(%i1) batch("temp/diffeq.sing5_back.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.sing5_back.max
(%i2) load("stringproc")
(%i3) keepfloat:true
(%i4) alias(convfloat,float)
(%i5) alias(int_trunc,truncate)
(%i6) alias(elapsed_time_seconds,elapsed_real_time)
(%i7) alias(ln,log)
(%i8) alias(arcsin,asin)
(%i9) alias(arccos,acos)
(%i10) alias(arctan,atan)
(%i11) alias(float_abs,abs)
(%i12) mode_declare(display_poles(),fixnum)
(%i13) mode_declare(est_size_answer(),convfloat)
(%i14) mode_declare(test_suggested_h(),convfloat)
(%i15) mode_declare(reached_interval(),boolean)
(%i16) mode_declare(display_alot([iter],fixnum),fixnum)
(%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum)
(%i18) mode_declare(check_for_pole(),fixnum)
(%i19) mode_declare(atomall(),fixnum)
(%i20) mode_declare(log10([x],convfloat),convfloat)
(%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum)
(%i22) mode_declare(omniout_timestr(secs_in,number),fixnum)
(%i23) mode_declare(zero_ats_ar(ar,array([20],convfloat)),fixnum)
(%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a],
completearray([20],convfloat),[arr_b],
completearray([20],convfloat),[jjj_ats],fixnum),
convfloat)
(%i25) mode_declare(att([mmm_att],fixnum,[arr_a],
completearray([20],convfloat),[arr_b],
completearray([20],convfloat),[jjj_att],fixnum),
convfloat)
(%i26) mode_declare(logitem_ditto([file],fixnum),fixnum)
(%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum)
(%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum)
(%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum)
(%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum)
(%i31) mode_declare(logstart([file],fixnum),fixnum)
(%i32) mode_declare(logend([file],fixnum),fixnum)
(%i33) mode_declare(chk_data(),fixnum)
(%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat,
[t2],convfloat,[clock_sec2],convfloat),
convfloat)
(%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2],
convfloat),convfloat)
(%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i42) mode_declare(neg([nnn],convfloat),convfloat)
(%i43) mode_declare(factorial_2([nnn],fixnum),convfloat)
(%i44) mode_declare(factorial_1([nnn],fixnum),convfloat)
(%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat)
(%i46) mode_declare(convfloat([mmm],fixnum),convfloat)
(%i47) mode_declare(elaped_time_seconds(),convfloat)
(%i48) mode_declare(Si([x],convfloat),convfloat)
(%i49) mode_declare(Ci([x],convfloat),convfloat)
(%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end],
convfloat,[estimated_h],
convfloat,[estimated_answer],
convfloat),convfloat)
(%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat)
(%i52) mode_declare(main_prog(),fixnum)
(%i53) define_variable(always,1,fixnum)
(%i54) define_variable(info,2,fixnum)
(%i55) define_variable(debugl,3,fixnum)
(%i56) define_variable(debugmassive,4,fixnum)
(%i57) define_variable(glob_iolevel,5,fixnum)
(%i58) define_variable(glob_yes_pole,4,fixnum)
(%i59) define_variable(glob_no_pole,3,fixnum)
(%i60) define_variable(glob_not_given,0,fixnum)
(%i61) define_variable(glob_no_sing_tests,4,fixnum)
(%i62) define_variable(glob_ratio_test,1,fixnum)
(%i63) define_variable(glob_three_term_test,2,fixnum)
(%i64) define_variable(glob_six_term_test,3,fixnum)
(%i65) define_variable(ats_max_terms,20,fixnum)
(%i66) define_variable(glob_log_10,0.0,convfloat)
(%i67) define_variable(max_unchanged,10,fixnum)
(%i68) define_variable(glob__small,1.0E-51,convfloat)
(%i69) define_variable(glob_small_float,1.0E-51,convfloat)
(%i70) define_variable(glob_smallish_float,1.0E-61,convfloat)
(%i71) define_variable(glob_large_float,1.0E+100,convfloat)
(%i72) define_variable(glob_larger_float,1.1E+100,convfloat)
(%i73) define_variable(glob__m2,-2.0,convfloat)
(%i74) define_variable(glob__m1,-1.0,convfloat)
(%i75) define_variable(glob__0,0.0,convfloat)
(%i76) define_variable(glob__1,1.0,convfloat)
(%i77) define_variable(glob__2,2.0,convfloat)
(%i78) define_variable(glob__3,3.0,convfloat)
(%i79) define_variable(glob__4,4.0,convfloat)
(%i80) define_variable(glob__5,5.0,convfloat)
(%i81) define_variable(glob__8,8.0,convfloat)
(%i82) define_variable(glob__10,10.0,convfloat)
(%i83) define_variable(glob__100,100.0,convfloat)
(%i84) define_variable(glob__pi,0.0,convfloat)
(%i85) define_variable(glob__0_5,0.5,convfloat)
(%i86) define_variable(glob__0_8,0.8,convfloat)
(%i87) define_variable(glob__m0_8,-0.8,convfloat)
(%i88) define_variable(glob__0_25,0.25,convfloat)
(%i89) define_variable(glob__0_125,0.125,convfloat)
(%i90) define_variable(glob_prec,1.0E-16,convfloat)
(%i91) define_variable(glob_check_sign,1.0,convfloat)
(%i92) define_variable(glob_desired_digits_correct,8.0,convfloat)
(%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat)
(%i94) define_variable(glob_ratio_of_radius,0.1,convfloat)
(%i95) define_variable(glob_percent_done,0.0,convfloat)
(%i96) define_variable(glob_total_exp_sec,0.1,convfloat)
(%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat)
(%i98) define_variable(glob_estimated_size_answer,100.0,convfloat)
(%i99) define_variable(glob_almost_1,0.999,convfloat)
(%i100) define_variable(glob_clock_sec,0.0,convfloat)
(%i101) define_variable(glob_clock_start_sec,0.0,convfloat)
(%i102) define_variable(glob_disp_incr,0.1,convfloat)
(%i103) define_variable(glob_h,0.1,convfloat)
(%i104) define_variable(glob_diff_rc_fm,0.1,convfloat)
(%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat)
(%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat)
(%i107) define_variable(glob_diff_ord_fm,0.1,convfloat)
(%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat)
(%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat)
(%i110) define_variable(glob_six_term_ord_save,0.1,convfloat)
(%i111) define_variable(glob_guess_error_rc,0.1,convfloat)
(%i112) define_variable(glob_guess_error_ord,0.1,convfloat)
(%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat)
(%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat)
(%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat)
(%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat)
(%i117) define_variable(glob_last_good_h,0.1,convfloat)
(%i118) define_variable(glob_max_h,0.1,convfloat)
(%i119) define_variable(glob_min_h,1.0E-6,convfloat)
(%i120) define_variable(glob_display_interval,0.1,convfloat)
(%i121) define_variable(glob_abserr,1.0E-11,convfloat)
(%i122) define_variable(glob_relerr,1.0E-11,convfloat)
(%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat)
(%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat)
(%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat)
(%i126) define_variable(glob_max_hours,0.0,convfloat)
(%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat)
(%i128) define_variable(glob_optimal_start,0.0,convfloat)
(%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat)
(%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat)
(%i131) define_variable(glob_max_sec,10000.0,convfloat)
(%i132) define_variable(glob_orig_start_sec,0.0,convfloat)
(%i133) define_variable(glob_normmax,0.0,convfloat)
(%i134) define_variable(glob_max_minutes,0.0,convfloat)
(%i135) define_variable(glob_next_display,0.0,convfloat)
(%i136) define_variable(glob_est_digits,1,fixnum)
(%i137) define_variable(glob_subiter_method,3,fixnum)
(%i138) define_variable(glob_html_log,true,boolean)
(%i139) define_variable(glob_min_good_digits,99999,fixnum)
(%i140) define_variable(glob_good_digits,0,fixnum)
(%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum)
(%i142) define_variable(glob_apfp_est_good_digits,0,fixnum)
(%i143) define_variable(glob_max_opt_iter,10,fixnum)
(%i144) define_variable(glob_dump,false,boolean)
(%i145) define_variable(glob_djd_debug,true,boolean)
(%i146) define_variable(glob_display_flag,true,boolean)
(%i147) define_variable(glob_djd_debug2,true,boolean)
(%i148) define_variable(glob_h_reason,0,fixnum)
(%i149) define_variable(glob_sec_in_minute,60,fixnum)
(%i150) define_variable(glob_min_in_hour,60,fixnum)
(%i151) define_variable(glob_hours_in_day,24,fixnum)
(%i152) define_variable(glob_days_in_year,365,fixnum)
(%i153) define_variable(glob_sec_in_hour,3600,fixnum)
(%i154) define_variable(glob_sec_in_day,86400,fixnum)
(%i155) define_variable(glob_sec_in_year,31536000,fixnum)
(%i156) define_variable(glob_not_yet_finished,true,boolean)
(%i157) define_variable(glob_initial_pass,true,boolean)
(%i158) define_variable(glob_not_yet_start_msg,true,boolean)
(%i159) define_variable(glob_reached_optimal_h,false,boolean)
(%i160) define_variable(glob_optimal_done,false,boolean)
(%i161) define_variable(glob_type_given_pole,0,fixnum)
(%i162) define_variable(glob_optimize,false,boolean)
(%i163) define_variable(glob_look_poles,false,boolean)
(%i164) define_variable(glob_dump_closed_form,false,boolean)
(%i165) define_variable(glob_max_iter,1000,fixnum)
(%i166) define_variable(glob_no_eqs,0,fixnum)
(%i167) define_variable(glob_unchanged_h_cnt,0,fixnum)
(%i168) define_variable(glob_warned,false,boolean)
(%i169) define_variable(glob_warned2,false,boolean)
(%i170) define_variable(glob_start,0,fixnum)
(%i171) define_variable(glob_iter,0,fixnum)
(%i172) completearray(array_y_init,[20],convfloat)
(%i173) completearray(array_norms,[20],convfloat)
(%i174) completearray(array_fact_1,[20],convfloat)
(%i175) completearray(array_1st_rel_error,[2],convfloat)
(%i176) completearray(array_last_rel_error,[2],convfloat)
(%i177) completearray(array_est_rel_error,[2],convfloat)
(%i178) completearray(array_max_est_error,[2],convfloat)
(%i179) completearray(array_type_pole,[2],convfloat)
(%i180) completearray(array_type_real_pole,[2],convfloat)
(%i181) completearray(array_type_complex_pole,[2],convfloat)
(%i182) completearray(array_est_digits,[2],convfloat)
(%i183) completearray(array_y,[20],convfloat)
(%i184) completearray(array_x,[20],convfloat)
(%i185) completearray(array_tmp0,[20],convfloat)
(%i186) completearray(array_tmp1,[20],convfloat)
(%i187) completearray(array_tmp2,[20],convfloat)
(%i188) completearray(array_tmp3,[20],convfloat)
(%i189) completearray(array_tmp4,[20],convfloat)
(%i190) completearray(array_tmp5,[20],convfloat)
(%i191) completearray(array_tmp6,[20],convfloat)
(%i192) completearray(array_m1,[20],convfloat)
(%i193) completearray(array_y_higher,[2,20],convfloat)
(%i194) completearray(array_y_higher_work,[2,20],convfloat)
(%i195) completearray(array_y_higher_work2,[2,20],convfloat)
(%i196) completearray(array_y_set_initial,[2,20],convfloat)
(%i197) completearray(array_given_rad_poles,[2,3],convfloat)
(%i198) completearray(array_given_ord_poles,[2,3],convfloat)
(%i199) completearray(array_rad_test_poles,[2,4],convfloat)
(%i200) completearray(array_ord_test_poles,[2,4],convfloat)
(%i201) completearray(array_fact_2,[20,20],convfloat)
(%i202) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i203) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i204) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i205) 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))
(%i206) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i207) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i208) logitem_time(fd,secs_in):=(
block(mode_declare(
[[days_int,hours_int,minutes_int,sec_int,
years_int],fixnum,[secs,secs_temp],convfloat]),
secs:secs_in,printf(fd,"
~%"),
if secs >= 0
then (years_int
:truncate(secs/glob_sec_in_year),
sec_temp
:mod(truncate(secs),
truncate(glob_sec_in_year)),
days_int
:truncate(sec_temp/glob_sec_in_day),
sec_temp
:mod(sec_temp,
truncate(glob_sec_in_day)),
hours_int
:truncate(sec_temp/glob_sec_in_hour),
sec_temp
:mod(sec_temp,
truncate(glob_sec_in_hour)),
minutes_int
:truncate(sec_temp/glob_sec_in_minute),
sec_int
:mod(sec_temp,
truncate(glob_sec_in_minute)),
if truncate(years_int) > 0.1
then printf(fd,
"~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%",
years_int,days_int,
hours_int,minutes_int,
sec_int)
elseif days_int > 0.1
then printf(fd,
"~d Days ~d Hours ~d Minutes ~d Seconds~%",
days_int,hours_int,
minutes_int,sec_int)
elseif hours_int > 0.1
then printf(fd,
"~d Hours ~d Minutes ~d Seconds~%",
hours_int,minutes_int,
sec_int)
elseif minutes_int > 0.1
then printf(fd,
"~d Minutes ~d Seconds~%",
minutes_int,sec_int)
