(%i1) batch("temp/diffeq.sing1_back.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.sing1_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_tmp7,[20],convfloat)
(%i193) completearray(array_tmp8,[20],convfloat)
(%i194) completearray(array_tmp9,[20],convfloat)
(%i195) completearray(array_m1,[20],convfloat)
(%i196) completearray(array_y_higher,[2,20],convfloat)
(%i197) completearray(array_y_higher_work,[2,20],convfloat)
(%i198) completearray(array_y_higher_work2,[2,20],convfloat)
(%i199) completearray(array_y_set_initial,[2,20],convfloat)
(%i200) completearray(array_given_rad_poles,[2,3],convfloat)
(%i201) completearray(array_given_ord_poles,[2,3],convfloat)
(%i202) completearray(array_rad_test_poles,[2,4],convfloat)
(%i203) completearray(array_ord_test_poles,[2,4],convfloat)
(%i204) completearray(array_fact_2,[20,20],convfloat)
(%i205) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i206) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i207) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i208) 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))
(%i209) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i210) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i211) 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)
(%i212) 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)
(%i213) 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)
(%i214) 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)
(%i215) 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)
(%i216) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i217) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i218) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i219) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i220) log_revs(file,revs):=printf(file,revs)
(%i221) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i222) 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)
(%i223) logstart(file):=(printf(file,""),0)
(%i224) logend(file):=(printf(file,"
~%"),0)
(%i225) 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)
(%i226) 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)
(%i227) 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)
(%i228) 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)
(%i229) 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)
(%i230) c(in_val):=(ret:in_val,ret)
(%i231) 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)
(%i232) 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)
(%i233) 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)
(%i234) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i235) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i236) 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)
(%i237) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i238) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i239) 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)
(%i240) log10(x):=log(x)/glob_log_10
(%i241) c(x):=x
(%i242) 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
(%i243) 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)
(%i244) exact_soln_y(x):=block(c(1.0)/(c(1.0E-6)+c(x)*c(x)))
c(1.0)
(%o244) exact_soln_y(x) := block(---------------------)
c(1.0E-6) + c(x) c(x)
(%i245) 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)
(%i246) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i247) 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)
(%i248) 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)
(%i249) 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))
(%i250) 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))
(%i251) 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(35)
*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)
(%i252) 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)
(%i253) 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)
(%i254) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),
array_tmp1[1]:neg(array_const_2D0[1]),
array_tmp2[1]:array_tmp1[1]*array_x[1],
array_tmp3[1]:array_x[1]*array_x[1],
array_tmp4[1]:array_const_0D000001[1]+array_tmp3[1],
array_tmp5[1]:array_tmp2[1]/array_tmp4[1],
array_tmp6[1]:array_x[1]*array_x[1],
array_tmp7[1]:array_const_0D000001[1]+array_tmp6[1],
array_tmp8[1]:array_tmp5[1]/array_tmp7[1],
array_tmp9[1]:array_tmp8[1]+array_const_0D0[1],
if not array_y_set_initial[1,2]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp9[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]:array_tmp1[1]*array_x[2],
array_tmp3[2]:array_x[2]*array_x[1]
+array_x[1]*array_x[2],
array_tmp4[2]:array_tmp3[2],
array_tmp5[2]:(array_tmp2[2]
-array_tmp5[1]*array_tmp4[2])
/array_tmp4[1],
array_tmp6[2]:array_x[2]*array_x[1]
+array_x[1]*array_x[2],
array_tmp7[2]:array_tmp6[2],
array_tmp8[2]:(array_tmp5[2]
-ats(2,array_tmp7,array_tmp8,2))
/array_tmp7[1],
array_tmp9[2]:array_tmp8[2],
if not array_y_set_initial[1,3]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp9[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_tmp3[3]:array_x[2]*array_x[2],
array_tmp4[3]:array_tmp3[3],
array_tmp5[3]:neg(ats(3,array_tmp4,array_tmp5,2))
/array_tmp4[1],
array_tmp6[3]:array_x[2]*array_x[2],
array_tmp7[3]:array_tmp6[3],
array_tmp8[3]:(array_tmp5[3]
-ats(3,array_tmp7,array_tmp8,2))
/array_tmp7[1],
array_tmp9[3]:array_tmp8[3],
if not array_y_set_initial[1,4]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp9[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_tmp4[4]:array_tmp3[4],
array_tmp5[4]:neg(ats(4,array_tmp4,array_tmp5,2))
/array_tmp4[1],
array_tmp7[4]:array_tmp6[4],
array_tmp8[4]:(array_tmp5[4]
-ats(4,array_tmp7,array_tmp8,2))
/array_tmp7[1],
array_tmp9[4]:array_tmp8[4],
if not array_y_set_initial[1,5]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp9[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_tmp4[5]:array_tmp3[5],
array_tmp5[5]:neg(ats(5,array_tmp4,array_tmp5,2))
/array_tmp4[1],
array_tmp7[5]:array_tmp6[5],
array_tmp8[5]:(array_tmp5[5]
-ats(5,array_tmp7,array_tmp8,2))
/array_tmp7[1],
array_tmp9[5]:array_tmp8[5],
if not array_y_set_initial[1,6]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp9[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_tmp4[kkk]:array_tmp3[kkk],
array_tmp5[kkk]
:neg(ats(kkk,array_tmp4,array_tmp5,2))
/array_tmp4[1],array_tmp7[kkk]:array_tmp6[kkk],
array_tmp8[kkk]
:(array_tmp5[kkk]
-ats(kkk,array_tmp7,array_tmp8,2))
/array_tmp7[1],array_tmp9[kkk]:array_tmp8[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_tmp9[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)
(%i255) exact_soln_y(x):=block(c(1.0)/(c(1.0E-6)+c(x)*c(x)))
c(1.0)
(%o255) exact_soln_y(x) := block(---------------------)
c(1.0E-6) + c(x) c(x)
(%i256) 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_tmp7[term]:c(0.0),term:1+term),
term:1,
while term <= 20 do (array_tmp8[term]:c(0.0),term:1+term),
term:1,
while term <= 20 do (array_tmp9[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_tmp7),
zero_ats_ar(array_tmp8),zero_ats_ar(array_tmp9),
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_2D0),
array_const_2D0[1]:c(2.0),zero_ats_ar(array_const_0D000001),
array_const_0D000001[1]:c(1.0E-6),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/sing1_backpostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; "),
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(-1.5),"),
omniout_str(always,"x_end:c(-2.0),"),
omniout_str(always,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(always,"glob_look_poles:true,"),
omniout_str(always,"glob_max_h:c(0.1),"),
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:2,"),
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(0.001),"),
omniout_str(always,""),
omniout_str(always,"array_given_ord_poles[1,1]:c(1.0),"),
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,""),
omniout_str(always,
" (c(1.0) / (c(x) * c(x) + c(0.000001))) "),
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(-1.5),x_end:c(-2.0),
array_y_init[1+0]:exact_soln_y(x_start),
glob_look_poles:true,glob_max_h:c(0.1),
glob_type_given_pole:2,array_given_rad_poles[1,1]:c(0.0),
array_given_rad_poles[1,2]:c(0.001),
array_given_ord_poles[1,1]:c(1.0),
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 ( 2.0 ) * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; "),
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,
"2015-04-24T23:03:56-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"sing1_back"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; "),
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,
"sing1_back diffeq.max"),
logitem_str(html_log_file,
"sing1_back maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i257) main():=(glob_iolevel:2,compile(all),main_prog())
(%i258) 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_2D0 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_const_0D000001 in translation.
warning: encountered undefined variable array_tmp4 in translation.
warning: encountered undefined variable array_tmp5 in translation.
warning: encountered undefined variable array_tmp6 in translation.
warning: encountered undefined variable array_tmp7 in translation.
warning: encountered undefined variable array_tmp8 in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp9 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_max_h (declared type convfloat) assigned type any.
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/sing1_backpostode.ode#################"
"diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:20,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:c(-1.5),"
"x_end:c(-2.0),"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
"glob_max_h:c(0.1),"
""
""
""
""
""
""
""
"glob_type_given_pole:2,"
""
"array_given_rad_poles[1,1]:c(0.0),"
""
"array_given_rad_poles[1,2]:c(0.001),"
""
"array_given_ord_poles[1,1]:c(1.0),"
""
"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(0.000001))) "
"));"
""
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.501 " "
y[1] (closed_form) = 0.44385224691322955 " "
y[1] (numeric) = 0.44385224691322955 " "
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] = -1.5019999999999998 " "
y[1] (closed_form) = 0.44326142894186854 " "
y[1] (numeric) = 0.4432614289418685 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.252334347334738000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5029999999999997 " "
y[1] (closed_form) = 0.4426717898548481 " "
y[1] (numeric) = 0.44267178985484795 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 3.76200737228771060000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5039999999999996 " "
y[1] (closed_form) = 0.4420833265178823 " "
y[1] (numeric) = 0.44208332651788207 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 5.022686710987042000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5049999999999994 " "
y[1] (closed_form) = 0.4414960358070948 " "
y[1] (numeric) = 0.4414960358070945 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 6.28671004143654500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5059999999999993 " "
y[1] (closed_form) = 0.44090991460897716 " "
y[1] (numeric) = 0.4409099146089769 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 6.29506724525441100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5069999999999992 " "
y[1] (closed_form) = 0.4403249598203478 " "
y[1] (numeric) = 0.4403249598203475 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 7.56411600022487900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5079999999999991 " "
y[1] (closed_form) = 0.4397411683483107 " "
y[1] (numeric) = 0.43974116834831023 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.00988772899768170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.508999999999999 " "
y[1] (closed_form) = 0.43915853711021446 " "
y[1] (numeric) = 0.4391585371102139 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 1.26403443267974870000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.509999999999999 " "
y[1] (closed_form) = 0.4385770630336119 " "
y[1] (numeric) = 0.43857706303361127 " "
absolute error = 6.1062266354383610000000000000000E-16 " "
relative error = 1.39228134576896230000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5109999999999988 " "
y[1] (closed_form) = 0.4379967430562193 " "
y[1] (numeric) = 0.43799674305621866 " "
absolute error = 6.1062266354383610000000000000000E-16 " "
relative error = 1.3941260368355280000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5119999999999987 " "
y[1] (closed_form) = 0.43741757412587634 " "
y[1] (numeric) = 0.4374175741258757 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 1.52287848997900460000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5129999999999986 " "
y[1] (closed_form) = 0.43683955320050577 " "
y[1] (numeric) = 0.436839553200505 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 1.77904246889681570000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5139999999999985 " "
y[1] (closed_form) = 0.4362626772480734 " "
y[1] (numeric) = 0.4362626772480725 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.03587990910136380000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5149999999999983 " "
y[1] (closed_form) = 0.43568694324654833 " "
y[1] (numeric) = 0.4356869432465474 " "
absolute error = 9.436895709313831000000000000000E-16 " "
relative error = 2.165980839130550200000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5159999999999982 " "
y[1] (closed_form) = 0.43511234818386385 " "
y[1] (numeric) = 0.4351123481838628 " "
absolute error = 1.0547118733938987000000000000000E-15 " "
relative error = 2.4239989460106360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5169999999999981 " "
y[1] (closed_form) = 0.4345388890578773 " "
y[1] (numeric) = 0.4345388890578762 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 2.55494514433962040000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.517999999999998 " "
y[1] (closed_form) = 0.43396656287633145 " "
y[1] (numeric) = 0.43396656287633034 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 2.55831467121935800000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.518999999999998 " "
y[1] (closed_form) = 0.43339536665681533 " "
y[1] (numeric) = 0.4333953666568141 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 2.8178550603996577000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5199999999999978 " "
y[1] (closed_form) = 0.432825297426725 " "
y[1] (numeric) = 0.4328252974267237 " "
absolute error = 1.27675647831893000000000000000E-15 " "
relative error = 2.9498194442645260000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5209999999999977 " "
y[1] (closed_form) = 0.4322563522232254 " "
y[1] (numeric) = 0.43225635222322406 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.08212388944183700000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5219999999999976 " "
y[1] (closed_form) = 0.43168852809321157 " "
y[1] (numeric) = 0.4316885280932101 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 3.3433594781584370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5229999999999975 " "
y[1] (closed_form) = 0.4311218220932703 " "
y[1] (numeric) = 0.4311218220932688 " "
absolute error = 1.4988010832439613000000000000000E-15 " "
relative error = 3.4765140766168540000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5239999999999974 " "
y[1] (closed_form) = 0.43055623128964227 " "
y[1] (numeric) = 0.4305562312896407 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 3.61000984661073900000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5249999999999972 " "
y[1] (closed_form) = 0.42999175275818363 " "
y[1] (numeric) = 0.429991752758182 " "
absolute error = 1.609823385706477000000000000000E-15 " "
relative error = 3.7438471212069980000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5259999999999971 " "
y[1] (closed_form) = 0.42942838358432867 " "
y[1] (numeric) = 0.429428383584327 " "
absolute error = 1.6653345369377348000000000000000E-15 " "
relative error = 3.87802623347253900000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.526999999999997 " "
y[1] (closed_form) = 0.4288661208630518 " "
y[1] (numeric) = 0.4288661208630501 " "
absolute error = 1.7208456881689926000000000000000E-15 " "
relative error = 4.01254751647426970000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.527999999999997 " "
y[1] (closed_form) = 0.4283049616988305 " "
y[1] (numeric) = 0.4283049616988287 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 4.14741130327909770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5289999999999968 " "
y[1] (closed_form) = 0.4277449032056076 " "
y[1] (numeric) = 0.42774490320560576 " "
absolute error = 1.8318679906315083000000000000000E-15 " "
relative error = 4.2826179269539290000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5299999999999967 " "
