|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 1 > ret := 1.0; > else > ret := -1.0; > fi;# end if 1; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 3 > # Begin Function number 4 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 1 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > if (min_size < 1.0) then # if number 1 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 4 > # Begin Function number 5 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms; > max_value3 := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > value3 := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (value3 > max_value3) then # if number 1 > max_value3 := value3; > omniout_float(ALWAYS,"value3",32,value3,32,""); > fi;# end if 1; > omniout_float(ALWAYS,"max_value3",32,max_value3,32,""); > max_value3; > end; test_suggested_h := proc() local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; max_value3 := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); value3 := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_value3 < value3 then max_value3 := value3; omniout_float(ALWAYS, "value3", 32, value3, 32, "") end if; omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""); max_value3 end proc > # End Function number 5 > # Begin Function number 6 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1 > ret := true; > else > ret := false; > fi;# end if 1; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 6 > # Begin Function number 7 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 1 > if (iter >= 0) then # if number 2 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 4 > glob_good_digits := -trunc(log10(relerr)) + 2; > else > glob_good_digits := Digits; > fi;# end if 4; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 3; > if (glob_iter = 1) then # if number 3 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 3; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 2; > #BOTTOM DISPLAY ALOT > fi;# end if 1; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 2 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 7 > # Begin Function number 8 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 2 > fi;# end if 1; > if ( not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 8 > # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 1; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 9 > # Begin Function number 10 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc,hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float * glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2; > if (m > 10) then # if number 1 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > glob_small_float * glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1; > n := n - 1; > od;# end do number 2; > m := n + cnt; > if (m <= 10) then # if number 1 > rad_c := glob_large_float; > ord_no := glob_large_float; > elif > (((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-5]) <= (glob_small_float)))) then # if number 2 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2; > #BOTTOM RADII COMPLEX EQ = 1 > found_sing := 0; > #TOP WHICH RADII EQ = 1 > if (1 <> found_sing and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found_sing := 1; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found_sing := 1; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found_sing := 1; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 3 > omniout_str(ALWAYS,"NO POLE for equation 1"); > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found_sing := 1; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found_sing := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing ) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 3 > omniout_str(ALWAYS,"NO POLE for equation 1"); > fi;# end if 3; > fi;# end if 2; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if (array_pole[1] > array_poles[1,1]) then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2; > #BOTTOM WHICH RADIUS EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 2 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 2 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 2; > #BOTTOM ADJUST ALL SERIES > if (reached_interval()) then # if number 2 > display_pole(); > fi;# end if 2 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and ( omniabs(array_y_higher[1, m]) < glob_small_float*glob_small_float or omniabs(array_y_higher[1, m - 1]) < glob_small_float*glob_small_float or omniabs(array_y_higher[1, m - 2]) < glob_small_float*glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if glob_small_float*glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float elif glob_large_float <= omniabs(array_y_higher[1, m]) or glob_large_float <= omniabs(array_y_higher[1, m - 1]) or glob_large_float <= omniabs(array_y_higher[1, m - 2]) or glob_large_float <= omniabs(array_y_higher[1, m - 3]) or glob_large_float <= omniabs(array_y_higher[1, m - 4]) or glob_large_float <= omniabs(array_y_higher[1, m - 5]) or omniabs(array_y_higher[1, m]) <= glob_small_float or omniabs(array_y_higher[1, m - 1]) <= glob_small_float or omniabs(array_y_higher[1, m - 2]) <= glob_small_float or omniabs(array_y_higher[1, m - 3]) <= glob_small_float or omniabs(array_y_higher[1, m - 4]) <= glob_small_float or omniabs(array_y_higher[1, m - 5]) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(dr1) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found_sing := 0; if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found_sing := 1; array_type_pole[1] := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1") end if end if end if; if 1 <> found_sing and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and -1.0*glob_smallish_float < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found_sing := 1; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1") end if end if end if; if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1") end if end if; if 1 <> found_sing and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and -1.0*glob_smallish_float < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found_sing := 1; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1") end if end if end if; if 1 <> found_sing and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found_sing := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1") end if end if end if; if 1 <> found_sing then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_pole() end if end proc > # End Function number 10 > # Begin Function number 11 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 2 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 3; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 2; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 11 > # Begin Function number 12 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D1[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp3[1] := sqrt(array_tmp2[1]); > #emit pre ln 1 FULL $eq_no = 1 > array_tmp4[1] := ln(array_tmp3[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D1[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/2.0; > #emit pre ln 2 FULL $eq_no = 1 > array_tmp4[2] := array_tmp3[2] / array_tmp3[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := 0.0; > array_tmp3[3] := -ats(3,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre ln ID_FULL iii = 3 $eq_no = 1 > #emit pre ln 3 $eq_no = 1 > array_tmp4[3] := ( array_tmp3[3] - att(2,array_tmp3,array_tmp4,2) ) / array_tmp3[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := 0.0; > array_tmp3[4] := -ats(4,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre ln ID_FULL iii = 4 $eq_no = 1 > #emit pre ln 4 $eq_no = 1 > array_tmp4[4] := ( array_tmp3[4] - att(3,array_tmp3,array_tmp4,2) ) / array_tmp3[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := 0.0; > array_tmp3[5] := -ats(5,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre ln ID_FULL iii = 5 $eq_no = 1 > #emit pre ln 5 $eq_no = 1 > array_tmp4[5] := ( array_tmp3[5] - att(4,array_tmp3,array_tmp4,2) ) / array_tmp3[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sqrt LINEAR $eq_no = 1 > array_tmp3[kkk] := 0.0; > array_tmp3[kkk] := -ats(kkk,array_tmp3,array_tmp3,2) /array_tmp3[1] / 2.0; > #emit ln FULL $eq_no = 1 > array_tmp4[kkk] := (array_tmp3[kkk] - att(kkk-1,array_tmp3,array_tmp4,2))/array_tmp3[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 2 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; array_tmp1[1] := array_const_0D1[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; array_tmp3[1] := sqrt(array_tmp2[1]); array_tmp4[1] := ln(array_tmp3[1]); array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_const_0D1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*2.0); array_tmp4[2] := array_tmp3[2]/array_tmp3[1]; array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp3[3] := 0.; array_tmp3[3] := -ats(3, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4[3] := (array_tmp3[3] - att(2, array_tmp3, array_tmp4, 2))/array_tmp3[1]; array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp3[4] := 0.; array_tmp3[4] := -ats(4, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4[4] := (array_tmp3[4] - att(3, array_tmp3, array_tmp4, 2))/array_tmp3[1]; array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp3[5] := 0.; array_tmp3[5] := -ats(5, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4[5] := (array_tmp3[5] - att(4, array_tmp3, array_tmp4, 2))/array_tmp3[1]; array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp3[kkk] := 0.; array_tmp3[kkk] := -ats(kkk, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0); array_tmp4[kkk] := ( array_tmp3[kkk] - att(kkk - 1, array_tmp3, array_tmp4, 2))/ array_tmp3[1]; array_tmp5[kkk] := array_tmp4[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp5[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 12 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, "\n") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 6 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 6 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # End Function number 16 > # Begin Function number 17 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 20 > # Begin Function number 21 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 21 > # Begin Function number 22 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 8 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 24 > # Begin Function number 25 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc > # End Function number 25 > # Begin Function number 26 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 8 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 8; > if (glob_max_iter < 2) then # if number 8 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 8; > if (errflag) then # if number 8 > quit; > fi;# end if 8 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 26 > # Begin Function number 27 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 8 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 9 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 9 > fi;# end if 8; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 27 > # Begin Function number 28 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 8 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 8; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 28 > # Begin Function number 29 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 29 > # Begin Function number 30 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 8 > if (array_fact_1[nnn] = 0) then # if number 9 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 9; > else > ret := factorial_2(nnn); > fi;# end if 8; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 8 > if (array_fact_2[mmm,nnn] = 0) then # if number 9 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 9; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 8; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 31 > # Begin Function number 32 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 33 > # Begin Function number 34 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 34 > # Begin Function number 35 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 35 > # Begin Function number 36 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 36 > # Begin Function number 37 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0,- glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 37 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(5.0 * ln(0.1 * x + 0.2) * ( 0.1 * x + 0.2) - 0.5 * x - 1.0); > end; exact_soln_y := proc(x) return 5.0*ln(0.1*x + 0.2)*(0.1*x + 0.2) - 0.5*x - 1.0 end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_value3 := 0.0; > glob_ratio_of_radius := 0.01; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.1e-200; > glob_smallish_float := 0.1e-100; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/ln_sqrtpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = ln(sqrt(0.1 * x + 0.2));"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 0.5 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.001;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(5.0 * ln(0.1 * x + 0.2) * ( 0.1 * x + 0.2) - 0.5 * x - 1.0);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D0[1] := 0.0; > array_const_0D1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D1[1] := 0.1; > array_const_0D2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D2[1] := 0.2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3; > iiif := iiif + 1; > od;# end do number 2; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 0.5 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 1000000; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.001; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > if (glob_display_interval < glob_h) then # if number 2 > glob_h := glob_display_interval; > fi;# end if 2; > if (glob_max_h < glob_h) then # if number 2 > glob_h := glob_max_h; > fi;# end if 2; > found_h := -1.0; > best_h := 0.0; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 3 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 3; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 3 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 4 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 4; > r_order := r_order + 1; > od;# end do number 3 > ; > atomall(); > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > value3 := test_suggested_h(); > omniout_float(ALWAYS,"value3",32,value3,32,""); > if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2 > best_h := glob_h; > found_h := 1.0; > fi;# end if 2; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > glob_h := glob_h * 0.5; > od;# end do number 2; > if (found_h > 0.0) then # if number 2 > glob_h := best_h ; > else > omniout_str(ALWAYS,"No increment to obtain desired accuracy found"); > fi;# end if 2; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2; > #BEGIN SOLUTION CODE > if (found_h > 0.0) then # if number 2 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > if (reached_interval()) then # if number 3 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 3; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 3 > #left paren 0004C > check_for_pole(); > fi;# end if 3;#was right paren 0004C > if (reached_interval()) then # if number 3 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 3; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4; > term_no := term_no - 1; > od;# end do number 3; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 2;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 3 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 3; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 3; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = ln(sqrt(0.1 * x + 0.2));"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 3 > logstart(html_log_file); > logitem_str(html_log_file,"2013-01-28T16:19:24-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"ln_sqrt") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = ln(sqrt(0.1 * x + 0.2));") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 4 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 4; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 4 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 4; > log_revs(html_log_file," 165 ") > ; > logitem_str(html_log_file,"ln_sqrt diffeq.mxt") > ; > logitem_str(html_log_file,"ln_sqrt maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 3; > if (glob_html_log) then # if number 3 > fclose(html_log_file); > fi;# end if 3 > ; > ;; > fi;# end if 2 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_value3 := 0.; glob_ratio_of_radius := 0.01; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.1*10^(-200); glob_smallish_float := 0.1*10^(-100); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/ln_sqrtpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = ln(sqrt(0.1 * x + 0.2));"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 0.5 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.001;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(5.0 * ln(0.1 * x + 0.2) * ( 0.1 * x + 0.2\ ) - 0.5 * x - 1.0);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_0D1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D1[term] := 0.; term := term + 1 end do; array_const_0D1[1] := 0.1; array_const_0D2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D2[term] := 0.; term := term + 1 end do; array_const_0D2[1] := 0.2; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 0.5; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_desired_digits_correct := 10; glob_display_interval := 0.001; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_max_h < glob_h then glob_h := glob_max_h end if; found_h := -1.0; best_h := 0.; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; while opt_iter <= 20 and found_h < 0. do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer) ; omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); value3 := test_suggested_h(); omniout_float(ALWAYS, "value3", 32, value3, 32, ""); if value3 < est_needed_step_err and found_h < 0. then best_h := glob_h; found_h := 1.0 end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1; glob_h := glob_h*0.5 end do; if 0. < found_h then glob_h := best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found") end if; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; if 0. < found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = ln(sqrt(0.1 * x + 0.2));"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-01-28T16:19:24-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "ln_sqrt"); logitem_str(html_log_file, "diff ( y , x , 1 ) = ln(sqrt(0.1 * x + 0.2));"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 165 "); logitem_str(html_log_file, "ln_sqrt diffeq.mxt") ; logitem_str(html_log_file, "ln_sqrt maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 12 > main(); ##############ECHO OF PROBLEM################# ##############temp/ln_sqrtpostode.ode################# diff ( y , x , 1 ) = ln(sqrt(0.1 * x + 0.2)); ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 0.5 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.001; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(5.0 * ln(0.1 * x + 0.2) * ( 0.1 * x + 0.2) - 0.5 * x - 1.0); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 0.4 estimated_steps = 400 step_error = 2.5000000000000000000000000000000e-13 est_needed_step_err = 2.5000000000000000000000000000000e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 6.7682835704795934185673433857193e-90 max_value3 = 6.7682835704795934185673433857193e-90 value3 = 6.7682835704795934185673433857193e-90 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = -2.6886801356779017901121541754532 y[1] (numeric) = -2.6886801356779017901121541754532 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.101 y[1] (analytic) = -2.6894603405233070262776559391428 y[1] (numeric) = -2.6894603405233070262776559391428 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.102 y[1] (analytic) = -2.6902403073867899023929870640188 y[1] (numeric) = -2.6902403073867899023929870640188 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.8MB, time=0.13 x[1] = 0.103 y[1] (analytic) = -2.6910200363815673263164553239129 y[1] (numeric) = -2.691020036381567326316455323913 absolute error = 1e-31 relative error = 3.7160630039181439135042762581851e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.104 y[1] (analytic) = -2.6917995276207485340845290360461 y[1] (numeric) = -2.6917995276207485340845290360461 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.105 y[1] (analytic) = -2.6925787812173352434363209956127 y[1] (numeric) = -2.6925787812173352434363209956127 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.106 y[1] (analytic) = -2.6933577972842218070463393693492 y[1] (numeric) = -2.6933577972842218070463393693492 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.107 y[1] (analytic) = -2.6941365759341953654661981717953 y[1] (numeric) = -2.6941365759341953654661981717954 absolute error = 1e-31 relative error = 3.7117643141504387096700316713965e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.108 y[1] (analytic) = -2.6949151172799359997759779756095 y[1] (numeric) = -2.6949151172799359997759779756096 absolute error = 1e-31 relative error = 3.7106920124791610353439975575064e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.109 y[1] (analytic) = -2.6956934214340168839459255414954 y[1] (numeric) = -2.6956934214340168839459255414955 absolute error = 1e-31 relative error = 3.7096206565954155667329572843530e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = -2.6964714885089044369091790940217 y[1] (numeric) = -2.6964714885089044369091790940218 absolute error = 1e-31 relative error = 3.7085502452428313329509601272512e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.9MB, time=0.28 x[1] = 0.111 y[1] (analytic) = -2.6972493186169584743462040168404 y[1] (numeric) = -2.6972493186169584743462040168404 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.112 y[1] (analytic) = -2.6980269118704323601816217945063 y[1] (numeric) = -2.6980269118704323601816217945064 absolute error = 1e-31 relative error = 3.7064122511170233603552560992387e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.113 y[1] (analytic) = -2.6988042683814731577941130882528 y[1] (numeric) = -2.6988042683814731577941130882529 absolute error = 1e-31 relative error = 3.7053446658424027916964617187099e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.114 y[1] (analytic) = -2.6995813882621217809400738996496 y[1] (numeric) = -2.6995813882621217809400738996497 absolute error = 1e-31 relative error = 3.7042780200961394568168615150909e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.115 y[1] (analytic) = -2.7003582716243131443917018490529 y[1] (numeric) = -2.700358271624313144391701849053 absolute error = 1e-31 relative error = 3.7032123126331764725858910176439e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.116 y[1] (analytic) = -2.7011349185798763142901876751083 y[1] (numeric) = -2.7011349185798763142901876751084 absolute error = 1e-31 relative error = 3.7021475422107043111662813225366e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.117 y[1] (analytic) = -2.7019113292405346582146851472798 y[1] (numeric) = -2.7019113292405346582146851472799 absolute error = 1e-31 relative error = 3.7010837075881556790242627788459e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.118 y[1] (analytic) = -2.7026875037179059949677306754158 y[1] (numeric) = -2.7026875037179059949677306754158 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.1MB, time=0.42 x[1] = 0.119 y[1] (analytic) = -2.703463442123502744077781998709 y[1] (numeric) = -2.703463442123502744077781998709 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = -2.7042391445687320750195434410342 y[1] (numeric) = -2.7042391445687320750195434410342 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.121 y[1] (analytic) = -2.7050146111648960561527433305321 y[1] (numeric) = -2.7050146111648960561527433305321 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.122 y[1] (analytic) = -2.7057898420231918033800272984291 y[1] (numeric) = -2.7057898420231918033800272984291 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.123 y[1] (analytic) = -2.7065648372547116285246292954137 y[1] (numeric) = -2.7065648372547116285246292954137 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.124 y[1] (analytic) = -2.7073395969704431874284802934083 y[1] (numeric) = -2.7073395969704431874284802934082 absolute error = 1e-31 relative error = 3.6936629638890377090458638350857e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.125 y[1] (analytic) = -2.7081141212812696277714127762599 y[1] (numeric) = -2.7081141212812696277714127762598 absolute error = 1e-31 relative error = 3.6926065712728440531593883857443e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.126 y[1] (analytic) = -2.7088884102979697366121172646987 y[1] (numeric) = -2.7088884102979697366121172646987 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.1MB, time=0.57 x[1] = 0.127 y[1] (analytic) = -2.7096624641312180876515052688542 y[1] (numeric) = -2.7096624641312180876515052688542 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.128 y[1] (analytic) = -2.7104362828915851882191312156584 y[1] (numeric) = -2.7104362828915851882191312156584 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.129 y[1] (analytic) = -2.7112098666895376259833240585772 y[1] (numeric) = -2.7112098666895376259833240585772 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = -2.7119832156354382153856774432676 y[1] (numeric) = -2.7119832156354382153856774432676 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.131 y[1] (analytic) = -2.7127563298395461438005454749481 y[1] (numeric) = -2.7127563298395461438005454749481 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.132 y[1] (analytic) = -2.7135292094120171174201893114588 y[1] (numeric) = -2.7135292094120171174201893114587 absolute error = 1e-31 relative error = 3.6852376474572229332823500690593e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.133 y[1] (analytic) = -2.71430185446290350686621799016 y[1] (numeric) = -2.7143018544629035068662179901599 absolute error = 1e-31 relative error = 3.6841886187263298271449267513262e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.134 y[1] (analytic) = -2.7150742651021544925279650869501 y[1] (numeric) = -2.71507426510215449252796508695 absolute error = 1e-31 relative error = 3.6831405050438834500160713104698e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.2MB, time=0.72 x[1] = 0.135 y[1] (analytic) = -2.7158464414396162096284410017509 y[1] (numeric) = -2.7158464414396162096284410017508 absolute error = 1e-31 relative error = 3.6820933052088168845279133963314e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.136 y[1] (analytic) = -2.716618383585031893018498866791 y[1] (numeric) = -2.7166183835850318930184988667909 absolute error = 1e-31 relative error = 3.6810470180222107754014877089139e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.137 y[1] (analytic) = -2.7173900916480420216998502818944 y[1] (numeric) = -2.7173900916480420216998502818944 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.138 y[1] (analytic) = -2.7181615657381844630775652947251 y[1] (numeric) = -2.7181615657381844630775652947251 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.139 y[1] (analytic) = -2.718932805964894616942689263532 y[1] (numeric) = -2.718932805964894616942689263532 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = -2.7197038124375055591856074653616 y[1] (numeric) = -2.7197038124375055591856074653616 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.141 y[1] (analytic) = -2.7204745852652481852407865439264 y[1] (numeric) = -2.7204745852652481852407865439264 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.142 y[1] (analytic) = -2.7212451245572513532635201283283 y[1] (numeric) = -2.7212451245572513532635201283282 absolute error = 1e-31 relative error = 3.6747883936501338108346705543632e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.143 y[1] (analytic) = -2.7220154304225420270393041966038 