else printf(fd,"~d Seconds~%",
sec_int))
else printf(fd," 0.0 Seconds~%"),
printf(fd," | ~%")),0)
(%i209) omniout_timestr(secs_in):=(
block(mode_declare(
[[days_int,hours_int,minutes_int,sec_int,
years_int],fixnum,[secs,secs_temp],
convfloat]),secs:secs_in,
if secs >= 0
then (
years_int:truncate(secs/glob_sec_in_year),
sec_temp
:mod(truncate(secs),
truncate(glob_sec_in_year)),
days_int:truncate(sec_temp/glob_sec_in_day),
sec_temp
:mod(sec_temp,truncate(glob_sec_in_day)),
hours_int
:truncate(sec_temp/glob_sec_in_hour),
sec_temp
:mod(sec_temp,truncate(glob_sec_in_hour)),
minutes_int
:truncate(sec_temp/glob_sec_in_minute),
sec_int
:mod(sec_temp,
truncate(glob_sec_in_minute)),
if years_int > 0
then printf(true,
"= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%",
years_int,days_int,
hours_int,minutes_int,
sec_int)
elseif days_int > 0.1
then printf(true,
"= ~d Days ~d Hours ~d Minutes ~d Seconds~%",
days_int,hours_int,
minutes_int,sec_int)
elseif hours_int > 0.1
then printf(true,
"= ~d Hours ~d Minutes ~d Seconds~%",
hours_int,minutes_int,
sec_int)
elseif minutes_int > 0.1
then printf(true,
"= ~d Minutes ~d Seconds~%",
minutes_int,sec_int)
else printf(true,"= ~d Seconds~%",
sec_int))
else printf(true,"= 0.0 Seconds~%")),0)
(%i210) zero_ats_ar(arr_a):=(
block(mode_declare([iii],fixnum),iii:1,
while iii <= ats_max_terms do
(arr_a[iii]:glob__0,iii:1+iii)),0)
(%i211) ats(mmm_ats,arr_a,arr_b,jjj_ats):=block(
mode_declare([[iii_ats,lll_ats,ma_ats],fixnum,[ret_ats],
convfloat]),ret_ats:glob__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,
if lll_ats <= ats_max_terms
and iii_ats <= ats_max_terms
then ret_ats
:c(arr_a[iii_ats])*c(arr_b[lll_ats])+ret_ats,
iii_ats:1+iii_ats)),ret_ats)
(%i212) att(mmm_att,arr_aa,arr_bb,jjj_att):=block(
mode_declare([[al_att,iii_att,lll_att,ma_att],convfloat,[ret_att],
fixnum]),ret_att:glob__0,
if jjj_att < mmm_att
then (ma_att:2+mmm_att,iii_att:jjj_att,
while iii_att < mmm_att and iii_att <= ats_max_terms do
(lll_att:ma_att-iii_att,al_att:lll_att-1,
if lll_att <= ats_max_terms
and iii_att <= ats_max_terms
then ret_att
:c(arr_aa[iii_att])*c(arr_bb[lll_att])
*c(al_att)
+ret_att,iii_att:1+iii_att),
ret_att:ret_att/c(mmm_att)),ret_att)
(%i213) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i214) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i215) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i216) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i217) log_revs(file,revs):=printf(file,revs)
(%i218) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i219) logitem_h_reason(file):=(printf(file,""),
if glob_h_reason = 1 then printf(file,"Max H")
elseif glob_h_reason = 2
then printf(file,"Display_interval")
elseif glob_h_reason = 3
then printf(file,"Optimal")
elseif glob_h_reason = 4
then printf(file,"Pole Accuracy")
elseif glob_h_reason = 5
then printf(file,"Min H (Pole)")
elseif glob_h_reason = 6 then printf(file,"Pole")
elseif glob_h_reason = 7
then printf(file,"Opt Iter")
else printf(file,"Impossible"),
printf(file," | "),0)
(%i220) logstart(file):=(printf(file,""),0)
(%i221) logend(file):=(printf(file,"
~%"),0)
(%i222) chk_data():=(
block(mode_declare([[errflag],boolean]),errflag:false,
if glob_max_iter < 2
then (omniout_str(always,"Illegal max_iter"),
errflag:true),if errflag then quit()),0)
(%i223) comp_expect_sec(t_end2,t_start2,t2,clock_sec2):=block(
mode_declare([[ms2,rrr,sec_left,sub1,sub2],
convfloat]),ms2:c(clock_sec2),
sub1:c(t_end2-t_start2),sub2:c(t2-t_start2),
if sub1 = glob__0 then sec_left:glob__0
else (if sub2 > glob__0
then (rrr:sub1/sub2,
sec_left:rrr*c(ms2)-c(ms2))
else sec_left:glob__0),sec_left)
(%i224) comp_percent(t_end2,t_start2,t2):=block(
mode_declare([[rrr,sub1,sub2],convfloat]),
sub1:t_end2-t_start2,sub2:t2-t_start2,
if sub2 > glob_small_float then rrr:glob__100*sub2/sub1
else rrr:0.0,rrr)
(%i225) comp_rad_from_ratio(term1,term2,last_no):=(
if abs(term2) > glob__0
then ret:abs(term1*glob_h/term2)
else ret:glob_larger_float,ret)
(%i226) comp_ord_from_ratio(term1,term2,last_no):=(
if abs(term2) > glob__0
then ret
:abs(term2)*c(last_no)
*log(abs(term1*glob_h/term2))
/log(c(last_no))
+glob__1 else ret:glob_larger_float,ret)
(%i227) c(in_val):=(ret:in_val,ret)
(%i228) comp_rad_from_three_terms(term1,term2,term3,last_no):=(
temp:abs(
term1*term3-term1*term3*c(last_no)
+glob__m2*term2*term2
+term2*term2*c(last_no)),
if abs(temp) > glob__0
then ret:abs(term2*glob_h*term1/temp)
else ret:glob_larger_float,ret)
(%i229) comp_ord_from_three_terms(term1,term2,term3,last_no):=(
ret:abs(
(-term1*term3*c(last_no*last_no)
+term2*term2*c(last_no*last_no)
+glob__4*term2*term2
-glob__4*term2*term2*c(last_no)
-glob__3*term1*term3
+glob__4*term1*term3*c(last_no))
/(term1*term3-term1*term3*c(last_no)
-glob__2*term2*term2
+term2*term2*c(last_no))),
ret)
(%i230) comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=
(
if term5 # glob__0 and term4 # glob__0
and term3 # glob__0
and term2 # glob__0
and term1 # glob__0
then (rm0:term6/term5,rm1:term5/term4,
rm2:term4/term3,rm3:term3/term2,
rm4:term2/term1,
nr1
:c(last_no-3)*rm2
-glob__2*c(last_no-2)*rm1
+c(last_no-1)*rm0,
nr2
:c(last_no-4)*rm3
-glob__2*c(last_no-3)*rm2
+c(last_no-2)*rm1,
dr1
:(-glob__1)/rm3+glob__2/rm2
+glob__m1/rm1,
dr2
:(-glob__1)/rm4+glob__2/rm3
+glob__m1/rm2,
ds1
:glob__5/rm3-glob__8/rm2
+glob__3/rm1,
ds2
:glob__5/rm4-glob__8/rm3
+glob__3/rm2,
if
abs(nr1*dr2-nr2*dr1) = glob__0
or abs(dr1) = glob__0
then (rad_c:glob_larger_float,
ord_no:glob_larger_float)
else (if
abs(nr1*dr2-nr2*dr1) > glob__0
then (
rcs
:(dr1*dr2-ds2*dr1+ds1*dr2)
/(nr1*dr2-nr2*dr1),
ord_no
:(rcs*nr1-ds1)/(glob__2*dr1)
-c(last_no)/glob__2,
if abs(rcs) # glob__0
then (if rcs > glob__0
then rad_c
:sqrt(rcs)
*abs(glob_h)
else (
rad_c
:glob_larger_float,
ord_no
:glob_larger_float))
else (
rad_c:glob_larger_float,
ord_no:glob_larger_float))
else (rad_c:glob_larger_float,
ord_no:glob_larger_float)))
else (rad_c:glob_larger_float,
ord_no:glob_larger_float),
glob_six_term_ord_save:ord_no,rad_c)
(%i231) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i232) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i233) factorial_1(nnn):=block(mode_declare([[ret],convfloat]),
if nnn <= ats_max_terms
then (if array_fact_1[nnn] = 0
then (ret:factorial_2(nnn),
array_fact_1[nnn]:ret)
else ret:array_fact_1[nnn])
else ret:factorial_2(nnn),ret)
(%i234) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i235) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i236) factorial_3(mmm,nnn):=block(mode_declare([[ret],convfloat]),
if nnn <= ats_max_terms and mmm <= ats_max_terms
then (if array_fact_2[mmm,nnn] = 0
then (ret:factorial_1(mmm)/factorial_1(nnn),
array_fact_2[mmm,nnn]:ret)
else ret:array_fact_2[mmm,nnn])
else ret:factorial_2(mmm)/factorial_2(nnn),ret)
(%i237) log10(x):=log(x)/glob_log_10
(%i238) c(x):=x
(%i239) expt(x,y):=if y = 0.0 then 1.0 elseif x <= 0.0 and y < 0.0
then print("expt error x = ",x,"y = ",y) else x^y
(%i240) estimated_needed_step_error(x_start,x_end,estimated_h,
estimated_answer):=block(
[desired_abs_gbl_error,range,
estimated_steps,step_error],
omniout_float(always,
"glob_desired_digits_correct",
32,
glob_desired_digits_correct,
32,""),
desired_abs_gbl_error
:expt(glob__10,
c(-glob_desired_digits_correct))
*c(abs(c(estimated_answer))),
omniout_float(always,"estimated_h",32,
estimated_h,32,""),
omniout_float(always,"estimated_answer",
32,estimated_answer,32,""),
omniout_float(always,
"desired_abs_gbl_error",32,
desired_abs_gbl_error,32,
""),range:x_end-x_start,
omniout_float(always,"range",32,range,32,
""),
estimated_steps:range/estimated_h,
omniout_float(always,"estimated_steps",32,
estimated_steps,32,""),
step_error
:c(
abs(desired_abs_gbl_error)
/sqrt(c(estimated_steps))
/c(ats_max_terms)),
omniout_float(always,"step_error",32,
step_error,32,""),
step_error)
(%i241) exact_soln_y(x):=block(c(1.0)/c(x)/c(x)/c(x))
c(1.0)
------
c(x)
------
c(x)
(%o241) exact_soln_y(x) := block(------)
c(x)
(%i242) display_poles():=(
block(mode_declare([[rad_given],convfloat]),
if glob_type_given_pole = 1
or glob_type_given_pole = 2
then (rad_given
:sqrt(
array_given_rad_poles[1,2]
*array_given_rad_poles[1,2]
+(array_x[1]
-array_given_rad_poles[1,1])
*(array_x[1]
-array_given_rad_poles[1,1])),
omniout_float(always,
"Radius of convergence (given) for eq 1 ",
4,rad_given,4," "),
omniout_float(always,
"Order of pole (given) ",
4,
array_given_ord_poles[
1,1],4," "),
if rad_given < glob_least_given_sing
then glob_least_given_sing
:rad_given)
elseif glob_type_given_pole = 3
then omniout_str(always,
"NO POLE (given) for Equation 1")
elseif glob_type_given_pole = 5
then omniout_str(always,
"SOME POLE (given) for Equation 1")
else omniout_str(always,
"NO info (given) for Equation 1"),
if array_rad_test_poles[1,1] < glob_large_float
then (omniout_float(always,
"Radius of convergence (ratio test) for eq 1 ",
4,
array_rad_test_poles[1,1],
4," "),
if
array_rad_test_poles[1,1]
< glob_least_ratio_sing
then glob_least_ratio_sing
:array_rad_test_poles[1,1],
omniout_float(always,
"Order of pole (ratio test) ",
4,
array_ord_test_poles[1,1],
4," "))
else omniout_str(always,
"NO POLE (ratio test) for Equation 1"),
if array_rad_test_poles[1,2] > glob__small
and array_rad_test_poles[1,2]
< glob_large_float
then (omniout_float(always,
"Radius of convergence (three term test) for eq 1 ",
4,
array_rad_test_poles[1,2],
4," "),
if
array_rad_test_poles[1,2]
< glob_least_3_sing
then glob_least_3_sing
:array_rad_test_poles[1,2],
omniout_float(always,
"Order of pole (three term test) ",
4,
array_ord_test_poles[1,2],
4," "))
else omniout_str(always,
"NO REAL POLE (three term test) for Equation 1"),
if array_rad_test_poles[1,3] > glob__small
and array_rad_test_poles[1,3]
< glob_large_float
then (omniout_float(always,
"Radius of convergence (six term test) for eq 1 ",
4,
array_rad_test_poles[1,3],
4," "),
if
array_rad_test_poles[1,3]
< glob_least_6_sing
then glob_least_6_sing
:array_rad_test_poles[1,3],
omniout_float(always,
"Order of pole (six term test) ",
4,
array_ord_test_poles[1,3],
4," "))
else omniout_str(always,
"NO COMPLEX POLE (six term test) for Equation 1")),
0)
(%i243) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i244) est_size_answer():=block([min_size],
min_size:glob_estimated_size_answer,
if abs(array_y[1]) < min_size
then (min_size:abs(array_y[1]),
omniout_float(always,"min_size",32,min_size,
32,"")),
if min_size < glob__1
then (min_size:glob__1,
omniout_float(always,"min_size",32,min_size,
32,"")),min_size)
(%i245) test_suggested_h():=block(
[max_estimated_step_error,hn_div_ho,hn_div_ho_2,
hn_div_ho_3,no_terms,est_tmp],
max_estimated_step_error:glob__small,
no_terms:ats_max_terms,hn_div_ho:glob__0_5,
hn_div_ho_2:glob__0_25,hn_div_ho_3:glob__0_125,
omniout_float(always,"hn_div_ho",32,hn_div_ho,32,""),
omniout_float(always,"hn_div_ho_2",32,hn_div_ho_2,32,
""),
omniout_float(always,"hn_div_ho_3",32,hn_div_ho_3,32,
""),
est_tmp:abs(array_y[no_terms]*hn_div_ho_3
+array_y[no_terms-1]*hn_div_ho_2
+array_y[no_terms-2]*hn_div_ho
+array_y[no_terms-3]),
if est_tmp >= max_estimated_step_error
then max_estimated_step_error:est_tmp,
omniout_float(always,"max_estimated_step_error",32,
max_estimated_step_error,32,""),
max_estimated_step_error)
(%i246) track_estimated_error():=block(
[hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,
est_tmp],no_terms:ats_max_terms,
hn_div_ho:glob__0_5,hn_div_ho_2:glob__0_25,
hn_div_ho_3:glob__0_125,
est_tmp:c(abs(array_y[no_terms]))*c(hn_div_ho_3)
+c(abs(array_y[no_terms-1]))
*c(hn_div_ho_2)
+c(abs(array_y[no_terms-2]))
*c(hn_div_ho)
+c(abs(array_y[no_terms-3])),
if glob_prec*c(abs(array_y[1])) > c(est_tmp)
then est_tmp
:c(glob_prec)*c(abs(array_y[1])),
if c(est_tmp) >= c(array_max_est_error[1])
then array_max_est_error[1]:c(est_tmp))
(%i247) reached_interval():=block(mode_declare([[ret],boolean]),
if glob_check_sign*array_x[1]
>= glob_check_sign*glob_next_display
-glob_h/glob__10 then ret:true else ret:false,
return(ret))
(%i248) display_alot(iter):=(
block(mode_declare(
[[abserr,est_rel_err],convfloat,
[closed_form_val_y],convfloat,[ind_var],
convfloat,[numeric_val],convfloat,[relerr],
convfloat,[term_no],fixnum]),
