##############ECHO OF PROBLEM################# ##############temp/add_sin_cpostode.ode################# diff ( y , x , 1 ) = sin ( x ) + 1.0 ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-5.0 x_end=5.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=3 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=16 $glob_max_minutes=3.0 $glob_subiter_method=3 $glob_max_iter=100000000 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(2.0 - cos(x) + 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 16 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 10.0 estimated_steps 10000000.0 step_error 7.905694150420948e-22 est_needed_step_err 7.905694150420948e-22 opt_iter 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 3.283662185463226 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 3.283662185463226 desired_abs_gbl_error 3.283662185463226e-16 range 10.0 estimated_steps 10000000.0 step_error 2.595962893157509e-21 est_needed_step_err 2.595962893157509e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.625464009062711e-259 estimated_step_error 7.625464009062711e-259 Double H and LOOP opt_iter 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 3.283662185463226 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 3.283662185463226 desired_abs_gbl_error 3.283662185463226e-16 range 10.0 estimated_steps 5000000.0 step_error 3.6712459309206475e-21 est_needed_step_err 3.6712459309206475e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.240178726334705e-248 estimated_step_error 5.240178726334705e-248 Double H and LOOP opt_iter 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 3.283662185463226 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 3.283662185463226 desired_abs_gbl_error 3.283662185463226e-16 range 10.0 estimated_steps 2500000.0 step_error 5.191925786315018e-21 est_needed_step_err 5.191925786315018e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.601023071759884e-237 estimated_step_error 3.601023071759884e-237 Double H and LOOP opt_iter 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 3.283662185463226 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 3.283662185463226 desired_abs_gbl_error 3.283662185463226e-16 range 10.0 estimated_steps 1250000.0 step_error 7.342491861841295e-21 est_needed_step_err 7.342491861841295e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.4746037598701562e-226 estimated_step_error 2.4746037598701562e-226 Double H and LOOP opt_iter 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 3.283662185463226 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 3.283662185463226 desired_abs_gbl_error 3.283662185463226e-16 range 10.0 estimated_steps 625000.0 step_error 1.0383851572630036e-20 est_needed_step_err 1.0383851572630036e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.7005341335925973e-215 estimated_step_error 1.7005341335925973e-215 Double H and LOOP opt_iter 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 3.283662185463226 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 3.283662185463226 desired_abs_gbl_error 3.283662185463226e-16 range 10.0 estimated_steps 312500.0 step_error 1.468498372368259e-20 est_needed_step_err 1.468498372368259e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1685973041668257e-204 estimated_step_error 1.1685973041668257e-204 Double H and LOOP opt_iter 7 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 3.283662185463226 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 3.283662185463226 desired_abs_gbl_error 3.283662185463226e-16 range 10.0 estimated_steps 156250.0 step_error 2.0767703145260073e-20 est_needed_step_err 2.0767703145260073e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.030527786324255e-194 estimated_step_error 8.030527786324255e-194 Double H and LOOP opt_iter 8 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size 3.283662185463226 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 3.283662185463226 desired_abs_gbl_error 3.283662185463226e-16 range 10.0 estimated_steps 78125.0 step_error 2.936996744736518e-20 est_needed_step_err 2.936996744736518e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.518520539358821e-183 estimated_step_error 5.518520539358821e-183 Double H and LOOP opt_iter 9 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.27201055544472436 Order of pole (three term test) 32.9195357645382 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] -5.0 