric) 1.9950041652780257 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 0.11 y[1] (analytic) 1.9939560979566968 y[1] (numeric) 1.9939560979566968 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 0.12 y[1] (analytic) 1.9928086358538661 y[1] (numeric) 1.9928086358538661 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 0.13 y[1] (analytic) 1.991561893714788 y[1] (numeric) 1.9915618937147879 absolute error 2.220446049250313e-16 relative error 1.1149269607225692e-14% Correct digits 16 h 0.01 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] 0.14 y[1] (analytic) 1.9902159962126371 y[1] (numeric) 1.990215996212637 absolute error 2.220446049250313e-16 relative error 1.1156809378860393e-14% Correct digits 16 h 0.01 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] 0.15000000000000002 y[1] (analytic) 1.9887710779360424 y[1] (numeric) 1.988771077936042 absolute error 4.440892098500626e-16 relative error 2.2329830455445925e-14% Correct digits 16 h 0.01 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] 0.16000000000000003 y[1] (analytic) 1.9872272833756268 y[1] (numeric) 1.9872272833756266 absolute error 2.220446049250313e-16 relative error 1.1173588787884023e-14% Correct digits 16 h 0.01 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] 0.17000000000000004 y[1] (analytic) 1.9855847669095605 y[1] (numeric) 1.9855847669095603 absolute error 2.220446049250313e-16 relative error 1.118283180982648e-14% Correct digits 16 h 0.01 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] 0.18000000000000005 y[1] (analytic) 1.9838436927881213 y[1] (numeric) 1.9838436927881211 absolute error 2.220446049250313e-16 relative error 1.1192646161198656e-14% Correct digits 16 h 0.01 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] 0.19000000000000006 y[1] (analytic) 1.9820042351172704 y[1] (numeric) 1.98200423511727 absolute error 4.440892098500626e-16 relative error 2.240606765523823e-14% Correct digits 16 h 0.01 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] 0.20000000000000007 y[1] (analytic) 1.9800665778412416 y[1] (numeric) 1.9800665778412412 absolute error 4.440892098500626e-16 relative error 2.2427993827067613e-14% Correct digits 16 h 0.01 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] 0.21000000000000008 y[1] (analytic) 1.9780309147241484 y[1] (numeric) 1.9780309147241477 absolute error 6.661338147750939e-16 relative error 3.3676612929378375e-14% Correct digits 16 h 0.01 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] 0.22000000000000008 y[1] (analytic) 1.9758974493306054 y[1] (numeric) 1.975897449330605 absolute error 4.440892098500626e-16 relative error 2.2475316722561242e-14% Correct digits 16 h 0.01 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] 0.2300000000000001 y[1] (analytic) 1.9736663950053748 y[1] (numeric) 1.9736663950053743 absolute error 4.440892098500626e-16 relative error 2.2500723069202038e-14% Correct digits 16 h 0.01 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] 0.2400000000000001 y[1] (analytic) 1.9713379748520294 y[1] (numeric) 1.971337974852029 absolute error 4.440892098500626e-16 relative error 2.252729950496674e-14% Correct digits 16 h 0.01 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] 0.2500000000000001 y[1] (analytic) 1.9689124217106446 y[1] (numeric) 1.9689124217106442 absolute error 4.440892098500626e-16 relative error 2.255505145649017e-14% Correct digits 16 h 0.01 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] 0.2600000000000001 y[1] (analytic) 1.9663899781345133 y[1] (numeric) 1.9663899781345127 absolute error 6.661338147750939e-16 relative error 3.3875976900932224e-14% Correct digits 16 h 0.01 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] 0.27000000000000013 y[1] (analytic) 1.9637708963658906 y[1] (numeric) 1.96377089636589 absolute error 6.661338147750939e-16 relative error 3.392115730036665e-14% Correct digits 16 h 0.01 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] 0.28000000000000014 y[1] (analytic) 1.9610554383107708 y[1] (numeric) 1.9610554383107703 absolute error 4.440892098500626e-16 relative error 2.2645418440214808e-14% Correct digits 16 h 0.01 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] 0.29000000000000015 y[1] (analytic) 1.958243875512697 y[1] (numeric) 1.9582438755126965 absolute error 4.440892098500626e-16 relative error 2.2677931763417034e-14% Correct digits 16 h 0.01 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] 0.30000000000000016 y[1] (analytic) 1.955336489125606 y[1] (numeric) 1.9553364891256053 absolute error 6.661338147750939e-16 relative error 3.40674773104131e-14% Correct digits 16 h 0.01 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] 0.31000000000000016 y[1] (analytic) 1.9523335698857134 y[1] (numeric) 1.9523335698857127 