y[1] (closed_form) = 0.42718594250675457 " "
y[1] (numeric) = 0.4271859425067526 " "
absolute error = 1.942890293094024000000000000000E-15 " "
relative error = 4.5481138299940740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5309999999999966 " "
y[1] (closed_form) = 0.4266280767350343 " "
y[1] (numeric) = 0.4266280767350323 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 4.6841770462435556000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5319999999999965 " "
y[1] (closed_form) = 0.42607130303256446 " "
y[1] (numeric) = 0.42607130303256235 " "
absolute error = 2.1094237467877974000000000000000E-15 " "
relative error = 4.9508702693046080000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5329999999999964 " "
y[1] (closed_form) = 0.42551561855078085 " "
y[1] (numeric) = 0.42551561855077874 " "
absolute error = 2.1094237467877974000000000000000E-15 " "
relative error = 4.9573356530885120000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5339999999999963 " "
y[1] (closed_form) = 0.4249610204504012 " "
y[1] (numeric) = 0.424961020450399 " "
absolute error = 2.1649348980190553000000000000000E-15 " "
relative error = 5.0944317098178020000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5349999999999961 " "
y[1] (closed_form) = 0.4244075059013885 " "
y[1] (numeric) = 0.4244075059013862 " "
absolute error = 2.275957200481571000000000000000E-15 " "
relative error = 5.3626695306618630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.535999999999996 " "
y[1] (closed_form) = 0.423855072082915 " "
y[1] (numeric) = 0.4238550720829127 " "
absolute error = 2.3314683517128287000000000000000E-15 " "
relative error = 5.5006262877909930000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.536999999999996 " "
y[1] (closed_form) = 0.42330371618332663 " "
y[1] (numeric) = 0.4233037161833242 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 5.7700666467041780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5379999999999958 " "
y[1] (closed_form) = 0.4227534354001067 " "
y[1] (numeric) = 0.42275343540010424 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 5.7775773054657660000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5389999999999957 " "
y[1] (closed_form) = 0.4222042269398407 " "
y[1] (numeric) = 0.4222042269398382 " "
absolute error = 2.4980018054066022000000000000000E-15 " "
relative error = 5.9165722321452240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5399999999999956 " "
y[1] (closed_form) = 0.4216560880181808 " "
y[1] (numeric) = 0.4216560880181782 " "
absolute error = 2.55351295663786000000000000000E-15 " "
relative error = 6.0559138814752710000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5409999999999955 " "
y[1] (closed_form) = 0.4211090158598102 " "
y[1] (numeric) = 0.42110901585980753 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 6.3274239181509620000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5419999999999954 " "
y[1] (closed_form) = 0.4205630076984083 " "
y[1] (numeric) = 0.42056300769840566 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 6.3356386803547670000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5429999999999953 " "
y[1] (closed_form) = 0.42001806077661596 " "
y[1] (numeric) = 0.4200180607766132 " "
absolute error = 2.7755575615628914000000000000000E-15 " "
relative error = 6.6081862204469700000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5439999999999952 " "
y[1] (closed_form) = 0.419474172346 " "
y[1] (numeric) = 0.4194741723459972 " "
absolute error = 2.7755575615628914000000000000000E-15 " "
relative error = 6.6167543666395130000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.544999999999995 " "
y[1] (closed_form) = 0.41893133966701923 " "
y[1] (numeric) = 0.4189313396670164 " "
absolute error = 2.831068712794149000000000000000E-15 " "
relative error = 6.7578346252261250000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.545999999999995 " "
y[1] (closed_form) = 0.41838956000898975 " "
y[1] (numeric) = 0.4183895600089868 " "
absolute error = 2.942091015256665000000000000000E-15 " "
relative error = 7.0319417511121680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5469999999999948 " "
y[1] (closed_form) = 0.4178488306500502 " "
y[1] (numeric) = 0.41784883065004724 " "
absolute error = 2.942091015256665000000000000000E-15 " "
relative error = 7.0410416386223570000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5479999999999947 " "
y[1] (closed_form) = 0.4173091488771282 " "
y[1] (numeric) = 0.4173091488771252 " "
absolute error = 2.9976021664879227000000000000000E-15 " "
relative error = 7.1831690595657940000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5489999999999946 " "
y[1] (closed_form) = 0.41677051198590603 " "
y[1] (numeric) = 0.416770511985903 " "
absolute error = 3.0531133177191805000000000000000E-15 " "
relative error = 7.3256462007619860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5499999999999945 " "
y[1] (closed_form) = 0.4162329172807866 " "
y[1] (numeric) = 0.4162329172807835 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 7.4684733952778450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5509999999999944 " "
y[1] (closed_form) = 0.41569636207485994 " "
y[1] (numeric) = 0.4156963620748568 " "
absolute error = 3.164135620181696000000000000000E-15 " "
relative error = 7.6116509761802740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5519999999999943 " "
y[1] (closed_form) = 0.41516084368986955 " "
y[1] (numeric) = 0.4151608436898664 " "
absolute error = 3.164135620181696000000000000000E-15 " "
relative error = 7.6214692890096970000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5529999999999942 " "
y[1] (closed_form) = 0.4146263594561792 " "
y[1] (numeric) = 0.4146263594561759 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 8.0329409790635360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.553999999999994 " "
y[1] (closed_form) = 0.414092906712739 " "
y[1] (numeric) = 0.4140929067127357 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 8.0432893678760680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.554999999999994 " "
y[1] (closed_form) = 0.41356048280705326 " "
y[1] (numeric) = 0.4135604828070498 " "
absolute error = 3.4416913763379850000000000000000E-15 " "
relative error = 8.3220992319609680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5559999999999938 " "
y[1] (closed_form) = 0.4130290850951466 " "
y[1] (numeric) = 0.4130290850951431 " "
absolute error = 3.497202527569243000000000000000E-15 " "
relative error = 8.4672064359913480000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5569999999999937 " "
y[1] (closed_form) = 0.41249871094153157 " "
y[1] (numeric) = 0.41249871094152807 " "
absolute error = 3.497202527569243000000000000000E-15 " "
relative error = 8.478093227459670000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5579999999999936 " "
y[1] (closed_form) = 0.41196935771917614 " "
y[1] (numeric) = 0.4119693577191726 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 8.6237328389415080000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5589999999999935 " "
y[1] (closed_form) = 0.4114410228094708 " "
y[1] (numeric) = 0.41144102280946715 " "
absolute error = 3.6637359812630166000000000000000E-15 " "
relative error = 8.9046443552120260000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5599999999999934 " "
y[1] (closed_form) = 0.41091370360219626 " "
y[1] (numeric) = 0.41091370360219254 " "
absolute error = 3.7192471324942744000000000000000E-15 " "
relative error = 9.0511635408851220000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5609999999999933 " "
y[1] (closed_form) = 0.4103873974954913 " "
y[1] (numeric) = 0.4103873974954875 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 9.1980365546361690000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5619999999999932 " "
y[1] (closed_form) = 0.40986210189582073 " "
y[1] (numeric) = 0.4098621018958169 " "
absolute error = 3.83026943495679000000000000000E-15 " "
relative error = 9.3452637295320680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.562999999999993 " "
y[1] (closed_form) = 0.40933781421794324 " "
y[1] (numeric) = 0.40933781421793936 " "
absolute error = 3.885780586188048000000000000000E-15 " "
relative error = 9.4928453986397310000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.563999999999993 " "
y[1] (closed_form) = 0.4088145318848798 " "
y[1] (numeric) = 0.4088145318848759 " "
absolute error = 3.941291737419305700000000000000E-15 " "
relative error = 9.6407818950260650000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5649999999999928 " "
y[1] (closed_form) = 0.408292252327882 " "
y[1] (numeric) = 0.40829225232787797 " "
absolute error = 4.052314039881821400000000000000E-15 " "
relative error = 9.9250329066435030000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5659999999999927 " "
y[1] (closed_form) = 0.4077709729864001 " "
y[1] (numeric) = 0.40777097298639603 " "
absolute error = 4.052314039881821400000000000000E-15 " "
relative error = 9.9377207019023730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5669999999999926 " "
y[1] (closed_form) = 0.4072506913080523 " "
y[1] (numeric) = 0.40725069130804814 " "
absolute error = 4.163336342344337000000000000000E-15 " "
relative error = 1.0223030755263000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5679999999999925 " "
y[1] (closed_form) = 0.40673140474859304 " "
y[1] (numeric) = 0.40673140474858877 " "
absolute error = 4.274358644806852700000000000000E-15 " "
relative error = 1.0509045023088148000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5689999999999924 " "
y[1] (closed_form) = 0.40621311077188194 " "
y[1] (numeric) = 0.40621311077187766 " "
absolute error = 4.274358644806852700000000000000E-15 " "
relative error = 1.0522453686156906000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5699999999999923 " "
y[1] (closed_form) = 0.4056958068498531 " "
y[1] (numeric) = 0.4056958068498488 " "
absolute error = 4.3298697960381105000000000000000E-15 " "
relative error = 1.067270039012403000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5709999999999922 " "
y[1] (closed_form) = 0.40517949046248397 " "
y[1] (numeric) = 0.40517949046247964 " "
absolute error = 4.3298697960381105000000000000000E-15 " "
relative error = 1.0686300511153385000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.571999999999992 " "
y[1] (closed_form) = 0.4046641590977648 " "
y[1] (numeric) = 0.40466415909776043 " "
absolute error = 4.385380947269368300000000000000E-15 " "
relative error = 1.0837087616177747000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.572999999999992 " "
y[1] (closed_form) = 0.4041498102516682 " "
y[1] (numeric) = 0.40414981025166374 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.0988232546082943000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5739999999999919 " "
y[1] (closed_form) = 0.4036364414281183 " "
y[1] (numeric) = 0.40363644142811383 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.1002208033516922000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5749999999999917 " "
y[1] (closed_form) = 0.403124050138961 " "
y[1] (numeric) = 0.4031240501389565 " "
absolute error = 4.496403249731884000000000000000E-15 " "
relative error = 1.1153894807769289000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5759999999999916 " "
y[1] (closed_form) = 0.40261263390393365 " "
y[1] (numeric) = 0.40261263390392904 " "
absolute error = 4.6074255521943996000000000000E-15 " "
relative error = 1.1443817615752627000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5769999999999915 " "
y[1] (closed_form) = 0.4021021902506346 " "
y[1] (numeric) = 0.40210219025062993 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 1.1596397175850247000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5779999999999914 " "
y[1] (closed_form) = 0.40159271671449404 " "
y[1] (numeric) = 0.4015927167144893 " "
absolute error = 4.718447854656915300000000000000E-15 " "
relative error = 1.1749336226163237000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5789999999999913 " "
y[1] (closed_form) = 0.4010842108387436 " "
y[1] (numeric) = 0.4010842108387389 " "
absolute error = 4.718447854656915300000000000000E-15 " "
relative error = 1.1764232366040388000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5799999999999912 " "
y[1] (closed_form) = 0.40057667017438753 " "
y[1] (numeric) = 0.40057667017438264 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 1.2194872223147832000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.580999999999991 " "
y[1] (closed_form) = 0.40007009228017193 " "
y[1] (numeric) = 0.4000700922801671 " "
absolute error = 4.829470157119431000000000000000E-15 " "
relative error = 1.2071560084869623000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.581999999999991 " "
y[1] (closed_form) = 0.39956447472255696 " "
y[1] (numeric) = 0.399564474722552 " "
absolute error = 4.9404924595819466000000000000000E-15 " "
relative error = 1.2364693990907087000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5829999999999909 " "
y[1] (closed_form) = 0.3990598150756863 " "
y[1] (numeric) = 0.3990598150756813 " "
absolute error = 4.9960036108132044000000000000000E-15 " "
relative error = 1.2519435488300557000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5839999999999907 " "
y[1] (closed_form) = 0.39855611092135873 " "
y[1] (numeric) = 0.3985561109213537 " "
absolute error = 5.051514762044462000000000000000E-15 " "
relative error = 1.2674538474310845000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5849999999999906 " "
y[1] (closed_form) = 0.3980533598489992 " "
y[1] (numeric) = 0.39805335984899404 " "
absolute error = 5.162537064506978000000000000000E-15 " "
relative error = 1.2969459839417952000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5859999999999905 " "
y[1] (closed_form) = 0.3975515594556295 " "
y[1] (numeric) = 0.39755155945562426 " "
absolute error = 5.218048215738236000000000000000E-15 " "
relative error = 1.3125462827723156000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5869999999999904 " "
y[1] (closed_form) = 0.3970507073458399 " "
y[1] (numeric) = 0.3970507073458347 " "
absolute error = 5.218048215738236000000000000000E-15 " "
relative error = 1.3142019694711690000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5879999999999903 " "
y[1] (closed_form) = 0.3965508011317608 " "
y[1] (numeric) = 0.39655080113175556 " "
absolute error = 5.218048215738236000000000000000E-15 " "
relative error = 1.3158586997796660000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5889999999999902 " "
y[1] (closed_form) = 0.39605183843303365 " "
y[1] (numeric) = 0.3960518384330284 " "
absolute error = 5.2735593669694940000000000000000E-15 " "
relative error = 1.3315326063967184000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.58999999999999 " "
y[1] (closed_form) = 0.3955538168767832 " "
y[1] (numeric) = 0.3955538168767778 " "
absolute error = 5.384581669432009000000000000000E-15 " "
relative error = 1.3612766303072563000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.59099999999999 " "
y[1] (closed_form) = 0.39505673409758874 " "
y[1] (numeric) = 0.3950567340975833 " "
absolute error = 5.440092820663267000000000000000E-15 " "
relative error = 1.3770409035273984000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5919999999999899 " "
y[1] (closed_form) = 0.3945605877374565 " "
y[1] (numeric) = 0.394560587737451 " "
absolute error = 5.495603971894525000000000000000E-15 " "
relative error = 1.3928415920627482000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5929999999999898 " "
y[1] (closed_form) = 0.3940653754457915 " "
y[1] (numeric) = 0.39406537544578596 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 1.408678729219996200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5939999999999896 " "
y[1] (closed_form) = 0.3935710948793697 " "
y[1] (numeric) = 0.39357109487936404 " "
absolute error = 5.662137425588298000000000000000E-15 " "
relative error = 1.4386568270019310000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5949999999999895 " "
y[1] (closed_form) = 0.3930777437023101 " "
y[1] (numeric) = 0.3930777437023044 " "
absolute error = 5.662137425588298000000000000000E-15 " "
relative error = 1.440462482626951000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5959999999999894 " "
y[1] (closed_form) = 0.3925853195860475 " "
y[1] (numeric) = 0.3925853195860418 " "
absolute error = 5.662137425588298000000000000000E-15 " "
relative error = 1.442269270679456000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5969999999999893 " "
