(%i1) batch("temp/diffeq.div_c_lin_back.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.div_c_lin_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([30],convfloat)),fixnum)
(%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a],
completearray([30],convfloat),[arr_b],
completearray([30],convfloat),[jjj_ats],fixnum),
convfloat)
(%i25) mode_declare(att([mmm_att],fixnum,[arr_a],
completearray([30],convfloat),[arr_b],
completearray([30],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,30,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,[30],convfloat)
(%i173) completearray(array_norms,[30],convfloat)
(%i174) completearray(array_fact_1,[30],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,[30],convfloat)
(%i184) completearray(array_x,[30],convfloat)
(%i185) completearray(array_tmp0,[30],convfloat)
(%i186) completearray(array_tmp1,[30],convfloat)
(%i187) completearray(array_tmp2,[30],convfloat)
(%i188) completearray(array_tmp3,[30],convfloat)
(%i189) completearray(array_tmp4,[30],convfloat)
(%i190) completearray(array_m1,[30],convfloat)
(%i191) completearray(array_y_higher,[2,30],convfloat)
(%i192) completearray(array_y_higher_work,[2,30],convfloat)
(%i193) completearray(array_y_higher_work2,[2,30],convfloat)
(%i194) completearray(array_y_set_initial,[2,30],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,[30,30],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(c(10.0)*log(c(0.3)+c(0.2)*c(x)))
(%o239) exact_soln_y(x) := block(c(10.0) log(c(0.3) + c(0.2) 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_const_0D2[1]*array_x[1],
array_tmp2[1]:array_const_0D3[1]+array_tmp1[1],
array_tmp3[1]:array_const_2D0[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_const_0D2[1]*array_x[2],
array_tmp2[2]:array_tmp1[2],
array_tmp3[2]:neg(array_tmp3[1])*array_tmp2[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_tmp3[3]:neg(array_tmp3[2])*array_tmp2[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_tmp3[4]:neg(array_tmp3[3])*array_tmp2[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_tmp3[5]:neg(array_tmp3[4])*array_tmp2[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_tmp3[kkk]
:array_const_2D0[1]*array_tmp2[kkk],
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(c(10.0)*log(c(0.3)+c(0.2)*c(x)))
(%o250) exact_soln_y(x) := block(c(10.0) log(c(0.3) + c(0.2) 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:30,
glob_html_log:true,term:1,
while term <= 30 do (array_y_init[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_norms[term]:c(0.0),term:1+term),
term:1,
while term <= 30 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 <= 30 do (array_y[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_x[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp0[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp1[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp2[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp3[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp4[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_m1[term]:c(0.0),term:1+term),
ord:1,
while ord <= 2 do
(term:1,
while term <= 30 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 <= 30 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 <= 30 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 <= 30 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 <= 30 do
(term:1,
while term <= 30 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_2D0),array_const_2D0[1]:c(2.0),
zero_ats_ar(array_const_0D2),array_const_0D2[1]:c(0.2),
zero_ats_ar(array_const_0D3),array_const_0D3[1]:c(0.3),
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,
array_y_set_initial[1,21]:false,
array_y_set_initial[1,22]:false,
array_y_set_initial[1,23]:false,
array_y_set_initial[1,24]:false,
array_y_set_initial[1,25]:false,
array_y_set_initial[1,26]:false,
array_y_set_initial[1,27]:false,
array_y_set_initial[1,28]:false,
array_y_set_initial[1,29]:false,
array_y_set_initial[1,30]: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/div_c_lin_backpostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; "),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(always,"Digits:32,"),
omniout_str(always,"max_terms:30,"),omniout_str(always,"!"),
omniout_str(always,"/* END FIRST INPUT BLOCK */"),
omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(always,"x_start:c(3.1),"),
omniout_str(always,"x_end:c(2.5),"),
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,"glob_display_interval:c(0.1),"),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),
omniout_str(always,"glob_type_given_pole:1,"),
omniout_str(always,""),
omniout_str(always,"array_given_rad_poles[1,1]:c(-1.5),"),
omniout_str(always,""),
omniout_str(always,"array_given_rad_poles[1,2]:c(0.0),"),
omniout_str(always,""),
omniout_str(always,"array_given_ord_poles[1,1]:c(1.0),"),
omniout_str(always,""),
omniout_str(always,"array_given_ord_poles[1,2]:c(0.0),"),
omniout_str(always,"/* END SECOND INPUT BLOCK */"),
omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"),
omniout_str(always,"glob_desired_digits_correct:8,"),
omniout_str(always,"glob_max_minutes:(3.0),"),
omniout_str(always,"glob_subiter_method:3,"),
omniout_str(always,"glob_max_iter:100000,"),
omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"),
omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"),
omniout_str(always,"glob_look_poles:false,"),
omniout_str(always,"glob_h:c(0.001),"),
omniout_str(always,"glob_display_interval:c(0.01),"),
omniout_str(always,"/* END OVERRIDE BLOCK */"),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN USER DEF BLOCK */"),
omniout_str(always,"exact_soln_y (x) := (block("),
omniout_str(always,""),
omniout_str(always,
" (c(10.0)* ln(c(0.2)* c(x) + c(0.3))) "),
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(3.1),x_end:c(2.5),
array_y_init[1+0]:exact_soln_y(x_start),
glob_look_poles:true,glob_display_interval:c(0.1),
glob_type_given_pole:1,array_given_rad_poles[1,1]:c(-1.5),
array_given_rad_poles[1,2]:c(0.0),
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 ) = 2.0 / ( 0.2 * x + 0.3 ) ; "),
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,
"2015-04-24T23:02:15-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"div_c_lin_back"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; "),
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,
"div_c_lin_back diffeq.max"),
logitem_str(html_log_file,
"div_c_lin_back maxima results"),
logitem_str(html_log_file,
"PROBLEM - missing singularity"),
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_const_0D2 in translation.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_const_0D3 in translation.
warning: encountered undefined variable array_tmp2 in translation.
warning: encountered undefined variable array_const_2D0 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_display_interval (declared type convfloat) assigned type any.
warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_h (declared type convfloat) assigned type any.
warning: 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/div_c_lin_backpostode.ode#################"
"diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:c(3.1),"
"x_end:c(2.5),"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
""
""
""
"glob_display_interval:c(0.1),"
""
""
""
""
""
""
""
"glob_type_given_pole:1,"
""
"array_given_rad_poles[1,1]:c(-1.5),"
""
"array_given_rad_poles[1,2]:c(0.0),"
""
"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("
""
" (c(10.0)* ln(c(0.2)* c(x) + c(0.3))) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.099 " "
y[1] (closed_form) = -0.8359902387631342 " "
y[1] (numeric) = -0.8359902387631344 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.6560669566375700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 15
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0980000000000003 " "
y[1] (closed_form) = -0.8381648609311037 " "
y[1] (numeric) = -0.838164860931104 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 3.97376367004396200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0970000000000004 " "
y[1] (closed_form) = -0.8403399561000919 " "
y[1] (numeric) = -0.8403399561000926 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 7.92695634593568600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0960000000000005 " "
y[1] (closed_form) = -0.8425155244759086 " "
y[1] (numeric) = -0.8425155244759095 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.05419828347094430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0950000000000006 " "
y[1] (closed_form) = -0.8446915662644972 " "
y[1] (numeric) = -0.8446915662644983 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.31435315441223900000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0940000000000007 " "
y[1] (closed_form) = -0.8468680816719355 " "
y[1] (numeric) = -0.846868081671937 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.70426771683646170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.093000000000001 " "
y[1] (closed_form) = -0.8490450709044364 " "
y[1] (numeric) = -0.849045070904438 " "
absolute error = 1.6653345369377348000000000000000E-15 " "
relative error = 1.96142065245576950000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.092000000000001 " "
y[1] (closed_form) = -0.8512225341683473 " "
y[1] (numeric) = -0.851222534168349 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.08683013911957650000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.091000000000001 " "
y[1] (closed_form) = -0.85340047167015 " "
y[1] (numeric) = -0.853400471670152 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 2.3416924535022862000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.090000000000001 " "
y[1] (closed_form) = -0.8555788836164618 " "
y[1] (numeric) = -0.8555788836164641 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.5952557873619670000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0890000000000013 " "
y[1] (closed_form) = -0.857757770214035 " "
y[1] (numeric) = -0.8577577702140374 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.84752961615943550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0880000000000014 " "
y[1] (closed_form) = -0.8599371316697567 " "
y[1] (numeric) = -0.8599371316697594 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.0985233233580640000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0870000000000015 " "
y[1] (closed_form) = -0.8621169681906495 " "
y[1] (numeric) = -0.8621169681906525 " "
absolute error = 2.9976021664879227000000000000000E-15 " "
relative error = 3.47702490159668140000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0860000000000016 " "
y[1] (closed_form) = -0.8642972799838717 " "
y[1] (numeric) = -0.864297279983875 " "
absolute error = 3.219646771412954000000000000000E-15 " "
relative error = 3.7251612911162170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0850000000000017 " "
y[1] (closed_form) = -0.8664780672567168 " "
y[1] (numeric) = -0.8664780672567202 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.84391619330933500000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.084000000000002 " "
y[1] (closed_form) = -0.8686593302166139 " "
y[1] (numeric) = -0.8686593302166175 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.08988144744220460000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.083000000000002 " "
y[1] (closed_form) = -0.8708410690711279 " "
y[1] (numeric) = -0.8708410690711318 " "
absolute error = 3.885780586188048000000000000000E-15 " "
relative error = 4.46210074857030850000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.082000000000002 " "
y[1] (closed_form) = -0.87302328402796 " "
y[1] (numeric) = -0.873023284027964 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 4.578117172557060000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.081000000000002 " "
y[1] (closed_form) = -0.8752059752949468 " "
y[1] (numeric) = -0.875205975294951 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 4.8204052676329495000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0800000000000023 " "
y[1] (closed_form) = -0.8773891430800613 " "
y[1] (numeric) = -0.8773891430800659 " "
absolute error = 4.551914400963142000000000000000E-15 " "
relative error = 5.1880222554198870000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0790000000000024 " "
y[1] (closed_form) = -0.879572787591413 " "
y[1] (numeric) = -0.8795727875914178 " "
absolute error = 4.773959005888173000000000000000E-15 " "
relative error = 5.4275883397450160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0780000000000025 " "
y[1] (closed_form) = -0.8817569090372472 " "
y[1] (numeric) = -0.8817569090372522 " "
absolute error = 4.9960036108132044000000000000000E-15 " "
relative error = 5.6659648023264460000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0770000000000026 " "
y[1] (closed_form) = -0.8839415076259461 " "
y[1] (numeric) = -0.8839415076259515 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.0287592247063390000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0760000000000027 " "
y[1] (closed_form) = -0.8861265835660286 " "
y[1] (numeric) = -0.886126583566034 " "
absolute error = 5.440092820663267000000000000000E-15 " "
relative error = 6.1391825068273730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.075000000000003 " "
y[1] (closed_form) = -0.8883121370661496 " "
y[1] (numeric) = -0.8883121370661554 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 6.4990215569022520000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.074000000000003 " "
y[1] (closed_form) = -0.8904981683351019 " "
y[1] (numeric) = -0.8904981683351079 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 6.7324162431289800000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.073000000000003 " "
y[1] (closed_form) = -0.8926846775818142 " "
y[1] (numeric) = -0.8926846775818205 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 6.96466411268840000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.072000000000003 " "
y[1] (closed_form) = -0.8948716650153531 " "
y[1] (numeric) = -0.8948716650153595 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 7.1957731980657020000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0710000000000033 " "
y[1] (closed_form) = -0.8970591308449221 " "
y[1] (numeric) = -0.8970591308449286 " "
absolute error = 6.5503158452884240000000000000000E-15 " "
relative error = 7.3019889325677030000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0700000000000034 " "
y[1] (closed_form) = -0.8992470752798616 " "
y[1] (numeric) = -0.8992470752798685 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 7.6546067725977770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0690000000000035 " "
y[1] (closed_form) = -0.9014354985296501 " "
y[1] (numeric) = -0.9014354985296573 " "
absolute error = 7.216449660063518000000000000000E-15 " "
relative error = 8.0055086268894630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0680000000000036 " "
y[1] (closed_form) = -0.9036244008039035 " "
y[1] (numeric) = -0.9036244008039109 " "
absolute error = 7.438494264988549000000000000000E-15 " "
relative error = 8.2318430737051160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0670000000000037 " "
y[1] (closed_form) = -0.9058137823123751 " "
y[1] (numeric) = -0.9058137823123827 " "
absolute error = 7.66053886991358000000000000000E-15 " "
relative error = 8.4570791695812360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.066000000000004 " "
y[1] (closed_form) = -0.9080036432649561 " "
y[1] (numeric) = -0.9080036432649641 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 8.8034952685411050000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.065000000000004 " "
y[1] (closed_form) = -0.9101939838716757 " "
y[1] (numeric) = -0.910193983871684 " "
absolute error = 8.326672684688674000000000000000E-15 " "
relative error = 9.1482396414769270000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.064000000000004 " "
y[1] (closed_form) = -0.9123848043427013 " "
y[1] (numeric) = -0.9123848043427099 " "
absolute error = 8.548717289613705000000000000000E-15 " "
relative error = 9.3696401440753490000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.063000000000004 " "
y[1] (closed_form) = -0.9145761048883382 " "
y[1] (numeric) = -0.914576104888347 " "
absolute error = 8.770761894538737000000000000000E-15 " "
relative error = 9.5899749049419670000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0620000000000043 " "
y[1] (closed_form) = -0.91676788571903 " "
y[1] (numeric) = -0.916767885719039 " "
absolute error = 8.992806499463768000000000000000E-15 " "
relative error = 9.809251217837569000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0610000000000044 " "
y[1] (closed_form) = -0.9189601470453589 " "
y[1] (numeric) = -0.9189601470453681 " "
absolute error = 9.2148511043887990000000000000E-15 " "
relative error = 1.0027476310062404000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0600000000000045 " "
y[1] (closed_form) = -0.9211528890780453 " "
y[1] (numeric) = -0.9211528890780548 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 1.036518272371981100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0590000000000046 " "
y[1] (closed_form) = -0.9233461120279486 " "
y[1] (numeric) = -0.9233461120279584 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 1.0581040510631023000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0580000000000047 " "
y[1] (closed_form) = -0.9255398161060668 " "
y[1] (numeric) = -0.9255398161060767 " "
absolute error = 9.880984919163893000000000000000E-15 " "
relative error = 1.067591555459515000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.057000000000005 " "
y[1] (closed_form) = -0.9277340015235368 " "
y[1] (numeric) = -0.9277340015235469 " "
absolute error = 1.010302952408892500000000000000E-14 " "
relative error = 1.0890006734147503000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.056000000000005 " "
y[1] (closed_form) = -0.9299286684916344 " "
y[1] (numeric) = -0.9299286684916448 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 1.1222469835674664000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.055000000000005 " "
y[1] (closed_form) = -0.9321238172217748 " "
y[1] (numeric) = -0.9321238172217854 " "
absolute error = 1.054711873393898700000000000000E-14 " "
relative error = 1.131514777229383000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.054000000000005 " "
y[1] (closed_form) = -0.9343194479255122 " "
y[1] (numeric) = -0.934319447925523 " "
absolute error = 1.076916333886401800000000000000E-14 " "
relative error = 1.1526211257589683000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0530000000000053 " "
y[1] (closed_form) = -0.9365155608145403 " "
y[1] (numeric) = -0.9365155608145515 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 1.185482730964484000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0520000000000054 " "
y[1] (closed_form) = -0.9387121561006926 " "
y[1] (numeric) = -0.9387121561007038 " "
absolute error = 1.121325254871408100000000000000E-14 " "
relative error = 1.194535777111133000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0510000000000055 " "
y[1] (closed_form) = -0.9409092339959413 " "
y[1] (numeric) = -0.9409092339959529 " "
absolute error = 1.165734175856414400000000000000E-14 " "
relative error = 1.238944346316664000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0500000000000056 " "
y[1] (closed_form) = -0.9431067947123994 " "
y[1] (numeric) = -0.9431067947124113 " "
absolute error = 1.187938636348917500000000000000E-14 " "
relative error = 1.259601397221594100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0490000000000057 " "
y[1] (closed_form) = -0.9453048384623195 " "