if reached_interval()
then (if iter >= 0
then (ind_var:array_x[1],
omniout_float(always,
"x[1] ",
33,ind_var,20,
" "),
closed_form_val_y
:exact_soln_y(ind_var),
omniout_float(always,
"y[1] (closed_form) ",
33,
closed_form_val_y,
20," "),
term_no:1,
numeric_val:array_y[term_no],
abserr
:abs(
numeric_val
-closed_form_val_y),
omniout_float(always,
"y[1] (numeric) ",
33,numeric_val,
20," "),
if
c(abs(closed_form_val_y))
> c(glob_prec)
then (
relerr
:abserr*glob__100
/abs(closed_form_val_y),
if c(relerr) > c(glob_prec)
then glob_good_digits
:3
-floor(log10(c(relerr)))
else glob_good_digits:16)
else (relerr:glob__m1,
glob_good_digits:-16),
if
glob_good_digits
< glob_min_good_digits
then glob_min_good_digits
:glob_good_digits,
if
glob_apfp_est_good_digits
< glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits
:glob_apfp_est_good_digits,
if
c(abs(numeric_val))
> c(glob_prec)
then (
est_rel_err
:c(array_max_est_error[1])
*glob__100
*c(sqrt(glob_iter))*c(25)
*c(ats_max_terms)
/c(abs(numeric_val)),
if est_rel_err > glob_prec
then glob_est_digits
:3
-floor(
log10(est_rel_err))
else glob_est_digits:16)
else (relerr:glob__m1,
glob_est_digits:-16),
array_est_digits[1]
:glob_est_digits,
if glob_iter = 1
then array_1st_rel_error[1]
:relerr
else array_last_rel_error[
1]
:relerr,
array_est_rel_error[1]
:est_rel_err,
omniout_float(always,
"absolute error ",
4,abserr,20," "),
omniout_float(always,
"relative error ",
4,relerr,20,"%"),
omniout_int(info,
"Desired digits ",
32,
glob_desired_digits_correct,
4," "),
omniout_int(info,
"Estimated correct digits ",
32,glob_est_digits,
4," "),
omniout_int(info,
"Correct digits ",
32,
glob_good_digits,4,
" "),
omniout_float(always,
"h ",
4,glob_h,20,
" ")))),0)
(%i249) prog_report(x_start,x_end):=(
block(mode_declare([[clock_sec],convfloat,[opt_clock_sec],
convfloat,[clock_sec1],convfloat,
[expect_sec],convfloat,[left_sec],
convfloat,[percent_done],convfloat,
[total_clock_sec],convfloat]),
clock_sec1:elapsed_time_seconds(),
total_clock_sec:clock_sec1-glob_orig_start_sec,
glob_clock_sec:clock_sec1-glob_clock_start_sec,
left_sec:-clock_sec1+glob_orig_start_sec
+glob_max_sec,
expect_sec:comp_expect_sec(x_end,x_start,
glob_h+array_x[1],
clock_sec1
-glob_orig_start_sec),
opt_clock_sec:clock_sec1
-glob_optimal_clock_start_sec,
glob_optimal_expect_sec
:comp_expect_sec(x_end,x_start,glob_h+array_x[1],
opt_clock_sec),
glob_total_exp_sec
:c(total_clock_sec)+glob_optimal_expect_sec,
percent_done:comp_percent(x_end,x_start,
glob_h+array_x[1]),
glob_percent_done:percent_done,
omniout_str_noeol(info,
"Total Elapsed Time "),
omniout_timestr(total_clock_sec),
omniout_str_noeol(info,
"Elapsed Time(since restart) "),
omniout_timestr(glob_clock_sec),
if c(percent_done) < glob__100
then (omniout_str_noeol(info,
"Expected Time Remaining "),
omniout_timestr(expect_sec),
omniout_str_noeol(info,
"Optimized Time Remaining "),
omniout_timestr(glob_optimal_expect_sec),
omniout_str_noeol(info,
"Expected Total Time "),
omniout_timestr(glob_total_exp_sec)),
omniout_str_noeol(info,
"Time to Timeout "),
omniout_timestr(left_sec),
omniout_float(info,
"Percent Done ",33,
percent_done,4,"%")),0)
(%i250) check_for_pole():=(
block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc],
convfloat,[m,n],fixnum,[nr1,nr2],
convfloat,[ord_no],fixnum,
[term1,term2,term3,part1,part2,
part3,part4,part5,part6,part7,
part8,part9,part10,part11,part12,
part13,part14,rad_c,rcs,rm0,rm1,
rm2,rm3,rm4],convfloat,
[found_sing],fixnum,
[h_new,ratio,term,local_test,
tmp_rad,tmp_ord,tmp_ratio,
prev_tmp_rad],convfloat,[last_no],
fixnum),tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,1]:glob_larger_float,
array_ord_test_poles[1,1]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-3
and found_sing = 1 do
(tmp_rad
:comp_rad_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,1]
then (
array_rad_test_poles[1,1]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,1]:rad_c,
array_ord_test_poles[1,1]
:tmp_ord)),
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,2]:glob_larger_float,
array_ord_test_poles[1,2]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-4
and found_sing = 1 do
(tmp_rad
:comp_rad_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,2]
then (
array_rad_test_poles[1,2]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,2]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,2]
:tmp_ord)),
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,3]:glob_larger_float,
array_ord_test_poles[1,3]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-7
and found_sing = 1 do
(tmp_rad
:comp_rad_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,3]
then (
array_rad_test_poles[1,3]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,3]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,3]
:tmp_ord)),
if abs(glob_min_pole_est)*glob_ratio_of_radius
< abs(glob_h)
then (h_new
:glob_check_sign*glob_min_pole_est
*glob_ratio_of_radius,
omniout_str(always,
"SETTING H FOR POLE"),
glob_h_reason:6,
if
glob_check_sign*glob_min_h
> glob_check_sign*h_new
then (
omniout_str(always,
"SETTING H FOR MIN H"),
h_new:glob_min_h,glob_h_reason:5),
term:1,ratio:c(1.0),
while term <= ats_max_terms do
(
array_y[term]
:array_y[term]*ratio,
array_y_higher[1,term]
:array_y_higher[1,term]*ratio,
array_x[term]
:array_x[term]*ratio,
ratio:ratio*h_new/abs(glob_h),
term:1+term),glob_h:h_new),
if reached_interval() then display_poles()),0)
(%i251) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),
array_tmp1[1]:neg(array_const_3D0[1]),
array_tmp2[1]:array_tmp1[1]/array_x[1],
array_tmp3[1]:array_tmp2[1]/array_x[1],
array_tmp4[1]:array_tmp3[1]/array_x[1],
array_tmp5[1]:array_tmp4[1]/array_x[1],
array_tmp6[1]:array_tmp5[1]+array_const_0D0[1],
if not array_y_set_initial[1,2]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp6[1])*expt(glob_h,c(1))
*c(factorial_3(0,1)),
if 2 <= ats_max_terms
then (array_y[2]:temporary,
array_y_higher[1,2]:temporary),
temporary:c(temporary)*c(1)/c(glob_h),
array_y_higher[2,1]:c(temporary),0)),
kkk:2,
array_tmp2[2]:neg(array_tmp2[1])*array_x[2]/array_x[1],
array_tmp3[2]:(array_tmp2[2]-array_tmp3[1]*array_x[2])
/array_x[1],
array_tmp4[2]:(array_tmp3[2]-array_tmp4[1]*array_x[2])
/array_x[1],
array_tmp5[2]:(array_tmp4[2]-array_tmp5[1]*array_x[2])
/array_x[1],array_tmp6[2]:array_tmp5[2],
if not array_y_set_initial[1,3]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp6[2])*expt(glob_h,c(1))
*c(factorial_3(1,2)),
if 3 <= ats_max_terms
then (array_y[3]:temporary,
array_y_higher[1,3]:temporary),
temporary:c(temporary)*c(2)/c(glob_h),
array_y_higher[2,2]:c(temporary),0)),
kkk:3,
array_tmp2[3]:neg(array_tmp2[2])*array_x[2]/array_x[1],
array_tmp3[3]:(array_tmp2[3]-array_tmp3[2]*array_x[2])
/array_x[1],
array_tmp4[3]:(array_tmp3[3]-array_tmp4[2]*array_x[2])
/array_x[1],
array_tmp5[3]:(array_tmp4[3]-array_tmp5[2]*array_x[2])
/array_x[1],array_tmp6[3]:array_tmp5[3],
if not array_y_set_initial[1,4]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp6[3])*expt(glob_h,c(1))
*c(factorial_3(2,3)),
if 4 <= ats_max_terms
then (array_y[4]:temporary,
array_y_higher[1,4]:temporary),
temporary:c(temporary)*c(3)/c(glob_h),
array_y_higher[2,3]:c(temporary),0)),
kkk:4,
array_tmp2[4]:neg(array_tmp2[3])*array_x[2]/array_x[1],
array_tmp3[4]:(array_tmp2[4]-array_tmp3[3]*array_x[2])
/array_x[1],
array_tmp4[4]:(array_tmp3[4]-array_tmp4[3]*array_x[2])
/array_x[1],
array_tmp5[4]:(array_tmp4[4]-array_tmp5[3]*array_x[2])
/array_x[1],array_tmp6[4]:array_tmp5[4],
if not array_y_set_initial[1,5]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp6[4])*expt(glob_h,c(1))
*c(factorial_3(3,4)),
if 5 <= ats_max_terms
then (array_y[5]:temporary,
array_y_higher[1,5]:temporary),
temporary:c(temporary)*c(4)/c(glob_h),
array_y_higher[2,4]:c(temporary),0)),
kkk:5,
array_tmp2[5]:neg(array_tmp2[4])*array_x[2]/array_x[1],
array_tmp3[5]:(array_tmp2[5]-array_tmp3[4]*array_x[2])
/array_x[1],
array_tmp4[5]:(array_tmp3[5]-array_tmp4[4]*array_x[2])
/array_x[1],
array_tmp5[5]:(array_tmp4[5]-array_tmp5[4]*array_x[2])
/array_x[1],array_tmp6[5]:array_tmp5[5],
if not array_y_set_initial[1,6]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp6[5])*expt(glob_h,c(1))
*c(factorial_3(4,5)),
if 6 <= ats_max_terms
then (array_y[6]:temporary,
array_y_higher[1,6]:temporary),
temporary:c(temporary)*c(5)/c(glob_h),
array_y_higher[2,5]:c(temporary),0)),
kkk:6,
while kkk <= ats_max_terms do
(array_tmp2[kkk]:array_tmp1[1]*array_x[kkk],
array_tmp3[kkk]
:neg(ats(kkk,array_x,array_tmp3,2))/array_x[1],
array_tmp4[kkk]
:neg(ats(kkk,array_x,array_tmp4,2))/array_x[1],
array_tmp5[kkk]
:neg(ats(kkk,array_x,array_tmp5,2))/array_x[1],
array_tmp6[kkk]:array_tmp5[kkk],order_d:1,
if order_d+kkk <= ats_max_terms
then (if
not array_y_set_initial[1,order_d+kkk]
then (
temporary
:c(array_tmp6[kkk])*expt(glob_h,c(order_d))
*c(
factorial_3(
kkk-1,
-1+order_d+kkk)),
array_y[order_d+kkk]:c(temporary),
array_y_higher[1,order_d+kkk]:c(temporary),
term:-1+order_d+kkk,adj2:-1+order_d+kkk,
adj3:2,
while term >= 1 and term <= ats_max_terms
and adj3 < 1+order_d do
(
if adj3 <= 1+order_d
then (
if adj2 > 0
then temporary
:c(temporary)*c(adj2)
/c(glob_h)
else temporary:c(temporary),
array_y_higher[adj3,term]
:c(temporary)),term:term-1,
adj2:adj2-1,adj3:1+adj3))),
kkk:1+kkk)),0)
(%i252) exact_soln_y(x):=block(c(1.0)/c(x)/c(x)/c(x))
c(1.0)
------
c(x)
------
c(x)
(%o252) exact_soln_y(x) := block(------)
c(x)
(%i253) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat,
[niii,done_once,term,ord,order_diff,term_no,
html_log_file,iiif,jjjf,rows,r_order,
sub_iter,calc_term,iii],fixnum,[temp_sum],
convfloat,[current_iter],fixnum,
[x_start,x_end],convfloat,[it,opt_iter],
fixnum,[tmp],convfloat,[subiter],fixnum,
[est_needed_step_err,estimated_step_error,
min_value,est_answer,last_min_pole_est],
convfloat,[repeat_it],fixnum],[found_h],
boolean),Digits:32,max_terms:20,
glob_html_log:true,term:1,
while term <= 20 do (array_y_init[term]:c(0.0),term:1+term),
term:1,
while term <= 20 do (array_norms[term]:c(0.0),term:1+term),
term:1,
while term <= 20 do (array_fact_1[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_1st_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_last_rel_error[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_est_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_max_est_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do (array_type_pole[term]:0,term:1+term),
term:1,
while term <= 2 do
(array_type_real_pole[term]:0,term:1+term),term:1,
while term <= 2 do
(array_type_complex_pole[term]:0,term:1+term),term:1,
while term <= 2 do (array_est_digits[term]:0,term:1+term),
term:1,
while term <= 20 do (array_y[term]:c(0.0),term:1+term),
term:1,
while term <= 20 do (array_x[term]:c(0.0),term:1+term),
term:1,
while term <= 20 do (array_tmp0[term]:c(0.0),term:1+term),
term:1,
while term <= 20 do (array_tmp1[term]:c(0.0),term:1+term),
term:1,
while term <= 20 do (array_tmp2[term]:c(0.0),term:1+term),
term:1,
while term <= 20 do (array_tmp3[term]:c(0.0),term:1+term),
term:1,
while term <= 20 do (array_tmp4[term]:c(0.0),term:1+term),
term:1,
while term <= 20 do (array_tmp5[term]:c(0.0),term:1+term),
term:1,
while term <= 20 do (array_tmp6[term]:c(0.0),term:1+term),
term:1,
while term <= 20 do (array_m1[term]:c(0.0),term:1+term),
ord:1,
while ord <= 2 do
(term:1,
while term <= 20 do
(array_y_higher[ord,term]:c(0.0),term:1+term),
ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 20 do
(array_y_higher_work[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 20 do
(array_y_higher_work2[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 20 do
(array_y_set_initial[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_rad_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_ord_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_rad_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_ord_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 20 do
(term:1,
while term <= 20 do
(array_fact_2[ord,term]:c(0.0),term:1+term),
ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x),
zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1),
zero_ats_ar(array_tmp2),zero_ats_ar(array_tmp3),