absolute error 6.661338147750939e-16 relative error 3.411987710758302e-14% Correct digits 16 h 0.01 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] 0.3200000000000002 y[1] (analytic) 1.949235418082441 y[1] (numeric) 1.9492354180824403 absolute error 6.661338147750939e-16 relative error 3.4174107888435693e-14% Correct digits 16 h 0.01 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] 0.3300000000000002 y[1] (analytic) 1.946042343528387 y[1] (numeric) 1.9460423435283865 absolute error 4.440892098500626e-16 relative error 2.2820120606670893e-14% Correct digits 16 h 0.01 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] 0.3400000000000002 y[1] (analytic) 1.942754665528346 y[1] (numeric) 1.9427546655283456 absolute error 4.440892098500626e-16 relative error 2.285873855972902e-14% Correct digits 16 h 0.01 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] 0.3500000000000002 y[1] (analytic) 1.939372712847379 y[1] (numeric) 1.9393727128473783 absolute error 6.661338147750939e-16 relative error 3.434790075998744e-14% Correct digits 16 h 0.01 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] 0.3600000000000002 y[1] (analytic) 1.9358968236779348 y[1] (numeric) 1.9358968236779344 absolute error 4.440892098500626e-16 relative error 2.2939714783267988e-14% Correct digits 16 h 0.01 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] 0.3700000000000002 y[1] (analytic) 1.9323273456060344 y[1] (numeric) 1.932327345606034 absolute error 4.440892098500626e-16 relative error 2.2982090009743315e-14% Correct digits 16 h 0.01 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] 0.3800000000000002 y[1] (analytic) 1.92866463557651 y[1] (numeric) 1.9286646355765098 absolute error 2.220446049250313e-16 relative error 1.1512867547273633e-14% Correct digits 16 h 0.01 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] 0.39000000000000024 y[1] (analytic) 1.9249090598573129 y[1] (numeric) 1.9249090598573126 absolute error 2.220446049250313e-16 relative error 1.1535329619233583e-14% Correct digits 16 h 0.01 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] 0.40000000000000024 y[1] (analytic) 1.921060994002885 y[1] (numeric) 1.9210609940028847 absolute error 4.440892098500626e-16 relative error 2.311687193880923e-14% Correct digits 16 h 0.01 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] 0.41000000000000025 y[1] (analytic) 1.917120822816605 y[1] (numeric) 1.9171208228166048 absolute error 2.220446049250313e-16 relative error 1.1582191496872207e-14% Correct digits 16 h 0.01 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] 0.42000000000000026 y[1] (analytic) 1.9130889403123081 y[1] (numeric) 1.913088940312308 absolute error 2.220446049250313e-16 relative error 1.1606601253404505e-14% Correct digits 16 h 0.01 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] 0.43000000000000027 y[1] (analytic) 1.908965749674885 y[1] (numeric) 1.9089657496748849 absolute error 2.220446049250313e-16 relative error 1.1631670445781838e-14% Correct digits 16 h 0.01 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] 0.4400000000000003 y[1] (analytic) 1.9047516632199633 y[1] (numeric) 1.9047516632199633 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 0.4500000000000003 y[1] (analytic) 1.9004471023526768 y[1] (numeric) 1.9004471023526768 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 0.4600000000000003 y[1] (analytic) 1.896052497525525 y[1] (numeric) 1.896052497525525 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 0.4700000000000003 y[1] (analytic) 1.8915682881953289 y[1] (numeric) 1.8915682881953289 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 0.4800000000000003 y[1] (analytic) 1.8869949227792842 y[1] (numeric) 1.8869949227792842 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 0.4900000000000003 y[1] (analytic) 1.8823328586101213 y[1] (numeric) 1.8823328586101216 absolute error 2.220446049250313e-16 relative error 1.1796245489173727e-14% Correct digits 16 h 0.01 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] 0.5000000000000003 y[1] (analytic) 1.8775825618903725 y[1] (numeric) 1.8775825618903728 absolute error 2.220446049250313e-16 relative error 1.1826090070919393e-14% Correct digits 16 h 0.01 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] 0.5100000000000003 y[1] (analytic) 1.8727445076457512 y[1] (numeric) 1.8727445076457514 absolute error 2.220446049250313e-16 relative error 1.18566416304254e-14% Correct digits 16 h 0.01 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] 0.5200000000000004 y[1] (analytic) 1.8678191796776498 y[1] (numeric) 1.86781917967765 absolute error 2.220446049250313e-16 relative error 1.1887906888468294e-14% Correct digits 16 h 0.01 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] 0.5300000000000004 