y[1] (numeric) = -0.9453048384623315 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.268417147367604000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.048000000000006 " "
y[1] (closed_form) = -0.9475033654580934 " "
y[1] (numeric) = -0.9475033654581058 " "
absolute error = 1.232347557333923800000000000000E-14 " "
relative error = 1.3006260476321532000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.047000000000006 " "
y[1] (closed_form) = -0.9497023759122541 " "
y[1] (numeric) = -0.9497023759122667 " "
absolute error = 1.254552017826427000000000000000E-14 " "
relative error = 1.3209949239321883000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.046000000000006 " "
y[1] (closed_form) = -0.9519018700374744 " "
y[1] (numeric) = -0.9519018700374872 " "
absolute error = 1.2767564783189300000000000000E-14 " "
relative error = 1.3412690094501725000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.045000000000006 " "
y[1] (closed_form) = -0.9541018480465673 " "
y[1] (numeric) = -0.9541018480465803 " "
absolute error = 1.298960938811433200000000000000E-14 " "
relative error = 1.3614489286137868000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0440000000000063 " "
y[1] (closed_form) = -0.9563023101524863 " "
y[1] (numeric) = -0.9563023101524996 " "
absolute error = 1.321165399303936300000000000000E-14 " "
relative error = 1.3815353003730285000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0430000000000064 " "
y[1] (closed_form) = -0.9585032565683258 " "
y[1] (numeric) = -0.9585032565683393 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.4131116203945200000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0420000000000065 " "
y[1] (closed_form) = -0.9607046875073209 " "
y[1] (numeric) = -0.9607046875073346 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.4329861906962990000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0410000000000066 " "
y[1] (closed_form) = -0.962906603182847 " "
y[1] (numeric) = -0.9629066031828611 " "
absolute error = 1.409983241273948800000000000000E-14 " "
relative error = 1.4642990676492493000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0400000000000067 " "
y[1] (closed_form) = -0.9651090038084214 " "
y[1] (numeric) = -0.9651090038084357 " "
absolute error = 1.43218770176645200000000000000E-14 " "
relative error = 1.4839647087685318000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.039000000000007 " "
y[1] (closed_form) = -0.9673118895977018 " "
y[1] (numeric) = -0.9673118895977163 " "
absolute error = 1.45439216225895500000000000000E-14 " "
relative error = 1.5035400452524433000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.038000000000007 " "
y[1] (closed_form) = -0.9695152607644872 " "
y[1] (numeric) = -0.969515260764502 " "
absolute error = 1.476596622751458200000000000000E-14 " "
relative error = 1.5230256629350264000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.037000000000007 " "
y[1] (closed_form) = -0.9717191175227182 " "
y[1] (numeric) = -0.9717191175227334 " "
absolute error = 1.521005543736464500000000000000E-14 " "
relative error = 1.5652728409975983000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.036000000000007 " "
y[1] (closed_form) = -0.9739234600864771 " "
y[1] (numeric) = -0.9739234600864924 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 1.5731295494685757000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0350000000000072 " "
y[1] (closed_form) = -0.9761282886699871 " "
y[1] (numeric) = -0.9761282886700027 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 1.5923237268259383000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0340000000000074 " "
y[1] (closed_form) = -0.9783336034876134 " "
y[1] (numeric) = -0.9783336034876294 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.634126794542294000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0330000000000075 " "
y[1] (closed_form) = -0.9805394047538638 " "
y[1] (numeric) = -0.9805394047538799 " "
absolute error = 1.60982338570647700000000000000E-14 " "
relative error = 1.6417732708157473000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0320000000000076 " "
y[1] (closed_form) = -0.9827456926833867 " "
y[1] (numeric) = -0.9827456926834032 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 1.671978914462261000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0310000000000077 " "
y[1] (closed_form) = -0.9849524674909739 " "
y[1] (numeric) = -0.9849524674909905 " "
absolute error = 1.665334536937734800000000000000E-14 " "
relative error = 1.690776552070515000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.030000000000008 " "
y[1] (closed_form) = -0.9871597293915585 " "
y[1] (numeric) = -0.9871597293915755 " "
absolute error = 1.698641227676489500000000000000E-14 " "
relative error = 1.7207359428280739000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.029000000000008 " "
y[1] (closed_form) = -0.9893674786002167 " "
y[1] (numeric) = -0.9893674786002338 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 1.7281177064175704000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.028000000000008 " "
y[1] (closed_form) = -0.9915757153321665 " "
y[1] (numeric) = -0.9915757153321838 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 1.7466622988392383000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.027000000000008 " "
y[1] (closed_form) = -0.993784439802769 " "
y[1] (numeric) = -0.9937844398027865 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.7651236109672683000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0260000000000082 " "
y[1] (closed_form) = -0.9959936522275277 " "
y[1] (numeric) = -0.9959936522275455 " "
absolute error = 1.78745906964650200000000000000E-14 " "
relative error = 1.7946490579019972000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0250000000000083 " "
y[1] (closed_form) = -0.9982033528220893 " "
y[1] (numeric) = -0.9982033528221074 " "
absolute error = 1.809663530139005200000000000000E-14 " "
relative error = 1.8129207090146320000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0240000000000085 " "
y[1] (closed_form) = -1.0004135418022433 " "
y[1] (numeric) = -1.0004135418022615 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 1.820013108884102000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0230000000000086 " "
y[1] (closed_form) = -1.0026242193839223 " "
y[1] (numeric) = -1.0026242193839408 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 1.838146521146478000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0220000000000087 " "
y[1] (closed_form) = -1.0048353857832022 " "
y[1] (numeric) = -1.0048353857832208 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 1.8561992419449713000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.021000000000009 " "
y[1] (closed_form) = -1.007047041216302 " "
y[1] (numeric) = -1.0070470412163208 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 1.8741717761100887000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.020000000000009 " "
y[1] (closed_form) = -1.0092591858995843 " "
y[1] (numeric) = -1.0092591858996036 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.9140653757101148000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.019000000000009 " "
y[1] (closed_form) = -1.011471820049556 " "
y[1] (numeric) = -1.0114718200495756 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.931830906811167200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.018000000000009 " "
y[1] (closed_form) = -1.0136849438828668 " "
y[1] (numeric) = -1.0136849438828865 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.9495179402221957000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0170000000000092 " "
y[1] (closed_form) = -1.0158985576163106 " "
y[1] (numeric) = -1.0158985576163306 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.967126962965969000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0160000000000093 " "
y[1] (closed_form) = -1.0181126614668259 " "
y[1] (numeric) = -1.0181126614668459 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.9628490244351976000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0150000000000095 " "
y[1] (closed_form) = -1.020327255651494 " "
y[1] (numeric) = -1.0203272556515144 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 2.002112904458211000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0140000000000096 " "
y[1] (closed_form) = -1.0225423403875415 " "
y[1] (numeric) = -1.0225423403875622 " "
absolute error = 2.065014825802791200000000000000E-14 " "
relative error = 2.0194907772915835000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0130000000000097 " "
y[1] (closed_form) = -1.0247579158923394 " "
y[1] (numeric) = -1.0247579158923603 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 2.036792547708971800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.01200000000001 " "
y[1] (closed_form) = -1.026973982383403 " "
y[1] (numeric) = -1.0269739823834239 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 2.0323974337220035000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.01100000000001 " "
y[1] (closed_form) = -1.0291905400783916 " "
y[1] (numeric) = -1.029190540078413 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 2.07116964669918000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.01000000000001 " "
y[1] (closed_form) = -1.0314075891951104 " "
y[1] (numeric) = -1.031407589195132 " "
absolute error = 2.153832667772803700000000000000E-14 " "
relative error = 2.0882458984557314000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.00900000000001 " "
y[1] (closed_form) = -1.0336251299515085 " "
y[1] (numeric) = -1.0336251299515304 " "
absolute error = 2.1982415887578100000000000000E-14 " "
relative error = 2.126730015611113000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.00800000000001 " "
y[1] (closed_form) = -1.035843162565681 " "
y[1] (numeric) = -1.035843162565703 " "
absolute error = 2.1982415887578100000000000000E-14 " "
relative error = 2.1221760863034356000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0070000000000103 " "
y[1] (closed_form) = -1.038061687255867 " "
y[1] (numeric) = -1.0380616872558894 " "
absolute error = 2.242650509742816200000000000000E-14 " "
relative error = 2.1604212324522826000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0060000000000104 " "
y[1] (closed_form) = -1.0402807042404523 " "
y[1] (numeric) = -1.0402807042404747 " "
absolute error = 2.242650509742816200000000000000E-14 " "
relative error = 2.1558128499367474000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0050000000000106 " "
y[1] (closed_form) = -1.0425002137379664 " "
y[1] (numeric) = -1.0425002137379893 " "
absolute error = 2.287059430727822500000000000000E-14 " "
relative error = 2.19382154611498000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0040000000000107 " "
y[1] (closed_form) = -1.0447202159670859 " "
y[1] (numeric) = -1.0447202159671092 " "
absolute error = 2.331468351712828700000000000000E-14 " "
relative error = 2.231667690621468900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0030000000000108 " "
y[1] (closed_form) = -1.0469407111466325 " "
y[1] (numeric) = -1.0469407111466558 " "
absolute error = 2.331468351712828700000000000000E-14 " "
relative error = 2.226934464282465000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.002000000000011 " "
y[1] (closed_form) = -1.049161699495573 " "
y[1] (numeric) = -1.0491616994955968 " "
absolute error = 2.37587727269783500000000000000E-14 " "
relative error = 2.2645482329750832000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.001000000000011 " "
y[1] (closed_form) = -1.0513831812330214 " "
y[1] (numeric) = -1.0513831812330454 " "
absolute error = 2.39808173319033800000000000000E-14 " "
relative error = 2.2808827228698494000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.000000000000011 " "
y[1] (closed_form) = -1.053605156578237 " "
y[1] (numeric) = -1.0536051565782611 " "
absolute error = 2.420286193682841300000000000000E-14 " "
relative error = 2.297147255375187000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.999000000000011 " "
y[1] (closed_form) = -1.0558276257506274 " "
y[1] (numeric) = -1.0558276257506496 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 2.10303840806563000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9980000000000113 " "
y[1] (closed_form) = -1.0580505889697402 " "
y[1] (numeric) = -1.0580505889697625 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 2.09861992649372000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9970000000000114 " "
y[1] (closed_form) = -1.0602740464552758 " "
y[1] (numeric) = -1.0602740464552984 " "
absolute error = 2.264854970235319300000000000000E-14 " "
relative error = 2.1361033761103712000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9960000000000115 " "
y[1] (closed_form) = -1.0624979984270795 " "
y[1] (numeric) = -1.0624979984271024 " "
absolute error = 2.287059430727822500000000000000E-14 " "
relative error = 2.152530578046812000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9950000000000117 " "
y[1] (closed_form) = -1.064722445105143 " "
y[1] (numeric) = -1.064722445105166 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 2.1688881471755606000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9940000000000118 " "
y[1] (closed_form) = -1.0669473867096042 " "
y[1] (numeric) = -1.0669473867096277 " "
absolute error = 2.35367281220533200000000000000E-14 " "
relative error = 2.2059877005406092000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.993000000000012 " "
y[1] (closed_form) = -1.0691728234607494 " "
y[1] (numeric) = -1.0691728234607731 " "
absolute error = 2.37587727269783500000000000000E-14 " "
relative error = 2.2221639201485524000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.992000000000012 " "
y[1] (closed_form) = -1.0713987555790105 " "
y[1] (numeric) = -1.0713987555790345 " "
absolute error = 2.39808173319033800000000000000E-14 " "
relative error = 2.2382719045574725000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.991000000000012 " "
y[1] (closed_form) = -1.073625183284968 " "
y[1] (numeric) = -1.0736251832849921 " "
absolute error = 2.420286193682841300000000000000E-14 " "
relative error = 2.2543120554209603000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.990000000000012 " "
y[1] (closed_form) = -1.0758521067993483 " "
y[1] (numeric) = -1.075852106799373 " "
absolute error = 2.464695114667847500000000000000E-14 " "
relative error = 2.2909237237079885000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9890000000000123 " "
y[1] (closed_form) = -1.0780795263430267 " "
y[1] (numeric) = -1.0780795263430516 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 2.306786757741525800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9880000000000124 " "
y[1] (closed_form) = -1.0803074421370251 " "
y[1] (numeric) = -1.0803074421370504 " "
absolute error = 2.53130849614535700000000000000E-14 " "
relative error = 2.3431371454203945000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9870000000000125 " "
y[1] (closed_form) = -1.0825358544025139 " "
y[1] (numeric) = -1.0825358544025394 " "
absolute error = 2.5535129566378600000000000000E-14 " "
relative error = 2.3588252954884575000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9860000000000126 " "
y[1] (closed_form) = -1.0847647633608108 " "
y[1] (numeric) = -1.0847647633608366 " "
absolute error = 2.575717417130363000000000000000E-14 " "
relative error = 2.374447902557503000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9850000000000128 " "
y[1] (closed_form) = -1.086994169233382 " "
y[1] (numeric) = -1.086994169233408 " "
absolute error = 2.597921877622866300000000000000E-14 " "
relative error = 2.390005347917448000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.984000000000013 " "
y[1] (closed_form) = -1.0892240722418414 " "
y[1] (numeric) = -1.0892240722418676 " "
absolute error = 2.620126338115369400000000000000E-14 " "
relative error = 2.405498009902246000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.983000000000013 " "
y[1] (closed_form) = -1.0914544726079514 " "
y[1] (numeric) = -1.091454472607978 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 2.4412701821026592000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.982000000000013 " "
y[1] (closed_form) = -1.093685370553623 " "
y[1] (numeric) = -1.0936853705536498 " "
absolute error = 2.686739719592879000000000000000E-14 " "
relative error = 2.456592903160854000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.981000000000013 " "
y[1] (closed_form) = -1.0959167663009155 " "
y[1] (numeric) = -1.0959167663009426 " "
absolute error = 2.70894418008538200000000000000E-14 " "
relative error = 2.4718521181393835000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9800000000000133 " "
y[1] (closed_form) = -1.0981486600720372 " "
y[1] (numeric) = -1.0981486600720645 " "
absolute error = 2.73114864057788500000000000000E-14 " "
relative error = 2.48704819290926000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9790000000000134 " "
y[1] (closed_form) = -1.1003810520893444 " "
y[1] (numeric) = -1.1003810520893722 " "
absolute error = 2.775557561562891400000000000000E-14 " "
relative error = 2.522360373520438000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9780000000000135 " "
y[1] (closed_form) = -1.1026139425753436 " "
y[1] (numeric) = -1.1026139425753716 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 2.5373903902582096000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9770000000000136 " "
y[1] (closed_form) = -1.1048473317526895 " "
y[1] (numeric) = -1.1048473317527177 " "
absolute error = 2.819966482547897600000000000000E-14 " "
relative error = 2.5523585037530980000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9760000000000137 " "
y[1] (closed_form) = -1.1070812198441862 " "
y[1] (numeric) = -1.1070812198442144 " "
absolute error = 2.819966482547897600000000000000E-14 " "
relative error = 2.5472083095626785000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.975000000000014 " "
y[1] (closed_form) = -1.1093156070727868 " "
y[1] (numeric) = -1.1093156070728154 " "
absolute error = 2.86437540353290400000000000000E-14 " "
relative error = 2.582110433919966000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.974000000000014 " "
y[1] (closed_form) = -1.1115504936615948 " "
y[1] (numeric) = -1.1115504936616236 " "
absolute error = 2.88657986402540700000000000000E-14 " "
relative error = 2.596894950328914000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.973000000000014 " "
y[1] (closed_form) = -1.1137858798338627 " "
y[1] (numeric) = -1.1137858798338918 " "
absolute error = 2.9087843245179100000000000000E-14 " "
relative error = 2.611618963019891600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.972000000000014 " "
y[1] (closed_form) = -1.1160217658129927 " "
y[1] (numeric) = -1.116021765813022 " "
absolute error = 2.93098878501041300000000000000E-14 " "
relative error = 2.626282815259669000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9710000000000143 " "
y[1] (closed_form) = -1.118258151822537 " "
y[1] (numeric) = -1.1182581518225665 " "
absolute error = 2.953193245502916400000000000000E-14 " "
relative error = 2.6408868477191980000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9700000000000144 " "
y[1] (closed_form) = -1.120495038086198 " "
y[1] (numeric) = -1.1204950380862277 " "
absolute error = 2.975397705995419500000000000000E-14 " "
relative error = 2.6554313984981043000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9690000000000145 " "
y[1] (closed_form) = -1.1227324248278276 " "
y[1] (numeric) = -1.1227324248278578 " "
absolute error = 3.01980662698042600000000000000E-14 " "
