(%i1) batch("temp/diffeq.sing2_back.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.sing2_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_m1,[20],convfloat)
(%i191) completearray(array_y_higher,[2,20],convfloat)
(%i192) completearray(array_y_higher_work,[2,20],convfloat)
(%i193) completearray(array_y_higher_work2,[2,20],convfloat)
(%i194) completearray(array_y_set_initial,[2,20],convfloat)
(%i195) completearray(array_given_rad_poles,[2,3],convfloat)
(%i196) completearray(array_given_ord_poles,[2,3],convfloat)
(%i197) completearray(array_rad_test_poles,[2,4],convfloat)
(%i198) completearray(array_ord_test_poles,[2,4],convfloat)
(%i199) completearray(array_fact_2,[20,20],convfloat)
(%i200) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i201) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i202) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i203) 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))
(%i204) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i205) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i206) 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)
(%i207) 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)
(%i208) 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)
(%i209) 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)
(%i210) 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)
(%i211) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i212) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i213) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i214) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i215) log_revs(file,revs):=printf(file,revs)
(%i216) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i217) 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)
(%i218) logstart(file):=(printf(file,""),0)
(%i219) logend(file):=(printf(file,"
~%"),0)
(%i220) 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)
(%i221) 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)
(%i222) 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)
(%i223) 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)
(%i224) 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)
(%i225) c(in_val):=(ret:in_val,ret)
(%i226) 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)
(%i227) 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)
(%i228) 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)
(%i229) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i230) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i231) 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)
(%i232) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i233) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i234) 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)
(%i235) log10(x):=log(x)/glob_log_10
(%i236) c(x):=x
(%i237) 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
(%i238) 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)
(%i239) exact_soln_y(x):=block(atan(c(x)))
(%o239) exact_soln_y(x) := block(atan(c(x)))
(%i240) 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)
(%i241) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i242) 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)
(%i243) 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)
(%i244) 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))
(%i245) 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))
(%i246) 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(22)
*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)
(%i247) 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)
(%i248) 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)
(%i249) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),
array_tmp1[1]:array_x[1]*array_x[1],
array_tmp2[1]:array_const_1D0[1]+array_tmp1[1],
array_tmp3[1]:array_const_1D0[1]/array_tmp2[1],
array_tmp4[1]:array_tmp3[1]+array_const_0D0[1],
if not array_y_set_initial[1,2]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp4[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_tmp1[2]:array_x[2]*array_x[1]
+array_x[1]*array_x[2],
array_tmp2[2]:array_tmp1[2],
array_tmp3[2]:neg(ats(2,array_tmp2,array_tmp3,2))
/array_tmp2[1],
array_tmp4[2]:array_tmp3[2],
if not array_y_set_initial[1,3]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp4[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_tmp1[3]:array_x[2]*array_x[2],
array_tmp2[3]:array_tmp1[3],
array_tmp3[3]:neg(ats(3,array_tmp2,array_tmp3,2))
/array_tmp2[1],
array_tmp4[3]:array_tmp3[3],
if not array_y_set_initial[1,4]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp4[3])*expt(glob_h,c(1))
*c(factorial_3(2,3)),
if 4 <= ats_max_terms
then (array_y[4]:temporary,
array_y_higher[1,4]:temporary),
temporary:c(temporary)*c(3)/c(glob_h),
array_y_higher[2,3]:c(temporary),0)),
kkk:4,array_tmp2[4]:array_tmp1[4],
array_tmp3[4]:neg(ats(4,array_tmp2,array_tmp3,2))
/array_tmp2[1],
array_tmp4[4]:array_tmp3[4],
if not array_y_set_initial[1,5]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp4[4])*expt(glob_h,c(1))
*c(factorial_3(3,4)),
if 5 <= ats_max_terms
then (array_y[5]:temporary,
array_y_higher[1,5]:temporary),
temporary:c(temporary)*c(4)/c(glob_h),
array_y_higher[2,4]:c(temporary),0)),
kkk:5,array_tmp2[5]:array_tmp1[5],
array_tmp3[5]:neg(ats(5,array_tmp2,array_tmp3,2))
/array_tmp2[1],
array_tmp4[5]:array_tmp3[5],
if not array_y_set_initial[1,6]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp4[5])*expt(glob_h,c(1))
*c(factorial_3(4,5)),
if 6 <= ats_max_terms
then (array_y[6]:temporary,
array_y_higher[1,6]:temporary),
temporary:c(temporary)*c(5)/c(glob_h),
array_y_higher[2,5]:c(temporary),0)),
kkk:6,
while kkk <= ats_max_terms do
(array_tmp2[kkk]:array_tmp1[kkk],
array_tmp3[kkk]
:neg(ats(kkk,array_tmp2,array_tmp3,2))
/array_tmp2[1],array_tmp4[kkk]:array_tmp3[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_tmp4[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)
(%i250) exact_soln_y(x):=block(atan(c(x)))
(%o250) exact_soln_y(x) := block(atan(c(x)))
(%i251) 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_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_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_1D0),array_const_1D0[1]:c(1.0),
zero_ats_ar(array_m1),array_m1[1]:glob__m1,iiif:0,
while iiif <= ats_max_terms do
(jjjf:0,
while jjjf <= ats_max_terms do
(array_fact_1[iiif]:0,
array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf),
iiif:1+iiif),array_y_set_initial[1,1]:true,
array_y_set_initial[1,2]:false,
array_y_set_initial[1,3]:false,
array_y_set_initial[1,4]:false,
array_y_set_initial[1,5]:false,
array_y_set_initial[1,6]:false,
array_y_set_initial[1,7]:false,
array_y_set_initial[1,8]:false,
array_y_set_initial[1,9]:false,
array_y_set_initial[1,10]:false,
array_y_set_initial[1,11]:false,
array_y_set_initial[1,12]:false,
array_y_set_initial[1,13]:false,
array_y_set_initial[1,14]:false,
array_y_set_initial[1,15]:false,
array_y_set_initial[1,16]:false,
array_y_set_initial[1,17]:false,
array_y_set_initial[1,18]:false,
array_y_set_initial[1,19]:false,
array_y_set_initial[1,20]:false,glob_log_10:log(10.0),
glob_orig_start_sec:elapsed_time_seconds(),
glob_display_flag:true,glob_no_eqs:1,glob_iter:-1,
opt_iter:-1,glob_max_iter:50000,glob_max_hours:0.0,
glob_max_minutes:15.0,
omniout_str(always,
"##############ECHO OF PROBLEM#################"),
omniout_str(always,
"##############temp/sing2_backpostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; "),
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,""),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(1.0),"),
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," (arctan(c(x))) "),
omniout_str(always,"));"),omniout_str(always,""),
omniout_str(always,""),
omniout_str(always,"/* END USER DEF BLOCK */"),
omniout_str(always,
"#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false,
glob_small_float:glob__0,glob_smallish_float:glob__0,
glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100),
glob_almost_1:c(0.99),x_start:c(-1.5),x_end:c(-2.0),
array_y_init[1+0]:exact_soln_y(x_start),
glob_look_poles:true,glob_type_given_pole:2,
array_given_rad_poles[1,1]:c(0.0),
array_given_rad_poles[1,2]:c(1.0),
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 ) = 1.0 / ( x * x + 1.0 ) ; "),
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,
"2015-04-24T23:04:41-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"sing2_back"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; "),
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,
"sing2_back diffeq.max"),
logitem_str(html_log_file,
"sing2_back maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i252) main():=(glob_iolevel:2,compile(all),main_prog())
(%i253) 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_tmp1 in translation.
warning: encountered undefined variable array_const_1D0 in translation.
warning: encountered undefined variable array_tmp2 in translation.
warning: encountered undefined variable array_tmp3 in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp4 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temporary in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable array_y_set_initial in translation.
warning: encountered undefined variable kkk in translation.
warning: encountered undefined variable order_d in translation.
warning: encountered undefined variable adj3 in translation.
warning: encountered undefined variable adj2 in translation.
modedeclare: [found_h]
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: variable term (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable array_y_init in translation.
warning: variable term (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_norms in translation.
warning: encountered undefined variable array_fact_1 in translation.
warning: encountered undefined variable array_type_pole in translation.
warning: encountered undefined variable array_type_real_pole in translation.
warning: encountered undefined variable array_type_complex_pole in translation.
warning: encountered undefined variable array_tmp0 in translation.
warning: encountered undefined variable array_m1 in translation.
warning: variable ord (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable ord in translation.
warning: variable ord (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_y_higher_work in translation.
warning: encountered undefined variable array_y_higher_work2 in translation.
warning: encountered undefined variable array_const_1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: variable iiif (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable iiif in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: variable jjjf (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable jjjf in translation.
warning: variable jjjf (declared type [found_h]) assigned type any.
warning: variable iiif (declared type [found_h]) assigned type any.
warning: variable glob_orig_start_sec (declared type convfloat) assigned type any.
warning: variable opt_iter (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__0 in translation.
warning: variable glob_large_float (declared type convfloat) assigned type any.
warning: variable glob_larger_float (declared type convfloat) assigned type any.
warning: variable glob_almost_1 (declared type convfloat) assigned type any.
warning: variable x_start (declared type [found_h]) assigned type any.
warning: variable x_end (declared type [found_h]) assigned type any.
warning: encountered undefined variable x_start in translation.
warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_h (declared type convfloat) assigned type any.
warning: variable glob_display_interval (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_max_minutes in translation.
warning: encountered undefined variable glob_max_hours in translation.
warning: encountered undefined variable x_end in translation.
warning: variable glob_check_sign (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_larger_float in translation.
warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_max_h in translation.
warning: encountered undefined variable glob_display_interval in translation.
warning: encountered undefined variable glob__10 in translation.
warning: variable display_max (declared type [found_h]) assigned type any.
warning: encountered undefined variable display_max in translation.
warning: variable min_value (declared type [found_h]) assigned type convfloat.
warning: variable est_answer (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_answer in translation.
warning: variable est_needed_step_err (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_needed_step_err in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable opt_iter in translation.
warning: encountered undefined variable found_h in translation.
warning: variable glob_next_display (declared type convfloat) assigned type any.
warning: variable order_diff (declared type [found_h]) assigned type fixnum.
warning: variable term_no (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable order_diff in translation.
warning: variable term_no (declared type [found_h]) assigned type any.
warning: variable r_order (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable r_order in translation.
warning: encountered undefined variable rows in translation.
warning: variable it (declared type [found_h]) assigned type any.
warning: encountered undefined variable it in translation.
warning: variable r_order (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_look_poles in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type any.
warning: encountered undefined variable estimated_step_error in translation.
warning: encountered undefined variable glob__2 in translation.
warning: variable opt_iter (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_optimize in translation.
warning: variable html_log_file (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_html_log in translation.
warning: variable current_iter (declared type [found_h]) assigned type fixnum.
warning: variable glob_clock_start_sec (declared type convfloat) assigned type any.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable debugl in translation.
warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable current_iter in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: variable calc_term (declared type [found_h]) assigned type fixnum.
warning: variable iii (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable calc_term in translation.
warning: variable iii (declared type [found_h]) assigned type any.
warning: variable temp_sum (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable temp_sum in translation.
warning: variable temp_sum (declared type [found_h]) assigned type any.
warning: encountered undefined variable html_log_file in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob_percent_done in translation.
warning: encountered undefined variable glob__100 in translation.
WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB__PI is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $LAST_MIN_POLE_EST is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H is neither declared nor
bound,
it will be treated as if it were declared SPECIAL.
"##############ECHO OF PROBLEM#################"
"##############temp/sing2_backpostode.ode#################"
"diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; "
"!"
"/* 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_type_given_pole:2,"
""
"array_given_rad_poles[1,1]:c(0.0),"
""
"array_given_rad_poles[1,2]:c(1.0),"
""
"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("
" (arctan(c(x))) "
"));"
""
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.501 " "
y[1] (closed_form) = -0.9831012735990038 " "
y[1] (numeric) = -0.9831012735990039 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.129306872486063000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 15
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5019999999999998 " "
y[1] (closed_form) = -0.983408540261777 " "
y[1] (numeric) = -0.9834085402617773 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.25790803958164200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 15
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5029999999999997 " "
y[1] (closed_form) = -0.9837155235700465 " "
y[1] (numeric) = -0.9837155235700465 " "
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] = -1.5039999999999996 " "
y[1] (closed_form) = -0.9840222238578064 " "
y[1] (numeric) = -0.9840222238578066 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.256499899509559200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 15
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5049999999999994 " "
y[1] (closed_form) = -0.9843286414586492 " "
y[1] (numeric) = -0.9843286414586494 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.255797460043320600000000000000E-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) = -0.9846347767057649 " "
y[1] (numeric) = -0.9846347767057649 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5069999999999992 " "
y[1] (closed_form) = -0.9849406299319406 " "
y[1] (numeric) = -0.984940629931941 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.38159374550892300000000000000E-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) = -0.9852462014695632 " "
y[1] (numeric) = -0.9852462014695633 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.126848317678547500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.508999999999999 " "
y[1] (closed_form) = -0.9855514916506161 " "
y[1] (numeric) = -0.9855514916506165 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.505997034272613600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.509999999999999 " "
y[1] (closed_form) = -0.9858565008066833 " "
y[1] (numeric) = -0.9858565008066835 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.252301473321339200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5109999999999988 " "
y[1] (closed_form) = -0.9861612292689461 " "
y[1] (numeric) = -0.9861612292689466 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.50321100312645160000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5119999999999987 " "
y[1] (closed_form) = -0.9864656773681864 " "
y[1] (numeric) = -0.9864656773681868 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.5018211990391600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5129999999999986 " "
y[1] (closed_form) = -0.9867698454347846 " "
y[1] (numeric) = -0.9867698454347852 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 5.625541912136446000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5139999999999985 " "
y[1] (closed_form) = -0.9870737337987218 " "
y[1] (numeric) = -0.9870737337987223 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 5.62380998809733600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5149999999999983 " "
y[1] (closed_form) = -0.9873773427895782 " "
y[1] (numeric) = -0.9873773427895788 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 5.62208072087470500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5159999999999982 " "
y[1] (closed_form) = -0.987680672736535 " "
y[1] (numeric) = -0.9876806727365356 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 5.62035410467786800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5169999999999981 " "
y[1] (closed_form) = -0.9879837239683735 " "
y[1] (numeric) = -0.9879837239683742 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.7423561604787900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.517999999999998 " "
y[1] (closed_form) = -0.9882864968134766 " "
y[1] (numeric) = -0.988286496813477 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.493527041823758000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.518999999999998 " "
y[1] (closed_form) = -0.988588991599827 " "
y[1] (numeric) = -0.9885889915998277 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.73822812549322400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5199999999999978 " "
y[1] (closed_form) = -0.9888912086550105 " "
y[1] (numeric) = -0.988891208655011 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 5.613474034900003000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5209999999999977 " "
y[1] (closed_form) = -0.989193148306213 " "
y[1] (numeric) = -0.9891931483062136 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.73411270504359300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5219999999999976 " "
y[1] (closed_form) = -0.9894948108802232 " "
y[1] (numeric) = -0.989494810880224 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 7.8540696595091400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5229999999999975 " "
y[1] (closed_form) = -0.9897961967034321 " "
y[1] (numeric) = -0.9897961967034329 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 7.85167815178486900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5239999999999974 " "
y[1] (closed_form) = -0.9900973061018331 " "
y[1] (numeric) = -0.9900973061018337 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 5.60663592246441500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5249999999999972 " "
y[1] (closed_form) = -0.9903981394010213 " "
y[1] (numeric) = -0.9903981394010224 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.12098658151418150000000000000E-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) = -0.9906986969261972 " "
y[1] (numeric) = -0.9906986969261982 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 1.00858184760192250000000000000E-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) = -0.9909989790021624 " "
y[1] (numeric) = -0.9909989790021634 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 1.00827623775025170000000000000E-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) = -0.9912989859533232 " "
y[1] (numeric) = -0.9912989859533242 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 1.00797109279973550000000000000E-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) = -0.9915987181036896 " "
y[1] (numeric) = -0.9915987181036907 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.1196293463835060000000000000E-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) = -0.9918981757768761 " "
y[1] (numeric) = -0.9918981757768771 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 1.00736219358407940000000000000E-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) = -0.9921973592961009 " "
y[1] (numeric) = -0.9921973592961021 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.23084920116504420000000000000E-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) = -0.9924962689841881 " "
y[1] (numeric) = -0.9924962689841891 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 1.00675514194659380000000000000E-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) = -0.9927949051635656 " "
y[1] (numeric) = -0.9927949051635667 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.11828034053241280000000000000E-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) = -0.9930932681562677 " "
y[1] (numeric) = -0.9930932681562689 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.1179443665813450000000000000E-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) = -0.9933913582839342 " "
y[1] (numeric) = -0.9933913582839351 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.94087121146732600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.535999999999996 " "
y[1] (closed_form) = -0.9936891758678097 " "
y[1] (numeric) = -0.9936891758678109 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.22900133839249390000000000000E-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) = -0.9939867212287469 " "
y[1] (numeric) = -0.993986721228748 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.11693949316819900000000000000E-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) = -0.9942839946872032 " "
y[1] (numeric) = -0.9942839946872045 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.33992665744288970000000000000E-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) = -0.9945809965632445 " "
y[1] (numeric) = -0.9945809965632456 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.11627210700939490000000000000E-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) = -0.9948777271765422 " "
y[1] (numeric) = -0.9948777271765434 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.22753308645632260000000000000E-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) = -0.9951741868463763 " "
y[1] (numeric) = -0.9951741868463775 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.22716740770547570000000000000E-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) = -0.9954703758916336 " "
y[1] (numeric) = -0.995470375891635 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.44985724032215660000000000000E-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) = -0.99576629463081 " "
y[1] (numeric) = -0.9957662946308112 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.22643770297573770000000000000E-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) = -0.9960619433820084 " "
y[1] (numeric) = -0.9960619433820098 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.44899616093371300000000000000E-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) = -0.9963573224629414 " "
y[1] (numeric) = -0.9963573224629428 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.44856659300196530000000000000E-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) = -0.9966524321909299 " "
y[1] (numeric) = -0.9966524321909314 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.44813767106345750000000000000E-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) = -0.9969472728829042 " "
y[1] (numeric) = -0.9969472728829056 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.44770939373663750000000000000E-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) = -0.997241844855404 " "
y[1] (numeric) = -0.9972418448554055 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.4472817596437448000000000000E-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) = -0.9975361484245789 " "
y[1] (numeric) = -0.9975361484245805 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.5581512879808550000000000000E-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) = -0.9978301839061887 " "
y[1] (numeric) = -0.9978301839061904 " "
absolute error = 1.6653345369377348000000000000000E-15 " "
relative error = 1.66895586423180600000000000000E-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) = -0.9981239516156035 " "
y[1] (numeric) = -0.9981239516156052 " "
absolute error = 1.6653345369377348000000000000000E-15 " "
relative error = 1.66846465736260220000000000000E-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) = -0.9984174518678042 " "
y[1] (numeric) = -0.9984174518678058 " "
absolute error = 1.6653345369377348000000000000000E-15 " "
relative error = 1.6679741863709271000000000000E-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) = -0.9987106849773826 " "
y[1] (numeric) = -0.9987106849773841 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.5563188197094530000000000000E-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) = -0.9990036512585415 " "
y[1] (numeric) = -0.9990036512585434 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 1.8892615051857440000000000000E-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) = -0.9992963510250967 " "
y[1] (numeric) = -0.9992963510250984 " "
absolute error = 1.6653345369377348000000000000000E-15 " "
relative error = 1.66650717300168670000000000000E-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) = -0.9995887845904743 " "
y[1] (numeric) = -0.9995887845904761 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7770876052075890000000000000E-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) = -0.9998809522677136 " "
y[1] (numeric) = -0.9998809522677156 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.99863937781086850000000000000E-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) = -1.0001728543694668 " "
y[1] (numeric) = -1.0001728543694686 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.77604984142476940000000000000E-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) = -1.0004644912079974 " "
y[1] (numeric) = -1.0004644912079996 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.2194151504260440000000000000E-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) = -1.0007558630951843 " "
y[1] (numeric) = -1.0007558630951865 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.21876896367393160000000000000E-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) = -1.0010469703425184 " "
y[1] (numeric) = -1.0010469703425207 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.21812373947904230000000000000E-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) = -1.0013378132611048 " "
y[1] (numeric) = -1.0013378132611073 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.4392274233814942000000000000E-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) = -1.0016283921616633 " "
y[1] (numeric) = -1.0016283921616655 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.2168361706064060000000000000E-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) = -1.0019187073545268 " "
y[1] (numeric) = -1.0019187073545295 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.6594325862382920000000000000E-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) = -1.002208759149645 " "
y[1] (numeric) = -1.0022087591496476 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.65866291306532100000000000000E-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) = -1.002498547856581 " "
y[1] (numeric) = -1.0024985478565835 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.436403184221640000000000000E-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) = -1.0027880737845138 " "
y[1] (numeric) = -1.0027880737845165 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.6571269929890990000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5679999999999925 " "
y[1] (closed_form) = -1.0030773372422388 " "
y[1] (numeric) = -1.0030773372422415 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.6563607412624680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5689999999999924 " "
y[1] (closed_form) = -1.0033663385381666 " "
y[1] (numeric) = -1.0033663385381695 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.87689526063924840000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5699999999999923 " "
y[1] (closed_form) = -1.0036550779803248 " "
y[1] (numeric) = -1.0036550779803277 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.87606761262457770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5709999999999922 " "
y[1] (closed_form) = -1.0039435558763574 " "
y[1] (numeric) = -1.0039435558763603 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.875241189735680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.571999999999992 " "
y[1] (closed_form) = -1.0042317725335255 " "
y[1] (numeric) = -1.0042317725335284 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.8744159893915733000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.572999999999992 " "
y[1] (closed_form) = -1.0045197282587077 " "