y[1] (numeric) = -2.7220154304225420270393041966037 absolute error = 1e-31 relative error = 3.6737484616123894926627126149864e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 memory used=22.8MB, alloc=4.2MB, time=0.87 TOP MAIN SOLVE Loop x[1] = 0.144 y[1] (analytic) = -2.7227855029700454186264660065689 y[1] (numeric) = -2.7227855029700454186264660065687 absolute error = 2e-31 relative error = 7.3454188654169681566454352881304e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.145 y[1] (analytic) = -2.723555342308585130732668670665 y[1] (numeric) = -2.7235553423085851307326686706649 absolute error = 1e-31 relative error = 3.6716713057586097070411911388377e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.146 y[1] (analytic) = -2.7243249485468832988259117114396 y[1] (numeric) = -2.7243249485468832988259117114395 absolute error = 1e-31 relative error = 3.6706340795850581939367495850716e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.147 y[1] (analytic) = -2.7250943217935607329806461998863 y[1] (numeric) = -2.7250943217935607329806461998862 absolute error = 1e-31 relative error = 3.6695977530122163127048303464373e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.148 y[1] (analytic) = -2.7258634621571370594596213501341 y[1] (numeric) = -2.725863462157137059459621350134 absolute error = 1e-31 relative error = 3.6685623248665610911021178851306e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.149 y[1] (analytic) = -2.7266323697460308620320777208587 y[1] (numeric) = -2.7266323697460308620320777208586 absolute error = 1e-31 relative error = 3.6675277939766551191899943445354e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = -2.7274010446685598230289004562922 y[1] (numeric) = -2.7274010446685598230289004562921 absolute error = 1e-31 relative error = 3.6664941591731418702964708151105e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.151 y[1] (analytic) = -2.7281694870329408641353442878031 y[1] (numeric) = -2.7281694870329408641353442878031 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.2MB, time=1.03 x[1] = 0.152 y[1] (analytic) = -2.7289376969472902869219403106816 y[1] (numeric) = -2.7289376969472902869219403106816 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.153 y[1] (analytic) = -2.7297056745196239131141928499805 y[1] (numeric) = -2.7297056745196239131141928499804 absolute error = 1e-31 relative error = 3.6633986196185085388721282691734e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.154 y[1] (analytic) = -2.730473419857857224601673034008 y[1] (numeric) = -2.7304734198578572246016730340079 absolute error = 1e-31 relative error = 3.6623685575084555231802326462075e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.155 y[1] (analytic) = -2.7312409330698055031871140043231 y[1] (numeric) = -2.7312409330698055031871140043231 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.156 y[1] (analytic) = -2.7320082142631839700761110068252 y[1] (numeric) = -2.7320082142631839700761110068252 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.157 y[1] (analytic) = -2.7327752635456079251080279297426 y[1] (numeric) = -2.7327752635456079251080279297426 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.158 y[1] (analytic) = -2.733542081024592885728710180984 y[1] (numeric) = -2.733542081024592885728710180984 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.159 y[1] (analytic) = -2.7343086668075547257056021294033 y[1] (numeric) = -2.7343086668075547257056021294033 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.3MB, time=1.18 x[1] = 0.16 y[1] (analytic) = -2.7350750210018098135858656720239 y[1] (numeric) = -2.7350750210018098135858656720239 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.161 y[1] (analytic) = -2.7358411437145751508980948321504 y[1] (numeric) = -2.7358411437145751508980948321504 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.162 y[1] (analytic) = -2.7366070350529685100982196415483 y[1] (numeric) = -2.7366070350529685100982196415484 absolute error = 1e-31 relative error = 3.6541600134439633158464722751048e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.163 y[1] (analytic) = -2.7373726951240085722601909134687 y[1] (numeric) = -2.7373726951240085722601909134688 absolute error = 1e-31 relative error = 3.6531379222904755327762184268268e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.164 y[1] (analytic) = -2.7381381240346150645120358722219 y[1] (numeric) = -2.7381381240346150645120358722219 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.165 y[1] (analytic) = -2.7389033218916088972178729692406 y[1] (numeric) = -2.7389033218916088972178729692407 absolute error = 1e-31 relative error = 3.6510963786387150042109010041251e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.166 y[1] (analytic) = -2.7396682888017123009064725850972 y[1] (numeric) = -2.7396682888017123009064725850973 absolute error = 1e-31 relative error = 3.6500769238650575024951798818145e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.167 y[1] (analytic) = -2.7404330248715489629469486917289 y[1] (numeric) = -2.7404330248715489629469486917289 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.3MB, time=1.34 x[1] = 0.168 y[1] (analytic) = -2.7411975302076441639721649291743 y[1] (numeric) = -2.7411975302076441639721649291743 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.169 y[1] (analytic) = -2.7419618049164249140504369363939 y[1] (numeric) = -2.741961804916424914050436936394 absolute error = 1e-31 relative error = 3.6470238141427357806419489679950e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = -2.7427258491042200886061111662333 y[1] (numeric) = -2.7427258491042200886061111662334 absolute error = 1e-31 relative error = 3.6460078586658672417358566551207e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.171 y[1] (analytic) = -2.7434896628772605640895988102639 y[1] (numeric) = -2.743489662877260564089598810264 absolute error = 1e-31 relative error = 3.6449927751914348500042022900972e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.172 y[1] (analytic) = -2.7442532463416793533974418600884 y[1] (numeric) = -2.7442532463416793533974418600885 absolute error = 1e-31 relative error = 3.6439785625947029529134434248863e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.173 y[1] (analytic) = -2.745016599603511741042986737698 y[1] (numeric) = -2.7450165996035117410429867376981 absolute error = 1e-31 relative error = 3.6429652197529125825398598790572e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.174 y[1] (analytic) = -2.7457797227686954180782393386095 y[1] (numeric) = -2.7457797227686954180782393386096 absolute error = 1e-31 relative error = 3.6419527455452770699870008110949e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.175 y[1] (analytic) = -2.7465426159430706167674737477632 y[1] (numeric) = -2.7465426159430706167674737477633 absolute error = 1e-31 relative error = 3.6409411388529776715544805310192e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.176 y[1] (analytic) = -2.7473052792323802450131653095149 y[1] (numeric) = -2.747305279232380245013165309515 absolute error = 1e-31 relative error = 3.6399303985591592066212289785585e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.3MB, time=1.49 x[1] = 0.177 y[1] (analytic) = -2.7480677127422700205348171594844 y[1] (numeric) = -2.7480677127422700205348171594844 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.178 y[1] (analytic) = -2.7488299165782886048012477575119 y[1] (numeric) = -2.7488299165782886048012477575119 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.179 y[1] (analytic) = -2.7495918908458877367169053975064 y[1] (numeric) = -2.7495918908458877367169053975064 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = -2.7503536356504223660627741115204 y[1] (numeric) = -2.7503536356504223660627741115205 absolute error = 1e-31 relative error = 3.6358960791000724783063642512075e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.181 y[1] (analytic) = -2.7511151510971507866924338319456 y[1] (numeric) = -2.7511151510971507866924338319457 absolute error = 1e-31 relative error = 3.6348896541142517994742459007967e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.182 y[1] (analytic) = -2.7518764372912347694838361272643 y[1] (numeric) = -2.7518764372912347694838361272644 absolute error = 1e-31 relative error = 3.6338840888667729833277777704016e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.183 y[1] (analytic) = -2.752637494337739695047355283306 y[1] (numeric) = -2.7526374943377396950473552833062 absolute error = 2e-31 relative error = 7.2657587645088092557192879217658e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.184 y[1] (analytic) = -2.7533983223416346861906729634156 y[1] (numeric) = -2.7533983223416346861906729634158 absolute error = 2e-31 relative error = 7.2637510663516888290889917524872e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.3MB, time=1.64 x[1] = 0.185 y[1] (analytic) = -2.7541589214077927401410531473309 y[1] (numeric) = -2.7541589214077927401410531473311 absolute error = 2e-31 relative error = 7.2617450810634297000275859862154e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.186 y[1] (analytic) = -2.7549192916409908605255625198752 y[1] (numeric) = -2.7549192916409908605255625198754 absolute error = 2e-31 relative error = 7.2597408064491180381667444683757e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.187 y[1] (analytic) = -2.755679433145910189109789956766 y[1] (numeric) = -2.7556794331459101891097899567661 absolute error = 1e-31 relative error = 3.6288691201588363490982831944195e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.188 y[1] (analytic) = -2.7564393460271361372956172359204 y[1] (numeric) = -2.7564393460271361372956172359206 absolute error = 2e-31 relative error = 7.2557373804818367711191069039344e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.189 y[1] (analytic) = -2.7571990303891585173785915885752 y[1] (numeric) = -2.7571990303891585173785915885754 absolute error = 2e-31 relative error = 7.2537382247581691579953493343640e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = -2.7579584863363716735654491953127 y[1] (numeric) = -2.757958486336371673565449195313 absolute error = 3e-31 relative error = 1.0877611156450554249173178399354e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.191 y[1] (analytic) = -2.7587177139730746127523372276936 y[1] (numeric) = -2.7587177139730746127523372276938 absolute error = 2e-31 relative error = 7.2497450169326031275223557873359e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.192 y[1] (analytic) = -2.7594767134034711350642805365977 y[1] (numeric) = -2.7594767134034711350642805365979 absolute error = 2e-31 relative error = 7.2477509604828260398190809841563e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.3MB, time=1.79 x[1] = 0.193 y[1] (analytic) = -2.7602354847316699641564375935785 y[1] (numeric) = -2.7602354847316699641564375935787 absolute error = 2e-31 relative error = 7.2457585994494432291903057115143e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.194 y[1] (analytic) = -2.7609940280616848772776888015007 y[1] (numeric) = -2.760994028061684877277688801501 absolute error = 3e-31 relative error = 1.0865651897501950553353571295706e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.195 y[1] (analytic) = -2.7617523434974348350970988054559 y[1] (numeric) = -2.7617523434974348350970988054562 absolute error = 3e-31 relative error = 1.0862668432466513279819297394101e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.196 y[1] (analytic) = -2.7625104311427441112937929544083 y[1] (numeric) = -2.7625104311427441112937929544086 absolute error = 3e-31 relative error = 1.0859687500832406289931350753091e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.197 y[1] (analytic) = -2.7632682911013424219107865882046 y[1] (numeric) = -2.7632682911013424219107865882048 absolute error = 2e-31 relative error = 7.2378060662465377683900013263389e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.198 y[1] (analytic) = -2.7640259234768650544733043534584 y[1] (numeric) = -2.7640259234768650544733043534587 absolute error = 3e-31 relative error = 1.0853733224854502898412593558952e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.199 y[1] (analytic) = -2.7647833283728529968721252853913 y[1] (numeric) = -2.7647833283728529968721252853915 absolute error = 2e-31 relative error = 7.2338399160452551413856483757320e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = -2.7655405058927530660124879309399 y[1] (numeric) = -2.7655405058927530660124879309402 absolute error = 3e-31 relative error = 1.0847789043796920657176787349754e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.201 y[1] (analytic) = -2.7662974561399180362290883313312 y[1] (numeric) = -2.7662974561399180362290883313313 absolute error = 1e-31 relative error = 3.6149402436113886445436518253270e-30 % Correct digits = 31 memory used=49.5MB, alloc=4.3MB, time=1.95 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.202 y[1] (analytic) = -2.7670541792176067674677022298393 y[1] (numeric) = -2.7670541792176067674677022298395 absolute error = 2e-31 relative error = 7.2279032879851534449959804455213e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.203 y[1] (analytic) = -2.7678106752289843332339614225834 y[1] (numeric) = -2.7678106752289843332339614225835 absolute error = 1e-31 relative error = 3.6129638813437584110163583233953e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.204 y[1] (analytic) = -2.7685669442771221483098127269516 y[1] (numeric) = -2.7685669442771221483098127269517 absolute error = 1e-31 relative error = 3.6119769546013337023702264830418e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.205 y[1] (analytic) = -2.7693229864649980962381866035698 y[1] (numeric) = -2.7693229864649980962381866035699 absolute error = 1e-31 relative error = 3.6109908627035445851419241808687e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.206 y[1] (analytic) = -2.7700788018954966565764010336116 y[1] (numeric) = -2.7700788018954966565764010336117 absolute error = 1e-31 