y[1] (analytic) 1.8628070705147608 y[1] (numeric) 1.862807070514761 absolute error 2.220446049250313e-16 relative error 1.1919892748940038e-14% Correct digits 16 h 0.01 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] 0.5400000000000004 y[1] (analytic) 1.857708681363824 y[1] (numeric) 1.8577086813638242 absolute error 2.220446049250313e-16 relative error 1.1952606302190438e-14% Correct digits 16 h 0.01 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] 0.5500000000000004 y[1] (analytic) 1.8525245220595057 y[1] (numeric) 1.8525245220595057 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 0.5600000000000004 y[1] (analytic) 1.8472551110134159 y[1] (numeric) 1.847255111013416 absolute error 2.220446049250313e-16 relative error 1.20202458015242e-14% Correct digits 16 h 0.01 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] 0.5700000000000004 y[1] (analytic) 1.8419009751622686 y[1] (numeric) 1.8419009751622688 absolute error 2.220446049250313e-16 relative error 1.2055186892198128e-14% Correct digits 16 h 0.01 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] 0.5800000000000004 y[1] (analytic) 1.8364626499151866 y[1] (numeric) 1.836462649915187 absolute error 4.440892098500626e-16 relative error 2.418177194458989e-14% Correct digits 16 h 0.01 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] 0.5900000000000004 y[1] (analytic) 1.8309406791001632 y[1] (numeric) 1.8309406791001637 absolute error 4.440892098500626e-16 relative error 2.4254702236902364e-14% Correct digits 16 h 0.01 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] 0.6000000000000004 y[1] (analytic) 1.8253356149096782 y[1] (numeric) 1.8253356149096784 absolute error 2.220446049250313e-16 relative error 1.2164590616176554e-14% Correct digits 16 h 0.01 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] 0.6100000000000004 y[1] (analytic) 1.8196480178454792 y[1] (numeric) 1.8196480178454797 absolute error 4.440892098500626e-16 relative error 2.440522592802746e-14% Correct digits 16 h 0.01 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] 0.6200000000000004 y[1] (analytic) 1.8138784566625337 y[1] (numeric) 1.8138784566625341 absolute error 4.440892098500626e-16 relative error 2.4482853755657347e-14% Correct digits 16 h 0.01 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] 0.6300000000000004 y[1] (analytic) 1.8080275083121515 y[1] (numeric) 1.808027508312152 absolute error 4.440892098500626e-16 relative error 2.4562082590470837e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.124065126337456 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] 0.6400000000000005 y[1] (analytic) 1.8020957578842922 y[1] (numeric) 1.8020957578842927 absolute error 4.440892098500626e-16 relative error 2.4642930760318475e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.401788799977366 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] 0.6500000000000005 y[1] (analytic) 1.7960837985490556 y[1] (numeric) 1.7960837985490559 absolute error 2.220446049250313e-16 relative error 1.2362708527542386e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.683679184406184 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] 0.6600000000000005 y[1] (analytic) 1.7899922314973646 y[1] (numeric) 1.789992231497365 absolute error 4.440892098500626e-16 relative error 2.480956073639342e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.969888431185957 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] 0.6700000000000005 y[1] (analytic) 1.783821665880849 y[1] (numeric) 1.7838216658808492 absolute error 2.220446049250313e-16 relative error 1.2447690773807591e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.260575145108636 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] 0.6800000000000005 y[1] (analytic) 1.7775727187509276 y[1] (numeric) 1.7775727187509278 absolute error 2.220446049250313e-16 relative error 1.2491449862093888e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.555904752566185 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] 0.6900000000000005 y[1] (analytic) 1.7712460149971063 y[1] (numeric) 1.7712460149971065 absolute error 2.220446049250313e-16 relative error 1.2536068002128663e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.856049894842467 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] 0.7000000000000005 y[1] (analytic) 1.7648421872844882 y[1] (numeric) 1.7648421872844884 absolute error 2.220446049250313e-16 relative error 1.2581555819825735e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.161190848335446 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] 0.7100000000000005 y[1] (analytic) 1.758361875990508 y[1] (numeric) 1.7583618759905082 absolute error 2.220446049250313e-16 relative error 1.262792420359721e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.471515973904948 