(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/local/share/maxima/5.26.0/share/contrib/stringproc/stringproc.mac (%i3) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if iter >= 0 then (ind_var : array_x , omniout_float(ALWAYS, 1 "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) relerr if relerr # 0.0 then glob_good_digits : - floor(log10(------)) 100.0 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, " "))) (%o3) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if iter >= 0 then (ind_var : array_x , omniout_float(ALWAYS, 1 "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) relerr if relerr # 0.0 then glob_good_digits : - floor(log10(------)) 100.0 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, " "))) (%i4) 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 (%o4) 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 (%i5) 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)), 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, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o5) 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)), 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, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i6) 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], 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) 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 omniout_str(ALWAYS, "Complex estimate of poles used")), if (not found) and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float) 1, 1 1, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 1, 1 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 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 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 glob_display_flag 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 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 omniout_str(ALWAYS, "Complex estimate of poles used")), if not found then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 array_type_pole : 3, if glob_display_flag 1 then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, 1 array_pole : glob_large_float, if array_pole > array_poles 2 1 1, 1 then (array_pole : array_poles , array_pole : array_poles ), 1 1, 1 2 1, 2 display_pole()) (%o6) 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], 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) 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 omniout_str(ALWAYS, "Complex estimate of poles used")), if (not found) and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float) 1, 1 1, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 1, 1 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 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 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 glob_display_flag 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 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 omniout_str(ALWAYS, "Complex estimate of poles used")), if not found then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 array_type_pole : 3, if glob_display_flag 1 then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, 1 array_pole : glob_large_float, if array_pole > array_poles 2 1 1, 1 then (array_pole : array_poles , array_pole : array_poles ), 1 1, 1 2 1, 2 display_pole()) (%i7) 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 (%o7) 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 (%i8) atomall() := block([kkk, order_d, adj2, temporary, term, temp, temp2], array_tmp1 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , omniout_str(ALWAYS, "WARNING: ar\ 1 1 1 ccos of linear function has low precision in testing."), array_tmp3 : arccos(array_tmp2 ), array_tmp3_a1 : sin(array_tmp3 ), 1 1 1 1 array_tmp4 : array_tmp3 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 - array_tmp2 2 array_tmp3 : --------------, array_tmp3_a1 : array_tmp2 array_tmp3 , 2 array_tmp3_a1 2 1 2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 3 glob_h array_y_higher : temporary)), kkk : 3, 2, 2 att(2, array_tmp3_a1, array_tmp3, 2) array_tmp3 : ------------------------------------, 3 array_tmp3_a1 1 array_tmp3 array_tmp2 1 2 2 array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 , 3 2 3 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary)), kkk : 4, 2, 3 att(3, array_tmp3_a1, array_tmp3, 2) array_tmp3 : ------------------------------------, 4 array_tmp3_a1 1 array_tmp3 array_tmp2 2 3 2 array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 , 4 3 4 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary)), kkk : 5, 2, 4 att(4, array_tmp3_a1, array_tmp3, 2) array_tmp3 : ------------------------------------, 5 array_tmp3_a1 1 array_tmp3 array_tmp2 3 4 2 array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 , 5 4 5 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp3 : kkk att(kkk - 1, array_tmp3_a1, array_tmp3, 2) ------------------------------------------, array_tmp3_a1 1 array_tmp3 array_tmp2 (kkk - 2) kkk - 1 2 array_tmp3_a1 : --------------------------------------- kkk kkk - 1 + array_tmp3 array_tmp2 , array_tmp4 : array_tmp3 , order_d : 1, kkk 1 kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp4 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) temporary convfp(adj2) and (term >= 1) do (temporary : ----------------------, glob_h array_y_higher : temporary, adj2 : 1 + adj2, term : term - 1))), adj2, term kkk : 1 + kkk)) (%o8) atomall() := block([kkk, order_d, adj2, temporary, term, temp, temp2], array_tmp1 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , omniout_str(ALWAYS, "WARNING: ar\ 1 1 1 ccos of linear function has low precision in testing."), array_tmp3 : arccos(array_tmp2 ), array_tmp3_a1 : sin(array_tmp3 ), 1 1 1 1 array_tmp4 : array_tmp3 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 - array_tmp2 2 array_tmp3 : --------------, array_tmp3_a1 : array_tmp2 array_tmp3 , 2 array_tmp3_a1 2 1 2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 3 glob_h array_y_higher : temporary)), kkk : 3, 2, 2 att(2, array_tmp3_a1, array_tmp3, 2) array_tmp3 : ------------------------------------, 3 array_tmp3_a1 1 array_tmp3 array_tmp2 1 2 2 array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 , 3 2 3 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary)), kkk : 4, 2, 3 att(3, array_tmp3_a1, array_tmp3, 2) array_tmp3 : ------------------------------------, 4 array_tmp3_a1 1 array_tmp3 array_tmp2 2 3 2 array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 , 4 3 4 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary)), kkk : 5, 2, 4 att(4, array_tmp3_a1, array_tmp3, 2) array_tmp3 : ------------------------------------, 5 array_tmp3_a1 1 array_tmp3 array_tmp2 3 4 2 array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 , 5 4 5 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp3 : kkk att(kkk - 1, array_tmp3_a1, array_tmp3, 2) ------------------------------------------, array_tmp3_a1 1 array_tmp3 array_tmp2 (kkk - 2) kkk - 1 2 array_tmp3_a1 : --------------------------------------- kkk kkk - 1 + array_tmp3 array_tmp2 , array_tmp4 : array_tmp3 , order_d : 1, kkk 1 kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp4 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) temporary convfp(adj2) and (term >= 1) do (temporary : ----------------------, glob_h array_y_higher : temporary, adj2 : 1 + adj2, term : term - 1))), adj2, term kkk : 1 + kkk)) log(x) (%i9) log10(x) := --------- log(10.0) log(x) (%o9) log10(x) := --------- log(10.0) (%i10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i11) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o11) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i12) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o12) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i13) 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)) (%o13) 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)) (%i14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i16) dump_series(iolevel, dump_label, series_name, array_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 (%o16) dump_series(iolevel, dump_label, series_name, array_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 (%i17) dump_series_2(iolevel, dump_label, series_name, 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 (%o17) dump_series_2(iolevel, dump_label, series_name, 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 (%i18) 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)) (%o18) 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)) (%i19) logitem_time(fd, secs_in) := block([cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int], secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_minute min_in_hour hours_in_day days_in_year years_in_century secs centuries_in_millinium, milliniums : ----------------, sec_in_millinium millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) centuries_in_millinium, cent_int : floor(centuries), years : (centuries - cent_int) years_in_century, years_int : floor(years), days : (years - years_int) days_in_year, days_int : floor(days), hours : (days - days_int) hours_in_day, hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour, minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_minute, sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\ Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(fd, "~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif 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, "")) (%o19) logitem_time(fd, secs_in) := block([cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int], secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_minute min_in_hour hours_in_day days_in_year years_in_century secs centuries_in_millinium, milliniums : ----------------, sec_in_millinium millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) centuries_in_millinium, cent_int : floor(centuries), years : (centuries - cent_int) years_in_century, years_int : floor(years), days : (years - years_int) days_in_year, days_int : floor(days), hours : (days - days_int) hours_in_day, hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour, minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_minute, sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\ Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(fd, "~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif 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, "")) (%i20) omniout_timestr(secs_in) := block([cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_minute) convfloat(min_in_hour) convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century) secs convfloat(centuries_in_millinium), milliniums : ---------------------------, convfloat(sec_in_millinium) millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) convfloat(centuries_in_millinium), cent_int : floor(centuries), years : (centuries - cent_int) convfloat(years_in_century), years_int : floor(years), days : (years - years_int) convfloat(days_in_year), days_int : floor(days), hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours), minutes : (hours - hours_int) convfloat(min_in_hour), minutes_int : floor(minutes), seconds : (minutes - minutes_int) convfloat(sec_in_minute), sec_int : floor(seconds), if millinium_int > 0 then printf(true, "= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(true, "= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif 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~%")) (%o20) omniout_timestr(secs_in) := block([cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_minute) convfloat(min_in_hour) convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century) secs convfloat(centuries_in_millinium), milliniums : ---------------------------, convfloat(sec_in_millinium) millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) convfloat(centuries_in_millinium), cent_int : floor(centuries), years : (centuries - cent_int) convfloat(years_in_century), years_int : floor(years), days : (years - years_int) convfloat(days_in_year), days_int : floor(days), hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours), minutes : (hours - hours_int) convfloat(min_in_hour), minutes_int : floor(minutes), seconds : (minutes - minutes_int) convfloat(sec_in_minute), sec_int : floor(seconds), if millinium_int > 0 then printf(true, "= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(true, "= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif 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~%")) (%i21) ats(mmm_ats, array_a, array_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 : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o21) ats(mmm_ats, array_a, array_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 : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i22) att(mmm_att, array_aa, array_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 : array_aa array_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o22) att(mmm_att, array_aa, array_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 : array_aa array_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i23) 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 (%o23) 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 (%i24) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o24) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i25) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o25) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i26) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o26) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i27) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error # 0.0 rel_error then (good_digits : - floor(log10(---------)), 100.0 printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o27) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error # 0.0 rel_error then (good_digits : - floor(log10(---------)), 100.0 printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i28) log_revs(file, revs) := printf(file, revs) (%o28) log_revs(file, revs) := printf(file, revs) (%i29) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o29) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i30) 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, "")) (%o30) 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, "")) (%i31) logstart(file) := printf(file, "") (%o31) logstart(file) := printf(file, "") (%i32) logend(file) := printf(file, "~%") (%o32) logend(file) := printf(file, "~%") (%i33) 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()) (%o33) 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()) (%i34) 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 (%o34) 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 (%i35) 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 (%o35) 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 (%i36) factorial_2(nnn) := block([ret], ret : nnn!) (%o36) factorial_2(nnn) := block([ret], ret : nnn!) (%i37) 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 (%o37) 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 (%i38) 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) (%o38) 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) (%i39) convfp(mmm) := mmm (%o39) convfp(mmm) := mmm (%i40) convfloat(mmm) := mmm (%o40) convfloat(mmm) := mmm (%i41) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o41) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i42) arcsin(x) := asin(x) (%o42) arcsin(x) := asin(x) (%i43) arccos(x) := acos(x) (%o43) arccos(x) := acos(x) (%i44) arctan(x) := atan(x) (%o44) arctan(x) := atan(x) (%i45) omniabs(x) := abs(x) (%o45) omniabs(x) := abs(x) y (%i46) expt(x, y) := x y (%o46) expt(x, y) := x (%i47) exact_soln_y(x) := 10.0 (0.2 + 0.1 x) arccos(0.2 + 0.1 x) - 10.0 sqrt(1.0 - expt(0.2 + 0.1 x, 2)) (%o47) exact_soln_y(x) := 10.0 (0.2 + 0.1 x) arccos(0.2 + 0.1 x) - 10.0 sqrt(1.0 - expt(0.2 + 0.1 x, 2)) (%i48) 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], define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_hmin_init, 0.001, float), define_variable(djd_debug2, true, boolean), define_variable(glob_percent_done, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_iter, 0, fixnum), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_dump, false, boolean), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(min_in_hour, 60, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_almost_1, 0.999, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_optimal_done, false, boolean), define_variable(glob_clock_sec, 0.0, float), define_variable(years_in_century, 100, fixnum), define_variable(glob_start, 0, fixnum), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(hours_in_day, 24, fixnum), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_h, 0.1, float), define_variable(days_in_year, 365, fixnum), define_variable(djd_debug, true, boolean), define_variable(glob_html_log, true, boolean), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_warned, false, boolean), define_variable(centuries_in_millinium, 10, fixnum), define_variable(sec_in_minute, 60, fixnum), 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/lin_arccospostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : -0.8,"), omniout_str(ALWAYS, "x_end : 0.8 ,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100,"), omniout_str(ALWAYS, "glob_max_minutes : 1,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := ("), omniout_str(ALWAYS, " (10.0 * (\ 0.1 * x + 0.2) * arccos(0.1 * x + 0.2 ) - 10.0 * sqrt(1.0 -"), omniout_str(ALWAYS, "expt((0.1 * x + 0.2) , 2 ))) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, max_terms : 30, Digits : 32, glob_max_terms : max_terms, glob_html_log : true, array(array_1st_rel_error, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y_init, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_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_a1, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_fact_2, 1 + max_terms, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_real_pole, 1 + 1, 1 + 3), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3), array(array_y_higher_work2, 1 + 2, 1 + max_terms), term : 1, while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_fact_1 : 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_init : 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_pole : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp0 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3_a1 : 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_norms : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 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), 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 <= 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 <= 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_complex_pole : 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_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term term : 1 + 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_tmp3_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a1 : 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_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 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_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term 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_const_0D2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, 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_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_1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, 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 : - 0.8, x_end : 0.8, array_y_init : exact_soln_y(x_start), 1 + 0 glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 100, glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 100, glob_max_minutes : 1, 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), chk_data(), array_y_set_initial : true, array_y_set_initial : false, 1, 1 1, 2 array_y_set_initial : false, array_y_set_initial : false, 1, 3 1, 4 array_y_set_initial : false, array_y_set_initial : false, 1, 5 1, 6 array_y_set_initial : false, array_y_set_initial : false, 1, 7 1, 8 array_y_set_initial : false, array_y_set_initial : false, 1, 9 1, 10 array_y_set_initial : false, array_y_set_initial : false, 1, 11 1, 12 array_y_set_initial : false, array_y_set_initial : false, 1, 13 1, 14 array_y_set_initial : false, array_y_set_initial : false, 1, 15 1, 16 array_y_set_initial : false, array_y_set_initial : false, 1, 17 1, 18 array_y_set_initial : false, array_y_set_initial : false, 1, 19 1, 20 array_y_set_initial : false, array_y_set_initial : false, 1, 21 1, 22 array_y_set_initial : false, array_y_set_initial : false, 1, 23 1, 24 array_y_set_initial : false, array_y_set_initial : false, 1, 25 1, 26 array_y_set_initial : false, array_y_set_initial : false, 1, 27 1, 28 array_y_set_initial : false, array_y_set_initial : false, 1, 29 1, 30 if glob_html_log then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, order_diff : 1, term_no : 1, 2 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), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), 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 (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < 1 convfloat(glob_max_sec)) do (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(), 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 ) = arccos(0.1 * x + 0.2) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-09-02T21:40:38-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "lin_arccos"), logitem_str(html_log_file, "diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), 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_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 126 "), logitem_str(html_log_file, "lin_arccos diffeq.max"), logitem_str(html_log_file, "lin_arccos maxima results"), logitem_str(html_log_file, "c c++ Maple and Maxima"), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%o48) 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], define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_hmin_init, 0.001, float), define_variable(djd_debug2, true, boolean), define_variable(glob_percent_done, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_iter, 0, fixnum), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_dump, false, boolean), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(min_in_hour, 60, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_almost_1, 0.999, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_optimal_done, false, boolean), define_variable(glob_clock_sec, 0.0, float), define_variable(years_in_century, 100, fixnum), define_variable(glob_start, 0, fixnum), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(hours_in_day, 24, fixnum), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_h, 0.1, float), define_variable(days_in_year, 365, fixnum), define_variable(djd_debug, true, boolean), define_variable(glob_html_log, true, boolean), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_warned, false, boolean), define_variable(centuries_in_millinium, 10, fixnum), define_variable(sec_in_minute, 60, fixnum), 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/lin_arccospostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : -0.8,"), omniout_str(ALWAYS, "x_end : 0.8 ,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100,"), omniout_str(ALWAYS, "glob_max_minutes : 1,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := ("), omniout_str(ALWAYS, " (10.0 * (\ 0.1 * x + 0.2) * arccos(0.1 * x + 0.2 ) - 10.0 * sqrt(1.0 -"), omniout_str(ALWAYS, "expt((0.1 * x + 0.2) , 2 ))) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, max_terms : 30, Digits : 32, glob_max_terms : max_terms, glob_html_log : true, array(array_1st_rel_error, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y_init, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_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_a1, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_fact_2, 1 + max_terms, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_real_pole, 1 + 1, 1 + 3), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3), array(array_y_higher_work2, 1 + 2, 1 + max_terms), term : 1, while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_fact_1 : 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_init : 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_pole : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp0 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3_a1 : 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_norms : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 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), 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 <= 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 <= 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_complex_pole : 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_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term term : 1 + 