##############ECHO OF PROBLEM################# ##############temp/div_c_exppostode.ode################# diff ( y , x , 1 ) = 2.0 / exp ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=1.0 # ELIMINATED in preodein.rb 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/exp(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 4.0 estimated_steps 4000000.0 step_error 1.6666666666666666e-21 est_needed_step_err 1.6666666666666666e-21 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 0.7357588823428847 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 4.0 estimated_steps 4000000.0 step_error 1.6666666666666666e-21 est_needed_step_err 1.6666666666666666e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.8244027295195666e-183 estimated_step_error 1.8244027295195666e-183 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 0.7357588823428847 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 2000000.0 step_error 2.3570226039551582e-21 est_needed_step_err 2.3570226039551582e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.22433592389236e-175 estimated_step_error 1.22433592389236e-175 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 0.7357588823428847 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 1000000.0 step_error 3.3333333333333333e-21 est_needed_step_err 3.3333333333333333e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.216378996365963e-168 estimated_step_error 8.216378996365963e-168 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 0.7357588823428847 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 500000.0 step_error 4.7140452079103165e-21 est_needed_step_err 4.7140452079103165e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.5139181979515537e-160 estimated_step_error 5.5139181979515537e-160 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 0.7357588823428847 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 250000.0 step_error 6.6666666666666666e-21 est_needed_step_err 6.6666666666666666e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.700327316330089e-152 estimated_step_error 3.700327316330089e-152 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 0.7357588823428847 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 125000.0 step_error 9.428090415820633e-21 est_needed_step_err 9.428090415820633e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.483246890483541e-144 estimated_step_error 2.483246890483541e-144 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 0.7357588823428847 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 62500.0 step_error 1.3333333333333333e-20 est_needed_step_err 1.3333333333333333e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6664777909627203e-136 estimated_step_error 1.6664777909627203e-136 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 0.7357588823428847 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 31250.0 step_error 1.8856180831641266e-20 est_needed_step_err 1.8856180831641266e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1183529888542776e-128 estimated_step_error 1.1183529888542776e-128 Double H and LOOP opt_iter 9 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 0.7357588823428847 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 15625.0 step_error 2.6666666666666666e-20 est_needed_step_err 2.6666666666666666e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.505122073163736e-121 estimated_step_error 7.505122073163736e-121 Double H and LOOP opt_iter 10 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 0.7357588823428847 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 7812.5 step_error 3.771236166328253e-20 est_needed_step_err 3.771236166328253e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.036578287758422e-113 estimated_step_error 5.036578287758422e-113 Double H and LOOP opt_iter 11 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 0.7357588823428847 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.001024 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 3906.25 step_error 5.333333333333333e-20 est_needed_step_err 5.333333333333333e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.379958426181443e-105 estimated_step_error 3.379958426181443e-105 Double H and LOOP opt_iter 12 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 0.7357588823428847 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.002048 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 1953.125 step_error 7.542472332656506e-20 est_needed_step_err 7.542472332656506e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.268208691633485e-97 estimated_step_error 2.268208691633485e-97 Double H and LOOP opt_iter 13 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 0.7357588823428847 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.004096 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 976.5625 step_error 1.0666666666666666e-19 est_needed_step_err 1.0666666666666666e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.5221113597445369e-89 estimated_step_error 1.5221113597445369e-89 Double H and LOOP opt_iter 14 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 0.7357588823428847 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.008192 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 488.28125 step_error 