(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac (%i3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%o4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i5) test_suggested_h() := block([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 hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%o5) test_suggested_h() := block([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 hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%i6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%o6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 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) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr # 0.0 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "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, " ")))) (%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 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) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr # 0.0 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "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, " ")))) (%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 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))), 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 ), hnew : sz2), return(hnew)) 1 (%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 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))), 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 ), hnew : sz2), return(hnew)) 1 (%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], 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(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 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(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 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))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], 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(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 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(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 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))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 elseif (omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 5 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 elseif (omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 5 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%i11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%o11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ), 1 1 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , array_tmp3 : sin(array_x ), 1 1 1 1 1 array_tmp3_g : cos(array_x ), array_tmp4 : array_tmp3 + array_tmp2 , 1 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), 1 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 2 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1_g array_x - array_tmp1 array_x 1 2 1 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 2 1 2 1 array_tmp3_g array_x 1 2 array_tmp2 : array_tmp1 , array_tmp3 : ----------------------, 2 2 2 1 - array_tmp3 array_x 1 2 array_tmp3_g : ----------------------, 2 1 array_tmp4 : array_tmp3 + array_tmp2 , 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), 2 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 3 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 array_tmp1_g array_x - array_tmp1 array_x 2 2 2 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 3 2 3 2 array_tmp3_g array_x 2 2 array_tmp2 : array_tmp1 , array_tmp3 : ----------------------, 3 3 3 2 - array_tmp3 array_x 2 2 array_tmp3_g : ----------------------, 3 2 array_tmp4 : array_tmp3 + array_tmp2 , 3 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp1_g array_x - array_tmp1 array_x 3 2 3 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 4 3 4 3 array_tmp3_g array_x 3 2 array_tmp2 : array_tmp1 , array_tmp3 : ----------------------, 4 4 4 3 - array_tmp3 array_x 3 2 array_tmp3_g : ----------------------, 4 3 array_tmp4 : array_tmp3 + array_tmp2 , 4 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp1_g array_x - array_tmp1 array_x 4 2 4 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 5 4 5 4 array_tmp3_g array_x 4 2 array_tmp2 : array_tmp1 , array_tmp3 : ----------------------, 5 5 5 4 - array_tmp3 array_x 4 2 array_tmp3_g : ----------------------, 5 4 array_tmp4 : array_tmp3 + array_tmp2 , 5 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 array_tmp1_g array_x kkk - 1 2 while kkk <= glob_max_terms do (array_tmp1 : ----------------------------, kkk kkk - 1 - array_tmp1 array_x kkk - 1 2 array_tmp1_g : ----------------------------, array_tmp2 : array_tmp1 , kkk kkk - 1 kkk kkk array_tmp3_g array_x kkk - 1 2 array_tmp3 : ----------------------------, kkk kkk - 1 - array_tmp3 array_x kkk - 1 2 array_tmp3_g : ----------------------------, kkk kkk - 1 array_tmp4 : array_tmp3 + array_tmp2 , order_d : 1, kkk kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp4 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d temporary convfp(adj2) then (if adj2 > 1 then temporary : ---------------------- glob_h temporary else temporary : ---------, array_y_higher : temporary), glob_h adj3, term term : term - 1, adj2 : adj2 - 1, adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ), 1 1 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , array_tmp3 : sin(array_x ), 1 1 1 1 1 array_tmp3_g : cos(array_x ), array_tmp4 : array_tmp3 + array_tmp2 , 1 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), 1 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 2 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1_g array_x - array_tmp1 array_x 1 2 1 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 2 1 2 1 array_tmp3_g array_x 1 2 array_tmp2 : array_tmp1 , array_tmp3 : ----------------------, 2 2 2 1 - array_tmp3 array_x 1 2 array_tmp3_g : ----------------------, 2 1 array_tmp4 : array_tmp3 + array_tmp2 , 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), 2 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 3 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 array_tmp1_g array_x - array_tmp1 array_x 2 2 2 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 3 2 3 2 array_tmp3_g array_x 2 2 array_tmp2 : array_tmp1 , array_tmp3 : ----------------------, 3 3 3 2 - array_tmp3 array_x 2 2 array_tmp3_g : ----------------------, 3 2 array_tmp4 : array_tmp3 + array_tmp2 , 3 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp1_g array_x - array_tmp1 array_x 3 2 3 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 4 3 4 3 array_tmp3_g array_x 3 2 array_tmp2 : array_tmp1 , array_tmp3 : ----------------------, 4 4 4 3 - array_tmp3 array_x 3 2 array_tmp3_g : ----------------------, 4 3 array_tmp4 : array_tmp3 + array_tmp2 , 4 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp1_g array_x - array_tmp1 array_x 4 2 4 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 5 4 5 4 array_tmp3_g array_x 4 2 array_tmp2 : array_tmp1 , array_tmp3 : ----------------------, 5 5 5 4 - array_tmp3 array_x 4 2 array_tmp3_g : ----------------------, 5 4 array_tmp4 : array_tmp3 + array_tmp2 , 5 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 array_tmp1_g array_x kkk - 1 2 while kkk <= glob_max_terms do (array_tmp1 : ----------------------------, kkk kkk - 1 - array_tmp1 array_x kkk - 1 2 array_tmp1_g : ----------------------------, array_tmp2 : array_tmp1 , kkk kkk - 1 kkk kkk array_tmp3_g array_x kkk - 1 2 array_tmp3 : ----------------------------, kkk kkk - 1 - array_tmp3 array_x kkk - 1 2 array_tmp3_g : ----------------------------, kkk kkk - 1 array_tmp4 : array_tmp3 + array_tmp2 , order_d : 1, kkk kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp4 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d temporary convfp(adj2) then (if adj2 > 1 then temporary : ---------------------- glob_h temporary else temporary : ---------, array_y_higher : temporary), glob_h adj3, term term : term - 1, adj2 : adj2 - 1, adj3 : 1 + adj3))), kkk : 1 + kkk)) log(x) (%i13) log10(x) := --------- log(10.0) log(x) (%o13) log10(x) := --------- log(10.0) (%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, 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 : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, 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 : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%o27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error # 0.0 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error # 0.0 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i32) log_revs(file, revs) := printf(file, revs) (%o32) log_revs(file, revs) := printf(file, revs) (%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%o34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%i35) logstart(file) := printf(file, "") (%o35) logstart(file) := printf(file, "") (%i36) logend(file) := printf(file, "~%") (%o36) logend(file) := printf(file, "~%") (%i37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i40) factorial_2(nnn) := nnn! (%o40) factorial_2(nnn) := nnn! (%i41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%o41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%o42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i46) arcsin(x) := asin(x) (%o46) arcsin(x) := asin(x) (%i47) arccos(x) := acos(x) (%o47) arccos(x) := acos(x) (%i48) arctan(x) := atan(x) (%o48) arctan(x) := atan(x) (%i49) omniabs(x) := abs(x) (%o49) omniabs(x) := abs(x) y (%i50) expt(x, y) := x y (%o50) expt(x, y) := x (%i51) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], 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, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%o51) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], 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, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%i52) exact_soln_y(x) := block(- cos(x) - cos(x) + 2.0) (%o52) exact_soln_y(x) := block(- cos(x) - cos(x) + 2.0) (%i53) main() := block([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, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, 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/addpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-5.0,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:100,"), omniout_str(ALWAYS, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), 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, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (2.0 - cos(x) - cos(x)) "), omniout_str(ALWAYS, "));"), 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 : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, max_terms : 30, Digits : 32, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3_g, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3_g : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0, term term : 1 + term), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_g : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), iiif, jjjf x_start : - 5.0, x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_h : 0.05, glob_look_poles : true, glob_max_iter : 100, glob_display_interval : 0.1, glob_max_minutes : 10, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 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, 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 (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), 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 (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), 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 < glob_check_sign x_end) 1 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")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;"), 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, "2012-12-14T19:35:41-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "add"), logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 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) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), 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), log_revs(html_log_file, " 151 "), logitem_str(html_log_file, "add diffeq.max"), logitem_str(html_log_file, "add maxima results"), logitem_str(html_log_file, "Languages compared"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o53) main() := block([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, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, 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/addpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-5.0,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:100,"), omniout_str(ALWAYS, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), 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, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (2.0 - cos(x) - cos(x)) "), omniout_str(ALWAYS, "));"), 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 : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, max_terms : 30, Digits : 32, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3_g, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3_g : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_m1 : 0.0, term term : 1 + term), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_g : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), iiif, jjjf x_start : - 5.0, x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_h : 0.05, glob_look_poles : true, glob_max_iter : 100, glob_display_interval : 0.1, glob_max_minutes : 10, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 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, 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 (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), 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 (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), 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 < glob_check_sign x_end) 1 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")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;"), 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, "2012-12-14T19:35:41-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "add"), logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 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) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), 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), log_revs(html_log_file, " 151 "), logitem_str(html_log_file, "add diffeq.max"), logitem_str(html_log_file, "add maxima results"), logitem_str(html_log_file, "Languages compared"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i54) main() "##############ECHO OF PROBLEM#################" "##############temp/addpostode.ode#################" "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "max_terms:30," "Digits:32," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-5.0," "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_h:0.05," "glob_look_poles:true," "glob_max_iter:100," "glob_display_interval:0.1," "glob_max_minutes:10," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.001," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (2.0 - cos(x) - cos(x)) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 10. "" estimated_steps = 10000. "" step_error = 1.00000000000000E-14 "" est_needed_step_err = 1.00000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 9.50888924284450000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-103 "" max_value3 = 9.50888924284450000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-103 "" value3 = 9.50888924284450000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-103 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = -5. " " y[1] (analytic) = 1.4326756290735476 " " y[1] (numeric) = 1.4326756290735476 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.999 " " y[1] (analytic) = 1.4345937609653947 " " y[1] (numeric) = 1.4345937609653943 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.095574663249738000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.998000000000000 " " y[1] (analytic) = 1.4365124582634339 " " y[1] (numeric) = 1.4365124582634328 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 7.72860004268448100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.996999999999999 " " y[1] (analytic) = 1.438431719048968 " " y[1] (numeric) = 1.4384317190489662 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.23492607669601780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.995999999999999 " " y[1] (analytic) = 1.4403515414027361 " " y[1] (numeric) = 1.4403515414027337 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.6957600863165948000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.994999999999998 " " y[1] (analytic) = 1.4422719234049164 " " y[1] (numeric) = 1.4422719234049133 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.15536641773598130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.993999999999998 " " y[1] (analytic) = 1.4441928631351266 " " y[1] (numeric) = 1.4441928631351229 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 2.61374943754471730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.992999999999998 " " y[1] (analytic) = 1.4461143586724274 " " y[1] (numeric) = 1.446114358672423 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 3.070913494405440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.991999999999997 " " y[1] (analytic) = 1.4480364080953234 " " y[1] (numeric) = 1.4480364080953183 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 3.52686291913975660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.990999999999997 " " y[1] (analytic) = 1.4499590094817654 " " y[1] (numeric) = 1.4499590094817596 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 3.98160202481463100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.989999999999997 " " y[1] (analytic) = 1.4518821609091521 " " y[1] (numeric) = 1.4518821609091455 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 4.5880708001672010000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.988999999999996 " " y[1] (analytic) = 1.4538058604543318 " " y[1] (numeric) = 1.4538058604543247 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.8874664429956760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.987999999999996 " " y[1] (analytic) = 1.4557301061936059 " " y[1] (numeric) = 1.455730106193598 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 5.3386002936333520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.986999999999996 " " y[1] (analytic) = 1.4576548962027283 " " y[1] (numeric) = 1.45765489620272 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.6362108779165650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.985999999999995 " " y[1] (analytic) = 1.4595802285569093 " " y[1] (numeric) = 1.4595802285569004 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 6.0851634074152230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.984999999999995 " " y[1] (analytic) = 1.461506101330817 " " y[1] (numeric) = 1.4615061013308073 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 6.6848592748296110000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.983999999999995 " " y[1] (analytic) = 1.4634325125985783 " " y[1] (numeric) = 1.4634325125985679 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 7.131245439494420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.982999999999994 " " y[1] (analytic) = 1.465359460433782 " " y[1] (numeric) = 1.4653594604337712 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 7.4249260574642440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.981999999999994 " " y[1] (analytic) = 1.4672869429094813 " " y[1] (numeric) = 1.4672869429094695 " " absolute error = 1.17683640610266600000000000000E-14 " " relative error = 8.0204925954641060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.980999999999994 " " y[1] (analytic) = 1.4692149580981928 " " y[1] (numeric) = 1.4692149580981806 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 8.3122304218063380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.979999999999993 " " y[1] (analytic) = 1.471143504071902 " " y[1] (numeric) = 1.4711435040718892 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 8.7541338081606860000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.978999999999993 " " y[1] (analytic) = 1.4730725789020633 " " y[1] (numeric) = 1.4730725789020498 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 9.1948768135527330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.977999999999993 " " y[1] (analytic) = 1.4750021806596019 " " y[1] (numeric) = 1.4750021806595874 " " absolute error = 1.443289932012703500000000000000E-14 " " relative error = 9.7850020219446920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.976999999999992 " " y[1] (analytic) = 1.4769323074149159 " " y[1] (numeric) = 1.4769323074149008 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 1.0223239791761388000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.975999999999992 " " y[1] (analytic) = 1.4788629572378786 " " y[1] (numeric) = 1.478862957237863 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 1.0510184374205028000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.974999999999992 " " y[1] (analytic) = 1.4807941281978412 " " y[1] (numeric) = 1.4807941281978247 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 1.1096276282814255000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.973999999999991 " " y[1] (analytic) = 1.4827258183636318 " " y[1] (numeric) = 1.482725818363615 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 1.138132874284635000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.972999999999991 " " y[1] (analytic) = 1.484658025803561 " " y[1] (numeric) = 1.4846580258035438 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 1.166563537403058900000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.971999999999990 " " y[1] (analytic) = 1.4865907485854217 " " y[1] (numeric) = 1.4865907485854037 " " absolute error = 1.798561299892753600000000000000E-14 " " relative error = 1.2098563788347197000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.97099999999999 " " y[1] (analytic) = 1.4885239847764913 " " y[1] (numeric) = 1.4885239847764724 " " absolute error = 1.88737914186276600000000000000E-14 " " relative error = 1.267953463407689000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.96999999999999 " " y[1] (analytic) = 1.490457732443533 " " y[1] (numeric) = 1.4904577324435135 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.3110016344688954000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.96899999999999 " " y[1] (analytic) = 1.4923919896528002 " " y[1] (numeric) = 1.4923919896527797 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 1.368816222194774000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.967999999999990 " " y[1] (analytic) = 1.494326754470035 " " y[1] (numeric) = 1.494326754470014 " " absolute error = 2.087219286295294300000000000000E-14 " " relative error = 1.396762307876586000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.966999999999989 " " y[1] (analytic) = 1.4962620249604734 " " y[1] (numeric) = 1.496262024960452 " " absolute error = 2.153832667772803700000000000000E-14 " " relative error = 1.4394755944098100000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.965999999999989 " " y[1] (analytic) = 1.4981977991888447 " " y[1] (numeric) = 1.4981977991888227 " " absolute error = 2.1982415887578100000000000000E-14 " " relative error = 1.4672572539807385000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.964999999999988 " " y[1] (analytic) = 1.5001340752193753 " " y[1] (numeric) = 1.5001340752193524 " " absolute error = 2.287059430727822500000000000000E-14 " " relative error = 1.5245700157790026000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.963999999999988 " " y[1] (analytic) = 1.5020708511157888 " " y[1] (numeric) = 1.5020708511157652 " " absolute error = 2.35367281220533200000000000000E-14 " " relative error = 1.5669519253748546000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.962999999999988 " " y[1] (analytic) = 1.5040081249413095 " " y[1] (numeric) = 1.5040081249412856 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 1.5944606238639290000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.961999999999987 " " y[1] (analytic) = 1.5059458947586646 " " y[1] (numeric) = 1.5059458947586395 " " absolute error = 2.509104035652854000000000000000E-14 " " relative error = 1.6661315950231734000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.960999999999987 " " y[1] (analytic) = 1.507884158630083 " " y[1] (numeric) = 1.5078841586300575 " " absolute error = 2.5535129566378600000000000000E-14 " " relative error = 1.6934410657631244000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.959999999999987 " " y[1] (analytic) = 1.5098229146173026 " " y[1] (numeric) = 1.509822914617276 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 1.7647998538793935000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.958999999999986 " " y[1] (analytic) = 1.511762160781566 " " y[1] (numeric) = 1.511762160781539 " " absolute error = 2.686739719592879000000000000000E-14 " " relative error = 1.7772238181989297000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.957999999999986 " " y[1] (analytic) = 1.5137018951836283 " " y[1] (numeric) = 1.5137018951836005 " " absolute error = 2.775557561562891400000000000000E-14 " " relative error = 1.833622307268226200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.956999999999986 " " y[1] (analytic) = 1.5156421158837547 " " y[1] (numeric) = 1.5156421158837263 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 1.8752256309420126000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.955999999999985 " " y[1] (analytic) = 1.5175828209417248 " " y[1] (numeric) = 1.517582820941696 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 1.9020904982531110000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.954999999999985 " " y[1] (analytic) = 1.519524008416834 " " y[1] (numeric) = 1.5195240084168045 " " absolute error = 2.953193245502916400000000000000E-14 " " relative error = 1.9434989043574227000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.953999999999985 " " y[1] (analytic) = 1.5214656763678946 " " y[1] (numeric) = 1.5214656763678645 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 1.9848010204143626000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.952999999999984 " " y[1] (analytic) = 1.523407822853239 " " y[1] (numeric) = 1.5234078228532082 " " absolute error = 3.08642000845793500000000000000E-14 " " relative error = 2.0259972163443934000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.951999999999984 " " y[1] (analytic) = 1.5253504459307208 " " y[1] (numeric) = 1.5253504459306895 " " absolute error = 3.130828929442941400000000000000E-14 " " relative error = 2.0525309038295184000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.950999999999984 " " y[1] (analytic) = 1.5272935436577173 " " y[1] (numeric) = 1.527293543657685 " " absolute error = 3.21964677141295400000000000000E-14 " " relative error = 2.1080733201439572000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.949999999999983 " " y[1] (analytic) = 1.5292371140911305 " " y[1] (numeric) = 1.5292371140910976 " " absolute error = 3.286260152890463400000000000000E-14 " " relative error = 2.1489539605135613000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.948999999999983 " " y[1] (analytic) = 1.5311811552873902 " " y[1] (numeric) = 1.5311811552873569 " " absolute error = 3.330669073875469600000000000000E-14 " " relative error = 2.1752286216259825000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.947999999999983 " " y[1] (analytic) = 1.5331256653024559 " " y[1] (numeric) = 1.533125665302422 " " absolute error = 3.39728245535297900000000000000E-14 " " relative error = 2.215919107115568000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.946999999999982 " " y[1] (analytic) = 1.5350706421918172 " " y[1] (numeric) = 1.5350706421917826 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 2.256505819096794000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.945999999999982 " " y[1] (analytic) = 1.537016084010498 " " y[1] (numeric) = 1.5370160840104623 " " absolute error = 3.57491813929300400000000000000E-14 " " relative error = 2.325882062317174000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.944999999999982 " " y[1] (analytic) = 1.538961988813056 " " y[1] (numeric) = 1.5389619888130195 " " absolute error = 3.641531520770513500000000000000E-14 " " relative error = 2.3662257724630945000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.943999999999981 " " y[1] (analytic) = 1.5409083546535864 " " y[1] (numeric) = 1.5409083546535496 " " absolute error = 3.6859404417555197000000000000E-14 " " relative error = 2.392056886851107200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.942999999999981 " " y[1] (analytic) = 1.5428551795857244 " " y[1] (numeric) = 1.5428551795856866 " " absolute error = 3.77475828372553200000000000000E-14 " " relative error = 2.446605704586675100000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.941999999999980 " " y[1] (analytic) = 1.5448024616626443 " " y[1] (numeric) = 1.544802461662606 " " absolute error = 3.841371665203041600000000000000E-14 " " relative error = 2.4866426358931606000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.94099999999998 " " y[1] (analytic) = 1.5467501989370644 " " y[1] (numeric) = 1.5467501989370258 " " absolute error = 3.86357612569554500000000000000E-14 " " relative error = 2.497866900777265800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.93999999999998 " " y[1] (analytic) = 1.5486983894612485 " " y[1] (numeric) = 1.548698389461209 " " absolute error = 3.95239396766555730000000000000E-14 " " relative error = 2.5520746935369976000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.93899999999998 " " y[1] (analytic) = 1.550647031287005 " " y[1] (numeric) = 1.550647031286965 " " absolute error = 4.019007349143066700000000000000E-14 " " relative error = 2.5918260365206214000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.937999999999980 " " y[1] (analytic) = 1.552596122465693 " " y[1] (numeric) = 1.5525961224656522 " " absolute error = 4.08562073062057600000000000000E-14 " " relative error = 2.6314768351554050000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.936999999999979 " " y[1] (analytic) = 1.5545456610482211 " " y[1] (numeric) = 1.5545456610481796 " " absolute error = 4.152234112098085500000000000000E-14 " " relative error = 2.6710274365940840000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.935999999999979 " " y[1] (analytic) = 1.5564956450850511 " " y[1] (numeric) = 1.556495645085009 " " absolute error = 4.21884749357559500000000000000E-14 " " relative error = 2.7104781866222730000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.934999999999978 " " y[1] (analytic) = 1.5584460726261993 " " y[1] (numeric) = 1.5584460726261562 " " absolute error = 4.307665335545607400000000000000E-14 " " relative error = 2.764077250543928000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.933999999999978 " " y[1] (analytic) = 1.5603969417212378 " " y[1] (numeric) = 1.560396941721194 " " absolute error = 4.37427871702311700000000000000E-14 " " relative error = 2.803311516490125000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.932999999999978 " " y[1] (analytic) = 1.5623482504192978 " " y[1] (numeric) = 1.5623482504192536 " " absolute error = 4.41868763800812300000000000000E-14 " " relative error = 2.8282347657266876000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.931999999999977 " " y[1] (analytic) = 1.5642999967690714 " " y[1] (numeric) = 1.5642999967690263 " " absolute error = 4.507505479978135600000000000000E-14 " " relative error = 2.881484043526181000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.930999999999977 " " y[1] (analytic) = 1.5662521788188117 " " y[1] (numeric) = 1.566252178818766 " " absolute error = 4.57411886145564500000000000000E-14 " " relative error = 2.9204229838040600000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.929999999999977 " " y[1] (analytic) = 1.5682047946163369 " " y[1] (numeric) = 1.5682047946162907 " " absolute error = 4.61852778244065100000000000000E-14 " " relative error = 2.9451050005051027000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.928999999999976 " " y[1] (analytic) = 1.5701578422090314 " " y[1] (numeric) = 1.5701578422089848 " " absolute error = 4.662936703425657500000000000000E-14 " " relative error = 2.9697248124210507000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.927999999999976 " " y[1] (analytic) = 1.5721113196438479 " " y[1] (numeric) = 1.5721113196438008 " " absolute error = 4.70734562441066400000000000000E-14 " " relative error = 2.9942826348181784000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.926999999999976 " " y[1] (analytic) = 1.5740652249673093 " " y[1] (numeric) = 1.5740652249672615 " " absolute error = 4.77395900588817300000000000000E-14 " " relative error = 3.032885124558495000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.925999999999975 " " y[1] (analytic) = 1.5760195562255102 " " y[1] (numeric) = 1.5760195562254617 " " absolute error = 4.840572387365682500000000000000E-14 " " relative error = 3.0713910676074460000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.924999999999975 " " y[1] (analytic) = 1.5779743114641196 " " y[1] (numeric) = 1.5779743114640705 " " absolute error = 4.90718576884319200000000000000E-14 " " relative error = 3.1098007953564666000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.923999999999975 " " y[1] (analytic) = 1.5799294887283821 " " y[1] (numeric) = 1.5799294887283326 " " absolute error = 4.95159468982819800000000000000E-14 " " relative error = 3.1340605546982514000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.922999999999974 " " y[1] (analytic) = 1.5818850860631213 " " y[1] (numeric) = 1.5818850860630709 " " absolute error = 5.04041253179821100000000000000E-14 " " relative error = 3.1863329240573457000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.921999999999974 " " y[1] (analytic) = 1.5838411015127392 " " y[1] (numeric) = 1.5838411015126883 " " absolute error = 5.08482145278321700000000000000E-14 " " relative error = 3.2104366075148977000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.920999999999974 " " y[1] (analytic) = 1.5857975331212213 " " y[1] (numeric) = 1.5857975331211696 " " absolute error = 5.173639294753230000000000000000E-14 " " relative error = 3.262484136023528000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.919999999999973 " " y[1] (analytic) = 1.5877543789321353 " " y[1] (numeric) = 1.5877543789320832 " " absolute error = 5.21804821573823600000000000000E-14 " " relative error = 3.286432892251067700000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.918999999999973 " " y[1] (analytic) = 1.5897116369886364 " " y[1] (numeric) = 1.5897116369885835 " " absolute error = 5.28466159721574500000000000000E-14 " " relative error = 3.3242894335392730000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.917999999999973 " " y[1] (analytic) = 1.591669305333466 " " y[1] (numeric) = 1.5916693053334126 " " absolute error = 5.351274978693255000000000000000E-14 " " relative error = 3.3620520046229857000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.916999999999972 " " y[1] (analytic) = 1.5936273820089566 " " y[1] (numeric) = 1.5936273820089022 " " absolute error = 5.44009282066326700000000000000E-14 " " relative error = 3.41365420930794030000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.915999999999972 " " y[1] (analytic) = 1.5955858650570311 " " y[1] (numeric) = 1.595585865056976 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 3.4512127004484020000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.914999999999972 " " y[1] (analytic) = 1.597544752519207 " " y[1] (numeric) = 1.5975447525191513 " " absolute error = 5.57331958361828600000000000000E-14 " " relative error = 3.4886782200183020000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.913999999999971 " " y[1] (analytic) = 1.5995040424365965 " " y[1] (numeric) = 1.5995040424365403 " " absolute error = 5.61772850460329200000000000000E-14 " " relative error = 3.512168994612576000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.912999999999971 " " y[1] (analytic) = 1.6014637328499104 " " y[1] (numeric) = 1.6014637328498535 " " absolute error = 5.68434188608080100000000000000E-14 " " relative error = 3.549466509594407000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.911999999999970 " " y[1] (analytic) = 1.603423821799458 " " y[1] (numeric) = 1.6034238217994008 " " absolute error = 5.72875080706580800000000000000E-14 " " relative error = 3.5728238093885000000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.91099999999997 " " y[1] (analytic) = 1.6053843073251515 " " y[1] (numeric) = 1.605384307325093 " " absolute error = 5.83977310952832300000000000000E-14 " " relative error = 3.637616913833173000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.90999999999997 " " y[1] (analytic) = 1.6073451874665041 " " y[1] (numeric) = 1.6073451874664453 " " absolute error = 5.8841820305133300000000000000E-14 " " relative error = 3.660807943680083000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.90899999999997 " " y[1] (analytic) = 1.6093064602626366 " " y[1] (numeric) = 1.6093064602625773 " " absolute error = 5.92859095149833600000000000000E-14 " " relative error = 3.683941559851066000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.907999999999970 " " y[1] (analytic) = 1.6112681237522763 " " y[1] (numeric) = 1.6112681237522164 " " absolute error = 5.99520433297584500000000000000E-14 " " relative error = 3.72079869551095000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.906999999999969 " " y[1] (analytic) = 1.6132301759737602 " " y[1] (numeric) = 1.6132301759736993 " " absolute error = 6.08402217494585800000000000000E-14 " " relative error = 3.771329265691108500000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.905999999999969 " " y[1] (analytic) = 1.6151926149650357 " " y[1] (numeric) = 1.615192614964974 " " absolute error = 6.1728400169158700000000000000E-14 " " relative error = 3.82173615686665000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.904999999999968 " " y[1] (analytic) = 1.617155438763664 " " y[1] (numeric) = 1.6171554387636018 " " absolute error = 6.21724893790087700000000000000E-14 " " relative error = 3.8445586545805654000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.903999999999968 " " y[1] (analytic) = 1.6191186454068216 " " y[1] (numeric) = 1.6191186454067588 " " absolute error = 6.28386231937838600000000000000E-14 " " relative error = 3.881038821462955000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.902999999999968 " " y[1] (analytic) = 1.6210822329313022 " " y[1] (numeric) = 1.6210822329312387 " " absolute error = 6.35047570085589500000000000000E-14 " " relative error = 3.917429709517404000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.901999999999967 " " y[1] (analytic) = 1.6230461993735181 " " y[1] (numeric) = 1.623046199373454 " " absolute error = 6.41708908233340500000000000000E-14 " " relative error = 3.953731621940488000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.900999999999967 " " y[1] (analytic) = 1.6250105427695036 " " y[1] (numeric) = 1.6250105427694386 " " absolute error = 6.50590692430341700000000000000E-14 " " relative error = 4.0036090554929000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.899999999999967 " " y[1] (analytic) = 1.6269752611549149 " " y[1] (numeric) = 1.6269752611548491 " " absolute error = 6.57252030578092700000000000000E-14 " " relative error = 4.0397174208508846000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.898999999999966 " " y[1] (analytic) = 1.6289403525650337 " " y[1] (numeric) = 1.6289403525649675 " " absolute error = 6.61692922676593300000000000000E-14 " " relative error = 4.06210651995114000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.897999999999966 " " y[1] (analytic) = 1.6309058150347693 " " y[1] (numeric) = 1.6309058150347024 " " absolute error = 6.68354260824344200000000000000E-14 " " relative error = 4.0980555386032247000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.896999999999966 " " y[1] (analytic) = 1.6328716465986592 " " y[1] (numeric) = 1.6328716465985915 " " absolute error = 6.77236045021345500000000000000E-14 " " relative error = 4.1475154916925455000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.895999999999965 " " y[1] (analytic) = 1.6348378452908716 " " y[1] (numeric) = 1.6348378452908034 " " absolute error = 6.81676937119846100000000000000E-14 " " relative error = 4.169691441162849000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.894999999999965 " " y[1] (analytic) = 1.6368044091452085 " " y[1] (numeric) = 1.6368044091451397 " " absolute error = 6.8833827526759700000000000000E-14 " " relative error = 4.2053789165137284000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.893999999999965 " " y[1] (analytic) = 1.6387713361951057 " " y[1] (numeric) = 1.6387713361950365 " " absolute error = 6.92779167366097700000000000000E-14 " " relative error = 4.227430344092973400000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.892999999999964 " " y[1] (analytic) = 1.640738624473637 " " y[1] (numeric) = 1.6407386244735669 " " absolute error = 7.01660951563098900000000000000E-14 " " relative error = 4.276494385497859300000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.891999999999964 " " y[1] (analytic) = 1.642706272013514 " " y[1] (numeric) = 1.6427062720134429 " " absolute error = 7.10542735760100200000000000000E-14 " " relative error = 4.325439963707977700000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.890999999999964 " " y[1] (analytic) = 1.6446742768470886 " " y[1] (numeric) = 1.644674276847017 " " absolute error = 7.14983627858600800000000000000E-14 " " relative error = 4.347265825968016400000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.889999999999963 " " y[1] (analytic) = 1.646642637006357 " " y[1] (numeric) = 1.6466426370062848 " " absolute error = 7.21644966006351800000000000000E-14 " " relative error = 4.3825232615033144000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.888999999999963 " " y[1] (analytic) = 1.6486113505229594 " " y[1] (numeric) = 1.648611350522886 " " absolute error = 7.32747196252603300000000000000E-14 " " relative error = 4.444632726932076000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.887999999999963 " " y[1] (analytic) = 1.6505804154281813 " " y[1] (numeric) = 1.6505804154281076 " " absolute error = 7.3718808835110390000000000000E-14 " " relative error = 4.466235522126125000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.886999999999962 " " y[1] (analytic) = 1.6525498297529593 " " y[1] (numeric) = 1.6525498297528847 " " absolute error = 7.46069872548105200000000000000E-14 " " relative error = 4.5146588569715660000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.885999999999962 " " y[1] (analytic) = 1.6545195915278779 " " y[1] (numeric) = 1.654519591527803 " " absolute error = 7.48290318597355500000000000000E-14 " " relative error = 4.522704490349017000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.884999999999962 " " y[1] (analytic) = 1.6564896987831768 " " y[1] (numeric) = 1.656489698783101 " " absolute error = 7.57172102794356800000000000000E-14 " " relative error = 4.570943624645295600000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.883999999999961 " " y[1] (analytic) = 1.6584601495487479 " " y[1] (numeric) = 1.6584601495486717 " " absolute error = 7.61612994892857400000000000000E-14 " " relative error = 4.5922899932210337000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.882999999999961 " " y[1] (analytic) = 1.6604309418541412 " " y[1] (numeric) = 1.6604309418540644 " " absolute error = 7.68274333040608300000000000000E-14 " " relative error = 4.626957458301187400000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.881999999999960 " " y[1] (analytic) = 1.6624020737285643 " " y[1] (numeric) = 1.6624020737284868 " " absolute error = 7.74935671188359300000000000000E-14 " " relative error = 4.661541774008218000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.88099999999996 " " y[1] (analytic) = 1.6643735432008855 " " y[1] (numeric) = 1.6643735432008073 " " absolute error = 7.81597009336110200000000000000E-14 " " relative error = 4.696043220159343300000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.87999999999996 " " y[1] (analytic) = 1.6663453482996355 " " y[1] (numeric) = 1.6663453482995567 " " absolute error = 7.88258347483861100000000000000E-14 " " relative error = 4.73046207551281000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.87899999999996 " " y[1] (analytic) = 1.6683174870530095 " " y[1] (numeric) = 1.66831748705293 " " absolute error = 7.94919685631612100000000000000E-14 " " relative error = 4.76479861777265000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.877999999999960 " " y[1] (analytic) = 1.6702899574888685 " " y[1] (numeric) = 1.6702899574887886 " " absolute error = 7.99360577730112700000000000000E-14 " " relative error = 4.785759347627761000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.876999999999959 " " y[1] (analytic) = 1.6722627576347429 " " y[1] (numeric) = 1.6722627576346623 " " absolute error = 8.06021915877863600000000000000E-14 " " relative error = 4.819947775539205000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.875999999999959 " " y[1] (analytic) = 1.6742358855178323 " " y[1] (numeric) = 1.6742358855177508 " " absolute error = 8.14903700074864900000000000000E-14 " " relative error = 4.867317127316378400000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.874999999999958 " " y[1] (analytic) = 1.676209339165009 " " y[1] (numeric) = 1.6762093391649269 " " absolute error = 8.21565038222615800000000000000E-14 " " relative error = 4.90132717332235000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.873999999999958 " " y[1] (analytic) = 1.6781831166028196 " " y[1] (numeric) = 1.6781831166027368 " " absolute error = 8.28226376370366800000000000000E-14 " " relative error = 4.935256279105956000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.872999999999958 " " y[1] (analytic) = 1.6801572158574865 " " y[1] (numeric) = 1.6801572158574032 " " absolute error = 8.32667268468867400000000000000E-14 " " relative error = 4.955889012111921000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.871999999999957 " " y[1] (analytic) = 1.682131634954911 " " y[1] (numeric) = 1.6821316349548272 " " absolute error = 8.3710816056736800000000000000E-14 " " relative error = 4.976472370961661000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.870999999999957 " " y[1] (analytic) = 1.6841063719206741 " " y[1] (numeric) = 1.6841063719205898 " " absolute error = 8.4376949871511900000000000000E-14 " " relative error = 5.010191237224668000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.869999999999957 " " y[1] (analytic) = 1.6860814247800393 " " y[1] (numeric) = 1.686081424779954 " " absolute error = 8.52651282912120200000000000000E-14 " " relative error = 5.056999444871735000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.868999999999956 " " y[1] (analytic) = 1.688056791557953 " " y[1] (numeric) = 1.6880567915578673 " " absolute error = 8.57092175010620800000000000000E-14 " " relative error = 5.077389453346457000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.867999999999956 " " y[1] (analytic) = 1.6900324702790495 " " y[1] (numeric) = 1.690032470278963 " " absolute error = 8.63753513158371800000000000000E-14 " " relative error = 5.110869337414288000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.866999999999956 " " y[1] (analytic) = 1.6920084589676496 " " y[1] (numeric) = 1.6920084589675628 " " absolute error = 8.68194405256872400000000000000E-14 " " relative error = 5.131146955297059000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.865999999999955 " " y[1] (analytic) = 1.6939847556477656 " " y[1] (numeric) = 1.6939847556476777 " " absolute error = 8.7929663550312400000000000000E-14 " " relative error = 5.190699813392880000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.864999999999955 " " y[1] (analytic) = 1.6959613583431001 " " y[1] (numeric) = 1.6959613583430115 " " absolute error = 8.85957973650874900000000000000E-14 " " relative error = 5.223927828853526000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.863999999999955 " " y[1] (analytic) = 1.6979382650770507 " " y[1] (numeric) = 1.6979382650769617 " " absolute error = 8.90398865749375500000000000000E-14 " " relative error = 5.24400023288815100000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.862999999999954 " " y[1] (analytic) = 1.6999154738727116 " " y[1] (numeric) = 1.6999154738726217 " " absolute error = 8.99280649946376800000000000000E-14 " " relative error = 5.290149208993636000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.861999999999954 " " y[1] (analytic) = 1.7018929827528733 " " y[1] (numeric) = 1.7018929827527827 " " absolute error = 9.05941988094127700000000000000E-14 " " relative error = 5.323143095805789000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.860999999999954 " " y[1] (analytic) = 1.7038707897400274 " " y[1] (numeric) = 1.703870789739936 " " absolute error = 9.12603326241878700000000000000E-14 " " relative error = 5.356059460243001000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.859999999999953 " " y[1] (analytic) = 1.705848892856367 " " y[1] (numeric) = 1.7058488928562752 " " absolute error = 9.19264664389629600000000000000E-14 " " relative error = 5.388898560940896000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.858999999999953 " " y[1] (analytic) = 1.707827290123789 " " y[1] (numeric) = 1.7078272901236968 " " absolute error = 9.21485110438879900000000000000E-14 " " relative error = 5.395657486958694000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.857999999999953 " " y[1] (analytic) = 1.709805979563897 " " y[1] (numeric) = 1.709805979563804 " " absolute error = 9.28146448586630900000000000000E-14 " " relative error = 5.428372924648234000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.856999999999952 " " y[1] (analytic) = 1.7117849591980012 " " y[1] (numeric) = 1.7117849591979075 " " absolute error = 9.37028232783632100000000000000E-14 " " relative error = 5.473983328038148000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.855999999999952 " " y[1] (analytic) = 1.7137642270471218 " " y[1] (numeric) = 1.7137642270470277 " " absolute error = 9.41469124882132700000000000000E-14 " " relative error = 5.4935743786898750000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.854999999999952 " " y[1] (analytic) = 1.7157437811319922 " " y[1] (numeric) = 1.715743781131897 " " absolute error = 9.52571355128384300000000000000E-14 " " relative error = 5.551944093306919000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.853999999999951 " " y[1] (analytic) = 1.7177236194730572 " " y[1] (numeric) = 1.7177236194729615 " " absolute error = 9.5701224722688490000000000000E-14 " " relative error = 5.571398310983613000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.852999999999951 " " y[1] (analytic) = 1.7197037400904795 " " y[1] (numeric) = 1.719703740090383 " " absolute error = 9.65894031423886200000000000000E-14 " " relative error = 5.616630405031667000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.851999999999950 " " y[1] (analytic) = 1.721684141004138 " " y[1] (numeric) = 1.721684141004041 " " absolute error = 9.68114477473136500000000000000E-14 " " relative error = 5.623066707860265000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.85099999999995 " " y[1] (analytic) = 1.7236648202336324 " " y[1] (numeric) = 1.723664820233535 " " absolute error = 9.74775815620887400000000000000E-14 " " relative error = 5.655251555744826000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.84999999999995 " " y[1] (analytic) = 1.725645775798284 " " y[1] (numeric) = 1.7256457757981856 " " absolute error = 9.83657599817888700000000000000E-14 " " relative error = 5.700228943931721000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.84899999999995 " " y[1] (analytic) = 