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_tmp3_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a1 : 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_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 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_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term 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_const_0D2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, 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_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_1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, 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 : - 0.8, x_end : 0.8, array_y_init : exact_soln_y(x_start), 1 + 0 glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 100, glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 100, glob_max_minutes : 1, 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), chk_data(), array_y_set_initial : true, array_y_set_initial : false, 1, 1 1, 2 array_y_set_initial : false, array_y_set_initial : false, 1, 3 1, 4 array_y_set_initial : false, array_y_set_initial : false, 1, 5 1, 6 array_y_set_initial : false, array_y_set_initial : false, 1, 7 1, 8 array_y_set_initial : false, array_y_set_initial : false, 1, 9 1, 10 array_y_set_initial : false, array_y_set_initial : false, 1, 11 1, 12 array_y_set_initial : false, array_y_set_initial : false, 1, 13 1, 14 array_y_set_initial : false, array_y_set_initial : false, 1, 15 1, 16 array_y_set_initial : false, array_y_set_initial : false, 1, 17 1, 18 array_y_set_initial : false, array_y_set_initial : false, 1, 19 1, 20 array_y_set_initial : false, array_y_set_initial : false, 1, 21 1, 22 array_y_set_initial : false, array_y_set_initial : false, 1, 23 1, 24 array_y_set_initial : false, array_y_set_initial : false, 1, 25 1, 26 array_y_set_initial : false, array_y_set_initial : false, 1, 27 1, 28 array_y_set_initial : false, array_y_set_initial : false, 1, 29 1, 30 if glob_html_log then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, order_diff : 1, term_no : 1, 2 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), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), 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 (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < 1 convfloat(glob_max_sec)) do (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(), 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 ) = arccos(0.1 * x + 0.2) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-09-02T21:40:38-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "lin_arccos"), logitem_str(html_log_file, "diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), 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_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 126 "), logitem_str(html_log_file, "lin_arccos diffeq.max"), logitem_str(html_log_file, "lin_arccos maxima results"), logitem_str(html_log_file, "c c++ Maple and Maxima"), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%i49) main() "##############ECHO OF PROBLEM#################" "##############temp/lin_arccospostode.ode#################" "diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "max_terms : 30," "Digits : 32," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start : -0.8," "x_end : 0.8 ," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_h : 0.00001 ," "glob_look_poles : true," "glob_max_iter : 100," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_h : 0.00001 ," "glob_look_poles : true," "glob_max_iter : 100," "glob_max_minutes : 1," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (" " (10.0 * (0.1 * x + 0.2) * arccos(0.1 * x + 0.2 ) - 10.0 * sqrt(1.0 -" "expt((0.1 * x + 0.2) , 2 ))) " ");" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" x[1] = -0.8 " " y[1] (analytic) = -8.187131183512555 " " y[1] (numeric) = -8.187131183512555 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.89091590562615 " " Order of pole = 0.3248634603939333 " " x[1] = -0.7999900000000001 " " y[1] (analytic) = -8.187116678453148 " " y[1] (numeric) = -8.187116678453148 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890914654055923 " " Order of pole = 0.3248633438279338 " " x[1] = -0.7999800000000001 " " y[1] (analytic) = -8.187102173403813 " " y[1] (numeric) = -8.187102173403813 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890913402478 " " Order of pole = 0.32486322726792416 " " x[1] = -0.7999700000000002 " " y[1] (analytic) = -8.187087668364551 " " y[1] (numeric) = -8.187087668364551 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890912150892298 " " Order of pole = 0.3248631107137072 " " x[1] = -0.7999600000000002 " " y[1] (analytic) = -8.187073163335363 " " y[1] (numeric) = -8.187073163335363 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890910899299023 " " Order of pole = 0.324862994165775 " " x[1] = -0.7999500000000003 " " y[1] (analytic) = -8.187058658316245 " " y[1] (numeric) = -8.187058658316246 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.169713096651462200000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890909647698182 " " Order of pole = 0.3248628776241542 " " x[1] = -0.7999400000000003 " " y[1] (analytic) = -8.187044153307202 " " y[1] (numeric) = -8.187044153307202 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890908396089532 " " Order of pole = 0.3248627610882533 " " x[1] = -0.7999300000000004 " " y[1] (analytic) = -8.18702964830823 " " y[1] (numeric) = -8.187029648308231 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.169720784835947600000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890907144473339 " " Order of pole = 0.3248626445587064 " " x[1] = -0.7999200000000004 " " y[1] (analytic) = -8.187015143319332 " " y[1] (numeric) = -8.187015143319332 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890905892849402 " " Order of pole = 0.3248625280350481 " " x[1] = -0.7999100000000005 " " y[1] (analytic) = -8.187000638340507 " " y[1] (numeric) = -8.187000638340507 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890904641217794 " " Order of pole = 0.32486241151742945 " " x[1] = -0.7999000000000005 " " y[1] (analytic) = -8.186986133371756 " " y[1] (numeric) = -8.186986133371754 