y[1] (closed_form) = 0.3920938202093049 " "
y[1] (numeric) = 0.39209382020929917 " "
absolute error = 5.717648576819556000000000000000E-15 " "
relative error = 1.4582348106806173000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5979999999999892 " "
y[1] (closed_form) = 0.39160324325806595 " "
y[1] (numeric) = 0.3916032432580601 " "
absolute error = 5.828670879282072000000000000000E-15 " "
relative error = 1.4884123100688892000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.598999999999989 " "
y[1] (closed_form) = 0.3911135864255479 " "
y[1] (numeric) = 0.391113586425542 " "
absolute error = 5.88418203051333000000000000000E-15 " "
relative error = 1.5044688383980337000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.599999999999989 " "
y[1] (closed_form) = 0.3906248474121743 " "
y[1] (numeric) = 0.39062484741216846 " "
absolute error = 5.828670879282072000000000000000E-15 " "
relative error = 1.492140327963278000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6009999999999889 " "
y[1] (closed_form) = 0.39013702392554855 " "
y[1] (numeric) = 0.3901370239255426 " "
absolute error = 5.9396931817445870000000000000000E-15 " "
relative error = 1.522463344283388000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6019999999999888 " "
y[1] (closed_form) = 0.3896501136804261 " "
y[1] (numeric) = 0.38965011368042013 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 1.538612237617066000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6029999999999887 " "
y[1] (closed_form) = 0.38916411439868853 " "
y[1] (numeric) = 0.38916411439868254 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 1.5405337006057845000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6039999999999885 " "
y[1] (closed_form) = 0.3886790238093165 " "
y[1] (numeric) = 0.3886790238093104 " "
absolute error = 6.106226635438361000000000000000E-15 " "
relative error = 1.5710203693508393000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6049999999999884 " "
y[1] (closed_form) = 0.3881948396483632 " "
y[1] (numeric) = 0.38819483964835705 " "
absolute error = 6.161737786669619000000000000000E-15 " "
relative error = 1.5872796743643160000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6059999999999883 " "
y[1] (closed_form) = 0.387711559658928 " "
y[1] (numeric) = 0.38771155965892184 " "
absolute error = 6.161737786669619000000000000000E-15 " "
relative error = 1.5892582083676157000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6069999999999882 " "
y[1] (closed_form) = 0.38722918159113034 " "
y[1] (numeric) = 0.3872291815911241 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.6055734519681886000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.607999999999988 " "
y[1] (closed_form) = 0.3867477032020833 " "
y[1] (numeric) = 0.386747703202077 " "
absolute error = 6.2727600891321340000000000000000E-15 " "
relative error = 1.62192562158656020000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.608999999999988 " "
y[1] (closed_form) = 0.3862671222558675 " "
y[1] (numeric) = 0.3862671222558612 " "
absolute error = 6.328271240363392000000000000000E-15 " "
relative error = 1.6383147505294215000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6099999999999879 " "
y[1] (closed_form) = 0.3857874365235055 " "
y[1] (numeric) = 0.38578743652349906 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 1.6691299231652326000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6109999999999878 " "
y[1] (closed_form) = 0.3853086437829353 " "
y[1] (numeric) = 0.38530864378292884 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 1.6712040196153768000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6119999999999877 " "
y[1] (closed_form) = 0.3848307418189853 " "
y[1] (numeric) = 0.38483074181897886 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 1.6732794039242294000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6129999999999876 " "
y[1] (closed_form) = 0.3843537284233485 " "
y[1] (numeric) = 0.384353728423342 " "
absolute error = 6.494804694057166000000000000000E-15 " "
relative error = 1.6897988008856854000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6139999999999874 " "
y[1] (closed_form) = 0.3838776013945565 " "
y[1] (numeric) = 0.38387760139454996 " "
absolute error = 6.5503158452884240000000000000000E-15 " "
relative error = 1.7063553126028544000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6149999999999873 " "
y[1] (closed_form) = 0.3834023585379548 " "
y[1] (numeric) = 0.3834023585379482 " "
absolute error = 6.6058269965196810000000000000000E-15 " "
relative error = 1.7229489723824273000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6159999999999872 " "
y[1] (closed_form) = 0.382927997665677 " "
y[1] (numeric) = 0.3829279976656703 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 1.739579813531095000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6169999999999871 " "
y[1] (closed_form) = 0.3824545165966198 " "
y[1] (numeric) = 0.3824545165966131 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 1.7417334241542629000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.617999999999987 " "
y[1] (closed_form) = 0.3819819131564182 " "
y[1] (numeric) = 0.3819819131564114 " "
absolute error = 6.827871601444713000000000000000E-15 " "
relative error = 1.7874855762211860000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.618999999999987 " "
y[1] (closed_form) = 0.3815101851774198 " "
y[1] (numeric) = 0.38151018517741303 " "
absolute error = 6.772360450213455000000000000000E-15 " "
relative error = 1.7751453862402114000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6199999999999868 " "
y[1] (closed_form) = 0.38103933049866096 " "
y[1] (numeric) = 0.38103933049865407 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 1.8064756579505276000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6209999999999867 " "
y[1] (closed_form) = 0.38056934696584105 " "
y[1] (numeric) = 0.3805693469658341 " "
absolute error = 6.938893903907228000000000000000E-15 " "
relative error = 1.8232929055450295000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6219999999999866 " "
y[1] (closed_form) = 0.3801002324312984 " "
y[1] (numeric) = 0.3801002324312915 " "
absolute error = 6.938893903907228000000000000000E-15 " "
relative error = 1.8255431888380666000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6229999999999865 " "
y[1] (closed_form) = 0.3796319847539858 " "
y[1] (numeric) = 0.37963198475397886 " "
absolute error = 6.938893903907228000000000000000E-15 " "
relative error = 1.8277948599098845000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6239999999999863 " "
y[1] (closed_form) = 0.3791646017994457 " "
y[1] (numeric) = 0.3791646017994387 " "
absolute error = 6.994405055138486000000000000000E-15 " "
relative error = 1.844688302110566700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6249999999999862 " "
y[1] (closed_form) = 0.3786980814397862 " "
y[1] (numeric) = 0.3786980814397792 " "
absolute error = 7.049916206369744000000000000000E-15 " "
relative error = 1.8616192032360995000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6259999999999861 " "
y[1] (closed_form) = 0.3782324215536566 " "
y[1] (numeric) = 0.37823242155364956 " "
absolute error = 7.049916206369744000000000000000E-15 " "
relative error = 1.86391113099479000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.626999999999986 " "
y[1] (closed_form) = 0.37776762002622355 " "
y[1] (numeric) = 0.37776762002621644 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 1.8808989921126015000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.627999999999986 " "
y[1] (closed_form) = 0.3773036747491467 " "
y[1] (numeric) = 0.37730367474913956 " "
absolute error = 7.16093850883226000000000000000E-15 " "
relative error = 1.8979244009731064000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6289999999999858 " "
y[1] (closed_form) = 0.3768405836205552 " "
y[1] (numeric) = 0.376840583620548 " "
absolute error = 7.216449660063518000000000000000E-15 " "
relative error = 1.914987390882994000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6299999999999857 " "
y[1] (closed_form) = 0.37637834454502356 " "
y[1] (numeric) = 0.37637834454501623 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 1.946836758470704000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6309999999999856 " "
y[1] (closed_form) = 0.3759169554335479 " "
y[1] (numeric) = 0.3759169554335406 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 1.949226247077683300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6319999999999855 " "
y[1] (closed_form) = 0.3754564142035228 " "
y[1] (numeric) = 0.37545641420351544 " "
absolute error = 7.382983113757291000000000000000E-15 " "
relative error = 1.9664021799758663000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6329999999999854 " "
y[1] (closed_form) = 0.3749967187787174 " "
y[1] (numeric) = 0.37499671877871 " "
absolute error = 7.382983113757291000000000000000E-15 " "
relative error = 1.968812723962507800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6339999999999852 " "
y[1] (closed_form) = 0.374537867089252 " "
y[1] (numeric) = 0.3745378670892445 " "
absolute error = 7.494005416219807000000000000000E-15 " "
relative error = 2.0008672219073625000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6349999999999851 " "
y[1] (closed_form) = 0.374079857071575 " "
y[1] (numeric) = 0.3740798570715675 " "
absolute error = 7.494005416219807000000000000000E-15 " "
relative error = 2.0033170122779245000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.635999999999985 " "
y[1] (closed_form) = 0.3736226866684395 " "
y[1] (numeric) = 0.3736226866684319 " "
absolute error = 7.605027718682322000000000000000E-15 " "
relative error = 2.035483387396970800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.636999999999985 " "
y[1] (closed_form) = 0.37316635382888025 " "
y[1] (numeric) = 0.3731663538288726 " "
absolute error = 7.66053886991358000000000000000E-15 " "
relative error = 2.0528482247427934000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6379999999999848 " "
y[1] (closed_form) = 0.37271085650819075 " "
y[1] (numeric) = 0.372710856508183 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 2.0851448345737433000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6389999999999847 " "
y[1] (closed_form) = 0.37225619266790005 " "
y[1] (numeric) = 0.3722561926678923 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 2.0876915751699307000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6399999999999846 " "
y[1] (closed_form) = 0.3718023602757505 " "
y[1] (numeric) = 0.37180236027574265 " "
absolute error = 7.827072323607354000000000000000E-15 " "
relative error = 2.1051701548646268000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6409999999999845 " "
y[1] (closed_form) = 0.3713493573056743 " "
y[1] (numeric) = 0.3713493573056664 " "
absolute error = 7.882583474838611000000000000000E-15 " "
relative error = 2.122686715288995300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6419999999999844 " "
y[1] (closed_form) = 0.37089718173777164 " "
y[1] (numeric) = 0.37089718173776365 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 2.1552080120556685000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6429999999999843 " "
y[1] (closed_form) = 0.37044583155828753 " "
y[1] (numeric) = 0.3704458315582795 " "
absolute error = 8.049116928532385000000000000000E-15 " "
relative error = 2.172818869272633000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6439999999999841 " "
y[1] (closed_form) = 0.3699953047595897 " "
y[1] (numeric) = 0.3699953047595817 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 2.16046140977251000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.644999999999984 " "
y[1] (closed_form) = 0.3695455993401465 " "
y[1] (numeric) = 0.3695455993401385 " "
absolute error = 8.049116928532385000000000000000E-15 " "
relative error = 2.1781119685648356000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.645999999999984 " "
y[1] (closed_form) = 0.3690967133045042 " "
y[1] (numeric) = 0.3690967133044961 " "
absolute error = 8.104628079763643000000000000000E-15 " "
relative error = 2.1958006635180566000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6469999999999838 " "
y[1] (closed_form) = 0.36864864466326513 " "
y[1] (numeric) = 0.368648644663257 " "
absolute error = 8.1601392309949010000000000000E-15 " "
relative error = 2.2135275279388644000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6479999999999837 " "
y[1] (closed_form) = 0.36820139143306546 " "
y[1] (numeric) = 0.3682013914330573 " "
absolute error = 8.1601392309949010000000000000E-15 " "
relative error = 2.216216293815477000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6489999999999836 " "
y[1] (closed_form) = 0.36775495163655364 " "
y[1] (numeric) = 0.36775495163654537 " "
absolute error = 8.271161533457416000000000000000E-15 " "
relative error = 2.2490958984100030000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6499999999999835 " "
y[1] (closed_form) = 0.36730932330236793 " "
y[1] (numeric) = 0.36730932330235966 " "
absolute error = 8.271161533457416000000000000000E-15 " "
relative error = 2.2518245545998897000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6509999999999834 " "
y[1] (closed_form) = 0.36686450446511526 " "
y[1] (numeric) = 0.36686450446510693 " "
absolute error = 8.326672684688674000000000000000E-15 " "
relative error = 2.26968610572693000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6519999999999833 " "
y[1] (closed_form) = 0.36642049316534914 " "
y[1] (numeric) = 0.3664204931653408 " "
absolute error = 8.326672684688674000000000000000E-15 " "
relative error = 2.2724364057146826000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6529999999999831 " "
y[1] (closed_form) = 0.3659772874495483 " "
y[1] (numeric) = 0.36597728744953995 " "
absolute error = 8.382183835919932000000000000000E-15 " "
relative error = 2.2903562935105515000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.653999999999983 " "
y[1] (closed_form) = 0.3655348853700951 " "
y[1] (numeric) = 0.36553488537008666 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 2.308314561716382200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.654999999999983 " "
y[1] (closed_form) = 0.3650932849852541 " "
y[1] (numeric) = 0.3650932849852456 " "
absolute error = 8.493206138382448000000000000000E-15 " "
relative error = 2.3263112436388642000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6559999999999828 " "
y[1] (closed_form) = 0.3646524843591509 " "
y[1] (numeric) = 0.3646524843591423 " "
absolute error = 8.548717289613705000000000000000E-15 " "
relative error = 2.3443463725846894000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6569999999999827 " "
y[1] (closed_form) = 0.36421248156175073 " "
y[1] (numeric) = 0.36421248156174213 " "
absolute error = 8.604228440844963000000000000000E-15 " "
relative error = 2.362419981860548000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6579999999999826 " "
y[1] (closed_form) = 0.3637732746688375 " "
y[1] (numeric) = 0.3637732746688289 " "
absolute error = 8.604228440844963000000000000000E-15 " "
relative error = 2.365272283588688000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6589999999999825 " "
y[1] (closed_form) = 0.3633348617619928 " "
y[1] (numeric) = 0.36333486176198415 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 2.3834045403958223000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6599999999999824 " "
y[1] (closed_form) = 0.3628972409285746 " "
y[1] (numeric) = 0.36289724092856596 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 2.386278707966432200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6609999999999823 " "
y[1] (closed_form) = 0.3624604102616969 " "
y[1] (numeric) = 0.3624604102616882 " "
absolute error = 8.715250743307479000000000000000E-15 " "
relative error = 2.4044697011226843000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6619999999999822 " "
y[1] (closed_form) = 0.3620243678602084 " "
y[1] (numeric) = 0.36202436786019965 " "
absolute error = 8.770761894538737000000000000000E-15 " "
relative error = 2.4226993189379634000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.662999999999982 " "
y[1] (closed_form) = 0.3615891118286724 " "
y[1] (numeric) = 0.3615891118286636 " "
absolute error = 8.826273045769994000000000000000E-15 " "
relative error = 2.4409675947189596000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.663999999999982 " "
y[1] (closed_form) = 0.3611546402773457 " "
y[1] (numeric) = 0.36115464027733685 " "
absolute error = 8.826273045769994000000000000000E-15 " "