y[1] (closed_form) -3.283662185463226 y[1] (numeric) -3.283662185463226 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -4.8999039999999 y[1] (closed_form) -3.086322053112261 y[1] (numeric) -3.086322053112453 absolute error 1.9229062786507711e-13 relative error 6.23041356527166e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -4.7999359999998 y[1] (closed_form) -2.8873712287249274 y[1] (numeric) -2.8873712287253213 absolute error 3.9390712913700554e-13 relative error 1.3642413736696968e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -4.6999679999997 y[1] (closed_form) -2.6875473389986158 y[1] (numeric) -2.6875473389992077 absolute error 5.919709167301335e-13 relative error 2.2026436823646898e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -4.5999999999996 y[1] (closed_form) -2.4878474730641478 y[1] (numeric) -2.4878474730649422 absolute error 7.94475596421762e-13 relative error 3.193425662238245e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -4.4999039999995 y[1] (closed_form) -2.2890143586484264 y[1] (numeric) -2.2890143586494234 absolute error 9.969802761133906e-13 relative error 4.3555003154373765e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -4.3999359999994 y[1] (closed_form) -2.0925422281171393 y[1] (numeric) -2.092542228118335 absolute error 1.1954881529163686e-12 relative error 5.713089737701799e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -4.2999679999993 y[1] (closed_form) -1.8991395108139213 y[1] (numeric) -1.8991395108153124 absolute error 1.3911094498553211e-12 relative error 7.324946071282189e-11% Desired digits 16 Estimated correct digits 12 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -4.1999999999992 y[1] (closed_form) -1.7097391786578031 y[1] (numeric) -1.709739178659386 absolute error 1.5829559885105482e-12 relative error 9.258464731171548e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -4.0999039999991 y[1] (closed_form) -1.5250015015113414 y[1] (numeric) -1.5250015015131086 absolute error 1.7672530105983242e-12 relative error 1.1588532921750577e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -3.999935999999 y[1] (closed_form) -1.3462439451136268 y[1] (numeric) -1.34624394511557 absolute error 1.943334382303874e-12 relative error 1.443523210899085e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -3.8999679999989 y[1] (closed_form) -1.1740136876525904 y[1] (numeric) -1.174013687654707 absolute error 2.1165291741453984e-12 relative error 1.8028147341087164e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -3.7999999999988 y[1] (closed_form) -1.0090322880836489 y[1] (numeric) -1.0090322880859295 absolute error 2.2806201371849966e-12 relative error 2.2602053116816943e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -3.6999039999987 y[1] (closed_form) -0.8517531079261986 y[1] (numeric) -0.8517531079286369 absolute error 2.4382718066817688e-12 relative error 2.862650906690952e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -3.5999359999986 y[1] (closed_form) -0.7031492641920432 y[1] (numeric) -0.703149264194628 absolute error 2.5848212459322895e-12 relative error 3.6760633588977585e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -3.4999679999985 y[1] (closed_form) -0.5635000881233587 y[1] (numeric) -0.5635000881260834 absolute error 2.724709347035059e-12 relative error 4.835330826849097e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -3.3999999999984 y[1] (closed_form) -0.43320180741852976 y[1] (numeric) -0.4332018074213846 absolute error 2.8548274855211275e-12 relative error 6.590063653088571e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -3.2999039999982998 y[1] (closed_form) -0.3124090910528592 y[1] (numeric) -0.312409091055835 absolute error 2.9757862840540383e-12 relative error 9.525287097200828e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -3.1999359999981998 y[1] (closed_form) -0.20163749030267253 y[1] (numeric) -0.20163749030575967 absolute error 3.0871416534239415e-12 relative error 1.5310355474023792e-09% Desired digits 16 Estimated correct digits 10 Correct digits 11 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -3.0999679999981 y[1] (closed_form) -0.10083418081765405 y[1] (numeric) -0.10083418082084192 absolute error 3.187866637333059e-12 relative error 3.1614940603305094e-09% Desired digits 16 Estimated correct digits 10 Correct digits 11 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.999999999998 