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] 0.7200000000000005 y[1] (analytic) 1.7518057291408946 y[1] (numeric) 1.751805729140895 absolute error 4.440892098500626e-16 relative error 2.5350368620374873e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.787222197747035 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] 0.7300000000000005 y[1] (analytic) 1.7451744023448699 y[1] (numeric) 1.7451744023448705 absolute error 6.661338147750939e-16 relative error 3.817004271206683e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 16.10851552642468 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] 0.7400000000000005 y[1] (analytic) 1.7384685587295876 y[1] (numeric) 1.738468558729588 absolute error 4.440892098500626e-16 relative error 2.5544851393492416e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 16.435611598937435 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] 0.7500000000000006 y[1] (analytic) 1.7316888688738206 y[1] (numeric) 1.731688868873821 absolute error 4.440892098500626e-16 relative error 2.5644861373906605e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 16.76873627899332 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] 0.7600000000000006 y[1] (analytic) 1.7248360107409049 y[1] (numeric) 1.7248360107409053 absolute error 4.440892098500626e-16 relative error 2.574674966690333e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 17.10812629095848 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] 0.7700000000000006 y[1] (analytic) 1.717910669610943 y[1] (numeric) 1.7179106696109434 absolute error 4.440892098500626e-16 relative error 2.5850541457469147e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 17.45402990330683 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] 0.7800000000000006 y[1] (analytic) 1.710913538012277 y[1] (numeric) 1.7109135380122773 absolute error 2.220446049250313e-16 relative error 1.2978131272665046e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 17.18453550076764 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] 0.7900000000000006 y[1] (analytic) 1.7038453156522357 y[1] (numeric) 1.703845315652236 absolute error 2.220446049250313e-16 relative error 1.3031969679714272e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 16.844253177528415 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] 0.8000000000000006 y[1] (analytic) 1.6967067093471648 y[1] (numeric) 1.6967067093471653 absolute error 4.440892098500626e-16 relative error 2.6173598972855662e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 16.51064821105805 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] 0.8100000000000006 y[1] (analytic) 1.6894984329517466 y[1] (numeric) 1.6894984329517468 absolute error 2.220446049250313e-16 relative error 1.3142634559127353e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 16.183461167005973 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] 0.8200000000000006 y[1] (analytic) 1.682221207287613 y[1] (numeric) 1.6822212072876135 absolute error 4.440892098500626e-16 relative error 2.6398978203711096e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.862445017598638 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] 0.8300000000000006 y[1] (analytic) 1.6748757600712665 y[1] (numeric) 1.674875760071267 absolute error 4.440892098500626e-16 relative error 2.6514755329145518e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.54736438966476 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] 0.8400000000000006 y[1] (analytic) 1.6674628258413078 y[1] (numeric) 1.667462825841308 absolute error 2.220446049250313e-16 relative error 1.3316315151613657e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 15.237994866247167 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] 0.8500000000000006 y[1] (analytic) 1.6599831458849816 y[1] (numeric) 1.659983145884982 absolute error 4.440892098500626e-16 relative error 2.675263366082592e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.93412233738417 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] 0.8600000000000007 y[1] (analytic) 1.6524374681640515 y[1] (numeric) 1.6524374681640517 absolute error 2.220446049250313e-16 relative error 1.3437398340509371e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.63554239605508 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] 0.8700000000000007 y[1] (analytic) 1.6448265472400005 y[1] (numeric) 1.644826547240001 absolute error 4.440892098500626e-16 relative error 2.6999151405674904e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.34205977565155 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] 0.8800000000000007 y[1] (analytic) 1.6371511441985795 y[1] (numeric) 1.63715114419858 absolute error 4.440892098500626e-16 