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.169732317194813500000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.89090338957861 " " Order of pole = 0.32486229500609554 " " x[1] = -0.7998900000000005 " " y[1] (analytic) = -8.186971628413076 " " y[1] (numeric) = -8.186971628413074 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.169736161336339200000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890902137931601 " " Order of pole = 0.32486217850043886 " " x[1] = -0.7998800000000006 " " y[1] (analytic) = -8.186957123464468 " " y[1] (numeric) = -8.186957123464467 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.169740005488817000000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890900886277114 " " Order of pole = 0.3248620620013227 " " x[1] = -0.7998700000000006 " " y[1] (analytic) = -8.186942618525935 " " y[1] (numeric) = -8.186942618525933 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.169743849652246400000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890899634614858 " " Order of pole = 0.32486194550800285 " " x[1] = -0.7998600000000007 " " y[1] (analytic) = -8.186928113597475 " " y[1] (numeric) = -8.186928113597471 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339495387653255500000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.89089838294494 " " Order of pole = 0.32486182902075456 " " x[1] = -0.7998500000000007 " " y[1] (analytic) = -8.186913608679086 " " y[1] (numeric) = -8.186913608679083 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33950307602392300000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890897131267343 " " Order of pole = 0.32486171253954765 " " x[1] = -0.7998400000000008 " " y[1] (analytic) = -8.18689910377077 " " y[1] (numeric) = -8.186899103770767 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339510764416495000000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890895879582098 " " Order of pole = 0.3248615960644443 " " x[1] = -0.7998300000000008 " " y[1] (analytic) = -8.186884598872526 " " y[1] (numeric) = -8.186884598872524 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.169759226415485500000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890894627889237 " " Order of pole = 0.3248614795955298 " " x[1] = -0.7998200000000009 " " y[1] (analytic) = -8.186870093984357 " " y[1] (numeric) = -8.186870093984354 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33952614126735100000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890893376188608 " " Order of pole = 0.32486136313243463 " " x[1] = -0.7998100000000009 " " y[1] (analytic) = -8.186855589106258 " " y[1] (numeric) = -8.186855589106257 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.16976691486281800000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890892124480478 " " Order of pole = 0.3248612466758072 " " x[1] = -0.799800000000001 " " y[1] (analytic) = -8.186841084238235 " " y[1] (numeric) = -8.186841084238232 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339541518205824500000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890890872764517 " " Order of pole = 0.32486113022484275 " " x[1] = -0.799790000000001 " " y[1] (analytic) = -8.186826579380284 " " y[1] (numeric) = -8.18682657938028 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33954920670791800000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890889621040984 " " Order of pole = 0.3248610137801595 " " x[1] = -0.799780000000001 " " y[1] (analytic) = -8.186812074532405 " " y[1] (numeric) = -8.186812074532401 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339556895231916300000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890888369309781 " " Order of pole = 0.32486089734154255 " " x[1] = -0.7997700000000011 " " y[1] (analytic) = -8.1867975696946 " " y[1] (numeric) = -8.186797569694596 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339564583777819600000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890887117570914 " " Order of pole = 0.32486078090899184 " " x[1] = -0.7997600000000011 " " y[1] (analytic) = -8.186783064866866 " " y[1] (numeric) = -8.186783064866862 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33957227234562800000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890885865824297 " " Order of pole = 0.3248606644822978 " " x[1] = -0.7997500000000012 " " y[1] (analytic) = -8.186768560049206 " " y[1] (numeric) = -8.186768560049202 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339579960935341000000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890884614070103 " " Order of pole = 0.32486054806189024 " " x[1] = -0.7997400000000012 " " y[1] (analytic) = -8.186754055241618 " " y[1] (numeric) = -8.186754055241614 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33958764954695900000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890883362308216 " " Order of pole = 0.32486043164748324 " " x[1] = -0.7997300000000013 " " y[1] (analytic) = -8.186739550444104 " " y[1] (numeric) = -8.1867395504441 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33959533818048200000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890882110538696 " " Order of pole = 0.3248603152392171 " " x[1] = -0.7997200000000013 " " y[1] (analytic) = -8.186725045656662 " " y[1] (numeric) = -8.186725045656658 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339603026835910400000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890880858761447 " " Order of pole = 0.32486019883686446 " " x[1] = -0.7997100000000014 " " y[1] (analytic) = -8.186710540879293 " " y[1] (numeric) = -8.18671054087929 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33961071551324400000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890879606976617 " " Order of pole = 0.3248600824407859 " " x[1] = -0.7997000000000014 " " y[1] (analytic) = -8.186696036111996 " " y[1] (numeric) = -8.186696036111993 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33961840421248400000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890878355184077 " " Order of pole = 0.32485996605065814 " " x[1] = -0.7996900000000015 " " y[1] (analytic) = -8.186681531354774 " " y[1] (numeric) = -8.18668153135477 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339626092933628300000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.89087710338392 " " Order of pole = 0.32485984966671744 " " x[1] = -0.7996800000000015 " " y[1] (analytic) = -8.186667026607623 " " y[1] (numeric) = -8.18666702660762 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33963378167667900000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.89087585157603 " " Order of pole = 0.3248597332886938 " " x[1] = -0.7996700000000015 " " y[1] (analytic) = -8.186652521870545 " " y[1] (numeric) = -8.186652521870542 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33964147044163500000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890874599760558 " " Order of pole = 0.324859616916914 " " x[1] = -0.7996600000000016 " " y[1] (analytic) = -8.18663801714354 " " y[1] (numeric) = -8.186638017143537 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33964915922849640000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.89087334793734 " " Order of pole = 0.3248595005510193 " " x[1] = -0.7996500000000016 " " y[1] (analytic) = -8.186623512426609 " " y[1] (numeric) = -8.186623512426605 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339656848037263000000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890872096106511 " " Order of pole = 0.32485938419131877 " " x[1] = -0.7996400000000017 " " y[1] (analytic) = -8.186609007719749 " " y[1] (numeric) = -8.186609007719746 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33966453686793700000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890870844268036 " " Order of pole = 0.32485926783773245 " " x[1] = -0.7996300000000017 " " y[1] (analytic) = -8.186594503022963 " " y[1] (numeric) = -8.18659450302296 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339672225720516000000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890869592421845 " " Order of pole = 0.32485915149009337 " " x[1] = -0.7996200000000018 " " y[1] (analytic) = -8.18657999833625 " " y[1] (numeric) = -8.186579998336246 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339679914595002700000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890868340568028 " " Order of pole = 0.3248590351486147 " " x[1] = -0.7996100000000018 " " y[1] (analytic) = -8.186565493659609 " " y[1] (numeric) = -8.186565493659606 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33968760349139400000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890867088706525 " " Order of pole = 0.324858918813149 " " x[1] = -0.7996000000000019 " " y[1] (analytic) = -8.18655098899304 " " y[1] (numeric) = -8.186550988993037 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339695292409692000000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890865836837373 " " Order of pole = 0.32485880248378507 " " x[1] = -0.7995900000000019 " " y[1] (analytic) = -8.186536484336546 " " y[1] (numeric) = -8.186536484336543 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339702981349896600000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890864584960626 " " Order of pole = 0.32485868616067926 " " x[1] = -0.799580000000002 " " y[1] (analytic) = -8.186521979690124 " " y[1] (numeric) = -8.18652197969012 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339710670312007500000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890863333076158 " " Order of pole = 0.32485856984348516 " " x[1] = -0.799570000000002 " " y[1] (analytic) = -8.186507475053773 " " y[1] (numeric) = -8.186507475053771 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.169859179648012700000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890862081183986 " " Order of pole = 0.3248584535322685 " " x[1] = -0.799560000000002 " " y[1] (analytic) = -8.186492970427498 " " y[1] (numeric) = -8.186492970427494 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33972604830194900000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890860829284293 " " Order of pole = 0.32485833722746804 " " x[1] = -0.7995500000000021 " " y[1] (analytic) = -8.186478465811293 " " y[1] (numeric) = -8.186478465811291 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.169866868664890300000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890859577376812 " " Order of pole = 0.3248582209284372 " " x[1] = -0.7995400000000021 " " y[1] (analytic) = -8.186463961205162 " " y[1] (numeric) = -8.18646396120516 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.16987071318975900000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890858325461702 " " Order of pole = 0.32485810463556675 " " x[1] = -0.7995300000000022 " " y[1] (analytic) = -8.186449456609104 " " y[1] (numeric) = -8.186449456609102 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.169874557725581200000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.89085707353885 " " Order of pole = 0.32485798834857604 " " x[1] = -0.7995200000000022 " " y[1] (analytic) = -8.18643495202312 " " y[1] (numeric) = -8.186434952023117 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339756804544713000000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.89085582160843 " " Order of pole = 0.32485787206788075 " " x[1] = -0.7995100000000023 " " y[1] (analytic) = -8.186420447447208 " " y[1] (numeric) = -8.186420447447205 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339764493660171500000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890854569670328 " " Order of pole = 0.32485775579321796 " " x[1] = -0.7995000000000023 " " y[1] (analytic) = -8.186405942881368 " " y[1] (numeric) = -8.186405942881365 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33977218279753800000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890853317724602 " " Order of pole = 0.32485763952471736 " " x[1] = -0.7994900000000024 " " y[1] (analytic) = -8.1863914383256 " " y[1] (numeric) = -8.186391438325598 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.169889935978405500000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890852065771243 " " Order of pole = 0.3248575232623683 " " x[1] = -0.7994800000000024 " " y[1] (analytic) = -8.186376933779908 " " y[1] (numeric) = -8.186376933779904 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339787561137990500000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.8908508138101 " " Order of pole = 0.32485740700579413 " " x[1] = -0.7994700000000025 " " y[1] (analytic) = -8.186362429244285 " " y[1] (numeric) = -8.186362429244284 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.169897625170539600000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890849561841344 " " Order of pole = 0.3248572907554159 " " x[1] = -0.7994600000000025 " " y[1] (analytic) = -8.186347924718739 " " y[1] (numeric) = -8.186347924718735 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33980293956607400000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.89084830986498 " " Order of pole = 0.3248571745112425 " " x[1] = -0.7994500000000025 " " y[1] (analytic) = -8.186333420203262 " " y[1] (numeric) = -8.18633342020326 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.169905314406489000000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.89084705788087 " " Order of pole = 0.3248570582729364 " " x[1] = -0.7994400000000026 " " y[1] (analytic) = -8.18631891569786 " " y[1] (numeric) = -8.186318915697857 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33981831808178730000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890845805889102 " " Order of pole = 0.3248569420407108 " " x[1] = -0.7994300000000026 " " y[1] (analytic) = -8.186304411202531 " " y[1] (numeric) = -8.186304411202528 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339826007372505300000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890844553889819 " " Order of pole = 0.32485682581493336 " " x[1] = -0.7994200000000027 " " y[1] (analytic) = -8.186289906717274 " " y[1] (numeric) = -8.18628990671727 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33983369668513200000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890843301882763 " " Order of pole = 0.3248567095949557 " " x[1] = -0.7994100000000027 " " y[1] (analytic) = -8.18627540224209 " " y[1] (numeric) = -8.186275402242087 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.339841386019665500000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890842049868036 " " Order of pole = 0.324856593381023 " " x[1] = -0.7994000000000028 " " y[1] (analytic) = -8.186260897776979 " " y[1] (numeric) = -8.186260897776975 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33984907537610800000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890840797845762 " " Order of pole = 0.3248564771734479 " " x[1] = -0.7993900000000028 " " y[1] (analytic) = -8.186246393321941 " " y[1] (numeric) = -8.186246393321937 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.33985676475445800000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.8908395458157 " " Order of pole = 0.3248563609716495 " " x[1] = -0.7993800000000029 " " y[1] (analytic) = -8.186231888876977 " " y[1] (numeric) = -8.186231888876971 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.50979668123207400000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890838293777994 " " Order of pole = 0.32485624477596176 " " x[1] = -0.7993700000000029 " " y[1] (analytic) = -8.186217384442084 " " y[1] (numeric) = -8.18621738444208 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.50980821536532400000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890837041732642 " " Order of pole = 0.3248561285863918 " " x[1] = -0.799360000000003 " " y[1] (analytic) = -8.186202880017266 " " y[1] (numeric) = -8.186202880017259 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 8.67975966604191400000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890835789679722 " " Order of pole = 0.32485601240312434 " " x[1] = -0.799350000000003 " " y[1] (analytic) = -8.186188375602518 " " y[1] (numeric) = -8.186188375602512 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.50983128373041200000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.89083453761905 " " Order of pole = 0.3248558962257082 " " x[1] = -0.799340000000003 " " y[1] (analytic) = -8.186173871197843 " " y[1] (numeric) = -8.186173871197838 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.5098428179622500000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890833285550709 " " Order of pole = 0.3248557800543601 " " x[1] = -0.7993300000000031 " " y[1] (analytic) = -8.186159366803244 " " y[1] (numeric) = -8.186159366803237 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 8.67980580296926800000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890832033474775 " " Order of pole = 0.3248556638892435 " " x[1] = -0.7993200000000031 " " y[1] (analytic) = -8.186144862418717 " " y[1] (numeric) = -8.18614486241871 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 8.67982118203268500000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890830781391164 " " Order of pole = 0.32485554773017356 " " x[1] = -0.7993100000000032 " " y[1] (analytic) = -8.18613035804426 " " y[1] (numeric) = -8.186130358044254 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.50987742085494300000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890829529299754 " " Order of pole = 0.32485543157684305 " " x[1] = -0.7993000000000032 " " y[1] (analytic) = -8.186115853679878 " " y[1] (numeric) = -8.186115853679873 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.50988895521823300000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890828277200876 " " Order of pole = 0.32485531543005486 " " x[1] = -0.7992900000000033 " " y[1] (analytic) = -8.186101349325568 " " y[1] (numeric) = -8.186101349325563 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.50990048961438700000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "WARNING: arccos of linear function has low precision in testing." "Complex estimate of poles used" Radius of convergence = 9.890827025094325 " " Order of pole = 0.3248551992893205 " " x[1] = -0.7992800000000033 " " y[1] (analytic) = -8.186086844981332 " " y[1] (numeric) = -8.186086844981327 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.50991202404340500000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;" Iterations = 72 "Total Elapsed Time "= 1 Minutes 1 Seconds "Elapsed Time(since restart) "= 1 Minutes 0 Seconds "Expected Time Remaining "= 1 Days 13 Hours 14 Minutes 29 Seconds "Optimized Time Remaining "= 1 Days 12 Hours 32 Minutes 29 Seconds "Time to Timeout " Unknown Percent Done = 4.56249999997923600E-2 "%" (%o49) true (%o49) diffeq.max