y[1] (closed_form) -0.010007503397836626 y[1] (numeric) -0.010007503401115092 absolute error 3.2784660403128996e-12 relative error 3.276007921238001e-08% Desired digits 16 Estimated correct digits 9 Correct digits 10 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.8999039999978997 y[1] (closed_form) 0.07103119274144376 y[1] (numeric) 0.0710311927380841 absolute error 3.359659772605994e-12 relative error 4.729837192563109e-09% Desired digits 16 Estimated correct digits 10 Correct digits 11 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.7999359999977997 y[1] (closed_form) 0.14226489949885446 y[1] (numeric) 0.1422648994954237 absolute error 3.4307556795454275e-12 relative error 2.4115264493425187e-09% Desired digits 16 Estimated correct digits 10 Correct digits 11 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.6999679999976998 y[1] (closed_form) 0.2040904653993283 y[1] (numeric) 0.20409046539583536 absolute error 3.4929281689244362e-12 relative error 1.7114607299709417e-09% Desired digits 16 Estimated correct digits 10 Correct digits 11 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.5999999999976 y[1] (closed_form) 0.2568887533701103 y[1] (numeric) 0.25688875336656486 absolute error 3.545441717989206e-12 relative error 1.3801467255676784e-09% Desired digits 16 Estimated correct digits 10 Correct digits 11 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.4999039999974997 y[1] (closed_form) 0.3011821585305219 y[1] (numeric) 0.3011821585269312 absolute error 3.5906833062426813e-12 relative error 1.1921965510047968e-09% Desired digits 16 Estimated correct digits 10 Correct digits 11 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.3999359999973997 y[1] (closed_form) 0.3374144843883813 y[1] (numeric) 0.33741448438475385 absolute error 3.627431688357774e-12 relative error 1.0750669743573946e-09% Desired digits 16 Estimated correct digits 10 Correct digits 11 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.2999679999972997 y[1] (closed_form) 0.36628415837259176 y[1] (numeric) 0.3662841583689356 absolute error 3.6561864646955655e-12 relative error 9.981830721099376e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.1999999999971998 y[1] (closed_form) 0.3885011172558821 y[1] (numeric) 0.3885011172522034 absolute error 3.678723992095456e-12 relative error 9.469017793512559e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -2.0999039999970996 y[1] (closed_form) 0.40485923417485203 y[1] (numeric) 0.4048592341711577 absolute error 3.69432262559144e-12 relative error 9.124955821054393e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.999935999997 y[1] (closed_form) 0.41615264065986834 y[1] (numeric) 0.4161526406561625 absolute error 3.705868945047541e-12 relative error 8.905071319916093e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.8999679999970733 y[1] (closed_form) 0.42329128509533565 y[1] (numeric) 0.4232912850916347 absolute error 3.700928452587959e-12 relative error 8.743219109163608e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.7999999999971468 y[1] (closed_form) 0.42720209469316184 y[1] (numeric) 0.42720209468946413 absolute error 3.697708805816546e-12 relative error 8.655642965590859e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.6999039999972203 y[1] (closed_form) 0.428845293880175 y[1] (numeric) 0.4288452938764792 absolute error 3.695821426674684e-12 relative error 8.618076214000251e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.5999359999972937 y[1] (closed_form) 0.4291995495309382 y[1] (numeric) 0.42919954952724304 absolute error 3.6951552928599085e-12 relative error 8.609410929946815e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.4999679999973672 y[1] (closed_form) 0.42926287852895517 y[1] (numeric) 0.42926287852525924 absolute error 3.695932448977146e-12 relative error 8.60995122998469e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.3999999999974406 y[1] (closed_form) 0.4300328570997962 y[1] (numeric) 0.4300328570961005 absolute error 3.695710404372221e-12 relative error 8.594018674053481e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.2999039999975142 y[1] (closed_form) 0.4325046710224798 y[1] (numeric) 0.4325046710187866 absolute error 3.6932124025668145e-12 relative error 8.539127204882503e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.1999359999975876 y[1] (closed_form) 0.437646595764138 y[1] (numeric) 