relative error = 3.6100056045904710170254698082718e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.207 y[1] (analytic) = -2.7708343906714090319188248236919 y[1] (numeric) = -2.770834390671409031918824823692 absolute error = 1e-31 relative error = 3.6090211792040269082614095509129e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.208 y[1] (analytic) = -2.7715897528954332746893230855561 y[1] (numeric) = -2.7715897528954332746893230855562 absolute error = 1e-31 relative error = 3.6080375854879561156727646056558e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.209 y[1] (analytic) = -2.7723448886701744137040062172688 y[1] (numeric) = -2.7723448886701744137040062172689 absolute error = 1e-31 relative error = 3.6070548223878284472693026608081e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.3MB, time=2.10 x[1] = 0.21 y[1] (analytic) = -2.7730997980981445805048022965991 y[1] (numeric) = -2.7730997980981445805048022965993 absolute error = 2e-31 relative error = 7.2121457777020713547749315763226e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.211 y[1] (analytic) = -2.7738544812817631354643713857759 y[1] (numeric) = -2.773854481281763135464371385776 absolute error = 1e-31 relative error = 3.6050917838267875723334026508853e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.212 y[1] (analytic) = -2.7746089383233567936628788397315 y[1] (numeric) = -2.7746089383233567936628788397317 absolute error = 2e-31 relative error = 7.2082230125322158529933364488856e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.213 y[1] (analytic) = -2.7753631693251597505371433073566 y[1] (numeric) = -2.7753631693251597505371433073568 absolute error = 2e-31 relative error = 7.2062641102436612178045381207812e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.214 y[1] (analytic) = -2.7761171743893138073026737171161 y[1] (numeric) = -2.7761171743893138073026737171162 absolute error = 1e-31 relative error = 3.6021534293485956201688464973003e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.215 y[1] (analytic) = -2.7768709536178684961491081446401 y[1] (numeric) = -2.7768709536178684961491081446402 absolute error = 1e-31 relative error = 3.6011756279028451598409041410606e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.216 y[1] (analytic) = -2.7776245071127812052095660705608 y[1] (numeric) = -2.777624507112781205209566070561 absolute error = 2e-31 relative error = 7.2003972994856394081261988011493e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.217 y[1] (analytic) = -2.7783778349759173033044241519151 y[1] (numeric) = -2.7783778349759173033044241519152 absolute error = 1e-31 relative error = 3.5992224938285540935647318763418e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.3MB, time=2.26 x[1] = 0.218 y[1] (analytic) = -2.7791309373090502644600242498567 y[1] (numeric) = -2.7791309373090502644600242498569 absolute error = 2e-31 relative error = 7.1964943182437472638453479212272e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.219 y[1] (analytic) = -2.7798838142138617922028210802022 y[1] (numeric) = -2.7798838142138617922028210802024 absolute error = 2e-31 relative error = 7.1945452891727803881422022414983e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = -2.7806364657919419436294754814514 y[1] (numeric) = -2.7806364657919419436294754814517 absolute error = 3e-31 relative error = 1.0788896847562495035079473012141e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.221 y[1] (analytic) = -2.7813888921447892532533979273756 y[1] (numeric) = -2.7813888921447892532533979273759 absolute error = 3e-31 relative error = 1.0785978215677114406389415173997e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.222 y[1] (analytic) = -2.7821410933738108566282455480177 y[1] (numeric) = -2.782141093373810856628245548018 absolute error = 3e-31 relative error = 1.0783062035009873722323631419764e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.223 y[1] (analytic) = -2.7828930695803226137488745640047 y[1] (numeric) = -2.782893069580322613748874564005 absolute error = 3e-31 relative error = 1.0780148302472931330768431788580e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.224 y[1] (analytic) = -2.7836448208655492322302486844005 y[1] (numeric) = -2.7836448208655492322302486844008 absolute error = 3e-31 relative error = 1.0777237014983747379134885577584e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.225 y[1] (analytic) = -2.7843963473306243902648026679219 y[1] (numeric) = -2.7843963473306243902648026679223 absolute error = 4e-31 relative error = 1.4365770892620096429807458965551e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.3MB, time=2.41 x[1] = 0.226 y[1] (analytic) = -2.7851476490765908593587589011854 y[1] (numeric) = -2.7851476490765908593587589011858 absolute error = 4e-31 relative error = 1.4361895683793247281288901211093e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.227 y[1] (analytic) = -2.7858987262044006268478935057252 y[1] (numeric) = -2.7858987262044006268478935057255 absolute error = 3e-31 relative error = 1.0768517792056633509182677296324e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.228 y[1] (analytic) = -2.7866495788149150181932471478196 y[1] (numeric) = -2.78664957881491501819324714782 absolute error = 4e-31 relative error = 1.4354155005384958923829936462685e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.229 y[1] (analytic) = -2.7874002070089048190572743916601 y[1] (numeric) = -2.7874002070089048190572743916605 absolute error = 4e-31 relative error = 1.4350289527646653169792495087780e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = -2.788150610887050397160924107078 y[1] (numeric) = -2.7881506108870503971609241070783 absolute error = 3e-31 relative error = 1.0759820464094476224849545024663e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.231 y[1] (analytic) = -2.7889007905499418239221421179066 y[1] (numeric) = -2.788900790549941823922142117907 absolute error = 4e-31 relative error = 1.4342568274761907842282760164139e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.232 y[1] (analytic) = -2.7896507460980789958762859560687 y[1] (numeric) = -2.7896507460980789958762859560691 absolute error = 4e-31 relative error = 1.4338712491500422926660827273634e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.233 y[1] (analytic) = -2.7904004776318717558789402696359 y[1] (numeric) = -2.7904004776318717558789402696363 absolute error = 4e-31 relative error = 1.4334859931627730611488037026434e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.234 y[1] (analytic) = -2.7911499852516400140916201203974 y[1] (numeric) = -2.7911499852516400140916201203977 absolute error = 3e-31 relative error = 1.0748257943327724188809811878207e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 memory used=64.8MB, alloc=4.3MB, time=2.57 TOP MAIN SOLVE Loop x[1] = 0.235 y[1] (analytic) = -2.791899269057613868750848097869 y[1] (numeric) = -2.7918992690576138687508480978694 absolute error = 4e-31 relative error = 1.4327164465894831905158581301832e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.236 y[1] (analytic) = -2.7926483291499337267210898721773 y[1] (numeric) = -2.7926483291499337267210898721776 absolute error = 3e-31 relative error = 1.0742491163981191083052377214195e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.237 y[1] (analytic) = -2.7933971656286504238320315078285 y[1] (numeric) = -2.7933971656286504238320315078288 absolute error = 3e-31 relative error = 1.0739611383993274279585415717878e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.238 y[1] (analytic) = -2.7941457785937253450006805640305 y[1] (numeric) = -2.7941457785937253450006805640307 absolute error = 2e-31 relative error = 7.1578226709652438417719047729615e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.239 y[1] (analytic) = -2.7948941681450305441387717149349 y[1] (numeric) = -2.7948941681450305441387717149351 absolute error = 2e-31 relative error = 7.1559060188937268755551430822178e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = -2.7956423343823488638459563349173 y[1] (numeric) = -2.7956423343823488638459563349176 absolute error = 3e-31 relative error = 1.0730986446672194199277184951127e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.241 y[1] (analytic) = -2.7963902774053740548892542097823 y[1] (numeric) = -2.7963902774053740548892542097826 absolute error = 3e-31 relative error = 1.0728116258448534153228062956138e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.242 y[1] (analytic) = -2.797137997313710895469244254564 y[1] (numeric) = -2.7971379973137108954692442545643 absolute error = 3e-31 relative error = 1.0725248460680566380104043895280e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.3MB, time=2.72 x[1] = 0.243 y[1] (analytic) = -2.7978854942068753102734698423747 y[1] (numeric) = -2.797885494206875310273469842375 absolute error = 3e-31 relative error = 1.0722383050384335592677670372328e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.244 y[1] (analytic) = -2.7986327681842944893175330765137 y[1] (numeric) = -2.798632768184294489317533076514 absolute error = 3e-31 relative error = 1.0719520024580964075719984428619e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.245 y[1] (analytic) = -2.7993798193453070065743510697841 y[1] (numeric) = -2.7993798193453070065743510697844 absolute error = 3e-31 relative error = 1.0716659380296640778531248960655e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.246 y[1] (analytic) = -2.8001266477891629383920460306488 y[1] (numeric) = -2.8001266477891629383920460306491 absolute error = 3e-31 relative error = 1.0713801114562610435771404793689e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.247 y[1] (analytic) = -2.800873253615023981700939695485 y[1] (numeric) = -2.8008732536150239817009396954853 absolute error = 3e-31 relative error = 1.0710945224415162716504230741560e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.248 y[1] (analytic) = -2.8016196369219635720101213897489 y[1] (numeric) = -2.8016196369219635720101213897491 absolute error = 2e-31 relative error = 7.1387278045970809342463158673648e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.249 y[1] (analytic) = -2.8023657978089670011940577483281 y[1] (numeric) = -2.8023657978089670011940577483285 absolute error = 4e-31 relative error = 1.4273654078733778117063353691904e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = -2.8031117363749315350697108767252 y[1] (numeric) = -2.8031117363749315350697108767254 absolute error = 2e-31 relative error = 7.1349278519537726154542906912919e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.3MB, time=2.88 x[1] = 0.251 y[1] (analytic) = -2.8038574527186665307646304899576 y[1] (numeric) = -2.8038574527186665307646304899579 absolute error = 3e-31 relative error = 1.0699545360592958865921640619126e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.252 y[1] (analytic) = -2.804602946938893553876484325191 y[1] (numeric) = -2.8046029469388935538764843251913 absolute error = 3e-31 relative error = 1.0696701304098585974258494602630e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.253 y[1] (analytic) = -2.8053482191342464954244898870849 y[1] (numeric) = -2.8053482191342464954244898870852 absolute error = 3e-31 relative error = 1.0693859605513873222808724191939e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.254 y[1] (analytic) = -2.8060932694032716885932093516627 y[1] (numeric) = -2.806093269403271688593209351663 absolute error = 3e-31 relative error = 1.0691020261910123346721619343116e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.255 y[1] (analytic) = -2.8068380978444280252691682251586 y[1] (numeric) = -2.8068380978444280252691682251589 absolute error = 3e-31 relative error = 1.0688183270363598213371373663429e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.256 y[1] (analytic) = -2.807582704556087072370757128765 y[1] (numeric) = -2.8075827045560870723707571287652 absolute error = 2e-31 relative error = 7.1235657519703388143347898588278e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.257 y[1] (analytic) = -2.8083270896365331879718748584704 y[1] (numeric) = -2.8083270896365331879718748584707 absolute error = 3e-31 relative error = 1.0682516331772001727743028345948e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.258 y[1] (analytic) = -2.8090712531839636372197696512368 y[1] (numeric) = -2.8090712531839636372197696512371 absolute error = 3e-31 relative error = 1.0679686378904154500409306888053e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.3MB, time=3.03 x[1] = 0.259 y[1] (analytic) = -2.8098151952964887080475343745962 y[1] (numeric) = -2.8098151952964887080475343745965 absolute error = 3e-31 relative error = 1.0676858766447959200508862300209e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = -2.8105589160721318266817101463462 y[1] (numeric) = -2.8105589160721318266817101463465 absolute error = 3e-31 relative error = 1.0674033491504314889870126225995e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.261 y[1] (analytic) = -2.8113024156088296729454516843654 y[1] (numeric) = -2.8113024156088296729454516843657 absolute error = 3e-31 relative error = 1.0671210551179016566310467933355e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.262 y[1] (analytic) = -2.8120456940044322953577064836518 y[1] (numeric) = -2.8120456940044322953577064836521 absolute error = 3e-31 relative error = 1.0668389942582744725763082838752e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.263 y[1] (analytic) = -2.8127887513567032260288587184901 y[1] (numeric) = -2.8127887513567032260288587184904 absolute error = 3e-31 relative error = 1.0665571662831054951281047581145e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.264 y[1] (analytic) = -2.8135315877633195953532875721667 y[1] (numeric) = -2.8135315877633195953532875721671 absolute error = 4e-31 relative error = 1.4217007612059156705116598815377e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.265 y[1] (analytic) = -2.8142742033218722464992885048606 y[1] (numeric) = -2.8142742033218722464992885048609 absolute error = 