relative error = 2.443904095761287000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6649999999999818 " "
y[1] (closed_form) = 0.36072095132215837 " "
y[1] (numeric) = 0.3607209513221495 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 2.4622313077315458000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6659999999999817 " "
y[1] (closed_form) = 0.36028804308469325 " "
y[1] (numeric) = 0.3602880430846843 " "
absolute error = 8.93729534823251000000000000000E-15 " "
relative error = 2.4805972664853637000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6669999999999816 " "
y[1] (closed_form) = 0.3598559136921656 " "
y[1] (numeric) = 0.35985591369215664 " "
absolute error = 8.93729534823251000000000000000E-15 " "
relative error = 2.483576067024929000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6679999999999815 " "
y[1] (closed_form) = 0.35942456127740285 " "
y[1] (numeric) = 0.35942456127739386 " "
absolute error = 8.992806499463768000000000000000E-15 " "
relative error = 2.5020011062970027000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6689999999999814 " "
y[1] (closed_form) = 0.3589939839788245 " "
y[1] (numeric) = 0.35899398397881543 " "
absolute error = 9.048317650695026000000000000000E-15 " "
relative error = 2.5204649811704777000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6699999999999813 " "
y[1] (closed_form) = 0.35856417994042183 " "
y[1] (numeric) = 0.35856417994041273 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 2.5389677249520440000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6709999999999812 " "
y[1] (closed_form) = 0.3581351473117382 " "
y[1] (numeric) = 0.3581351473117291 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 2.542009314154768000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.671999999999981 " "
y[1] (closed_form) = 0.35770688424784886 " "
y[1] (numeric) = 0.3577068842478397 " "
absolute error = 9.159339953157541000000000000000E-15 " "
relative error = 2.5605713382947350000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.672999999999981 " "
y[1] (closed_form) = 0.3572793889093413 " "
y[1] (numeric) = 0.3572793889093321 " "
absolute error = 9.2148511043887990000000000000E-15 " "
relative error = 2.5791723201606354000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6739999999999808 " "
y[1] (closed_form) = 0.3568526594622954 " "
y[1] (numeric) = 0.3568526594622861 " "
absolute error = 9.270362255620057000000000000000E-15 " "
relative error = 2.5978122930591613000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6749999999999807 " "
y[1] (closed_form) = 0.3564266940782638 " "
y[1] (numeric) = 0.35642669407825445 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 2.616491290297003000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6759999999999806 " "
y[1] (closed_form) = 0.35600149093425226 " "
y[1] (numeric) = 0.3560014909342428 " "
absolute error = 9.43689570931383100000000000000E-15 " "
relative error = 2.6508022998860625000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6769999999999805 " "
y[1] (closed_form) = 0.3555770482127002 " "
y[1] (numeric) = 0.35557704821269076 " "
absolute error = 9.43689570931383100000000000000E-15 " "
relative error = 2.653966491017395000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6779999999999804 " "
y[1] (closed_form) = 0.35515336410146137 " "
y[1] (numeric) = 0.3551533641014519 " "
absolute error = 9.492406860545088000000000000000E-15 " "
relative error = 2.6727627611133276000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6789999999999803 " "
y[1] (closed_form) = 0.35473043679378435 " "
y[1] (numeric) = 0.3547304367937748 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 2.691598188775338000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6799999999999802 " "
y[1] (closed_form) = 0.35430826448829333 " "
y[1] (numeric) = 0.35430826448828373 " "
absolute error = 9.603429163007604000000000000000E-15 " "
relative error = 2.7104728073101186000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.68099999999998 " "
y[1] (closed_form) = 0.353886845388969 " "
y[1] (numeric) = 0.3538868453889593 " "
absolute error = 9.658940314238862000000000000000E-15 " "
relative error = 2.7293866500243585000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.68199999999998 " "
y[1] (closed_form) = 0.3534661777051292 " "
y[1] (numeric) = 0.35346617770511957 " "
absolute error = 9.658940314238862000000000000000E-15 " "
relative error = 2.732634951652037000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6829999999999798 " "
y[1] (closed_form) = 0.35304625965141057 " "
y[1] (numeric) = 0.35304625965140085 " "
absolute error = 9.71445146547012000000000000000E-15 " "
relative error = 2.7516086631428804000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6839999999999797 " "
y[1] (closed_form) = 0.3526270894477486 " "
y[1] (numeric) = 0.35262708944773885 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 2.7706216876310250000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6849999999999796 " "
y[1] (closed_form) = 0.3522086653193596 " "
y[1] (numeric) = 0.3522086653193498 " "
absolute error = 9.825473767932635000000000000000E-15 " "
relative error = 2.7896740584231633000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6859999999999795 " "
y[1] (closed_form) = 0.35179098549672155 " "
y[1] (numeric) = 0.35179098549671173 " "
absolute error = 9.825473767932635000000000000000E-15 " "
relative error = 2.792986225630333000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6869999999999794 " "
y[1] (closed_form) = 0.35137404821555546 " "
y[1] (numeric) = 0.3513740482155456 " "
absolute error = 9.880984919163893000000000000000E-15 " "
relative error = 2.812098665039218000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6879999999999793 " "
y[1] (closed_form) = 0.35095785171680666 " "
y[1] (numeric) = 0.3509578517167967 " "
absolute error = 9.936496070395151000000000000000E-15 " "
relative error = 2.831250539569938000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6889999999999792 " "
y[1] (closed_form) = 0.3505423942466264 " "
y[1] (numeric) = 0.35054239424661643 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 2.850441882529183000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.689999999999979 " "
y[1] (closed_form) = 0.35012767405635326 " "
y[1] (numeric) = 0.35012767405634326 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 2.8538181817693703000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.690999999999979 " "
y[1] (closed_form) = 0.34971368940249487 " "
y[1] (numeric) = 0.34971368940248476 " "
absolute error = 1.010302952408892500000000000000E-14 " "
relative error = 2.8889431069600124000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6919999999999789 " "
y[1] (closed_form) = 0.3493004385467093 " "
y[1] (numeric) = 0.3493004385466992 " "
absolute error = 1.010302952408892500000000000000E-14 " "
relative error = 2.8923609618480120000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6929999999999787 " "
y[1] (closed_form) = 0.3488879197557872 " "
y[1] (numeric) = 0.34888791975577704 " "
absolute error = 1.015854067532018200000000000000E-14 " "
relative error = 2.911691721063574000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6939999999999786 " "
y[1] (closed_form) = 0.34847613130163335 " "
y[1] (numeric) = 0.34847613130162314 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 2.9310621041388857000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6949999999999785 " "
y[1] (closed_form) = 0.3480650714612486 " "
y[1] (numeric) = 0.3480650714612384 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 2.9345236463029040000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6959999999999784 " "
y[1] (closed_form) = 0.3476547385167121 " "
y[1] (numeric) = 0.3476547385167018 " "
absolute error = 1.026956297778269800000000000000E-14 " "
relative error = 2.953954553186402000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6969999999999783 " "
y[1] (closed_form) = 0.34724513075516283 " "
y[1] (numeric) = 0.3472451307551525 " "
absolute error = 1.032507412901395600000000000000E-14 " "
relative error = 2.9734251727474925000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6979999999999782 " "
y[1] (closed_form) = 0.34683624646878236 " "
y[1] (numeric) = 0.346836246468772 " "
absolute error = 1.038058528024521400000000000000E-14 " "
relative error = 2.9929355382928635000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.698999999999978 " "
y[1] (closed_form) = 0.3464280839547765 " "
y[1] (numeric) = 0.3464280839547661 " "
absolute error = 1.038058528024521400000000000000E-14 " "
relative error = 2.9964618231125620000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.699999999999978 " "
y[1] (closed_form) = 0.3460206415153579 " "
y[1] (numeric) = 0.34602064151534745 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 3.0160329123062650000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7009999999999779 " "
y[1] (closed_form) = 0.3456139174577283 " "
y[1] (numeric) = 0.3456139174577178 " "
absolute error = 1.04916075827077300000000000000E-14 " "
relative error = 3.035643836302092000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7019999999999778 " "
y[1] (closed_form) = 0.3452079100940609 " "
y[1] (numeric) = 0.3452079100940504 " "
absolute error = 1.04916075827077300000000000000E-14 " "
relative error = 3.0392141303624876000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7029999999999776 " "
y[1] (closed_form) = 0.3448026177414829 " "
y[1] (numeric) = 0.34480261774147236 " "
absolute error = 1.054711873393898700000000000000E-14 " "
relative error = 3.058885922335639000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7039999999999775 " "
y[1] (closed_form) = 0.34439803872205815 " "
y[1] (numeric) = 0.34439803872204755 " "
absolute error = 1.060262988517024500000000000000E-14 " "
relative error = 3.0785976379287560000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7049999999999774 " "
y[1] (closed_form) = 0.3439941713627695 " "
y[1] (numeric) = 0.3439941713627589 " "
absolute error = 1.060262988517024500000000000000E-14 " "
relative error = 3.0822120744566100000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7059999999999773 " "
y[1] (closed_form) = 0.3435910139955019 " "
y[1] (numeric) = 0.34359101399549125 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 3.1019848023560453000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7069999999999772 " "
y[1] (closed_form) = 0.34318856495702477 " "
y[1] (numeric) = 0.3431885649570141 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 3.105622425891769000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.707999999999977 " "
y[1] (closed_form) = 0.3427868225889752 " "
y[1] (numeric) = 0.3427868225889645 " "
absolute error = 1.07136521876327600000000000000E-14 " "
relative error = 3.1254562549153650000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.708999999999977 " "
y[1] (closed_form) = 0.34238578523784063 " "
y[1] (numeric) = 0.34238578523782986 " "
absolute error = 1.076916333886401800000000000000E-14 " "
relative error = 3.1453301518879195000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7099999999999769 " "
y[1] (closed_form) = 0.3419854512549419 " "
y[1] (numeric) = 0.3419854512549311 " "
absolute error = 1.076916333886401800000000000000E-14 " "
relative error = 3.149012128833477000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7109999999999768 " "
y[1] (closed_form) = 0.34158581899641643 " "
y[1] (numeric) = 0.3415858189964056 " "
absolute error = 1.082467449009527600000000000000E-14 " "
relative error = 3.1689472712591843000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7119999999999767 " "
y[1] (closed_form) = 0.34118688682320114 " "
y[1] (numeric) = 0.3411868868231902 " "
absolute error = 1.093569679255779200000000000000E-14 " "
relative error = 3.2051925835662420000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7129999999999765 " "
y[1] (closed_form) = 0.34078865310101564 " "
y[1] (numeric) = 0.3407886531010047 " "
absolute error = 1.093569679255779200000000000000E-14 " "
relative error = 3.208938059717693000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7139999999999764 " "
y[1] (closed_form) = 0.34039111620034584 " "
y[1] (numeric) = 0.34039111620033485 " "
absolute error = 1.09912079437890500000000000000E-14 " "
relative error = 3.2289937723638750000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7149999999999763 " "
y[1] (closed_form) = 0.33999427449642683 " "
y[1] (numeric) = 0.3399942744964158 " "
absolute error = 1.104671909502030800000000000000E-14 " "
relative error = 3.2490897416969305000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7159999999999762 " "
y[1] (closed_form) = 0.3395981263692266 " "
y[1] (numeric) = 0.3395981263692155 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 3.269226001023549000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.716999999999976 " "
y[1] (closed_form) = 0.33920267020342926 " "
y[1] (numeric) = 0.3392026702034181 " "
absolute error = 1.115774139748282300000000000000E-14 " "
relative error = 3.289402583650422000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.717999999999976 " "
y[1] (closed_form) = 0.33880790438841885 " "
y[1] (numeric) = 0.33880790438840763 " "
absolute error = 1.121325254871408100000000000000E-14 " "
relative error = 3.3096195228842400000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7189999999999759 " "
y[1] (closed_form) = 0.33841382731826264 " "
y[1] (numeric) = 0.33841382731825137 " "
absolute error = 1.126876369994533900000000000000E-14 " "
relative error = 3.3298768520316940000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7199999999999758 " "
y[1] (closed_form) = 0.33802043739169507 " "
y[1] (numeric) = 0.33802043739168375 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 3.350174604399475000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7209999999999757 " "
y[1] (closed_form) = 0.3376277330121013 " "
y[1] (numeric) = 0.33762773301209 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 3.354071287375765000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7219999999999756 " "
y[1] (closed_form) = 0.3372357125875012 " "
y[1] (numeric) = 0.33723571258748974 " "
absolute error = 1.143529715363911200000000000000E-14 " "
relative error = 3.3908915120227795000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7229999999999754 " "
y[1] (closed_form) = 0.33684437453053273 " "
y[1] (numeric) = 0.3368443745305213 " "
absolute error = 1.143529715363911200000000000000E-14 " "
relative error = 3.3948309718922076000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7239999999999753 " "
y[1] (closed_form) = 0.3364537172584367 " "
y[1] (numeric) = 0.3364537172584252 " "
absolute error = 1.14908083048703700000000000000E-14 " "
relative error = 3.4152716155143725000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7249999999999752 " "
y[1] (closed_form) = 0.33606373919303995 " "
y[1] (numeric) = 0.33606373919302845 " "
absolute error = 1.14908083048703700000000000000E-14 " "
relative error = 3.4192347952987223000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.725999999999975 " "
y[1] (closed_form) = 0.33567443876073993 " "
y[1] (numeric) = 0.3356744387607284 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 3.4397374726323876000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.726999999999975 " "
y[1] (closed_form) = 0.33528581439248856 " "
y[1] (numeric) = 0.335285814392477 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 3.4437244167405795000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.727999999999975 " "
y[1] (closed_form) = 0.33489786452377657 " "
y[1] (numeric) = 0.33489786452376497 " "
absolute error = 1.160183060733288600000000000000E-14 " "
relative error = 3.464289216603588000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7289999999999748 " "
y[1] (closed_form) = 0.3345105875946177 " "
y[1] (numeric) = 0.33451058759460606 " "
absolute error = 1.165734175856414400000000000000E-14 " "
relative error = 3.4848947061404495000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7299999999999747 " "
y[1] (closed_form) = 0.334123982049533 " "
y[1] (numeric) = 0.33412398204952126 " "
absolute error = 1.171285290979540200000000000000E-14 " "
relative error = 3.505540918657854000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7309999999999746 " "
y[1] (closed_form) = 0.3337380463375351 " "
y[1] (numeric) = 0.33373804633752335 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 3.526227887462493000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7319999999999744 " "
y[1] (closed_form) = 0.333352778912113 " "