relative error = 2.689693964653703000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9680000000000146 " "
y[1] (closed_form) = -1.1249703122714292 " "
y[1] (numeric) = -1.1249703122714596 " "
absolute error = 3.04201108747292900000000000000E-14 " "
relative error = 2.7040812137795883000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9670000000000147 " "
y[1] (closed_form) = -1.1272087006411555 " "
y[1] (numeric) = -1.1272087006411862 " "
absolute error = 3.06421554796543200000000000000E-14 " "
relative error = 2.7184101277984350000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.966000000000015 " "
y[1] (closed_form) = -1.1294475901613101 " "
y[1] (numeric) = -1.129447590161341 " "
absolute error = 3.08642000845793500000000000000E-14 " "
relative error = 2.7326810339354710000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.965000000000015 " "
y[1] (closed_form) = -1.1316869810563475 " "
y[1] (numeric) = -1.1316869810563785 " "
absolute error = 3.10862446895043830000000000000E-14 " "
relative error = 2.746894256969152000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.964000000000015 " "
y[1] (closed_form) = -1.1339268735508727 " "
y[1] (numeric) = -1.133926873550904 " "
absolute error = 3.130828929442941400000000000000E-14 " "
relative error = 2.76105011925399000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.963000000000015 " "
y[1] (closed_form) = -1.1361672678696422 " "
y[1] (numeric) = -1.1361672678696737 " "
absolute error = 3.153033389935444600000000000000E-14 " "
relative error = 2.775148940743122300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9620000000000153 " "
y[1] (closed_form) = -1.1384081642375627 " "
y[1] (numeric) = -1.1384081642375945 " "
absolute error = 3.17523785042794770000000000000E-14 " "
relative error = 2.7891910390106260000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9610000000000154 " "
y[1] (closed_form) = -1.140649562879693 " "
y[1] (numeric) = -1.140649562879725 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 2.803176729273592000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9600000000000155 " "
y[1] (closed_form) = -1.142891464021243 " "
y[1] (numeric) = -1.1428914640212753 " "
absolute error = 3.21964677141295400000000000000E-14 " "
relative error = 2.8171063244139427000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9590000000000156 " "
y[1] (closed_form) = -1.1451338678875738 " "
y[1] (numeric) = -1.1451338678876062 " "
absolute error = 3.24185123190545700000000000000E-14 " "
relative error = 2.830980135000019000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9580000000000157 " "
y[1] (closed_form) = -1.1473767747041983 " "
y[1] (numeric) = -1.147376774704231 " "
absolute error = 3.2640556923979600000000000000E-14 " "
relative error = 2.844798469307919000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.957000000000016 " "
y[1] (closed_form) = -1.1496201846967815 " "
y[1] (numeric) = -1.1496201846968144 " "
absolute error = 3.286260152890463400000000000000E-14 " "
relative error = 2.8585616333426084000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.956000000000016 " "
y[1] (closed_form) = -1.15186409809114 " "
y[1] (numeric) = -1.151864098091173 " "
absolute error = 3.286260152890463400000000000000E-14 " "
relative error = 2.8529929514570573000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.955000000000016 " "
y[1] (closed_form) = -1.1541085151132424 " "
y[1] (numeric) = -1.1541085151132755 " "
absolute error = 3.308464613382966500000000000000E-14 " "
relative error = 2.8666841722923570000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.954000000000016 " "
y[1] (closed_form) = -1.1563534359892096 " "
y[1] (numeric) = -1.156353435989243 " "
absolute error = 3.330669073875469600000000000000E-14 " "
relative error = 2.8803209902915440000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9530000000000163 " "
y[1] (closed_form) = -1.1585988609453148 " "
y[1] (numeric) = -1.1585988609453484 " "
absolute error = 3.35287353436797300000000000000E-14 " "
relative error = 2.8939037033338033000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9520000000000164 " "
y[1] (closed_form) = -1.160844790207984 " "
y[1] (numeric) = -1.1608447902080177 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 2.907432607123797000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9510000000000165 " "
y[1] (closed_form) = -1.163091224003795 " "
y[1] (numeric) = -1.163091224003829 " "
absolute error = 3.39728245535297900000000000000E-14 " "
relative error = 2.9209079952114697000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9500000000000166 " "
y[1] (closed_form) = -1.165338162559479 " "
y[1] (numeric) = -1.1653381625595132 " "
absolute error = 3.41948691584548200000000000000E-14 " "
relative error = 2.9343301590116344000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9490000000000167 " "
y[1] (closed_form) = -1.1675856061019199 " "
y[1] (numeric) = -1.1675856061019543 " "
absolute error = 3.44169137633798500000000000000E-14 " "
relative error = 2.947699387823351000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.948000000000017 " "
y[1] (closed_form) = -1.1698335548581544 " "
y[1] (numeric) = -1.169833554858189 " "
absolute error = 3.463895836830488400000000000000E-14 " "
relative error = 2.9610159688490856000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.947000000000017 " "
y[1] (closed_form) = -1.1720820090553727 " "
y[1] (numeric) = -1.1720820090554076 " "
absolute error = 3.486100297322991500000000000000E-14 " "
relative error = 2.974280187213673000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.946000000000017 " "
y[1] (closed_form) = -1.174330968920918 " "
y[1] (numeric) = -1.1743309689209531 " "
absolute error = 3.508304757815494700000000000000E-14 " "
relative error = 2.9874923259830605000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.945000000000017 " "
y[1] (closed_form) = -1.176580434682287 " "
y[1] (numeric) = -1.1765804346823225 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 3.019524695529926000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9440000000000173 " "
y[1] (closed_form) = -1.1788304065671302 " "
y[1] (numeric) = -1.178830406567166 " "
absolute error = 3.57491813929300400000000000000E-14 " "
relative error = 3.0325974961093144000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9430000000000174 " "
y[1] (closed_form) = -1.1810808848032515 " "
y[1] (numeric) = -1.1810808848032874 " "
absolute error = 3.59712259978550700000000000000E-14 " "
relative error = 3.0456191832998200000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9420000000000175 " "
y[1] (closed_form) = -1.1833318696186084 " "
y[1] (numeric) = -1.1833318696186446 " "
absolute error = 3.619327060278010300000000000000E-14 " "
relative error = 3.058590031420797000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9410000000000176 " "
y[1] (closed_form) = -1.185583361241313 " "
y[1] (numeric) = -1.1855833612413493 " "
absolute error = 3.641531520770513500000000000000E-14 " "
relative error = 3.0715103128284527000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9400000000000177 " "
y[1] (closed_form) = -1.187835359899631 " "
y[1] (numeric) = -1.1878353598996676 " "
absolute error = 3.663735981263016600000000000000E-14 " "
relative error = 3.0843802979333710000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.939000000000018 " "
y[1] (closed_form) = -1.1900878658219827 " "
y[1] (numeric) = -1.1900878658220195 " "
absolute error = 3.6859404417555197000000000000E-14 " "
relative error = 3.0972002552178574000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.938000000000018 " "
y[1] (closed_form) = -1.1923408792369425 " "
y[1] (numeric) = -1.1923408792369796 " "
absolute error = 3.70814490224802300000000000000E-14 " "
relative error = 3.109970451253092000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.937000000000018 " "
y[1] (closed_form) = -1.1945944003732398 " "
y[1] (numeric) = -1.194594400373277 " "
absolute error = 3.70814490224802300000000000000E-14 " "
relative error = 3.1041037033904123000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.936000000000018 " "
y[1] (closed_form) = -1.196848429459758 " "
y[1] (numeric) = -1.1968484294597952 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 3.1168101748893620000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9350000000000183 " "
y[1] (closed_form) = -1.1991029667255355 " "
y[1] (numeric) = -1.199102966725573 " "
absolute error = 3.75255382323302900000000000000E-14 " "
relative error = 3.129467549797128000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9340000000000184 " "
y[1] (closed_form) = -1.201358012399766 " "
y[1] (numeric) = -1.201358012399804 " "
absolute error = 3.796962744218035400000000000000E-14 " "
relative error = 3.1605588883811850000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9330000000000185 " "
y[1] (closed_form) = -1.2036135667117984 " "
y[1] (numeric) = -1.2036135667118364 " "
absolute error = 3.796962744218035400000000000000E-14 " "
relative error = 3.1546360470089374000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9320000000000186 " "
y[1] (closed_form) = -1.205869629891136 " "
y[1] (numeric) = -1.2058696298911742 " "
absolute error = 3.819167204710538500000000000000E-14 " "
relative error = 3.1671476833323410000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9310000000000187 " "
y[1] (closed_form) = -1.2081262021674382 " "
y[1] (numeric) = -1.2081262021674766 " "
absolute error = 3.841371665203041600000000000000E-14 " "
relative error = 3.1796112511353786000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.930000000000019 " "
y[1] (closed_form) = -1.2103832837705195 " "
y[1] (numeric) = -1.2103832837705584 " "
absolute error = 3.88578058618804800000000000000E-14 " "
relative error = 3.2103719857095825000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.929000000000019 " "
y[1] (closed_form) = -1.2126408749303506 " "
y[1] (numeric) = -1.2126408749303896 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 3.2227060191295387000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.928000000000019 " "
y[1] (closed_form) = -1.2148989758770572 " "
y[1] (numeric) = -1.2148989758770965 " "
absolute error = 3.93018950717305400000000000000E-14 " "
relative error = 3.234992855546512000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.927000000000019 " "
y[1] (closed_form) = -1.217157586840922 " "
y[1] (numeric) = -1.2171575868409612 " "
absolute error = 3.93018950717305400000000000000E-14 " "
relative error = 3.228989861020120600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9260000000000193 " "
y[1] (closed_form) = -1.2194167080523821 " "
y[1] (numeric) = -1.2194167080524219 " "
absolute error = 3.974598428158060400000000000000E-14 " "
relative error = 3.259425922174034000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9250000000000194 " "
y[1] (closed_form) = -1.2216763397420325 " "
y[1] (numeric) = -1.2216763397420727 " "
absolute error = 4.019007349143066700000000000000E-14 " "
relative error = 3.2897480440619115000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9240000000000195 " "
y[1] (closed_form) = -1.223936482140624 " "
y[1] (numeric) = -1.2239364821406644 " "
absolute error = 4.0412118096355700000000000000E-14 " "
relative error = 3.301814978639762000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9230000000000196 " "
y[1] (closed_form) = -1.2261971354790633 " "
y[1] (numeric) = -1.2261971354791041 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 3.331944442215944000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9220000000000197 " "
y[1] (closed_form) = -1.2284582999884148 " "
y[1] (numeric) = -1.2284582999884557 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 3.3258114912481000000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.92100000000002 " "
y[1] (closed_form) = -1.2307199758998983 " "
y[1] (numeric) = -1.2307199758999396 " "
absolute error = 4.130029651605582300000000000000E-14 " "
relative error = 3.3557833889758054000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.92000000000002 " "
y[1] (closed_form) = -1.232982163444892 " "
y[1] (numeric) = -1.2329821634449336 " "
absolute error = 4.152234112098085500000000000000E-14 " "
relative error = 3.3676351817587900000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.91900000000002 " "
y[1] (closed_form) = -1.2352448628549304 " "
y[1] (numeric) = -1.2352448628549721 " "
absolute error = 4.174438572590588600000000000000E-14 " "
relative error = 3.379442164157248000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.91800000000002 " "
y[1] (closed_form) = -1.2375080743617048 " "
y[1] (numeric) = -1.2375080743617468 " "
absolute error = 4.19664303308309200000000000000E-14 " "
relative error = 3.391204566683479000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9170000000000202 " "
y[1] (closed_form) = -1.2397717981970648 " "
y[1] (numeric) = -1.239771798197107 " "
absolute error = 4.21884749357559500000000000000E-14 " "
relative error = 3.40292261826801000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9160000000000204 " "
y[1] (closed_form) = -1.2420360345930168 " "
y[1] (numeric) = -1.2420360345930592 " "
absolute error = 4.24105195406809800000000000000E-14 " "
relative error = 3.414596546273137000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9150000000000205 " "
y[1] (closed_form) = -1.244300783781725 " "
y[1] (numeric) = -1.2443007837817677 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 3.4262265765063280000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9140000000000206 " "
y[1] (closed_form) = -1.2465660459955117 " "
y[1] (numeric) = -1.2465660459955545 " "
absolute error = 4.28546087505310400000000000000E-14 " "
relative error = 3.4378129332334906000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9130000000000207 " "
y[1] (closed_form) = -1.2488318214668563 " "
y[1] (numeric) = -1.2488318214668996 " "
absolute error = 4.329869796038110500000000000000E-14 " "
relative error = 3.4671360239302035000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.912000000000021 " "
y[1] (closed_form) = -1.2510981104283971 " "
y[1] (numeric) = -1.2510981104284409 " "
absolute error = 4.37427871702311700000000000000E-14 " "
relative error = 3.4963514696103964000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.911000000000021 " "
y[1] (closed_form) = -1.2533649131129307 " "
y[1] (numeric) = -1.2533649131129745 " "
absolute error = 4.37427871702311700000000000000E-14 " "
relative error = 3.4900280606698186000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.910000000000021 " "
y[1] (closed_form) = -1.2556322297534108 " "
y[1] (numeric) = -1.255632229753455 " "
absolute error = 4.41868763800812300000000000000E-14 " "
relative error = 3.5190938344071443000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.909000000000021 " "
y[1] (closed_form) = -1.257900060582951 " "
y[1] (numeric) = -1.2579000605829955 " "
absolute error = 4.46309655899312930000000000000E-14 " "
relative error = 3.548053377885035000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9080000000000212 " "
y[1] (closed_form) = -1.2601684058348228 " "
y[1] (numeric) = -1.2601684058348677 " "
absolute error = 4.485301019485632400000000000000E-14 " "
relative error = 3.55928699586327000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9070000000000213 " "
y[1] (closed_form) = -1.2624372657424567 " "
y[1] (numeric) = -1.2624372657425018 " "
absolute error = 4.507505479978135600000000000000E-14 " "
relative error = 3.5704787891596410000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9060000000000215 " "
y[1] (closed_form) = -1.2647066405394423 " "
y[1] (numeric) = -1.2647066405394873 " "
absolute error = 4.507505479978135600000000000000E-14 " "
relative error = 3.5640719637998614000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9050000000000216 " "
y[1] (closed_form) = -1.2669765304595275 " "
y[1] (numeric) = -1.2669765304595728 " "
absolute error = 4.52970994047063870000000000000E-14 " "
relative error = 3.575212193415872000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9040000000000217 " "
y[1] (closed_form) = -1.26924693573662 " "
y[1] (numeric) = -1.2692469357366658 " "
absolute error = 4.57411886145564500000000000000E-14 " "
relative error = 3.603805321618531000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.903000000000022 " "
y[1] (closed_form) = -1.2715178566047873 " "
y[1] (numeric) = -1.2715178566048333 " "
absolute error = 4.59632332194814800000000000000E-14 " "
relative error = 3.6148319098099585000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.902000000000022 " "
y[1] (closed_form) = -1.2737892932982557 " "
y[1] (numeric) = -1.2737892932983017 " "
absolute error = 4.59632332194814800000000000000E-14 " "
relative error = 3.608385897204998700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.901000000000022 " "
y[1] (closed_form) = -1.2760612460514111 " "
y[1] (numeric) = -1.2760612460514573 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 3.6193621557993580000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.900000000000022 " "
y[1] (closed_form) = -1.2783337150987997 " "
y[1] (numeric) = -1.278333715098846 " "
absolute error = 4.640732242933154300000000000000E-14 " "
relative error = 3.630297932472572000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8990000000000222 " "
y[1] (closed_form) = -1.280606700675127 " "
y[1] (numeric) = -1.2806067006751738 " "
absolute error = 4.685141163918160600000000000000E-14 " "
relative error = 3.658532445166956000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8980000000000223 " "
y[1] (closed_form) = -1.2828802030152595 " "
y[1] (numeric) = -1.2828802030153064 " "
absolute error = 4.685141163918160600000000000000E-14 " "
relative error = 3.652048845173762600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8970000000000224 " "
y[1] (closed_form) = -1.2851542223542232 " "
y[1] (numeric) = -1.28515422235427 " "
absolute error = 4.685141163918160600000000000000E-14 " "
relative error = 3.645586718250543000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8960000000000226 " "
y[1] (closed_form) = -1.287428758927204 " "
y[1] (numeric) = -1.2874287589272513 " "
absolute error = 4.72955008490316700000000000000E-14 " "
relative error = 3.673640232213108000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8950000000000227 " "
y[1] (closed_form) = -1.2897038129695502 " "
y[1] (numeric) = -1.2897038129695975 " "
absolute error = 4.72955008490316700000000000000E-14 " "
relative error = 3.667159883797933000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8940000000000228 " "
y[1] (closed_form) = -1.2919793847167682 " "
y[1] (numeric) = -1.291979384716816 " "
absolute error = 4.77395900588817300000000000000E-14 " "
relative error = 3.6950736694105496000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.893000000000023 " "
y[1] (closed_form) = -1.2942554744045276 " "
y[1] (numeric) = -1.2942554744045756 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 3.705731643582451700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.892000000000023 " "
y[1] (closed_form) = -1.2965320822686575 " "
y[1] (numeric) = -1.2965320822687056 " "
absolute error = 4.818367926873179400000000000000E-14 " "
relative error = 3.71635071184822000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.891000000000023 " "
y[1] (closed_form) = -1.2988092085451484 " "
y[1] (numeric) = -1.2988092085451968 " "
absolute error = 4.840572387365682500000000000000E-14 " "
relative error = 3.726931065408609000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.890000000000023 " "
y[1] (closed_form) = -1.301086853470152 " "
y[1] (numeric) = -1.301086853470201 " "
absolute error = 4.88498130835068900000000000000E-14 " "