0.43764659576044773 absolute error 3.690270311551558e-12 relative error 8.432078181959319e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -1.099967999997661 y[1] (closed_form) 0.44640736017140115 y[1] (numeric) 0.4464073601677173 absolute error 3.683831018008732e-12 relative error 8.252173567645255e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9999999999977344 y[1] (closed_form) 0.4596976941322194 y[1] (numeric) 0.4596976941285449 absolute error 3.674505144601881e-12 relative error 7.993307757478136e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8999039999977211 y[1] (closed_form) 0.47841083521099936 y[1] (numeric) 0.4784108352073221 absolute error 3.6772807021634435e-12 relative error 7.686449452052246e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7999359999977078 y[1] (closed_form) 0.5033113812905516 y[1] (numeric) 0.5033113812868707 absolute error 3.6809444381447065e-12 relative error 7.313453609386533e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.6999679999976945 y[1] (closed_form) 0.535169198141943 y[1] (numeric) 0.535169198138257 absolute error 3.68594044175552e-12 relative error 6.887430096038332e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.5999999999976813 y[1] (closed_form) 0.5746643850913313 y[1] (numeric) 0.5746643850876386 absolute error 3.692712802205733e-12 relative error 6.425859854911403e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.499903999997668 y[1] (closed_form) 0.6224674173031066 y[1] (numeric) 0.6224674172994067 absolute error 3.699929251865797e-12 relative error 5.943972566300831e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.3999359999976547 y[1] (closed_form) 0.6789780851109891 y[1] (numeric) 0.6789780851072811 absolute error 3.70803387994556e-12 relative error 5.461198175990359e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.29996799999764145 y[1] (closed_form) 0.7446860547185763 y[1] (numeric) 0.7446860547148599 absolute error 3.716360552630249e-12 relative error 4.99050644104608e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.19999999999763904 y[1] (closed_form) 0.8199334221606501 y[1] (numeric) 0.8199334221569327 absolute error 3.717470775654874e-12 relative error 4.533869062025511e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.09990399999764472 y[1] (closed_form) 0.9050822553010904 y[1] (numeric) 0.9050822552973781 absolute error 3.7123637497415984e-12 relative error 4.1016865903603646e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 6.400000235686883e-05 y[1] (closed_form) 1.0000640020503568 y[1] (numeric) 1.0000640020466431 absolute error 3.713696017371149e-12 relative error 3.713458348422935e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.10003200000235847 y[1] (closed_form) 1.1050310299033426 y[1] (numeric) 1.1050310298996247 absolute error 3.717914864864724e-12 relative error 3.3645343562795076e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.20000000000235277 y[1] (closed_form) 1.2199334221615785 y[1] (numeric) 1.219933422157868 absolute error 3.710587392902198e-12 relative error 3.0416310640358337e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3000960000023552 y[1] (closed_form) 1.344787885219432 y[1] (numeric) 1.344787885215721 absolute error 3.711031482112048e-12 relative error 2.759566414079133e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.40006400000236847 y[1] (closed_form) 1.4790279306606295 y[1] (numeric) 1.4790279306569003 absolute error 3.729239139715901e-12 relative error 2.521412248144754e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5000320000023817 y[1] (closed_form) 1.6224647801797059 y[1] (numeric) 1.6224647801759584 absolute error 3.747446797319753e-12 relative error 2.3097245888472738e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.600000000002395 y[1] (closed_form) 1.774664385094069 y[1] (numeric) 1.7746643850903008 absolute error 3.768318990182706e-12 relative error 2.1233981037958116e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7000960000024082 y[1] (closed_form) 1.9353156611417441 y[1] (numeric) 1.935315661137954 absolute error 3.790079361465359e-12 relative error 1.9583778695974553e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8000640000024215 y[1] (closed_form) 2.103403202873635 y[1] (numeric) 2.103403202869822 absolute error 3.812949955772638e-12 relative error 1.8127527573236781e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9000320000024348 