zero_ats_ar(array_tmp4),zero_ats_ar(array_tmp5),
zero_ats_ar(array_tmp6),zero_ats_ar(array_m1),
zero_ats_ar(array_const_1),array_const_1[1]:c(1),
zero_ats_ar(array_const_0D0),array_const_0D0[1]:c(0.0),
zero_ats_ar(array_const_3D0),array_const_3D0[1]:c(3.0),
zero_ats_ar(array_m1),array_m1[1]:glob__m1,iiif:0,
while iiif <= ats_max_terms do
(jjjf:0,
while jjjf <= ats_max_terms do
(array_fact_1[iiif]:0,
array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf),
iiif:1+iiif),array_y_set_initial[1,1]:true,
array_y_set_initial[1,2]:false,
array_y_set_initial[1,3]:false,
array_y_set_initial[1,4]:false,
array_y_set_initial[1,5]:false,
array_y_set_initial[1,6]:false,
array_y_set_initial[1,7]:false,
array_y_set_initial[1,8]:false,
array_y_set_initial[1,9]:false,
array_y_set_initial[1,10]:false,
array_y_set_initial[1,11]:false,
array_y_set_initial[1,12]:false,
array_y_set_initial[1,13]:false,
array_y_set_initial[1,14]:false,
array_y_set_initial[1,15]:false,
array_y_set_initial[1,16]:false,
array_y_set_initial[1,17]:false,
array_y_set_initial[1,18]:false,
array_y_set_initial[1,19]:false,
array_y_set_initial[1,20]:false,glob_log_10:log(10.0),
glob_orig_start_sec:elapsed_time_seconds(),
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/sing5_backpostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; "),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(always,"Digits:32,"),
omniout_str(always,"max_terms:20,"),omniout_str(always,"!"),
omniout_str(always,"/* END FIRST INPUT BLOCK */"),
omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(always,"x_start:c(-0.7),"),
omniout_str(always,"x_end:c(-1.0),"),
omniout_str(always,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(always,"glob_look_poles:true,"),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,"glob_type_given_pole:1,"),
omniout_str(always,""),
omniout_str(always,"array_given_rad_poles[1,1]:c(0.0),"),
omniout_str(always,""),
omniout_str(always,"array_given_rad_poles[1,2]:c(0.0),"),
omniout_str(always,""),
omniout_str(always,"array_given_ord_poles[1,1]:c(4.0),"),
omniout_str(always,""),
omniout_str(always,"array_given_ord_poles[1,2]:c(0.0),"),
omniout_str(always,"/* END SECOND INPUT BLOCK */"),
omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"),
omniout_str(always,"glob_desired_digits_correct:8,"),
omniout_str(always,"glob_max_minutes:(3.0),"),
omniout_str(always,"glob_subiter_method:3,"),
omniout_str(always,"glob_max_iter:100000,"),
omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"),
omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"),
omniout_str(always,"glob_look_poles:false,"),
omniout_str(always,"glob_h:c(0.001),"),
omniout_str(always,"glob_display_interval:c(0.01),"),
omniout_str(always,"/* END OVERRIDE BLOCK */"),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN USER DEF BLOCK */"),
omniout_str(always,"exact_soln_y (x) := (block("),
omniout_str(always," (c(1.0)/c(x)/c(x)/c(x)) "),
omniout_str(always,"));"),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:glob__0,glob_smallish_float:glob__0,
glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100),
glob_almost_1:c(0.99),x_start:c(-0.7),x_end:c(-1.0),
array_y_init[1+0]:exact_soln_y(x_start),
glob_look_poles:true,glob_type_given_pole:1,
array_given_rad_poles[1,1]:c(0.0),
array_given_rad_poles[1,2]:c(0.0),
array_given_ord_poles[1,1]:c(4.0),
array_given_ord_poles[1,2]:c(0.0),
glob_desired_digits_correct:8,glob_max_minutes:3.0,
glob_subiter_method:3,glob_max_iter:100000,
glob_upper_ratio_limit:c(1.000001),
glob_lower_ratio_limit:c(0.999999),glob_look_poles:false,
glob_h:c(0.001),glob_display_interval:c(0.01),
glob_last_good_h:glob_h,
glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes,
glob_check_sign:c(my_check_sign(x_start,x_end)),
glob__pi:3.141592654,glob_prec:1.0E-16,
if glob_optimize
then (omniout_str(always,"START of Optimize"),
found_h:false,glob_min_pole_est:glob_larger_float,
last_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,
glob_min_h:abs(glob_min_h)*glob_check_sign,
glob_max_h:abs(glob_max_h)*glob_check_sign,
glob_h:abs(glob_min_h)*glob_check_sign,
glob_display_interval
:c(abs(c(glob_display_interval))
*glob_check_sign),
display_max:c(x_end)-c(x_start)/glob__10,
if glob_display_interval > display_max
then glob_display_interval:c(display_max),
chk_data(),min_value:glob_larger_float,
est_answer:est_size_answer(),opt_iter:1,
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,est_answer),
omniout_float(always,"est_needed_step_err",32,
est_needed_step_err,16,""),
estimated_step_error:glob_small_float,
while opt_iter <= 100 and not found_h do
(omniout_int(always,"opt_iter",32,opt_iter,
4,""),array_x[1]:c(x_start),
array_x[2]:c(glob_h),
glob_next_display:c(x_start),order_diff:1,
term_no:1,
while term_no <= order_diff do
(
array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,
c(term_no-1))
/c(
factorial_1(
term_no-1)),
term_no:1+term_no),
r_order:1+r_order),atomall(),
if glob_check_sign*glob_min_h
>= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR MIN H"),
glob_h:glob_check_sign*abs(glob_min_h),
glob_h_reason:1,found_h:true),
if glob_check_sign*glob_display_interval
<= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR DISPLAY INTERVAL"),
glob_h_reason:2,
glob_h:glob_display_interval,
found_h:true),
if glob_look_poles then check_for_pole(),
if not found_h
then (est_answer:est_size_answer(),
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,
est_answer),
omniout_float(always,
"est_needed_step_err",
32,
est_needed_step_err,
16,""),
estimated_step_error
:test_suggested_h(),
omniout_float(always,
"estimated_step_error",
32,
estimated_step_error,
32,""),
if
estimated_step_error
< est_needed_step_err
then (
omniout_str(always,
"Double H and LOOP"),
glob_h:glob_h*glob__2)
else (
omniout_str(always,
"Found H for OPTIMAL"),
found_h:true,glob_h_reason:3,
glob_h:glob_h/glob__2)),
opt_iter:1+opt_iter),
if not found_h and opt_iter = 1
then (omniout_str(always,
"Beginning glob_h too large."),
found_h:false),
if glob_check_sign*glob_max_h
<= glob_check_sign*glob_h
then (omniout_str(always,
"SETTING H FOR MAX H"),
glob_h:glob_check_sign*abs(glob_max_h),
glob_h_reason:1,found_h:true))
else (found_h:true,glob_h:glob_h*glob_check_sign),
if glob_html_log then html_log_file:openw("entry.html"),
if found_h
then (omniout_str(always,"START of Soultion"),
array_x[1]:c(x_start),array_x[2]:c(glob_h),
glob_next_display:c(x_start),
glob_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,order_diff:1,
term_no:1,
while term_no <= order_diff do
(array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),
r_order:1+r_order),current_iter:1,
glob_clock_start_sec:elapsed_time_seconds(),
glob_clock_sec:elapsed_time_seconds(),glob_iter:0,
omniout_str(debugl," "),
glob_reached_optimal_h:true,
glob_optimal_clock_start_sec
:elapsed_time_seconds(),
while glob_iter < glob_max_iter
and glob_check_sign*array_x[1]
< glob_check_sign*x_end
and glob_clock_sec-glob_orig_start_sec
< glob_max_sec do
(if reached_interval()
then (omniout_str(info," "),
omniout_str(info,
"TOP MAIN SOLVE Loop")),
glob_iter:1+glob_iter,
glob_clock_sec:elapsed_time_seconds(),
track_estimated_error(),atomall(),
track_estimated_error(),
display_alot(current_iter),
if glob_look_poles then check_for_pole(),
if reached_interval()
then glob_next_display
:glob_display_interval
+glob_next_display,
array_x[1]:glob_h+array_x[1],
array_x[2]:glob_h,order_diff:2,ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[2,iii]
:array_y_higher[2,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),
term_no:ats_max_terms,
while term_no >= 1 do
(
array_y[term_no]
:array_y_higher_work2[1,term_no],
ord:1,
while ord <= order_diff do
(
array_y_higher[ord,term_no]
:array_y_higher_work2[
ord,term_no],ord:1+ord),
term_no:term_no-1)),
omniout_str(always,"Finished!"),
if glob_iter >= glob_max_iter
then omniout_str(always,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds()-glob_orig_start_sec
>= 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 ) = neg ( 3.0 ) / x / x / x / x ; "),
omniout_int(info,
"Iterations ",32,
glob_iter,4," "),
prog_report(x_start,x_end),
if glob_html_log
then (logstart(html_log_file),
logitem_str(html_log_file,
"2015-04-24T23:07:49-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"sing5_back"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; "),
logitem_float(html_log_file,x_start),
logitem_float(html_log_file,x_end),
logitem_float(html_log_file,array_x[1]),
logitem_float(html_log_file,glob_h),
logitem_h_reason(html_log_file),
logitem_str(html_log_file,"16"),
logitem_float(html_log_file,
glob_desired_digits_correct),
if array_est_digits[1] # -16
then (
logitem_integer(html_log_file,
array_est_digits[
1]),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_min_good_digits # -16
then (
logitem_integer(html_log_file,
glob_min_good_digits),
0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_good_digits # -16
then (
logitem_integer(html_log_file,
glob_good_digits),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
logitem_str(html_log_file,"NA"),
logitem_str(html_log_file,"NA"),
logitem_integer(html_log_file,
ats_max_terms),
if glob_type_given_pole = 0
then (
logitem_str(html_log_file,
"Not Given"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 4
then (
logitem_str(html_log_file,
"No Solution"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 5
then (
logitem_str(html_log_file,
"Some Pole"),
logitem_str(html_log_file,"????"),0)
elseif glob_type_given_pole = 3
then (
logitem_str(html_log_file,
"No Pole"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 1
then (
logitem_str(html_log_file,
"Real Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0) elseif glob_type_given_pole = 2
then (
logitem_str(html_log_file,
"Complex Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0),
if
glob_least_ratio_sing
< glob_large_float
then (
logitem_float(html_log_file,
glob_least_ratio_sing),
0)
else (
logitem_str(html_log_file,"NONE"),0),
if glob_least_3_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_3_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
if glob_least_6_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_6_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
logitem_integer(html_log_file,
glob_iter),
logitem_time(html_log_file,
glob_clock_sec),
if c(glob_percent_done) < glob__100
then (
logitem_time(html_log_file,
glob_total_exp_sec),0)
else (
logitem_str(html_log_file,"Done"),
0),
log_revs(html_log_file,
" 308.maple.seems.ok | "),
logitem_str(html_log_file,
"sing5_back diffeq.max"),
logitem_str(html_log_file,
"sing5_back maxima results"),
logitem_str(html_log_file,
"Poor Accuracy"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i254) main():=(glob_iolevel:2,compile(all),main_prog())
(%i255) main()
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable secs in translation.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable sec_temp in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable years_int in translation.
warning: encountered undefined variable days_int in translation.
warning: encountered undefined variable hours_int in translation.
warning: encountered undefined variable minutes_int in translation.
warning: encountered undefined variable sec_int in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable iii in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_ats in translation.
warning: encountered undefined variable ma_ats in translation.
warning: encountered undefined variable ret_ats in translation.
warning: encountered undefined variable lll_ats in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_att in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable ma_att in translation.
warning: encountered undefined variable lll_att in translation.
warning: encountered undefined variable ret_att in translation.
warning: encountered undefined variable al_att in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_h_reason in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable errflag in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable sub1 in translation.