y[1] (numeric) = -1.0045197282587104 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.6525464698630010000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5739999999999919 " "
y[1] (closed_form) = -1.0048074233584 " "
y[1] (numeric) = -1.0048074233584026 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.6517869963526090000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5749999999999917 " "
y[1] (closed_form) = -1.0050948581387162 " "
y[1] (numeric) = -1.0050948581387191 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.87194769792267900000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5759999999999916 " "
y[1] (closed_form) = -1.00538203290539 " "
y[1] (numeric) = -1.0053820329053926 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.65027141115731300000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5769999999999915 " "
y[1] (closed_form) = -1.005668947963771 " "
y[1] (numeric) = -1.0056689479637742 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.09110117722599300000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5779999999999914 " "
y[1] (closed_form) = -1.0059556036188309 " "
y[1] (numeric) = -1.0059556036188337 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.8694903171086350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5789999999999913 " "
y[1] (closed_form) = -1.0062420001751582 " "
y[1] (numeric) = -1.006242000175161 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.8686736028936727000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5799999999999912 " "
y[1] (closed_form) = -1.0065281379369622 " "
y[1] (numeric) = -1.0065281379369653 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0884625593498590000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.580999999999991 " "
y[1] (closed_form) = -1.0068140172080722 " "
y[1] (numeric) = -1.0068140172080753 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0875856074896080000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.581999999999991 " "
y[1] (closed_form) = -1.0070996382919377 " "
y[1] (numeric) = -1.0070996382919408 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0867099448300180000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5829999999999909 " "
y[1] (closed_form) = -1.0073850014916286 " "
y[1] (numeric) = -1.0073850014916317 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.0858355686728690000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5839999999999907 " "
y[1] (closed_form) = -1.0076701071098357 " "
y[1] (numeric) = -1.007670107109839 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.30531693892198330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5849999999999906 " "
y[1] (closed_form) = -1.007954955448872 " "
y[1] (numeric) = -1.0079549554488751 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08409066510921260000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5859999999999905 " "
y[1] (closed_form) = -1.0082395468106709 " "
y[1] (numeric) = -1.008239546810674 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08322013234240100000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5869999999999904 " "
y[1] (closed_form) = -1.0085238814967887 " "
y[1] (numeric) = -1.0085238814967916 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.86218295568898550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5879999999999903 " "
y[1] (closed_form) = -1.008807959808403 " "
y[1] (numeric) = -1.008807959808406 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08148289149189700000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5889999999999902 " "
y[1] (closed_form) = -1.0090917820463154 " "
y[1] (numeric) = -1.0090917820463186 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08061617809088250000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.58999999999999 " "
y[1] (closed_form) = -1.0093753485109493 " "
y[1] (numeric) = -1.0093753485109527 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.2997329276853643000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.59099999999999 " "
y[1] (closed_form) = -1.0096586595023522 " "
y[1] (numeric) = -1.0096586595023556 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.2988070201043130000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5919999999999899 " "
y[1] (closed_form) = -1.0099417153201948 " "
y[1] (numeric) = -1.0099417153201982 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.29788246524652660000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5929999999999898 " "
y[1] (closed_form) = -1.0102245162637717 " "
y[1] (numeric) = -1.0102245162637753 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.51675654431740200000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5939999999999896 " "
y[1] (closed_form) = -1.0105070626320023 " "
y[1] (numeric) = -1.0105070626320058 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.51577322928053300000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5949999999999895 " "
y[1] (closed_form) = -1.0107893547234301 " "
y[1] (numeric) = -1.0107893547234337 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.51479134816629200000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5959999999999894 " "
y[1] (closed_form) = -1.0110713928362245 " "
y[1] (numeric) = -1.0110713928362278 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.29419771687178840000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5969999999999893 " "
y[1] (closed_form) = -1.0113531772681785 " "
y[1] (numeric) = -1.011353177268182 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.51283187580122100000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5979999999999892 " "
y[1] (closed_form) = -1.0116347083167128 " "
y[1] (numeric) = -1.0116347083167163 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.51185427861798070000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.598999999999989 " "
y[1] (closed_form) = -1.011915986278873 " "
y[1] (numeric) = -1.0119159862788765 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.5108781034924890000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.599999999999989 " "
y[1] (closed_form) = -1.012197011451331 " "
y[1] (numeric) = -1.0121970114513346 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.5099033474782440000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6009999999999889 " "
y[1] (closed_form) = -1.012477784130386 " "
y[1] (numeric) = -1.0124777841303896 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.5089300076365780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6019999999999888 " "
y[1] (closed_form) = -1.012758304611964 " "
y[1] (numeric) = -1.0127583046119673 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.28871070097184500000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6029999999999887 " "
y[1] (closed_form) = -1.0130385731916176 " "
y[1] (numeric) = -1.0130385731916212 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.50698756475534560000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6039999999999885 " "
y[1] (closed_form) = -1.0133185901645287 " "
y[1] (numeric) = -1.013318590164532 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.2868923023850590000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6049999999999884 " "
y[1] (closed_form) = -1.0135983558255057 " "
y[1] (numeric) = -1.0135983558255093 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.5050507514952130000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6059999999999883 " "
y[1] (closed_form) = -1.0138778704689866 " "
y[1] (numeric) = -1.0138778704689904 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.7230897267532360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6069999999999882 " "
y[1] (closed_form) = -1.0141571343890379 " "
y[1] (numeric) = -1.0141571343890416 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.7220645161655080000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.607999999999988 " "
y[1] (closed_form) = -1.0144361478793547 " "
y[1] (numeric) = -1.0144361478793584 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.7210407886356770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.608999999999988 " "
y[1] (closed_form) = -1.0147149112332616 " "
y[1] (numeric) = -1.0147149112332656 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.9388431611721750000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6099999999999879 " "
y[1] (closed_form) = -1.0149934247437138 " "
y[1] (numeric) = -1.0149934247437178 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.93776234526815600000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6109999999999878 " "
y[1] (closed_form) = -1.015271688703296 " "
y[1] (numeric) = -1.0152716887033 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.9366830899769070000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6119999999999877 " "
y[1] (closed_form) = -1.0155497034042231 " "
y[1] (numeric) = -1.0155497034042273 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 4.15425013609240450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6129999999999876 " "
y[1] (closed_form) = -1.015827469138342 " "
y[1] (numeric) = -1.0158274691383462 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 4.153114206641959600000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6139999999999874 " "
y[1] (closed_form) = -1.0161049861971296 " "
y[1] (numeric) = -1.0161049861971339 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 4.1519799143640030000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6149999999999873 " "
y[1] (closed_form) = -1.0163822548716948 " "
y[1] (numeric) = -1.0163822548716992 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.3693129009431910000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6159999999999872 " "
y[1] (closed_form) = -1.0166592754527786 " "
y[1] (numeric) = -1.016659275452783 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.3681223451414770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6169999999999871 " "
y[1] (closed_form) = -1.0169360482307543 " "
y[1] (numeric) = -1.0169360482307586 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 4.14858682698431600000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.617999999999987 " "
y[1] (closed_form) = -1.017212573495627 " "
y[1] (numeric) = -1.0172125734956314 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.3657463682734526000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.618999999999987 " "
y[1] (closed_form) = -1.0174888515370357 " "
y[1] (numeric) = -1.0174888515370402 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.3645609401932417000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6199999999999868 " "
y[1] (closed_form) = -1.0177648826442525 " "
y[1] (numeric) = -1.017764882644257 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.3633772143550040000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6209999999999867 " "
y[1] (closed_form) = -1.0180406671061824 " "
y[1] (numeric) = -1.018040667106187 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 4.580304946638550400000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6219999999999866 " "
y[1] (closed_form) = -1.0183162052113652 " "
y[1] (numeric) = -1.0183162052113701 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.7971163410256690000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6229999999999865 " "
y[1] (closed_form) = -1.0185914972479755 " "
y[1] (numeric) = -1.0185914972479801 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 4.5778280262734890000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6239999999999863 " "
y[1] (closed_form) = -1.018866543503821 " "
y[1] (numeric) = -1.0188665435038258 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 4.576592227074310300000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6249999999999862 " "
y[1] (closed_form) = -1.019141344266346 " "
y[1] (numeric) = -1.0191413442663506 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 4.5753581970343743000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6259999999999861 " "
y[1] (closed_form) = -1.0194158998226293 " "
y[1] (numeric) = -1.019415899822634 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 4.5741259325433054000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.626999999999986 " "
y[1] (closed_form) = -1.0196902104593857 " "
y[1] (numeric) = -1.0196902104593906 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.7906523552382957000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.627999999999986 " "
y[1] (closed_form) = -1.019964276462967 " "
y[1] (numeric) = -1.0199642764629717 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 4.571666685813539600000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6289999999999858 " "
y[1] (closed_form) = -1.02023809811936 " "
y[1] (numeric) = -1.0202380981193648 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.7880796819441884000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6299999999999857 " "
y[1] (closed_form) = -1.0205116757141894 " "
y[1] (numeric) = -1.020511675714194 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 4.5692144581906646000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6309999999999856 " "
y[1] (closed_form) = -1.0207850095327164 " "
y[1] (numeric) = -1.0207850095327213 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.7855143470287453000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6319999999999855 " "
y[1] (closed_form) = -1.0210580998598406 " "
y[1] (numeric) = -1.0210580998598455 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.7842344221364524000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6329999999999854 " "
y[1] (closed_form) = -1.0213309469800986 " "
y[1] (numeric) = -1.0213309469801037 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 5.0003634261512630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6339999999999852 " "
y[1] (closed_form) = -1.021603551177666 " "
y[1] (numeric) = -1.021603551177671 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.9990291315927143000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6349999999999851 " "
y[1] (closed_form) = -1.0218759127363568 " "
y[1] (numeric) = -1.0218759127363617 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.7804055731872510000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.635999999999985 " "
y[1] (closed_form) = -1.0221480319396234 " "
y[1] (numeric) = -1.0221480319396286 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.9963662343355990000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.636999999999985 " "
y[1] (closed_form) = -1.0224199090705588 " "
y[1] (numeric) = -1.0224199090705637 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.7778620750758180000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6379999999999848 " "
y[1] (closed_form) = -1.0226915444118942 " "
y[1] (numeric) = -1.0226915444118991 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.7765930353514660000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6389999999999847 " "
y[1] (closed_form) = -1.0229629382460022 " "
y[1] (numeric) = -1.022962938246007 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.7753257969703190000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6399999999999846 " "
y[1] (closed_form) = -1.0232340908548947 " "
y[1] (numeric) = -1.0232340908548998 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.9910630997535340000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6409999999999845 " "
y[1] (closed_form) = -1.0235050025202255 " "
y[1] (numeric) = -1.0235050025202306 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.9897420146461860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6419999999999844 " "
y[1] (closed_form) = -1.0237756735232888 " "
y[1] (numeric) = -1.0237756735232937 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.7715348534696017000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6429999999999843 " "
y[1] (closed_form) = -1.0240461041450204 " "
y[1] (numeric) = -1.0240461041450253 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.7702747840920470000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6439999999999841 " "
y[1] (closed_form) = -1.0243162946659976 " "
y[1] (numeric) = -1.0243162946660027 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.985789975098449700000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.644999999999984 " "