y[1] (closed_form) 2.2784470985130456 y[1] (numeric) 2.278447098509203 absolute error 3.842703932832592e-12 relative error 1.6865451628613222e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.000000000002448 y[1] (closed_form) 2.459697694136368 y[1] (numeric) 2.4596976941325095 absolute error 3.858691144387194e-12 relative error 1.568766419379854e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1000960000023745 y[1] (closed_form) 2.646585436575519 y[1] (numeric) 2.6465854365717973 absolute error 3.721467578543525e-12 relative error 1.4061392189019306e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.200064000002301 y[1] (closed_form) 2.837765896771342 y[1] (numeric) 2.8377658967677557 absolute error 3.5864644587491057e-12 relative error 1.263833800677354e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.3000320000022276 y[1] (closed_form) 3.032564005378674 y[1] (numeric) 3.032564005375231 absolute error 3.4430236439675355e-12 relative error 1.1353506926352928e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.4000000000021542 y[1] (closed_form) 3.230032857104036 y[1] (numeric) 3.2300328571007384 absolute error 3.297806472346565e-12 relative error 1.0209823299764488e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.5000960000020807 y[1] (closed_form) 3.429454558180977 y[1] (numeric) 3.429454558177827 absolute error 3.150368854676344e-12 relative error 9.186209647132157e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.6000640000020072 y[1] (closed_form) 3.629327494956053 y[1] (numeric) 3.629327494953052 absolute error 3.001154880166723e-12 relative error 8.269176271189778e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.7000320000019338 y[1] (closed_form) 3.8289082275073367 y[1] (numeric) 3.8289082275044852 absolute error 2.851496816447252e-12 relative error 7.447284309301948e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.8000000000018603 y[1] (closed_form) 4.027202094696759 y[1] (numeric) 4.027202094694056 absolute error 2.702726931147481e-12 relative error 6.711177804328669e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.9000960000017868 y[1] (closed_form) 4.223476410185541 y[1] (numeric) 4.223476410182993 absolute error 2.5481838861196593e-12 relative error 6.033380179357306e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0000640000017134 y[1] (closed_form) 4.416269030733422 y[1] (numeric) 4.416269030731026 absolute error 2.3954171979312378e-12 relative error 5.4240744421619265e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1000320000018133 y[1] (closed_form) 4.604905727044483 y[1] (numeric) 4.60490572704191 absolute error 2.573052881871263e-12 relative error 5.587634219653608e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2000000000019133 y[1] (closed_form) 4.7885011172588055 y[1] (numeric) 4.788501117256045 absolute error 2.7604585284279892e-12 relative error 5.764765342705451e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3000960000020134 y[1] (closed_form) 4.966443605913398 y[1] (numeric) 4.966443605910459 absolute error 2.9389823907877144e-12 relative error 5.917679981885539e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4000640000021134 y[1] (closed_form) 5.13750094367813 y[1] (numeric) 5.137500943675025 absolute error 3.1041835768519377e-12 relative error 6.042205365765902e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5000320000022134 y[1] (closed_form) 5.301194766248894 y[1] (numeric) 5.301194766245626 absolute error 3.268496584496461e-12 relative error 6.165584794782473e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6000000000023133 y[1] (closed_form) 5.4568887533724535 y[1] (numeric) 5.456888753369027 absolute error 3.426592343203083e-12 relative error 6.279388307275622e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7000960000024135 y[1] (closed_form) 5.604209166322981 y[1] (numeric) 5.604209166319402 absolute error 3.5793590313915047e-12 relative error 6.386911917743399e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8000640000025134 y[1] (closed_form) 5.742307777983937 y[1] (numeric) 5.742307777980211 absolute error 3.725908470642025e-12 relative error 6.488521017503092e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9000320000026134 y[1] (closed_form) 5.870997820634232 y[1] (numeric) 5.870997820630389 absolute error 3.842259843622742e-12 relative error 6.544474995576937e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.0000000000027134 