warning: encountered undefined variable sub2 in translation.
warning: encountered undefined variable rrr in translation.
warning: encountered undefined variable ms2 in translation.
warning: encountered undefined variable sec_left in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ret in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__m2 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temp in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm0 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm1 in translation.
warning: encountered undefined variable rm2 in translation.
warning: encountered undefined variable rm3 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable rm4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__8 in translation.
warning: encountered undefined variable glob__5 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable nr1 in translation.
warning: encountered undefined variable dr2 in translation.
warning: encountered undefined variable nr2 in translation.
warning: encountered undefined variable dr1 in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable ds1 in translation.
warning: encountered undefined variable ds2 in translation.
warning: encountered undefined variable rcs in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable ord_no in translation.
warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any.
warning: encountered undefined variable rad_c in translation.
warning: encountered undefined variable glob_six_term_ord_save in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_fact_2 in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob_log_10 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob__10 in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_x in translation.
warning: encountered undefined variable array_given_rad_poles in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable rad_given in translation.
warning: encountered undefined variable array_given_ord_poles in translation.
warning: variable glob_least_given_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable array_rad_test_poles in translation.
warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable array_ord_test_poles in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: variable glob_least_3_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob__small in translation.
warning: variable glob_least_6_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_estimated_size_answer in translation.
warning: encountered undefined variable array_y in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__small in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable array_max_est_error in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__10 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ind_var in translation.
warning: encountered undefined variable closed_form_val_y in translation.
warning: encountered undefined variable term_no in translation.
warning: encountered undefined variable numeric_val in translation.
warning: encountered undefined variable abserr in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable relerr in translation.
warning: variable glob_good_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_min_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable est_rel_err in translation.
warning: variable glob_est_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_est_digits in translation.
warning: encountered undefined variable array_est_digits in translation.
warning: encountered undefined variable array_1st_rel_error in translation.
warning: encountered undefined variable array_last_rel_error in translation.
warning: encountered undefined variable array_est_rel_error in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable clock_sec1 in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_clock_start_sec in translation.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_optimal_clock_start_sec in translation.
warning: encountered undefined variable opt_clock_sec in translation.
warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_optimal_expect_sec in translation.
warning: encountered undefined variable total_clock_sec in translation.
warning: variable glob_total_exp_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable percent_done in translation.
warning: variable glob_percent_done (declared type convfloat) assigned type any.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable expect_sec in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable left_sec in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable last_no in translation.
warning: encountered undefined variable found_sing in translation.
warning: encountered undefined variable array_y_higher in translation.
warning: variable tmp_rad (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_rad in translation.
warning: encountered undefined variable prev_tmp_rad in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable cnt in translation.
warning: encountered undefined variable tmp_ratio in translation.
warning: encountered undefined variable glob_upper_ratio_limit in translation.
warning: encountered undefined variable glob_lower_ratio_limit in translation.
warning: variable tmp_ord (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_ord in translation.
warning: encountered undefined variable glob_min_pole_est in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_ratio_of_radius in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable h_new in translation.
warning: variable ratio (declared type convfloat) assigned type any.
warning: encountered undefined variable term in translation.
warning: encountered undefined variable ratio in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_const_3D0 in translation.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_tmp2 in translation.
warning: encountered undefined variable array_tmp3 in translation.
warning: encountered undefined variable array_tmp4 in translation.
warning: encountered undefined variable array_tmp5 in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp6 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temporary in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable array_y_set_initial in translation.
warning: encountered undefined variable kkk in translation.
warning: encountered undefined variable order_d in translation.
warning: encountered undefined variable adj3 in translation.
warning: encountered undefined variable adj2 in translation.
modedeclare: [found_h]
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: variable term (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable array_y_init in translation.
warning: variable term (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_norms in translation.
warning: encountered undefined variable array_fact_1 in translation.
warning: encountered undefined variable array_type_pole in translation.
warning: encountered undefined variable array_type_real_pole in translation.
warning: encountered undefined variable array_type_complex_pole in translation.
warning: encountered undefined variable array_tmp0 in translation.
warning: encountered undefined variable array_m1 in translation.
warning: variable ord (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable ord in translation.
warning: variable ord (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_y_higher_work in translation.
warning: encountered undefined variable array_y_higher_work2 in translation.
warning: encountered undefined variable array_const_1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: variable iiif (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable iiif in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: variable jjjf (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable jjjf in translation.
warning: variable jjjf (declared type [found_h]) assigned type any.
warning: variable iiif (declared type [found_h]) assigned type any.
warning: variable glob_orig_start_sec (declared type convfloat) assigned type any.
warning: variable opt_iter (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__0 in translation.
warning: variable glob_large_float (declared type convfloat) assigned type any.
warning: variable glob_larger_float (declared type convfloat) assigned type any.
warning: variable glob_almost_1 (declared type convfloat) assigned type any.
warning: variable x_start (declared type [found_h]) assigned type any.
warning: variable x_end (declared type [found_h]) assigned type any.
warning: encountered undefined variable x_start in translation.
warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_h (declared type convfloat) assigned type any.
warning: variable glob_display_interval (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_max_minutes in translation.
warning: encountered undefined variable glob_max_hours in translation.
warning: encountered undefined variable x_end in translation.
warning: variable glob_check_sign (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_larger_float in translation.
warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_max_h in translation.
warning: encountered undefined variable glob_display_interval in translation.
warning: encountered undefined variable glob__10 in translation.
warning: variable display_max (declared type [found_h]) assigned type any.
warning: encountered undefined variable display_max in translation.
warning: variable min_value (declared type [found_h]) assigned type convfloat.
warning: variable est_answer (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_answer in translation.
warning: variable est_needed_step_err (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_needed_step_err in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable opt_iter in translation.
warning: encountered undefined variable found_h in translation.
warning: variable glob_next_display (declared type convfloat) assigned type any.
warning: variable order_diff (declared type [found_h]) assigned type fixnum.
warning: variable term_no (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable order_diff in translation.
warning: variable term_no (declared type [found_h]) assigned type any.
warning: variable r_order (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable r_order in translation.
warning: encountered undefined variable rows in translation.
warning: variable it (declared type [found_h]) assigned type any.
warning: encountered undefined variable it in translation.
warning: variable r_order (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_look_poles in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type any.
warning: encountered undefined variable estimated_step_error in translation.
warning: encountered undefined variable glob__2 in translation.
warning: variable opt_iter (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_optimize in translation.
warning: variable html_log_file (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_html_log in translation.
warning: variable current_iter (declared type [found_h]) assigned type fixnum.
warning: variable glob_clock_start_sec (declared type convfloat) assigned type any.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable debugl in translation.
warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable current_iter in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: variable calc_term (declared type [found_h]) assigned type fixnum.
warning: variable iii (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable calc_term in translation.
warning: variable iii (declared type [found_h]) assigned type any.
warning: variable temp_sum (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable temp_sum in translation.
warning: variable temp_sum (declared type [found_h]) assigned type any.
warning: encountered undefined variable html_log_file in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob_percent_done in translation.
warning: encountered undefined variable glob__100 in translation.
WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB__PI is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $LAST_MIN_POLE_EST is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H is neither declared nor
bound,
it will be treated as if it were declared SPECIAL.
"##############ECHO OF PROBLEM#################"
"##############temp/sing5_backpostode.ode#################"
"diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:20,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:c(-0.7),"
"x_end:c(-1.0),"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
""
""
""
""
""
""
""
""
"glob_type_given_pole:1,"
""
"array_given_rad_poles[1,1]:c(0.0),"
""
"array_given_rad_poles[1,2]:c(0.0),"
""
"array_given_ord_poles[1,1]:c(4.0),"
""
"array_given_ord_poles[1,2]:c(0.0),"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:8,"
"glob_max_minutes:(3.0),"
"glob_subiter_method:3,"
"glob_max_iter:100000,"
"glob_upper_ratio_limit:c(1.000001),"
"glob_lower_ratio_limit:c(0.999999),"
"glob_look_poles:false,"
"glob_h:c(0.001),"
"glob_display_interval:c(0.01),"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (c(1.0)/c(x)/c(x)/c(x)) "
"));"
""
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.701 " "
y[1] (closed_form) = -2.9029927158019686 " "
y[1] (numeric) = -2.9029927158019686 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 15
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.702 " "
y[1] (closed_form) = -2.8906044279296133 " "
y[1] (numeric) = -2.890604427929612 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.608958654728211000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 15
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.703 " "
y[1] (closed_form) = -2.878286527937843 " "
y[1] (numeric) = -2.8782865279378416 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.62868313011455100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.704 " "
y[1] (closed_form) = -2.866038516622841 " "
y[1] (numeric) = -2.8660385166228393 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 6.19795173406600600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.705 " "
y[1] (closed_form) = -2.8538598990233024 " "
y[1] (numeric) = -2.853859899023301 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.668300745969133400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.706 " "
y[1] (closed_form) = -2.8417501843784363 " "
y[1] (numeric) = -2.841750184378434 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 7.81365674384914900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.707 " "
y[1] (closed_form) = -2.829708886086427 " "
y[1] (numeric) = -2.8297088860864252 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 6.27752504200884600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.708 " "
y[1] (closed_form) = -2.817735521663382 " "
y[1] (numeric) = -2.81773552166338 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 7.88025005249437500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.709 " "
y[1] (closed_form) = -2.8058296127027247 " "
y[1] (numeric) = -2.8058296127027225 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 7.91368812702586400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.71 " "
y[1] (closed_form) = -2.7939906848350575 " "
y[1] (numeric) = -2.7939906848350544 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.11261089230652000000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.711 " "
y[1] (closed_form) = -2.782218267688465 " "
y[1] (numeric) = -2.782218267688463 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 7.9808477826404100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.712 " "
y[1] (closed_form) = -2.7705118948492777 " "
y[1] (numeric) = -2.770511894849274 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.28233114082831860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.713 " "
y[1] (closed_form) = -2.7588711038232527 " "
y[1] (numeric) = -2.7588711038232496 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.1267740869236320000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.714 " "
y[1] (closed_form) = -2.747295435997215 " "
y[1] (numeric) = -2.747295435997211 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 1.45481364555166660000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.715 " "
y[1] (closed_form) = -2.7357844366011035 " "
y[1] (numeric) = -2.735784436601099 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.6232609700850270000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.716 " "
y[1] (closed_form) = -2.7243376546704563 " "
y[1] (numeric) = -2.7243376546704527 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.30406510834291100000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.717 " "
y[1] (closed_form) = -2.712954643009312 " "
y[1] (numeric) = -2.712954643009308 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 1.47322879096023480000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.718 " "
y[1] (closed_form) = -2.701634958153512 " "
y[1] (numeric) = -2.701634958153508 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 1.47940152928072170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.719 " "
y[1] (closed_form) = -2.690378160334427 " "
y[1] (numeric) = -2.6903781603344226 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.65065720647561360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.72 " "
y[1] (closed_form) = -2.6791838134430725 " "
y[1] (numeric) = -2.679183813443069 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.32604327518492940000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.721 " "
y[1] (closed_form) = -2.6680514849946344 " "
y[1] (numeric) = -2.6680514849946304 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 1.49802314952651730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.722 " "
y[1] (closed_form) = -2.6569807460933728 " "
y[1] (numeric) = -2.656980746093368 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 1.8385459945591262000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.723 " "
y[1] (closed_form) = -2.6459711713979237 " "
y[1] (numeric) = -2.6459711713979193 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.67835997100240770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.724 " "
y[1] (closed_form) = -2.6350223390869854 " "
y[1] (numeric) = -2.635022339086981 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.68533375699553320000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.725 " "
y[1] (closed_form) = -2.6241338308253725 " "
y[1] (numeric) = -2.624133830825367 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 2.03079220106872040000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.726 " "
y[1] (closed_form) = -2.6133052317304517 " "
y[1] (numeric) = -2.613305231730446 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 2.20914099813285220000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.727 " "
y[1] (closed_form) = -2.602536130338945 " "
y[1] (numeric) = -2.602536130338939 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 2.3889193565551628000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.728 " "
y[1] (closed_form) = -2.591826118574096 " "
y[1] (numeric) = -2.5918261185740903 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 2.22744870370661370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.729 " "
y[1] (closed_form) = -2.5811747917131975 " "
y[1] (numeric) = -2.5811747917131913 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 2.4086896237562880000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.73 " "
y[1] (closed_form) = -2.57058174835547 " "
y[1] (numeric) = -2.5705817483554645 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 2.0730990257789020000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.731 " "
y[1] (closed_form) = -2.560046590390301 " "
y[1] (numeric) = -2.5600465903902943 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 2.6020378585123180000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.732 " "
y[1] (closed_form) = -2.549568922965815 " "
y[1] (numeric) = -2.549568922965809 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 2.43854907466811740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.733 " "
y[1] (closed_form) = -2.5391483544578075 " "