y[1] (closed_form) = -1.0245862453664412 " "
y[1] (numeric) = -1.0245862453664463 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.9844763545983417000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.645999999999984 " "
y[1] (closed_form) = -1.024855956526213 " "
y[1] (numeric) = -1.0248559565262183 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.199823920879411000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6469999999999838 " "
y[1] (closed_form) = -1.0251254284248192 " "
y[1] (numeric) = -1.0251254284248243 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.9818546800883107000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6479999999999837 " "
y[1] (closed_form) = -1.0253946613414082 " "
y[1] (numeric) = -1.0253946613414133 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.9805466186012454000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6489999999999836 " "
y[1] (closed_form) = -1.0256636555547725 " "
y[1] (numeric) = -1.0256636555547776 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.9792404026575116000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6499999999999835 " "
y[1] (closed_form) = -1.0259324113433483 " "
y[1] (numeric) = -1.0259324113433537 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.1943680297836640000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6509999999999834 " "
y[1] (closed_form) = -1.0262009289852174 " "
y[1] (numeric) = -1.0262009289852225 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.9766334925519135000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6519999999999833 " "
y[1] (closed_form) = -1.0264692087581047 " "
y[1] (numeric) = -1.02646920875811 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.1916516079895270000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6529999999999831 " "
y[1] (closed_form) = -1.0267372509393813 " "
y[1] (numeric) = -1.0267372509393866 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.1902962645263760000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.653999999999983 " "
y[1] (closed_form) = -1.0270050558060637 " "
y[1] (numeric) = -1.027005055806069 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.1889428275678080000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.654999999999983 " "
y[1] (closed_form) = -1.0272726236348138 " "
y[1] (numeric) = -1.027272623634819 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.1875912932876790000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6559999999999828 " "
y[1] (closed_form) = -1.0275399547019402 " "
y[1] (numeric) = -1.0275399547019455 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.1862416578697050000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6569999999999827 " "
y[1] (closed_form) = -1.0278070492833975 " "
y[1] (numeric) = -1.027807049283403 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 5.4009311640702440000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6579999999999826 " "
y[1] (closed_form) = -1.0280739076547882 " "
y[1] (numeric) = -1.0280739076547936 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.1835480684042160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6589999999999825 " "
y[1] (closed_form) = -1.028340530091361 " "
y[1] (numeric) = -1.0283405300913666 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 5.398129277888720000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6599999999999824 " "
y[1] (closed_form) = -1.0286069168680134 " "
y[1] (numeric) = -1.028606916868019 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 5.3967312800387080000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6609999999999823 " "
y[1] (closed_form) = -1.02887306825929 " "
y[1] (numeric) = -1.0288730682592955 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 5.3953352404466160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6619999999999822 " "
y[1] (closed_form) = -1.029138984539384 " "
y[1] (numeric) = -1.0291389845393897 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 5.6096988014060430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.662999999999982 " "
y[1] (closed_form) = -1.0294046659821379 " "
y[1] (numeric) = -1.0294046659821439 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 5.8239529420200550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.663999999999982 " "
y[1] (closed_form) = -1.029670112861044 " "
y[1] (numeric) = -1.0296701128610493 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 5.1755124788398330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6649999999999818 " "
y[1] (closed_form) = -1.029935325449241 " "
y[1] (numeric) = -1.0299353254492467 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 5.6053614099823760000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6659999999999817 " "
y[1] (closed_form) = -1.0302003040195213 " "
y[1] (numeric) = -1.0302003040195271 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 5.6039196508928790000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6669999999999816 " "
y[1] (closed_form) = -1.0304650488443259 " "
y[1] (numeric) = -1.0304650488443314 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 5.3869999078099730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6679999999999815 " "
y[1] (closed_form) = -1.0307295601957454 " "
y[1] (numeric) = -1.0307295601957511 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 5.601042165662190000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6689999999999814 " "
y[1] (closed_form) = -1.0309938383455233 " "
y[1] (numeric) = -1.0309938383455288 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 5.3842369533787680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6699999999999813 " "
y[1] (closed_form) = -1.0312578835650528 " "
y[1] (numeric) = -1.0312578835650588 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 5.8134870322158970000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6709999999999812 " "
y[1] (closed_form) = -1.0315216961253806 " "
y[1] (numeric) = -1.0315216961253864 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 5.5967409602105860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.671999999999981 " "
y[1] (closed_form) = -1.0317852762972035 " "
y[1] (numeric) = -1.0317852762972095 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 5.8105154926139300000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.672999999999981 " "
y[1] (closed_form) = -1.0320486243508724 " "
y[1] (numeric) = -1.0320486243508784 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 5.8090328222147960000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6739999999999808 " "
y[1] (closed_form) = -1.0323117405563904 " "
y[1] (numeric) = -1.0323117405563962 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 5.5924576862210480000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6749999999999807 " "
y[1] (closed_form) = -1.032574625183413 " "
y[1] (numeric) = -1.0325746251834191 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 6.0211134248980080000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6759999999999806 " "
y[1] (closed_form) = -1.032837278501251 " "
y[1] (numeric) = -1.0328372785012572 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 6.01958223944310000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6769999999999805 " "
y[1] (closed_form) = -1.0330997007788678 " "
y[1] (numeric) = -1.033099700778874 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 6.0180531784237370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6779999999999804 " "
y[1] (closed_form) = -1.0333618922848813 " "
y[1] (numeric) = -1.0333618922848877 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.2314021746901200000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6789999999999803 " "
y[1] (closed_form) = -1.033623853287565 " "
y[1] (numeric) = -1.0336238532875712 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 6.0150014128700390000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6799999999999802 " "
y[1] (closed_form) = -1.033885584054846 " "
y[1] (numeric) = -1.0338855840548522 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 6.0134786999516400000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.68099999999998 " "
y[1] (closed_form) = -1.0341470848543075 " "
y[1] (numeric) = -1.034147084854314 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.2266708837970440000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.68199999999998 " "
y[1] (closed_form) = -1.0344083559531891 " "
y[1] (numeric) = -1.0344083559531956 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.2250981498425860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6829999999999798 " "
y[1] (closed_form) = -1.0346693976183858 " "
y[1] (numeric) = -1.0346693976183923 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.2235275902118580000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6839999999999797 " "
y[1] (closed_form) = -1.0349302101164495 " "
y[1] (numeric) = -1.034930210116456 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.2219592006125360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6849999999999796 " "
y[1] (closed_form) = -1.0351907937135887 " "
y[1] (numeric) = -1.0351907937135951 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.2203929767631790000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6859999999999795 " "
y[1] (closed_form) = -1.0354511486756692 " "
y[1] (numeric) = -1.0354511486756757 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.2188289143932040000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6869999999999794 " "
y[1] (closed_form) = -1.035711275268215 " "
y[1] (numeric) = -1.0357112752682214 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.2172670092428450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6879999999999793 " "
y[1] (closed_form) = -1.0359711737564072 " "
y[1] (numeric) = -1.0359711737564137 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.2157072570631290000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6889999999999792 " "
y[1] (closed_form) = -1.0362308444050863 " "
y[1] (numeric) = -1.0362308444050927 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.2141496536158310000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.689999999999979 " "
y[1] (closed_form) = -1.036490287478751 " "
y[1] (numeric) = -1.0364902874787572 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 5.9983668086502320000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.690999999999979 " "
y[1] (closed_form) = -1.0367495032415586 " "
y[1] (numeric) = -1.036749503241565 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.2110408760191880000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6919999999999789 " "
y[1] (closed_form) = -1.037008491957327 " "
y[1] (numeric) = -1.0370084919573337 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 6.4236100277036620000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6929999999999787 " "
y[1] (closed_form) = -1.0372672538895338 " "
y[1] (numeric) = -1.0372672538895404 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 6.4220075614768750000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6939999999999786 " "
y[1] (closed_form) = -1.037525789301316 " "
y[1] (numeric) = -1.0375257893013228 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.6344208728646010000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6949999999999785 " "
y[1] (closed_form) = -1.037784098455472 " "
y[1] (numeric) = -1.0377840984554787 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 6.4188092279164520000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6959999999999784 " "
y[1] (closed_form) = -1.0380421816144607 " "
y[1] (numeric) = -1.0380421816144676 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.6311204636889490000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6969999999999783 " "
y[1] (closed_form) = -1.0383000390404034 " "
y[1] (numeric) = -1.03830003904041 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 6.4156196641457770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6979999999999782 " "
y[1] (closed_form) = -1.0385576709950817 " "
y[1] (numeric) = -1.0385576709950883 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 6.4140281601968800000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.698999999999978 " "
y[1] (closed_form) = -1.0388150777399399 " "
y[1] (numeric) = -1.0388150777399467 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.6261867970298920000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.699999999999978 " "
y[1] (closed_form) = -1.0390722595360855 " "
y[1] (numeric) = -1.0390722595360922 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 6.4108516867970530000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7009999999999779 " "
y[1] (closed_form) = -1.0393292166442876 " "
y[1] (numeric) = -1.0393292166442945 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.622908932456020000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7019999999999778 " "
y[1] (closed_form) = -1.0395859493249797 " "
y[1] (numeric) = -1.0395859493249866 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.6212733609428490000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7029999999999776 " "
y[1] (closed_form) = -1.0398424578382583 " "
y[1] (numeric) = -1.0398424578382652 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.6196400241108850000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7039999999999775 " "
y[1] (closed_form) = -1.0400987424438841 " "
y[1] (numeric) = -1.040098742443891 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.6180089175978850000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7049999999999774 " "
y[1] (closed_form) = -1.0403548034012815 " "
y[1] (numeric) = -1.0403548034012886 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.8298116511510210000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7059999999999773 " "
y[1] (closed_form) = -1.040610640969541 " "
y[1] (numeric) = -1.040610640969548 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.6147533781344920000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7069999999999772 " "
y[1] (closed_form) = -1.0408662554074166 " "
y[1] (numeric) = -1.0408662554074237 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.8264556764017580000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.707999999999977 " "
y[1] (closed_form) = -1.0411216469733293 " "
y[1] (numeric) = -1.0411216469733362 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.6115067078730170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.708999999999977 " "
y[1] (closed_form) = -1.0413768159253647 " "
y[1] (numeric) = -1.0413768159253716 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.6098866879030860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7099999999999769 " "
y[1] (closed_form) = -1.0416317625212754 " "
y[1] (numeric) = -1.0416317625212823 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.6082688723073350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7109999999999768 " "
y[1] (closed_form) = -1.0418864870184803 " "
y[1] (numeric) = -1.0418864870184872 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.6066532567994410000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7119999999999767 " "
y[1] (closed_form) = -1.0421409896740652 " "
y[1] (numeric) = -1.042140989674072 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.6050398371037910000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7129999999999765 " "
y[1] (closed_form) = -1.0423952707447837 " "
y[1] (numeric) = -1.0423952707447905 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.6034286089554540000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7139999999999764 " "
y[1] (closed_form) = -1.0426493304870563 " "
y[1] (numeric) = -1.0426493304870634 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.8147814896517690000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7149999999999763 " "
y[1] (closed_form) = -1.0429031691569726 " "
y[1] (numeric) = -1.0429031691569797 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.8131227977230640000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7159999999999762 " "
y[1] (closed_form) = -1.04315678701029 " "