1.7276270057171366 " " y[1] (numeric) = 1.7276270057170375 " " absolute error = 9.90318937965639600000000000000E-14 " " relative error = 5.732249696771550000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.847999999999950 " " y[1] (analytic) = 1.729608508008961 " " y[1] (numeric) = 1.729608508008861 " " absolute error = 9.99200722162640900000000000000E-14 " " relative error = 5.777034037100517000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.846999999999949 " " y[1] (analytic) = 1.7315902806922545 " " y[1] (numeric) = 1.731590280692154 " " absolute error = 1.00586206031039180000000000000E-13 " " relative error = 5.808891811914471000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.845999999999949 " " y[1] (analytic) = 1.7335723217852452 " " y[1] (numeric) = 1.7335723217851438 " " absolute error = 1.01474384450739310000000000000E-13 " " relative error = 5.8534843441801300000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.844999999999948 " " y[1] (analytic) = 1.7355546293058914 " " y[1] (numeric) = 1.7355546293057897 " " absolute error = 1.01696429055664340000000000000E-13 " " relative error = 5.859592509417942000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.843999999999948 " " y[1] (analytic) = 1.7375372012718868 " " y[1] (numeric) = 1.7375372012717842 " " absolute error = 1.02584607475364460000000000000E-13 " " relative error = 5.904023660631379000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.842999999999948 " " y[1] (analytic) = 1.739520035700659 " " y[1] (numeric) = 1.7395200357005558 " " absolute error = 1.03250741290139560000000000000E-13 " " relative error = 5.93558793064153000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.841999999999947 " " y[1] (analytic) = 1.7415031306093738 " " y[1] (numeric) = 1.7415031306092699 " " absolute error = 1.03916875104914650000000000000E-13 " " relative error = 5.9670794314652100000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.840999999999947 " " y[1] (analytic) = 1.7434864840149364 " " y[1] (numeric) = 1.7434864840148319 " " absolute error = 1.04583008919689750000000000000E-13 " " relative error = 5.998498404120338000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.839999999999947 " " y[1] (analytic) = 1.7454700939339935 " " y[1] (numeric) = 1.7454700939338883 " " absolute error = 1.05249142734464840000000000000E-13 " " relative error = 6.029845088737735000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.838999999999946 " " y[1] (analytic) = 1.7474539583829354 " " y[1] (numeric) = 1.7474539583828297 " " absolute error = 1.0569323194431490000000000000E-13 " " relative error = 6.048412974618321000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.837999999999946 " " y[1] (analytic) = 1.7494380753778982 " " y[1] (numeric) = 1.7494380753777916 " " absolute error = 1.06581410364015030000000000000E-13 " " relative error = 6.092322549970353000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.836999999999946 " " y[1] (analytic) = 1.7514224429347642 " " y[1] (numeric) = 1.7514224429346572 " " absolute error = 1.07025499573865090000000000000E-13 " " relative error = 6.110775844263376000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.835999999999945 " " y[1] (analytic) = 1.753407059069167 " " y[1] (numeric) = 1.7534070590690591 " " absolute error = 1.07913677993565220000000000000E-13 " " relative error = 6.154513718614403000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.834999999999945 " " y[1] (analytic) = 1.7553919217964902 " " y[1] (numeric) = 1.7553919217963816 " " absolute error = 1.08579811808340310000000000000E-13 " " relative error = 6.185502534227135000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.833999999999945 " " y[1] (analytic) = 1.757377029131871 " " y[1] (numeric) = 1.7573770291317619 " " absolute error = 1.0924594562311540000000000000E-13 " " relative error = 6.216420484173618000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.832999999999944 " " y[1] (analytic) = 1.7593623790902027 " " y[1] (numeric) = 1.7593623790900927 " " absolute error = 1.0991207943789050000000000000E-13 " " relative error = 6.2472678024823960000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.831999999999944 " " y[1] (analytic) = 1.7613479696861352 " " y[1] (numeric) = 1.7613479696860246 " " absolute error = 1.10578213252665590000000000000E-13 " " relative error = 6.278044722325378000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.830999999999944 " " y[1] (analytic) = 1.7633337989340778 " " y[1] (numeric) = 1.7633337989339668 " " absolute error = 1.11022302462515650000000000000E-13 " " relative error = 6.296159157706148000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.829999999999943 " " y[1] (analytic) = 1.7653198648482018 " " y[1] (numeric) = 1.7653198648480903 " " absolute error = 1.11466391672365720000000000000E-13 " " relative error = 6.314231992282634000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.828999999999943 " " y[1] (analytic) = 1.7673061654424416 " " y[1] (numeric) = 1.7673061654423294 " " absolute error = 1.12132525487140810000000000000E-13 " " relative error = 6.344827380776361000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.827999999999943 " " y[1] (analytic) = 1.7692926987304967 " " y[1] (numeric) = 1.7692926987303836 " " absolute error = 1.13020703906840940000000000000E-13 " " relative error = 6.387903142760697000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.826999999999942 " " y[1] (analytic) = 1.7712794627258335 " " y[1] (numeric) = 1.77127946272572 " " absolute error = 1.134647931166910000000000000E-13 " " relative error = 6.405809783515432000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.825999999999942 " " y[1] (analytic) = 1.7732664554416888 " " y[1] (numeric) = 1.7732664554415745 " " absolute error = 1.14352971536391120000000000000E-13 " " relative error = 6.448719039683625000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.824999999999942 " " y[1] (analytic) = 1.7752536748910699 " " y[1] (numeric) = 1.7752536748909546 " " absolute error = 1.15241149956091250000000000000E-13 " " relative error = 6.491531412442365000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.823999999999941 " " y[1] (analytic) = 1.777241119086757 " " y[1] (numeric) = 1.7772411190866413 " " absolute error = 1.1568523916594131000000000000E-13 " " relative error = 6.5092596566405500000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.822999999999941 " " y[1] (analytic) = 1.7792287860413065 " " y[1] (numeric) = 1.7792287860411902 " " absolute error = 1.1635137298071640000000000000E-13 " " relative error = 6.539427300948311000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.821999999999940 " " y[1] (analytic) = 1.7812166737670516 " " y[1] (numeric) = 1.7812166737669346 " " absolute error = 1.1701750679549150000000000000E-13 " " relative error = 6.569526802599149000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.82099999999994 " " y[1] (analytic) = 1.7832047802761046 " " y[1] (numeric) = 1.7832047802759872 " " absolute error = 1.17461596005341560000000000000E-13 " " relative error = 6.58710638870956000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.81999999999994 " " y[1] (analytic) = 1.7851931035803594 " " y[1] (numeric) = 1.7851931035802413 " " absolute error = 1.18127729820116660000000000000E-13 " " relative error = 6.617084145306257000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8189999999999396 " " y[1] (analytic) = 1.7871816416914927 " " y[1] (numeric) = 1.787181641691374 " " absolute error = 1.18793863634891750000000000000E-13 " " relative error = 6.646994399654773000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.817999999999940 " " y[1] (analytic) = 1.7891703926209668 " " y[1] (numeric) = 1.789170392620847 " " absolute error = 1.19682042054591880000000000000E-13 " " relative error = 6.6892478518644000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.816999999999939 " " y[1] (analytic) = 1.7911593543800306 " " y[1] (numeric) = 1.79115935437991 " " absolute error = 1.205702204742920000000000000E-13 " " relative error = 6.731406682462637000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8159999999999386 " " y[1] (analytic) = 1.7931485249797223 " " y[1] (numeric) = 1.7931485249796013 " " absolute error = 1.21014309684142060000000000000E-13 " " relative error = 6.7487053079170090000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.814999999999938 " " y[1] (analytic) = 1.7951379024308722 " " y[1] (numeric) = 1.7951379024307503 " " absolute error = 1.2190248810384219000000000000E-13 " " relative error = 6.7907032623381670000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.813999999999938 " " y[1] (analytic) = 1.7971274847441023 " " y[1] (numeric) = 1.7971274847439798 " " absolute error = 1.22568621918617280000000000000E-13 " " relative error = 6.8202519275403630000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8129999999999376 " " y[1] (analytic) = 1.7991172699298308 " " y[1] (numeric) = 1.7991172699297076 " " absolute error = 1.23234755733392380000000000000E-13 " " relative error = 6.8497344666253350000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.811999999999937 " " y[1] (analytic) = 1.8011072559982728 " " y[1] (numeric) = 1.8011072559981487 " " absolute error = 1.2412293415309250000000000000E-13 " " relative error = 6.891479324161444000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.810999999999937 " " y[1] (analytic) = 1.803097440959442 " " y[1] (numeric) = 1.8030974409593172 " " absolute error = 1.2478906796786760000000000000E-13 " " relative error = 6.920816653229033000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8099999999999365 " " y[1] (analytic) = 1.805087822823154 " " y[1] (numeric) = 1.8050878228230285 " " absolute error = 1.2545520178264270000000000000E-13 " " relative error = 6.9500885328909370000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.808999999999936 " " y[1] (analytic) = 1.807078399599027 " " y[1] (numeric) = 1.8070783995989006 " " absolute error = 1.26343380202342810000000000000E-13 " " relative error = 6.9915826690406560000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.807999999999936 " " y[1] (analytic) = 1.809069169296484 " " y[1] (numeric) = 1.8090691692963572 " " absolute error = 1.26787469412192880000000000000E-13 " " relative error = 7.008436800760822000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8069999999999355 " " y[1] (analytic) = 1.8110601299247562 " " y[1] (numeric) = 1.8110601299246285 " " absolute error = 1.276756478318930000000000000E-13 " " relative error = 7.049774092105794000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.805999999999935 " " y[1] (analytic) = 1.8130512794928824 " " y[1] (numeric) = 1.8130512794927542 " " absolute error = 1.28119737041743060000000000000E-13 " " relative error = 7.0665258335979700000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.804999999999935 " " y[1] (analytic) = 1.8150426160097135 " " y[1] (numeric) = 1.8150426160095847 " " absolute error = 1.28785870856518160000000000000E-13 " " relative error = 7.0954736665989640000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8039999999999345 " " y[1] (analytic) = 1.8170341374839136 " " y[1] (numeric) = 1.817034137483784 " " absolute error = 1.29674049276218280000000000000E-13 " " relative error = 7.136577491922124000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.802999999999934 " " y[1] (analytic) = 1.8190258419239607 " " y[1] (numeric) = 1.8190258419238303 " " absolute error = 1.30340183090993380000000000000E-13 " " relative error = 7.1653838052753670000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.801999999999934 " " y[1] (analytic) = 1.821017727338151 " " y[1] (numeric) = 1.8210177273380197 " " absolute error = 1.3122836151069350000000000000E-13 " " relative error = 7.206319825481043000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8009999999999335 " " y[1] (analytic) = 1.8230097917345987 " " y[1] (numeric) = 1.823009791734467 " " absolute error = 1.31672450720543570000000000000E-13 " " relative error = 7.222805457081878000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.799999999999933 " " y[1] (analytic) = 1.82500203312124 " " y[1] (numeric) = 1.8250020331211076 " " absolute error = 1.32338584535318660000000000000E-13 " " relative error = 7.251421211240209000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.798999999999933 " " y[1] (analytic) = 1.8269944495058335 " " y[1] (numeric) = 1.8269944495057007 " " absolute error = 1.32782673745168720000000000000E-13 " " relative error = 7.26782031445601000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7979999999999325 " " y[1] (analytic) = 1.8289870388959635 " " y[1] (numeric) = 1.8289870388958298 " " absolute error = 1.33670852164868850000000000000E-13 " " relative error = 7.308463609756193000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.796999999999932 " " y[1] (analytic) = 1.83097979929904 " " y[1] (numeric) = 1.8309797992989056 " " absolute error = 1.34336985979643940000000000000E-13 " " relative error = 7.336890665373402000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.795999999999932 " " y[1] (analytic) = 1.8329727287223032 " " y[1] (numeric) = 1.8329727287221682 " " absolute error = 1.35003119794419040000000000000E-13 " " relative error = 7.365255231512619000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7949999999999315 " " y[1] (analytic) = 1.8349658251728238 " " y[1] (numeric) = 1.8349658251726881 " " absolute error = 1.35669253609194130000000000000E-13 " " relative error = 7.393557511972535000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.793999999999931 " " y[1] (analytic) = 1.8369590866575054 " " y[1] (numeric) = 1.836959086657369 " " absolute error = 1.36335387423969220000000000000E-13 " " relative error = 7.421797709825013000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.792999999999930 " " y[1] (analytic) = 1.838952511183087 " " y[1] (numeric) = 1.83895251118295 " " absolute error = 1.37001521238744320000000000000E-13 " " relative error = 7.449976027418165000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7919999999999305 " " y[1] (analytic) = 1.8409460967561433 " " y[1] (numeric) = 1.840946096756006 " " absolute error = 1.37223565843669350000000000000E-13 " " relative error = 7.453969786810458000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.79099999999993 " " y[1] (analytic) = 1.8429398413830902 " " y[1] (numeric) = 1.842939841382952 " " absolute error = 1.38111744263369470000000000000E-13 " " relative error = 7.494099436242005000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.78999999999993 " " y[1] (analytic) = 1.8449337430701824 " " y[1] (numeric) = 1.8449337430700437 " " absolute error = 1.38777878078144570000000000000E-13 " " relative error = 7.522106341185033000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7889999999999295 " " y[1] (analytic) = 1.846927799823519 " " y[1] (numeric) = 1.8469277998233793 " " absolute error = 1.3966605649784470000000000000E-13 " " relative error = 7.562074517000087000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.787999999999930 " " y[1] (analytic) = 1.8489220096490424 " " y[1] (numeric) = 1.8489220096489023 " " absolute error = 1.40110145707694760000000000000E-13 " " relative error = 7.577937034471783000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.786999999999929 " " y[1] (analytic) = 1.850916370552544 " " y[1] (numeric) = 1.8509163705524032 " " absolute error = 1.40776279522469850000000000000E-13 " " relative error = 7.60576121980296000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7859999999999285 " " y[1] (analytic) = 1.8529108805396626 " " y[1] (numeric) = 1.8529108805395211 " " absolute error = 1.41442413337244940000000000000E-13 " " relative error = 7.633524894410986000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.784999999999928 " " y[1] (analytic) = 1.8549055376158883 " " y[1] (numeric) = 1.8549055376157462 " " absolute error = 1.42108547152020040000000000000E-13 " " relative error = 7.661228255034068000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.783999999999928 " " y[1] (analytic) = 1.8569003397865642 " " y[1] (numeric) = 1.8569003397864214 " " absolute error = 1.42774680966795130000000000000E-13 " " relative error = 7.688871497713546000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7829999999999275 " " y[1] (analytic) = 1.8588952850568887 " " y[1] (numeric) = 1.858895285056745 " " absolute error = 1.43662859386495260000000000000E-13 " " relative error = 7.728399794294957000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.781999999999927 " " y[1] (analytic) = 1.8608903714319163 " " y[1] (numeric) = 1.860890371431772 " " absolute error = 1.44328993201270350000000000000E-13 " " relative error = 7.755910580063468000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.780999999999927 " " y[1] (analytic) = 1.8628855969165605 " " y[1] (numeric) = 1.8628855969164158 " " absolute error = 1.44773082411120400000000000000E-13 " " relative error = 7.771442468112273000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7799999999999265 " " y[1] (analytic) = 1.8648809595155966 " " y[1] (numeric) = 1.8648809595154512 " " absolute error = 1.4543921622589550000000000000E-13 " " relative error = 7.798847185595877000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.778999999999926 " " y[1] (analytic) = 1.866876457233662 " " y[1] (numeric) = 1.866876457233516 " " absolute error = 1.4610535004067060000000000000E-13 " " relative error = 7.826192754991915000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.777999999999926 " " y[1] (analytic) = 1.8688720880752592 " " y[1] (numeric) = 1.8688720880751122 " " absolute error = 1.46993528460370730000000000000E-13 " " relative error = 7.865360577553412000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7769999999999255 " " y[1] (analytic) = 1.8708678500447569 " " y[1] (numeric) = 1.8708678500446094 " " absolute error = 1.4743761767022080000000000000E-13 " " relative error = 7.880707216530213000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.775999999999925 " " y[1] (analytic) = 1.8728637411463942 " " y[1] (numeric) = 1.8728637411462459 " " absolute error = 1.48325796089920900000000000000E-13 " " relative error = 7.919732377280665000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.774999999999925 " " y[1] (analytic) = 1.8748597593842797 " " y[1] (numeric) = 1.8748597593841307 " " absolute error = 1.489919299046960000000000000E-13 " " relative error = 7.94683064474253100000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7739999999999245 " " y[1] (analytic) = 1.8768559027623954 " " y[1] (numeric) = 1.8768559027622458 " " absolute error = 1.4965806371947110000000000000E-13 " " relative error = 7.973870743044325000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.772999999999924 " " y[1] (analytic) = 1.878852169284598 " " y[1] (numeric) = 1.8788521692844478 " " absolute error = 1.5032419753424620000000000000E-13 " " relative error = 8.000852860684853000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.771999999999924 " " y[1] (analytic) = 1.8808485569546214 " " y[1] (numeric) = 1.8808485569544704 " " absolute error = 1.5099033134902130000000000000E-13 " " relative error = 8.02777718550065000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7709999999999235 " " y[1] (analytic) = 1.8828450637760779 " " y[1] (numeric) = 1.8828450637759262 " " absolute error = 1.51656465163796380000000000000E-13 " " relative error = 8.054643904668756000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.769999999999923 " " y[1] (analytic) = 1.8848416877524605 " " y[1] (numeric) = 1.8848416877523084 " " absolute error = 1.52100554373646450000000000000E-13 " " relative error = 8.069672660679292000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.768999999999923 " " y[1] (analytic) = 1.886838426887146 " " y[1] (numeric) = 1.8868384268869933 " " absolute error = 1.52766688188421540000000000000E-13 " " relative error = 8.096437194172043000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7679999999999225 " " y[1] (analytic) = 1.8888352791833949 " " y[1] (numeric) = 1.888835279183242 " " absolute error = 1.52988732793346570000000000000E-13 " " relative error = 8.099633381450213000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.766999999999922 " " y[1] (analytic) = 1.8908322426443558 " " y[1] (numeric) = 1.890832242644202 " " absolute error = 1.5387691121304670000000000000E-13 " " relative error = 8.138052003907426000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.765999999999922 " " y[1] (analytic) = 1.8928293152730649 " " y[1] (numeric) = 1.8928293152729103 " " absolute error = 1.5454304502782180000000000000E-13 " " relative error = 8.164658259507512000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7649999999999215 " " y[1] (analytic) = 1.8948264950724494 " " y[1] (numeric) = 1.8948264950722944 " " absolute