relative error 2.7125730658634683e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 14.053487825668238 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] 0.8900000000000007 y[1] (analytic) 1.6294120265736964 y[1] (numeric) 1.6294120265736967 absolute error 2.220446049250313e-16 relative error 1.362728403275281e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.769648022602286 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] 0.9000000000000007 y[1] (analytic) 1.621609968270664 y[1] (numeric) 1.6216099682706642 absolute error 2.220446049250313e-16 relative error 1.3692849037048451e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.490369513319372 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] 0.9100000000000007 y[1] (analytic) 1.613745749488811 y[1] (numeric) 1.6137457494888112 absolute error 2.220446049250313e-16 relative error 1.3759577987757289e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 13.215488688384472 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] 0.9200000000000007 y[1] (analytic) 1.6058201566434622 y[1] (numeric) 1.6058201566434624 absolute error 2.220446049250313e-16 relative error 1.382748896297056e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 12.944848783073242 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] 0.9300000000000007 y[1] (analytic) 1.5978339822872978 y[1] (numeric) 1.5978339822872978 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 12.678299503975994 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] 0.9400000000000007 y[1] (analytic) 1.5897880250310976 y[1] (numeric) 1.5897880250310978 absolute error 2.220446049250313e-16 relative error 1.396693152979863e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 12.415696679283977 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] 0.9500000000000007 y[1] (analytic) 1.581683089463883 y[1] (numeric) 1.5816830894638831 absolute error 2.220446049250313e-16 relative error 1.4038501543333445e-14% Correct digits 16 h 0.01 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] 0.9600000000000007 y[1] (analytic) 1.573519986072456 y[1] (numeric) 1.5735199860724562 absolute error 2.220446049250313e-16 relative error 1.4111330449590286e-14% Correct digits 16 h 0.01 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] 0.9700000000000008 y[1] (analytic) 1.5652995311603537 y[1] (numeric) 1.565299531160354 absolute error 2.220446049250313e-16 relative error 1.4185438665558792e-14% Correct digits 16 h 0.01 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] 0.9800000000000008 y[1] (analytic) 1.5570225467662167 y[1] (numeric) 1.5570225467662169 absolute error 2.220446049250313e-16 relative error 1.426084711401233e-14% Correct digits 16 h 0.01 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] 0.9900000000000008 y[1] (analytic) 1.5486898605815869 y[1] (numeric) 1.548689860581587 absolute error 2.220446049250313e-16 relative error 1.4337577237165215e-14% Correct digits 16 h 0.01 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] 1.0000000000000007 y[1] (analytic) 1.5403023058681393 y[1] (numeric) 1.5403023058681393 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 1.0100000000000007 y[1] (analytic) 1.531860721374355 y[1] (numeric) 1.5318607213743551 absolute error 2.220446049250313e-16 relative error 1.449509095877968e-14% Correct digits 16 h 0.01 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] 1.0200000000000007 y[1] (analytic) 1.523365951251649 y[1] (numeric) 1.5233659512516493 absolute error 2.220446049250313e-16 relative error 1.4575920168268952e-14% Correct digits 16 h 0.01 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] 1.0300000000000007 y[1] (analytic) 1.514818844969955 y[1] (numeric) 1.5148188449699551 absolute error 2.220446049250313e-16 relative error 1.465816230517223e-14% Correct digits 16 h 0.01 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] 1.0400000000000007 y[1] (analytic) 1.5062202572327776 y[1] (numeric) 1.506220257232778 absolute error 4.440892098500626e-16 relative error 2.948368326063691e-14% Correct digits 16 h 0.01 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] 1.0500000000000007 y[1] (analytic) 1.4975710478917263 y[1] (numeric) 1.4975710478917266 absolute error 2.220446049250313e-16 relative error 1.4826983016106292e-14% Correct digits 16 h 0.01 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] 1.0600000000000007 y[1] (analytic) 1.488872081860527 y[1] (numeric) 1.4888720818605272 absolute error 2.220446049250313e-16 relative error 1.4913611963732943e-14% Correct digits 16 h 0.01 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] 1.0700000000000007 y[1] (analytic) 1.4801242290285335 y[1] (numeric) 1.4801242290285337 absolute error 2.220446049250313e-16 relative error 1.500175462101369e-14% Correct