y[1] (numeric) = -1.0431567870102971 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.811466354895039000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.716999999999976 " "
y[1] (closed_form) = -1.043410184302435 " "
y[1] (numeric) = -1.0434101843024421 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.8098121568089620000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.717999999999976 " "
y[1] (closed_form) = -1.043663361288503 " "
y[1] (numeric) = -1.0436633612885102 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 7.0209152053393580000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7189999999999759 " "
y[1] (closed_form) = -1.0439163182232596 " "
y[1] (numeric) = -1.0439163182232667 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.8065104774819540000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7199999999999758 " "
y[1] (closed_form) = -1.0441690553611398 " "
y[1] (numeric) = -1.044169055361147 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.8048629875777110000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7209999999999757 " "
y[1] (closed_form) = -1.0444215729562492 " "
y[1] (numeric) = -1.0444215729562565 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 7.0158182789977490000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7219999999999756 " "
y[1] (closed_form) = -1.0446738712623642 " "
y[1] (numeric) = -1.0446738712623715 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 7.0141238946386720000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7229999999999754 " "
y[1] (closed_form) = -1.044925950532932 " "
y[1] (numeric) = -1.0449259505329396 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 7.2249297317199060000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7239999999999753 " "
y[1] (closed_form) = -1.0451778110210719 " "
y[1] (numeric) = -1.0451778110210794 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 7.2231887128140140000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7249999999999752 " "
y[1] (closed_form) = -1.045429452979574 " "
y[1] (numeric) = -1.0454294529795818 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 7.4338456317893120000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.725999999999975 " "
y[1] (closed_form) = -1.0456808766609016 " "
y[1] (numeric) = -1.0456808766609096 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 7.6444027577768660000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.726999999999975 " "
y[1] (closed_form) = -1.0459320823171905 " "
y[1] (numeric) = -1.0459320823171983 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 7.4302732498258750000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.727999999999975 " "
y[1] (closed_form) = -1.0461830702002486 " "
y[1] (numeric) = -1.0461830702002564 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 7.4284906664457410000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7289999999999748 " "
y[1] (closed_form) = -1.046433840561558 " "
y[1] (numeric) = -1.0464338405615659 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 7.4267104819599170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7299999999999747 " "
y[1] (closed_form) = -1.0466843936522743 " "
y[1] (numeric) = -1.0466843936522823 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 7.637073625802749000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7309999999999746 " "
y[1] (closed_form) = -1.0469347297232272 " "
y[1] (numeric) = -1.0469347297232352 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 7.6352474995402590000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7319999999999744 " "
y[1] (closed_form) = -1.0471848490249207 " "
y[1] (numeric) = -1.047184849024929 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 7.845463377240520000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7329999999999743 " "
y[1] (closed_form) = -1.047434751807534 " "
y[1] (numeric) = -1.0474347518075422 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 7.843591563148540000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7339999999999742 " "
y[1] (closed_form) = -1.0476844383209212 " "
y[1] (numeric) = -1.0476844383209294 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 7.8417222607534640000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7349999999999741 " "
y[1] (closed_form) = -1.047933908814612 " "
y[1] (numeric) = -1.0479339088146202 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 7.8398554652358080000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.735999999999974 " "
y[1] (closed_form) = -1.0481831635378123 " "
y[1] (numeric) = -1.0481831635378205 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 7.837991171787970000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.736999999999974 " "
y[1] (closed_form) = -1.048432202739404 " "
y[1] (numeric) = -1.0484322027394124 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.0479166560362170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7379999999999738 " "
y[1] (closed_form) = -1.0486810266679463 " "
y[1] (numeric) = -1.0486810266679547 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.0460071009017090000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7389999999999737 " "
y[1] (closed_form) = -1.048929635571675 " "
y[1] (numeric) = -1.0489296355716833 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 7.8324132559650320000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7399999999999736 " "
y[1] (closed_form) = -1.0491780296985034 " "
y[1] (numeric) = -1.0491780296985118 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.0421956506045830000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7409999999999735 " "
y[1] (closed_form) = -1.049426209296023 " "
y[1] (numeric) = -1.0494262092960314 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.0402937456759080000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7419999999999733 " "
y[1] (closed_form) = -1.0496741746115026 " "
y[1] (numeric) = -1.0496741746115112 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.2499310753084850000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7429999999999732 " "
y[1] (closed_form) = -1.0499219258918915 " "
y[1] (numeric) = -1.0499219258918997 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 7.8250107742507590000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7439999999999731 " "
y[1] (closed_form) = -1.0501694633838152 " "
y[1] (numeric) = -1.0501694633838239 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.2460401811467120000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.744999999999973 " "
y[1] (closed_form) = -1.0504167873335812 " "
y[1] (numeric) = -1.05041678733359 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.2440986249452850000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.745999999999973 " "
y[1] (closed_form) = -1.0506638979871756 " "
y[1] (numeric) = -1.050663897987184 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.030822228988570000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7469999999999728 " "
y[1] (closed_form) = -1.050910795590264 " "
y[1] (numeric) = -1.0509107955902726 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.2402232695804730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7479999999999727 " "
y[1] (closed_form) = -1.0511574803881936 " "
y[1] (numeric) = -1.051157480388202 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.0270512692685590000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7489999999999726 " "
y[1] (closed_form) = -1.0514039526259917 " "
y[1] (numeric) = -1.051403952626 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 7.813980879286889000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7499999999999725 " "
y[1] (closed_form) = -1.0516502125483669 " "
y[1] (numeric) = -1.0516502125483753 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.0232903359615190000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7509999999999724 " "
y[1] (closed_form) = -1.0518962603997095 " "
y[1] (numeric) = -1.0518962603997182 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.2325034493283690000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7519999999999722 " "
y[1] (closed_form) = -1.0521420964240924 " "
y[1] (numeric) = -1.0521420964241008 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.0195393909513960000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7529999999999721 " "
y[1] (closed_form) = -1.0523877208652697 " "
y[1] (numeric) = -1.052387720865278 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.0176676521973710000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.753999999999972 " "
y[1] (closed_form) = -1.0526331339666788 " "
y[1] (numeric) = -1.0526331339666872 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.0157983963084010000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.754999999999972 " "
y[1] (closed_form) = -1.0528783359714402 " "
y[1] (numeric) = -1.0528783359714486 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.0139316185721820000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7559999999999718 " "
y[1] (closed_form) = -1.053123327122358 " "
y[1] (numeric) = -1.0531233271223663 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.0120673142879210000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7569999999999717 " "
y[1] (closed_form) = -1.0533681076619197 " "
y[1] (numeric) = -1.0533681076619281 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.0102054787662900000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7579999999999716 " "
y[1] (closed_form) = -1.0536126778322974 " "
y[1] (numeric) = -1.0536126778323058 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.0083461073294050000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7589999999999715 " "
y[1] (closed_form) = -1.053857037875348 " "
y[1] (numeric) = -1.0538570378753562 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 7.7957921112236470000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7599999999999714 " "
y[1] (closed_form) = -1.0541011880326125 " "
y[1] (numeric) = -1.0541011880326208 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 7.7939864554748770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7609999999999713 " "
y[1] (closed_form) = -1.0543451285453176 " "
y[1] (numeric) = -1.0543451285453262 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.2133822764696450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7619999999999711 " "
y[1] (closed_form) = -1.0545888596543769 " "
y[1] (numeric) = -1.0545888596543853 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.0009331692698680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.762999999999971 " "
y[1] (closed_form) = -1.0548323816003882 " "
y[1] (numeric) = -1.0548323816003966 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 7.9990860484862500000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.763999999999971 " "
y[1] (closed_form) = -1.0550756946236368 " "
y[1] (numeric) = -1.0550756946236453 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 7.9972413639583050000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7649999999999708 " "
y[1] (closed_form) = -1.0553187989640946 " "
y[1] (numeric) = -1.0553187989641033 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.2058043508527070000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7659999999999707 " "
y[1] (closed_form) = -1.0555616948614208 " "
y[1] (numeric) = -1.0555616948614297 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.4142729318794540000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7669999999999706 " "
y[1] (closed_form) = -1.0558043825549626 " "
y[1] (numeric) = -1.0558043825549714 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.4123388231331650000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7679999999999705 " "
y[1] (closed_form) = -1.0560468622837542 " "
y[1] (numeric) = -1.056046862283763 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.4104072595736410000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7689999999999704 " "
y[1] (closed_form) = -1.0562891342865186 " "
y[1] (numeric) = -1.0562891342865277 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 8.6186901923170490000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7699999999999703 " "
y[1] (closed_form) = -1.056531198801668 " "
y[1] (numeric) = -1.056531198801677 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 8.6167155425717390000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7709999999999702 " "
y[1] (closed_form) = -1.0567730560673025 " "
y[1] (numeric) = -1.0567730560673116 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 8.6147434869369810000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.77199999999997 " "
y[1] (closed_form) = -1.0570147063212127 " "
y[1] (numeric) = -1.057014706321222 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 8.8228416795719640000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.77299999999997 " "
y[1] (closed_form) = -1.057256149800879 " "
y[1] (numeric) = -1.0572561498008883 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 8.8208268248027940000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7739999999999698 " "
y[1] (closed_form) = -1.0574973867434712 " "
y[1] (numeric) = -1.0574973867434807 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 9.0287863889468790000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7749999999999697 " "
y[1] (closed_form) = -1.0577384173858504 " "
y[1] (numeric) = -1.05773841738586 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 9.0267289670479830000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7759999999999696 " "
y[1] (closed_form) = -1.057979241964568 " "
y[1] (numeric) = -1.0579792419645777 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.2345503854683150000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7769999999999695 " "
y[1] (closed_form) = -1.0582198607158677 " "
y[1] (numeric) = -1.0582198607158773 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 9.0226222037803580000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7779999999999694 " "
y[1] (closed_form) = -1.0584602738756836 " "
y[1] (numeric) = -1.0584602738756934 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.23035361632179900000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7789999999999693 " "
y[1] (closed_form) = -1.0587004816796428 " "
y[1] (numeric) = -1.0587004816796528 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.4379925149121990000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7799999999999692 " "
y[1] (closed_form) = -1.058940484363065 " "
y[1] (numeric) = -1.0589404843630748 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.2261678167662520000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.780999999999969 " "
y[1] (closed_form) = -1.0591802821609617 " "
y[1] (numeric) = -1.0591802821609713 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 9.0144408582611490000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.781999999999969 " "
y[1] (closed_form) = -1.059419875308038 " "
y[1] (numeric) = -1.0594198753080477 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.2219929457720010000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7829999999999688 " "
y[1] (closed_form) = -1.059659264038693 " "
y[1] (numeric) = -1.0596592640387028 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.2199095957175840000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7839999999999687 " "
y[1] (closed_form) = -1.059898448587019 " "
y[1] (numeric) = -1.059898448587029 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.4273250752909770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7849999999999686 " "
y[1] (closed_form) = -1.060137429186804 " "
y[1] (numeric) = -1.0601374291868138 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.2157510410660510000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7859999999999685 " "
y[1] (closed_form) = -1.0603762060715285 " "
y[1] (numeric) = -1.0603762060715383 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.2136758263343550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7869999999999684 " "
y[1] (closed_form) = -1.0606147794743697 " "
y[1] (numeric) = -1.0606147794743794 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.2116033132625920000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7879999999999683 " "