error = 1.54987134237671850000000000000E-13 " " relative error = 8.179489501583408000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.763999999999921 " " y[1] (analytic) = 1.8968237800453305 " " y[1] (numeric) = 1.8968237800451746 " " absolute error = 1.55875312657371980000000000000E-13 " " relative error = 8.217701311908208000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.762999999999920 " " y[1] (analytic) = 1.8988211681944227 " " y[1] (numeric) = 1.8988211681942662 " " absolute error = 1.56541446472147070000000000000E-13 " " relative error = 8.244138473608936000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7619999999999205 " " y[1] (analytic) = 1.9008186575223385 " " y[1] (numeric) = 1.9008186575221813 " " absolute error = 1.57207580286922170000000000000E-13 " " relative error = 8.270519634515668000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.76099999999992 " " y[1] (analytic) = 1.9028162460315885 " " y[1] (numeric) = 1.9028162460314304 " " absolute error = 1.5809575870662230000000000000E-13 " " relative error = 8.308514237059849000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.75999999999992 " " y[1] (analytic) = 1.904813931724584 " " y[1] (numeric) = 1.9048139317244255 " " absolute error = 1.58539847916472350000000000000E-13 " " relative error = 8.32311467676705000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7589999999999195 " " y[1] (analytic) = 1.9068117126036404 " " y[1] (numeric) = 1.906811712603481 " " absolute error = 1.59428026336172480000000000000E-13 " " relative error = 8.360973728154983000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.757999999999920 " " y[1] (analytic) = 1.908809586670976 " " y[1] (numeric) = 1.908809586670816 " " absolute error = 1.60094160150947570000000000000E-13 " " relative error = 8.387120500068151000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.756999999999919 " " y[1] (analytic) = 1.910807551928717 " " y[1] (numeric) = 1.9108075519285568 " " absolute error = 1.6031620475587260000000000000E-13 " " relative error = 8.389971276492696000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7559999999999185 " " y[1] (analytic) = 1.9128056063788996 " " y[1] (numeric) = 1.9128056063787382 " " absolute error = 1.61426427780497760000000000000E-13 " " relative error = 8.43924898809197100000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.754999999999918 " " y[1] (analytic) = 1.9148037480234676 " " y[1] (numeric) = 1.914803748023306 " " absolute error = 1.6164847238542280000000000000E-13 " " relative error = 8.442038645071717000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.753999999999918 " " y[1] (analytic) = 1.9168019748642813 " " y[1] (numeric) = 1.9168019748641187 " " absolute error = 1.62536650805122920000000000000E-13 " " relative error = 8.479574464995596000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7529999999999175 " " y[1] (analytic) = 1.9188002849031127 " " y[1] (numeric) = 1.9188002849029495 " " absolute error = 1.632027846198980000000000000E-13 " " relative error = 8.505459682487941000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.751999999999917 " " y[1] (analytic) = 1.9207986761416525 " " y[1] (numeric) = 1.9207986761414888 " " absolute error = 1.63646873829748070000000000000E-13 " " relative error = 8.519730665291215000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.750999999999917 " " y[1] (analytic) = 1.9227971465815097 " " y[1] (numeric) = 1.9227971465813452 " " absolute error = 1.6453505224944820000000000000E-13 " " relative error = 8.557067631495643000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7499999999999165 " " y[1] (analytic) = 1.9247956942242137 " " y[1] (numeric) = 1.9247956942240485 " " absolute error = 1.6520118606422330000000000000E-13 " " relative error = 8.582790711759535000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.748999999999916 " " y[1] (analytic) = 1.9267943170712174 " " y[1] (numeric) = 1.9267943170710515 " " absolute error = 1.65867319878998400000000000000E-13 " " relative error = 8.60846009402402100000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.747999999999916 " " y[1] (analytic) = 1.9287930131238977 " " y[1] (numeric) = 1.9287930131237312 " " absolute error = 1.66533453693773480000000000000E-13 " " relative error = 8.634075951159415000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7469999999999155 " " y[1] (analytic) = 1.9307917803835593 " " y[1] (numeric) = 1.9307917803833918 " " absolute error = 1.6742163211347360000000000000E-13 " " relative error = 8.67113863931068900000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.745999999999915 " " y[1] (analytic) = 1.9327906168514346 " " y[1] (numeric) = 1.9327906168512663 " " absolute error = 1.68309810533173730000000000000E-13 " " relative error = 8.708124359965836000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.744999999999915 " " y[1] (analytic) = 1.9347895205286871 " " y[1] (numeric) = 1.9347895205285184 " " absolute error = 1.6875389974302380000000000000E-13 " " relative error = 8.722080513280395000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7439999999999145 " " y[1] (analytic) = 1.936788489416414 " " y[1] (numeric) = 1.9367884894162446 " " absolute error = 1.6942003355779890000000000000E-13 " " relative error = 8.747472141826282000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.742999999999914 " " y[1] (analytic) = 1.9387875215156463 " " y[1] (numeric) = 1.938787521515476 " " absolute error = 1.70308211977499000000000000000E-13 " " relative error = 8.784263880776407000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.741999999999914 " " y[1] (analytic) = 1.9407866148273518 " " y[1] (numeric) = 1.9407866148271808 " " absolute error = 1.7097434579227410000000000000E-13 " " relative error = 8.809538590489693000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7409999999999135 " " y[1] (analytic) = 1.9427857673524374 " " y[1] (numeric) = 1.942785767352266 " " absolute error = 1.71418435002124170000000000000E-13 " " relative error = 8.823331830134179000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.739999999999913 " " y[1] (analytic) = 1.944784977091751 " " y[1] (numeric) = 1.9447849770915788 " " absolute error = 1.72084568816899260000000000000E-13 " " relative error = 8.848513889398513000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.738999999999913 " " y[1] (analytic) = 1.9467842420460828 " " y[1] (numeric) = 1.94678424204591 " " absolute error = 1.72750702631674360000000000000E-13 " " relative error = 8.873643976597646000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7379999999999125 " " y[1] (analytic) = 1.9487835602161683 " " y[1] (numeric) = 1.9487835602159949 " " absolute error = 1.73416836446449450000000000000E-13 " " relative error = 8.898722258679831000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.736999999999912 " " y[1] (analytic) = 1.9507829296026893 " " y[1] (numeric) = 1.9507829296025152 " " absolute error = 1.74082970261224550000000000000E-13 " " relative error = 8.923748902020562000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.735999999999912 " " y[1] (analytic) = 1.9527823482062767 " " y[1] (numeric) = 1.9527823482061017 " " absolute error = 1.74971148680924670000000000000E-13 " " relative error = 8.960094751042991000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7349999999999115 " " y[1] (analytic) = 1.9547818140275117 " " y[1] (numeric) = 1.9547818140273363 " " absolute error = 1.75415237890774730000000000000E-13 " " relative error = 8.973647935129907000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.733999999999911 " " y[1] (analytic) = 1.9567813250669293 " " y[1] (numeric) = 1.956781325066753 " " absolute error = 1.76303416310474860000000000000E-13 " " relative error = 9.009868095733417000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.732999999999910 " " y[1] (analytic) = 1.9587808793250177 " " y[1] (numeric) = 1.958780879324841 " " absolute error = 1.76747505520324920000000000000E-13 " " relative error = 9.023342395563453000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7319999999999105 " " y[1] (analytic) = 1.9607804748022235 " " y[1] (numeric) = 1.960780474802046 " " absolute error = 1.77413639335100020000000000000E-13 " " relative error = 9.048113320946602000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.73099999999991 " " y[1] (analytic) = 1.9627801094989517 " " y[1] (numeric) = 1.9627801094987734 " " absolute error = 1.78301817754800140000000000000E-13 " " relative error = 9.084146354036373000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.72999999999991 " " y[1] (analytic) = 1.9647797814155665 " " y[1] (numeric) = 1.964779781415388 " " absolute error = 1.78523862359725170000000000000E-13 " " relative error = 9.086202130556531000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7289999999999095 " " y[1] (analytic) = 1.9667794885523975 " " y[1] (numeric) = 1.9667794885522183 " " absolute error = 1.79189996174500270000000000000E-13 " " relative error = 9.110833075973804000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.727999999999910 " " y[1] (analytic) = 1.968779228909737 " " y[1] (numeric) = 1.9687792289095571 " " absolute error = 1.79856129989275360000000000000E-13 " " relative error = 9.135413831487617000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.726999999999909 " " y[1] (analytic) = 1.9707790004878452 " " y[1] (numeric) = 1.9707790004876644 " " absolute error = 1.80744308408975480000000000000E-13 " " relative error = 9.17121140240656900000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7259999999999085 " " y[1] (analytic) = 1.97277880128695 " " y[1] (numeric) = 1.9727788012867689 " " absolute error = 1.81188397618825550000000000000E-13 " " relative error = 9.184425415592797000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.724999999999908 " " y[1] (analytic) = 1.9747786293072518 " " y[1] (numeric) = 1.9747786293070697 " " absolute error = 1.82076576038525670000000000000E-13 " " relative error = 9.220100589320117000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;" Iterations = 275 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds "Expected Time Remaining "= 0 Years 0 Days 1 Hours 46 Minutes 26 Seconds "Optimized Time Remaining "= 0 Years 0 Days 1 Hours 45 Minutes 34 Seconds "Expected Total Time "= 0 Years 0 Days 1 Hours 48 Minutes 35 Seconds "Time to Timeout " Unknown Percent Done = 2.7600000000009217 "%" (%o54) true (%o54) diffeq.max