y[1] (numeric) = 0.33335277891210124 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 3.5303032719368255000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7329999999999743 " "
y[1] (closed_form) = 0.33296817823121627 " "
y[1] (numeric) = 0.33296817823120445 " "
absolute error = 1.182387521225791700000000000000E-14 " "
relative error = 3.5510526186221030000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7339999999999742 " "
y[1] (closed_form) = 0.3325842427572397 " "
y[1] (numeric) = 0.3325842427572278 " "
absolute error = 1.187938636348917500000000000000E-14 " "
relative error = 3.571842810412456000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7349999999999741 " "
y[1] (closed_form) = 0.33220097095700785 " "
y[1] (numeric) = 0.3322009709569959 " "
absolute error = 1.193489751472043300000000000000E-14 " "
relative error = 3.5926738806145760000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.735999999999974 " "
y[1] (closed_form) = 0.3318183613017599 " "
y[1] (numeric) = 0.33181836130174797 " "
absolute error = 1.193489751472043300000000000000E-14 " "
relative error = 3.5968164835419350000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.736999999999974 " "
y[1] (closed_form) = 0.33143641226713444 " "
y[1] (numeric) = 0.33143641226712245 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 3.6177101314648380000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7379999999999738 " "
y[1] (closed_form) = 0.33105512233315404 " "
y[1] (numeric) = 0.331055122333142 " "
absolute error = 1.204591981718294800000000000000E-14 " "
relative error = 3.638644746617349400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7389999999999737 " "
y[1] (closed_form) = 0.33067448998421034 " "
y[1] (numeric) = 0.3306744899841983 " "
absolute error = 1.204591981718294800000000000000E-14 " "
relative error = 3.642833112937784000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7399999999999736 " "
y[1] (closed_form) = 0.33029451370904894 " "
y[1] (numeric) = 0.33029451370903684 " "
absolute error = 1.210143096841420600000000000000E-14 " "
relative error = 3.663830450140071000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7409999999999735 " "
y[1] (closed_form) = 0.3299151920007543 " "
y[1] (numeric) = 0.32991519200074215 " "
absolute error = 1.215694211964546400000000000000E-14 " "
relative error = 3.68486884338980970000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7419999999999733 " "
y[1] (closed_form) = 0.329536523356735 " "
y[1] (numeric) = 0.3295365233567228 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 3.7059483259936890000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7429999999999732 " "
y[1] (closed_form) = 0.3291585062787086 " "
y[1] (numeric) = 0.32915850627869636 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 3.710204365958588700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7439999999999731 " "
y[1] (closed_form) = 0.3287811392726871 " "
y[1] (numeric) = 0.32878113927267477 " "
absolute error = 1.232347557333923800000000000000E-14 " "
relative error = 3.748230692490635000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.744999999999973 " "
y[1] (closed_form) = 0.3284044208489619 " "
y[1] (numeric) = 0.3284044208489495 " "
absolute error = 1.237898672457049500000000000000E-14 " "
relative error = 3.769433642997083000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.745999999999973 " "
y[1] (closed_form) = 0.32802834952208926 " "
y[1] (numeric) = 0.3280283495220769 " "
absolute error = 1.237898672457049500000000000000E-14 " "
relative error = 3.773755147262631000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7469999999999728 " "
y[1] (closed_form) = 0.3276529238108758 " "
y[1] (numeric) = 0.3276529238108634 " "
absolute error = 1.237898672457049500000000000000E-14 " "
relative error = 3.778079127325522000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7479999999999727 " "
y[1] (closed_form) = 0.3272781422383636 " "
y[1] (numeric) = 0.32727814223835117 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 3.799367043200045400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7489999999999726 " "
y[1] (closed_form) = 0.32690400333181585 " "
y[1] (numeric) = 0.32690400333180336 " "
absolute error = 1.249000902703301100000000000000E-14 " "
relative error = 3.820696259371083600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7499999999999725 " "
y[1] (closed_form) = 0.3265305056227023 " "
y[1] (numeric) = 0.32653050562268976 " "
absolute error = 1.254552017826427000000000000000E-14 " "
relative error = 3.84206680914532970000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7509999999999724 " "
y[1] (closed_form) = 0.32615764764668503 " "
y[1] (numeric) = 0.32615764764667243 " "
absolute error = 1.260103132949552700000000000000E-14 " "
relative error = 3.8634787258294720000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7519999999999722 " "
y[1] (closed_form) = 0.3257854279436038 " "
y[1] (numeric) = 0.3257854279435912 " "
absolute error = 1.260103132949552700000000000000E-14 " "
relative error = 3.867892867104194000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7529999999999721 " "
y[1] (closed_form) = 0.3254138450574622 " "
y[1] (numeric) = 0.3254138450574495 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 3.889368160869698000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.753999999999972 " "
y[1] (closed_form) = 0.32504289753641274 " "
y[1] (numeric) = 0.32504289753640003 " "
absolute error = 1.271205363195804200000000000000E-14 " "
relative error = 3.910884910362941000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.754999999999972 " "
y[1] (closed_form) = 0.3246725839327434 " "
y[1] (numeric) = 0.3246725839327307 " "
absolute error = 1.271205363195804200000000000000E-14 " "
relative error = 3.915345569982395000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7559999999999718 " "
y[1] (closed_form) = 0.3243029028028631 " "
y[1] (numeric) = 0.32430290280285035 " "
absolute error = 1.2767564783189300000000000000E-14 " "
relative error = 3.936925840885992500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7569999999999717 " "
y[1] (closed_form) = 0.3239338527072876 " "
y[1] (numeric) = 0.3239338527072748 " "
absolute error = 1.2767564783189300000000000000E-14 " "
relative error = 3.941411086394326000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7579999999999716 " "
y[1] (closed_form) = 0.32356543221062567 " "
y[1] (numeric) = 0.32356543221061285 " "
absolute error = 1.282307593442055800000000000000E-14 " "
relative error = 3.96305496752611950000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7589999999999715 " "
y[1] (closed_form) = 0.32319763988156497 " "
y[1] (numeric) = 0.32319763988155215 " "
absolute error = 1.282307593442055800000000000000E-14 " "
relative error = 3.967564843332254700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7599999999999714 " "
y[1] (closed_form) = 0.32283047429285844 " "
y[1] (numeric) = 0.3228304742928455 " "
absolute error = 1.293409823688307400000000000000E-14 " "
relative error = 4.006467563266594000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7609999999999713 " "
y[1] (closed_form) = 0.3224639340213099 " "
y[1] (numeric) = 0.32246393402129697 " "
absolute error = 1.293409823688307400000000000000E-14 " "
relative error = 4.011021659255800700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7619999999999711 " "
y[1] (closed_form) = 0.3220980176477609 " "
y[1] (numeric) = 0.322098017647748 " "
absolute error = 1.293409823688307400000000000000E-14 " "
relative error = 4.015578342064654000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.762999999999971 " "
y[1] (closed_form) = 0.3217327237570766 " "
y[1] (numeric) = 0.32173272375706363 " "
absolute error = 1.298960938811433200000000000000E-14 " "
relative error = 4.0373914211853995000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.763999999999971 " "
y[1] (closed_form) = 0.32136805093813214 " "
y[1] (numeric) = 0.3213680509381191 " "
absolute error = 1.30451205393455900000000000000E-14 " "
relative error = 4.059246244691871500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7649999999999708 " "
y[1] (closed_form) = 0.321003997783799 " "
y[1] (numeric) = 0.3210039977837859 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 4.08114284589076000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7659999999999707 " "
y[1] (closed_form) = 0.3206405628909316 " "
y[1] (numeric) = 0.32064056289091847 " "
absolute error = 1.315614284180810500000000000000E-14 " "
relative error = 4.103081258088756000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7669999999999706 " "
y[1] (closed_form) = 0.32027774486035354 " "
y[1] (numeric) = 0.3202777448603404 " "
absolute error = 1.315614284180810500000000000000E-14 " "
relative error = 4.107729323354766000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7679999999999705 " "
y[1] (closed_form) = 0.31991554229684427 " "
y[1] (numeric) = 0.3199155422968311 " "
absolute error = 1.315614284180810500000000000000E-14 " "
relative error = 4.112380019849345000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7689999999999704 " "
y[1] (closed_form) = 0.31955395380912577 " "
y[1] (numeric) = 0.31955395380911256 " "
absolute error = 1.321165399303936300000000000000E-14 " "
relative error = 4.134404796296426000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7699999999999703 " "
y[1] (closed_form) = 0.3191929780098489 " "
y[1] (numeric) = 0.3191929780098356 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 4.173862588885273000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7709999999999702 " "
y[1] (closed_form) = 0.3188326135155803 " "
y[1] (numeric) = 0.31883261351556696 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 4.178580148561509300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.77199999999997 " "
y[1] (closed_form) = 0.3184728589467892 " "
y[1] (numeric) = 0.3184728589467758 " "
absolute error = 1.337818744673313600000000000000E-14 " "
relative error = 4.2007307909928926000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.77299999999997 " "
y[1] (closed_form) = 0.31811371292783397 " "
y[1] (numeric) = 0.31811371292782054 " "
absolute error = 1.343369859796439400000000000000E-14 " "
relative error = 4.2229234553657585000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7739999999999698 " "
y[1] (closed_form) = 0.31775517408694925 " "
y[1] (numeric) = 0.31775517408693577 " "
absolute error = 1.348920974919565200000000000000E-14 " "
relative error = 4.245158174986795600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7749999999999697 " "
y[1] (closed_form) = 0.3173972410562327 " "
y[1] (numeric) = 0.31739724105621914 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 4.267434983162698000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7759999999999696 " "
y[1] (closed_form) = 0.31703991247163177 " "
y[1] (numeric) = 0.3170399124716182 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 4.272244713554439000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7769999999999695 " "
y[1] (closed_form) = 0.3166831869729313 " "
y[1] (numeric) = 0.31668318697291764 " "
absolute error = 1.365574320288942500000000000000E-14 " "
relative error = 4.3121149984058543000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7779999999999694 " "
y[1] (closed_form) = 0.31632706320373977 " "
y[1] (numeric) = 0.31632706320372606 " "
absolute error = 1.371125435412068300000000000000E-14 " "
relative error = 4.334518272086490500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7789999999999693 " "
y[1] (closed_form) = 0.315971539811477 " "
y[1] (numeric) = 0.31597153981146325 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 4.356963767548754000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7799999999999692 " "
y[1] (closed_form) = 0.31561661544736114 " "
y[1] (numeric) = 0.31561661544734737 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 4.361863359392109000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.780999999999969 " "
y[1] (closed_form) = 0.3152622887663959 " "
y[1] (numeric) = 0.31526228876638207 " "
absolute error = 1.382227665658320000000000000000E-14 " "
relative error = 4.384373630816743600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.781999999999969 " "
y[1] (closed_form) = 0.31490855842735765 " "
y[1] (numeric) = 0.3149085584273437 " "
absolute error = 1.393329895904571500000000000000E-14 " "
relative error = 4.4245539176922094000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7829999999999688 " "
y[1] (closed_form) = 0.31455542309278284 " "
y[1] (numeric) = 0.31455542309276885 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 4.447168633347887000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7839999999999687 " "
y[1] (closed_form) = 0.31420288142895547 " "
y[1] (numeric) = 0.3142028814289414 " "
absolute error = 1.40443212615082300000000000000E-14 " "
relative error = 4.469825737318643400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7849999999999686 " "
y[1] (closed_form) = 0.31385093210589426 " "
y[1] (numeric) = 0.3138509321058802 " "
absolute error = 1.40443212615082300000000000000E-14 " "
relative error = 4.474838155576874600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7859999999999685 " "
y[1] (closed_form) = 0.31349957379734045 " "
y[1] (numeric) = 0.31349957379732635 " "
absolute error = 1.409983241273948800000000000000E-14 " "
relative error = 4.49756031306576000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7869999999999684 " "
y[1] (closed_form) = 0.3131488051807449 " "
y[1] (numeric) = 0.31314880518073074 " "
absolute error = 1.415534356397074600000000000000E-14 " "
relative error = 4.520324947687566000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7879999999999683 " "
y[1] (closed_form) = 0.31279862493725585 " "
y[1] (numeric) = 0.31279862493724164 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 4.543132092748986600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7889999999999682 " "
y[1] (closed_form) = 0.31244903175170663 " "
y[1] (numeric) = 0.31244903175169236 " "
absolute error = 1.42663658664332620000000000000E-14 " "
relative error = 4.565981781556709000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.789999999999968 " "
y[1] (closed_form) = 0.312100024312603 " "
y[1] (numeric) = 0.3121000243125887 " "
absolute error = 1.42663658664332620000000000000E-14 " "
relative error = 4.571087713900306000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.790999999999968 " "
y[1] (closed_form) = 0.3117516013121113 " "
y[1] (numeric) = 0.31175160131209695 " "
absolute error = 1.437738816889577700000000000000E-14 " "
relative error = 4.611808923637828500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7919999999999678 " "
y[1] (closed_form) = 0.31140376144604565 " "
y[1] (numeric) = 0.3114037614460313 " "
absolute error = 1.43218770176645200000000000000E-14 " "
relative error = 4.599134240112880400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7929999999999677 " "
y[1] (closed_form) = 0.3110565034138563 " "
y[1] (numeric) = 0.31105650341384194 " "
absolute error = 1.437738816889577700000000000000E-14 " "
relative error = 4.622114635477293000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7939999999999676 " "
y[1] (closed_form) = 0.31070982591861707 " "
y[1] (numeric) = 0.31070982591860263 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 4.645137718917001000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7949999999999675 " "
y[1] (closed_form) = 0.31036372766701326 " "
y[1] (numeric) = 0.3103637276669988 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 4.650317686482995400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7959999999999674 " "
y[1] (closed_form) = 0.31001820736933006 " "
y[1] (numeric) = 0.3100182073693155 " "
absolute error = 1.45439216225895500000000000000E-14 " "
relative error = 4.691312083249073500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7969999999999673 " "
y[1] (closed_form) = 0.3096732637394398 " "
y[1] (numeric) = 0.3096732637394252 " "
absolute error = 1.45994327738208090000000000000E-14 " "
relative error = 4.714463430754818000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7979999999999672 " "
y[1] (closed_form) = 0.3093288954947906 " "
y[1] (numeric) = 0.309328895494776 " "
absolute error = 1.45994327738208090000000000000E-14 " "
relative error = 4.719711926837006000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.798999999999967 " "
y[1] (closed_form) = 0.30898510135639407 " "
y[1] (numeric) = 0.30898510135637947 " "
absolute error = 1.45994327738208090000000000000E-14 " "