y[1] (closed_form) = -1.0608531496281994 " "
y[1] (numeric) = -1.0608531496282092 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.209533496813850000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7889999999999682 " "
y[1] (closed_form) = -1.0610913167655855 " "
y[1] (numeric) = -1.0610913167655955 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.4167269713260940000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.789999999999968 " "
y[1] (closed_form) = -1.0613292811187924 " "
y[1] (numeric) = -1.0613292811188022 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.205401933698130000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.790999999999968 " "
y[1] (closed_form) = -1.0615670429197799 " "
y[1] (numeric) = -1.0615670429197899 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.4125069992225450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7919999999999678 " "
y[1] (closed_form) = -1.0618046024002061 " "
y[1] (numeric) = -1.0618046024002161 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.41040112186320100000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7929999999999677 " "
y[1] (closed_form) = -1.0620419597914252 " "
y[1] (numeric) = -1.0620419597914355 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 9.6173712652157170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7939999999999676 " "
y[1] (closed_form) = -1.0622791153244897 " "
y[1] (numeric) = -1.0622791153245 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 9.615224171503550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7949999999999675 " "
y[1] (closed_form) = -1.06251606923015 " "
y[1] (numeric) = -1.06251606923016 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.4040998635118570000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7959999999999674 " "
y[1] (closed_form) = -1.0627528217388544 " "
y[1] (numeric) = -1.0627528217388644 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.402004885084840000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7969999999999673 " "
y[1] (closed_form) = -1.0629893730807507 " "
y[1] (numeric) = -1.0629893730807605 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.1910256716735740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7979999999999672 " "
y[1] (closed_form) = -1.0632257234856848 " "
y[1] (numeric) = -1.0632257234856948 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.3978230594991250000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.798999999999967 " "
y[1] (closed_form) = -1.0634618731832033 " "
y[1] (numeric) = -1.0634618731832133 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.395736202293619000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.799999999999967 " "
y[1] (closed_form) = -1.0636978224025517 " "
y[1] (numeric) = -1.0636978224025617 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.393652042135120000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8009999999999668 " "
y[1] (closed_form) = -1.0639335713726763 " "
y[1] (numeric) = -1.0639335713726863 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.3915705740301280000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8019999999999667 " "
y[1] (closed_form) = -1.0641691203222234 " "
y[1] (numeric) = -1.0641691203222334 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.389491792997051000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8029999999999666 " "
y[1] (closed_form) = -1.0644044694795407 " "
y[1] (numeric) = -1.064404469479551 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 9.5960249317120770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8039999999999665 " "
y[1] (closed_form) = -1.0646396190726777 " "
y[1] (numeric) = -1.0646396190726877 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.385342272279559000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8049999999999664 " "
y[1] (closed_form) = -1.0648745693293842 " "
y[1] (numeric) = -1.0648745693293942 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.3832715226911470000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8059999999999663 " "
y[1] (closed_form) = -1.065109320477113 " "
y[1] (numeric) = -1.0651093204771231 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 9.5896746279302880000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8069999999999662 " "
y[1] (closed_form) = -1.0653438727430196 " "
y[1] (numeric) = -1.0653438727430298 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 9.587563309725120000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.807999999999966 " "
y[1] (closed_form) = -1.0655782263539622 " "
y[1] (numeric) = -1.065578226353972 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.168695807656271000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.808999999999966 " "
y[1] (closed_form) = -1.065812381536501 " "
y[1] (numeric) = -1.0658123815365108 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.166681477857070000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8099999999999659 " "
y[1] (closed_form) = -1.066046338516901 " "
y[1] (numeric) = -1.066046338516911 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.3729576854299170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8109999999999657 " "
y[1] (closed_form) = -1.066280097521131 " "
y[1] (numeric) = -1.066280097521141 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.3709028658188860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8119999999999656 " "
y[1] (closed_form) = -1.0665136587748636 " "
y[1] (numeric) = -1.0665136587748736 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.3688506841108150000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8129999999999655 " "
y[1] (closed_form) = -1.0667470225034765 " "
y[1] (numeric) = -1.0667470225034863 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.1586499991093580000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8139999999999654 " "
y[1] (closed_form) = -1.0669801889320518 " "
y[1] (numeric) = -1.0669801889320616 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.1566485657809680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8149999999999653 " "
y[1] (closed_form) = -1.0672131582853774 " "
y[1] (numeric) = -1.0672131582853872 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.1546496975338530000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8159999999999652 " "
y[1] (closed_form) = -1.067445930787947 " "
y[1] (numeric) = -1.0674459307879567 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.1526533896565350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.816999999999965 " "
y[1] (closed_form) = -1.0676785066639598 " "
y[1] (numeric) = -1.06767850666397 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 9.5665987118781640000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.817999999999965 " "
y[1] (closed_form) = -1.067910886137323 " "
y[1] (numeric) = -1.067910886137333 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.3565927188624360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8189999999999649 " "
y[1] (closed_form) = -1.068143069431649 " "
y[1] (numeric) = -1.068143069431659 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.3545588672340320000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8199999999999648 " "
y[1] (closed_form) = -1.068375056770258 " "
y[1] (numeric) = -1.068375056770268 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.3525276150050350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8209999999999646 " "
y[1] (closed_form) = -1.0686068483761773 " "
y[1] (numeric) = -1.0686068483761877 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 9.7660766888541370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8219999999999645 " "
y[1] (closed_form) = -1.0688384444721435 " "
y[1] (numeric) = -1.068838444472154 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 9.7639605736959070000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8229999999999644 " "
y[1] (closed_form) = -1.0690698452806005 " "
y[1] (numeric) = -1.0690698452806109 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 9.761847158580450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8239999999999643 " "
y[1] (closed_form) = -1.0693010510237007 " "
y[1] (numeric) = -1.069301051023711 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 9.7597364385693090000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8249999999999642 " "
y[1] (closed_form) = -1.0695320619233057 " "
y[1] (numeric) = -1.0695320619233164 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 9.9652375238151380000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.825999999999964 " "
y[1] (closed_form) = -1.0697628782009874 " "
y[1] (numeric) = -1.069762878200998 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 9.9630873846783920000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.826999999999964 " "
y[1] (closed_form) = -1.0699935000780258 " "
y[1] (numeric) = -1.0699935000780367 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 1.0168459565906833000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8279999999999639 " "
y[1] (closed_form) = -1.0702239277754129 " "
y[1] (numeric) = -1.0702239277754237 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 1.0166270215937227000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8289999999999638 " "
y[1] (closed_form) = -1.0704541615138496 " "
y[1] (numeric) = -1.0704541615138605 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 1.016408365019539100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8299999999999637 " "
y[1] (closed_form) = -1.0706842015137483 " "
y[1] (numeric) = -1.0706842015137594 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 1.0369285575107091000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8309999999999635 " "
y[1] (closed_form) = -1.0709140479952333 " "
y[1] (numeric) = -1.0709140479952441 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 1.015971885110145000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8319999999999634 " "
y[1] (closed_form) = -1.071143701178139 " "
y[1] (numeric) = -1.07114370117815 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 1.0157540607632326000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8329999999999633 " "
y[1] (closed_form) = -1.0713731612820132 " "
y[1] (numeric) = -1.071373161282024 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 1.015536512815686100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8339999999999632 " "
y[1] (closed_form) = -1.0716024285261152 " "
y[1] (numeric) = -1.071602428526126 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 1.0153192407646154000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.834999999999963 " "
y[1] (closed_form) = -1.071831503129417 " "
y[1] (numeric) = -1.071831503129428 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 1.0358186164370503000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.835999999999963 " "
y[1] (closed_form) = -1.0720603853106043 " "
y[1] (numeric) = -1.0720603853106152 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 1.0148855223462303000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8369999999999629 " "
y[1] (closed_form) = -1.0722890752880754 " "
y[1] (numeric) = -1.0722890752880863 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 1.0146690749790135000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8379999999999628 " "
y[1] (closed_form) = -1.0725175732799423 " "
y[1] (numeric) = -1.0725175732799537 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 1.0558591423863596000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8389999999999627 " "
y[1] (closed_form) = -1.0727458795040326 " "
y[1] (numeric) = -1.0727458795040439 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 1.0556344300676503000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8399999999999626 " "
y[1] (closed_form) = -1.0729739941778869 " "
y[1] (numeric) = -1.072973994177898 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 1.0347156880310132000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8409999999999624 " "
y[1] (closed_form) = -1.0732019175187606 " "
y[1] (numeric) = -1.073201917518772 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 1.0551858570434057000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8419999999999623 " "
y[1] (closed_form) = -1.0734296497436253 " "
y[1] (numeric) = -1.0734296497436366 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 1.0549619953092643000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8429999999999622 " "
y[1] (closed_form) = -1.0736571910691677 " "
y[1] (numeric) = -1.073657191069179 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 1.0547384160767065000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8439999999999621 " "
y[1] (closed_form) = -1.0738845417117902 " "
y[1] (numeric) = -1.0738845417118017 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 1.0751918858703935000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.844999999999962 " "
y[1] (closed_form) = -1.0741117018876125 " "
y[1] (numeric) = -1.0741117018876236 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 1.033619708894413100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.845999999999962 " "
y[1] (closed_form) = -1.074338671812469 " "
y[1] (numeric) = -1.0743386718124803 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 1.0540693682814113000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8469999999999618 " "
y[1] (closed_form) = -1.0745654517019128 " "
y[1] (numeric) = -1.0745654517019245 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 1.0951742439129929000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8479999999999617 " "
y[1] (closed_form) = -1.0747920417712147 " "
y[1] (numeric) = -1.0747920417712262 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 1.0742840482028274000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8489999999999616 " "
y[1] (closed_form) = -1.0750184422353612 " "
y[1] (numeric) = -1.075018442235373 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 1.0947127601416655000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8499999999999615 " "
y[1] (closed_form) = -1.0752446533090594 " "
y[1] (numeric) = -1.075244653309071 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 1.073831841020357000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8509999999999613 " "
y[1] (closed_form) = -1.0754706752067327 " "
y[1] (numeric) = -1.0754706752067444 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 1.0942524359173701000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8519999999999612 " "
y[1] (closed_form) = -1.0756965081425247 " "
y[1] (numeric) = -1.0756965081425365 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 1.0940227073292132000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8529999999999611 " "
y[1] (closed_form) = -1.0759221523302978 " "
y[1] (numeric) = -1.0759221523303095 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 1.093793267062865000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.853999999999961 " "
y[1] (closed_form) = -1.0761476079836334 " "
y[1] (numeric) = -1.0761476079836454 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.114197399780314100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.854999999999961 " "
y[1] (closed_form) = -1.0763728753158341 " "
y[1] (numeric) = -1.076372875315846 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 1.093335249420284000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8559999999999608 " "
y[1] (closed_form) = -1.0765979545399214 " "
y[1] (numeric) = -1.0765979545399333 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.1137313251793916000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8569999999999607 " "
y[1] (closed_form) = -1.0768228458686382 " "
y[1] (numeric) = -1.0768228458686502 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.1134987256218004000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8579999999999606 " "
y[1] (closed_form) = -1.077047549514448 " "
y[1] (numeric) = -1.07704754951446 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.1132664171936679000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8589999999999605 " "
y[1] (closed_form) = -1.0772720656895358 " "
