(%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 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , 1 1 1 array_tmp3 : array_tmp2 + array_const_0D0 , 1 1 1 array_tmp4 : array_const_0D3 array_x , 1 1 1 array_tmp5 : array_const_0D1 + array_tmp4 , 1 1 1 array_tmp6 : array_tmp5 + array_tmp3 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp6 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 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3 : array_tmp2 , array_tmp4 : array_const_0D3 array_x , 2 2 2 1 2 array_tmp5 : array_tmp4 , array_tmp6 : array_tmp5 + array_tmp3 , 2 2 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp6 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 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp6 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 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp6 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 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp6 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 while kkk <= glob_max_terms do (order_d : 1, if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp6 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 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , 1 1 1 array_tmp3 : array_tmp2 + array_const_0D0 , 1 1 1 array_tmp4 : array_const_0D3 array_x , 1 1 1 array_tmp5 : array_const_0D1 + array_tmp4 , 1 1 1 array_tmp6 : array_tmp5 + array_tmp3 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp6 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 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3 : array_tmp2 , array_tmp4 : array_const_0D3 array_x , 2 2 2 1 2 array_tmp5 : array_tmp4 , array_tmp6 : array_tmp5 + array_tmp3 , 2 2 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp6 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 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp6 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 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp6 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 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp6 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 while kkk <= glob_max_terms do (order_d : 1, if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp6 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) 0.4 x x (%i52) exact_soln_y(x) := block(0.3 x + -------) 2.0 0.4 x x (%o52) exact_soln_y(x) := block(0.3 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/add_lin_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.1 * x + 0.2) + (0.3 * x + 0.1) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-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:1000000,"), 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, " (0.4 * x * x / 2.0 + 0.3 * 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, Digits : 32, max_terms : 30, 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, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 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 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term 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, 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, 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_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 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_const_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, 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 : 1000000, 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 ) = (0.1 * x + 0.2) + (0.3 * x + 0.1) ;"), 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, "2012-12-14T19:28:39-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "add_lin_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.1 * x + 0.2) + (0.3 * x + 0.1) ;"), 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_lin_lin diffeq.max"), logitem_str(html_log_file, "add_lin_lin 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/add_lin_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.1 * x + 0.2) + (0.3 * x + 0.1) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-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:1000000,"), 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, " (0.4 * x * x / 2.0 + 0.3 * 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, Digits : 32, max_terms : 30, 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, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 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 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term 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, 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, 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_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 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_const_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, 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 : 1000000, 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 ) = (0.1 * x + 0.2) + (0.3 * x + 0.1) ;"), 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, "2012-12-14T19:28:39-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "add_lin_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.1 * x + 0.2) + (0.3 * x + 0.1) ;"), 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_lin_lin diffeq.max"), logitem_str(html_log_file, "add_lin_lin 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/add_lin_linpostode.ode#################" "diff ( y , x , 1 ) = (0.1 * x + 0.2) + (0.3 * x + 0.1) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* 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:1000000," "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(" " (0.4 * x * x / 2.0 + 0.3 * 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 "" max_value3 = 0.0 "" value3 = 0.0 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = -5. " " y[1] (analytic) = 3.5 " " y[1] (numeric) = 3.5 " " 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) = 3.4983002 " " y[1] (numeric) = 3.4983002 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.998000000000000 " " y[1] (analytic) = 3.4966007999999995 " " y[1] (numeric) = 3.4966008 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.270059795931130200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.996999999999999 " " y[1] (analytic) = 3.494901799999999 " " y[1] (numeric) = 3.4949018 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.541354437197993500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.995999999999999 " " y[1] (analytic) = 3.493203199999998 " " y[1] (numeric) = 3.4932032 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 5.085180385155526000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.994999999999998 " " y[1] (analytic) = 3.491504999999997 " " y[1] (numeric) = 3.491505 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 8.90339400616765900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.993999999999998 " " y[1] (analytic) = 3.4898071999999973 " " y[1] (numeric) = 3.4898072 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 7.63519331125334900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.992999999999998 " " y[1] (analytic) = 3.4881097999999957 " " y[1] (numeric) = 3.4881098 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 1.2731514640108610000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.991999999999997 " " y[1] (analytic) = 3.4864127999999956 " " y[1] (numeric) = 3.4864128 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 1.27377116631186980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.990999999999997 " " y[1] (analytic) = 3.484716199999995 " " y[1] (numeric) = 3.4847162000000003 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 1.52926959107911260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.989999999999997 " " y[1] (analytic) = 3.4830199999999945 " " y[1] (numeric) = 3.4830200000000002 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 1.6575155261958940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.988999999999996 " " y[1] (analytic) = 3.481324199999994 " " y[1] (numeric) = 3.4813242000000004 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 1.78588622625289740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.987999999999996 " " y[1] (analytic) = 3.4796287999999933 " " y[1] (numeric) = 3.4796288000000004 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 2.04200728468537070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.986999999999996 " " y[1] (analytic) = 3.4779337999999935 " " y[1] (numeric) = 3.4779338000000006 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 2.04300247394042260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.985999999999995 " " y[1] (analytic) = 3.476239199999992 " " y[1] (numeric) = 3.4762392000000006 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 2.42724809821809970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.984999999999995 " " y[1] (analytic) = 3.4745449999999916 " " y[1] (numeric) = 3.4745450000000004 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 2.5562438238679520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.983999999999995 " " y[1] (analytic) = 3.4728511999999916 " " y[1] (numeric) = 3.4728512000000005 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 2.5574905705724660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.982999999999994 " " y[1] (analytic) = 3.4711577999999905 " " y[1] (numeric) = 3.4711578000000003 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 2.8146120630705420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.981999999999994 " " y[1] (analytic) = 3.46946479999999 " " y[1] (numeric) = 3.4694648000000003 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 2.94398485511409960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.980999999999994 " " y[1] (analytic) = 3.467772199999989 " " y[1] (numeric) = 