relative error = 4.7249633428057486000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.799999999999967 " "
y[1] (closed_form) = 0.30864188004881377 " "
y[1] (numeric) = 0.3086418800487991 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 4.7482032972110880000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8009999999999668 " "
y[1] (closed_form) = 0.308299230300153 " "
y[1] (numeric) = 0.3082992303001383 " "
absolute error = 1.471045507628332400000000000000E-14 " "
relative error = 4.771486150634099000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8019999999999667 " "
y[1] (closed_form) = 0.3079571508420432 " "
y[1] (numeric) = 0.30795715084202846 " "
absolute error = 1.476596622751458200000000000000E-14 " "
relative error = 4.7948119363814710000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8029999999999666 " "
y[1] (closed_form) = 0.30761564040963235 " "
y[1] (numeric) = 0.3076156404096176 " "
absolute error = 1.476596622751458200000000000000E-14 " "
relative error = 4.800135067206491300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8039999999999665 " "
y[1] (closed_form) = 0.30727469774157307 " "
y[1] (numeric) = 0.3072746977415583 " "
absolute error = 1.476596622751458200000000000000E-14 " "
relative error = 4.805461151224755000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8049999999999664 " "
y[1] (closed_form) = 0.3069343215800111 " "
y[1] (numeric) = 0.3069343215799962 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 4.846961543236535400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8059999999999663 " "
y[1] (closed_form) = 0.3065945106705735 " "
y[1] (numeric) = 0.3065945106705586 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 4.852333623794710700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8069999999999662 " "
y[1] (closed_form) = 0.30625526376235734 " "
y[1] (numeric) = 0.30625526376234247 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 4.857708679750591000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.807999999999966 " "
y[1] (closed_form) = 0.3059165796079182 " "
y[1] (numeric) = 0.30591657960790325 " "
absolute error = 1.493249968120835500000000000000E-14 " "
relative error = 4.881232557041132000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.808999999999966 " "
y[1] (closed_form) = 0.30557845696325836 " "
y[1] (numeric) = 0.3055784569632434 " "
absolute error = 1.498801083243961300000000000000E-14 " "
relative error = 4.90479956649617970000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8099999999999659 " "
y[1] (closed_form) = 0.3052408945878157 " "
y[1] (numeric) = 0.30524089458780074 " "
absolute error = 1.498801083243961300000000000000E-14 " "
relative error = 4.91022372761644000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8109999999999657 " "
y[1] (closed_form) = 0.30490389124445233 " "
y[1] (numeric) = 0.30490389124443734 " "
absolute error = 1.498801083243961300000000000000E-14 " "
relative error = 4.915650886338866500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8119999999999656 " "
y[1] (closed_form) = 0.3045674456994431 " "
y[1] (numeric) = 0.304567445699428 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 4.957533494831334000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8129999999999655 " "
y[1] (closed_form) = 0.30423155672246416 " "
y[1] (numeric) = 0.30423155672244906 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 4.963006894342736300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8139999999999654 " "
y[1] (closed_form) = 0.3038962230865822 " "
y[1] (numeric) = 0.30389622308656705 " "
absolute error = 1.515454428613338700000000000000E-14 " "
relative error = 4.986749796431576000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8149999999999653 " "
y[1] (closed_form) = 0.3035614435682428 " "
y[1] (numeric) = 0.3035614435682276 " "
absolute error = 1.515454428613338700000000000000E-14 " "
relative error = 4.992249380553014000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8159999999999652 " "
y[1] (closed_form) = 0.30322721694725946 " "
y[1] (numeric) = 0.30322721694724425 " "
absolute error = 1.521005543736464500000000000000E-14 " "
relative error = 5.016058779449913000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.816999999999965 " "
y[1] (closed_form) = 0.3028935420068025 " "
y[1] (numeric) = 0.30289354200678725 " "
absolute error = 1.526556658859590200000000000000E-14 " "
relative error = 5.039911543658155000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.817999999999965 " "
y[1] (closed_form) = 0.30256041753338786 " "
y[1] (numeric) = 0.30256041753337254 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 5.063807706484429000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8189999999999649 " "
y[1] (closed_form) = 0.3022278423168661 " "
y[1] (numeric) = 0.3022278423168508 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 5.069379982458404000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8199999999999648 " "
y[1] (closed_form) = 0.30189581515041164 " "
y[1] (numeric) = 0.30189581515039626 " "
absolute error = 1.537658889105841800000000000000E-14 " "
relative error = 5.0933428419328830000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8209999999999646 " "
y[1] (closed_form) = 0.3015643348305114 " "
y[1] (numeric) = 0.301564334830496 " "
absolute error = 1.543210004228967600000000000000E-14 " "
relative error = 5.117349188843235000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8219999999999645 " "
y[1] (closed_form) = 0.3012334001569543 " "
y[1] (numeric) = 0.30123340015693884 " "
absolute error = 1.548761119352093400000000000000E-14 " "
relative error = 5.141399056496154000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8229999999999644 " "
y[1] (closed_form) = 0.3009030099328201 " "
y[1] (numeric) = 0.30090300993280455 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 5.1654924781983280000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8239999999999643 " "
y[1] (closed_form) = 0.3005731629644687 " "
y[1] (numeric) = 0.3005731629644531 " "
absolute error = 1.55986334959834500000000000000E-14 " "
relative error = 5.1896294872564500000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8249999999999642 " "
y[1] (closed_form) = 0.3002438580615293 " "
y[1] (numeric) = 0.3002438580615137 " "
absolute error = 1.55986334959834500000000000000E-14 " "
relative error = 5.1953214286191330000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.825999999999964 " "
y[1] (closed_form) = 0.29991509403688993 " "
y[1] (numeric) = 0.2999150940368743 " "
absolute error = 1.565414464721470700000000000000E-14 " "
relative error = 5.2195254451879070000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.826999999999964 " "
y[1] (closed_form) = 0.2995868697066863 " "
y[1] (numeric) = 0.2995868697066706 " "
absolute error = 1.570965579844596500000000000000E-14 " "
relative error = 5.243773137930468000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8279999999999639 " "
y[1] (closed_form) = 0.29925918389029144 " "
y[1] (numeric) = 0.29925918389027567 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 5.2680645401535090000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8289999999999638 " "
y[1] (closed_form) = 0.29893203541030505 " "
y[1] (numeric) = 0.29893203541028923 " "
absolute error = 1.58206781009084800000000000000E-14 " "
relative error = 5.292399685163719000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8299999999999637 " "
y[1] (closed_form) = 0.29860542309254284 " "
y[1] (numeric) = 0.29860542309252697 " "
absolute error = 1.58761892521397390000000000000E-14 " "
relative error = 5.3167786062677900000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8309999999999635 " "
y[1] (closed_form) = 0.29827934576602605 " "
y[1] (numeric) = 0.2982793457660102 " "
absolute error = 1.58761892521397390000000000000E-14 " "
relative error = 5.322590879152999000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8319999999999634 " "
y[1] (closed_form) = 0.297953802262971 " "
y[1] (numeric) = 0.2979538022629551 " "
absolute error = 1.593170040337099600000000000000E-14 " "
relative error = 5.347037118630169000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8329999999999633 " "
y[1] (closed_form) = 0.2976287914187786 " "
y[1] (numeric) = 0.29762879141876264 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 5.371527223019040000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8339999999999632 " "
y[1] (closed_form) = 0.2973043120720238 " "
y[1] (numeric) = 0.2973043120720078 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 5.377389733496114000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.834999999999963 " "
y[1] (closed_form) = 0.2969803630644454 " "
y[1] (numeric) = 0.2969803630644294 " "
absolute error = 1.604272270583351200000000000000E-14 " "
relative error = 5.401947300587078000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.835999999999963 " "
y[1] (closed_form) = 0.29665694324093567 " "
y[1] (numeric) = 0.2966569432409196 " "
absolute error = 1.604272270583351200000000000000E-14 " "
relative error = 5.4078365840923880000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8369999999999629 " "
y[1] (closed_form) = 0.29633405144952996 " "
y[1] (numeric) = 0.2963340514495139 " "
absolute error = 1.604272270583351200000000000000E-14 " "
relative error = 5.4137290761422420000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8379999999999628 " "
y[1] (closed_form) = 0.29601168654139665 " "
y[1] (numeric) = 0.29601168654138055 " "
absolute error = 1.60982338570647700000000000000E-14 " "
relative error = 5.4383778036457560000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8389999999999627 " "
y[1] (closed_form) = 0.2956898473708266 " "
y[1] (numeric) = 0.29568984737081044 " "
absolute error = 1.615374500829602800000000000000E-14 " "
relative error = 5.46307056259443000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8399999999999626 " "
y[1] (closed_form) = 0.2953685327952233 " "
y[1] (numeric) = 0.2953685327952071 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 5.48780738629495000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8409999999999624 " "
y[1] (closed_form) = 0.29504774167509246 " "
y[1] (numeric) = 0.29504774167507625 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 5.493774013487273000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8419999999999623 " "
y[1] (closed_form) = 0.2947274728740323 " "
y[1] (numeric) = 0.294727472874016 " "
absolute error = 1.626476731075854300000000000000E-14 " "
relative error = 5.51857862185456100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8429999999999622 " "
y[1] (closed_form) = 0.2944077252587229 " "
y[1] (numeric) = 0.29440772525870657 " "
absolute error = 1.6320278461989800000000000000E-14 " "
relative error = 5.543427383791538000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8439999999999621 " "
y[1] (closed_form) = 0.2940884976989166 " "
y[1] (numeric) = 0.29408849769890033 " "
absolute error = 1.626476731075854300000000000000E-14 " "
relative error = 5.530569008316051000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.844999999999962 " "
y[1] (closed_form) = 0.2937697890674281 " "
y[1] (numeric) = 0.2937697890674118 " "
absolute error = 1.6320278461989800000000000000E-14 " "
relative error = 5.555465221185101000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.845999999999962 " "
y[1] (closed_form) = 0.2934515982401242 " "
y[1] (numeric) = 0.2934515982401078 " "
absolute error = 1.63757896132210600000000000000E-14 " "
relative error = 5.580405665339453000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8469999999999618 " "
y[1] (closed_form) = 0.2931339240959138 " "
y[1] (numeric) = 0.2931339240958974 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 5.605390374085796000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8479999999999617 " "
y[1] (closed_form) = 0.2928167655167386 " "
y[1] (numeric) = 0.2928167655167221 " "
absolute error = 1.648681191568357500000000000000E-14 " "
relative error = 5.630419380730822000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8489999999999616 " "
y[1] (closed_form) = 0.29250012138756254 " "
y[1] (numeric) = 0.292500121387546 " "
absolute error = 1.654232306691483200000000000000E-14 " "
relative error = 5.655492718581221000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8499999999999615 " "
y[1] (closed_form) = 0.29218399059636263 " "
y[1] (numeric) = 0.29218399059634603 " "
absolute error = 1.65978342181460900000000000000E-14 " "
relative error = 5.680610420943685000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8509999999999613 " "
y[1] (closed_form) = 0.29186837203411875 " "
y[1] (numeric) = 0.29186837203410215 " "
absolute error = 1.65978342181460900000000000000E-14 " "
relative error = 5.68675327938782000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8519999999999612 " "
y[1] (closed_form) = 0.2915532645948042 " "
y[1] (numeric) = 0.29155326459478753 " "
absolute error = 1.665334536937734800000000000000E-14 " "
relative error = 5.711939254915182000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8529999999999611 " "
y[1] (closed_form) = 0.2912386671753758 " "
y[1] (numeric) = 0.29123866717535907 " "
absolute error = 1.670885652060860600000000000000E-14 " "
relative error = 5.737169683772452000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.853999999999961 " "
y[1] (closed_form) = 0.29092457867576427 " "
y[1] (numeric) = 0.29092457867574756 " "
absolute error = 1.670885652060860600000000000000E-14 " "
relative error = 5.7433636568846390000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.854999999999961 " "
y[1] (closed_form) = 0.2906109979988649 " "
y[1] (numeric) = 0.29061099799884815 " "
absolute error = 1.676436767183986400000000000000E-14 " "
relative error = 5.768662503235801000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8559999999999608 " "
y[1] (closed_form) = 0.29029792405052757 " "
y[1] (numeric) = 0.2902979240505108 " "
absolute error = 1.676436767183986400000000000000E-14 " "
relative error = 5.77488376007882000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8569999999999607 " "
y[1] (closed_form) = 0.2899853557395474 " "
y[1] (numeric) = 0.2899853557395306 " "
absolute error = 1.681987882307112200000000000000E-14 " "
relative error = 5.8002511127417160000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8579999999999606 " "
y[1] (closed_form) = 0.2896732919776553 " "
y[1] (numeric) = 0.28967329197763847 " "
absolute error = 1.681987882307112200000000000000E-14 " "
relative error = 5.806499697724486000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8589999999999605 " "
y[1] (closed_form) = 0.2893617316795083 " "
y[1] (numeric) = 0.2893617316794914 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 5.831935645516958000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8599999999999604 " "
y[1] (closed_form) = 0.2890506737626803 " "
y[1] (numeric) = 0.2890506737626634 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 5.838211603048401000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8609999999999602 " "
y[1] (closed_form) = 0.28874011714765263 " "
y[1] (numeric) = 0.2887401171476357 " "
absolute error = 1.693090112553363700000000000000E-14 " "
relative error = 5.863716234788291000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8619999999999601 " "
y[1] (closed_form) = 0.28843006075780464 " "
y[1] (numeric) = 0.28843006075778765 " "
absolute error = 1.698641227676489500000000000000E-14 " "
relative error = 5.889265575209383000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.86299999999996 " "
y[1] (closed_form) = 0.2881205035194043 " "
y[1] (numeric) = 0.2881205035193873 " "
absolute error = 1.704192342799615300000000000000E-14 " "
relative error = 5.914859657618367000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.86399999999996 " "
y[1] (closed_form) = 0.2878114443615991 " "
y[1] (numeric) = 0.287811444361582 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 5.940498515321934000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8649999999999598 " "
y[1] (closed_form) = 0.28750288221640663 " "
y[1] (numeric) = 0.2875028822163895 " "
absolute error = 1.71529457304586690000000000000E-14 " "
relative error = 5.966182181626776000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8659999999999597 " "
y[1] (closed_form) = 0.28719481601870533 " "
y[1] (numeric) = 0.2871948160186882 " "
absolute error = 1.71529457304586690000000000000E-14 " "
relative error = 5.97258194567881000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8669999999999596 " "
y[1] (closed_form) = 0.2868872447062255 " "
y[1] (numeric) = 0.28688724470620836 " "