relative error = 3.754538980485328500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8890000000000233 " "
y[1] (closed_form) = -1.3033650172799822 " "
y[1] (numeric) = -1.3033650172800313 " "
absolute error = 4.90718576884319200000000000000E-14 " "
relative error = 3.765012643260974300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8880000000000234 " "
y[1] (closed_form) = -1.3056437002111132 " "
y[1] (numeric) = -1.3056437002111627 " "
absolute error = 4.95159468982819800000000000000E-14 " "
relative error = 3.792454778457216600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8870000000000235 " "
y[1] (closed_form) = -1.3079229025001817 " "
y[1] (numeric) = -1.3079229025002317 " "
absolute error = 4.996003610813204400000000000000E-14 " "
relative error = 3.819799776625221000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8860000000000237 " "
y[1] (closed_form) = -1.3102026243839862 " "
y[1] (numeric) = -1.3102026243840363 " "
absolute error = 5.018208071305708000000000000000E-14 " "
relative error = 3.830100762975576000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8850000000000238 " "
y[1] (closed_form) = -1.312482866099487 " "
y[1] (numeric) = -1.3124828660995371 " "
absolute error = 5.018208071305708000000000000000E-14 " "
relative error = 3.8234465385587174000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.884000000000024 " "
y[1] (closed_form) = -1.3147636278838062 " "
y[1] (numeric) = -1.3147636278838566 " "
absolute error = 5.04041253179821100000000000000E-14 " "
relative error = 3.833702442705285700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.883000000000024 " "
y[1] (closed_form) = -1.3170449099742287 " "
y[1] (numeric) = -1.3170449099742794 " "
absolute error = 5.06261699229071400000000000000E-14 " "
relative error = 3.8439213074288986000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.882000000000024 " "
y[1] (closed_form) = -1.319326712608202 " "
y[1] (numeric) = -1.3193267126082528 " "
absolute error = 5.08482145278321700000000000000E-14 " "
relative error = 3.85410331208328000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.881000000000024 " "
y[1] (closed_form) = -1.3216090360233355 " "
y[1] (numeric) = -1.3216090360233865 " "
absolute error = 5.1070259132757200000000000000E-14 " "
relative error = 3.864248634862955000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8800000000000243 " "
y[1] (closed_form) = -1.3238918804574016 " "
y[1] (numeric) = -1.3238918804574529 " "
absolute error = 5.12923037376822300000000000000E-14 " "
relative error = 3.874357452812602000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8790000000000244 " "
y[1] (closed_form) = -1.3261752461483358 " "
y[1] (numeric) = -1.3261752461483873 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 3.884429941836304300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8780000000000245 " "
y[1] (closed_form) = -1.3284591333342368 " "
y[1] (numeric) = -1.3284591333342883 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 3.877751829167212500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8770000000000246 " "
y[1] (closed_form) = -1.3307435422533656 " "
y[1] (numeric) = -1.3307435422534175 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 3.90446663107419000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8760000000000248 " "
y[1] (closed_form) = -1.3330284731441475 " "
y[1] (numeric) = -1.3330284731441995 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 3.897774023528962000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.875000000000025 " "
y[1] (closed_form) = -1.3353139262451705 " "
y[1] (numeric) = -1.3353139262452227 " "
absolute error = 5.21804821573823600000000000000E-14 " "
relative error = 3.90773144290578970000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.874000000000025 " "
y[1] (closed_form) = -1.3375999017951867 " "
y[1] (numeric) = -1.3375999017952394 " "
absolute error = 5.26245713672324200000000000000E-14 " "
relative error = 3.934253531015158300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.873000000000025 " "
y[1] (closed_form) = -1.339886400033112 " "
y[1] (numeric) = -1.339886400033165 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 3.944111677740103600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.872000000000025 " "
y[1] (closed_form) = -1.3421734211980256 " "
y[1] (numeric) = -1.3421734211980791 " "
absolute error = 5.351274978693255000000000000000E-14 " "
relative error = 3.987022015319525700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8710000000000253 " "
y[1] (closed_form) = -1.3444609655291724 " "
y[1] (numeric) = -1.3444609655292257 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 3.96372275196793000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8700000000000254 " "
y[1] (closed_form) = -1.3467490332659589 " "
y[1] (numeric) = -1.3467490332660126 " "
absolute error = 5.373479439185758000000000000000E-14 " "
relative error = 3.989963464948403000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8690000000000255 " "
y[1] (closed_form) = -1.3490376246479578 " "
y[1] (numeric) = -1.349037624648012 " "
absolute error = 5.41788836017076400000000000000E-14 " "
relative error = 4.016113606605008000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8680000000000256 " "
y[1] (closed_form) = -1.3513267399149067 " "
y[1] (numeric) = -1.351326739914961 " "
absolute error = 5.44009282066326700000000000000E-14 " "
relative error = 4.025742005968025000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8670000000000258 " "
y[1] (closed_form) = -1.3536163793067069 " "
y[1] (numeric) = -1.3536163793067613 " "
absolute error = 5.44009282066326700000000000000E-14 " "
relative error = 4.018932471435936000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.866000000000026 " "
y[1] (closed_form) = -1.355906543063424 " "
y[1] (numeric) = -1.3559065430634787 " "
absolute error = 5.4622972811557700000000000000E-14 " "
relative error = 4.028520482550887000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.865000000000026 " "
y[1] (closed_form) = -1.35819723142529 " "
y[1] (numeric) = -1.358197231425345 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 4.054423079895434500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.864000000000026 " "
y[1] (closed_form) = -1.3604884446327012 " "
y[1] (numeric) = -1.3604884446327563 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 4.047594982423723400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.863000000000026 " "
y[1] (closed_form) = -1.3627801829262194 " "
y[1] (numeric) = -1.3627801829262747 " "
absolute error = 5.528910662633280000000000000000E-14 " "
relative error = 4.057081789053733000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8620000000000263 " "
y[1] (closed_form) = -1.3650724465465713 " "
y[1] (numeric) = -1.365072446546627 " "
absolute error = 5.57331958361828600000000000000E-14 " "
relative error = 4.082801317774707500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8610000000000264 " "
y[1] (closed_form) = -1.3673652357346502 " "
y[1] (numeric) = -1.3673652357347061 " "
absolute error = 5.59552404411078900000000000000E-14 " "
relative error = 4.092194168666616300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8600000000000265 " "
y[1] (closed_form) = -1.3696585507315144 " "
y[1] (numeric) = -1.3696585507315706 " "
absolute error = 5.61772850460329200000000000000E-14 " "
relative error = 4.101553997967556400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8590000000000266 " "
y[1] (closed_form) = -1.3719523917783882 " "
y[1] (numeric) = -1.3719523917784446 " "
absolute error = 5.63993296509579500000000000000E-14 " "
relative error = 4.110880959786843000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8580000000000267 " "
y[1] (closed_form) = -1.374246759116662 " "
y[1] (numeric) = -1.3742467591167187 " "
absolute error = 5.662137425588298000000000000000E-14 " "
relative error = 4.120175207273405000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.857000000000027 " "
y[1] (closed_form) = -1.3765416529878924 " "
y[1] (numeric) = -1.3765416529879493 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 4.129436892623255000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.856000000000027 " "
y[1] (closed_form) = -1.3788370736338025 " "
y[1] (numeric) = -1.3788370736338595 " "
absolute error = 5.70654634657330500000000000000E-14 " "
relative error = 4.138666167086883500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.855000000000027 " "
y[1] (closed_form) = -1.3811330212962813 " "
y[1] (numeric) = -1.3811330212963386 " "
absolute error = 5.72875080706580800000000000000E-14 " "
relative error = 4.147863180976593700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.854000000000027 " "
y[1] (closed_form) = -1.3834294962173854 " "
y[1] (numeric) = -1.383429496217443 " "
absolute error = 5.75095526755831100000000000000E-14 " "
relative error = 4.157028083673759000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8530000000000273 " "
y[1] (closed_form) = -1.3857264986393372 " "
y[1] (numeric) = -1.3857264986393951 " "
absolute error = 5.79536418854331700000000000000E-14 " "
relative error = 4.18218471988077050000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8520000000000274 " "
y[1] (closed_form) = -1.3880240288045267 " "
y[1] (numeric) = -1.3880240288045849 " "
absolute error = 5.8175686490358200000000000000E-14 " "
relative error = 4.1912593213867916000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8510000000000275 " "
y[1] (closed_form) = -1.390322086955511 " "
y[1] (numeric) = -1.3903220869555692 " "
absolute error = 5.8175686490358200000000000000E-14 " "
relative error = 4.1843316046103907000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8500000000000276 " "
y[1] (closed_form) = -1.3926206733350142 " "
y[1] (numeric) = -1.3926206733350726 " "
absolute error = 5.83977310952832300000000000000E-14 " "
relative error = 4.193369537982928300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8490000000000277 " "
y[1] (closed_form) = -1.3949197881859274 " "
y[1] (numeric) = -1.3949197881859863 " "
absolute error = 5.8841820305133300000000000000E-14 " "
relative error = 4.218294184618043000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.848000000000028 " "
y[1] (closed_form) = -1.3972194317513107 " "
y[1] (numeric) = -1.3972194317513698 " "
absolute error = 5.90638649100583300000000000000E-14 " "
relative error = 4.227243306803009000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.847000000000028 " "
y[1] (closed_form) = -1.3995196042743903 " "
y[1] (numeric) = -1.3995196042744498 " "
absolute error = 5.95079541199083900000000000000E-14 " "
relative error = 4.252027191199048000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.846000000000028 " "
y[1] (closed_form) = -1.4018203059985612 " "
y[1] (numeric) = -1.401820305998621 " "
absolute error = 5.97299987248334200000000000000E-14 " "
relative error = 4.260888394128792300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.845000000000028 " "
y[1] (closed_form) = -1.4041215371673863 " "
y[1] (numeric) = -1.4041215371674463 " "
absolute error = 5.99520433297584500000000000000E-14 " "
relative error = 4.2697189483114906000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8440000000000283 " "
y[1] (closed_form) = -1.4064232980245968 " "
y[1] (numeric) = -1.4064232980246567 " "
absolute error = 5.99520433297584500000000000000E-14 " "
relative error = 4.262731100513237300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8430000000000284 " "
y[1] (closed_form) = -1.4087255888140913 " "
y[1] (numeric) = -1.4087255888141517 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 4.2872886685086653000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8420000000000285 " "
y[1] (closed_form) = -1.411028409779938 " "
y[1] (numeric) = -1.4110284097799988 " "
absolute error = 6.08402217494585800000000000000E-14 " "
relative error = 4.311764478147335000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8410000000000286 " "
y[1] (closed_form) = -1.4133317611663738 " "
y[1] (numeric) = -1.4133317611664347 " "
absolute error = 6.08402217494585800000000000000E-14 " "
relative error = 4.304737459465939300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8400000000000287 " "
y[1] (closed_form) = -1.4156356432178034 " "
y[1] (numeric) = -1.4156356432178647 " "
absolute error = 6.12843109593086400000000000000E-14 " "
relative error = 4.3291020011340386000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.839000000000029 " "
y[1] (closed_form) = -1.4179400561788018 " "
y[1] (numeric) = -1.417940056178863 " "
absolute error = 6.12843109593086400000000000000E-14 " "
relative error = 4.322066415449421000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.838000000000029 " "
y[1] (closed_form) = -1.4202450002941116 " "
y[1] (numeric) = -1.4202450002941733 " "
absolute error = 6.1728400169158700000000000000E-14 " "
relative error = 4.34632054021494000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.837000000000029 " "
y[1] (closed_form) = -1.422550475808646 " "
y[1] (numeric) = -1.4225504758087077 " "
absolute error = 6.1728400169158700000000000000E-14 " "
relative error = 4.3392766175182160000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.836000000000029 " "
y[1] (closed_form) = -1.4248564829674868 " "
y[1] (numeric) = -1.4248564829675487 " "
absolute error = 6.19504447740837300000000000000E-14 " "
relative error = 4.347837520103234300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8350000000000293 " "
y[1] (closed_form) = -1.4271630220158853 " "
y[1] (numeric) = -1.427163022015948 " "
absolute error = 6.26165785888588300000000000000E-14 " "
relative error = 4.387486056106761300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8340000000000294 " "
y[1] (closed_form) = -1.4294700931992637 " "
y[1] (numeric) = -1.4294700931993265 " "
absolute error = 6.28386231937838600000000000000E-14 " "
relative error = 4.395938291590711400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8330000000000295 " "
y[1] (closed_form) = -1.4317776967632132 " "
y[1] (numeric) = -1.431777696763276 " "
absolute error = 6.28386231937838600000000000000E-14 " "
relative error = 4.3888533349724396000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8320000000000296 " "
y[1] (closed_form) = -1.4340858329534947 " "
y[1] (numeric) = -1.4340858329535577 " "
absolute error = 6.30606677987088900000000000000E-14 " "
relative error = 4.397272907217532000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8310000000000297 " "
y[1] (closed_form) = -1.4363945020160398 " "
y[1] (numeric) = -1.4363945020161033 " "
absolute error = 6.35047570085589500000000000000E-14 " "
relative error = 4.421122255719259000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.83000000000003 " "
y[1] (closed_form) = -1.438703704196951 " "
y[1] (numeric) = -1.4387037041970148 " "
absolute error = 6.37268016134839900000000000000E-14 " "
relative error = 4.4294597579461104000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.82900000000003 " "
y[1] (closed_form) = -1.4410134397425005 " "
y[1] (numeric) = -1.4410134397425645 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 4.437768896162152000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.82800000000003 " "
y[1] (closed_form) = -1.4433237088991313 " "
y[1] (numeric) = -1.4433237088991955 " "
absolute error = 6.41708908233340500000000000000E-14 " "
relative error = 4.446049796568451000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.82700000000003 " "
y[1] (closed_form) = -1.445634511913458 " "
y[1] (numeric) = -1.445634511913522 " "
absolute error = 6.41708908233340500000000000000E-14 " "
relative error = 4.438942920530912000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8260000000000303 " "
y[1] (closed_form) = -1.4479458490322648 " "
y[1] (numeric) = -1.4479458490323291 " "
absolute error = 6.43929354282590800000000000000E-14 " "
relative error = 4.447192239357302000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8250000000000304 " "
y[1] (closed_form) = -1.450257720502508 " "
y[1] (numeric) = -1.4502577205025728 " "
absolute error = 6.48370246381091400000000000000E-14 " "
relative error = 4.470724321718721500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8240000000000305 " "
y[1] (closed_form) = -1.4525701265713158 " "
y[1] (numeric) = -1.4525701265713808 " "
absolute error = 6.50590692430341700000000000000E-14 " "
relative error = 4.478893517974329000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8230000000000306 " "
y[1] (closed_form) = -1.4548830674859867 " "
y[1] (numeric) = -1.454883067486052 " "
absolute error = 6.5281113847959200000000000000E-14 " "
relative error = 4.48703509628192000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8220000000000307 " "
y[1] (closed_form) = -1.4571965434939915 " "
y[1] (numeric) = -1.457196543494057 " "
absolute error = 6.55031584528842400000000000000E-14 " "
relative error = 4.495149178423392000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.821000000000031 " "
y[1] (closed_form) = -1.4595105548429723 " "
y[1] (numeric) = -1.4595105548430383 " "
absolute error = 6.5947247662734300000000000000E-14 " "
relative error = 4.518449520211213500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.820000000000031 " "
y[1] (closed_form) = -1.4618251017807438 " "
y[1] (numeric) = -1.46182510178081 " "
absolute error = 6.61692922676593300000000000000E-14 " "
relative error = 4.526484884344525000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.819000000000031 " "
y[1] (closed_form) = -1.4641401845552924 " "
y[1] (numeric) = -1.4641401845553588 " "
absolute error = 6.63913368725843600000000000000E-14 " "
relative error = 4.5344931839808494000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.818000000000031 " "
y[1] (closed_form) = -1.4664558034147765 " "
y[1] (numeric) = -1.4664558034148434 " "
absolute error = 6.68354260824344200000000000000E-14 " "
relative error = 4.557616119544960500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8170000000000313 " "
y[1] (closed_form) = -1.4687719586075278 " "
y[1] (numeric) = -1.468771958607595 " "
absolute error = 6.70574706873594600000000000000E-14 " "
relative error = 4.565546768126852500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8160000000000314 " "
y[1] (closed_form) = -1.4710886503820497 " "
y[1] (numeric) = -1.4710886503821172 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 4.58854467265987000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8150000000000315 " "
y[1] (closed_form) = -1.4734058789870192 " "
y[1] (numeric) = -1.4734058789870867 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 4.581328258552728000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8140000000000316 " "
y[1] (closed_form) = -1.4757236446712851 " "
y[1] (numeric) = -1.475723644671353 " "
absolute error = 6.79456491070595800000000000000E-14 " "
relative error = 4.6042258218471765000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8130000000000317 " "
y[1] (closed_form) = -1.4780419476838704 " "
y[1] (numeric) = -1.4780419476839386 " "
absolute error = 6.81676937119846100000000000000E-14 " "
relative error = 4.612027000911925000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.812000000000032 " "
y[1] (closed_form) = -1.4803607882739709 " "
y[1] (numeric) = -1.480360788274039 " "
absolute error = 6.81676937119846100000000000000E-14 " "
relative error = 4.604802711065107400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.811000000000032 " "
y[1] (closed_form) = -1.482680166690955 " "
y[1] (numeric) = -1.4826801666910236 " "
absolute error = 6.86117829218346700000000000000E-14 " "