3.4677722 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 3.2015454320360490000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.979999999999993 " " y[1] (analytic) = 3.4660799999999883 " " y[1] (numeric) = 3.4660800000000003 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 3.45935716023627050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.978999999999993 " " y[1] (analytic) = 3.4643881999999886 " " y[1] (numeric) = 3.4643882 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 3.332859595844850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.977999999999993 " " y[1] (analytic) = 3.4626967999999883 " " y[1] (numeric) = 3.4626968000000002 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 3.46273709726815600000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.976999999999992 " " y[1] (analytic) = 3.4610057999999873 " " y[1] (numeric) = 3.4610058 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 3.7210533093159980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.975999999999992 " " y[1] (analytic) = 3.4593151999999865 " " y[1] (numeric) = 3.4593152000000003 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 3.9796216041117020000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.974999999999992 " " y[1] (analytic) = 3.4576249999999855 " " y[1] (numeric) = 3.457625 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 4.23844226168312850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.973999999999991 " " y[1] (analytic) = 3.455935199999986 " " y[1] (numeric) = 3.4559352000000003 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 4.11201422850812200000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.972999999999991 " " y[1] (analytic) = 3.4542457999999847 " " y[1] (numeric) = 3.4542458000000003 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 4.4997152040402744000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.971999999999990 " " y[1] (analytic) = 3.452556799999984 " " y[1] (numeric) = 3.4525568000000004 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 4.7591688468245890000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.97099999999999 " " y[1] (analytic) = 3.4508681999999835 " " y[1] (numeric) = 3.4508682000000004 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 4.8901867577273620000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.96999999999999 " " y[1] (analytic) = 3.4491799999999833 " " y[1] (numeric) = 3.4491800000000006 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 5.0213323700568040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.96899999999999 " " y[1] (analytic) = 3.4474921999999832 " " y[1] (numeric) = 3.4474922000000006 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 5.0237906801217780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.967999999999990 " " y[1] (analytic) = 3.4458047999999826 " " y[1] (numeric) = 3.445804800000001 " " absolute error = 1.820765760385256700000000000000E-14 " " relative error = 5.2840072669968590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.966999999999989 " " y[1] (analytic) = 3.444117799999982 " " y[1] (numeric) = 3.444117800000001 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 5.4155368360811370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.965999999999989 " " y[1] (analytic) = 3.442431199999981 " " y[1] (numeric) = 3.4424312000000006 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 5.6761992028781470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.964999999999988 " " y[1] (analytic) = 3.4407449999999806 " " y[1] (numeric) = 3.4407450000000006 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 5.8080486764502840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.963999999999988 " " y[1] (analytic) = 3.43905919999998 " " y[1] (numeric) = 3.4390592000000004 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 5.9400267529861070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.962999999999988 " " y[1] (analytic) = 3.437373799999979 " " y[1] (numeric) = 3.4373738000000005 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 6.2013279070210910000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.961999999999987 " " y[1] (analytic) = 3.435688799999979 " " y[1] (numeric) = 3.4356888000000003 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 6.2043692876965850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.960999999999987 " " y[1] (analytic) = 3.434004199999978 " " y[1] (numeric) = 3.4340042000000004 " " absolute error = 2.22044604925031300000000000000E-14 " " relative error = 6.466055135431480000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.959999999999987 " " y[1] (analytic) = 3.4323199999999776 " " y[1] (numeric) = 3.4323200000000003 " " absolute error = 2.264854970235319300000000000000E-14 " " relative error = 6.5986125135049590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.958999999999986 " " y[1] (analytic) = 3.4306361999999773 " " y[1] (numeric) = 3.4306362000000004 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 6.7312992593628580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.957999999999986 " " y[1] (analytic) = 3.428952799999977 " " y[1] (numeric) = 3.4289528000000002 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 6.7346039036184480000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.956999999999986 " " y[1] (analytic) = 3.4272697999999764 " " y[1] (numeric) = 3.4272698000000004 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 6.9970614312020450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.955999999999985 " " y[1] (analytic) = 3.425587199999976 " " y[1] (numeric) = 3.4255872000000003 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 7.130137146050060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.954999999999985 " " y[1] (analytic) = 3.423904999999975 " " y[1] (numeric) = 3.4239050000000004 " " absolute error = 2.53130849614535700000000000000E-14 " " relative error = 7.393045356531139000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.953999999999985 " " y[1] (analytic) = 3.422223199999975 " " y[1] (numeric) = 3.4222232000000004 " " absolute error = 2.53130849614535700000000000000E-14 " " relative error = 7.3966785572179370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.952999999999984 " " y[1] (analytic) = 3.420541799999974 " " y[1] (numeric) = 3.4205418000000005 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 7.7898047002389970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.951999999999984 " " y[1] (analytic) = 3.4188607999999734 " " y[1] (numeric) = 3.4188608000000005 " " absolute error = 2.70894418008538200000000000000E-14 " " relative error = 7.9235287382434620000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.950999999999984 " " y[1] (analytic) = 3.4171801999999722 " " y[1] (numeric) = 3.4171802000000007 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 8.3172989912572470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.949999999999983 " " y[1] (analytic) = 3.4154999999999722 " " y[1] (numeric) = 3.4155000000000006 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 8.3213905520141230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.948999999999983 " " y[1] (analytic) = 3.4138201999999715 " " y[1] (numeric) = 3.413820200000001 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 8.5856565762029240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.947999999999983 " " y[1] (analytic) = 3.412140799999971 " " y[1] (numeric) = 3.412140800000001 " " absolute error = 2.975397705995419500000000000000E-14 " " relative error = 8.7200320279733030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.946999999999982 " " y[1] (analytic) = 3.410461799999971 " " y[1] (numeric) = 3.4104618000000007 " " absolute error = 2.975397705995419500000000000000E-14 " " relative error = 8.7243249755661970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.945999999999982 " " y[1] (analytic) = 3.40878319999997 " " y[1] (numeric) = 3.4087832000000007 " " absolute error = 3.06421554796543200000000000000E-14 " " relative error = 8.9891769824653530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.944999999999982 " " y[1] (analytic) = 3.407104999999969 " " y[1] (numeric) = 3.4071050000000005 " " absolute error = 3.153033389935444600000000000000E-14 " " relative error = 9.254288875557030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.943999999999981 " " y[1] (analytic) = 3.4054271999999695 " " y[1] (numeric) = 3.4054272000000005 " " absolute error = 3.10862446895043830000000000000E-14 " " relative error = 9.1284420026669970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.942999999999981 " " y[1] (analytic) = 3.403749799999968 " " y[1] (numeric) = 3.4037498000000004 " " absolute error = 3.24185123190545700000000000000E-14 " " relative error = 9.524352324326211000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.941999999999980 " " y[1] (analytic) = 3.402072799999967 " " y[1] (numeric) = 3.4020728000000005 " " absolute error = 3.330669073875469600000000000000E-14 " " relative error = 9.7901169953667710000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.94099999999998 " " y[1] (analytic) = 3.4003961999999666 " " y[1] (numeric) = 3.4003962000000003 " " absolute error = 3.37507799486047600000000000000E-14 " " relative error = 9.9255433671538320000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.93999999999998 " " y[1] (analytic) = 3.398719999999966 " " y[1] (numeric) = 3.3987200000000004 " " absolute error = 3.41948691584548200000000000000E-14 " " relative error = 1.0061102167420428000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.93899999999998 " " y[1] (analytic) = 3.397044199999966 " " y[1] (numeric) = 3.3970442000000003 " " absolute error = 3.41948691584548200000000000000E-14 " " relative error = 1.0066065421949812000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.937999999999980 " " y[1] (analytic) = 