absolute error = 1.71529457304586690000000000000E-14 " "
relative error = 5.978985140319989000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8679999999999595 " "
y[1] (closed_form) = 0.28658016721954 " "
y[1] (numeric) = 0.2865801672195228 " "
absolute error = 1.720845688168992600000000000000E-14 " "
relative error = 6.004761965438827000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8689999999999594 " "
y[1] (closed_form) = 0.286273582502055 " "
y[1] (numeric) = 0.28627358250203777 " "
absolute error = 1.720845688168992600000000000000E-14 " "
relative error = 6.0111927657755140000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8699999999999593 " "
y[1] (closed_form) = 0.2859674895000011 " "
y[1] (numeric) = 0.2859674894999839 " "
absolute error = 1.720845688168992600000000000000E-14 " "
relative error = 6.0176270078035780000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8709999999999591 " "
y[1] (closed_form) = 0.2856618871624244 " "
y[1] (numeric) = 0.2856618871624071 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 6.062929625016712000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.871999999999959 " "
y[1] (closed_form) = 0.2853567744411769 " "
y[1] (numeric) = 0.2853567744411596 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 6.06941230607534000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.872999999999959 " "
y[1] (closed_form) = 0.2850521502909082 " "
y[1] (numeric) = 0.28505215029089087 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 6.075898451029804000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8739999999999588 " "
y[1] (closed_form) = 0.28474801366905617 " "
y[1] (numeric) = 0.2847480136690388 " "
absolute error = 1.7374990335383700000000000000E-14 " "
relative error = 6.101882893405363000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8749999999999587 " "
y[1] (closed_form) = 0.284444363535838 " "
y[1] (numeric) = 0.2844443635358206 " "
absolute error = 1.743050148661495800000000000000E-14 " "
relative error = 6.1279124219379500000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8759999999999586 " "
y[1] (closed_form) = 0.2841411988542416 " "
y[1] (numeric) = 0.2841411988542241 " "
absolute error = 1.748601263784621600000000000000E-14 " "
relative error = 6.1539870699342580000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8769999999999585 " "
y[1] (closed_form) = 0.2838385185900163 " "
y[1] (numeric) = 0.28383851858999887 " "
absolute error = 1.743050148661495800000000000000E-14 " "
relative error = 6.1409922702535050000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8779999999999584 " "
y[1] (closed_form) = 0.28353632171166465 " "
y[1] (numeric) = 0.28353632171164717 " "
absolute error = 1.748601263784621600000000000000E-14 " "
relative error = 6.167115568222751000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8789999999999583 " "
y[1] (closed_form) = 0.2832346071904329 " "
y[1] (numeric) = 0.2832346071904154 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 6.193284063371332000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8799999999999581 " "
y[1] (closed_form) = 0.2829333740003029 " "
y[1] (numeric) = 0.28293337400028534 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 6.199877922163646000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.880999999999958 " "
y[1] (closed_form) = 0.2826326211179829 " "
y[1] (numeric) = 0.28263262111796533 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 6.206475289260717000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.881999999999958 " "
y[1] (closed_form) = 0.28233234752289915 " "
y[1] (numeric) = 0.2823323475228816 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 6.213076164662547000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8829999999999578 " "
y[1] (closed_form) = 0.2820325521971872 " "
y[1] (numeric) = 0.2820325521971696 " "
absolute error = 1.75970349403087300000000000000E-14 " "
relative error = 6.239363081750048000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8839999999999577 " "
y[1] (closed_form) = 0.28173323412568313 " "
y[1] (numeric) = 0.2817332341256655 " "
absolute error = 1.76525460915399900000000000000E-14 " "
relative error = 6.2656953292436450000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8849999999999576 " "
y[1] (closed_form) = 0.28143439229591505 " "
y[1] (numeric) = 0.28143439229589734 " "
absolute error = 1.770805724277124700000000000000E-14 " "
relative error = 6.292072940450028000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8859999999999575 " "
y[1] (closed_form) = 0.28113602569809454 " "
y[1] (numeric) = 0.2811360256980768 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 6.318495948675887000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8869999999999574 " "
y[1] (closed_form) = 0.2808381333251081 " "
y[1] (numeric) = 0.28083813332509033 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 6.325198143030943000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8879999999999573 " "
y[1] (closed_form) = 0.28054071417250875 " "
y[1] (numeric) = 0.280540714172491 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 6.331903890099679000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8889999999999572 " "
y[1] (closed_form) = 0.28024376723850747 " "
y[1] (numeric) = 0.28024376723848965 " "
absolute error = 1.781907954523376200000000000000E-14 " "
relative error = 6.3584213561004730000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.889999999999957 " "
y[1] (closed_form) = 0.2799472915239646 " "
y[1] (numeric) = 0.27994729152394676 " "
absolute error = 1.781907954523376200000000000000E-14 " "
relative error = 6.365155186260618000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.890999999999957 " "
y[1] (closed_form) = 0.27965128603238176 " "
y[1] (numeric) = 0.27965128603236394 " "
absolute error = 1.781907954523376200000000000000E-14 " "
relative error = 6.3718925802366710000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8919999999999568 " "
y[1] (closed_form) = 0.2793557497698934 " "
y[1] (numeric) = 0.27935574976987554 " "
absolute error = 1.78745906964650200000000000000E-14 " "
relative error = 6.398504670545855000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8929999999999567 " "
y[1] (closed_form) = 0.2790606817452583 " "
y[1] (numeric) = 0.27906068174524035 " "
absolute error = 1.793010184769627800000000000000E-14 " "
relative error = 6.425162346612429000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8939999999999566 " "
y[1] (closed_form) = 0.2787660809698511 " "
y[1] (numeric) = 0.2787660809698332 " "
absolute error = 1.793010184769627800000000000000E-14 " "
relative error = 6.431952476182151000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8949999999999565 " "
y[1] (closed_form) = 0.2784719464576547 " "
y[1] (numeric) = 0.27847194645763673 " "
absolute error = 1.798561299892753600000000000000E-14 " "
relative error = 6.458680390508378000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8959999999999564 " "
y[1] (closed_form) = 0.27817827722525124 " "
y[1] (numeric) = 0.27817827722523325 " "
absolute error = 1.798561299892753600000000000000E-14 " "
relative error = 6.465498736396271000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8969999999999563 " "
y[1] (closed_form) = 0.27788507229181436 " "
y[1] (numeric) = 0.2778850722917963 " "
absolute error = 1.804112415015879400000000000000E-14 " "
relative error = 6.492296977799995000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8979999999999562 " "
y[1] (closed_form) = 0.27759233067910083 " "
y[1] (numeric) = 0.27759233067908273 " "
absolute error = 1.809663530139005200000000000000E-14 " "
relative error = 6.519140949290102000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.898999999999956 " "
y[1] (closed_form) = 0.27730005141144237 " "
y[1] (numeric) = 0.2773000514114242 " "
absolute error = 1.81521464526213100000000000000E-14 " "
relative error = 6.546030684173284000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.899999999999956 " "
y[1] (closed_form) = 0.2770082335157376 " "
y[1] (numeric) = 0.27700823351571946 " "
absolute error = 1.81521464526213100000000000000E-14 " "
relative error = 6.552926684610635000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9009999999999558 " "
y[1] (closed_form) = 0.276716876021444 " "
y[1] (numeric) = 0.2767168760214258 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 6.579886946411456000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9019999999999557 " "
y[1] (closed_form) = 0.2764259779605696 " "
y[1] (numeric) = 0.2764259779605514 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 6.586811318598200000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9029999999999556 " "
y[1] (closed_form) = 0.27613553836766525 " "
y[1] (numeric) = 0.276135538367647 " "
absolute error = 1.826316875508382500000000000000E-14 " "
relative error = 6.6138421961345040000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9039999999999555 " "
y[1] (closed_form) = 0.2758455562798163 " "
y[1] (numeric) = 0.27584555627979795 " "
absolute error = 1.831867990631508300000000000000E-14 " "
relative error = 6.640918981392874000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9049999999999554 " "
y[1] (closed_form) = 0.2755560307366348 " "
y[1] (numeric) = 0.27555603073661644 " "
absolute error = 1.83741910575463400000000000000E-14 " "
relative error = 6.6680417076800050000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9059999999999553 " "
y[1] (closed_form) = 0.2752669607802516 " "
y[1] (numeric) = 0.2752669607802332 " "
absolute error = 1.83741910575463400000000000000E-14 " "
relative error = 6.675044111892035000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9069999999999552 " "
y[1] (closed_form) = 0.2749783454553083 " "
y[1] (numeric) = 0.2749783454552899 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 6.702237653754791000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.907999999999955 " "
y[1] (closed_form) = 0.2746901838089494 " "
y[1] (numeric) = 0.27469018380893095 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 6.7092685851474400000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.908999999999955 " "
y[1] (closed_form) = 0.2744024748908145 " "
y[1] (numeric) = 0.274402474890796 " "
absolute error = 1.848521336000885600000000000000E-14 " "
relative error = 6.736533031403662000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9099999999999548 " "
y[1] (closed_form) = 0.2741152177530302 " "
y[1] (numeric) = 0.2741152177530117 " "
absolute error = 1.854072451124011400000000000000E-14 " "
relative error = 6.763843563017637000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9109999999999547 " "
y[1] (closed_form) = 0.27382841145020276 " "
y[1] (numeric) = 0.2738284114501842 " "
absolute error = 1.854072451124011400000000000000E-14 " "
relative error = 6.770927973853381000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9119999999999546 " "
y[1] (closed_form) = 0.27354205503940987 " "
y[1] (numeric) = 0.2735420550393913 " "
absolute error = 1.859623566247137200000000000000E-14 " "
relative error = 6.798309554189818000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9129999999999545 " "
y[1] (closed_form) = 0.2732561475801932 " "
y[1] (numeric) = 0.2732561475801745 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 6.825737308701848000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9139999999999544 " "
y[1] (closed_form) = 0.2729706881345504 " "
y[1] (numeric) = 0.27297068813453174 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 6.832875332207453000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9149999999999543 " "
y[1] (closed_form) = 0.27268567576692787 " "
y[1] (numeric) = 0.2726856757669091 " "
absolute error = 1.876276911616514600000000000000E-14 " "
relative error = 6.880731473479454000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9159999999999542 " "
y[1] (closed_form) = 0.2724011095442124 " "
y[1] (numeric) = 0.27240110954419366 " "
absolute error = 1.876276911616514600000000000000E-14 " "
relative error = 6.887919490327857000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.916999999999954 " "
y[1] (closed_form) = 0.2721169885357243 " "
y[1] (numeric) = 0.27211698853570554 " "
absolute error = 1.876276911616514600000000000000E-14 " "
relative error = 6.895111259730083000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.917999999999954 " "
y[1] (closed_form) = 0.2718333118132092 " "
y[1] (numeric) = 0.27183331181319037 " "
absolute error = 1.881828026739640300000000000000E-14 " "
relative error = 6.922727807667453000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9189999999999539 " "
y[1] (closed_form) = 0.2715500784508307 " "
y[1] (numeric) = 0.27155007845081186 " "
absolute error = 1.881828026739640300000000000000E-14 " "
relative error = 6.929948381806051000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9199999999999537 " "
y[1] (closed_form) = 0.27126728752516294 " "
y[1] (numeric) = 0.27126728752514406 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 6.957636355941708000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9209999999999536 " "
y[1] (closed_form) = 0.27098493811518276 " "
y[1] (numeric) = 0.27098493811516383 " "
absolute error = 1.89293025698589200000000000000E-14 " "
relative error = 6.985370737399795000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9219999999999535 " "
y[1] (closed_form) = 0.2707030293022625 " "
y[1] (numeric) = 0.27070302930224355 " "
absolute error = 1.89293025698589200000000000000E-14 " "
relative error = 6.992645268377391000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9229999999999534 " "
y[1] (closed_form) = 0.27042156017016233 " "
y[1] (numeric) = 0.27042156017014335 " "
absolute error = 1.898481372109017700000000000000E-14 " "
relative error = 7.02045122036276000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9239999999999533 " "
y[1] (closed_form) = 0.27014052980502296 " "
y[1] (numeric) = 0.27014052980500397 " "
absolute error = 1.898481372109017700000000000000E-14 " "
relative error = 7.0277546782012620000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9249999999999532 " "
y[1] (closed_form) = 0.2698599372953581 " "
y[1] (numeric) = 0.2698599372953391 " "
absolute error = 1.904032487232143500000000000000E-14 " "
relative error = 7.055632289531755000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.925999999999953 " "
y[1] (closed_form) = 0.26957978173204705 " "
y[1] (numeric) = 0.269579781732028 " "
absolute error = 1.904032487232143500000000000000E-14 " "
relative error = 7.062964718640086000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.926999999999953 " "
y[1] (closed_form) = 0.26930006220832753 " "
y[1] (numeric) = 0.26930006220830843 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 7.090914078133546000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9279999999999529 " "
y[1] (closed_form) = 0.26902077781978806 " "
y[1] (numeric) = 0.26902077781976896 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 7.0982755229206240000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9289999999999528 " "
y[1] (closed_form) = 0.26874192766436095 " "
y[1] (numeric) = 0.2687419276643418 " "
absolute error = 1.91513471747839500000000000000E-14 " "
relative error = 7.126296719394892000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9299999999999526 " "
y[1] (closed_form) = 0.26846351084231473 " "
y[1] (numeric) = 0.2684635108422956 " "
absolute error = 1.91513471747839500000000000000E-14 " "
relative error = 7.133687224269643000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9309999999999525 " "
y[1] (closed_form) = 0.26818552645624716 " "
y[1] (numeric) = 0.268185526456228 " "
absolute error = 1.91513471747839500000000000000E-14 " "
relative error = 7.141081559413824000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9319999999999524 " "
y[1] (closed_form) = 0.26790797361107777 " "
y[1] (numeric) = 0.2679079736110586 " "
absolute error = 1.91513471747839500000000000000E-14 " "
relative error = 7.148479724827442000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9329999999999523 " "
y[1] (closed_form) = 0.2676308514140408 " "
y[1] (numeric) = 0.2676308514140216 " "
absolute error = 1.920685832601520800000000000000E-14 " "
relative error = 7.176623406656902000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9339999999999522 " "
y[1] (closed_form) = 0.2673541589746779 " "
y[1] (numeric) = 0.2673541589746587 " "
absolute error = 1.920685832601520800000000000000E-14 " "
relative error = 7.1840506987715720000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.934999999999952 " "
y[1] (closed_form) = 0.2670778954048312 " "