1.5084944665313013e-19 est_needed_step_err 1.5084944665313013e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0213941718303649e-81 estimated_step_error 1.0213941718303649e-81 Double H and LOOP opt_iter 15 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 0.7357588823428847 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.016384 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 244.140625 step_error 2.1333333333333333e-19 est_needed_step_err 2.1333333333333333e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.8534206933073786e-74 estimated_step_error 6.8534206933073786e-74 Double H and LOOP opt_iter 16 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 0.7357588823428847 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.032768 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 122.0703125 step_error 3.0169889330626025e-19 est_needed_step_err 3.0169889330626025e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.5978581059609457e-66 estimated_step_error 4.5978581059609457e-66 Double H and LOOP opt_iter 17 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 0.7357588823428847 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.065536 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.0 estimated_steps 61.03515625 step_error 4.2666666666666666e-19 est_needed_step_err 4.2666666666666666e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.0837000948334615e-58 estimated_step_error 3.0837000948334615e-58 Double H and LOOP opt_iter 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL 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 START of Soultion TOP MAIN SOLVE Loop x[1] 1.0 y[1] (closed_form) -0.7357588823428847 y[1] (numeric) -0.7357588823428847 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.1 y[1] (closed_form) -0.665742167396159 y[1] (numeric) -0.6657421673961591 absolute error 1.1102230246251565e-16 relative error 1.66764714479097e-14% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.2000000000000002 y[1] (closed_form) -0.602388423824404 y[1] (numeric) -0.6023884238244042 absolute error 1.1102230246251565e-16 relative error 1.843035126034869e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.3000000000000003 y[1] (closed_form) -0.5450635860680251 y[1] (numeric) -0.5450635860680252 absolute error 1.1102230246251565e-16 relative error 2.036868822285623e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.4000000000000004 y[1] (closed_form) -0.49319392788321276 y[1] (numeric) -0.4931939278832129 absolute error 1.6653345369377348e-16 relative error 3.376632279487598e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.5000000000000004 y[1] (closed_form) -0.4462603202968594 y[1] (numeric) -0.44626032029685964 absolute error 2.220446049250313e-16 relative error 4.975674395100235e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.6000000000000005 y[1] (closed_form) -0.4037930359893106 y[1] (numeric) -0.4037930359893108 absolute error 2.220446049250313e-16 relative error 5.498970639278419e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.7000000000000006 y[1] (closed_form) -0.36536704810546905 y[1] (numeric) -0.3653670481054693 absolute error 2.7755575615628914e-16 relative error 7.596628037352953e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.8000000000000007 y[1] (closed_form) -0.33059777644317284 y[1] (numeric) -0.3305977764431731 absolute error 2.7755575615628914e-16 relative error 8.395572382320568e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.9000000000000008 y[1] (closed_form) -0.29913723844526985 y[1] (numeric) -0.2991372384452702 absolute error 3.3306690738754696e-16 relative error 1.1134250925047731e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.000000000000001 y[1] (closed_form) -0.2706705664732251 y[1] (numeric) -0.27067056647322546 absolute error 3.3306690738754696e-16 relative error 1.230525031691963e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.100000000000001 y[1] (closed_form) -0.24491285650596356 y[1] (numeric) -0.24491285650596392 absolute error 3.608224830031759e-16 relative error 1.473268852239245e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.200000000000001 y[1] (closed_form) -0.22160631672466752 y[1] (numeric) -0.2216063167246679 absolute error 3.885780586188048e-16 relative error 1.7534611123093102e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.300000000000001 y[1] (closed_form) -0.20051768744560725 y[1] (numeric) -0.20051768744560763 absolute error 3.885780586188048e-16 relative error 1.9378742273008266e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.4000000000000012 y[1] (closed_form) -0.18143590657882477 y[1] (numeric) -0.1814359065788252 absolute error 4.163336342344337e-16 relative error 2.2946595416798475e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.5000000000000013 y[1] (closed_form) -0.16416999724779738 y[1] (numeric) -0.1641699972477978 absolute error 4.163336342344337e-16 relative error 2.535990992349362e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.6000000000000014 y[1] (closed_form) -0.14854715642866756 y[1] (numeric) -0.14854715642866798 absolute error 4.163336342344337e-16 relative error 2.8027034932463174e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.7000000000000015 y[1] (closed_form) -0.13441102547949932 y[1] (numeric) -0.13441102547949976 