3.395368799999966 " " y[1] (numeric) = 3.3953688000000004 " " absolute error = 3.41948691584548200000000000000E-14 " " relative error = 1.0071032389310747000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.936999999999979 " " y[1] (analytic) = 3.3936937999999657 " " y[1] (numeric) = 3.3936938000000003 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 1.0206860256015211000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.935999999999979 " " y[1] (analytic) = 3.3920191999999645 " " y[1] (numeric) = 3.3920192000000005 " " absolute error = 3.59712259978550700000000000000E-14 " " relative error = 1.0604664619190672000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.934999999999978 " " y[1] (analytic) = 3.390344999999964 " " y[1] (numeric) = 3.3903450000000004 " " absolute error = 3.641531520770513500000000000000E-14 " " relative error = 1.07408877880290990000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.933999999999978 " " y[1] (analytic) = 3.3886711999999632 " " y[1] (numeric) = 3.3886712000000005 " " absolute error = 3.73034936274052600000000000000E-14 " " relative error = 1.1008295413082764000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.932999999999978 " " y[1] (analytic) = 3.3869977999999623 " " y[1] (numeric) = 3.3869978000000005 " " absolute error = 3.819167204710538500000000000000E-14 " " relative error = 1.1275966003611167000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.931999999999977 " " y[1] (analytic) = 3.385324799999962 " " y[1] (numeric) = 3.3853248000000007 " " absolute error = 3.86357612569554500000000000000E-14 " " relative error = 1.1412719174525257000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.930999999999977 " " y[1] (analytic) = 3.383652199999961 " " y[1] (numeric) = 3.3836522000000007 " " absolute error = 3.95239396766555730000000000000E-14 " " relative error = 1.1680851736669634000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.929999999999977 " " y[1] (analytic) = 3.3819799999999614 " " y[1] (numeric) = 3.381980000000001 " " absolute error = 3.95239396766555730000000000000E-14 " " relative error = 1.1686627264695837000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.928999999999976 " " y[1] (analytic) = 3.380308199999961 " " y[1] (numeric) = 3.380308200000001 " " absolute error = 3.996802888650563500000000000000E-14 " " relative error = 1.182378248424392100000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.927999999999976 " " y[1] (analytic) = 3.3786367999999607 " " y[1] (numeric) = 3.3786368000000007 " " absolute error = 3.996802888650563500000000000000E-14 " " relative error = 1.1829631668756493000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.926999999999976 " " y[1] (analytic) = 3.37696579999996 " " y[1] (numeric) = 3.3769658000000007 " " absolute error = 4.08562073062057600000000000000E-14 " " relative error = 1.2098496024510005000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.925999999999975 " " y[1] (analytic) = 3.375295199999959 " " y[1] (numeric) = 3.3752952000000005 " " absolute error = 4.130029651605582300000000000000E-14 " " relative error = 1.2236054646733216000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.924999999999975 " " y[1] (analytic) = 3.3736249999999584 " " y[1] (numeric) = 3.3736250000000005 " " absolute error = 4.21884749357559500000000000000E-14 " " relative error = 1.2505383655787608000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.923999999999975 " " y[1] (analytic) = 3.371955199999958 " " y[1] (numeric) = 3.3719552000000004 " " absolute error = 4.21884749357559500000000000000E-14 " " relative error = 1.2511576350645606000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.922999999999974 " " y[1] (analytic) = 3.370285799999957 " " y[1] (numeric) = 3.3702858000000004 " " absolute error = 4.352074256530613600000000000000E-14 " " relative error = 1.2913071812873167000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.921999999999974 " " y[1] (analytic) = 3.3686167999999563 " " y[1] (numeric) = 3.3686168000000003 " " absolute error = 4.3964831775156200000000000000E-14 " " relative error = 1.3051300989520911000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.920999999999974 " " y[1] (analytic) = 3.366948199999956 " " y[1] (numeric) = 3.3669482000000004 " " absolute error = 4.44089209850062600000000000000E-14 " " relative error = 1.3189665639942677000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.919999999999973 " " y[1] (analytic) = 3.365279999999956 " " y[1] (numeric) = 3.3652800000000003 " " absolute error = 4.44089209850062600000000000000E-14 " " relative error = 1.3196203877539714000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.918999999999973 " " y[1] (analytic) = 3.363612199999955 " " y[1] (numeric) = 3.3636122000000004 " " absolute error = 4.52970994047063870000000000000E-14 " " relative error = 1.3466801971020023000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.917999999999973 " " y[1] (analytic) = 3.3619447999999545 " " y[1] (numeric) = 3.3619448000000003 " " absolute error = 4.57411886145564500000000000000E-14 " " relative error = 1.3605573956644698000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.916999999999972 " " y[1] (analytic) = 3.3602777999999542 " " y[1] (numeric) = 3.3602778000000004 " " absolute error = 4.61852778244065100000000000000E-14 " " relative error = 1.3744482025982238000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.915999999999972 " " y[1] (analytic) = 3.3586111999999533 " " y[1] (numeric) = 3.3586112000000004 " " absolute error = 4.70734562441066400000000000000E-14 " " relative error = 1.4015750392336956000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.914999999999972 " " y[1] (analytic) = 3.356944999999953 " " y[1] (numeric) = 3.3569450000000005 " " absolute error = 4.7517545453956700000000000000E-14 " " relative error = 1.4154996716942747000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.913999999999971 " " y[1] (analytic) = 3.3552791999999525 " " y[1] (numeric) = 3.3552792000000005 " " absolute error = 4.79616346638067600000000000000E-14 " " relative error = 1.4294379634281237000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.912999999999971 " " y[1] (analytic) = 3.353613799999952 " " y[1] (numeric) = 3.3536138000000006 " " absolute error = 4.88498130835068900000000000000E-14 " " relative error = 1.4566320392499457000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.911999999999970 " " y[1] (analytic) = 3.351948799999951 " " y[1] (numeric) = 3.3519488000000006 " " absolute error = 4.97379915032070130000000000000E-14 " " relative error = 1.4838529604989117000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.91099999999997 " " y[1] (analytic) = 3.35028419999995 " " y[1] (numeric) = 3.350284200000001 " " absolute error = 5.06261699229071400000000000000E-14 " " relative error = 1.5111007574494095000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.90999999999997 " " y[1] (analytic) = 3.3486199999999497 " " y[1] (numeric) = 3.348620000000001 " " absolute error = 5.1070259132757200000000000000E-14 " " relative error = 1.5251136029993836000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.90899999999997 " " y[1] (analytic) = 3.3469561999999495 " " y[1] (numeric) = 3.346956200000001 " " absolute error = 5.151434834260726000000000000000E-14 " " relative error = 1.5391401997614443000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.907999999999970 " " y[1] (analytic) = 3.3452927999999496 " " y[1] (numeric) = 3.345292800000001 " " absolute error = 5.151434834260726000000000000000E-14 " " relative error = 1.5399055156728894000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.906999999999969 " " y[1] (analytic) = 3.343629799999949 " " y[1] (numeric) = 3.343629800000001 " " absolute error = 5.195843755245733000000000000000E-14 " " relative error = 1.553953058812256000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.905999999999969 " " y[1] (analytic) = 3.3419671999999485 " " y[1] (numeric) = 3.341967200000001 " " absolute error = 5.24025267623073900000000000000E-14 " " relative error = 1.5680143947046576000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.904999999999968 " " y[1] (analytic) = 3.340304999999947 " " y[1] (numeric) = 3.3403050000000007 " " absolute error = 5.373479439185758000000000000000E-14 " " relative error = 1.6086792790436333000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.903999999999968 " " y[1] (analytic) = 3.338643199999947 " " y[1] (numeric) = 3.338643200000001 " " absolute error = 5.373479439185758000000000000000E-14 " " relative error = 1.6094799945037083000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.902999999999968 " " y[1] (analytic) = 3.336981799999946 " " y[1] (numeric) = 3.3369818000000007 " " absolute error = 5.4622972811557700000000000000E-14 " " relative error = 1.6368975345193248000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.901999999999967 " " y[1] (analytic) = 3.3353207999999457 " " y[1] (numeric) = 3.3353208000000008 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 1.6510274520342588000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.900999999999967 " " y[1] (analytic) = 3.3336601999999456 " " y[1] (numeric) = 3.3336602000000006 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 1.6518498802430034000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.899999999999967 " " y[1] (analytic) = 3.331999999999945 " " y[1] (numeric) = 3.3320000000000007 " " absolute error = 5.59552404411078900000000000000E-14 " " relative error = 1.679328944811189000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.898999999999966 " " y[1] (analytic) = 3.3303401999999442 " " y[1] (numeric) = 3.3303402000000006 " " absolute error = 5.63993296509579500000000000000E-14 " " relative error = 1.6935005514139034000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.897999999999966 " " y[1] (analytic) = 3.328680799999944 " " y[1] (numeric) = 