y[1] (numeric) = 0.2670778954048119 " "
absolute error = 1.926236947724646600000000000000E-14 " "
relative error = 7.2122664618309060000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.935999999999952 " "
y[1] (closed_form) = 0.26680205981863586 " "
y[1] (numeric) = 0.26680205981861654 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 7.240529042995187000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9369999999999519 " "
y[1] (closed_form) = 0.26652665133251324 " "
y[1] (numeric) = 0.26652665133249387 " "
absolute error = 1.937339177970898200000000000000E-14 " "
relative error = 7.2688384755711100000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9379999999999518 " "
y[1] (closed_form) = 0.2662516690651637 " "
y[1] (numeric) = 0.2662516690651443 " "
absolute error = 1.937339177970898200000000000000E-14 " "
relative error = 7.276345664885747000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9389999999999517 " "
y[1] (closed_form) = 0.2659771121375596 " "
y[1] (numeric) = 0.26597711213754016 " "
absolute error = 1.94289029309402400000000000000E-14 " "
relative error = 7.304727378531686000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9399999999999515 " "
y[1] (closed_form) = 0.2657029796729382 " "
y[1] (numeric) = 0.2657029796729187 " "
absolute error = 1.948441408217149700000000000000E-14 " "
relative error = 7.333156032407108000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9409999999999514 " "
y[1] (closed_form) = 0.2654292707967948 " "
y[1] (numeric) = 0.26542927079677525 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 7.3616316598186990000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9419999999999513 " "
y[1] (closed_form) = 0.2651559846368755 " "
y[1] (numeric) = 0.26515598463685597 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 7.36921901278683100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9429999999999512 " "
y[1] (closed_form) = 0.2648831203231707 " "
y[1] (numeric) = 0.2648831203231511 " "
absolute error = 1.959543638463401300000000000000E-14 " "
relative error = 7.397767121108585000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.943999999999951 " "
y[1] (closed_form) = 0.26461067698790763 " "
y[1] (numeric) = 0.264610676987888 " "
absolute error = 1.96509475358652700000000000000E-14 " "
relative error = 7.426362291784354000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.944999999999951 " "
y[1] (closed_form) = 0.2643386537655439 " "
y[1] (numeric) = 0.2643386537655242 " "
absolute error = 1.97064586870965290000000000000E-14 " "
relative error = 7.455004558120827000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9459999999999509 " "
y[1] (closed_form) = 0.2640670497927603 " "
y[1] (numeric) = 0.2640670497927406 " "
absolute error = 1.97064586870965290000000000000E-14 " "
relative error = 7.462672341195976000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9469999999999508 " "
y[1] (closed_form) = 0.26379586420845424 " "
y[1] (numeric) = 0.26379586420843454 " "
absolute error = 1.97064586870965290000000000000E-14 " "
relative error = 7.470344065562862000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9479999999999507 " "
y[1] (closed_form) = 0.2635250961537328 " "
y[1] (numeric) = 0.26352509615371306 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 7.499084575534785000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9489999999999505 " "
y[1] (closed_form) = 0.26325474477190575 " "
y[1] (numeric) = 0.263254744771886 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 7.50678581518078000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9499999999999504 " "
y[1] (closed_form) = 0.26298480920847905 " "
y[1] (numeric) = 0.26298480920845924 " "
absolute error = 1.981748098955904400000000000000E-14 " "
relative error = 7.535599128027544000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9509999999999503 " "
y[1] (closed_form) = 0.26271528861114796 " "
y[1] (numeric) = 0.26271528861112814 " "
absolute error = 1.981748098955904400000000000000E-14 " "
relative error = 7.54332992736157000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9519999999999502 " "
y[1] (closed_form) = 0.2624461821297904 " "
y[1] (numeric) = 0.2624461821297705 " "
absolute error = 1.987299214079030200000000000000E-14 " "
relative error = 7.572216131901014000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.95299999999995 " "
y[1] (closed_form) = 0.26217748891646003 " "
y[1] (numeric) = 0.2621774889164401 " "
absolute error = 1.99285032920215600000000000000E-14 " "
relative error = 7.601149654145768000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.95399999999995 " "
y[1] (closed_form) = 0.26190920812537993 " "
y[1] (numeric) = 0.26190920812535995 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 7.630130527402521000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9549999999999499 " "
y[1] (closed_form) = 0.2616413389129355 " "
y[1] (numeric) = 0.2616413389129155 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 7.637942278648387000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9559999999999498 " "
y[1] (closed_form) = 0.2613738804376683 " "
y[1] (numeric) = 0.2613738804376483 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 7.645758026697144000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9569999999999497 " "
y[1] (closed_form) = 0.26110683186026906 " "
y[1] (numeric) = 0.261106831860249 " "
absolute error = 2.003952559448407600000000000000E-14 " "
relative error = 7.674837709803090000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9579999999999496 " "
y[1] (closed_form) = 0.26084019234357125 " "
y[1] (numeric) = 0.2608401923435512 " "
absolute error = 2.003952559448407600000000000000E-14 " "
relative error = 7.68268318407333000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9589999999999494 " "
y[1] (closed_form) = 0.26057396105254466 " "
y[1] (numeric) = 0.26057396105252456 " "
absolute error = 2.009503674571533300000000000000E-14 " "
relative error = 7.711836080836633000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9599999999999493 " "
y[1] (closed_form) = 0.2603081371542884 " "
y[1] (numeric) = 0.26030813715426837 " "
absolute error = 2.003952559448407600000000000000E-14 " "
relative error = 7.698386156329164000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9609999999999492 " "
y[1] (closed_form) = 0.2600427198180252 " "
y[1] (numeric) = 0.26004271981800503 " "
absolute error = 2.01505478969465900000000000000E-14 " "
relative error = 7.748937524975783000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9619999999999491 " "
y[1] (closed_form) = 0.2597777082150938 " "
y[1] (numeric) = 0.2597777082150737 " "
absolute error = 2.01505478969465900000000000000E-14 " "
relative error = 7.756842584915755000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.962999999999949 " "
y[1] (closed_form) = 0.25951310151894363 " "
y[1] (numeric) = 0.2595131015189235 " "
absolute error = 2.01505478969465900000000000000E-14 " "
relative error = 7.764751674965307000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.963999999999949 " "
y[1] (closed_form) = 0.25924889890512764 " "
y[1] (numeric) = 0.2592488989051074 " "
absolute error = 2.026157019940910700000000000000E-14 " "
relative error = 7.815489394546608000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9649999999999488 " "
y[1] (closed_form) = 0.2589850995512959 " "
y[1] (numeric) = 0.25898509955127563 " "
absolute error = 2.026157019940910700000000000000E-14 " "
relative error = 7.823450165477956000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9659999999999487 " "
y[1] (closed_form) = 0.2587217026371897 " "
y[1] (numeric) = 0.25872170263716937 " "
absolute error = 2.031708135064036500000000000000E-14 " "
relative error = 7.852870920199297000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9669999999999486 " "
y[1] (closed_form) = 0.2584587073446346 " "
y[1] (numeric) = 0.25845870734461424 " "
absolute error = 2.037259250187162300000000000000E-14 " "
relative error = 7.882339392306235000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9679999999999485 " "
y[1] (closed_form) = 0.25819611285753447 " "
y[1] (numeric) = 0.25819611285751404 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 7.911855615105463000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9689999999999483 " "
y[1] (closed_form) = 0.25793391836186486 " "
y[1] (numeric) = 0.2579339183618444 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 7.919898159513691000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9699999999999482 " "
y[1] (closed_form) = 0.2576721230456671 " "
y[1] (numeric) = 0.25767212304564663 " "
absolute error = 2.048361480433413800000000000000E-14 " "
relative error = 7.949488117775098000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9709999999999481 " "
y[1] (closed_form) = 0.25741072609904153 " "
y[1] (numeric) = 0.257410726099021 " "
absolute error = 2.053912595556539600000000000000E-14 " "
relative error = 7.979125915546638000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.971999999999948 " "
y[1] (closed_form) = 0.2571497267141415 " "
y[1] (numeric) = 0.25714972671412095 " "
absolute error = 2.053912595556539600000000000000E-14 " "
relative error = 7.987224492910917000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.972999999999948 " "
y[1] (closed_form) = 0.2568891240851672 " "
y[1] (numeric) = 0.2568891240851466 " "
absolute error = 2.059463710679665400000000000000E-14 " "
relative error = 8.01693617047363100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9739999999999478 " "
y[1] (closed_form) = 0.2566289174083592 " "
y[1] (numeric) = 0.2566289174083386 " "
absolute error = 2.059463710679665400000000000000E-14 " "
relative error = 8.025064873739682000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9749999999999477 " "
y[1] (closed_form) = 0.2563691058819925 " "
y[1] (numeric) = 0.25636910588197187 " "
absolute error = 2.065014825802791200000000000000E-14 " "
relative error = 8.054850519911411000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9759999999999476 " "
y[1] (closed_form) = 0.25610968870637024 " "
y[1] (numeric) = 0.2561096887063496 " "
absolute error = 2.065014825802791200000000000000E-14 " "
relative error = 8.063009393488157000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9769999999999475 " "
y[1] (closed_form) = 0.2558506650838175 " "
y[1] (numeric) = 0.2558506650837968 " "
absolute error = 2.07056594092591700000000000000E-14 " "
relative error = 8.092869097086745000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9779999999999474 " "
y[1] (closed_form) = 0.25559203421867516 " "
y[1] (numeric) = 0.2555920342186544 " "
absolute error = 2.076117056049042700000000000000E-14 " "
relative error = 8.122776840035607000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9789999999999472 " "
y[1] (closed_form) = 0.25533379531729394 " "
y[1] (numeric) = 0.2553337953172732 " "
absolute error = 2.076117056049042700000000000000E-14 " "
relative error = 8.130992035226392000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9799999999999471 " "
y[1] (closed_form) = 0.2550759475880282 " "
y[1] (numeric) = 0.25507594758800745 " "
absolute error = 2.076117056049042700000000000000E-14 " "
relative error = 8.139211382651288000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.980999999999947 " "
y[1] (closed_form) = 0.2548184902412299 " "
y[1] (numeric) = 0.2548184902412091 " "
absolute error = 2.076117056049042700000000000000E-14 " "
relative error = 8.1474348823102990000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.981999999999947 " "
y[1] (closed_form) = 0.2545614224892425 " "
y[1] (numeric) = 0.2545614224892217 " "
absolute error = 2.081668171172168500000000000000E-14 " "
relative error = 8.177469118519471000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9829999999999468 " "
y[1] (closed_form) = 0.254304743546395 " "
y[1] (numeric) = 0.25430474354637417 " "
absolute error = 2.081668171172168500000000000000E-14 " "
relative error = 8.185722932818169000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9839999999999467 " "
y[1] (closed_form) = 0.25404845262899595 " "
y[1] (numeric) = 0.2540484526289751 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 8.215831526214414000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9849999999999466 " "
y[1] (closed_form) = 0.2537925489553274 " "
y[1] (numeric) = 0.2537925489553065 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 8.22411569956171900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9859999999999465 " "
y[1] (closed_form) = 0.2535370317456389 " "
y[1] (numeric) = 0.25353703174561804 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 8.232404047347599000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9869999999999464 " "
y[1] (closed_form) = 0.25328190022214186 " "
y[1] (numeric) = 0.25328190022212094 " "
absolute error = 2.0927704014184200000000000000E-14 " "
relative error = 8.262613315767718000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9879999999999463 " "
y[1] (closed_form) = 0.2530271536090032 " "
y[1] (numeric) = 0.25302715360898226 " "
absolute error = 2.0927704014184200000000000000E-14 " "
relative error = 8.270932078113357000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9889999999999461 " "
y[1] (closed_form) = 0.2527727911323397 " "
y[1] (numeric) = 0.25277279113231876 " "
absolute error = 2.0927704014184200000000000000E-14 " "
relative error = 8.279255025999797000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.989999999999946 " "
y[1] (closed_form) = 0.25251881202021215 " "
y[1] (numeric) = 0.25251881202019116 " "
absolute error = 2.09832151654154600000000000000E-14 " "
relative error = 8.309565135977243000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.990999999999946 " "
y[1] (closed_form) = 0.2522652155026193 " "
y[1] (numeric) = 0.25226521550259834 " "
absolute error = 2.09832151654154600000000000000E-14 " "
relative error = 8.317918553934593000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9919999999999458 " "
y[1] (closed_form) = 0.25201200081149233 " "
y[1] (numeric) = 0.2520120008114713 " "
absolute error = 2.103872631664671600000000000000E-14 " "
relative error = 8.348303354166021000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9929999999999457 " "
y[1] (closed_form) = 0.2517591671806887 " "
y[1] (numeric) = 0.2517591671806676 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 8.378736593428014000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9939999999999456 " "
y[1] (closed_form) = 0.2515067138459865 " "
y[1] (numeric) = 0.25150671384596535 " "
absolute error = 2.114974861910923200000000000000E-14 " "
relative error = 8.409218305027262000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9949999999999455 " "
y[1] (closed_form) = 0.25125464004507875 " "
y[1] (numeric) = 0.2512546400450576 " "
absolute error = 2.114974861910923200000000000000E-14 " "
relative error = 8.417654939751424000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9959999999999454 " "
y[1] (closed_form) = 0.25100294501756765 " "
y[1] (numeric) = 0.25100294501754644 " "
absolute error = 2.12052597703404900000000000000E-14 " "
relative error = 8.448211541444798000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9969999999999453 " "
y[1] (closed_form) = 0.25075162800495854 " "
y[1] (numeric) = 0.25075162800493733 " "
absolute error = 2.12052597703404900000000000000E-14 " "
relative error = 8.456678801671095000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9979999999999452 " "
y[1] (closed_form) = 0.25050068825065475 " "
y[1] (numeric) = 0.2505006882506335 " "
absolute error = 2.126077092157174800000000000000E-14 " "
relative error = 8.487310382276435000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.998999999999945 " "
y[1] (closed_form) = 0.2502501249999512 " "
y[1] (numeric) = 0.25025012499992993 " "
absolute error = 2.126077092157174800000000000000E-14 " "
relative error = 8.495808312413787000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.999999999999945 " "
y[1] (closed_form) = 0.24999993750002938 " "
y[1] (numeric) = 0.2499999375000081 " "
absolute error = 2.128852649718737700000000000000E-14 " "
relative error = 8.515412727727131000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
"Finished!"
"diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; "
Iterations = 501
"Total Elapsed Time "= 11 Seconds
"Elapsed Time(since restart) "= 11 Seconds
"Expected Time Remaining "= 0 Seconds
"Optimized Time Remaining "= 0 Seconds
"Expected Total Time "= 11 Seconds
"Time to Timeout "= 2 Minutes 48 Seconds
Percent Done = 0.0 "%"
(%o258) temp/diffeq.sing1_back.max