relative error = 4.6275511376780887000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.810000000000032 " "
y[1] (closed_form) = -1.4850000831843664 " "
y[1] (numeric) = -1.485000083184435 " "
absolute error = 6.86117829218346700000000000000E-14 " "
relative error = 4.620321823464595400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.809000000000032 " "
y[1] (closed_form) = -1.4873205380039205 " "
y[1] (numeric) = -1.4873205380039896 " "
absolute error = 6.90558721316847400000000000000E-14 " "
relative error = 4.642971731188634000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8080000000000322 " "
y[1] (closed_form) = -1.4896415313995086 " "
y[1] (numeric) = -1.4896415313995777 " "
absolute error = 6.90558721316847400000000000000E-14 " "
relative error = 4.635737570152679300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8070000000000324 " "
y[1] (closed_form) = -1.4919630636211945 " "
y[1] (numeric) = -1.4919630636212637 " "
absolute error = 6.92779167366097700000000000000E-14 " "
relative error = 4.643406959986192000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8060000000000325 " "
y[1] (closed_form) = -1.4942851349192166 " "
y[1] (numeric) = -1.494285134919286 " "
absolute error = 6.9499961341534800000000000000E-14 " "
relative error = 4.651050841464208000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8050000000000326 " "
y[1] (closed_form) = -1.496607745543988 " "
y[1] (numeric) = -1.4966077455440576 " "
absolute error = 6.97220059464598300000000000000E-14 " "
relative error = 4.65866932428023960000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8040000000000327 " "
y[1] (closed_form) = -1.4989308957460958 " "
y[1] (numeric) = -1.498930895746166 " "
absolute error = 7.01660951563098900000000000000E-14 " "
relative error = 4.681076049298763000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.803000000000033 " "
y[1] (closed_form) = -1.5012545857763027 " "
y[1] (numeric) = -1.501254585776373 " "
absolute error = 7.03881397612349200000000000000E-14 " "
relative error = 4.688621132493463500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.802000000000033 " "
y[1] (closed_form) = -1.503578815885545 " "
y[1] (numeric) = -1.5035788158856158 " "
absolute error = 7.08322289710849900000000000000E-14 " "
relative error = 4.710908947554423000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.801000000000033 " "
y[1] (closed_form) = -1.5059035863249353 " "
y[1] (numeric) = -1.5059035863250063 " "
absolute error = 7.10542735760100200000000000000E-14 " "
relative error = 4.7183813240935024000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.800000000000033 " "
y[1] (closed_form) = -1.5082288973457603 " "
y[1] (numeric) = -1.5082288973458315 " "
absolute error = 7.12763181809350500000000000000E-14 " "
relative error = 4.725828971077924000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7990000000000332 " "
y[1] (closed_form) = -1.5105547491994824 " "
y[1] (numeric) = -1.5105547491995541 " "
absolute error = 7.17204073907851100000000000000E-14 " "
relative error = 4.7479515342819110000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7980000000000333 " "
y[1] (closed_form) = -1.51288114213774 " "
y[1] (numeric) = -1.5128811421378119 " "
absolute error = 7.19424519957101400000000000000E-14 " "
relative error = 4.755327433988212300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7970000000000335 " "
y[1] (closed_form) = -1.5152080764123463 " "
y[1] (numeric) = -1.5152080764124185 " "
absolute error = 7.21644966006351800000000000000E-14 " "
relative error = 4.76267898277730970000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7960000000000336 " "
y[1] (closed_form) = -1.517535552275291 " "
y[1] (numeric) = -1.5175355522753635 " "
absolute error = 7.26085858104852400000000000000E-14 " "
relative error = 4.7846382051228253000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7950000000000337 " "
y[1] (closed_form) = -1.5198635699787393 " "
y[1] (numeric) = -1.5198635699788121 " "
absolute error = 7.28306304154102700000000000000E-14 " "
relative error = 4.791918949437617400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.794000000000034 " "
y[1] (closed_form) = -1.5221921297750332 " "
y[1] (numeric) = -1.5221921297751062 " "
absolute error = 7.3052675020335300000000000000E-14 " "
relative error = 4.799175714509301700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.793000000000034 " "
y[1] (closed_form) = -1.5245212319166903 " "
y[1] (numeric) = -1.5245212319167636 " "
absolute error = 7.32747196252603300000000000000E-14 " "
relative error = 4.806408601678598000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.792000000000034 " "
y[1] (closed_form) = -1.526850876656405 " "
y[1] (numeric) = -1.5268508766564786 " "
absolute error = 7.34967642301853600000000000000E-14 " "
relative error = 4.813617711713486500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.791000000000034 " "
y[1] (closed_form) = -1.529181064247049 " "
y[1] (numeric) = -1.5291810642471224 " "
absolute error = 7.34967642301853600000000000000E-14 " "
relative error = 4.806282653413206000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7900000000000342 " "
y[1] (closed_form) = -1.531511794941669 " "
y[1] (numeric) = -1.531511794941743 " "
absolute error = 7.39408534400354300000000000000E-14 " "
relative error = 4.827965000612458600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7890000000000343 " "
y[1] (closed_form) = -1.5338430689934905 " "
y[1] (numeric) = -1.533843068993565 " "
absolute error = 7.43849426498854900000000000000E-14 " "
relative error = 4.849579735604697000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7880000000000345 " "
y[1] (closed_form) = -1.5361748866559157 " "
y[1] (numeric) = -1.5361748866559903 " "
absolute error = 7.46069872548105200000000000000E-14 " "
relative error = 4.856672759259966000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7870000000000346 " "
y[1] (closed_form) = -1.5385072481825237 " "
y[1] (numeric) = -1.5385072481825985 " "
absolute error = 7.48290318597355500000000000000E-14 " "
relative error = 4.863742562677747000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7860000000000347 " "
y[1] (closed_form) = -1.540840153827071 " "
y[1] (numeric) = -1.5408401538271461 " "
absolute error = 7.50510764646605800000000000000E-14 " "
relative error = 4.8707892430147300000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.785000000000035 " "
y[1] (closed_form) = -1.5431736038434927 " "
y[1] (numeric) = -1.5431736038435677 " "
absolute error = 7.50510764646605800000000000000E-14 " "
relative error = 4.8634240682795016000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.784000000000035 " "
y[1] (closed_form) = -1.5455075984859 " "
y[1] (numeric) = -1.5455075984859754 " "
absolute error = 7.54951656745106400000000000000E-14 " "
relative error = 4.884813620358231000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.783000000000035 " "
y[1] (closed_form) = -1.5478421380085838 " "
y[1] (numeric) = -1.5478421380086596 " "
absolute error = 7.57172102794356800000000000000E-14 " "
relative error = 4.891791508974655500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.782000000000035 " "
y[1] (closed_form) = -1.5501772226660124 " "
y[1] (numeric) = -1.5501772226660882 " "
absolute error = 7.57172102794356800000000000000E-14 " "
relative error = 4.884422837100932000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.781000000000035 " "
y[1] (closed_form) = -1.552512852712832 " "
y[1] (numeric) = -1.5525128527129082 " "
absolute error = 7.61612994892857400000000000000E-14 " "
relative error = 4.90567916112274960000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7800000000000353 " "
y[1] (closed_form) = -1.554849028403868 " "
y[1] (numeric) = -1.5548490284039445 " "
absolute error = 7.63833440942107700000000000000E-14 " "
relative error = 4.912589113080783600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7790000000000354 " "
y[1] (closed_form) = -1.5571857499941242 " "
y[1] (numeric) = -1.5571857499942008 " "
absolute error = 7.6605388699135800000000000000E-14 " "
relative error = 4.91947660704093000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7780000000000356 " "
y[1] (closed_form) = -1.5595230177387829 " "
y[1] (numeric) = -1.5595230177388597 " "
absolute error = 7.68274333040608300000000000000E-14 " "
relative error = 4.926341735914620500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7770000000000357 " "
y[1] (closed_form) = -1.5618608318932057 " "
y[1] (numeric) = -1.5618608318932827 " "
absolute error = 7.70494779089858600000000000000E-14 " "
relative error = 4.933184592099063000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7760000000000358 " "
y[1] (closed_form) = -1.564199192712933 " "
y[1] (numeric) = -1.5641991927130106 " "
absolute error = 7.74935671188359300000000000000E-14 " "
relative error = 4.95420068491608000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.775000000000036 " "
y[1] (closed_form) = -1.5665381004536854 " "
y[1] (numeric) = -1.566538100453763 " "
absolute error = 7.77156117237609600000000000000E-14 " "
relative error = 4.960978076514942500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.774000000000036 " "
y[1] (closed_form) = -1.5688775553713619 " "
y[1] (numeric) = -1.5688775553714396 " "
absolute error = 7.77156117237609600000000000000E-14 " "
relative error = 4.9535804408499710000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.773000000000036 " "
y[1] (closed_form) = -1.5712175577220413 " "
y[1] (numeric) = -1.5712175577221195 " "
absolute error = 7.81597009336110200000000000000E-14 " "
relative error = 4.974467128977818000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.772000000000036 " "
y[1] (closed_form) = -1.573558107761983 " "
y[1] (numeric) = -1.5735581077620613 " "
absolute error = 7.83817455385360500000000000000E-14 " "
relative error = 4.981178969616551500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7710000000000363 " "
y[1] (closed_form) = -1.5758992057476253 " "
y[1] (numeric) = -1.575899205747704 " "
absolute error = 7.86037901434610800000000000000E-14 " "
relative error = 4.98786913888763060000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7700000000000364 " "
y[1] (closed_form) = -1.5782408519355875 " "
y[1] (numeric) = -1.5782408519356665 " "
absolute error = 7.90478793533111500000000000000E-14 " "
relative error = 5.008606845803363000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7690000000000365 " "
y[1] (closed_form) = -1.5805830465826691 " "
y[1] (numeric) = -1.5805830465827484 " "
absolute error = 7.92699239582361800000000000000E-14 " "
relative error = 5.015233089436413000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7680000000000367 " "
y[1] (closed_form) = -1.5829257899458495 " "
y[1] (numeric) = -1.582925789945929 " "
absolute error = 7.94919685631612100000000000000E-14 " "
relative error = 5.021837983060504000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7670000000000368 " "
y[1] (closed_form) = -1.5852690822822897 " "
y[1] (numeric) = -1.5852690822823692 " "
absolute error = 7.94919685631612100000000000000E-14 " "
relative error = 5.014414868213902000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.766000000000037 " "
y[1] (closed_form) = -1.58761292384933 " "
y[1] (numeric) = -1.58761292384941 " "
absolute error = 8.0158102377936300000000000000E-14 " "
relative error = 5.048970134583232000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.765000000000037 " "
y[1] (closed_form) = -1.5899573149044937 " "
y[1] (numeric) = -1.589957314904574 " "
absolute error = 8.03801469828613300000000000000E-14 " "
relative error = 5.05549087572138000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.764000000000037 " "
y[1] (closed_form) = -1.5923022557054836 " "
y[1] (numeric) = -1.5923022557055642 " "
absolute error = 8.06021915877863600000000000000E-14 " "
relative error = 5.061990667850611000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.763000000000037 " "
y[1] (closed_form) = -1.5946477465101847 " "
y[1] (numeric) = -1.5946477465102655 " "
absolute error = 8.0824236192711400000000000000E-14 " "
relative error = 5.068469595845956000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7620000000000373 " "
y[1] (closed_form) = -1.5969937875766633 " "
y[1] (numeric) = -1.5969937875767444 " "
absolute error = 8.10462807976364300000000000000E-14 " "
relative error = 5.074927744122224000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7610000000000374 " "
y[1] (closed_form) = -1.5993403791631673 " "
y[1] (numeric) = -1.5993403791632486 " "
absolute error = 8.12683254025614600000000000000E-14 " "
relative error = 5.081365196637128000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7600000000000375 " "
y[1] (closed_form) = -1.601687521528126 " "
y[1] (numeric) = -1.6016875215282078 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 5.1016452032074240000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7590000000000376 " "
y[1] (closed_form) = -1.604035214930152 " "
y[1] (numeric) = -1.604035214930234 " "
absolute error = 8.19344592173365500000000000000E-14 " "
relative error = 5.10802122389217000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7580000000000378 " "
y[1] (closed_form) = -1.6063834596280389 " "
y[1] (numeric) = -1.606383459628121 " "
absolute error = 8.21565038222615800000000000000E-14 " "
relative error = 5.114376852540866000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.757000000000038 " "
y[1] (closed_form) = -1.6087322558807629 " "
y[1] (numeric) = -1.6087322558808452 " "
absolute error = 8.23785484271866200000000000000E-14 " "
relative error = 5.120712171093088000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.756000000000038 " "
y[1] (closed_form) = -1.611081603947483 " "
y[1] (numeric) = -1.6110816039475655 " "
absolute error = 8.26005930321116500000000000000E-14 " "
relative error = 5.127027261047679000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.755000000000038 " "
y[1] (closed_form) = -1.6134315040875409 " "
y[1] (numeric) = -1.6134315040876235 " "
absolute error = 8.26005930321116500000000000000E-14 " "
relative error = 5.119559945547582000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.754000000000038 " "
y[1] (closed_form) = -1.6157819565604605 " "
y[1] (numeric) = -1.6157819565605436 " "
absolute error = 8.30446822419617100000000000000E-14 " "
relative error = 5.139597078973465000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7530000000000383 " "
y[1] (closed_form) = -1.6181329616259499 " "
y[1] (numeric) = -1.6181329616260332 " "
absolute error = 8.32667268468867400000000000000E-14 " "
relative error = 5.145851967765230000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7520000000000384 " "
y[1] (closed_form) = -1.6204845195438993 " "
y[1] (numeric) = -1.620484519543983 " "
absolute error = 8.3710816056736800000000000000E-14 " "
relative error = 5.165789308514839000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7510000000000385 " "
y[1] (closed_form) = -1.6228366305743835 " "
y[1] (numeric) = -1.6228366305744673 " "
absolute error = 8.3710816056736800000000000000E-14 " "
relative error = 5.158302103835822000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7500000000000386 " "
y[1] (closed_form) = -1.6251892949776592 " "
y[1] (numeric) = -1.6251892949777433 " "
absolute error = 8.41549052665868700000000000000E-14 " "
relative error = 5.178160201193285000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7490000000000387 " "
y[1] (closed_form) = -1.6275425130141685 " "
y[1] (numeric) = -1.6275425130142527 " "
absolute error = 8.41549052665868700000000000000E-14 " "
relative error = 5.17067324470278000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.748000000000039 " "
y[1] (closed_form) = -1.6298962849445362 " "
y[1] (numeric) = -1.6298962849446208 " "
absolute error = 8.45989944764369300000000000000E-14 " "
relative error = 5.1904526231444070000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.747000000000039 " "
y[1] (closed_form) = -1.632250611029572 " "
y[1] (numeric) = -1.6322506110296569 " "
absolute error = 8.48210390813619600000000000000E-14 " "
relative error = 5.196569602008575000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.746000000000039 " "
y[1] (closed_form) = -1.6346054915302695 " "
y[1] (numeric) = -1.6346054915303543 " "
absolute error = 8.48210390813619600000000000000E-14 " "
relative error = 5.189083208203039000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.745000000000039 " "
y[1] (closed_form) = -1.6369609267078062 " "
y[1] (numeric) = -1.6369609267078915 " "
absolute error = 8.52651282912120200000000000000E-14 " "
relative error = 5.208745480730198000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7440000000000393 " "
y[1] (closed_form) = -1.6393169168235453 " "
y[1] (numeric) = -1.6393169168236308 " "
absolute error = 8.54871728961370500000000000000E-14 " "
relative error = 5.214804533450613000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7430000000000394 " "
y[1] (closed_form) = -1.6416734621390339 " "
y[1] (numeric) = -1.6416734621391198 " "
absolute error = 8.59312621059871200000000000000E-14 " "
relative error = 5.2343699333497270000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7420000000000395 " "
y[1] (closed_form) = -1.6440305629160046 " "
y[1] (numeric) = -1.6440305629160907 " "
absolute error = 8.61533067109121500000000000000E-14 " "
relative error = 5.240371356485167000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7410000000000396 " "
y[1] (closed_form) = -1.6463882194163748 " "
y[1] (numeric) = -1.6463882194164612 " "
absolute error = 8.63753513158371800000000000000E-14 " "
relative error = 5.246353824522397000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7400000000000397 " "
y[1] (closed_form) = -1.6487464319022471 " "
y[1] (numeric) = -1.648746431902334 " "
absolute error = 8.68194405256872400000000000000E-14 " "
relative error = 5.265784892436067000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.73900000000004 " "
y[1] (closed_form) = -1.65110520063591 " "
y[1] (numeric) = -1.651105200635997 " "
absolute error = 8.70414851306122700000000000000E-14 " "
relative error = 5.271710433538029000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.73800000000004 " "
y[1] (closed_form) = -1.6534645258798373 " "
y[1] (numeric) = -1.6534645258799245 " "
absolute error = 8.7263529735537300000000000000E-14 " "
relative error = 5.277617292037328000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.73700000000004 " "
y[1] (closed_form) = -1.6558244078966886 " "
y[1] (numeric) = -1.655824407896776 " "
absolute error = 8.74855743404623400000000000000E-14 " "
relative error = 5.283505541000625000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.73600000000004 " "
y[1] (closed_form) = -1.6581848469493097 " "
y[1] (numeric) = -1.6581848469493974 " "
absolute error = 8.77076189453873700000000000000E-14 " "
relative error = 5.289375253111848000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7350000000000403 " "
y[1] (closed_form) = -1.6605458433007325 " "
y[1] (numeric) = -1.6605458433008204 " "
absolute error = 8.7929663550312400000000000000E-14 " "
relative error = 5.29522650067469000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7340000000000404 " "
y[1] (closed_form) = -1.6629073972141752 " "
y[1] (numeric) = -1.6629073972142634 " "
absolute error = 8.81517081552374300000000000000E-14 " "
relative error = 5.30105935561509000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7330000000000405 " "
y[1] (closed_form) = -1.6652695089530425 " "
y[1] (numeric) = -1.665269508953131 " "
absolute error = 8.85957973650874900000000000000E-14 " "
relative error = 5.320207743477379000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7320000000000406 " "