3.3286808000000008 " " absolute error = 5.68434188608080100000000000000E-14 " " relative error = 1.707686085755323000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.896999999999966 " " y[1] (analytic) = 3.327021799999944 " " y[1] (numeric) = 3.3270218000000007 " " absolute error = 5.68434188608080100000000000000E-14 " " relative error = 1.7085376134538396000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.895999999999965 " " y[1] (analytic) = 3.325363199999943 " " y[1] (numeric) = 3.325363200000001 " " absolute error = 5.77315972805081400000000000000E-14 " " relative error = 1.7360990005695956000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.894999999999965 " " y[1] (analytic) = 3.323704999999942 " " y[1] (numeric) = 3.323705000000001 " " absolute error = 5.86197757002082700000000000000E-14 " " relative error = 1.7636876828782724000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.893999999999965 " " y[1] (analytic) = 3.322047199999942 " " y[1] (numeric) = 3.322047200000001 " " absolute error = 5.90638649100583300000000000000E-14 " " relative error = 1.7779357532927093000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.892999999999964 " " y[1] (analytic) = 3.3203897999999405 " " y[1] (numeric) = 3.320389800000001 " " absolute error = 6.03961325396085200000000000000E-14 " " relative error = 1.8189470567464577000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.891999999999964 " " y[1] (analytic) = 3.31873279999994 " " y[1] (numeric) = 3.318732800000001 " " absolute error = 6.12843109593086400000000000000E-14 " " relative error = 1.846617810247024000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.890999999999964 " " y[1] (analytic) = 3.3170761999999394 " " y[1] (numeric) = 3.317076200000001 " " absolute error = 6.1728400169158700000000000000E-14 " " relative error = 1.8609280115168844000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.889999999999963 " " y[1] (analytic) = 3.315419999999939 " " y[1] (numeric) = 3.3154200000000014 " " absolute error = 6.21724893790087700000000000000E-14 " " relative error = 1.8752522871615032000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.888999999999963 " " y[1] (analytic) = 3.313764199999939 " " y[1] (numeric) = 3.3137642000000014 " " absolute error = 6.21724893790087700000000000000E-14 " " relative error = 1.8761893009469383000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.887999999999963 " " y[1] (analytic) = 3.3121087999999386 " " y[1] (numeric) = 3.312108800000001 " " absolute error = 6.26165785888588300000000000000E-14 " " relative error = 1.8905350750814706000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.886999999999962 " " y[1] (analytic) = 3.310453799999938 " " y[1] (numeric) = 3.3104538000000012 " " absolute error = 6.30606677987088900000000000000E-14 " " relative error = 1.9048949663248604000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.885999999999962 " " y[1] (analytic) = 3.308799199999937 " " y[1] (numeric) = 3.308799200000001 " " absolute error = 6.39488462184090200000000000000E-14 " " relative error = 1.9326904521256605000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.884999999999962 " " y[1] (analytic) = 3.3071449999999367 " " y[1] (numeric) = 3.307145000000001 " " absolute error = 6.43929354282590800000000000000E-14 " " relative error = 1.9470853388121873000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.883999999999961 " " y[1] (analytic) = 3.305491199999936 " " y[1] (numeric) = 3.305491200000001 " " absolute error = 6.48370246381091400000000000000E-14 " " relative error = 1.961494395692549000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.882999999999961 " " y[1] (analytic) = 3.3038377999999353 " " y[1] (numeric) = 3.303837800000001 " " absolute error = 6.57252030578092700000000000000E-14 " " relative error = 1.989359255403233000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.881999999999960 " " y[1] (analytic) = 3.302184799999935 " " y[1] (numeric) = 3.302184800000001 " " absolute error = 6.57252030578092700000000000000E-14 " " relative error = 1.9903550842403053000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.88099999999996 " " y[1] (analytic) = 3.3005321999999344 " " y[1] (numeric) = 3.300532200000001 " " absolute error = 6.66133814775093900000000000000E-14 " " relative error = 2.0182618269111485000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.87999999999996 " " y[1] (analytic) = 3.298879999999934 " " y[1] (numeric) = 3.298880000000001 " " absolute error = 6.70574706873594600000000000000E-14 " " relative error = 2.0327344640411535000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.87899999999996 " " y[1] (analytic) = 3.2972281999999336 " " y[1] (numeric) = 3.297228200000001 " " absolute error = 6.75015598972095200000000000000E-14 " " relative error = 2.047221356932798000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.877999999999960 " " y[1] (analytic) = 3.2955767999999335 " " y[1] (numeric) = 3.295576800000001 " " absolute error = 6.75015598972095200000000000000E-14 " " relative error = 2.048247211147101200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.876999999999959 " " y[1] (analytic) = 3.2939257999999327 " " y[1] (numeric) = 3.293925800000001 " " absolute error = 6.83897383169096400000000000000E-14 " " relative error = 2.0762379746657023000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.875999999999959 " " y[1] (analytic) = 3.2922751999999322 " " y[1] (numeric) = 3.292275200000001 " " absolute error = 6.8833827526759700000000000000E-14 " " relative error = 2.0907677318943788000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.874999999999958 " " y[1] (analytic) = 3.2906249999999315 " " y[1] (numeric) = 3.2906250000000012 " " absolute error = 6.97220059464598300000000000000E-14 " " relative error = 2.118807398183059000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.873999999999958 " " y[1] (analytic) = 3.2889751999999315 " " y[1] (numeric) = 3.288975200000001 " " absolute error = 6.97220059464598300000000000000E-14 " " relative error = 2.1198702242103035000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.872999999999958 " " y[1] (analytic) = 3.2873257999999304 " " y[1] (numeric) = 3.2873258000000014 " " absolute error = 7.10542735760100200000000000000E-14 " " relative error = 2.1614612575367956000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.871999999999957 " " y[1] (analytic) = 3.28567679999993 " " y[1] (numeric) = 3.2856768000000014 " " absolute error = 7.14983627858600800000000000000E-14 " " relative error = 2.17606195429391020000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.870999999999957 " " y[1] (analytic) = 3.284028199999929 " " y[1] (numeric) = 3.2840282000000016 " " absolute error = 7.28306304154102700000000000000E-14 " " relative error = 2.2177224426821865000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.869999999999957 " " y[1] (analytic) = 3.282379999999929 " " y[1] (numeric) = 3.2823800000000016 " " absolute error = 7.28306304154102700000000000000E-14 " " relative error = 2.218836040172431000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.868999999999956 " " y[1] (analytic) = 3.280732199999928 " " y[1] (numeric) = 3.2807322000000014 " " absolute error = 7.32747196252603300000000000000E-14 " " relative error = 2.2334867693639224000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.867999999999956 " " y[1] (analytic) = 3.2790847999999277 " " y[1] (numeric) = 3.2790848000000015 " " absolute error = 7.3718808835110390000000000000E-14 " " relative error = 2.248151948833772800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.866999999999956 " " y[1] (analytic) = 3.2774377999999276 " " y[1] (numeric) = 3.2774378000000013 " " absolute error = 7.3718808835110390000000000000E-14 " " relative error = 2.2492817052122857000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.865999999999955 " " y[1] (analytic) = 3.2757911999999267 " " y[1] (numeric) = 3.2757912000000013 " " absolute error = 7.46069872548105200000000000000E-14 " " relative error = 2.2775257243139363000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.864999999999955 " " y[1] (analytic) = 3.2741449999999257 " " y[1] (numeric) = 3.274145000000001 " " absolute error = 7.54951656745106400000000000000E-14 " " relative error = 2.305797870116087000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.863999999999955 " " y[1] (analytic) = 3.2724991999999262 " " y[1] (numeric) = 3.2724992000000013 " " absolute error = 7.50510764646605800000000000000E-14 " " relative error = 2.29338716002321030000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.862999999999954 " " y[1] (analytic) = 3.2708537999999248 " " y[1] (numeric) = 3.270853800000001 " " absolute error = 7.63833440942107700000000000000E-14 " " relative error = 2.3352723406412274000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.861999999999954 " " y[1] (analytic) = 3.269208799999924 " " y[1] (numeric) = 3.2692088000000012 " " absolute error = 7.7271522513910900000000000000E-14 " " relative error = 2.3636153956857295000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.860999999999954 " " y[1] (analytic) = 3.2675641999999234 " " y[1] (numeric) = 3.267564200000001 " " absolute error = 7.77156117237609600000000000000E-14 " " relative error = 2.3783958620847534000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.859999999999953 " " y[1] (analytic) = 3.265919999999923 " " y[1] (numeric) = 3.2659200000000013 " " absolute error = 7.81597009336110200000000000000E-14 " " relative error = 2.3931909211987085000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.858999999999953 " " y[1] (analytic) = 3.264276199999923 " " y[1] (numeric) = 3.264276200000001 " " absolute error = 7.81597009336110200000000000000E-14 " " relative error = 2.3943960665342245000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.857999999999953 " " y[1] (analytic) = 3.2626327999999223 " " y[1] (numeric) = 