y[1] (closed_form) 5.989992496603541 y[1] (numeric) 5.989992496599583 absolute error 3.958611216603458e-12 relative error 6.6087081391973e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.1000960000028135 y[1] (closed_form) 6.099235137415782 y[1] (numeric) 6.09923513741171 absolute error 4.072298054325074e-12 relative error 6.676735627625742e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.2000640000029135 y[1] (closed_form) 6.198355037807811 y[1] (numeric) 6.198355037803636 absolute error 4.175326751010289e-12 relative error 6.736185206465662e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.3000320000030134 y[1] (closed_form) 6.287506721543601 y[1] (numeric) 6.287506721539338 absolute error 4.263256414560601e-12 relative error 6.780519852094821e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.4000000000031134 y[1] (closed_form) 6.366798192581779 y[1] (numeric) 6.3667981925774395 absolute error 4.339639758654812e-12 relative error 6.816047293145094e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.5000960000032135 y[1] (closed_form) 6.436519007787883 y[1] (numeric) 6.43651900778346 absolute error 4.423128530106624e-12 relative error 6.871926463286828e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.6000640000033135 y[1] (closed_form) 6.496794093191081 y[1] (numeric) 6.496794093186598 absolute error 4.482636484226532e-12 relative error 6.899766900300145e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.7000320000034135 y[1] (closed_form) 6.548115076521279 y[1] (numeric) 6.54811507651676 absolute error 4.519051799434237e-12 relative error 6.901301743516406e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.8000000000035135 y[1] (closed_form) 6.590967711915781 y[1] (numeric) 6.590967711911229 absolute error 4.551914400963142e-12 relative error 6.906291458132553e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 3.9000960000036136 y[1] (closed_form) 6.625962275304992 y[1] (numeric) 6.625962275300408 absolute error 4.583888824072346e-12 relative error 6.918072626456888e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.0000640000037135 y[1] (closed_form) 6.653659184166186 y[1] (numeric) 6.6536591841615635 absolute error 4.622080496119452e-12 relative error 6.946674556338393e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.1000320000038135 y[1] (closed_form) 6.674829761372102 y[1] (numeric) 6.674829761367464 absolute error 4.638067707674054e-12 relative error 6.948593257786153e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.2000000000039135 y[1] (closed_form) 6.690260821341202 y[1] (numeric) 6.690260821336554 absolute error 4.647837670290755e-12 relative error 6.947169616264676e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.300096000004014 y[1] (closed_form) 6.700807218303636 y[1] (numeric) 6.700807218298982 absolute error 4.654054919228656e-12 relative error 6.945513827820387e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.400064000004114 y[1] (closed_form) 6.707335966816514 y[1] (numeric) 6.707335966811846 absolute error 4.667377595524158e-12 relative error 6.95861608634974e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.5000320000042136 y[1] (closed_form) 6.710796518359187 y[1] (numeric) 6.710796518354518 absolute error 4.669153952363558e-12 relative error 6.957674755284016e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.6000000000043135 y[1] (closed_form) 6.712152526935082 y[1] (numeric) 6.7121525269304065 absolute error 4.675371201301459e-12 relative error 6.965531820887177e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.700096000004414 y[1] (closed_form) 6.712388670773225 y[1] (numeric) 6.712388670768555 absolute error 4.6700421307832585e-12 relative error 6.957347614743082e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.800064000004514 y[1] (closed_form) 6.712501262204847 y[1] (numeric) 6.712501262200179 absolute error 4.667377595524158e-12 relative error 6.953261404663142e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 4.900032000004614 y[1] (closed_form) 6.713488192189401 y[1] (numeric) 6.713488192184729 absolute error 4.671818487622659e-12 relative error 6.958854106659398e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( x ) + 1.0 ; Iterations 78125 Total Elapsed Time 13 Seconds Elapsed Time(since restart) 13 Seconds Time to Timeout 2 Minutes 47.0 Seconds Percent Done 100.00128000004715%