3e-31 relative error = 1.0659942078347957089840775739002e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.266 y[1] (analytic) = -2.8150165981298658496968047822274 y[1] (numeric) = -2.8150165981298658496968047822277 absolute error = 3e-31 relative error = 1.0657130767871942280285037455618e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.267 y[1] (analytic) = -2.8157587722847190163234154027616 y[1] (numeric) = -2.8157587722847190163234154027619 absolute error = 3e-31 relative error = 1.0654321774751275456454361154827e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 memory used=80.1MB, alloc=4.3MB, time=3.18 TOP MAIN SOLVE Loop x[1] = 0.268 y[1] (analytic) = -2.816500725883764412789024381236 y[1] (numeric) = -2.8165007258837644127890243812363 absolute error = 3e-31 relative error = 1.0651515096125732407102083566203e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.269 y[1] (analytic) = -2.8172424590242488742196951683853 y[1] (numeric) = -2.8172424590242488742196951683856 absolute error = 3e-31 relative error = 1.0648710729139902102024640857804e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = -2.8179839718033335179410728134942 y[1] (numeric) = -2.8179839718033335179410728134946 absolute error = 4e-31 relative error = 1.4194544894590901955934438548059e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.271 y[1] (analytic) = -2.8187252643180938567618353066664 y[1] (numeric) = -2.8187252643180938567618353066668 absolute error = 4e-31 relative error = 1.4190811891586320246223043008407e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.272 y[1] (analytic) = -2.8194663366655199120576143712685 y[1] (numeric) = -2.8194663366655199120576143712689 absolute error = 4e-31 relative error = 1.4187081959384747363068390100319e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.273 y[1] (analytic) = -2.82020718894251632665582481436 y[1] (numeric) = -2.8202071889425163266558248143604 absolute error = 4e-31 relative error = 1.4183355094204502912909812709906e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.274 y[1] (analytic) = -2.8209478212459024775218403838114 y[1] (numeric) = -2.8209478212459024775218403838119 absolute error = 5e-31 relative error = 1.7724539115337820322840229165658e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.275 y[1] (analytic) = -2.8216882336724125882469529252771 y[1] (numeric) = -2.8216882336724125882469529252776 absolute error = 5e-31 relative error = 1.7719888187266266322681185803932e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.3MB, time=3.34 x[1] = 0.276 y[1] (analytic) = -2.8224284263186958413385504802053 y[1] (numeric) = -2.8224284263186958413385504802058 absolute error = 5e-31 relative error = 1.7715241078837627303525673777304e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.277 y[1] (analytic) = -2.8231683992813164903129488176308 y[1] (numeric) = -2.8231683992813164903129488176313 absolute error = 5e-31 relative error = 1.7710597785356450778860974078072e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.278 y[1] (analytic) = -2.8239081526567539715913097475853 y[1] (numeric) = -2.8239081526567539715913097475858 absolute error = 5e-31 relative error = 1.7705958302135154417105352732264e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.279 y[1] (analytic) = -2.8246476865414030161990784225702 y[1] (numeric) = -2.8246476865414030161990784225706 absolute error = 4e-31 relative error = 1.4161058099595207510884160994112e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = -2.8253870010315737612693706956521 y[1] (numeric) = -2.8253870010315737612693706956525 absolute error = 4e-31 relative error = 1.4157352598208899004153748945771e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.281 y[1] (analytic) = -2.8261260962234918613507404693517 y[1] (numeric) = -2.8261260962234918613507404693522 absolute error = 5e-31 relative error = 1.7692062667272425902172957882563e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.282 y[1] (analytic) = -2.8268649722132985995197558385833 y[1] (numeric) = -2.8268649722132985995197558385837 absolute error = 4e-31 relative error = 1.4149950702697318410099524544491e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.283 y[1] (analytic) = -2.8276036290970509982988117034633 y[1] (numeric) = -2.8276036290970509982988117034637 absolute error = 4e-31 relative error = 1.4146254301128247667094306410855e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.3MB, time=3.50 x[1] = 0.284 y[1] (analytic) = -2.8283420669707219303796054038247 y[1] (numeric) = -2.8283420669707219303796054038251 absolute error = 4e-31 relative error = 1.4142560925398160788797007833156e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.285 y[1] (analytic) = -2.8290802859302002291527008067288 y[1] (numeric) = -2.8290802859302002291527008067292 absolute error = 4e-31 relative error = 1.4138870571800693649862473550124e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.286 y[1] (analytic) = -2.8298182860712907990436051611656 y[1] (numeric) = -2.829818286071290799043605161166 absolute error = 4e-31 relative error = 1.4135183236635672617330903021831e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.287 y[1] (analytic) = -2.8305560674897147256557819204444 y[1] (numeric) = -2.8305560674897147256557819204447 absolute error = 3e-31 relative error = 1.0598624187156826123330684846533e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.288 y[1] (analytic) = -2.8312936302811093857210216225002 y[1] (numeric) = -2.8312936302811093857210216225006 absolute error = 4e-31 relative error = 1.4127817606833148517684652809859e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.289 y[1] (analytic) = -2.832030974541028556857591811463 y[1] (numeric) = -2.8320309745410285568575918114634 absolute error = 4e-31 relative error = 1.4124139304826133337005772111952e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = -2.832768100364942527136585880338 y[1] (numeric) = -2.8327681003649425271365858803383 absolute error = 3e-31 relative error = 1.0590348004884385571781040594625e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.291 y[1] (analytic) = -2.8335050078482382044568896145262 y[1] (numeric) = -2.8335050078482382044568896145266 absolute error = 4e-31 relative error = 1.4116791708222874493309522987605e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.4MB, time=3.65 x[1] = 0.292 y[1] (analytic) = -2.8342416970862192257291831191538 y[1] (numeric) = -2.8342416970862192257291831191542 absolute error = 4e-31 relative error = 1.4113122406293910901243844505706e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.293 y[1] (analytic) = -2.834978168174106065869394719764 y[1] (numeric) = -2.8349781681741060658693947197643 absolute error = 3e-31 relative error = 1.0582092072801314630983378567811e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.294 y[1] (analytic) = -2.8357144212070361466020223358562 y[1] (numeric) = -2.8357144212070361466020223358565 absolute error = 3e-31 relative error = 1.0579344582671462622585689582368e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.295 y[1] (analytic) = -2.836450456280063945073736740009 y[1] (numeric) = -2.8364504562800639450737367400093 absolute error = 3e-31 relative error = 1.0576599331597095192036969749520e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.296 y[1] (analytic) = -2.8371862734881611022776800318889 y[1] (numeric) = -2.8371862734881611022776800318893 absolute error = 4e-31 relative error = 1.4098475089131968622088044679355e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.297 y[1] (analytic) = -2.8379218729262165312888715763216 y[1] (numeric) = -2.837921872926216531288871576322 absolute error = 4e-31 relative error = 1.4094820714269876154254615798988e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.298 y[1] (analytic) = -2.8386572546890365253111325777617 y[1] (numeric) = -2.8386572546890365253111325777621 absolute error = 4e-31 relative error = 1.4091169313916286442367468015753e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.299 y[1] (analytic) = -2.8393924188713448655359393899417 y[1] (numeric) = -2.8393924188713448655359393899422 absolute error = 5e-31 relative error = 1.7609401105562908057855096182611e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = -2.8401273655677829288136145891923 y[1] (numeric) = -2.8401273655677829288136145891927 absolute error = 4e-31 relative error = 1.4083875422257133867552718590097e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.4MB, time=3.81 x[1] = 0.301 y[1] (analytic) = -2.8408620948729097951372637728926 y[1] (numeric) = -2.8408620948729097951372637728931 absolute error = 5e-31 relative error = 1.7600291154659805691303547433432e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.302 y[1] (analytic) = -2.841596606881202354939864980729 y[1] (numeric) = -2.8415966068812023549398649807294 absolute error = 4e-31 relative error = 1.4076593385259579930459113200905e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.303 y[1] (analytic) = -2.8423309016870554162049165758839 y[1] (numeric) = -2.8423309016870554162049165758843 absolute error = 4e-31 relative error = 1.4072956803255434475644651618763e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.304 y[1] (analytic) = -2.8430649793847818113910483659575 y[1] (numeric) = -2.8430649793847818113910483659579 absolute error = 4e-31 relative error = 1.4069323174124463211579074805478e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.305 y[1] (analytic) = -2.8437988400686125041709996893028 y[1] (numeric) = -2.8437988400686125041709996893033 absolute error = 5e-31 relative error = 1.7582115617852086548721964079685e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.306 y[1] (analytic) = -2.8445324838326966959853671415481 y[1] (numeric) = -2.8445324838326966959853671415486 absolute error = 5e-31 relative error = 1.7577580950184989122996641561803e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.307 y[1] (analytic) = -2.8452659107711019324115235693536 y[1] (numeric) = -2.845265910771101932411523569354 absolute error = 4e-31 relative error = 1.4058439968150291363757952755919e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.308 y[1] (analytic) = -2.8459991209778142093481089139072 y[1] (numeric) = -2.8459991209778142093481089139076 absolute error = 4e-31 relative error = 1.4054818114721342267183228077216e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.4MB, time=3.96 x[1] = 0.309 y[1] (analytic) = -2.8467321145467380790154924452885 y[1] (numeric) = -2.8467321145467380790154924452889 absolute error = 4e-31 relative error = 1.4051199196299815355071027807265e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = -2.8474648915716967557726048906093 y[1] (numeric) = -2.8474648915716967557726048906096 absolute error = 3e-31 relative error = 1.0535687406997701131474679999522e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.311 y[1] (analytic) = -2.8481974521464322217505379237684 y[1] (numeric) = -2.8481974521464322217505379237687 absolute error = 3e-31 relative error = 1.0532977612697349146608270406920e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.312 y[1] (analytic) = -2.8489297963646053323033074527209 y[1] (numeric) = -2.8489297963646053323033074527212 absolute error = 3e-31 relative error = 1.0530270011666025414110609960803e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.313 y[1] (analytic) = -2.8496619243197959212761761113467 y[1] (numeric) = -2.849661924319795921276176111347 absolute error = 3e-31 relative error = 1.0527564601250336873135933760882e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.314 y[1] (analytic) = -2.850393836105502906091929337306 y[1] (numeric) = -2.8503938361055029060919293373064 absolute error = 4e-31 relative error = 1.4033148505068357876948367942284e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.315 y[1] (analytic) = -2.8511255318151443926554983946724 y[1] (numeric) = -2.8511255318151443926554983946727 absolute error = 3e-31 relative error = 1.0522160341674173727870922769987e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.316 y[1] (analytic) = -2.8518570115420577800773226806269 y[1] (numeric) = -2.8518570115420577800773226806273 absolute error = 4e-31 relative error = 1.4025948649638355031643103484044e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.4MB, time=4.12 x[1] = 0.317 y[1] (analytic) = -2.8525882753794998652158426390788 y[1] (numeric) = -2.8525882753794998652158426390792 absolute error = 4e-31 relative error = 1.4022353083772146856594478178407e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.318 y[1] (analytic) = -2.8533193234206469470395135907184 y[1] (numeric) = -2.8533193234206469470395135907187 absolute error = 3e-31 relative error = 1.0514070315843611037950977566133e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.319 y[1] (analytic) = -2.8540501557585949308087297787226 y[1] (numeric) = -2.8540501557585949308087297787229 absolute error = 3e-31 relative error = 1.0511377993645007243471676441656e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = -2.8547807724863594320780469220874 y[1] (numeric) = -2.8547807724863594320780469220876 absolute error = 2e-31 relative error = 7.0057918957402404111228170202400e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.321 y[1] (analytic) = -2.8555111736968758805190905643565 y[1] (numeric) = -2.8555111736968758805190905643569 absolute error = 4e-31 relative error = 1.4007999817494730143320682431538e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.322 y[1] (analytic) = -2.8562413594829996235645365043456 y[1] (numeric) = -2.8562413594829996235645365043459 absolute error = 3e-31 relative error = 1.0503314049562750298330472461126e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.323 y[1] (analytic) = -2.8569713299375060298735485972966 y[1] (numeric) = -2.8569713299375060298735485972969 absolute error = 3e-31 relative error = 1.0500630400325447466967351733148e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.324 y[1] (analytic) = -2.8577010851530905926190582197586 y[1] (numeric) = -2.8577010851530905926190582197589 absolute error = 3e-31 relative