3.2626328000000013 " " absolute error = 7.90478793533111500000000000000E-14 " " relative error = 2.422824884041901200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.856999999999952 " " y[1] (analytic) = 3.260989799999922 " " y[1] (numeric) = 3.2609898000000013 " " absolute error = 7.94919685631612100000000000000E-14 " " relative error = 2.4376638210632587000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.855999999999952 " " y[1] (analytic) = 3.2593471999999215 " " y[1] (numeric) = 3.2593472000000014 " " absolute error = 7.99360577730112700000000000000E-14 " " relative error = 2.452517417383861300000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.854999999999952 " " y[1] (analytic) = 3.25770499999992 " " y[1] (numeric) = 3.2577050000000014 " " absolute error = 8.12683254025614600000000000000E-14 " " relative error = 2.4946496199798157000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.853999999999951 " " y[1] (analytic) = 3.2560631999999203 " " y[1] (numeric) = 3.2560632000000016 " " absolute error = 8.12683254025614600000000000000E-14 " " relative error = 2.4959074935205017000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.852999999999951 " " y[1] (analytic) = 3.2544217999999194 " " y[1] (numeric) = 3.2544218000000016 " " absolute error = 8.21565038222615800000000000000E-14 " " relative error = 2.5244577645793675000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.851999999999950 " " y[1] (analytic) = 3.252780799999919 " " y[1] (numeric) = 3.252780800000002 " " absolute error = 8.26005930321116500000000000000E-14 " " relative error = 2.5393839336518986000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.85099999999995 " " y[1] (analytic) = 3.2511401999999183 " " y[1] (numeric) = 3.251140200000002 " " absolute error = 8.34887714518117700000000000000E-14 " " relative error = 2.567984347516415000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.84999999999995 " " y[1] (analytic) = 3.2494999999999177 " " y[1] (numeric) = 3.249500000000002 " " absolute error = 8.4376949871511900000000000000E-14 " " relative error = 2.59661332117292030000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.84899999999995 " " y[1] (analytic) = 3.247860199999918 " " y[1] (numeric) = 3.247860200000002 " " absolute error = 8.39328606616618300000000000000E-14 " " relative error = 2.5842510296983820000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.847999999999950 " " y[1] (analytic) = 3.246220799999917 " " y[1] (numeric) = 3.246220800000002 " " absolute error = 8.48210390813619600000000000000E-14 " " relative error = 2.612916505290217000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.846999999999949 " " y[1] (analytic) = 3.244581799999917 " " y[1] (numeric) = 3.244581800000002 " " absolute error = 8.48210390813619600000000000000E-14 " " relative error = 2.61423641966321000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.845999999999949 " " y[1] (analytic) = 3.2429431999999165 " " y[1] (numeric) = 3.242943200000002 " " absolute error = 8.52651282912120200000000000000E-14 " " relative error = 2.6292513631202120000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.844999999999948 " " y[1] (analytic) = 3.241304999999915 " " y[1] (numeric) = 3.241305000000002 " " absolute error = 8.70414851306122700000000000000E-14 " " relative error = 2.6853839774601450000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.843999999999948 " " y[1] (analytic) = 3.2396671999999156 " " y[1] (numeric) = 3.2396672000000017 " " absolute error = 8.61533067109121500000000000000E-14 " " relative error = 2.659325831706244000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.842999999999948 " " y[1] (analytic) = 3.2380297999999144 " " y[1] (numeric) = 3.238029800000002 " " absolute error = 8.74855743404623400000000000000E-14 " " relative error = 2.701814984545992700000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.841999999999947 " " y[1] (analytic) = 3.236392799999914 " " y[1] (numeric) = 3.2363928000000017 " " absolute error = 8.7929663550312400000000000000E-14 " " relative error = 2.7169033236730333000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.840999999999947 " " y[1] (analytic) = 3.2347561999999135 " " y[1] (numeric) = 3.234756200000002 " " absolute error = 8.83737527601624600000000000000E-14 " " relative error = 2.732006596360023000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.839999999999947 " " y[1] (analytic) = 3.2331199999999125 " " y[1] (numeric) = 3.2331200000000018 " " absolute error = 8.92619311798625900000000000000E-14 " " relative error = 2.7608604437776824000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.838999999999946 " " y[1] (analytic) = 3.2314841999999127 " " y[1] (numeric) = 3.231484200000002 " " absolute error = 8.92619311798625900000000000000E-14 " " relative error = 2.762258010726618700000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.837999999999946 " " y[1] (analytic) = 3.229848799999912 " " y[1] (numeric) = 3.229848800000002 " " absolute error = 8.97060203897126500000000000000E-14 " " relative error = 2.7774061866213395000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.836999999999946 " " y[1] (analytic) = 3.228213799999912 " " y[1] (numeric) = 3.228213800000002 " " absolute error = 9.01501095995627100000000000000E-14 " " relative error = 2.7925693645063154000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.835999999999945 " " y[1] (analytic) = 3.226579199999911 " " y[1] (numeric) = 3.226579200000002 " " absolute error = 9.10382880192628400000000000000E-14 " " relative error = 2.8215110299869706000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.834999999999945 " " y[1] (analytic) = 3.22494499999991 " " y[1] (numeric) = 3.224945000000002 " " absolute error = 9.23705556488130200000000000000E-14 " " relative error = 2.864252123642903000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.833999999999945 " " y[1] (analytic) = 3.2233111999999102 " " y[1] (numeric) = 3.223311200000002 " " absolute error = 9.19264664389629600000000000000E-14 " " relative error = 2.8519265046131914000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.832999999999944 " " y[1] (analytic) = 3.2216777999999087 " " y[1] (numeric) = 3.2216778000000024 " " absolute error = 9.37028232783632100000000000000E-14 " " relative error = 2.9085100713164386000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.831999999999944 " " y[1] (analytic) = 3.2200447999999087 " " y[1] (numeric) = 3.2200448000000024 " " absolute error = 9.37028232783632100000000000000E-14 " " relative error = 2.9099850809021627000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.830999999999944 " " y[1] (analytic) = 3.218412199999908 " " y[1] (numeric) = 3.2184122000000026 " " absolute error = 9.45910016980633400000000000000E-14 " " relative error = 2.939058014323524000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.829999999999943 " " y[1] (analytic) = 3.2167799999999076 " " y[1] (numeric) = 3.2167800000000026 " " absolute error = 9.5035090907913400000000000000E-14 " " relative error = 2.954354693448608000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.828999999999943 " " y[1] (analytic) = 3.2151481999999074 " " y[1] (numeric) = 3.2151482000000025 " " absolute error = 9.5035090907913400000000000000E-14 " " relative error = 2.9558541316358650000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.827999999999943 " " y[1] (analytic) = 3.2135167999999066 " " y[1] (numeric) = 3.2135168000000025 " " absolute error = 9.59232693276135300000000000000E-14 " " relative error = 2.9849935537171085000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.826999999999942 " " y[1] (analytic) = 3.211885799999906 " " y[1] (numeric) = 3.2118858000000023 " " absolute error = 9.63673585374635900000000000000E-14 " " relative error = 3.0003357696424454000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.825999999999942 " " y[1] (analytic) = 3.2102551999999056 " " y[1] (numeric) = 3.2102552000000024 " " absolute error = 9.68114477473136500000000000000E-14 " " relative error = 3.0156931993231095000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.824999999999942 " " y[1] (analytic) = 3.208624999999905 " " y[1] (numeric) = 3.2086250000000023 " " absolute error = 9.72555369571637100000000000000E-14 " " relative error = 3.0310658602101080000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.823999999999941 " " y[1] (analytic) = 3.206995199999905 " " y[1] (numeric) = 3.2069952000000024 " " absolute error = 9.72555369571637100000000000000E-14 " " relative error = 3.032606252643178000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.822999999999941 " " y[1] (analytic) = 3.205365799999904 " " y[1] (numeric) = 3.2053658000000023 " " absolute error = 9.81437153768638400000000000000E-14 " " relative error = 3.061856945527614000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.821999999999940 " " y[1] (analytic) = 3.203736799999903 " " y[1] (numeric) = 3.2037368000000024 " " absolute error = 9.94759830064140300000000000000E-14 " " relative error = 3.1049986068274094000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.82099999999994 " " y[1] (analytic) = 3.202108199999903 " " y[1] (numeric) = 3.2021082000000023 " " absolute error = 9.94759830064140300000000000000E-14 " " relative error = 3.1065778166526990000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.81999999999994 " " y[1] (analytic) = 3.200479999999902 " " y[1] (numeric) = 3.2004800000000024 " " absolute error = 1.00364161426114150000000000000E-13 " " relative error = 3.1359096581174456000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8189999999999396 " " y[1] (analytic) = 3.1988521999999024 " " y[1] (numeric) = 3.1988522000000024 " " absolute error = 9.99200722162640900000000000000E-14 " " relative error = 3.1236226611616230000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.817999999999940 " " y[1] (analytic) = 3.1972247999999013 " " y[1] (numeric) = 3.1972248000000025 " " absolute error = 1.01252339845814280000000000000E-13 " " relative error = 3.1668820986818760000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.816999999999939 " " y[1] (analytic) = 3.1955977999999012 " " y[1] (numeric) = 3.1955978000000025 " " absolute error = 1.01252339845814280000000000000E-13 " " relative error = 3.1684944784295890000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8159999999999386 " " y[1] (analytic) = 3.1939711999999005 " " y[1] (numeric) = 3.1939712000000027 " " absolute error = 1.0214051826551440000000000000E-13 " " relative error = 3.1979160696726877000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.814999999999938 " " y[1] (analytic) = 3.1923449999998996 " " y[1] (numeric) = 3.1923450000000027 " " absolute error = 1.03028696685214530000000000000E-13 " " relative error = 3.227367238980053000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.813999999999938 " " y[1] (analytic) = 3.1907191999998994 " " y[1] (numeric) = 3.190719200000003 " " absolute error = 1.03472785895064590000000000000E-13 " " relative error = 3.2429298665663797000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8129999999999376 " " y[1] (analytic) = 3.189093799999899 " " y[1] (numeric) = 3.189093800000003 " " absolute error = 1.03916875104914650000000000000E-13 " " relative error = 3.2585079531031025000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.811999999999937 " " y[1] (analytic) = 3.1874687999998983 " " y[1] (numeric) = 3.187468800000003 " " absolute error = 1.04805053524614780000000000000E-13 " " relative error = 3.2880338632528144000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.810999999999937 " " y[1] (analytic) = 3.185844199999898 " " y[1] (numeric) = 3.185844200000003 " " absolute error = 1.05249142734464840000000000000E-13 " " relative error = 3.3036500257755297000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8099999999999365 " " y[1] (analytic) = 3.184219999999897 " " y[1] (numeric) = 3.184220000000003 " " absolute error = 1.06137321154164970000000000000E-13 " " relative error = 3.333228267964161000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.808999999999936 " " y[1] (analytic) = 3.182596199999897 " " y[1] (numeric) = 3.182596200000003 " " absolute error = 1.06137321154164970000000000000E-13 " " relative error = 3.3349289223109235000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.807999999999936 " " y[1] (analytic) = 3.1809727999998962 " " y[1] (numeric) = 3.180972800000003 " " absolute error = 1.06581410364015030000000000000E-13 " " relative error = 3.3505916920766665000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8069999999999355 " " y[1] (analytic) = 3.179349799999896 " " y[1] (numeric) = 3.179349800000003 " " absolute error = 1.07025499573865090000000000000E-13 " " relative error = 3.366270033384455000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.805999999999935 " " y[1] (analytic) = 3.1777271999998957 " " y[1] (numeric) = 3.1777272000000027 " " absolute error = 1.07025499573865090000000000000E-13 " " relative error = 3.3679889064696494000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.804999999999935 " " y[1] (analytic) = 3.1761049999998945 " " y[1] (numeric) = 3.176105000000003 " " absolute error = 1.08357767203415280000000000000E-13 " " relative error = 3.4116556978884160000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8039999999999345 " " y[1] (analytic) = 3.174483199999895 " " y[1] (numeric) = 3.1744832000000027 " " absolute error = 1.07913677993565220000000000000E-13 " " relative error = 3.399409327274713300000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.802999999999934 " " y[1] (analytic) = 3.172861799999893 " " y[1] (numeric) = 3.172861800000003 " " absolute error = 1.09690034832965470000000000000E-13 " " relative error = 3.457132448471886000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.801999999999934 " " y[1] (analytic) = 3.171240799999893 " " y[1] (numeric) = 3.1712408000000027 " " absolute error = 1.09690034832965470000000000000E-13 " " relative error = 3.4588995838149270000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8009999999999335 " " y[1] (analytic) = 3.1696201999998923 " " y[1] (numeric) = 3.169620200000003 " " absolute error = 1.10578213252665590000000000000E-13 " " relative error = 3.488689693884124000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.799999999999933 " " y[1] (analytic) = 3.167999999999892 " " y[1] (numeric) = 3.168000000000003 " " absolute error = 1.11022302462515650000000000000E-13 " " relative error = 3.504491870660335600000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.798999999999933 " " y[1] (analytic) = 3.1663801999998915 " " y[1] (numeric) = 3.166380200000003 " " absolute error = 1.11466391672365720000000000000E-13 " " relative error = 3.520309774308516000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7979999999999325 " " y[1] (analytic) = 3.1647607999998915 " " y[1] (numeric) = 3.164760800000003 " " absolute error = 1.11466391672365720000000000000E-13 " " relative error = 3.5221111078085120000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.796999999999932 " " y[1] (analytic) = 3.1631417999998908 " " y[1] (numeric) = 3.163141800000003 " " absolute error = 1.12354570092065840000000000000E-13 " " relative error = 3.55199283484761000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.795999999999932 " " y[1] (analytic) = 3.1615231999998903 " " y[1] (numeric) = 3.161523200000003 " " absolute error = 1.1279865930191590000000000000E-13 " " relative error = 3.5678580281150496000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7949999999999315 " " y[1] (analytic) = 3.1599049999998896 " " y[1] (numeric) = 3.1599050000000033 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 3.5977928995213465000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.793999999999931 " " y[1] (analytic) = 3.1582871999998896 " " y[1] (numeric) = 3.1582872000000033 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 3.5996358317767935000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.792999999999930 " " y[1] (analytic) = 3.1566697999998885 " " y[1] (numeric) = 3.1566698000000035 " " absolute error = 1.15019105351166220000000000000E-13 " " relative error = 3.643685042736186000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7919999999999305 " " y[1] (analytic) = 3.155052799999888 " " y[1] (numeric) = 3.1550528000000035 " " absolute error = 1.15463194561016280000000000000E-13 " " relative error = 3.659627964420132000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.79099999999993 " " y[1] (analytic) = 3.153436199999887 " " y[1] (numeric) = 3.1534362000000034 " " absolute error = 1.1635137298071640000000000000E-13 " " relative error = 3.689669478035439000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.78999999999993 " " y[1] (analytic) = 3.151819999999887 " " y[1] (numeric) = 3.1518200000000034 " " absolute error = 1.1635137298071640000000000000E-13 " " relative error = 3.6915614781529590000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7889999999999295 " " y[1] (analytic) = 3.1502041999998864 " " y[1] (numeric) = 3.1502042000000032 " " absolute error = 1.16795462190566470000000000000E-13 " " relative error = 3.707552106957723000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.787999999999930 " " y[1] (analytic) = 3.148588799999886 " " y[1] (numeric) = 3.1485888000000033 " " absolute error = 1.17239551400416530000000000000E-13 " " relative error = 3.723558674934649000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.786999999999929 " " y[1] (analytic) = 3.146973799999886 " " y[1] (numeric) = 3.146973800000003 " " absolute error = 1.17239551400416530000000000000E-13 " " relative error = 3.725469573353956000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7859999999999285 " " y[1] (analytic) = 3.145359199999885 " " y[1] (numeric) = 3.1453592000000032 " " absolute error = 1.18127729820116660000000000000E-13 " " relative error = 3.755619702198749000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.784999999999928 " " y[1] (analytic) = 3.143744999999884 " " y[1] (numeric) = 3.143745000000003 " " absolute error = 1.19015908239816780000000000000E-13 " " relative error = 3.785800319040545000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.783999999999928 " " y[1] (analytic) = 3.1421311999998838 " " y[1] (numeric) = 3.1421312000000032 " " absolute error = 1.19459997449666840000000000000E-13 " " relative error = 3.801878083565423700000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7829999999999275 " " y[1] (analytic) = 3.1405177999998832 " " y[1] (numeric) = 3.140517800000003 " " absolute error = 1.1990408665951690000000000000E-13 " " relative error = 3.817971885385313400000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.781999999999927 " " y[1] (analytic) = 3.1389047999998825 " " y[1] (numeric) = 3.1389048000000033 " " absolute error = 1.20792265079217030000000000000E-13 " " relative error = 3.8482296461881080000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.780999999999927 " " y[1] (analytic) = 3.137292199999882 " " y[1] (numeric) = 3.137292200000003 " " absolute error = 1.2123635428906710000000000000E-13 " " relative error = 3.86436285052032000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7799999999999265 " " y[1] (analytic) = 3.1356799999998817 " " y[1] (numeric) = 3.1356800000000034 " " absolute error = 1.21680443498917160000000000000E-13 " " relative error = 3.880512153629253000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.778999999999926 " " y[1] (analytic) = 3.1340681999998816 " " y[1] (numeric) = 3.1340682000000033 " " absolute error = 1.21680443498917160000000000000E-13 " " relative error = 3.882507837542328000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.777999999999926 " " y[1] (analytic) = 3.132456799999881 " " y[1] (numeric) = 3.1324568000000035 " " absolute