y[1] (closed_form) = -1.6676321787809263 " "
y[1] (numeric) = -1.6676321787810149 " "
absolute error = 8.85957973650874900000000000000E-14 " "
relative error = 5.312670173458326000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7310000000000407 " "
y[1] (closed_form) = -1.6699954069616043 " "
y[1] (numeric) = -1.6699954069616931 " "
absolute error = 8.88178419700125200000000000000E-14 " "
relative error = 5.318448278346348000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.730000000000041 " "
y[1] (closed_form) = -1.6723591937590423 " "
y[1] (numeric) = -1.6723591937591313 " "
absolute error = 8.90398865749375500000000000000E-14 " "
relative error = 5.324208274587131000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.729000000000041 " "
y[1] (closed_form) = -1.6747235394373927 " "
y[1] (numeric) = -1.674723539437482 " "
absolute error = 8.92619311798625900000000000000E-14 " "
relative error = 5.32995023225441000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.728000000000041 " "
y[1] (closed_form) = -1.6770884442609957 " "
y[1] (numeric) = -1.6770884442610852 " "
absolute error = 8.94839757847876200000000000000E-14 " "
relative error = 5.3356742210586560000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.727000000000041 " "
y[1] (closed_form) = -1.679453908494379 " "
y[1] (numeric) = -1.6794539084944686 " "
absolute error = 8.97060203897126500000000000000E-14 " "
relative error = 5.3413803103494270000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7260000000000413 " "
y[1] (closed_form) = -1.6818199324022576 " "
y[1] (numeric) = -1.6818199324023475 " "
absolute error = 8.99280649946376800000000000000E-14 " "
relative error = 5.347068569117701000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7250000000000414 " "
y[1] (closed_form) = -1.684186516249535 " "
y[1] (numeric) = -1.6841865162496255 " "
absolute error = 9.03721542044877400000000000000E-14 " "
relative error = 5.365923152367638000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7240000000000415 " "
y[1] (closed_form) = -1.6865536603013032 " "
y[1] (numeric) = -1.6865536603013935 " "
absolute error = 9.03721542044877400000000000000E-14 " "
relative error = 5.358391869271609000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7230000000000416 " "
y[1] (closed_form) = -1.688921364822841 " "
y[1] (numeric) = -1.6889213648229318 " "
absolute error = 9.0816243414337800000000000000E-14 " "
relative error = 5.377174171981889000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7220000000000417 " "
y[1] (closed_form) = -1.6912896300796174 " "
y[1] (numeric) = -1.6912896300797082 " "
absolute error = 9.0816243414337800000000000000E-14 " "
relative error = 5.369644666364012000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.721000000000042 " "
y[1] (closed_form) = -1.6936584563372885 " "
y[1] (numeric) = -1.69365845633738 " "
absolute error = 9.1482377229112900000000000000E-14 " "
relative error = 5.401465501312053000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.720000000000042 " "
y[1] (closed_form) = -1.696027843861701 " "
y[1] (numeric) = -1.6960278438617926 " "
absolute error = 9.17044218340379300000000000000E-14 " "
relative error = 5.40701157507151000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.719000000000042 " "
y[1] (closed_form) = -1.698397792918889 " "
y[1] (numeric) = -1.6983977929189809 " "
absolute error = 9.19264664389629600000000000000E-14 " "
relative error = 5.412540384957574000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.718000000000042 " "
y[1] (closed_form) = -1.7007683037750763 " "
y[1] (numeric) = -1.7007683037751684 " "
absolute error = 9.21485110438879900000000000000E-14 " "
relative error = 5.418051996815345000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7170000000000423 " "
y[1] (closed_form) = -1.7031393766966765 " "
y[1] (numeric) = -1.7031393766967688 " "
absolute error = 9.23705556488130200000000000000E-14 " "
relative error = 5.423546476153367000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7160000000000424 " "
y[1] (closed_form) = -1.7055110119502923 " "
y[1] (numeric) = -1.705511011950385 " "
absolute error = 9.25926002537380600000000000000E-14 " "
relative error = 5.429023888145772000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7150000000000425 " "
y[1] (closed_form) = -1.7078832098027161 " "
y[1] (numeric) = -1.7078832098028092 " "
absolute error = 9.30366894635881200000000000000E-14 " "
relative error = 5.447485456241187000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7140000000000426 " "
y[1] (closed_form) = -1.7102559705209308 " "
y[1] (numeric) = -1.710255970521024 " "
absolute error = 9.32587340685131500000000000000E-14 " "
relative error = 5.4529108902983260000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7130000000000427 " "
y[1] (closed_form) = -1.7126292943721086 " "
y[1] (numeric) = -1.7126292943722021 " "
absolute error = 9.34807786734381800000000000000E-14 " "
relative error = 5.458319496263814000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.712000000000043 " "
y[1] (closed_form) = -1.7150031816236124 " "
y[1] (numeric) = -1.7150031816237061 " "
absolute error = 9.37028232783632100000000000000E-14 " "
relative error = 5.463711337821177000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.711000000000043 " "
y[1] (closed_form) = -1.7173776325429957 " "
y[1] (numeric) = -1.7173776325430896 " "
absolute error = 9.39248678832882400000000000000E-14 " "
relative error = 5.469086478330896000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.710000000000043 " "
y[1] (closed_form) = -1.719752647398002 " "
y[1] (numeric) = -1.7197526473980964 " "
absolute error = 9.4368957093138310000000000000E-14 " "
relative error = 5.487356407674047000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.709000000000043 " "
y[1] (closed_form) = -1.7221282264565665 " "
y[1] (numeric) = -1.722128226456661 " "
absolute error = 9.45910016980633400000000000000E-14 " "
relative error = 5.49268052430060900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7080000000000433 " "
y[1] (closed_form) = -1.7245043699868146 " "
y[1] (numeric) = -1.7245043699869096 " "
absolute error = 9.5035090907913400000000000000E-14 " "
relative error = 5.510864023420249000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7070000000000434 " "
y[1] (closed_form) = -1.7268810782570634 " "
y[1] (numeric) = -1.7268810782571586 " "
absolute error = 9.52571355128384300000000000000E-14 " "
relative error = 5.516137544861005000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7060000000000435 " "
y[1] (closed_form) = -1.7292583515358209 " "
y[1] (numeric) = -1.7292583515359166 " "
absolute error = 9.5701224722688490000000000000E-14 " "
relative error = 5.534235219259895000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7050000000000436 " "
y[1] (closed_form) = -1.7316361900917874 " "
y[1] (numeric) = -1.731636190091883 " "
absolute error = 9.5701224722688490000000000000E-14 " "
relative error = 5.526635748910731000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7040000000000437 " "
y[1] (closed_form) = -1.7340145941938538 " "
y[1] (numeric) = -1.73401459419395 " "
absolute error = 9.61453139325385600000000000000E-14 " "
relative error = 5.5446657862321320000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.703000000000044 " "
y[1] (closed_form) = -1.7363935641111041 " "
y[1] (numeric) = -1.7363935641112005 " "
absolute error = 9.63673585374635900000000000000E-14 " "
relative error = 5.549856929284119000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.702000000000044 " "
y[1] (closed_form) = -1.7387731001128135 " "
y[1] (numeric) = -1.73877310011291 " "
absolute error = 9.65894031423886200000000000000E-14 " "
relative error = 5.5550320588765600000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.701000000000044 " "
y[1] (closed_form) = -1.7411532024684497 " "
y[1] (numeric) = -1.7411532024685468 " "
absolute error = 9.70334923522386800000000000000E-14 " "
relative error = 5.572943966945203000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.700000000000044 " "
y[1] (closed_form) = -1.7435338714476734 " "
y[1] (numeric) = -1.7435338714477706 " "
absolute error = 9.72555369571637100000000000000E-14 " "
relative error = 5.578069835627081000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6990000000000443 " "
y[1] (closed_form) = -1.7459151073203372 " "
y[1] (numeric) = -1.7459151073204346 " "
absolute error = 9.74775815620887400000000000000E-14 " "
relative error = 5.583179912550224000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6980000000000444 " "
y[1] (closed_form) = -1.7482969103564865 " "
y[1] (numeric) = -1.7482969103565844 " "
absolute error = 9.79216707719388100000000000000E-14 " "
relative error = 5.600974879717204000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6970000000000445 " "
y[1] (closed_form) = -1.7506792808263607 " "
y[1] (numeric) = -1.7506792808264586 " "
absolute error = 9.79216707719388100000000000000E-14 " "
relative error = 5.5933529255979730000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6960000000000446 " "
y[1] (closed_form) = -1.753062219000391 " "
y[1] (numeric) = -1.7530622190004894 " "
absolute error = 9.83657599817888700000000000000E-14 " "
relative error = 5.6110820777301180000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6950000000000447 " "
y[1] (closed_form) = -1.7554457251492033 " "
y[1] (numeric) = -1.7554457251493019 " "
absolute error = 9.8587804586713900000000000000E-14 " "
relative error = 5.616112373872139000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.694000000000045 " "
y[1] (closed_form) = -1.7578297995436158 " "
y[1] (numeric) = -1.7578297995437149 " "
absolute error = 9.90318937965639600000000000000E-14 " "
relative error = 5.633758957907958000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.693000000000045 " "
y[1] (closed_form) = -1.7602144424546418 " "
y[1] (numeric) = -1.7602144424547408 " "
absolute error = 9.90318937965639600000000000000E-14 " "
relative error = 5.626126647300014000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.692000000000045 " "
y[1] (closed_form) = -1.762599654153487 " "
y[1] (numeric) = -1.7625996541535864 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 5.643708301655644000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.691000000000045 " "
y[1] (closed_form) = -1.7649854349115526 " "
y[1] (numeric) = -1.7649854349116523 " "
absolute error = 9.96980276113390600000000000000E-14 " "
relative error = 5.648660076128909000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6900000000000452 " "
y[1] (closed_form) = -1.7673717850004331 " "
y[1] (numeric) = -1.7673717850005333 " "
absolute error = 1.00142116821189120000000000000E-13 " "
relative error = 5.666160208683233000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6890000000000454 " "
y[1] (closed_form) = -1.7697587046919183 " "
y[1] (numeric) = -1.7697587046920187 " "
absolute error = 1.00364161426114150000000000000E-13 " "
relative error = 5.67106471407839000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6880000000000455 " "
y[1] (closed_form) = -1.772146194257992 " "
y[1] (numeric) = -1.7721461942580927 " "
absolute error = 1.00808250635964210000000000000E-13 " "
relative error = 5.688483882571168000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6870000000000456 " "
y[1] (closed_form) = -1.774534253970833 " "
y[1] (numeric) = -1.7745342539709341 " "
absolute error = 1.01030295240889250000000000000E-13 " "
relative error = 5.6933415072048430000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6860000000000457 " "
y[1] (closed_form) = -1.776922884102816 " "
y[1] (numeric) = -1.776922884102917 " "
absolute error = 1.01030295240889250000000000000E-13 " "
relative error = 5.685688227933445000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.685000000000046 " "
y[1] (closed_form) = -1.779312084926509 " "
y[1] (numeric) = -1.7793120849266104 " "
absolute error = 1.01474384450739310000000000000E-13 " "
relative error = 5.703012153426166000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.684000000000046 " "
y[1] (closed_form) = -1.7817018567146772 " "
y[1] (numeric) = -1.781701856714779 " "
absolute error = 1.01918473660589370000000000000E-13 " "
relative error = 5.720287784204215000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.683000000000046 " "
y[1] (closed_form) = -1.7840921997402812 " "
y[1] (numeric) = -1.7840921997403831 " "
absolute error = 1.01918473660589370000000000000E-13 " "
relative error = 5.712623690380246000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.682000000000046 " "
y[1] (closed_form) = -1.786483114276476 " "
y[1] (numeric) = -1.7864831142765785 " "
absolute error = 1.02362562870439430000000000000E-13 " "
relative error = 5.729836574016328000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6810000000000462 " "
y[1] (closed_form) = -1.7888746005966147 " "
y[1] (numeric) = -1.788874600596717 " "
absolute error = 1.02362562870439430000000000000E-13 " "
relative error = 5.722176548110196000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6800000000000463 " "
y[1] (closed_form) = -1.7912666589742445 " "
y[1] (numeric) = -1.7912666589743473 " "
absolute error = 1.0280665208028950000000000000E-13 " "
relative error = 5.739327060280403000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6790000000000465 " "
y[1] (closed_form) = -1.7936592896831103 " "
y[1] (numeric) = -1.7936592896832133 " "
absolute error = 1.03028696685214530000000000000E-13 " "
relative error = 5.744050571801562000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6780000000000466 " "
y[1] (closed_form) = -1.796052492997153 " "
y[1] (numeric) = -1.7960524929972563 " "
absolute error = 1.03250741290139560000000000000E-13 " "
relative error = 5.748759665584185000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6770000000000467 " "
y[1] (closed_form) = -1.79844626919051 " "
y[1] (numeric) = -1.798446269190614 " "
absolute error = 1.03916875104914650000000000000E-13 " "
relative error = 5.778147331123114000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.676000000000047 " "
y[1] (closed_form) = -1.8008406185375168 " "
y[1] (numeric) = -1.800840618537621 " "
absolute error = 1.04138919709839680000000000000E-13 " "
relative error = 5.782794914655585000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.675000000000047 " "
y[1] (closed_form) = -1.8032355413127044 " "
y[1] (numeric) = -1.8032355413128087 " "
absolute error = 1.04360964314764710000000000000E-13 " "
relative error = 5.787428315592809000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.674000000000047 " "
y[1] (closed_form) = -1.8056310377908023 " "
y[1] (numeric) = -1.8056310377909066 " "
absolute error = 1.04360964314764710000000000000E-13 " "
relative error = 5.779750244127994000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.673000000000047 " "
y[1] (closed_form) = -1.8080271082467365 " "
y[1] (numeric) = -1.808027108246841 " "
absolute error = 1.04583008919689750000000000000E-13 " "
relative error = 5.78437172997395000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6720000000000472 " "
y[1] (closed_form) = -1.8104237529556313 " "
y[1] (numeric) = -1.8104237529557363 " "
absolute error = 1.05027098129539810000000000000E-13 " "
relative error = 5.801243932978476000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6710000000000473 " "
y[1] (closed_form) = -1.8128209721928092 " "
y[1] (numeric) = -1.8128209721929145 " "
absolute error = 1.05249142734464840000000000000E-13 " "
relative error = 5.805821112448531000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6700000000000474 " "
y[1] (closed_form) = -1.8152187662337902 " "
y[1] (numeric) = -1.8152187662338957 " "
absolute error = 1.05471187339389870000000000000E-13 " "
relative error = 5.8103843625537830000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6690000000000476 " "
y[1] (closed_form) = -1.8176171353542925 " "
y[1] (numeric) = -1.817617135354398 " "
absolute error = 1.05471187339389870000000000000E-13 " "
relative error = 5.802717485870933000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6680000000000477 " "
y[1] (closed_form) = -1.8200160798302325 " "
y[1] (numeric) = -1.8200160798303384 " "
absolute error = 1.05915276549239930000000000000E-13 " "
relative error = 5.8194692740912200000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6670000000000478 " "
y[1] (closed_form) = -1.822415599937726 " "
y[1] (numeric) = -1.8224155999378322 " "
absolute error = 1.06137321154164970000000000000E-13 " "
relative error = 5.8239910346351190000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.666000000000048 " "
y[1] (closed_form) = -1.8248156959530872 " "
y[1] (numeric) = -1.8248156959531938 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 5.840667120541638000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.665000000000048 " "
y[1] (closed_form) = -1.8272163681528295 " "
y[1] (numeric) = -1.827216368152936 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 5.832993411270739000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.664000000000048 " "
y[1] (closed_form) = -1.8296176168136646 " "
y[1] (numeric) = -1.8296176168137717 " "
absolute error = 1.07025499573865090000000000000E-13 " "
relative error = 5.849610245896806000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.663000000000048 " "
y[1] (closed_form) = -1.8320194422125051 " "
y[1] (numeric) = -1.8320194422126124 " "
absolute error = 1.07247544178790120000000000000E-13 " "
relative error = 5.854061463958522000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6620000000000483 " "
y[1] (closed_form) = -1.8344218446264617 " "
y[1] (numeric) = -1.8344218446265694 " "
absolute error = 1.07691633388640180000000000000E-13 " "
relative error = 5.870603520346169000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6610000000000484 " "
y[1] (closed_form) = -1.836824824332846 " "
y[1] (numeric) = -1.836824824332954 " "
absolute error = 1.07913677993565220000000000000E-13 " "
relative error = 5.8750119534540050000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6600000000000485 " "
y[1] (closed_form) = -1.839228381609169 " "
y[1] (numeric) = -1.839228381609277 " "
absolute error = 1.07913677993565220000000000000E-13 " "
relative error = 5.867334316532778000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6590000000000487 " "
y[1] (closed_form) = -1.8416325167331415 " "
y[1] (numeric) = -1.84163251673325 " "
absolute error = 1.08357767203415280000000000000E-13 " "
relative error = 5.883788769956686000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6580000000000488 " "
y[1] (closed_form) = -1.8440372299826757 " "
y[1] (numeric) = -1.8440372299827843 " "
absolute error = 1.08579811808340310000000000000E-13 " "
relative error = 5.88815724774496000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.657000000000049 " "
y[1] (closed_form) = -1.8464425216358835 " "
y[1] (numeric) = -1.846442521635992 " "
absolute error = 1.08579811808340310000000000000E-13 " "
relative error = 5.880486965396702000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.656000000000049 " "
y[1] (closed_form) = -1.8488483919710774 " "
y[1] (numeric) = -1.8488483919711864 " "
absolute error = 1.09023901018190370000000000000E-13 " "
relative error = 5.896854576699976000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.655000000000049 " "
y[1] (closed_form) = -1.8512548412667715 " "
y[1] (numeric) = -1.8512548412668808 " "
absolute error = 1.0924594562311540000000000000E-13 " "
relative error = 5.901183520922537000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.654000000000049 " "
y[1] (closed_form) = -1.8536618698016807 " "