y[1] (numeric) = -1.077272065689548 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1336461475086912000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8599999999999604 " "
y[1] (closed_form) = -1.0774963946058085 " "
y[1] (numeric) = -1.0774963946058207 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.133410128517834000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8609999999999602 " "
y[1] (closed_form) = -1.0777205364748947 " "
y[1] (numeric) = -1.077720536474907 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.133174404453896000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8619999999999601 " "
y[1] (closed_form) = -1.0779444915081458 " "
y[1] (numeric) = -1.077944491508158 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1329389747880572000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.86299999999996 " "
y[1] (closed_form) = -1.0781682599166353 " "
y[1] (numeric) = -1.0781682599166476 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1327038389927187000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.86399999999996 " "
y[1] (closed_form) = -1.0783918419111604 " "
y[1] (numeric) = -1.0783918419111727 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1324689965415005000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8649999999999598 " "
y[1] (closed_form) = -1.0786152377022418 " "
y[1] (numeric) = -1.078615237702254 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1322344469092363000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8659999999999597 " "
y[1] (closed_form) = -1.0788384475001238 " "
y[1] (numeric) = -1.0788384475001358 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.1114183679433909000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8669999999999596 " "
y[1] (closed_form) = -1.0790614715147744 " "
y[1] (numeric) = -1.0790614715147868 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.1523437917161794000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8679999999999595 " "
y[1] (closed_form) = -1.0792843099558875 " "
y[1] (numeric) = -1.0792843099559 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.1521058687779846000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8689999999999594 " "
y[1] (closed_form) = -1.0795069630328806 " "
y[1] (numeric) = -1.0795069630328933 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 1.1724373176035995000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8699999999999593 " "
y[1] (closed_form) = -1.0797294309548975 " "
y[1] (numeric) = -1.07972943095491 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.151630910422147100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8709999999999591 " "
y[1] (closed_form) = -1.0799517139308064 " "
y[1] (numeric) = -1.079951713930819 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 1.1719544788404958000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.871999999999959 " "
y[1] (closed_form) = -1.0801738121692026 " "
y[1] (numeric) = -1.0801738121692153 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 1.1717135092647679000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.872999999999959 " "
y[1] (closed_form) = -1.080395725878407 " "
y[1] (numeric) = -1.0803957258784198 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 1.1920249939142424000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8739999999999588 " "
y[1] (closed_form) = -1.0806174552664674 " "
y[1] (numeric) = -1.0806174552664805 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.2123283430903295000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8749999999999587 " "
y[1] (closed_form) = -1.080839000541159 " "
y[1] (numeric) = -1.080839000541172 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.212079845751085000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8759999999999586 " "
y[1] (closed_form) = -1.0810603619099837 " "
y[1] (numeric) = -1.081060361909997 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2323711760149814000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8769999999999585 " "
y[1] (closed_form) = -1.0812815395801718 " "
y[1] (numeric) = -1.0812815395801851 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2321190927456933000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8779999999999584 " "
y[1] (closed_form) = -1.0815025337586819 " "
y[1] (numeric) = -1.0815025337586945 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 1.1702739555070582000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8789999999999583 " "
y[1] (closed_form) = -1.081723344652199 " "
y[1] (numeric) = -1.0817233446522119 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 1.1905619999162172000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8799999999999581 " "
y[1] (closed_form) = -1.0819439724671394 " "
y[1] (numeric) = -1.0819439724671525 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.210841968156972900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.880999999999958 " "
y[1] (closed_form) = -1.0821644174096479 " "
y[1] (numeric) = -1.0821644174096607 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 1.1900767460529699000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.881999999999958 " "
y[1] (closed_form) = -1.0823846796855978 " "
y[1] (numeric) = -1.0823846796856107 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 1.189834568740633100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8829999999999578 " "
y[1] (closed_form) = -1.082604759500593 " "
y[1] (numeric) = -1.082604759500606 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.210102909266737900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8839999999999577 " "
y[1] (closed_form) = -1.0828246570599678 " "
y[1] (numeric) = -1.082824657059981 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2303632179631885000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8849999999999576 " "
y[1] (closed_form) = -1.083044372568787 " "
y[1] (numeric) = -1.0830443725688002 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.2096117225099925000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8859999999999575 " "
y[1] (closed_form) = -1.0832639062318454 " "
y[1] (numeric) = -1.0832639062318588 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2298643219679557000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8869999999999574 " "
y[1] (closed_form) = -1.0834832582536704 " "
y[1] (numeric) = -1.0834832582536837 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2296153349868105000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8879999999999573 " "
y[1] (closed_form) = -1.08370242883852 " "
y[1] (numeric) = -1.0837024288385335 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.24985609886874020000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8889999999999572 " "
y[1] (closed_form) = -1.083921418190385 " "
y[1] (numeric) = -1.0839214181903982 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2291182803403027000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.889999999999957 " "
y[1] (closed_form) = -1.0841402265129874 " "
y[1] (numeric) = -1.0841402265130007 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2288702115917917000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.890999999999957 " "
y[1] (closed_form) = -1.0843588540097826 " "
y[1] (numeric) = -1.0843588540097961 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2490994886370628000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8919999999999568 " "
y[1] (closed_form) = -1.0845773008839592 " "
y[1] (numeric) = -1.084577300883973 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.2693208214971550000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8929999999999567 " "
y[1] (closed_form) = -1.084795567338439 " "
y[1] (numeric) = -1.0847955673384526 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2485966303917585000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8939999999999566 " "
y[1] (closed_form) = -1.085013653575877 " "
y[1] (numeric) = -1.0850136535758905 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2483456642031743000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8949999999999565 " "
y[1] (closed_form) = -1.0852315597986628 " "
y[1] (numeric) = -1.0852315597986761 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2276344320444904000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8959999999999564 " "
y[1] (closed_form) = -1.08544928620892 " "
y[1] (numeric) = -1.0854492862089333 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2273881852217294000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8969999999999563 " "
y[1] (closed_form) = -1.085666833008507 " "
y[1] (numeric) = -1.0856668330085206 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2475946108524784000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8979999999999562 " "
y[1] (closed_form) = -1.0858842003990181 " "
y[1] (numeric) = -1.0858842003990317 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2473448730030123000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.898999999999956 " "
y[1] (closed_form) = -1.0861013885817823 " "
y[1] (numeric) = -1.0861013885817956 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.226651253332661900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.899999999999956 " "
y[1] (closed_form) = -1.0863183977578639 " "
y[1] (numeric) = -1.0863183977578774 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2468463139704622000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9009999999999558 " "
y[1] (closed_form) = -1.0865352281280645 " "
y[1] (numeric) = -1.086535228128078 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.246597491713399000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9019999999999557 " "
y[1] (closed_form) = -1.0867518798929212 " "
y[1] (numeric) = -1.086751879892935 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.2667809239684402000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9029999999999556 " "
y[1] (closed_form) = -1.0869683532527092 " "
y[1] (numeric) = -1.0869683532527228 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2461007590418686000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9039999999999555 " "
y[1] (closed_form) = -1.0871846484074394 " "
y[1] (numeric) = -1.0871846484074528 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2254290303875774000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9049999999999554 " "
y[1] (closed_form) = -1.0874007655568605 " "
y[1] (numeric) = -1.0874007655568743 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.266024996616767000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9059999999999553 " "
y[1] (closed_form) = -1.0876167049004606 " "
y[1] (numeric) = -1.0876167049004741 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2453579316498758000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9069999999999552 " "
y[1] (closed_form) = -1.087832466637464 " "
y[1] (numeric) = -1.0878324666374775 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2451109261607364000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.907999999999955 " "
y[1] (closed_form) = -1.0880480509668342 " "
y[1] (numeric) = -1.088048050966848 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.2652718318018089000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.908999999999955 " "
y[1] (closed_form) = -1.0882634580872748 " "
y[1] (numeric) = -1.0882634580872883 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2446178174752857000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9099999999999548 " "
y[1] (closed_form) = -1.088478688197227 " "
y[1] (numeric) = -1.0884786881972406 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.24437171322666000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9109999999999547 " "
y[1] (closed_form) = -1.0886937414948723 " "
y[1] (numeric) = -1.088693741494886 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.2645214150353212000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9119999999999546 " "
y[1] (closed_form) = -1.0889086181781324 " "
y[1] (numeric) = -1.088908618178146 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2438804022957192000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9129999999999545 " "
y[1] (closed_form) = -1.0891233184446687 " "
y[1] (numeric) = -1.0891233184446822 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2436351945681925000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9139999999999544 " "
y[1] (closed_form) = -1.0893378424918838 " "
y[1] (numeric) = -1.0893378424918971 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2230068373486383000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9149999999999543 " "
y[1] (closed_form) = -1.0895521905169203 " "
y[1] (numeric) = -1.089552190516934 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.263525109230474200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9159999999999542 " "
y[1] (closed_form) = -1.089766362716664 " "
y[1] (numeric) = -1.0897663627166776 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2429013560908098000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.916999999999954 " "
y[1] (closed_form) = -1.0899803592877402 " "
y[1] (numeric) = -1.0899803592877537 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.242657336438416100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.917999999999954 " "
y[1] (closed_form) = -1.0901941804265174 " "
y[1] (numeric) = -1.090194180426531 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2424136125114703000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9189999999999539 " "
y[1] (closed_form) = -1.0904078263291062 " "
y[1] (numeric) = -1.0904078263291197 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2421701837949621000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9199999999999537 " "
y[1] (closed_form) = -1.0906212971913598 " "
y[1] (numeric) = -1.0906212971913734 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2419270497750384000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9209999999999536 " "
y[1] (closed_form) = -1.0908345932088745 " "
y[1] (numeric) = -1.090834593208888 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2416842099389992000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9219999999999535 " "
y[1] (closed_form) = -1.0910477145769901 " "
y[1] (numeric) = -1.0910477145770037 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2414416637752941000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9229999999999534 " "
y[1] (closed_form) = -1.0912606614907894 " "
y[1] (numeric) = -1.0912606614908034 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.2818944734218335000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9239999999999533 " "
y[1] (closed_form) = -1.091473434145101 " "
y[1] (numeric) = -1.0914734341451144 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2409574504244206000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9249999999999532 " "
y[1] (closed_form) = -1.0916860327344948 " "
y[1] (numeric) = -1.0916860327345088 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.2813949881942974000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.925999999999953 " "
y[1] (closed_form) = -1.091898457453289 " "
y[1] (numeric) = -1.0918984574533028 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.2608100516472134000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.926999999999953 " "
y[1] (closed_form) = -1.0921107084955441 " "
y[1] (numeric) = -1.092110708495558 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.2605650139917213000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9279999999999529 " "
y[1] (closed_form) = -1.0923227860550675 " "
y[1] (numeric) = -1.0923227860550813 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.2603202717276205000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9289999999999528 " "
y[1] (closed_form) = -1.0925346903254116 " "
y[1] (numeric) = -1.0925346903254254 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.2600758243430704000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9299999999999526 " "
y[1] (closed_form) = -1.0927464214998752 " "
y[1] (numeric) = -1.092746421499889 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.2598316713273733000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9309999999999525 " "