error = 1.22568621918617280000000000000E-13 " " relative error = 3.912859130846495000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7769999999999255 " " y[1] (analytic) = 3.1308457999998804 " " y[1] (numeric) = 3.1308458000000035 " " absolute error = 1.23012711128467340000000000000E-13 " " relative error = 3.929056842354614000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.775999999999925 " " y[1] (analytic) = 3.12923519999988 " " y[1] (numeric) = 3.1292352000000037 " " absolute error = 1.2345680033831741000000000000E-13 " " relative error = 3.945270727439156300000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.774999999999925 " " y[1] (analytic) = 3.127624999999879 " " y[1] (numeric) = 3.1276250000000037 " " absolute error = 1.2478906796786760000000000000E-13 " " relative error = 3.989898660097436000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7739999999999245 " " y[1] (analytic) = 3.126015199999879 " " y[1] (numeric) = 3.126015200000004 " " absolute error = 1.2478906796786760000000000000E-13 " " relative error = 3.991953333044331300000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.772999999999924 " " y[1] (analytic) = 3.124405799999878 " " y[1] (numeric) = 3.124405800000004 " " absolute error = 1.25677246387567720000000000000E-13 " " relative error = 4.022436726611268000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.771999999999924 " " y[1] (analytic) = 3.122796799999877 " " y[1] (numeric) = 3.122796800000004 " " absolute error = 1.2700951401711790000000000000E-13 " " relative error = 4.067171902351216000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7709999999999235 " " y[1] (analytic) = 3.121188199999877 " " y[1] (numeric) = 3.121188200000004 " " absolute error = 1.2700951401711790000000000000E-13 " " relative error = 4.069268044045627000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.769999999999923 " " y[1] (analytic) = 3.1195799999998766 " " y[1] (numeric) = 3.119580000000004 " " absolute error = 1.27453603226967970000000000000E-13 " " relative error = 4.08560137027975000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.768999999999923 " " y[1] (analytic) = 3.117972199999876 " " y[1] (numeric) = 3.117972200000004 " " absolute error = 1.27897692436818030000000000000E-13 " " relative error = 4.101951019217654000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7679999999999225 " " y[1] (analytic) = 3.116364799999876 " " y[1] (numeric) = 3.116364800000004 " " absolute error = 1.27897692436818030000000000000E-13 " " relative error = 4.104066777959471400000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.766999999999922 " " y[1] (analytic) = 3.1147577999998752 " " y[1] (numeric) = 3.114757800000004 " " absolute error = 1.28785870856518160000000000000E-13 " " relative error = 4.13469936110356040000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.765999999999922 " " y[1] (analytic) = 3.1131511999998747 " " y[1] (numeric) = 3.113151200000004 " " absolute error = 1.29229960066368220000000000000E-13 " " relative error = 4.1510980920674010000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7649999999999215 " " y[1] (analytic) = 3.111544999999874 " " y[1] (numeric) = 3.111545000000004 " " absolute error = 1.30118138486068350000000000000E-13 " " relative error = 4.181785527320788000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.763999999999921 " " y[1] (analytic) = 3.109939199999874 " " y[1] (numeric) = 3.109939200000004 " " absolute error = 1.30118138486068350000000000000E-13 " " relative error = 4.183944769276314000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.762999999999920 " " y[1] (analytic) = 3.1083337999998726 " " y[1] (numeric) = 3.108333800000004 " " absolute error = 1.31450406115618530000000000000E-13 " " relative error = 4.228966854062582400000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7619999999999205 " " y[1] (analytic) = 3.106728799999872 " " y[1] (numeric) = 3.106728800000004 " " absolute error = 1.3189449532546860000000000000E-13 " " relative error = 4.245446056491124000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.76099999999992 " " y[1] (analytic) = 3.1051241999998718 " " y[1] (numeric) = 3.105124200000004 " " absolute error = 1.32338584535318660000000000000E-13 " " relative error = 4.261941745690047700000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.75999999999992 " " y[1] (analytic) = 3.1035199999998717 " " y[1] (numeric) = 3.103520000000004 " " absolute error = 1.32338584535318660000000000000E-13 " " relative error = 4.264144730348898000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7589999999999195 " " y[1] (analytic) = 3.101916199999872 " " y[1] (numeric) = 3.1019162000000042 " " absolute error = 1.32338584535318660000000000000E-13 " " relative error = 4.26634944346092060000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.757999999999920 " " y[1] (analytic) = 3.1003127999998705 " " y[1] (numeric) = 3.100312800000004 " " absolute error = 1.33670852164868850000000000000E-13 " " relative error = 4.311527925984579000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.756999999999919 " " y[1] (analytic) = 3.0987097999998703 " " y[1] (numeric) = 3.0987098000000044 " " absolute error = 1.3411494137471890000000000000E-13 " " relative error = 4.328089754475379400000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7559999999999185 " " y[1] (analytic) = 3.0971071999998703 " " y[1] (numeric) = 3.0971072000000044 " " absolute error = 1.3411494137471890000000000000E-13 " " relative error = 4.3303293271451676000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.754999999999918 " " y[1] (analytic) = 3.095504999999869 " " y[1] (numeric) = 3.0955050000000046 " " absolute error = 1.3544720900426910000000000000E-13 " " relative error = 4.3756094402779133000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.753999999999918 " " y[1] (analytic) = 3.0939031999998687 " " y[1] (numeric) = 3.0939032000000046 " " absolute error = 1.35891298214119160000000000000E-13 " " relative error = 4.392228503274599000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7529999999999175 " " y[1] (analytic) = 3.092301799999868 " " y[1] (numeric) = 3.092301800000005 " " absolute error = 1.36779476633819290000000000000E-13 " " relative error = 4.4232253344038125000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.751999999999917 " " y[1] (analytic) = 3.0907007999998672 " " y[1] (numeric) = 3.090700800000005 " " absolute error = 1.3766765505351940000000000000E-13 " " relative error = 4.454253710146428000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.750999999999917 " " y[1] (analytic) = 3.0891001999998666 " " y[1] (numeric) = 3.0891002000000047 " " absolute error = 1.38111744263369470000000000000E-13 " " relative error = 4.470937662150792400000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7499999999999165 " " y[1] (analytic) = 3.0874999999998662 " " y[1] (numeric) = 3.087500000000005 " " absolute error = 1.38555833473219540000000000000E-13 " " relative error = 4.487638331116617000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.748999999999916 " " y[1] (analytic) = 3.085900199999866 " " y[1] (numeric) = 3.0859002000000046 " " absolute error = 1.38555833473219540000000000000E-13 " " relative error = 4.489964823659091000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.747999999999916 " " y[1] (analytic) = 3.084300799999866 " " y[1] (numeric) = 3.0843008000000047 " " absolute error = 1.38555833473219540000000000000E-13 " " relative error = 4.492293147063527400000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7469999999999155 " " y[1] (analytic) = 3.0827017999998656 " " y[1] (numeric) = 3.0827018000000046 " " absolute error = 1.3899992268306960000000000000E-13 " " relative error = 4.509029147194051000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.745999999999915 " " y[1] (analytic) = 3.0811031999998653 " " y[1] (numeric) = 3.0811032000000047 " " absolute error = 1.39444011892919660000000000000E-13 " " relative error = 4.5257819307359054000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.744999999999915 " " y[1] (analytic) = 3.079504999999864 " " y[1] (numeric) = 3.0795050000000046 " " absolute error = 1.40776279522469850000000000000E-13 " " relative error = 4.571393114233491000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7439999999999145 " " y[1] (analytic) = 3.077907199999864 " " y[1] (numeric) = 3.0779072000000047 " " absolute error = 1.40776279522469850000000000000E-13 " " relative error = 4.573766211095515000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.742999999999914 " " y[1] (analytic) = 3.076309799999863 " " y[1] (numeric) = 3.0763098000000046 " " absolute error = 1.41664457942169970000000000000E-13 " " relative error = 4.605012731233255000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.741999999999914 " " y[1] (analytic) = 3.0747127999998627 " " y[1] (numeric) = 3.074712800000005 " " absolute error = 1.42108547152020040000000000000E-13 " " relative error = 4.6218478406186875000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7409999999999135 " " y[1] (analytic) = 3.0731161999998617 " " y[1] (numeric) = 3.0731162000000047 " " absolute error = 1.42996725571720160000000000000E-13 " " relative error = 4.65315062189079000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.739999999999913 " " y[1] (analytic) = 3.071519999999861 " " y[1] (numeric) = 3.071520000000005 " " absolute error = 1.4388490399142030000000000000E-13 " " relative error = 4.684485335971336000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.738999999999913 " " y[1] (analytic) = 3.0699241999998614 " " y[1] (numeric) = 3.069924200000005 " " absolute error = 1.43440814781570230000000000000E-13 " " relative error = 4.672454609191220600000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7379999999999125 " " y[1] (analytic) = 3.068328799999861 " " y[1] (numeric) = 3.068328800000005 " " absolute