absolute error 4.440892098500626e-16 relative error 3.3039641522398486e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.8000000000000016 y[1] (closed_form) -0.12162012525043574 y[1] (numeric) -0.12162012525043618 absolute error 4.440892098500626e-16 relative error 3.651445095419942e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.9000000000000017 y[1] (closed_form) -0.11004644011281427 y[1] (numeric) -0.11004644011281473 absolute error 4.579669976578771e-16 relative error 4.161579394920831e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.0000000000000018 y[1] (closed_form) -0.09957413673572771 y[1] (numeric) -0.09957413673572817 absolute error 4.579669976578771e-16 relative error 4.599256520529353e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.100000000000002 y[1] (closed_form) -0.09009840478711545 y[1] (numeric) -0.09009840478711591 absolute error 4.579669976578771e-16 relative error 5.082964551258834e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.200000000000002 y[1] (closed_form) -0.08152440795673227 y[1] (numeric) -0.08152440795673274 absolute error 4.718447854656915e-16 relative error 5.787773223892841e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.300000000000002 y[1] (closed_form) -0.07376633480247986 y[1] (numeric) -0.07376633480248034 absolute error 4.718447854656915e-16 relative error 6.396478647463302e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.400000000000002 y[1] (closed_form) -0.06674653992065202 y[1] (numeric) -0.06674653992065249 absolute error 4.718447854656915e-16 relative error 7.069202179268295e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.500000000000002 y[1] (closed_form) -0.06039476684463686 y[1] (numeric) -0.06039476684463735 absolute error 4.85722573273506e-16 relative error 8.042461270245616e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.6000000000000023 y[1] (closed_form) -0.05464744489458499 y[1] (numeric) -0.05464744489458548 absolute error 4.85722573273506e-16 relative error 8.888294305625187e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.7000000000000024 y[1] (closed_form) -0.049447052940678665 y[1] (numeric) -0.04944705294067915 absolute error 4.85722573273506e-16 relative error 9.82308437787434e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.8000000000000025 y[1] (closed_form) -0.04474154371233108 y[1] (numeric) -0.04474154371233157 absolute error 4.926614671774132e-16 relative error 1.1011275568518936e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.9000000000000026 y[1] (closed_form) -0.04048382289160867 y[1] (numeric) -0.040483822891609164 absolute error 4.926614671774132e-16 relative error 1.2169341529244023e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.000000000000003 y[1] (closed_form) -0.03663127777746826 y[1] (numeric) -0.03663127777746876 absolute error 4.996003610813204e-16 relative error 1.3638627735465522e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.100000000000002 y[1] (closed_form) -0.03314535080352242 y[1] (numeric) -0.033145350803522905 absolute error 4.85722573273506e-16 relative error 1.465431988192707e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.200000000000002 y[1] (closed_form) -0.029991153640955354 y[1] (numeric) -0.02999115364095583 absolute error 4.753142324176451e-16 relative error 1.584848112573319e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.300000000000002 y[1] (closed_form) -0.02713711802440182 y[1] (numeric) -0.027137118024402287 absolute error 4.683753385137379e-16 relative error 1.7259582911220442e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.400000000000001 y[1] (closed_form) -0.024554679806136855 y[1] (numeric) -0.02455467980613731 absolute error 4.544975507059235e-16 relative error 1.850961015554895e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.500000000000001 y[1] (closed_form) -0.02221799307648459 y[1] (numeric) -0.022217993076485042 absolute error 4.510281037539698e-16 relative error 2.030012801792326e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.6000000000000005 y[1] (closed_form) -0.02010367148926715 y[1] (numeric) -0.020103671489267595 absolute error 4.440892098500626e-16 relative error 2.2089955562950317e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.7 y[1] (closed_form) -0.01819055420339163 y[1] (numeric) -0.018190554203392068 absolute error 4.371503159461554e-16 relative error 2.4031720587416113e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.8 y[1] (closed_form) -0.01645949409804006 y[1] (numeric) -0.01645949409804049 absolute error 4.3021142204224816e-16 relative error 2.6137584756841114e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.8999999999999995 y[1] (closed_form) -0.014893166141848688 y[1] (numeric) -0.014893166141849113 absolute error 4.2500725161431774e-16 relative error 2.853706509189332e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.999999999999999 y[1] (closed_form) -0.013475893998170948 y[1] (numeric) -0.013475893998171366 absolute error 4.180683577104105e-16 relative error 3.1023422844314e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.1 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 Finished! diff ( y , x , 1 ) = 2.0 / exp ( x ) ; Iterations 41 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 104.99999999999996%