y[1] (numeric) = -1.8536618698017902 " "
absolute error = 1.09467990228040430000000000000E-13 " "
relative error = 5.905499379978734000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6530000000000493 " "
y[1] (closed_form) = -1.8560694778547213 " "
y[1] (numeric) = -1.8560694778548308 " "
absolute error = 1.09467990228040430000000000000E-13 " "
relative error = 5.897839037500122000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6520000000000494 " "
y[1] (closed_form) = -1.8584776657050106 " "
y[1] (numeric) = -1.8584776657051205 " "
absolute error = 1.0991207943789050000000000000E-13 " "
relative error = 5.914092026292688000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6510000000000495 " "
y[1] (closed_form) = -1.8608864336318685 " "
y[1] (numeric) = -1.8608864336319786 " "
absolute error = 1.10134124042815530000000000000E-13 " "
relative error = 5.918368904859398000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6500000000000496 " "
y[1] (closed_form) = -1.8632957819148157 " "
y[1] (numeric) = -1.8632957819149263 " "
absolute error = 1.10578213252665590000000000000E-13 " "
relative error = 5.934549647240113000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6490000000000498 " "
y[1] (closed_form) = -1.8657057108335764 " "
y[1] (numeric) = -1.865705710833687 " "
absolute error = 1.10578213252665590000000000000E-13 " "
relative error = 5.926883999473876000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.64800000000005 " "
y[1] (closed_form) = -1.8681162206680757 " "
y[1] (numeric) = -1.8681162206681865 " "
absolute error = 1.10800257857590620000000000000E-13 " "
relative error = 5.931122305547256000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.64700000000005 " "
y[1] (closed_form) = -1.8705273116984418 " "
y[1] (numeric) = -1.8705273116985528 " "
absolute error = 1.11022302462515650000000000000E-13 " "
relative error = 5.93534784379636900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.64600000000005 " "
y[1] (closed_form) = -1.8729389842050057 " "
y[1] (numeric) = -1.872938984205117 " "
absolute error = 1.11244347067440690000000000000E-13 " "
relative error = 5.939560658707729000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.64500000000005 " "
y[1] (closed_form) = -1.8753512384683009 " "
y[1] (numeric) = -1.8753512384684123 " "
absolute error = 1.11466391672365720000000000000E-13 " "
relative error = 5.943760794559544000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6440000000000503 " "
y[1] (closed_form) = -1.877764074769064 " "
y[1] (numeric) = -1.877764074769176 " "
absolute error = 1.11910480882215780000000000000E-13 " "
relative error = 5.959773242332322000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6430000000000504 " "
y[1] (closed_form) = -1.8801774933882356 " "
y[1] (numeric) = -1.8801774933883477 " "
absolute error = 1.12132525487140810000000000000E-13 " "
relative error = 5.963932973427348000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6420000000000505 " "
y[1] (closed_form) = -1.8825914946069586 " "
y[1] (numeric) = -1.882591494607071 " "
absolute error = 1.12354570092065840000000000000E-13 " "
relative error = 5.9680801923267400000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6410000000000506 " "
y[1] (closed_form) = -1.8850060787065805 " "
y[1] (numeric) = -1.8850060787066931 " "
absolute error = 1.12576614696990870000000000000E-13 " "
relative error = 5.972214942364359000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6400000000000508 " "
y[1] (closed_form) = -1.8874212459686521 " "
y[1] (numeric) = -1.887421245968765 " "
absolute error = 1.1279865930191590000000000000E-13 " "
relative error = 5.976337266672337000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.639000000000051 " "
y[1] (closed_form) = -1.8898369966749284 " "
y[1] (numeric) = -1.8898369966750415 " "
absolute error = 1.13020703906840940000000000000E-13 " "
relative error = 5.980447208182245000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.638000000000051 " "
y[1] (closed_form) = -1.8922533311073688 " "
y[1] (numeric) = -1.892253331107482 " "
absolute error = 1.13242748511765970000000000000E-13 " "
relative error = 5.984544809626257000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.637000000000051 " "
y[1] (closed_form) = -1.894670249548137 " "
y[1] (numeric) = -1.8946702495482504 " "
absolute error = 1.134647931166910000000000000E-13 " "
relative error = 5.988630113538301000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.636000000000051 " "
y[1] (closed_form) = -1.8970877522796008 " "
y[1] (numeric) = -1.8970877522797147 " "
absolute error = 1.13908882326541060000000000000E-13 " "
relative error = 6.004407660618996000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6350000000000513 " "
y[1] (closed_form) = -1.8995058395843345 " "
y[1] (numeric) = -1.8995058395844484 " "
absolute error = 1.13908882326541060000000000000E-13 " "
relative error = 5.996763997917876000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6340000000000514 " "
y[1] (closed_form) = -1.9019245117451153 " "
y[1] (numeric) = -1.9019245117452295 " "
absolute error = 1.1413092693146609000000000000E-13 " "
relative error = 6.000812662472338000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6330000000000515 " "
y[1] (closed_form) = -1.9043437690449272 " "
y[1] (numeric) = -1.9043437690450415 " "
absolute error = 1.14352971536391120000000000000E-13 " "
relative error = 6.004849197670955000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6320000000000516 " "
y[1] (closed_form) = -1.9067636117669586 " "
y[1] (numeric) = -1.9067636117670734 " "
absolute error = 1.14797060746241190000000000000E-13 " "
relative error = 6.02051874903681000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6310000000000517 " "
y[1] (closed_form) = -1.9091840401946047 " "
y[1] (numeric) = -1.9091840401947198 " "
absolute error = 1.15019105351166220000000000000E-13 " "
relative error = 6.024516386562828000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.630000000000052 " "
y[1] (closed_form) = -1.9116050546114653 " "
y[1] (numeric) = -1.9116050546115808 " "
absolute error = 1.15463194561016280000000000000E-13 " "
relative error = 6.040117663555992000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.629000000000052 " "
y[1] (closed_form) = -1.9140266553013472 " "
y[1] (numeric) = -1.9140266553014629 " "
absolute error = 1.1568523916594131000000000000E-13 " "
relative error = 6.044076703191349000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.628000000000052 " "
y[1] (closed_form) = -1.9164488425482626 " "
y[1] (numeric) = -1.9164488425483786 " "
absolute error = 1.15907283770866340000000000000E-13 " "
relative error = 6.0480238865519000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.627000000000052 " "
y[1] (closed_form) = -1.9188716166364308 " "
y[1] (numeric) = -1.918871616636547 " "
absolute error = 1.16129328375791370000000000000E-13 " "
relative error = 6.051959254019985000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6260000000000523 " "
y[1] (closed_form) = -1.9212949778502773 " "
y[1] (numeric) = -1.9212949778503938 " "
absolute error = 1.16573417585641440000000000000E-13 " "
relative error = 6.067439874124616000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6250000000000524 " "
y[1] (closed_form) = -1.9237189264744348 " "
y[1] (numeric) = -1.9237189264745516 " "
absolute error = 1.16795462190566470000000000000E-13 " "
relative error = 6.071337167983029000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6240000000000525 " "
y[1] (closed_form) = -1.9261434627937426 " "
y[1] (numeric) = -1.9261434627938596 " "
absolute error = 1.1701750679549150000000000000E-13 " "
relative error = 6.0752227991244970000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6230000000000526 " "
y[1] (closed_form) = -1.9285685870932476 " "
y[1] (numeric) = -1.9285685870933649 " "
absolute error = 1.17239551400416530000000000000E-13 " "
relative error = 6.0790968070843050000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6220000000000527 " "
y[1] (closed_form) = -1.9309942996582041 " "
y[1] (numeric) = -1.9309942996583216 " "
absolute error = 1.17461596005341560000000000000E-13 " "
relative error = 6.082959231217454000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.621000000000053 " "
y[1] (closed_form) = -1.9334206007740737 " "
y[1] (numeric) = -1.9334206007741914 " "
absolute error = 1.1768364061026660000000000000E-13 " "
relative error = 6.086810110699669000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.620000000000053 " "
y[1] (closed_form) = -1.935847490726526 " "
y[1] (numeric) = -1.935847490726644 " "
absolute error = 1.18127729820116660000000000000E-13 " "
relative error = 6.1021196342168040000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.619000000000053 " "
y[1] (closed_form) = -1.938274969801439 " "
y[1] (numeric) = -1.9382749698015573 " "
absolute error = 1.18349774425041690000000000000E-13 " "
relative error = 6.105933176094499000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.618000000000053 " "
y[1] (closed_form) = -1.9407030382848987 " "
y[1] (numeric) = -1.9407030382850172 " "
absolute error = 1.18571819029966720000000000000E-13 " "
relative error = 6.109735322244607000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6170000000000533 " "
y[1] (closed_form) = -1.9431316964631988 " "
y[1] (numeric) = -1.9431316964633178 " "
absolute error = 1.19015908239816780000000000000E-13 " "
relative error = 6.124953262634962000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6160000000000534 " "
y[1] (closed_form) = -1.9455609446228435 " "
y[1] (numeric) = -1.9455609446229625 " "
absolute error = 1.19015908239816780000000000000E-13 " "
relative error = 6.117305580622077000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6150000000000535 " "
y[1] (closed_form) = -1.9479907830505436 " "
y[1] (numeric) = -1.9479907830506629 " "
absolute error = 1.1923795284474181000000000000E-13 " "
relative error = 6.121073769046063000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6140000000000536 " "
y[1] (closed_form) = -1.95042121203322 " "
y[1] (numeric) = -1.95042121203334 " "
absolute error = 1.1990408665951690000000000000E-13 " "
relative error = 6.14759960155081900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6130000000000537 " "
y[1] (closed_form) = -1.952852231858004 " "
y[1] (numeric) = -1.9528522318581238 " "
absolute error = 1.1990408665951690000000000000E-13 " "
relative error = 6.139946725279692000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.612000000000054 " "
y[1] (closed_form) = -1.955283842812234 " "
y[1] (numeric) = -1.9552838428123542 " "
absolute error = 1.20126131264441940000000000000E-13 " "
relative error = 6.14366715635862000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.611000000000054 " "
y[1] (closed_form) = -1.9577160451834599 " "
y[1] (numeric) = -1.9577160451835804 " "
absolute error = 1.205702204742920000000000000E-13 " "
relative error = 6.158718511345358000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.610000000000054 " "
y[1] (closed_form) = -1.960148839259441 " "
y[1] (numeric) = -1.9601488392595616 " "
absolute error = 1.205702204742920000000000000E-13 " "
relative error = 6.151074758172156000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.609000000000054 " "
y[1] (closed_form) = -1.9625822253281462 " "
y[1] (numeric) = -1.962582225328267 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 6.1547620028516470000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6080000000000543 " "
y[1] (closed_form) = -1.9650162036777545 " "
y[1] (numeric) = -1.965016203677876 " "
absolute error = 1.21458398893992130000000000000E-13 " "
relative error = 6.181038032494017000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6070000000000544 " "
y[1] (closed_form) = -1.9674507745966572 " "
y[1] (numeric) = -1.9674507745967786 " "
absolute error = 1.21458398893992130000000000000E-13 " "
relative error = 6.173389467337095000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6060000000000545 " "
y[1] (closed_form) = -1.9698859383734537 " "
y[1] (numeric) = -1.9698859383735756 " "
absolute error = 1.2190248810384219000000000000E-13 " "
relative error = 6.188301856933797000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6050000000000546 " "
y[1] (closed_form) = -1.9723216952969564 " "
y[1] (numeric) = -1.9723216952970783 " "
absolute error = 1.2190248810384219000000000000E-13 " "
relative error = 6.180659493556315000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6040000000000547 " "
y[1] (closed_form) = -1.9747580456561875 " "
y[1] (numeric) = -1.9747580456563096 " "
absolute error = 1.22124532708767220000000000000E-13 " "
relative error = 6.184278270312693000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.603000000000055 " "
y[1] (closed_form) = -1.9771949897403809 " "
y[1] (numeric) = -1.9771949897405035 " "
absolute error = 1.22568621918617280000000000000E-13 " "
relative error = 6.199116554240883000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.602000000000055 " "
y[1] (closed_form) = -1.9796325278389824 " "
y[1] (numeric) = -1.9796325278391051 " "
absolute error = 1.22790666523542310000000000000E-13 " "
relative error = 6.202699985819276000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.601000000000055 " "
y[1] (closed_form) = -1.9820706602416485 " "
y[1] (numeric) = -1.9820706602417717 " "
absolute error = 1.23234755733392380000000000000E-13 " "
relative error = 6.217475401122579000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.600000000000055 " "
y[1] (closed_form) = -1.984509387238249 " "
y[1] (numeric) = -1.9845093872383726 " "
absolute error = 1.2345680033831741000000000000E-13 " "
relative error = 6.22102375187686000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5990000000000553 " "
y[1] (closed_form) = -1.986948709118865 " "
y[1] (numeric) = -1.9869487091189886 " "
absolute error = 1.23678844943242440000000000000E-13 " "
relative error = 6.224561528721556000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5980000000000554 " "
y[1] (closed_form) = -1.9893886261737894 " "
y[1] (numeric) = -1.9893886261739135 " "
absolute error = 1.2412293415309250000000000000E-13 " "
relative error = 6.2392502158725690000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5970000000000555 " "
y[1] (closed_form) = -1.9918291386935292 " "
y[1] (numeric) = -1.9918291386936533 " "
absolute error = 1.2412293415309250000000000000E-13 " "
relative error = 6.231605499782307000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5960000000000556 " "
y[1] (closed_form) = -1.9942702469688025 " "
y[1] (numeric) = -1.9942702469689269 " "
absolute error = 1.24344978758017530000000000000E-13 " "
relative error = 6.2351117631632970000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5950000000000557 " "
y[1] (closed_form) = -1.9967119512905414 " "
y[1] (numeric) = -1.996711951290666 " "
absolute error = 1.24567023362942560000000000000E-13 " "
relative error = 6.238607590966275000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.594000000000056 " "
y[1] (closed_form) = -1.9991542519498906 " "
y[1] (numeric) = -1.9991542519500154 " "
absolute error = 1.2478906796786760000000000000E-13 " "
relative error = 6.24209301739241000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.593000000000056 " "
y[1] (closed_form) = -2.0015971492382088 " "
y[1] (numeric) = -2.0015971492383335 " "
absolute error = 1.2478906796786760000000000000E-13 " "
relative error = 6.2344747051304150000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.592000000000056 " "
y[1] (closed_form) = -2.0040406434470674 " "
y[1] (numeric) = -2.0040406434471927 " "
absolute error = 1.25233157177717660000000000000E-13 " "
relative error = 6.2490328021645950000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.591000000000056 " "
y[1] (closed_form) = -2.0064847348682524 " "
y[1] (numeric) = -2.006484734868378 " "
absolute error = 1.25677246387567720000000000000E-13 " "
relative error = 6.263553577237646000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5900000000000563 " "
y[1] (closed_form) = -2.0089294237937634 " "
y[1] (numeric) = -2.0089294237938895 " "
absolute error = 1.26121335597417780000000000000E-13 " "
relative error = 6.278037152706137000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5890000000000564 " "
y[1] (closed_form) = -2.0113747105158146 " "
y[1] (numeric) = -2.0113747105159407 " "
absolute error = 1.26121335597417780000000000000E-13 " "
relative error = 6.270404760387691000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5880000000000565 " "
y[1] (closed_form) = -2.0138205953268336 " "
y[1] (numeric) = -2.01382059532696 " "
absolute error = 1.26565424807267850000000000000E-13 " "
relative error = 6.284841117474363000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5870000000000566 " "
y[1] (closed_form) = -2.016267078519464 " "
y[1] (numeric) = -2.0162670785195904 " "
absolute error = 1.26565424807267850000000000000E-13 " "
relative error = 6.277215263575314000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5860000000000567 " "
y[1] (closed_form) = -2.018714160386563 " "
y[1] (numeric) = -2.01871416038669 " "
absolute error = 1.2700951401711790000000000000E-13 " "
relative error = 6.2916046515865780000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.585000000000057 " "
y[1] (closed_form) = -2.0211618412212036 " "
y[1] (numeric) = -2.021161841221331 " "
absolute error = 1.27453603226967970000000000000E-13 " "
relative error = 6.305957327492360000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.584000000000057 " "
y[1] (closed_form) = -2.023610121316674 " "
y[1] (numeric) = -2.0236101213168016 " "
absolute error = 1.27453603226967970000000000000E-13 " "
relative error = 6.2983280170608900000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.583000000000057 " "
y[1] (closed_form) = -2.026059000966478 " "
y[1] (numeric) = -2.0260590009666055 " "
absolute error = 1.27453603226967970000000000000E-13 " "
relative error = 6.290715283521832000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.582000000000057 " "
y[1] (closed_form) = -2.0285084804643345 " "
y[1] (numeric) = -2.028508480464462 " "
absolute error = 1.27453603226967970000000000000E-13 " "
relative error = 6.2831190726791190000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5810000000000572 " "
y[1] (closed_form) = -2.030958560104178 " "
y[1] (numeric) = -2.030958560104306 " "
absolute error = 1.27897692436818030000000000000E-13 " "
relative error = 6.297405321271425000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5800000000000574 " "
y[1] (closed_form) = -2.033409240180161 " "
y[1] (numeric) = -2.0334092401802892 " "
absolute error = 1.2834178164666810000000000000E-13 " "
relative error = 6.3116552787621330000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5790000000000575 " "
y[1] (closed_form) = -2.03586052098665 " "
y[1] (numeric) = -2.0358605209867786 " "
absolute error = 1.28785870856518160000000000000E-13 " "
relative error = 6.325869062685295000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5780000000000576 " "
y[1] (closed_form) = -2.0383124028182293 " "
y[1] (numeric) = -2.038312402818358 " "
absolute error = 1.28785870856518160000000000000E-13 " "
relative error = 6.318259687693364000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5770000000000577 " "
y[1] (closed_form) = -2.0407648859696996 " "
y[1] (numeric) = -2.040764885969829 " "
absolute error = 1.29229960066368220000000000000E-13 " "
relative error = 6.332427657631059000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.576000000000058 " "
y[1] (closed_form) = -2.0432179707360794 " "
y[1] (numeric) = -2.0432179707362086 " "