error = 1.4388490399142030000000000000E-13 " " relative error = 4.689357411481676600000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.736999999999912 " " y[1] (analytic) = 3.0667337999998603 " " y[1] (numeric) = 3.066733800000005 " " absolute error = 1.44773082411120400000000000000E-13 " " relative error = 4.720758039420539000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.735999999999912 " " y[1] (analytic) = 3.0651391999998596 " " y[1] (numeric) = 3.0651392000000053 " " absolute error = 1.45661260830820540000000000000E-13 " " relative error = 4.752190726960368000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7349999999999115 " " y[1] (analytic) = 3.0635449999998587 " " y[1] (numeric) = 3.0635450000000053 " " absolute error = 1.46549439250520660000000000000E-13 " " relative error = 4.7836555118507296000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.733999999999911 " " y[1] (analytic) = 3.0619511999998585 " " y[1] (numeric) = 3.0619512000000055 " " absolute error = 1.46993528460370730000000000000E-13 " " relative error = 4.80064896071425050000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.732999999999910 " " y[1] (analytic) = 3.060357799999858 " " y[1] (numeric) = 3.0603578000000056 " " absolute error = 1.4743761767022080000000000000E-13 " " relative error = 4.817659479889169000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7319999999999105 " " y[1] (analytic) = 3.0587647999998575 " " y[1] (numeric) = 3.0587648000000054 " " absolute error = 1.47881706880070850000000000000E-13 " " relative error = 4.834687089379273000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.73099999999991 " " y[1] (analytic) = 3.057172199999857 " " y[1] (numeric) = 3.0571722000000054 " " absolute error = 1.48325796089920900000000000000E-13 " " relative error = 4.85173180921663000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.72999999999991 " " y[1] (analytic) = 3.055579999999856 " " y[1] (numeric) = 3.0555800000000053 " " absolute error = 1.49213974509621040000000000000E-13 " " relative error = 4.883327371877943500000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7289999999999095 " " y[1] (analytic) = 3.053988199999856 " " y[1] (numeric) = 3.0539882000000054 " " absolute error = 1.49213974509621040000000000000E-13 " " relative error = 4.885872660203077000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.727999999999910 " " y[1] (analytic) = 3.0523967999998556 " " y[1] (numeric) = 3.0523968000000052 " " absolute error = 1.4965806371947110000000000000E-13 " " relative error = 4.902968831558144300000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.726999999999909 " " y[1] (analytic) = 3.0508057999998552 " " y[1] (numeric) = 3.0508058000000053 " " absolute error = 1.50102152929321160000000000000E-13 " " relative error = 4.920082193672514000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7259999999999085 " " y[1] (analytic) = 3.049215199999855 " " y[1] (numeric) = 3.0492152000000052 " " absolute error = 1.50102152929321160000000000000E-13 " " relative error = 4.922648717261028400000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.724999999999908 " " y[1] (analytic) = 3.047624999999854 " " y[1] (numeric) = 3.0476250000000054 " " absolute error = 1.51434420558871350000000000000E-13 " " relative error = 4.968932219642463000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.723999999999908 " " y[1] (analytic) = 3.0460351999998543 " " y[1] (numeric) = 3.0460352000000053 " " absolute error = 1.5099033134902130000000000000E-13 " " relative error = 4.956946372419745000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7229999999999075 " " y[1] (analytic) = 3.0444457999998527 " " y[1] (numeric) = 3.0444458000000054 " " absolute error = 1.52766688188421540000000000000E-13 " " relative error = 5.01788168435874000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.721999999999907 " " y[1] (analytic) = 3.0428567999998526 " " y[1] (numeric) = 3.0428568000000054 " " absolute error = 1.52766688188421540000000000000E-13 " " relative error = 5.020502055450948000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.720999999999907 " " y[1] (analytic) = 3.041268199999852 " " y[1] (numeric) = 3.0412682000000055 " " absolute error = 1.53654866608121670000000000000E-13 " " relative error = 5.052328716294379000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7199999999999065 " " y[1] (analytic) = 3.0396799999998514 " " y[1] (numeric) = 3.0396800000000055 " " absolute error = 1.54098955817971730000000000000E-13 " " relative error = 5.069578239090275000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.718999999999906 " " y[1] (analytic) = 3.038092199999851 " " y[1] (numeric) = 3.0380922000000057 " " absolute error = 1.5454304502782180000000000000E-13 " " relative error = 5.086845126946093000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.717999999999906 " " y[1] (analytic) = 3.036504799999851 " " y[1] (numeric) = 3.0365048000000057 " " absolute error = 1.5454304502782180000000000000E-13 " " relative error = 5.0895043876706330000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7169999999999055 " " y[1] (analytic) = 3.0349177999998505 " " y[1] (numeric) = 3.034917800000006 " " absolute error = 1.55431223447521920000000000000E-13 " " relative error = 5.12143107953466100000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.715999999999905 " " y[1] (analytic) = 3.03333119999985 " " y[1] (numeric) = 3.033331200000006 " " absolute error = 1.55875312657371980000000000000E-13 " " relative error = 5.138750185188472000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.714999999999905 " " y[1] (analytic) = 3.0317449999998494 " " y[1] (numeric) = 3.031745000000006 " " absolute error = 1.5676349107707210000000000000E-13 " " relative error = 5.170734711431202000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7139999999999045 " " y[1] (analytic) = 3.0301591999998494 " " y[1] (numeric) = 3.030159200000006 " " absolute error = 1.5676349107707210000000000000E-13 " " relative error = 5.1734407577357610000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.712999999999904 " " y[1] (analytic) = 3.0285737999998483 " " y[1] (numeric) = 3.028573800000006 " " absolute error = 1.57651669496772230000000000000E-13 " " relative error = 5.205475577209977000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.711999999999904 " " y[1] (analytic) = 3.026988799999848 " " y[1] (numeric) = 3.026988800000006 " " absolute error = 1.5809575870662230000000000000E-13 " " relative error = 5.22287227183101000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7109999999999035 " " y[1] (analytic) = 3.025404199999847 " " y[1] (numeric) = 3.025404200000006 " " absolute error = 1.58983937126322420000000000000E-13 " " relative error = 5.254965175441035000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.709999999999903 " " y[1] (analytic) = 3.023819999999847 " " y[1] (numeric) = 3.023820000000006 " " absolute error = 1.58983937126322420000000000000E-13 " " relative error = 5.257718287673554000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.708999999999903 " " y[1] (analytic) = 3.0222361999998464 " " y[1] (numeric) = 3.022236200000006 " " absolute error = 1.59428026336172480000000000000E-13 " " relative error = 5.275167650237946000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7079999999999025 " " y[1] (analytic) = 3.020652799999846 " " y[1] (numeric) = 3.020652800000006 " " absolute error = 1.59872115546022540000000000000E-13 " " relative error = 5.292634610175346000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.706999999999902 " " y[1] (analytic) = 3.019069799999846 " " y[1] (numeric) = 3.019069800000006 " " absolute error = 1.59872115546022540000000000000E-13 " " relative error = 5.2954097167952430000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.705999999999902 " " y[1] (analytic) = 3.017487199999845 " " y[1] (numeric) = 3.017487200000006 " " absolute error = 1.60760293965722670000000000000E-13 " " relative error = 5.3276214051788160000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7049999999999015 " " y[1] (analytic) = 3.015904999999844 " " y[1] (numeric) = 3.015905000000006 " " absolute error = 1.6164847238542280000000000000E-13 " " relative error = 5.359866188936029000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.703999999999901 " " y[1] (analytic) = 3.014323199999844 " " y[1] (numeric) = 3.014323200000006 " " absolute error = 1.62092561595272850000000000000E-13 " " relative error = 5.377411473171864000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.702999999999900 " " y[1] (analytic) = 3.0127417999998434 " " y[1] (numeric) = 3.012741800000006 " " absolute error = 1.62536650805122920000000000000E-13 " " relative error = 5.39497446495851000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7019999999999005 " " y[1] (analytic) = 3.0111607999998427 " " y[1] (numeric) = 3.011160800000006 " " absolute error = 1.63424829224823040000000000000E-13 " " relative error = 5.42730329196738900000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7009999999999 " " y[1] (analytic) = 3.009580199999842 " " y[1] (numeric) = 3.009580200000006 " " absolute error = 1.6386891843467310000000000000E-13 " " relative error = 5.444909507135969000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.6999999999999 " " y[1] (analytic) = 3.007999999999842 " " y[1] (numeric) = 3.0080000000000062 " " absolute error = 1.64313007644523170000000000000E-13 " " relative error = 5.462533498820871000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = (0.1 * x + 0.2) + (0.3 * x + 0.1) ;" Iterations = 300 "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 37 Minutes 13 Seconds "Optimized Time Remaining "= 0 Years 0 Days 1 Hours 36 Minutes 25 Seconds "Expected Total Time "= 0 Years 0 Days 1 Hours 39 Minutes 26 Seconds "Time to Timeout " Unknown Percent Done = 3.010000000001005 "%" (%o54) true (%o54) diffeq.max