y[1] (numeric) = -2.5391483544578013 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 2.4485567875487390000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.734 " "
y[1] (closed_form) = -2.528784496438997 " "
y[1] (numeric) = -2.5287844964389894 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 2.985432953295230000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.735 " "
y[1] (closed_form) = -2.518476963648618 " "
y[1] (numeric) = -2.5184769636486117 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 2.4686542809959638000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.736 " "
y[1] (closed_form) = -2.5082253739623575 " "
y[1] (numeric) = -2.5082253739623503 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.83285044133663100000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.737 " "
y[1] (closed_form) = -2.4980293483625906 " "
y[1] (numeric) = -2.4980293483625835 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.84441308195937300000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.738 " "
y[1] (closed_form) = -2.4878885109089635 " "
y[1] (numeric) = -2.4878885109089564 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.8560071427818906000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.739 " "
y[1] (closed_form) = -2.4778024887092793 " "
y[1] (numeric) = -2.4778024887092727 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 2.68840562478445200000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.74 " "
y[1] (closed_form) = -2.467770911890707 " "
y[1] (numeric) = -2.4677709118907 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.87928969555650900000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.741 " "
y[1] (closed_form) = -2.4577934135712933 " "
y[1] (numeric) = -2.4577934135712853 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 3.2523505568704530000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.742 " "
y[1] (closed_form) = -2.4478696298317835 " "
y[1] (numeric) = -2.4478696298317764 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.9026984407209970000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.743 " "
y[1] (closed_form) = -2.4379991996877544 " "
y[1] (numeric) = -2.4379991996877473 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.91445024203085300000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.744 " "
y[1] (closed_form) = -2.4281817650620305 " "
y[1] (numeric) = -2.4281817650620234 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.92623371933586950000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.745 " "
y[1] (closed_form) = -2.4184169707574092 " "
y[1] (numeric) = -2.4184169707574013 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 3.3053050296771850000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.746 " "
y[1] (closed_form) = -2.4087044644296687 " "
y[1] (numeric) = -2.408704464429661 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 3.13426436449049100000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.747 " "
y[1] (closed_form) = -2.3990438965608756 " "
y[1] (numeric) = -2.3990438965608676 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 3.33199646274096040000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.748 " "
y[1] (closed_form) = -2.389434920432964 " "
y[1] (numeric) = -2.389434920432956 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 3.3453958963036706000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.749 " "
y[1] (closed_form) = -2.3798771921016093 " "
y[1] (numeric) = -2.3798771921016013 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 3.35883120516911050000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.75 " "
y[1] (closed_form) = -2.3703703703703702 " "
y[1] (numeric) = -2.3703703703703622 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 3.3723024372989130000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.751 " "
y[1] (closed_form) = -2.3609141167651133 " "
y[1] (numeric) = -2.360914116765105 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 3.57391017624664130000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.752 " "
y[1] (closed_form) = -2.351508095508702 " "
y[1] (numeric) = -2.351508095508694 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 3.39935286319814600000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.753 " "
y[1] (closed_form) = -2.342151973495964 " "
y[1] (numeric) = -2.3421519734959566 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 3.22332481106357760000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.754 " "
y[1] (closed_form) = -2.3328454202689146 " "
y[1] (numeric) = -2.332845420268906 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 3.6169113108996953000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.755 " "
y[1] (closed_form) = -2.323588107992243 " "
y[1] (numeric) = -2.3235881079922343 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 3.8224434728562070000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.756 " "
y[1] (closed_form) = -2.3143797114290665 " "
y[1] (numeric) = -2.3143797114290576 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 3.8376521160898840000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.757 " "
y[1] (closed_form) = -2.3052199079169307 " "
y[1] (numeric) = -2.3052199079169218 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 3.8529010470966790000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.758 " "
y[1] (closed_form) = -2.296108377344067 " "
y[1] (numeric) = -2.2961083773440585 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 3.6747808032089330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.759 " "
y[1] (closed_form) = -2.2870448021259016 " "
y[1] (numeric) = -2.2870448021258927 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 3.8835199855924430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.76 " "
y[1] (closed_form) = -2.2780288671818054 " "
y[1] (numeric) = -2.278028867181796 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 4.0938346046459617000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.761 " "
y[1] (closed_form) = -2.269060259912094 " "
y[1] (numeric) = -2.2690602599120853 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 3.91430071466913900000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.762 " "
y[1] (closed_form) = -2.26013867017527 " "
y[1] (numeric) = -2.2601386701752606 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 4.1262394780972045000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.763 " "
y[1] (closed_form) = -2.251263790265493 " "
y[1] (numeric) = -2.2512637902654844 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 3.7479814776197890000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.764 " "
y[1] (closed_form) = -2.2424353148903013 " "
y[1] (numeric) = -2.2424353148902925 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 3.96077609821077260000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.765 " "
y[1] (closed_form) = -2.23365294114855 " "
y[1] (numeric) = -2.2336529411485406 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 4.17516671236128840000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.766 " "
y[1] (closed_form) = -2.224916368508591 " "
y[1] (numeric) = -2.2249163685085813 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 4.39115948580592830000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.767 " "
y[1] (closed_form) = -2.216225298786674 " "
y[1] (numeric) = -2.216225298786665 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 4.2079988040732990000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.768 " "
y[1] (closed_form) = -2.2075794361255783 " "
y[1] (numeric) = -2.207579436125569 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 4.2244791984558117000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.769 " "
y[1] (closed_form) = -2.1989784869734565 " "
y[1] (numeric) = -2.198978486973447 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 4.2410025664629820000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.77 " "
y[1] (closed_form) = -2.190422160062909 " "
y[1] (numeric) = -2.190422160062899 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 4.6630517225310080000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.771 " "
y[1] (closed_form) = -2.181910166390266 " "
y[1] (numeric) = -2.181910166390255 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 4.8847753681968690000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.772 " "
y[1] (closed_form) = -2.17344221919509 " "
y[1] (numeric) = -2.17344221919508 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 4.6994816500500750000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.773 " "
y[1] (closed_form) = -2.1650180339398917 " "
y[1] (numeric) = -2.1650180339398815 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 4.7177675503995440000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.774 " "
y[1] (closed_form) = -2.1566373282900457 " "
y[1] (numeric) = -2.1566373282900346 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 5.1479356777406330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.775 " "
y[1] (closed_form) = -2.1482998220939207 " "
y[1] (numeric) = -2.14829982209391 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 4.9611981189912063000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.776 " "
y[1] (closed_form) = -2.140005237363217 " "
y[1] (numeric) = -2.140005237363207 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 4.7729097332194230000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.777 " "
y[1] (closed_form) = -2.1317532982535 " "
y[1] (numeric) = -2.1317532982534884 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 5.4163488174552290000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.778 " "
y[1] (closed_form) = -2.1235437310449305 " "
y[1] (numeric) = -2.123543731044919 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 5.4372882871689390000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.779 " "
y[1] (closed_form) = -2.115376264123207 " "
y[1] (numeric) = -2.1153762641231952 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 5.4582816551018700000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.78 " "
y[1] (closed_form) = -2.1072506279606866 " "
y[1] (numeric) = -2.107250627960676 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 5.0578421451064070000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.781 " "
y[1] (closed_form) = -2.0991665550977134 " "
y[1] (numeric) = -2.0991665550977023 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 5.2888753487856390000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.782 " "
y[1] (closed_form) = -2.091123780124123 " "
y[1] (numeric) = -2.0911237801241116 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 5.5215858409951570000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.783 " "
y[1] (closed_form) = -2.083122039660948 " "
y[1] (numeric) = -2.0831220396609367 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 5.542795494584140000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.784 " "
y[1] (closed_form) = -2.075161072342306 " "
y[1] (numeric) = -2.075161072342295 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 5.3500571084441630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.785 " "
y[1] (closed_form) = -2.06724061879747 " "
y[1] (numeric) = -2.067240618797459 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 5.3705553892946530000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.786 " "
y[1] (closed_form) = -2.0593604216331234 " "
y[1] (numeric) = -2.0593604216331114 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 5.8223944385815680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.787 " "
y[1] (closed_form) = -2.0515202254157905 " "
y[1] (numeric) = -2.0515202254157785 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 5.8446456034921820000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.788 " "
y[1] (closed_form) = -2.0437197766544553 " "
y[1] (numeric) = -2.043719776654443 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 6.0842479570055720000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.789 " "
y[1] (closed_form) = -2.0359588237833433 " "
y[1] (numeric) = -2.0359588237833317 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 5.6711949776300240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.79 " "
y[1] (closed_form) = -2.0282371171448905 " "
y[1] (numeric) = -2.028237117144879 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 5.6927857983168930000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.791 " "
y[1] (closed_form) = -2.020554408972873 " "
y[1] (numeric) = -2.020554408972861 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 5.9342171696563640000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.792 " "
y[1] (closed_form) = -2.0129104533757114 " "
y[1] (numeric) = -2.0129104533757 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 5.736131697631209000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.793 " "
y[1] (closed_form) = -2.00530500631995 " "
y[1] (numeric) = -2.005305006319937 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 6.422258481908469000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.794 " "
y[1] (closed_form) = -1.997737825613885 " "
y[1] (numeric) = -1.9977378256138727 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 6.113141131081080000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.795 " "
y[1] (closed_form) = -1.9902086708913818 " "
y[1] (numeric) = -1.9902086708913695 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 6.136267743928060000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.796 " "
y[1] (closed_form) = -1.98271730359583 " "
y[1] (numeric) = -1.982717303595818 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 6.0474625627193770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.797 " "
y[1] (closed_form) = -1.975263486964277 " "
y[1] (numeric) = -1.9752634869642645 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 6.2951084540685550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.798 " "
y[1] (closed_form) = -1.967846986011709 " "
y[1] (numeric) = -1.9678469860116963 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 6.4316700285615990000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.799 " "
y[1] (closed_form) = -1.9604675675154986 " "
y[1] (numeric) = -1.9604675675154855 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 6.6824016411448630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8 " "
y[1] (closed_form) = -1.953125 " "
y[1] (numeric) = -1.9531249999999867 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 6.8212102632969620000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.801 " "
y[1] (closed_form) = -1.9458190537213027 " "
y[1] (numeric) = -1.9458190537212896 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 6.7327080930379430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.802 " "
y[1] (closed_form) = -1.938549500652135 " "
y[1] (numeric) = -1.9385495006521223 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 6.5288724773182630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.803 " "
y[1] (closed_form) = -1.9313161144669193 " "
y[1] (numeric) = -1.9313161144669062 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 6.7832663914746430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.804 " "
y[1] (closed_form) = -1.9241186705269717 " "
y[1] (numeric) = -1.9241186705269584 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 6.9240408606674480000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.805 " "
y[1] (closed_form) = -1.9169569458658544 " "
y[1] (numeric) = -1.9169569458658409 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 7.0657407980068140000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.806 " "
y[1] (closed_form) = -1.9098307191748698 " "
y[1] (numeric) = -1.909830719174856 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 7.208369499522860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.807 " "
y[1] (closed_form) = -1.9027397707886982 " "
y[1] (numeric) = -1.9027397707886846 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 7.1185356549374770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.808 " "
y[1] (closed_form) = -1.8956838826711804 " "
y[1] (numeric) = -1.8956838826711664 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 7.379294743259380000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.809 " "
y[1] (closed_form) = -1.8886628384012343 " "
y[1] (numeric) = -1.8886628384012207 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 7.1715928460225360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.81 " "
y[1] (closed_form) = -1.8816764231589203 " "
y[1] (numeric) = -1.8816764231589065 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 7.3162236269297430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.811 " "
y[1] (closed_form) = -1.874724423711633 " "
y[1] (numeric) = -1.8747244237116194 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 7.2249130214086010000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.812 " "
y[1] (closed_form) = -1.8678066284004382 " "
y[1] (numeric) = -1.8678066284004247 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 7.251671931385320000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8130000000000001 " "
y[1] (closed_form) = -1.8609228271265388 " "
y[1] (numeric) = -1.8609228271265243 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 7.7557753119794630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8140000000000001 " "
y[1] (closed_form) = -1.8540728113378715 " "
y[1] (numeric) = -1.8540728113378573 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 7.6646691695714260000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8150000000000001 " "
y[1] (closed_form) = -1.8472563740158454 " "
y[1] (numeric) = -1.8472563740158308 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 7.9333568048234330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8160000000000001 " "
y[1] (closed_form) = -1.8404733096621957 " "
y[1] (numeric) = -1.8404733096621817 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 7.6006590461474880000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8170000000000001 " "
y[1] (closed_form) = -1.833723414285981 " "
y[1] (numeric) = -1.8337234142859666 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 7.8708158535167890000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8180000000000001 " "
y[1] (closed_form) = -1.8270064853906929 " "
y[1] (numeric) = -1.8270064853906787 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 7.7782179914720500000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8190000000000001 " "
y[1] (closed_form) = -1.8203223219615043 " "
y[1] (numeric) = -1.8203223219614901 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 7.8067793509717410000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8200000000000001 " "
y[1] (closed_form) = -1.8136707244526342 " "
y[1] (numeric) = -1.8136707244526193 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 8.2026954117964120000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8210000000000001 " "
y[1] (closed_form) = -1.807051494774835 " "
y[1] (numeric) = -1.8070514947748206 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 7.9869883962135920000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8220000000000001 " "
y[1] (closed_form) = -1.8004644362830107 " "
y[1] (numeric) = -1.8004644362829962 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 8.016209056549430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8230000000000001 " "
y[1] (closed_form) = -1.7939093537639414 " "
y[1] (numeric) = -1.7939093537639272 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 7.921723963022490000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8240000000000001 " "
y[1] (closed_form) = -1.7873860534241393 " "
y[1] (numeric) = -1.7873860534241248 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 8.0748640129968440000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8250000000000001 " "
y[1] (closed_form) = -1.780894342877813 " "
y[1] (numeric) = -1.780894342877799 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 7.8549354520784980000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8260000000000001 " "