absolute error = 1.29229960066368220000000000000E-13 " "
relative error = 6.324824953444027000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.575000000000058 " "
y[1] (closed_form) = -2.0456716574126026 " "
y[1] (numeric) = -2.045671657412732 " "
absolute error = 1.29229960066368220000000000000E-13 " "
relative error = 6.317238624199364000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.574000000000058 " "
y[1] (closed_form) = -2.0481259462947214 " "
y[1] (numeric) = -2.0481259462948516 " "
absolute error = 1.30118138486068350000000000000E-13 " "
relative error = 6.353034036869947000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.573000000000058 " "
y[1] (closed_form) = -2.050580837678107 " "
y[1] (numeric) = -2.050580837678237 " "
absolute error = 1.30118138486068350000000000000E-13 " "
relative error = 6.345428382789454000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5720000000000582 " "
y[1] (closed_form) = -2.0530363318586455 " "
y[1] (numeric) = -2.053036331858776 " "
absolute error = 1.3056222769591840000000000000E-13 " "
relative error = 6.359469906590420000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5710000000000583 " "
y[1] (closed_form) = -2.0554924291324435 " "
y[1] (numeric) = -2.0554924291325745 " "
absolute error = 1.31006316905768470000000000000E-13 " "
relative error = 6.373476012317981000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5700000000000585 " "
y[1] (closed_form) = -2.057949129795825 " "
y[1] (numeric) = -2.057949129795956 " "
absolute error = 1.31006316905768470000000000000E-13 " "
relative error = 6.365867601341826000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5690000000000586 " "
y[1] (closed_form) = -2.0604064341453316 " "
y[1] (numeric) = -2.060406434145463 " "
absolute error = 1.31450406115618530000000000000E-13 " "
relative error = 6.379828947202105000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5680000000000587 " "
y[1] (closed_form) = -2.0628643424777255 " "
y[1] (numeric) = -2.062864342477857 " "
absolute error = 1.31450406115618530000000000000E-13 " "
relative error = 6.3722273640995820000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.567000000000059 " "
y[1] (closed_form) = -2.0653228550899856 " "
y[1] (numeric) = -2.0653228550901175 " "
absolute error = 1.3189449532546860000000000000E-13 " "
relative error = 6.38614418081971000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.566000000000059 " "
y[1] (closed_form) = -2.0677819722793114 " "
y[1] (numeric) = -2.0677819722794433 " "
absolute error = 1.3189449532546860000000000000E-13 " "
relative error = 6.378549435755144000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.565000000000059 " "
y[1] (closed_form) = -2.0702416943431206 " "
y[1] (numeric) = -2.070241694343253 " "
absolute error = 1.32338584535318660000000000000E-13 " "
relative error = 6.392421952322294000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.564000000000059 " "
y[1] (closed_form) = -2.072702021579052 " "
y[1] (numeric) = -2.0727020215791843 " "
absolute error = 1.32338584535318660000000000000E-13 " "
relative error = 6.3848340551382690000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5630000000000592 " "
y[1] (closed_form) = -2.075162954284962 " "
y[1] (numeric) = -2.075162954285095 " "
absolute error = 1.33226762955018780000000000000E-13 " "
relative error = 6.420062707842848000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5620000000000593 " "
y[1] (closed_form) = -2.0776244927589294 " "
y[1] (numeric) = -2.0776244927590626 " "
absolute error = 1.33226762955018780000000000000E-13 " "
relative error = 6.412456313417043000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5610000000000595 " "
y[1] (closed_form) = -2.0800866372992513 " "
y[1] (numeric) = -2.0800866372993845 " "
absolute error = 1.33226762955018780000000000000E-13 " "
relative error = 6.404866055386911000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5600000000000596 " "
y[1] (closed_form) = -2.0825493882044457 " "
y[1] (numeric) = -2.082549388204579 " "
absolute error = 1.33226762955018780000000000000E-13 " "
relative error = 6.397291882229292000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5590000000000597 " "
y[1] (closed_form) = -2.085012745773251 " "
y[1] (numeric) = -2.0850127457733847 " "
absolute error = 1.33670852164868850000000000000E-13 " "
relative error = 6.411032855115496000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.55800000000006 " "
y[1] (closed_form) = -2.0874767103046272 " "
y[1] (numeric) = -2.0874767103047613 " "
absolute error = 1.3411494137471890000000000000E-13 " "
relative error = 6.42473952943635100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.55700000000006 " "
y[1] (closed_form) = -2.0899412820977554 " "
y[1] (numeric) = -2.0899412820978895 " "
absolute error = 1.3411494137471890000000000000E-13 " "
relative error = 6.417163129104877000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.55600000000006 " "
y[1] (closed_form) = -2.0924064614520366 " "
y[1] (numeric) = -2.092406461452171 " "
absolute error = 1.34559030584568970000000000000E-13 " "
relative error = 6.430826565656418000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.55500000000006 " "
y[1] (closed_form) = -2.094872248667094 " "
y[1] (numeric) = -2.094872248667229 " "
absolute error = 1.35003119794419040000000000000E-13 " "
relative error = 6.444455974836535000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5540000000000602 " "
y[1] (closed_form) = -2.0973386440427735 " "
y[1] (numeric) = -2.0973386440429085 " "
absolute error = 1.35003119794419040000000000000E-13 " "
relative error = 6.436877524660999000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5530000000000603 " "
y[1] (closed_form) = -2.099805647879141 " "
y[1] (numeric) = -2.0998056478792764 " "
absolute error = 1.3544720900426910000000000000E-13 " "
relative error = 6.4504640770480050000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5520000000000604 " "
y[1] (closed_form) = -2.1022732604764864 " "
y[1] (numeric) = -2.102273260476622 " "
absolute error = 1.3544720900426910000000000000E-13 " "
relative error = 6.442892632024896000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5510000000000606 " "
y[1] (closed_form) = -2.1047414821353203 " "
y[1] (numeric) = -2.104741482135456 " "
absolute error = 1.35891298214119160000000000000E-13 " "
relative error = 6.456436544228394000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5500000000000607 " "
y[1] (closed_form) = -2.1072103131563775 " "
y[1] (numeric) = -2.1072103131565134 " "
absolute error = 1.35891298214119160000000000000E-13 " "
relative error = 6.448872111420545000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5490000000000608 " "
y[1] (closed_form) = -2.109679753840614 " "
y[1] (numeric) = -2.1096797538407506 " "
absolute error = 1.36779476633819290000000000000E-13 " "
relative error = 6.483423675314512000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.548000000000061 " "
y[1] (closed_form) = -2.1121498044892104 " "
y[1] (numeric) = -2.112149804489347 " "
absolute error = 1.36779476633819290000000000000E-13 " "
relative error = 6.475841644522804000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.547000000000061 " "
y[1] (closed_form) = -2.114620465403569 " "
y[1] (numeric) = -2.114620465403706 " "
absolute error = 1.37223565843669350000000000000E-13 " "
relative error = 6.4892763542549300000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.546000000000061 " "
y[1] (closed_form) = -2.1170917368853166 " "
y[1] (numeric) = -2.1170917368854543 " "
absolute error = 1.3766765505351940000000000000E-13 " "
relative error = 6.502677831809841000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.545000000000061 " "
y[1] (closed_form) = -2.1195636192363034 " "
y[1] (numeric) = -2.1195636192364415 " "
absolute error = 1.38111744263369470000000000000E-13 " "
relative error = 6.516046180917763000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5440000000000613 " "
y[1] (closed_form) = -2.1220361127586034 " "
y[1] (numeric) = -2.122036112758742 " "
absolute error = 1.38555833473219540000000000000E-13 " "
relative error = 6.52938150487457100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5430000000000614 " "
y[1] (closed_form) = -2.1245092177545146 " "
y[1] (numeric) = -2.1245092177546536 " "
absolute error = 1.3899992268306960000000000000E-13 " "
relative error = 6.542683906544053000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5420000000000615 " "
y[1] (closed_form) = -2.1269829345265596 " "
y[1] (numeric) = -2.126982934526699 " "
absolute error = 1.39444011892919660000000000000E-13 " "
relative error = 6.5559534883601780000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5410000000000617 " "
y[1] (closed_form) = -2.129457263377486 " "
y[1] (numeric) = -2.1294572633776254 " "
absolute error = 1.39444011892919660000000000000E-13 " "
relative error = 6.548335779782242000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5400000000000618 " "
y[1] (closed_form) = -2.1319322046102647 " "
y[1] (numeric) = -2.1319322046104046 " "
absolute error = 1.39888101102769720000000000000E-13 " "
relative error = 6.561564237374164000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.539000000000062 " "
y[1] (closed_form) = -2.1344077585280936 " "
y[1] (numeric) = -2.1344077585282335 " "
absolute error = 1.39888101102769720000000000000E-13 " "
relative error = 6.5539539267434910000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.538000000000062 " "
y[1] (closed_form) = -2.1368839254343936 " "
y[1] (numeric) = -2.136883925434534 " "
absolute error = 1.40332190312619800000000000000E-13 " "
relative error = 6.567141464368147000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.537000000000062 " "
y[1] (closed_form) = -2.1393607056328134 " "
y[1] (numeric) = -2.1393607056329538 " "
absolute error = 1.40332190312619800000000000000E-13 " "
relative error = 6.559538554818419000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.536000000000062 " "
y[1] (closed_form) = -2.1418380994272255 " "
y[1] (numeric) = -2.1418380994273662 " "
absolute error = 1.40776279522469850000000000000E-13 " "
relative error = 6.572685375244586000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5350000000000623 " "
y[1] (closed_form) = -2.144316107121729 " "
y[1] (numeric) = -2.1443161071218704 " "
absolute error = 1.4122036873231990000000000000E-13 " "
relative error = 6.585799932355919000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5340000000000624 " "
y[1] (closed_form) = -2.14679472902065 " "
y[1] (numeric) = -2.146794729020791 " "
absolute error = 1.4122036873231990000000000000E-13 " "
relative error = 6.5781961741979620000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5330000000000625 " "
y[1] (closed_form) = -2.149273965428539 " "
y[1] (numeric) = -2.1492739654286805 " "
absolute error = 1.41664457942169970000000000000E-13 " "
relative error = 6.59127036482405000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5320000000000626 " "
y[1] (closed_form) = -2.1517538166501744 " "
y[1] (numeric) = -2.1517538166503165 " "
absolute error = 1.42108547152020040000000000000E-13 " "
relative error = 6.604312540421236000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5310000000000628 " "
y[1] (closed_form) = -2.154234282990562 " "
y[1] (numeric) = -2.154234282990704 " "
absolute error = 1.42108547152020040000000000000E-13 " "
relative error = 6.59670808667762100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.530000000000063 " "
y[1] (closed_form) = -2.1567153647549326 " "
y[1] (numeric) = -2.156715364755075 " "
absolute error = 1.4255263636187010000000000000E-13 " "
relative error = 6.609710242318803000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.529000000000063 " "
y[1] (closed_form) = -2.1591970622487464 " "
y[1] (numeric) = -2.159197062248889 " "
absolute error = 1.4255263636187010000000000000E-13 " "
relative error = 6.602113297310868000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.528000000000063 " "
y[1] (closed_form) = -2.1616793757776898 " "
y[1] (numeric) = -2.1616793757778323 " "
absolute error = 1.4255263636187010000000000000E-13 " "
relative error = 6.594531916213758000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.527000000000063 " "
y[1] (closed_form) = -2.1641623056476766 " "
y[1] (numeric) = -2.1641623056478196 " "
absolute error = 1.42996725571720160000000000000E-13 " "
relative error = 6.607486194475835000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5260000000000633 " "
y[1] (closed_form) = -2.16664585216485 " "
y[1] (numeric) = -2.166645852164993 " "
absolute error = 1.42996725571720160000000000000E-13 " "
relative error = 6.599912275872957000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5250000000000634 " "
y[1] (closed_form) = -2.1691300156355804 " "
y[1] (numeric) = -2.169130015635724 " "
absolute error = 1.43440814781570230000000000000E-13 " "
relative error = 6.612826974299205000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5240000000000635 " "
y[1] (closed_form) = -2.171614796366466 " "
y[1] (numeric) = -2.17161479636661 " "
absolute error = 1.4388490399142030000000000000E-13 " "
relative error = 6.625710242542450000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5230000000000636 " "
y[1] (closed_form) = -2.174100194664335 " "
y[1] (numeric) = -2.174100194664479 " "
absolute error = 1.4388490399142030000000000000E-13 " "
relative error = 6.618135831298937000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5220000000000637 " "
y[1] (closed_form) = -2.176586210836243 " "
y[1] (numeric) = -2.1765862108363874 " "
absolute error = 1.44328993201270350000000000000E-13 " "
relative error = 6.630979856562595000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.521000000000064 " "
y[1] (closed_form) = -2.1790728451894763 " "
y[1] (numeric) = -2.1790728451896206 " "
absolute error = 1.44328993201270350000000000000E-13 " "
relative error = 6.623412958400690000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.520000000000064 " "
y[1] (closed_form) = -2.181560098031549 " "
y[1] (numeric) = -2.181560098031693 " "
absolute error = 1.44328993201270350000000000000E-13 " "
relative error = 6.615861434736561000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.519000000000064 " "
y[1] (closed_form) = -2.1840479696702046 " "
y[1] (numeric) = -2.1840479696703494 " "
absolute error = 1.44773082411120400000000000000E-13 " "
relative error = 6.62865854695404900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.518000000000064 " "
y[1] (closed_form) = -2.1865364604134183 " "
y[1] (numeric) = -2.186536460413563 " "
absolute error = 1.44773082411120400000000000000E-13 " "
relative error = 6.621114490071092000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5170000000000643 " "
y[1] (closed_form) = -2.1890255705693935 " "
y[1] (numeric) = -2.1890255705695383 " "
absolute error = 1.44773082411120400000000000000E-13 " "
relative error = 6.613585714006214000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5160000000000644 " "
y[1] (closed_form) = -2.1915153004465635 " "
y[1] (numeric) = -2.191515300446709 " "
absolute error = 1.45661260830820540000000000000E-13 " "
relative error = 6.646600222281781000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5150000000000645 " "
y[1] (closed_form) = -2.1940056503535943 " "
y[1] (numeric) = -2.19400565035374 " "
absolute error = 1.45661260830820540000000000000E-13 " "
relative error = 6.639055866029571000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5140000000000646 " "
y[1] (closed_form) = -2.19649662059938 " "
y[1] (numeric) = -2.1964966205995258 " "
absolute error = 1.45661260830820540000000000000E-13 " "
relative error = 6.631526744214725000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5130000000000647 " "
y[1] (closed_form) = -2.1989882114930466 " "
y[1] (numeric) = -2.198988211493193 " "
absolute error = 1.46549439250520660000000000000E-13 " "
relative error = 6.6644031325214800000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.512000000000065 " "
y[1] (closed_form) = -2.201480423343952 " "
y[1] (numeric) = -2.201480423344099 " "
absolute error = 1.46993528460370730000000000000E-13 " "
relative error = 6.677030915273551000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.511000000000065 " "
y[1] (closed_form) = -2.2039732564616847 " "
y[1] (numeric) = -2.2039732564618317 " "
absolute error = 1.46993528460370730000000000000E-13 " "
relative error = 6.669478771097155000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.510000000000065 " "
y[1] (closed_form) = -2.2064667111560645 " "
y[1] (numeric) = -2.2064667111562115 " "
absolute error = 1.46993528460370730000000000000E-13 " "
relative error = 6.661941814810086000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.509000000000065 " "
y[1] (closed_form) = -2.2089607877371433 " "
y[1] (numeric) = -2.2089607877372908 " "
absolute error = 1.4743761767022080000000000000E-13 " "
relative error = 6.674523988325556000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5080000000000653 " "
y[1] (closed_form) = -2.2114554865152054 " "
y[1] (numeric) = -2.211455486515353 " "
absolute error = 1.4743761767022080000000000000E-13 " "
relative error = 6.666994591084980000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5070000000000654 " "
y[1] (closed_form) = -2.213950807800767 " "
y[1] (numeric) = -2.2139508078009147 " "
absolute error = 1.47881706880070850000000000000E-13 " "
relative error = 6.679538965320079000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5060000000000655 " "
y[1] (closed_form) = -2.2164467519045763 " "
y[1] (numeric) = -2.2164467519047246 " "
absolute error = 1.48325796089920900000000000000E-13 " "
relative error = 6.6920532136612640000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5050000000000656 " "
y[1] (closed_form) = -2.2189433191376158 " "
y[1] (numeric) = -2.218943319137764 " "
absolute error = 1.48325796089920900000000000000E-13 " "
relative error = 6.684523881735167000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5040000000000657 " "
y[1] (closed_form) = -2.2214405098110994 " "
y[1] (numeric) = -2.221440509811248 " "
absolute error = 1.48769885299770980000000000000E-13 " "
relative error = 6.697000646324832000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.503000000000066 " "
y[1] (closed_form) = -2.2239383242364745 " "
y[1] (numeric) = -2.223938324236624 " "
absolute error = 1.4965806371947110000000000000E-13 " "
relative error = 6.729416103337844000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.502000000000066 " "
y[1] (closed_form) = -2.2264367627254233 " "
y[1] (numeric) = -2.226436762725573 " "
absolute error = 1.4965806371947110000000000000E-13 " "
relative error = 6.721864560674602000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.501000000000066 " "
y[1] (closed_form) = -2.22893582558986 " "
y[1] (numeric) = -2.22893582559001 " "
absolute error = 1.50102152929321160000000000000E-13 " "
relative error = 6.734251888548587000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.500000000000066 " "
y[1] (closed_form) = -2.2314355131419332 " "
y[1] (numeric) = -2.2314355131420838 " "
absolute error = 1.50546242139171230000000000000E-13 " "
relative error = 6.7466095817036300000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = -1.000E-3 " "
"Finished!"
"diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; "
Iterations = 601
"Total Elapsed Time "= 12 Seconds
"Elapsed Time(since restart) "= 12 Seconds
"Expected Time Remaining "= 0 Seconds
"Optimized Time Remaining "= 0 Seconds
"Expected Total Time "= 12 Seconds
"Time to Timeout "= 2 Minutes 47 Seconds
Percent Done = 0.0 "%"
(%o253) temp/diffeq.div_c_lin_back.max