error = 1.0497948912803405671679733669916e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.325 y[1] (analytic) = -2.8584306252223690325972686993285 y[1] (numeric) = -2.8584306252223690325972686993288 absolute error = 3e-31 relative error = 1.0495269584395170358794524757118e-29 % Correct digits = 30 h = 0.001 memory used=106.8MB, alloc=4.4MB, time=4.27 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.326 y[1] (analytic) = -2.859159950237877401159767021229 y[1] (numeric) = -2.8591599502378774011597670212294 absolute error = 4e-31 relative error = 1.3990123216671409323327044003329e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.327 y[1] (analytic) = -2.8598890602920721829686241375098 y[1] (numeric) = -2.8598890602920721829686241375102 absolute error = 4e-31 relative error = 1.3986556526047522942454013893367e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.328 y[1] (analytic) = -2.8606179554773303985748642214372 y[1] (numeric) = -2.8606179554773303985748642214375 absolute error = 3e-31 relative error = 1.0487244527902754979926746002537e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.329 y[1] (analytic) = -2.861346635885949706820682229374 y[1] (numeric) = -2.8613466358859497068206822293742 absolute error = 2e-31 relative error = 6.9897158733469785534210102820972e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = -2.8620751016101485070657881551326 y[1] (numeric) = -2.8620751016101485070657881551328 absolute error = 2e-31 relative error = 6.9879368255390586895809413627373e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.331 y[1] (analytic) = -2.8628033527420660412382553874019 y[1] (numeric) = -2.8628033527420660412382553874021 absolute error = 2e-31 relative error = 6.9861592067940992455405342149518e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.332 y[1] (analytic) = -2.8635313893737624957102496093922 y[1] (numeric) = -2.8635313893737624957102496093924 absolute error = 2e-31 relative error = 6.9843830153976005789712382587256e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.333 y[1] (analytic) = -2.8642592115972191029990137113035 y[1] (numeric) = -2.8642592115972191029990137113036 absolute error = 1e-31 relative error = 3.4913041248189343720256188121646e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.4MB, time=4.43 x[1] = 0.334 y[1] (analytic) = -2.8649868195043382432934832205876 y[1] (numeric) = -2.8649868195043382432934832205878 absolute error = 2e-31 relative error = 6.9808349078060096952492444169684e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.335 y[1] (analytic) = -2.8657142131869435458069057922371 y[1] (numeric) = -2.8657142131869435458069057922374 absolute error = 3e-31 relative error = 1.0468594482293885258357188401757e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.336 y[1] (analytic) = -2.8664413927367799899558373414813 y[1] (numeric) = -2.8664413927367799899558373414816 absolute error = 3e-31 relative error = 1.0465938733656447898844112606935e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.337 y[1] (analytic) = -2.8671683582455140063658864442956 y[1] (numeric) = -2.8671683582455140063658864442958 absolute error = 2e-31 relative error = 6.9755234088306059986865175528339e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.338 y[1] (analytic) = -2.8678951098047335777045776770197 y[1] (numeric) = -2.86789510980473357770457767702 absolute error = 3e-31 relative error = 1.0460633618515640379062108283063e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.339 y[1] (analytic) = -2.8686216475059483393417036151307 y[1] (numeric) = -2.868621647505948339341703615131 absolute error = 3e-31 relative error = 1.0457984246923170568059066510392e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = -2.8693479714405896798375342628059 y[1] (numeric) = -2.8693479714405896798375342628062 absolute error = 3e-31 relative error = 1.0455336995930176229005581416662e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.341 y[1] (analytic) = -2.8700740817000108412592517393487 y[1] (numeric) = -2.8700740817000108412592517393491 absolute error = 4e-31 relative error = 1.3936922484003298159957102101410e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.4MB, time=4.58 x[1] = 0.342 y[1] (analytic) = -2.8707999783754870193259771058044 y[1] (numeric) = -2.8707999783754870193259771058047 absolute error = 3e-31 relative error = 1.0450048845610010070562648375441e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.343 y[1] (analytic) = -2.8715256615582154633827552751711 y[1] (numeric) = -2.8715256615582154633827552751713 absolute error = 2e-31 relative error = 6.9649386274845703204134622749316e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.344 y[1] (analytic) = -2.8722511313393155762038630124971 y[1] (numeric) = -2.8722511313393155762038630124974 absolute error = 3e-31 relative error = 1.0444769147331193839977979626117e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.345 y[1] (analytic) = -2.8729763878098290136258040968384 y[1] (numeric) = -2.8729763878098290136258040968387 absolute error = 3e-31 relative error = 1.0442132461405314769344863422753e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.346 y[1] (analytic) = -2.8737014310607197840103547855199 y[1] (numeric) = -2.8737014310607197840103547855203 absolute error = 4e-31 relative error = 1.3919330507914140109564747417217e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.347 y[1] (analytic) = -2.8744262611828743475380217924017 y[1] (numeric) = -2.8744262611828743475380217924022 absolute error = 5e-31 relative error = 1.7394775672354233945800972185319e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.348 y[1] (analytic) = -2.8751508782671017153322740658671 y[1] (numeric) = -2.8751508782671017153322740658676 absolute error = 5e-31 relative error = 1.7390391710551127655921100515975e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.349 y[1] (analytic) = -2.875875282404133548414908729036 y[1] (numeric) = -2.8758752824041335484149087290365 absolute error = 5e-31 relative error = 1.7386011245314402887464848052054e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.4MB, time=4.74 x[1] = 0.35 y[1] (analytic) = -2.8765994736846242564929106242393 y[1] (numeric) = -2.8765994736846242564929106242398 absolute error = 5e-31 relative error = 1.7381634272481879009080385835967e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.351 y[1] (analytic) = -2.8773234521991510965771639860651 y[1] (numeric) = -2.8773234521991510965771639860657 absolute error = 6e-31 relative error = 2.0852712945477761097503222487870e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.352 y[1] (analytic) = -2.8780472180382142714333738522968 y[1] (numeric) = -2.8780472180382142714333738522973 absolute error = 5e-31 relative error = 1.7372890787414491834048631864265e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.353 y[1] (analytic) = -2.8787707712922370278655539097913 y[1] (numeric) = -2.8787707712922370278655539097918 absolute error = 5e-31 relative error = 1.7368524266889006179170216470391e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.354 y[1] (analytic) = -2.8794941120515657548324365627964 y[1] (numeric) = -2.8794941120515657548324365627969 absolute error = 5e-31 relative error = 1.7364161222186449089549599169479e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.355 y[1] (analytic) = -2.8802172404064700813971601043482 y[1] (numeric) = -2.8802172404064700813971601043487 absolute error = 5e-31 relative error = 1.7359801649178296013053495854250e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.356 y[1] (analytic) = -2.8809401564471429745105869672425 y[1] (numeric) = -2.880940156447142974510586967243 absolute error = 5e-31 relative error = 1.7355445543742712320198008381330e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.357 y[1] (analytic) = -2.8816628602637008366286061296005 y[1] (numeric) = -2.881662860263700836628606129601 absolute error = 5e-31 relative error = 1.7351092901764539619108677298207e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.358 y[1] (analytic) = -2.8823853519461836031637718512601 y[1] (numeric) = -2.8823853519461836031637718512606 absolute error = 5e-31 relative error = 1.7346743719135282104294197962679e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 memory used=122.0MB, alloc=4.4MB, time=4.89 TOP MAIN SOLVE Loop x[1] = 0.359 y[1] (analytic) = -2.8831076315845548397716300211017 y[1] (numeric) = -2.8831076315845548397716300211023 absolute error = 6e-31 relative error = 2.0810877590103711526963080276713e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = -2.8838296992687018394720825019521 y[1] (numeric) = -2.8838296992687018394720825019526 absolute error = 5e-31 relative error = 1.7338055715522760671995416827805e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.361 y[1] (analytic) = -2.8845515550884357196061389688967 y[1] (numeric) = -2.8845515550884357196061389688972 absolute error = 5e-31 relative error = 1.7333716886355695685843289246267e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.362 y[1] (analytic) = -2.88527319913349151862840484866 y[1] (numeric) = -2.8852731991334915186284048486604 absolute error = 4e-31 relative error = 1.3863505200135933345049266013798e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.363 y[1] (analytic) = -2.8859946314935282927356530821698 y[1] (numeric) = -2.8859946314935282927356530821702 absolute error = 4e-31 relative error = 1.3860039642312029754459121217390e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.364 y[1] (analytic) = -2.8867158522581292123318265495076 y[1] (numeric) = -2.8867158522581292123318265495081 absolute error = 5e-31 relative error = 1.7320721040447252139456521604275e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.365 y[1] (analytic) = -2.8874368615168016583298171161419 y[1] (numeric) = -2.8874368615168016583298171161423 absolute error = 4e-31 relative error = 1.3853116767023459524147732133336e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.366 y[1] (analytic) = -2.8881576593589773182903663816446 y[1] (numeric) = -2.888157659358977318290366381645 absolute error = 4e-31 relative error = 1.3849659443064457165734618909883e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.4MB, time=5.05 x[1] = 0.367 y[1] (analytic) = -2.8888782458740122823984323369934 y[1] (numeric) = -2.8888782458740122823984323369939 absolute error = 5e-31 relative error = 1.7307756071551851993231940745349e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.368 y[1] (analytic) = -2.8895986211511871392773652640451 y[1] (numeric) = -2.8895986211511871392773652640455 absolute error = 4e-31 relative error = 1.3842753006320442098955190704022e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.369 y[1] (analytic) = -2.8903187852797070716412353408345 y[1] (numeric) = -2.890318785279707071641235340835 absolute error = 5e-31 relative error = 1.7299129858840574585699980493848e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = -2.8910387383487019517856535489943 y[1] (numeric) = -2.8910387383487019517856535489947 absolute error = 4e-31 relative error = 1.3835857496273856392173026807927e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.371 y[1] (analytic) = -2.8917584804472264369174266147808 y[1] (numeric) = -2.8917584804472264369174266147812 absolute error = 4e-31 relative error = 1.3832413830706144881271674827594e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.372 y[1] (analytic) = -2.8924780116642600643233858529548 y[1] (numeric) = -2.8924780116642600643233858529552 absolute error = 4e-31 relative error = 1.3828972887156017719662929081105e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.373 y[1] (analytic) = -2.8931973320887073463787289230526 y[1] (numeric) = -2.8931973320887073463787289230531 absolute error = 5e-31 relative error = 1.7281918328019171173764755694653e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.374 y[1] (analytic) = -2.8939164418093978653952126504238 y[1] (numeric) = -2.8939164418093978653952126504243 absolute error = 5e-31 relative error = 1.7277623941601404400247713664533e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.4MB, time=5.20 x[1] = 0.375 y[1] (analytic) = -2.8946353409150863683095342097656 y[1] (numeric) = -2.894635340915086368309534209766 absolute error = 4e-31 relative error = 1.3818666356555546920427787497282e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.376 y[1] (analytic) = -2.8953540294944528612122371167687 y[1] (numeric) = -2.8953540294944528612122371167691 absolute error = 4e-31 relative error = 1.3815236269045914626023502378258e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.377 y[1] (analytic) = -2.8960725076361027037174776238757 y[1] (numeric) = -2.8960725076361027037174776238761 absolute error = 4e-31 relative error = 1.3811808887564661730822829762690e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.378 y[1] (analytic) = -2.8967907754285667031739862690453 y[1] (numeric) = -2.8967907754285667031739862690457 absolute error = 4e-31 relative error = 1.3808384208929340540108361852508e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.379 y[1] (analytic) = -2.8975088329603012087175584818021 y[1] (numeric) = -2.8975088329603012087175584818026 absolute error = 5e-31 relative error = 1.7256202787453262749997143016060e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = -2.8982266803196882051654073087215 y[1] (numeric) = -2.898226680319688205165407308722 absolute error = 5e-31 relative error = 1.7251928684365282940274932545501e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.381 y[1] (analytic) = -2.8989443175950354067527104808456 y[1] (numeric) = -2.8989443175950354067527104808461 absolute error = 5e-31 relative error = 1.7247657947938788517757039485672e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.382 y[1] (analytic) = -2.8996617448745763507116832083443 y[1] (numeric) = -2.8996617448745763507116832083447 absolute error = 4e-31 relative error = 1.3794712459376941284418009756669e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.383 y[1] (analytic) = -2.9003789622464704906935072530092 memory