digits 16 h 0.01 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] 1.0800000000000007 y[1] (analytic) 1.4713283641737394 y[1] (numeric) 1.4713283641737396 absolute error 2.220446049250313e-16 relative error 1.509143780081518e-14% Correct digits 16 h 0.01 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] 1.0900000000000007 y[1] (analytic) 1.4624853668753002 y[1] (numeric) 1.4624853668753004 absolute error 2.220446049250313e-16 relative error 1.5182689000126186e-14% Correct digits 16 h 0.01 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] 1.1000000000000008 y[1] (analytic) 1.4535961214255768 y[1] (numeric) 1.4535961214255768 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 1.1100000000000008 y[1] (analytic) 1.4446615167417063 y[1] (numeric) 1.4446615167417063 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 1.1200000000000008 y[1] (analytic) 1.4356824462767115 y[1] (numeric) 1.4356824462767115 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 1.1300000000000008 y[1] (analytic) 1.4266598079301567 y[1] (numeric) 1.4266598079301567 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 1.1400000000000008 y[1] (analytic) 1.4175945039583575 y[1] (numeric) 1.4175945039583575 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 1.1500000000000008 y[1] (analytic) 1.4084874408841566 y[1] (numeric) 1.4084874408841568 absolute error 2.220446049250313e-16 relative error 1.576475575711532e-14% Correct digits 16 h 0.01 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] 1.1600000000000008 y[1] (analytic) 1.3993395294062725 y[1] (numeric) 1.3993395294062727 absolute error 2.220446049250313e-16 relative error 1.5867814798260068e-14% Correct digits 16 h 0.01 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] 1.1700000000000008 y[1] (analytic) 1.3901516843082296 y[1] (numeric) 1.3901516843082298 absolute error 2.220446049250313e-16 relative error 1.5972688982895103e-14% Correct digits 16 h 0.01 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] 1.1800000000000008 y[1] (analytic) 1.380924824366881 y[1] (numeric) 1.3809248243668812 absolute error 2.220446049250313e-16 relative error 1.6079412941745987e-14% Correct digits 16 h 0.01 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] 1.1900000000000008 y[1] (analytic) 1.3716598722605322 y[1] (numeric) 1.3716598722605324 absolute error 2.220446049250313e-16 relative error 1.6188022221507132e-14% Correct digits 16 h 0.01 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] 1.2000000000000008 y[1] (analytic) 1.3623577544766727 y[1] (numeric) 1.362357754476673 absolute error 2.220446049250313e-16 relative error 1.6298553312843005e-14% Correct digits 16 h 0.01 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] 1.2100000000000009 y[1] (analytic) 1.3530194012193295 y[1] (numeric) 1.3530194012193297 absolute error 2.220446049250313e-16 relative error 1.6411043679412625e-14% Correct digits 16 h 0.01 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] 1.2200000000000009 y[1] (analytic) 1.3436457463160463 y[1] (numeric) 1.3436457463160465 absolute error 2.220446049250313e-16 relative error 1.652553178796005e-14% Correct digits 16 h 0.01 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] 1.2300000000000009 y[1] (analytic) 1.3342377271245018 y[1] (numeric) 1.334237727124502 absolute error 2.220446049250313e-16 relative error 1.664205713951541e-14% Correct digits 16 h 0.01 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] 1.2400000000000009 y[1] (analytic) 1.3247962844387753 y[1] (numeric) 1.3247962844387757 absolute error 4.440892098500626e-16 relative error 3.352132060350641e-14% Correct digits 16 h 0.01 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] 1.2500000000000009 y[1] (analytic) 1.315322362395268 y[1] (numeric) 1.3153223623952681 absolute error 2.220446049250313e-16 relative error 1.6881382942556907e-14% Correct digits 16 h 0.01 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] 1.260000000000001 y[1] (analytic) 1.3058169083782885 y[1] (numeric) 1.3058169083782887 absolute error 2.220446049250313e-16 relative error 1.7004267864841134e-14% Correct digits 16 h 0.01 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] 1.270000000000001 y[1] (analytic) 1.296280872925318 y[1] (numeric) 1.2962808729253181 absolute error 2.220446049250313e-16 relative error 1.712935904268518e-14% Correct digits 16 h 0.01 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] 1.280000000000001 y[1] (analytic) 1.2867152096319545 y[1] (numeric) 1.286715209631955 absolute error 4.440892098500626e-16 relative error 3.451340331766869e-14% Correct digits 16 h 0.01 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] 1.290000000000001 y[1] (analytic) 1.2771208750565568 y[1] (numeric) 1.277120875056557 