y[1] (closed_form) = -1.7744340311349576 " "
y[1] (numeric) = -1.7744340311349427 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 8.384075298906170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8270000000000001 " "
y[1] (closed_form) = -1.7680049285895465 " "
y[1] (numeric) = -1.768004928589532 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 8.1633818360682430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8280000000000001 " "
y[1] (closed_form) = -1.761606847007855 " "
y[1] (numeric) = -1.7616068470078405 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 8.1930308937217010000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8290000000000001 " "
y[1] (closed_form) = -1.7552395995168795 " "
y[1] (numeric) = -1.7552395995168648 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 8.3492555256192740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8300000000000001 " "
y[1] (closed_form) = -1.7489030005928776 " "
y[1] (numeric) = -1.7489030005928627 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 8.5064686405900170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8310000000000001 " "
y[1] (closed_form) = -1.7425968660500166 " "
y[1] (numeric) = -1.7425968660500015 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 8.6646736425777280000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8320000000000001 " "
y[1] (closed_form) = -1.7363210130291304 " "
y[1] (numeric) = -1.7363210130291151 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 8.8238739408552660000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8330000000000001 " "
y[1] (closed_form) = -1.7300752599865836 " "
y[1] (numeric) = -1.7300752599865683 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 8.8557290507385060000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8340000000000001 " "
y[1] (closed_form) = -1.7238594266832443 " "
y[1] (numeric) = -1.7238594266832292 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 8.7588540580441120000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8350000000000001 " "
y[1] (closed_form) = -1.7176733341735615 " "
y[1] (numeric) = -1.7176733341735462 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 8.919669086671080000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8360000000000001 " "
y[1] (closed_form) = -1.7115168047947438 " "
y[1] (numeric) = -1.7115168047947287 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 8.822018628507070000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8370000000000001 " "
y[1] (closed_form) = -1.7053896621560487 " "
y[1] (numeric) = -1.7053896621560334 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 8.9839161570015620000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8380000000000001 " "
y[1] (closed_form) = -1.6992917311281652 " "
y[1] (numeric) = -1.69929173112815 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 9.0161550598821830000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8390000000000001 " "
y[1] (closed_form) = -1.6932228378327052 " "
y[1] (numeric) = -1.6932228378326895 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 9.3107455187979580000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8400000000000001 " "
y[1] (closed_form) = -1.6871828096317891 " "
y[1] (numeric) = -1.6871828096317734 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 9.344077511741489000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8410000000000001 " "
y[1] (closed_form) = -1.681171475117734 " "
y[1] (numeric) = -1.6811714751177191 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 8.8491797238798910000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8420000000000001 " "
y[1] (closed_form) = -1.6751886641028417 " "
y[1] (numeric) = -1.675188664102826 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 9.410979961543829000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8430000000000001 " "
y[1] (closed_form) = -1.6692342076092717 " "
y[1] (numeric) = -1.6692342076092561 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 9.31152876804120100000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8440000000000001 " "
y[1] (closed_form) = -1.6633079378590274 " "
y[1] (numeric) = -1.6633079378590125 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 8.9442178392573670000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8450000000000001 " "
y[1] (closed_form) = -1.6574096882640261 " "
y[1] (numeric) = -1.6574096882640112 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 8.9760477661737830000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8460000000000001 " "
y[1] (closed_form) = -1.6515392934162625 " "
y[1] (numeric) = -1.651539293416247 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 9.4112943038737760000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8470000000000001 " "
y[1] (closed_form) = -1.6456965890780682 " "
y[1] (numeric) = -1.6456965890780524 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 9.5796315398022360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8480000000000001 " "
y[1] (closed_form) = -1.6398814121724639 " "
y[1] (numeric) = -1.6398814121724485 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 9.3427961473935320000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8490000000000001 " "
y[1] (closed_form) = -1.6340936007736018 " "
y[1] (numeric) = -1.634093600773586 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 9.6476523390176560000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8500000000000001 " "
y[1] (closed_form) = -1.6283329940972922 " "
y[1] (numeric) = -1.6283329940972768 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 9.4090568669713580000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8510000000000001 " "
y[1] (closed_form) = -1.6225994324916295 " "
y[1] (numeric) = -1.6225994324916135 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 9.8528393603913860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8520000000000001 " "
y[1] (closed_form) = -1.6168927574276943 " "
y[1] (numeric) = -1.6168927574276786 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 9.7502860825216010000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8530000000000001 " "
y[1] (closed_form) = -1.6112128114903546 " "
y[1] (numeric) = -1.6112128114903388 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 9.7846583873018080000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8540000000000001 " "
y[1] (closed_form) = -1.605559438369143 " "
y[1] (numeric) = -1.6055594383691267 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 1.0095706064916499000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8550000000000001 " "
y[1] (closed_form) = -1.5999324828492234 " "
y[1] (numeric) = -1.5999324828492074 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 9.9924288843311640000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8560000000000001 " "
y[1] (closed_form) = -1.5943317908024446 " "
y[1] (numeric) = -1.5943317908024288 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 9.8882597967531230000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8570000000000001 " "
y[1] (closed_form) = -1.5887572091784725 " "
y[1] (numeric) = -1.588757209178457 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 9.783195478174639000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8580000000000001 " "
y[1] (closed_form) = -1.5832085859960079 " "
y[1] (numeric) = -1.583208585995992 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.0097981842704942000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8590000000000001 " "
y[1] (closed_form) = -1.5776857703340827 " "
y[1] (numeric) = -1.5776857703340665 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 1.0274071341909166000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8600000000000001 " "
y[1] (closed_form) = -1.5721886123234425 " "
y[1] (numeric) = -1.5721886123234265 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.0168761832574097000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8610000000000001 " "
y[1] (closed_form) = -1.5667169631380051 " "
y[1] (numeric) = -1.5667169631379894 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 1.0062549471667742000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8620000000000001 " "
y[1] (closed_form) = -1.5612706749863983 " "
y[1] (numeric) = -1.5612706749863825 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 1.0097651356844045000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8630000000000001 " "
y[1] (closed_form) = -1.555849601103577 " "
y[1] (numeric) = -1.5558496011035612 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 1.0132834779463813000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8640000000000001 " "
y[1] (closed_form) = -1.550453595742518 " "
y[1] (numeric) = -1.5504535957425023 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 1.0168099834118044000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8650000000000001 " "
y[1] (closed_form) = -1.5450825141659918 " "
y[1] (numeric) = -1.5450825141659759 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.034715713110756900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8660000000000001 " "
y[1] (closed_form) = -1.5397362126384084 " "
y[1] (numeric) = -1.539736212638392 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 1.0671503748227452000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8670000000000001 " "
y[1] (closed_form) = -1.5344145484177392 " "
y[1] (numeric) = -1.5344145484177232 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.0419095394453853000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8680000000000001 " "
y[1] (closed_form) = -1.5291173797475177 " "
y[1] (numeric) = -1.5291173797475013 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 1.0745611149332038000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8690000000000001 " "
y[1] (closed_form) = -1.523844565848903 " "
y[1] (numeric) = -1.5238445658488873 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 1.0345652898591245000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8700000000000001 " "
y[1] (closed_form) = -1.5185959669128308 " "
y[1] (numeric) = -1.5185959669128144 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 1.0820060847294145000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8710000000000001 " "
y[1] (closed_form) = -1.51337144409222 " "
y[1] (numeric) = -1.5133714440922035 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 1.0857414304066283000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8720000000000001 " "
y[1] (closed_form) = -1.5081708594942653 " "
y[1] (numeric) = -1.5081708594942493 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.0600398127280647000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8730000000000001 " "
y[1] (closed_form) = -1.5029940761727947 " "
y[1] (numeric) = -1.502994076172778 " "
absolute error = 1.665334536937734800000000000000E-14 " "
relative error = 1.108011377648487900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8740000000000001 " "
y[1] (closed_form) = -1.49784095812069 " "
y[1] (numeric) = -1.4978409581206735 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 1.0969990288600687000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8750000000000001 " "
y[1] (closed_form) = -1.4927113702623904 " "
y[1] (numeric) = -1.4927113702623738 " "
absolute error = 1.665334536937734800000000000000E-14 " "
relative error = 1.1156440354875842000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8760000000000001 " "
y[1] (closed_form) = -1.4876051784464521 " "
y[1] (numeric) = -1.4876051784464357 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 1.1045471609349992000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8770000000000001 " "
y[1] (closed_form) = -1.4825222494381838 " "
y[1] (numeric) = -1.4825222494381673 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 1.108334176480596900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8780000000000001 " "
y[1] (closed_form) = -1.4774624509123433 " "
y[1] (numeric) = -1.477462450912327 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 1.0971010565796753000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8790000000000001 " "
y[1] (closed_form) = -1.4724256514459058 " "
y[1] (numeric) = -1.4724256514458895 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 1.1008539645862578000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8800000000000001 " "
y[1] (closed_form) = -1.4674117205108934 " "
y[1] (numeric) = -1.4674117205108768 " "
absolute error = 1.665334536937734800000000000000E-14 " "
relative error = 1.1348788575560326000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8810000000000001 " "
y[1] (closed_form) = -1.4624205284672716 " "
y[1] (numeric) = -1.4624205284672551 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 1.123568798755415100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8820000000000001 " "
y[1] (closed_form) = -1.4574519465559126 " "
y[1] (numeric) = -1.457451946555896 " "
absolute error = 1.665334536937734800000000000000E-14 " "
relative error = 1.1426342672038463000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8830000000000001 " "
y[1] (closed_form) = -1.4525058468916163 " "
y[1] (numeric) = -1.4525058468915997 " "
absolute error = 1.665334536937734800000000000000E-14 " "
relative error = 1.146525186457304000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8840000000000001 " "
y[1] (closed_form) = -1.4475821024562008 " "
y[1] (numeric) = -1.4475821024561841 " "
absolute error = 1.665334536937734800000000000000E-14 " "
relative error = 1.1504249286531384000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8850000000000001 " "
y[1] (closed_form) = -1.4426805870916508 " "
y[1] (numeric) = -1.442680587091634 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 1.1697246171671344000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8860000000000001 " "
y[1] (closed_form) = -1.4378011754933295 " "
y[1] (numeric) = -1.4378011754933124 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 1.1891376130890313000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8870000000000001 " "
y[1] (closed_form) = -1.432943743203252 " "
y[1] (numeric) = -1.4329437432032346 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 1.208664280527571900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8880000000000001 " "
y[1] (closed_form) = -1.428108166603418 " "
y[1] (numeric) = -1.4281081666034008 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 1.2127568197684016000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8890000000000001 " "
y[1] (closed_form) = -1.4232943229092072 " "
y[1] (numeric) = -1.42329432290919 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 1.216858586827741000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8900000000000001 " "
y[1] (closed_form) = -1.4185020901628294 " "
y[1] (numeric) = -1.418502090162812 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 1.2209695920972767000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8910000000000001 " "
y[1] (closed_form) = -1.4137313472268367 " "
y[1] (numeric) = -1.4137313472268196 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 1.2093835658921755000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8920000000000001 " "
y[1] (closed_form) = -1.4089819737776954 " "
y[1] (numeric) = -1.4089819737776779 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.2449785813828389000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8930000000000001 " "
y[1] (closed_form) = -1.4042538502994077 " "
y[1] (numeric) = -1.4042538502993909 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 1.2017335733638398000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8940000000000001 " "
y[1] (closed_form) = -1.3995468580772032 " "
y[1] (numeric) = -1.3995468580771864 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 1.2057752748262382000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8950000000000001 " "
y[1] (closed_form) = -1.3948608791912733 " "
y[1] (numeric) = -1.3948608791912558 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.257582318836548000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8960000000000001 " "
y[1] (closed_form) = -1.3901957965105678 " "
y[1] (numeric) = -1.3901957965105507 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 1.229858025908471000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8970000000000001 " "
y[1] (closed_form) = -1.3855514936866513 " "
y[1] (numeric) = -1.3855514936866344 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 1.2179547314694625000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8980000000000001 " "
y[1] (closed_form) = -1.380927855147605 " "
y[1] (numeric) = -1.380927855147588 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 1.2220327015199936000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8990000000000001 " "
y[1] (closed_form) = -1.3763247660919886 " "
y[1] (numeric) = -1.376324766091971 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.2745192284002727000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9000000000000001 " "
y[1] (closed_form) = -1.3717421124828526 " "
y[1] (numeric) = -1.3717421124828355 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 1.2464029808256787000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9010000000000001 " "
y[1] (closed_form) = -1.3671797810418103 " "
y[1] (numeric) = -1.3671797810417927 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.2830444124700693000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9020000000000001 " "
y[1] (closed_form) = -1.3626376592431504 " "
y[1] (numeric) = -1.3626376592431335 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 1.2384356075756393000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9030000000000001 " "
y[1] (closed_form) = -1.3581156353080162 " "
y[1] (numeric) = -1.3581156353079993 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 1.242559141179101100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9040000000000001 " "
y[1] (closed_form) = -1.353613598198624 " "
y[1] (numeric) = -1.3536135981986062 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.312307176704052800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9050000000000001 " "
y[1] (closed_form) = -1.349131437612536 " "
y[1] (numeric) = -1.3491314376125187 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 1.2837503227114416000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9060000000000001 " "
y[1] (closed_form) = -1.3446690439769917 " "
y[1] (numeric) = -1.3446690439769744 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 1.2880105526136282000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9070000000000001 " "
y[1] (closed_form) = -1.3402263084432766 " "
y[1] (numeric) = -1.340226308443259 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.3088478922229646000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9080000000000001 " "
y[1] (closed_form) = -1.3358031228811487 " "
y[1] (numeric) = -1.3358031228811311 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.313181822126808000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9090000000000001 " "
y[1] (closed_form) = -1.3313993798733115 " "
y[1] (numeric) = -1.331399379873294 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.3175253086528121000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9100000000000001 " "
y[1] (closed_form) = -1.3270149727099367 " "
y[1] (numeric) = -1.327014972709919 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.3386109998236867000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9110000000000001 " "
y[1] (closed_form) = -1.3226497953832326 " "
y[1] (numeric) = -1.3226497953832148 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.343028854350337100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9120000000000001 " "
y[1] (closed_form) = -1.3183037425820627 " "
y[1] (numeric) = -1.318303742582045 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.3474564184434715000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9130000000000001 " "
y[1] (closed_form) = -1.3139767096866095 " "