y[1] (closed_form) = -1.0929579797715037 " "
y[1] (numeric) = -1.0929579797715174 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.2595878121709722000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9319999999999524 " "
y[1] (closed_form) = -1.0931693653330885 " "
y[1] (numeric) = -1.0931693653331023 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.2593442463654490000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9329999999999523 " "
y[1] (closed_form) = -1.093380578377169 " "
y[1] (numeric) = -1.0933805783771828 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.259100973403517200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9339999999999522 " "
y[1] (closed_form) = -1.0935916190960318 " "
y[1] (numeric) = -1.0935916190960453 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2385538316051693000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.934999999999952 " "
y[1] (closed_form) = -1.09380248768171 " "
y[1] (numeric) = -1.093802487681724 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.278915550825446000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.935999999999952 " "
y[1] (closed_form) = -1.0940131843259873 " "
y[1] (numeric) = -1.0940131843260013 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.278669243725373000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9369999999999519 " "
y[1] (closed_form) = -1.0942237092203935 " "
y[1] (numeric) = -1.0942237092204075 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.278423232141775000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9379999999999518 " "
y[1] (closed_form) = -1.0944340625562083 " "
y[1] (numeric) = -1.0944340625562223 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.2781775155649022000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9389999999999517 " "
y[1] (closed_form) = -1.0946442445244606 " "
y[1] (numeric) = -1.0946442445244744 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.2576474570815974000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9399999999999515 " "
y[1] (closed_form) = -1.0948542553159277 " "
y[1] (numeric) = -1.0948542553159417 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.277686965398002200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9409999999999514 " "
y[1] (closed_form) = -1.0950640951211381 " "
y[1] (numeric) = -1.095064095121152 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.2774421307941344000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9419999999999513 " "
y[1] (closed_form) = -1.0952737641303696 " "
y[1] (numeric) = -1.0952737641303836 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.2771975891693044000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9429999999999512 " "
y[1] (closed_form) = -1.0954832625336501 " "
y[1] (numeric) = -1.0954832625336643 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.2972224406546318000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.943999999999951 " "
y[1] (closed_form) = -1.0956925905207595 " "
y[1] (numeric) = -1.0956925905207735 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.2767093828414397000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.944999999999951 " "
y[1] (closed_form) = -1.0959017482812272 " "
y[1] (numeric) = -1.0959017482812414 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.2967270777229614000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9459999999999509 " "
y[1] (closed_form) = -1.0961107360043354 " "
y[1] (numeric) = -1.0961107360043496 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.2964798398932748000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9469999999999508 " "
y[1] (closed_form) = -1.096319553879118 " "
y[1] (numeric) = -1.0963195538791317 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.2557256191081206000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9479999999999507 " "
y[1] (closed_form) = -1.0965282020943592 " "
y[1] (numeric) = -1.0965282020943734 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.2959862489682800000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9489999999999505 " "
y[1] (closed_form) = -1.0967366808385983 " "
y[1] (numeric) = -1.0967366808386125 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.2957398948611760000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9499999999999504 " "
y[1] (closed_form) = -1.096944990300126 " "
y[1] (numeric) = -1.09694499030014 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.275251743157112000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9509999999999503 " "
y[1] (closed_form) = -1.0971531306669857 " "
y[1] (numeric) = -1.0971531306669997 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.275009815792335000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9519999999999502 " "
y[1] (closed_form) = -1.097361102126975 " "
y[1] (numeric) = -1.0973611021269891 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.2950025919141497000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.95299999999995 " "
y[1] (closed_form) = -1.097568904867645 " "
y[1] (numeric) = -1.0975689048676591 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.2947574090499295000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.95399999999995 " "
y[1] (closed_form) = -1.0977765390763012 " "
y[1] (numeric) = -1.0977765390763152 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.274285759654468000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9549999999999499 " "
y[1] (closed_form) = -1.0979840049400027 " "
y[1] (numeric) = -1.097984004940017 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.2942679174983546000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9559999999999498 " "
y[1] (closed_form) = -1.098191302645564 " "
y[1] (numeric) = -1.0981913026455787 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3344618455589680000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9569999999999497 " "
y[1] (closed_form) = -1.0983984323795557 " "
y[1] (numeric) = -1.0983984323795701 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.3139948942625304000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9579999999999496 " "
y[1] (closed_form) = -1.0986053943283016 " "
y[1] (numeric) = -1.098605394328316 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.3137473559331514000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9589999999999494 " "
y[1] (closed_form) = -1.0988121886778828 " "
y[1] (numeric) = -1.0988121886778972 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.3135001111967137000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9599999999999493 " "
y[1] (closed_form) = -1.0990188156141358 " "
y[1] (numeric) = -1.0990188156141505 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.333457054314655000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9609999999999492 " "
y[1] (closed_form) = -1.0992252753226546 " "
y[1] (numeric) = -1.099225275322669 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.3130065005001415000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9619999999999491 " "
y[1] (closed_form) = -1.099431567988788 " "
y[1] (numeric) = -1.0994315679888025 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.3127601335415012000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.962999999999949 " "
y[1] (closed_form) = -1.0996376937976438 " "
y[1] (numeric) = -1.0996376937976582 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.312514058178783000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.963999999999949 " "
y[1] (closed_form) = -1.0998436529340858 " "
y[1] (numeric) = -1.0998436529341005 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3324570165910976000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9649999999999488 " "
y[1] (closed_form) = -1.1000494455827368 " "
y[1] (numeric) = -1.1000494455827514 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3322077461062493000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9659999999999487 " "
y[1] (closed_form) = -1.1002550719279764 " "
y[1] (numeric) = -1.100255071927991 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3319587701942800000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9669999999999486 " "
y[1] (closed_form) = -1.1004605321539431 " "
y[1] (numeric) = -1.100460532153958 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3518875139354802000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9679999999999485 " "
y[1] (closed_form) = -1.1006658264445346 " "
y[1] (numeric) = -1.1006658264445495 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3516353622092572000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9689999999999483 " "
y[1] (closed_form) = -1.100870954983407 " "
y[1] (numeric) = -1.1008709549834217 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.331213604892769200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9699999999999482 " "
y[1] (closed_form) = -1.101075917953976 " "
y[1] (numeric) = -1.1010759179539904 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.3107996537556021000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9709999999999481 " "
y[1] (closed_form) = -1.101280715539416 " "
y[1] (numeric) = -1.1012807155394309 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3508806900963694000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.971999999999948 " "
y[1] (closed_form) = -1.1014853479226634 " "
y[1] (numeric) = -1.1014853479226783 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3506297254007257000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.972999999999948 " "
y[1] (closed_form) = -1.1016898152864134 " "
y[1] (numeric) = -1.1016898152864283 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3503790562055284000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9739999999999478 " "
y[1] (closed_form) = -1.1018941178131223 " "
y[1] (numeric) = -1.1018941178131372 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3501286820100974000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9749999999999477 " "
y[1] (closed_form) = -1.1020982556850072 " "
y[1] (numeric) = -1.102098255685022 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3498786023148482000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9759999999999476 " "
y[1] (closed_form) = -1.1023022290840467 " "
y[1] (numeric) = -1.1023022290840616 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.349628816621288000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9769999999999475 " "
y[1] (closed_form) = -1.1025060381919813 " "
y[1] (numeric) = -1.102506038191996 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3292393345151163000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9779999999999474 " "
y[1] (closed_form) = -1.1027096831903127 " "
y[1] (numeric) = -1.1027096831903274 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3289938547245733000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9789999999999472 " "
y[1] (closed_form) = -1.1029131642603054 " "
y[1] (numeric) = -1.10291316426032 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3287486630809006000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9799999999999471 " "
y[1] (closed_form) = -1.1031164815829861 " "
y[1] (numeric) = -1.103116481583001 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3486326039321278000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.980999999999947 " "
y[1] (closed_form) = -1.1033196353391452 " "
y[1] (numeric) = -1.10331963533916 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3483842808076300000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.981999999999947 " "
y[1] (closed_form) = -1.1035226257093358 " "
y[1] (numeric) = -1.1035226257093507 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.34813624871663000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9829999999999468 " "
y[1] (closed_form) = -1.1037254528738745 " "
y[1] (numeric) = -1.1037254528738891 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3277707682552398000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9839999999999467 " "
y[1] (closed_form) = -1.1039281170128414 " "
y[1] (numeric) = -1.103928117012856 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3275270100654202000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9849999999999466 " "
y[1] (closed_form) = -1.1041306183060817 " "
y[1] (numeric) = -1.1041306183060964 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3272835371176614000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9859999999999465 " "
y[1] (closed_form) = -1.1043329569332045 " "
y[1] (numeric) = -1.1043329569332192 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3270403489315105000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9869999999999464 " "
y[1] (closed_form) = -1.104535133073584 " "
y[1] (numeric) = -1.1045351330735989 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3469004366188860000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9879999999999463 " "
y[1] (closed_form) = -1.1047371469063596 " "
y[1] (numeric) = -1.1047371469063745 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.346654140456644800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9889999999999461 " "
y[1] (closed_form) = -1.1049389986104359 " "
y[1] (numeric) = -1.1049389986104508 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3464081319137347000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.989999999999946 " "
y[1] (closed_form) = -1.1051406883644834 " "
y[1] (numeric) = -1.1051406883644983 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3461624105066486000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.990999999999946 " "
y[1] (closed_form) = -1.1053422163469386 " "
y[1] (numeric) = -1.1053422163469537 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.3660052888238666000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9919999999999458 " "
y[1] (closed_form) = -1.105543582736005 " "
y[1] (numeric) = -1.1055435827360203 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 1.3858411354449254000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9929999999999457 " "
y[1] (closed_form) = -1.1057447877096525 " "
y[1] (numeric) = -1.1057447877096676 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.365507963747856000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9939999999999456 " "
y[1] (closed_form) = -1.1059458314456174 " "
y[1] (numeric) = -1.1059458314456325 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.3652597356568266000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9949999999999455 " "
y[1] (closed_form) = -1.1061467141214043 " "
y[1] (numeric) = -1.1061467141214196 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 1.38508549943996000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9959999999999454 " "
y[1] (closed_form) = -1.106347435914286 " "
y[1] (numeric) = -1.1063474359143008 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3446940849718467000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9969999999999453 " "
y[1] (closed_form) = -1.1065479970013015 " "
y[1] (numeric) = -1.1065479970013163 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3444503600650953000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9979999999999452 " "
y[1] (closed_form) = -1.106748397559259 " "
y[1] (numeric) = -1.1067483975592742 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 1.3843324981192773000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.998999999999945 " "
y[1] (closed_form) = -1.1069486377647364 " "
y[1] (numeric) = -1.1069486377647517 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 1.3840820808782098000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.999999999999945 " "
y[1] (closed_form) = -1.1071487177940795 " "
y[1] (numeric) = -1.1071487177940946 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.363776418852379000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
"Finished!"
"diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; "
Iterations = 501
"Total Elapsed Time "= 9 Seconds
"Elapsed Time(since restart) "= 9 Seconds
"Expected Time Remaining "= 0 Seconds
"Optimized Time Remaining "= 0 Seconds
"Expected Total Time "= 9 Seconds
"Time to Timeout "= 2 Minutes 50 Seconds
Percent Done = 0.0 "%"
(%o253) temp/diffeq.sing2_back.max