absolute error 2.220446049250313e-16 relative error 1.7386342143628193e-14% Correct digits 16 h 0.01 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] 1.300000000000001 y[1] (analytic) 1.2674988286245865 y[1] (numeric) 1.2674988286245867 absolute error 2.220446049250313e-16 relative error 1.751832821541782e-14% Correct digits 16 h 0.01 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] 1.310000000000001 y[1] (analytic) 1.2578500325326687 y[1] (numeric) 1.257850032532669 absolute error 2.220446049250313e-16 relative error 1.7652708922537186e-14% Correct digits 16 h 0.01 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] 1.320000000000001 y[1] (analytic) 1.248175451652372 y[1] (numeric) 1.2481754516523722 absolute error 2.220446049250313e-16 relative error 1.7789534686896946e-14% Correct digits 16 h 0.01 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] 1.330000000000001 y[1] (analytic) 1.2384760534337222 y[1] (numeric) 1.2384760534337225 absolute error 2.220446049250313e-16 relative error 1.792885734927245e-14% Correct digits 16 h 0.01 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] 1.340000000000001 y[1] (analytic) 1.2287528078084584 y[1] (numeric) 1.2287528078084586 absolute error 2.220446049250313e-16 relative error 1.8070730216361325e-14% Correct digits 16 h 0.01 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] 1.350000000000001 y[1] (analytic) 1.2190066870930407 y[1] (numeric) 1.2190066870930407 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 1.360000000000001 y[1] (analytic) 1.2092386658914185 y[1] (numeric) 1.2092386658914185 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 1.370000000000001 y[1] (analytic) 1.199449720997572 y[1] (numeric) 1.199449720997572 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 1.380000000000001 y[1] (analytic) 1.1896408312978335 y[1] (numeric) 1.1896408312978335 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 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] 1.390000000000001 y[1] (analytic) 1.1798129776729984 y[1] (numeric) 1.1798129776729986 absolute error 2.220446049250313e-16 relative error 1.8820322299130875e-14% Correct digits 16 h 0.01 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] 1.400000000000001 y[1] (analytic) 1.1699671429002398 y[1] (numeric) 1.16996714290024 absolute error 2.220446049250313e-16 relative error 1.8978704339901662e-14% Correct digits 16 h 0.01 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] 1.410000000000001 y[1] (analytic) 1.1601043115548302 y[1] (numeric) 1.1601043115548304 absolute error 2.220446049250313e-16 relative error 1.9140055141027445e-14% Correct digits 16 h 0.01 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] 1.420000000000001 y[1] (analytic) 1.1502254699116847 y[1] (numeric) 1.150225469911685 absolute error 2.220446049250313e-16 relative error 1.9304441671082113e-14% Correct digits 16 h 0.01 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] 1.430000000000001 y[1] (analytic) 1.1403316058467357 y[1] (numeric) 1.1403316058467359 absolute error 2.220446049250313e-16 relative error 1.947193288220364e-14% Correct digits 16 h 0.01 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] 1.440000000000001 y[1] (analytic) 1.1304237087381444 y[1] (numeric) 1.1304237087381448 absolute error 4.440892098500626e-16 relative error 3.9285199559887605e-14% Correct digits 16 h 0.01 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] 1.450000000000001 y[1] (analytic) 1.1205027693673655 y[1] (numeric) 1.120502769367366 absolute error 4.440892098500626e-16 relative error 3.9633030992042515e-14% Correct digits 16 h 0.01 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] 1.460000000000001 y[1] (analytic) 1.1105697798200684 y[1] (numeric) 1.1105697798200689 absolute error 4.440892098500626e-16 relative error 3.998751072823292e-14% Correct digits 16 h 0.01 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] 1.470000000000001 y[1] (analytic) 1.1006257333869307 y[1] (numeric) 1.100625733386931 absolute error 2.220446049250313e-16 relative error 2.017439699885432e-14% Correct digits 16 h 0.01 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] 1.480000000000001 y[1] (analytic) 1.0906716244643087 y[1] (numeric) 1.0906716244643089 absolute error 2.220446049250313e-16 relative error 2.035852037812849e-14% Correct digits 16 h 0.01 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] 1.490000000000001 y[1] (analytic) 1.0807084484547995 y[1] (numeric) 1.0807084484547997 absolute error 2.220446049250313e-16 relative error 2.054620792892953e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 3 ) = sin(x); Iterations 140 Total Elapsed Time 0.0 Seconds Elapsed Time(since restart) 0.0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.71428571428581%