y[1] (numeric) = -1.313976709686592 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.3349950314767162000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9140000000000001 " "
y[1] (closed_form) = -1.3096685927630873 " "
y[1] (numeric) = -1.3096685927630696 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.3563407179617576000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9150000000000001 " "
y[1] (closed_form) = -1.305379288558497 " "
y[1] (numeric) = -1.3053792885584792 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.360797474703191000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9160000000000001 " "
y[1] (closed_form) = -1.3011086944954313 " "
y[1] (numeric) = -1.3011086944954136 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.3652639836436722000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9170000000000001 " "
y[1] (closed_form) = -1.296856708666922 " "
y[1] (numeric) = -1.296856708666905 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 1.3183749958622937000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9180000000000001 " "
y[1] (closed_form) = -1.292623229831336 " "
y[1] (numeric) = -1.2926232298313185 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.3570484719949158000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9190000000000002 " "
y[1] (closed_form) = -1.2884081574073076 " "
y[1] (numeric) = -1.2884081574072903 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 1.3442540769847977000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9200000000000002 " "
y[1] (closed_form) = -1.2842113914687259 " "
y[1] (numeric) = -1.2842113914687086 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 1.3486470606949308000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9210000000000002 " "
y[1] (closed_form) = -1.2800328327397565 " "
y[1] (numeric) = -1.2800328327397388 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.3877431843667418000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9220000000000002 " "
y[1] (closed_form) = -1.2758723825899103 " "
y[1] (numeric) = -1.2758723825898926 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.3922684303224747000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9230000000000002 " "
y[1] (closed_form) = -1.2717299430291555 " "
y[1] (numeric) = -1.271729943029138 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.3793434592956907000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9240000000000002 " "
y[1] (closed_form) = -1.2676054167030715 " "
y[1] (numeric) = -1.2676054167030537 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.4013484133101892000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9250000000000002 " "
y[1] (closed_form) = -1.2634987068880417 " "
y[1] (numeric) = -1.2634987068880235 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 1.4410507509499132000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9260000000000002 " "
y[1] (closed_form) = -1.2594097174864913 " "
y[1] (numeric) = -1.2594097174864731 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 1.445729483506853200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9270000000000002 " "
y[1] (closed_form) = -1.255338353022166 " "
y[1] (numeric) = -1.255338353022148 " "
absolute error = 1.798561299892753600000000000000E-14 " "
relative error = 1.4327303037964265000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9280000000000002 " "
y[1] (closed_form) = -1.25128451863545 " "
y[1] (numeric) = -1.2512845186354316 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 1.472862641094253000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9290000000000002 " "
y[1] (closed_form) = -1.2472481200787222 " "
y[1] (numeric) = -1.247248120078704 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 1.4598264219234390000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9300000000000002 " "
y[1] (closed_form) = -1.243229063711759 " "
y[1] (numeric) = -1.243229063711741 " "
absolute error = 1.798561299892753600000000000000E-14 " "
relative error = 1.4466853714978367000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9310000000000002 " "
y[1] (closed_form) = -1.2392272564971691 " "
y[1] (numeric) = -1.2392272564971507 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 1.487193096516571000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9320000000000002 " "
y[1] (closed_form) = -1.2352426059958712 " "
y[1] (numeric) = -1.2352426059958526 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 1.5099662789452853000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9330000000000002 " "
y[1] (closed_form) = -1.2312750203626102 " "
y[1] (numeric) = -1.2312750203625917 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 1.49679818919335000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9340000000000002 " "
y[1] (closed_form) = -1.227324408341513 " "
y[1] (numeric) = -1.2273244083414943 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 1.5197079669349028000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9350000000000002 " "
y[1] (closed_form) = -1.223390679261677 " "
y[1] (numeric) = -1.2233906792616585 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 1.524594483992559000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9360000000000002 " "
y[1] (closed_form) = -1.2194737430328042 " "
y[1] (numeric) = -1.2194737430327858 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 1.5112832329577952000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9370000000000002 " "
y[1] (closed_form) = -1.2155735101408665 " "
y[1] (numeric) = -1.2155735101408474 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 1.5709322278123497000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9380000000000002 " "
y[1] (closed_form) = -1.2116898916438068 " "
y[1] (numeric) = -1.2116898916437882 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 1.5393168617094952000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9390000000000002 " "
y[1] (closed_form) = -1.207822799167286 " "
y[1] (numeric) = -1.2078227991672674 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 1.54424530043329000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9400000000000002 " "
y[1] (closed_form) = -1.2039721449004548 " "
y[1] (numeric) = -1.2039721449004361 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 1.5491842475512396000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9410000000000002 " "
y[1] (closed_form) = -1.2001378415917683 " "
y[1] (numeric) = -1.200137841591749 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.6096384897634763000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9420000000000002 " "
y[1] (closed_form) = -1.1963198025448316 " "
y[1] (numeric) = -1.196319802544813 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 1.5590937117337955000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9430000000000002 " "
y[1] (closed_form) = -1.19251794161429 " "
y[1] (numeric) = -1.192517941614271 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 1.5826840636945513000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9440000000000002 " "
y[1] (closed_form) = -1.1887321732017389 " "
y[1] (numeric) = -1.1887321732017198 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 1.6064035662566317000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9450000000000002 " "
y[1] (closed_form) = -1.1849624122516809 " "
y[1] (numeric) = -1.1849624122516624 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 1.555298465016898000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9460000000000002 " "
y[1] (closed_form) = -1.181208574247515 " "
y[1] (numeric) = -1.181208574247496 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 1.59783731934482000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9470000000000002 " "
y[1] (closed_form) = -1.1774705752075507 " "
y[1] (numeric) = -1.1774705752075323 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 1.5651942899319610000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9480000000000002 " "
y[1] (closed_form) = -1.1737483316810706 " "
y[1] (numeric) = -1.1737483316810517 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 1.6079930347245874000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9490000000000002 " "
y[1] (closed_form) = -1.17004176074441 " "
y[1] (numeric) = -1.1700417607443911 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 1.6130869898711720000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9500000000000002 " "
y[1] (closed_form) = -1.1663507799970831 " "
y[1] (numeric) = -1.1663507799970645 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 1.5991541424398306000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9510000000000002 " "
y[1] (closed_form) = -1.1626753075579352 " "
y[1] (numeric) = -1.162675307557916 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.661502614092037000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9520000000000002 " "
y[1] (closed_form) = -1.1590152620613243 " "
y[1] (numeric) = -1.159015262061305 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.6667494605826513000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9530000000000002 " "
y[1] (closed_form) = -1.1553705626533437 " "
y[1] (numeric) = -1.1553705626533244 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.6720073414466805000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9540000000000002 " "
y[1] (closed_form) = -1.1517411289880677 " "
y[1] (numeric) = -1.1517411289880486 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 1.6579972307084753000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9550000000000002 " "
y[1] (closed_form) = -1.1481268812238337 " "
y[1] (numeric) = -1.1481268812238146 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 1.6632165256158526000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9560000000000002 " "
y[1] (closed_form) = -1.1445277400195524 " "
y[1] (numeric) = -1.1445277400195335 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 1.6490462186880010000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9570000000000002 " "
y[1] (closed_form) = -1.1409436265310517 " "
y[1] (numeric) = -1.1409436265310329 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 1.6542264648089514000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9580000000000002 " "
y[1] (closed_form) = -1.1373744624074487 " "
y[1] (numeric) = -1.1373744624074293 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.6984626670435440000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9590000000000002 " "
y[1] (closed_form) = -1.1338201697875516 " "
y[1] (numeric) = -1.1338201697875323 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.7037869975533590000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9600000000000002 " "
y[1] (closed_form) = -1.1302806712962958 " "
y[1] (numeric) = -1.1302806712962763 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.7287675291299828000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9610000000000002 " "
y[1] (closed_form) = -1.126755890041204 " "
y[1] (numeric) = -1.1267558900411843 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.7538820975326888000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9620000000000002 " "
y[1] (closed_form) = -1.1232457496088786 " "
y[1] (numeric) = -1.123245749608859 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.7395948518128543000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9630000000000002 " "
y[1] (closed_form) = -1.1197501740615246 " "
y[1] (numeric) = -1.1197501740615052 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.7251955905850394000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9640000000000002 " "
y[1] (closed_form) = -1.1162690879334987 " "
y[1] (numeric) = -1.116269087933479 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.7703589620055035000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9650000000000002 " "
y[1] (closed_form) = -1.1128024162278853 " "
y[1] (numeric) = -1.1128024162278662 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 1.716013170449672000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9660000000000002 " "
y[1] (closed_form) = -1.10935008441311 " "
y[1] (numeric) = -1.1093500844130901 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.7814006701755156000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9670000000000002 " "
y[1] (closed_form) = -1.1059120184195657 " "
y[1] (numeric) = -1.1059120184195461 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.7668607364740307000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9680000000000002 " "
y[1] (closed_form) = -1.1024881446362838 " "
y[1] (numeric) = -1.1024881446362638 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.812628511288495000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9690000000000002 " "
y[1] (closed_form) = -1.0990783899076182 " "
y[1] (numeric) = -1.0990783899075982 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.818251966989593000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9700000000000002 " "
y[1] (closed_form) = -1.095682681529967 " "
y[1] (numeric) = -1.095682681529947 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.823887041396688700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9710000000000002 " "
y[1] (closed_form) = -1.0923009472485148 " "
y[1] (numeric) = -1.0923009472484948 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.8295337465001904000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9720000000000002 " "
y[1] (closed_form) = -1.0889331152540043 " "
y[1] (numeric) = -1.0889331152539845 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.8148010710206122000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9730000000000002 " "
y[1] (closed_form) = -1.0855791141795355 " "
y[1] (numeric) = -1.0855791141795157 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.8204080734607345000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9740000000000002 " "
y[1] (closed_form) = -1.082238873097388 " "
y[1] (numeric) = -1.0822388730973678 " "
absolute error = 2.02060590481778500000000000000E-14 " "
relative error = 1.8670609188475856000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9750000000000002 " "
y[1] (closed_form) = -1.0789123215158707 " "
y[1] (numeric) = -1.0789123215158511 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.8110762889378426000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9760000000000002 " "
y[1] (closed_form) = -1.0755993893762024 " "
y[1] (numeric) = -1.0755993893761826 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.8372983504377785000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9770000000000002 " "
y[1] (closed_form) = -1.0723000070494066 " "
y[1] (numeric) = -1.0723000070493869 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.842951572172959000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9780000000000002 " "
y[1] (closed_form) = -1.0690141053332431 " "
y[1] (numeric) = -1.0690141053332232 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.8693873489183957000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9790000000000002 " "
y[1] (closed_form) = -1.0657416154491575 " "
y[1] (numeric) = -1.0657416154491377 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.8542927809006587000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9800000000000002 " "
y[1] (closed_form) = -1.0624824690392602 " "
y[1] (numeric) = -1.06248246903924 " "
absolute error = 2.02060590481778500000000000000E-14 " "
relative error = 1.901778112767261700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9810000000000002 " "
y[1] (closed_form) = -1.0592365981633245 " "
y[1] (numeric) = -1.0592365981633047 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.865680422352691000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9820000000000002 " "
y[1] (closed_form) = -1.0560039352958164 " "
y[1] (numeric) = -1.0560039352957964 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.892418557858379000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9830000000000002 " "
y[1] (closed_form) = -1.0527844133229414 " "
y[1] (numeric) = -1.052784413322921 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 1.9403881169388634000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9840000000000002 " "
y[1] (closed_form) = -1.0495779655397186 " "
y[1] (numeric) = -1.0495779655396982 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 1.9463159787846965000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9850000000000002 " "
y[1] (closed_form) = -1.04638452564708 " "
y[1] (numeric) = -1.0463845256470603 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.8885953828595717000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9860000000000002 " "
y[1] (closed_form) = -1.043204027748993 " "
y[1] (numeric) = -1.043204027748973 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.915638160099321000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9870000000000002 " "
y[1] (closed_form) = -1.0400364063495995 " "
y[1] (numeric) = -1.0400364063495793 " "
absolute error = 2.02060590481778500000000000000E-14 " "
relative error = 1.942822282452462000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9880000000000002 " "
y[1] (closed_form) = -1.0368815963503883 " "
y[1] (numeric) = -1.0368815963503686 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.9059041946434277000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9890000000000002 " "
y[1] (closed_form) = -1.0337395330473855 " "
y[1] (numeric) = -1.0337395330473655 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.933176956514516300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9900000000000002 " "
y[1] (closed_form) = -1.0306101521283642 " "
y[1] (numeric) = -1.0306101521283442 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.939046923027377000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9910000000000002 " "
y[1] (closed_form) = -1.0274933896700826 " "
y[1] (numeric) = -1.027493389670063 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.901708120932712000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9920000000000002 " "
y[1] (closed_form) = -1.0243891821355435 " "
y[1] (numeric) = -1.024389182135524 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.9074708689004197000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9930000000000002 " "
y[1] (closed_form) = -1.0212974663712702 " "
y[1] (numeric) = -1.0212974663712509 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.891503823769904000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9940000000000002 " "
y[1] (closed_form) = -1.0182181796046117 " "
y[1] (numeric) = -1.0182181796045924 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.89722409356108000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9950000000000002 " "
y[1] (closed_form) = -1.0151512594410643 " "
y[1] (numeric) = -1.0151512594410452 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 1.8810828283921688000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9960000000000002 " "
y[1] (closed_form) = -1.0120966438616188 " "
y[1] (numeric) = -1.0120966438615993 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.9306382796457922000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9970000000000002 " "
y[1] (closed_form) = -1.009054271220123 " "
y[1] (numeric) = -1.0090542712201034 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.936459295670546000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9980000000000002 " "
y[1] (closed_form) = -1.0060240802406728 " "
y[1] (numeric) = -1.0060240802406537 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 1.898149000467699000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9990000000000002 " "
y[1] (closed_form) = -1.0030060100150204 " "
y[1] (numeric) = -1.003006010015001 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.9481364057938333000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
"Finished!"
"diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; "
Iterations = 300
"Total Elapsed Time "= 7 Seconds
"Elapsed Time(since restart) "= 7 Seconds
"Expected Time Remaining "= 0 Seconds
"Optimized Time Remaining "= 0 Seconds
"Expected Total Time "= 7 Seconds
"Time to Timeout "= 2 Minutes 52 Seconds
Percent Done = 0.0 "%"
(%o255) temp/diffeq.sing5_back.max