used=133.5MB, alloc=4.4MB, time=5.36 y[1] (numeric) = -2.9003789622464704906935072530096 absolute error = 4e-31 relative error = 1.3791301247412941072852863196957e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.384 y[1] (analytic) = -2.9010959697988032900334459968983 y[1] (numeric) = -2.9010959697988032900334459968988 absolute error = 5e-31 relative error = 1.7234865899133836070793784321350e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.385 y[1] (analytic) = -2.9018127676195863148594743956199 y[1] (numeric) = -2.9018127676195863148594743956203 absolute error = 4e-31 relative error = 1.3784486871912408460639661658723e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.386 y[1] (analytic) = -2.9025293557967573270447518773504 y[1] (numeric) = -2.9025293557967573270447518773508 absolute error = 4e-31 relative error = 1.3781083702087078663066649851534e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.387 y[1] (analytic) = -2.903245734418180377004265423721 y[1] (numeric) = -2.9032457344181803770042654237215 absolute error = 5e-31 relative error = 1.7222104008367778782370921256358e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.388 y[1] (analytic) = -2.9039619035716458963359692461538 y[1] (numeric) = -2.9039619035716458963359692461543 absolute error = 5e-31 relative error = 1.7217856728252499687697797238083e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.389 y[1] (analytic) = -2.9046778633448707903067466511004 y[1] (numeric) = -2.9046778633448707903067466511008 absolute error = 4e-31 relative error = 1.3770890226683571555933389622069e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = -2.9053936138254985301835188699005 y[1] (numeric) = -2.9053936138254985301835188699009 absolute error = 4e-31 relative error = 1.3767497735817095587033653886607e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.391 y[1] (analytic) = -2.906109155101099245409824813643 y[1] (numeric) = -2.9061091551010992454098248136434 absolute error = 4e-31 relative error = 1.3764107906885713340273500883731e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.4MB, time=5.51 x[1] = 0.392 y[1] (analytic) = -2.9068244872591698156281949004609 y[1] (numeric) = -2.9068244872591698156281949004614 absolute error = 5e-31 relative error = 1.7200900920971925774090555930784e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.393 y[1] (analytic) = -2.9075396103871339625486412921226 y[1] (numeric) = -2.907539610387133962548641292123 absolute error = 4e-31 relative error = 1.3757336222385657512715324484922e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.394 y[1] (analytic) = -2.9082545245723423416635860685795 y[1] (numeric) = -2.9082545245723423416635860685799 absolute error = 4e-31 relative error = 1.3753954360608098397001056389769e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.395 y[1] (analytic) = -2.9089692299020726338095480632988 y[1] (numeric) = -2.9089692299020726338095480632991 absolute error = 3e-31 relative error = 1.0312931361260881472407733344175e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.396 y[1] (analytic) = -2.9096837264635296365759082787216 y[1] (numeric) = -2.9096837264635296365759082787221 absolute error = 5e-31 relative error = 1.7183998228141001585403495409768e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.397 y[1] (analytic) = -2.9103980143438453555610730000623 y[1] (numeric) = -2.9103980143438453555610730000627 absolute error = 4e-31 relative error = 1.3743824660015813810615051931639e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.398 y[1] (analytic) = -2.9111120936300790954763529268588 y[1] (numeric) = -2.9111120936300790954763529268592 absolute error = 4e-31 relative error = 1.3740453377774631629169891193971e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.399 y[1] (analytic) = -2.9118259644092175510978758452352 y[1] (numeric) = -2.9118259644092175510978758452355 absolute error = 3e-31 relative error = 1.0302813549533933570571633905656e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.4MB, time=5.66 x[1] = 0.4 y[1] (analytic) = -2.912539626768174898066849569686 y[1] (numeric) = -2.9125396267681748980668495696864 absolute error = 4e-31 relative error = 1.3733718721755204720719192730377e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.401 y[1] (analytic) = -2.9132530807937928835384910913801 y[1] (numeric) = -2.9132530807937928835384910913806 absolute error = 5e-31 relative error = 1.7162944177296185009609225441887e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.402 y[1] (analytic) = -2.913966326572840916679937080461 y[1] (numeric) = -2.9139663265728409166799370804614 absolute error = 4e-31 relative error = 1.3726994589894452965570860407715e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.403 y[1] (analytic) = -2.914679364192016159017450102611 y[1] (numeric) = -2.9146793641920161590174501026115 absolute error = 5e-31 relative error = 1.7154545578587370836550744463111e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.404 y[1] (analytic) = -2.9153921937379436146332341252289 y[1] (numeric) = -2.9153921937379436146332341252293 absolute error = 4e-31 relative error = 1.3720280957710311833946699880608e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.405 y[1] (analytic) = -2.9161048152971762202121721059297 y[1] (numeric) = -2.9161048152971762202121721059302 absolute error = 5e-31 relative error = 1.7146160089209471352124882253467e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.406 y[1] (analytic) = -2.9168172289561949349387976757279 y[1] (numeric) = -2.9168172289561949349387976757284 absolute error = 5e-31 relative error = 1.7141972250998009039027207640371e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.407 y[1] (analytic) = -2.9175294348014088302448121511718 y[1] (numeric) = -2.9175294348014088302448121511723 absolute error = 5e-31 relative error = 1.7137787678705429514245897116249e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.4MB, time=5.82 x[1] = 0.408 y[1] (analytic) = -2.918241432919155179407457333879 y[1] (numeric) = -2.9182414329191551794074573338795 absolute error = 5e-31 relative error = 1.7133606368539680497699189829362e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.409 y[1] (analytic) = -2.9189532233956995469990537823524 y[1] (numeric) = -2.9189532233956995469990537823529 absolute error = 5e-31 relative error = 1.7129428316714718718438065714165e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = -2.9196648063172358781880134696375 y[1] (numeric) = -2.919664806317235878188013469638 absolute error = 5e-31 relative error = 1.7125253519450497894094474655395e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.411 y[1] (analytic) = -2.9203761817698865878916349713014 y[1] (numeric) = -2.920376181769886587891634971302 absolute error = 6e-31 relative error = 2.0545298367567548087250285099762e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.412 y[1] (analytic) = -2.9210873498397026497809885613684 y[1] (numeric) = -2.9210873498397026497809885613691 absolute error = 7e-31 relative error = 2.3963679142919609804927129124968e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.413 y[1] (analytic) = -2.9217983106126636851381978292243 y[1] (numeric) = -2.921798310612663685138197829225 absolute error = 7e-31 relative error = 2.3957848064236130151291672557647e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.414 y[1] (analytic) = -2.9225090641746780515664236681 y[1] (numeric) = -2.9225090641746780515664236681007 absolute error = 7e-31 relative error = 2.3952021520853051338786315307895e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.415 y[1] (analytic) = -2.9232196106115829315528557255525 y[1] (numeric) = -2.9232196106115829315528557255532 absolute error = 7e-31 relative error = 2.3946199507520036479791316823271e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.416 y[1] (analytic) = -2.9239299500091444208850156483717 y[1] (numeric) = -2.9239299500091444208850156483724 absolute error = 7e-31 relative error = 2.3940382018995044347991390362056e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 memory used=148.7MB, alloc=4.4MB, time=5.98 TOP MAIN SOLVE Loop x[1] = 0.417 y[1] (analytic) = -2.9246400824530576169206756985501 y[1] (numeric) = -2.9246400824530576169206756985508 absolute error = 7e-31 relative error = 2.3934569050044312831845940232997e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.418 y[1] (analytic) = -2.9253500080289467067116955633472 y[1] (numeric) = -2.9253500080289467067116955633479 absolute error = 7e-31 relative error = 2.3928760595442342427925073375225e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.419 y[1] (analytic) = -2.9260597268223650549820794310603 y[1] (numeric) = -2.926059726822365054982079431061 absolute error = 7e-31 relative error = 2.3922956649971879773998834750747e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = -2.9267692389187952919605546548643 y[1] (numeric) = -2.926769238918795291960554654865 absolute error = 7e-31 relative error = 2.3917157208423901221767480302428e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.421 y[1] (analytic) = -2.9274785444036494010679725800028 y[1] (numeric) = -2.9274785444036494010679725800035 absolute error = 7e-31 relative error = 2.3911362265597596449120964181420e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.422 y[1] (analytic) = -2.9281876433622688064598313646935 y[1] (numeric) = -2.9281876433622688064598313646942 absolute error = 7e-31 relative error = 2.3905571816300352111816178575071e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.423 y[1] (analytic) = -2.9288965358799244604242198823421 y[1] (numeric) = -2.9288965358799244604242198823429 absolute error = 8e-31 relative error = 2.7314040977540269182240965456905e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.424 y[1] (analytic) = -2.9296052220418169306354810520392 y[1] (numeric) = -2.92960522204181693063548105204 absolute error = 8e-31 relative error = 2.7307433574358261075078072135338e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.4MB, time=6.13 x[1] = 0.425 y[1] (analytic) = -2.9303137019330764872638922058296 y[1] (numeric) = -2.9303137019330764872638922058304 absolute error = 8e-31 relative error = 2.7300831288890812254226156718722e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.426 y[1] (analytic) = -2.931021975638763189941659364895 y[1] (numeric) = -2.9310219756387631899416593648957 absolute error = 7e-31 relative error = 2.3882454850835694248195643555358e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.427 y[1] (analytic) = -2.9317300432438669745855215625622 y[1] (numeric) = -2.931730043243866974585521562563 absolute error = 8e-31 relative error = 2.7287642047520350525772657269030e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.428 y[1] (analytic) = -2.9324379048333077400762606199429 y[1] (numeric) = -2.9324379048333077400762606199437 absolute error = 8e-31 relative error = 2.7281055079850886296725984561545e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.429 y[1] (analytic) = -2.9331455604919354347954110500093 y[1] (numeric) = -2.93314556049193543479541105001 absolute error = 7e-31 relative error = 2.3865164055567661682586426782627e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = -2.9338530103045301430194640380202 y[1] (numeric) = -2.9338530103045301430194640380209 absolute error = 7e-31 relative error = 2.3859409368547093861609792561830e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.431 y[1] (analytic) = -2.9345602543558021711718587204114 y[1] (numeric) = -2.9345602543558021711718587204121 absolute error = 7e-31 relative error = 2.3853659128688252277957585982598e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.432 y[1] (analytic) = -2.9352672927303921339330532605572 y[1] (numeric) = -2.9352672927303921339330532605579 absolute error = 7e-31 relative error = 2.3847913330879602801232160785769e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.4MB, time=6.29 x[1] = 0.433 y[1] (analytic) = -2.9359741255128710402089674981866 y[1] (numeric) = -2.9359741255128710402089674981874 absolute error = 8e-31 relative error = 2.7248196537163006877033298974657e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.434 y[1] (analytic) = -2.936680752787740378958088229689 y[1] (numeric) = -2.9366807527877403789580882296897 absolute error = 7e-31 relative error = 2.3836435041006826344938508066989e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.435 y[1] (analytic) = -2.9373871746394322048775274590624 y[1] (numeric) = -2.9373871746394322048775274590632 absolute error = 8e-31 relative error = 2.7235088615725332787339223020268e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.436 y[1] (analytic) = -2.9380933911523092239483232438479 y[1] (numeric) = -2.9380933911523092239483232438486 absolute error = 7e-31 relative error = 2.3824974458196600133083874728915e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.437 y[1] (analytic) = -2.9387994024106648788402720470237 y[1] (numeric) = -2.9387994024106648788402720470244 absolute error = 7e-31 relative error = 2.3819250794246034169607775989435e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.438 y[1] (analytic) = -2.9395052084987234341765807945304 y[1] (numeric) = -2.9395052084987234341765807945311 absolute error = 7e-31 relative error = 2.3813531541844314966622463023115e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.439 y[1] (analytic) = -2.9402108095006400616586261288217 y[1] (numeric) = -2.9402108095006400616586261288224 absolute error = 7e-31 relative error = 2.3807816695935714173272218406457e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = -2.9409162055005009250511076416075 y[1] (numeric) = -2.9409162055005009250511076416082 absolute error = 7e-31 relative error = 2.3802106251472412762257979834112e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.441 y[1] (analytic) = -2.9416213965823232650278811637472 y[1] (numeric) = -2.9416213965823232650278811637478 absolute error = 6e-31 memory used=160.2MB, alloc=4.4MB, time=6.45 relative error = 2.0396914460069558922639102469005e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.442 y[1] (analytic) = -2.9423263828300554838787574870708 y[1] (numeric) = -2.9423263828300554838787574870714 absolute error = 6e-31 relative error = 2.0392027325768472782174307843170e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.443 y[1] (analytic) = -2.9430311643275772300775511917398 y[1] (numeric) = -2.9430311643275772300775511917405 absolute error = 7e-31 relative error = 2.3785001276394426642397489114230e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.444 y[1] (analytic) = -2.943735741158699482711663553599 y[1] (numeric) = -2.9437357411586994827116635535996 absolute error = 6e-31 relative error = 2.0382264332050091174950768064728e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.445 y[1] (analytic) = -2.9444401134071646357734828088171 y[1] (numeric) = -2.9444401134071646357734828088177 absolute error = 6e-31 relative error = 2.0377388464040072683259343137139e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.446 y[1] (analytic) = -2.9451442811566465823138843579577 y[1] (numeric) = -2.9451442811566465823138843579582 absolute error = 5e-31 relative error = 1.6977096952399051510099931400954e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.447 y[1] (analytic) = -2.9458482444907507984581127984452 y[1] (numeric) = -2.9458482444907507984581127984457 absolute error = 5e-31 relative error = 1.6973039970239032816363819301933e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.448 y[1] (analytic) = -2.9465520034930144272843269832124 y[1] (numeric) = -2.9465520034930144272843269832129 absolute error = 5e-31 relative error = 1.6968986103325882836853189063498e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.449 y[1] (analytic) = -2.9472555582469063625650886140979 y[1] (numeric) = -2.9472555582469063625650886140984 absolute error = 5e-31 relative error = 1.6964935348104363307488809307829e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.4MB, time=6.61 x[1] = 0.45 y[1] (analytic) = -2.9479589088358273323720741913271 y[1] (numeric) = -2.9479589088358273323720741913277 absolute error = 6e-31 relative error = 2.0353065241229730117333157883451e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.451 y[1] (analytic) = -2.9486620553431099825442894551303 y[1] (numeric) = -2.9486620553431099825442894551308 absolute error = 5e-31 relative error = 1.6956843158542947316445212395333e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.452 y[1] (analytic) = -2.9493649978520189600200647722325 y[1] (numeric) = -2.9493649978520189600200647722329 absolute error = 4e-31 relative error = 1.3562241373696181154360626289336e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.453 y[1] (analytic) = -2.9500677364457509960331092385818 y[1] (numeric) = -2.9500677364457509960331092385823 absolute error = 5e-31 relative error = 1.6948763373223465484812908675322e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.454 y[1] (analytic) = -2.9507702712074349891729005902572 y[1] (numeric) = -2.9507702712074349891729005902577 absolute error = 5e-31 relative error = 1.6944728123325013160673914000308e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.455 y[1] (analytic) = -2.9514726022201320883096873370091 y[1] (numeric) = -2.9514726022201320883096873370096 absolute error = 5e-31 relative error = 1.6940695963902703109031471306073e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.456 y[1] (analytic) = -2.9521747295668357753843788573347 y[1] (numeric) = -2.9521747295668357753843788573353 absolute error = 6e-31 relative error = 2.0324000269727811747079185430268e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.457 y[1] (analytic) = -2.9528766533304719480635985203581 y[1] (numeric) = -2.9528766533304719480635985203586 absolute error = 5e-31 relative error = 1.6932640902425204407992646981670e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.4MB, time=6.76 x[1] = 0.458 y[1] (analytic) = -2.9535783735938990022601742280732 y[1] (numeric) = -2.9535783735938990022601742280737 absolute error = 5e-31 relative error = 1.6928617993353010871367188904803e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.459 y[1] (analytic) = -2.954279890439907914519340101717 y[1] (numeric) = -2.9542798904399079145193401017175 absolute error = 5e-31 relative error = 1.6924598160722928428774741885616e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = -2.954981203951222324270922368141 y[1] (numeric) = -2.9549812039512223242709223681416 absolute error = 6e-31 relative error = 2.0304697681248065210797487231763e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.461 y[1] (analytic) = -2.9556823142104986159477818360669 y[1] (numeric) = -2.9556823142104986159477818360674 absolute error = 5e-31 relative error = 1.6916567710814906581427183123967e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.462 y[1] (analytic) = -2.9563832213003260009707846880103 y[1] (numeric) = -2.9563832213003260009707846880109 absolute error = 6e-31 relative error = 2.0295068503876095850972483208995e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.463 y[1] (analytic) = -2.957083925303226599600572651455 y[1] (numeric) = -2.9570839253032265996005726514555 absolute error = 5e-31 relative error = 1.6908549524806901793771350137442e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.464 y[1] (analytic) = -2.9577844263016555226564029525272 y[1] (numeric) = -2.9577844263016555226564029525277 absolute error = 5e-31 relative error = 1.6904545022072088845361358750391e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.465 y[1] (analytic) = -2.9584847243780009531023277969779 y[1] (numeric) = -2.9584847243780009531023277969785 absolute error = 6e-31 relative error = 2.0280652289869283132689416671911e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.4MB, time=6.92 x[1] = 0.466 y[1] (analytic) = -2.9591848196145842275009824666953 y[1] (numeric) = -2.9591848196145842275009824666958 absolute error = 5e-31 relative error = 1.6896545179801305892424005951116e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.467 y[1] (analytic) = -2.9598847120936599173352504652544 y[1] (numeric) = -2.959884712093659917335250465255 absolute error = 6e-31 relative error = 2.0271059800014742673812864496879e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.468 y[1] (analytic) = -2.9605844018974159101980734931583 y[1] (numeric) = -2.9605844018974159101980734931588 absolute error = 5e-31 relative error = 1.6888557532072175425348705983471e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.469 y[1] (analytic) = -2.9612838891079734908506733824083 y[1] (numeric) = -2.9612838891079734908506733824087 absolute error = 4e-31 relative error = 1.3507654618027583297903236818893e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = -2.9619831738073874221494524708909 y[1] (numeric) = -2.9619831738073874221494524708914 absolute error = 5e-31 relative error = 1.6880582051291359707270542491171e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.471 y[1] (analytic) = -2.9626822560776460258418382497403 y[1] (numeric) = -2.9626822560776460258418382497408 absolute error = 5e-31 relative error = 1.6876598864906962594105837824865e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.472 y[1] (analytic) = -2.9633811360006712632313374713503 y[1] (numeric) = -2.9633811360006712632313374713507 absolute error = 4e-31 relative error = 1.3498094967960590819241452683659e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.473 y[1] (analytic) = -2.9640798136583188157120642620511 y[1] (numeric) = -2.9640798136583188157120642620515 absolute error = 4e-31 relative error = 1.3494913266397946579290670076503e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.474 y[1] (analytic) = -2.9647782891323781651730061416283 y[1] (numeric) = -2.9647782891323781651730061416287 absolute error = 4e-31 relative error = 1.3491733984501661672188998800325e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.4MB, time=7.08 x[1] = 0.475 y[1] (analytic) = -2.9654765625045726742722912118377 y[1] (numeric) = -2.965476562504572674272291211838 absolute error = 3e-31 relative error = 1.0116417839654984936815484208836e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.476 y[1] (analytic) = -2.9661746338565596665817191378612 y[1] (numeric) = -2.9661746338565596665817191378615 absolute error = 3e-31 relative error = 1.0114037001589017310608138080688e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.477 y[1] (analytic) = -2.9668725032699305066018179102406 y[1] (numeric) = -2.966872503269930506601817910241 absolute error = 4e-31 relative error = 1.3482210629514449362458077398145e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.478 y[1] (analytic) = -2.9675701708262106796476877402172 y[1] (numeric) = -2.9675701708262106796476877402176 absolute error = 4e-31 relative error = 1.3479040999008111870598315105702e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.479 y[1] (analytic) = -2.9682676366068598716058928085888 y[1] (numeric) = -2.9682676366068598716058928085892 absolute error = 4e-31 relative error = 1.3475873774551383806348427649318e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = -2.9689649006932720485626609571689 y[1] (numeric) = -2.9689649006932720485626609571693 absolute error = 4e-31 relative error = 1.3472708953433483657608975046326e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.481 y[1] (analytic) = -2.9696619631667755363036507826826 y[1] (numeric) = -2.969661963166775536303650782683 absolute error = 4e-31 relative error = 1.3469546532947800413740441130090e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.482 y[1] (analytic) = -2.9703588241086330996855449654618 y[1] (numeric) = -2.9703588241086330996855449654622 absolute error = 4e-31 relative error = 1.3466386510391885465960297159781e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.4MB, time=7.23 x[1] = 0.483 y[1] (analytic) = -2.9710554836000420218797280396 y[1] (numeric) = -2.9710554836000420218797280396004 absolute error = 4e-31 relative error = 1.3463228883067444526741831281675e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.484 y[1] (analytic) = -2.9717519417221341834883061872882 y[1] (numeric) = -2.9717519417221341834883061872886 absolute error = 4e-31 relative error = 1.3460073648280329568162505528759e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.485 y[1] (analytic) = -2.9724481985559761415327260178722 y[1] (numeric) = -2.9724481985559761415327260178725 absolute error = 3e-31 relative error = 1.0092690602505398084362325014048e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.486 y[1] (analytic) = -2.9731442541825692083152486717427 y[1] (numeric) = -2.9731442541825692083152486717431 absolute error = 4e-31 relative error = 1.3453770345562168541572401398601e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.487 y[1] (analytic) = -2.9738401086828495301535349704926 y[1] (numeric) = -2.9738401086828495301535349704929 absolute error = 3e-31 relative error = 1.0087966704197614068844267042117e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.488 y[1] (analytic) = -2.9745357621376881659885967178292 y[1] (numeric) = -2.9745357621376881659885967178295 absolute error = 3e-31 relative error = 1.0085607435575128650719078632587e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.489 y[1] (analytic) = -2.9752312146278911658663686405339 y[1] (numeric) = -2.9752312146278911658663686405341 absolute error = 2e-31 relative error = 6.7221666341993449369964058520928e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = -2.9759264662341996492931548452798 y[1] (numeric) = -2.97592646623419964929315484528 absolute error = 2e-31 relative error = 6.7205961662448008669393468338422e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.4MB, time=7.39 x[1] = 0.491 y[1] (analytic) = -2.9766215170372898834652030553755 y[1] (numeric) = -2.9766215170372898834652030553758 absolute error = 3e-31 relative error = 1.0078540327780669068407365626985e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.492 y[1] (analytic) = -2.9773163671177733613726592814683 y[1] (numeric) = -2.9773163671177733613726592814685 absolute error = 2e-31 relative error = 6.7174587896956475161362077915492e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.493 y[1] (analytic) = -2.978011016556196879778154971926 y[1] (numeric) = -2.9780110165561968797781549719262 absolute error = 2e-31 relative error = 6.7158918784418095961412701044847e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.494 y[1] (analytic) = -2.9787054654330426170702780820097 y[1] (numeric) = -2.9787054654330426170702780820099 absolute error = 2e-31 relative error = 6.7143261500990366068629442067945e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.495 y[1] (analytic) = -2.9793997138287282109921788960398 y[1] (numeric) = -2.97939971382872821099217889604 absolute error = 2e-31 relative error = 6.7127616033427956115416107578407e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.496 y[1] (analytic) = -2.9800937618236068362455608335527 y[1] (numeric) = -2.9800937618236068362455608335529 absolute error = 2e-31 relative error = 6.7111982368505791629455743347870e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.497 y[1] (analytic) = -2.9807876094979672819703058689276 y[1] (numeric) = -2.9807876094979672819703058689278 absolute error = 2e-31 relative error = 6.7096360493019013933773873850010e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.498 y[1] (analytic) = -2.9814812569320340290999835941314 y[1] (numeric) = -2.9814812569320340290999835941316 absolute error = 2e-31 relative error = 6.7080750393782941137977818062895e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.499 y[1] (analytic) = -2.9821747042059673275934923560807 y[1] (numeric) = -2.9821747042059673275934923560809 absolute error = 2e-31 relative error = 6.7065152057633029220422935999447e-30 % Correct digits = 31 h = 0.001 memory used=186.9MB, alloc=4.4MB, time=7.54 NO POLE for equation 1 Finished! diff ( y , x , 1 ) = ln(sqrt(0.1 * x + 0.2)); Iterations = 400 Total Elapsed Time = 7 Seconds Elapsed Time(since restart) = 7 Seconds Time to Timeout = 2 Minutes 52 Seconds Percent Done = 100.2 % > quit memory used=187.0MB, alloc=4.4MB, time=7.55