(%i1) batch("temp/diffeq.div_lin_exp.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.div_lin_exp.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_tmp5,[30],convfloat)
(%i191) completearray(array_m1,[30],convfloat)
(%i192) completearray(array_y_higher,[2,30],convfloat)
(%i193) completearray(array_y_higher_work,[2,30],convfloat)
(%i194) completearray(array_y_higher_work2,[2,30],convfloat)
(%i195) completearray(array_y_set_initial,[2,30],convfloat)
(%i196) completearray(array_given_rad_poles,[2,3],convfloat)
(%i197) completearray(array_given_ord_poles,[2,3],convfloat)
(%i198) completearray(array_rad_test_poles,[2,4],convfloat)
(%i199) completearray(array_ord_test_poles,[2,4],convfloat)
(%i200) completearray(array_fact_2,[30,30],convfloat)
(%i201) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i202) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i203) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i204) 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))
(%i205) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i206) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i207) 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)
(%i208) 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)
(%i209) 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)
(%i210) 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)
(%i211) 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)
(%i212) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i213) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i214) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i215) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i216) log_revs(file,revs):=printf(file,revs)
(%i217) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i218) 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)
(%i219) logstart(file):=(printf(file,""),0)
(%i220) logend(file):=(printf(file,"
~%"),0)
(%i221) 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)
(%i222) 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)
(%i223) 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)
(%i224) 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)
(%i225) 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)
(%i226) c(in_val):=(ret:in_val,ret)
(%i227) 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)
(%i228) 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)
(%i229) 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)
(%i230) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i231) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i232) 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)
(%i233) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i234) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i235) 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)
(%i236) log10(x):=log(x)/glob_log_10
(%i237) c(x):=x
(%i238) 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
(%i239) 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)
(%i240) exact_soln_y(x):=block(neg(c(0.1)*(c(2.0)*c(x)+c(5.0)))/exp(c(x)))
neg(c(0.1) (c(2.0) c(x) + c(5.0)))
(%o240) exact_soln_y(x) := block(----------------------------------)
exp(c(x))
(%i241) 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)
(%i242) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i243) 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)
(%i244) 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)
(%i245) 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))
(%i246) 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))
(%i247) display_alot(iter):=(
block(mode_declare(
[[abserr,est_rel_err],convfloat,
[closed_form_val_y],convfloat,[ind_var],
convfloat,[numeric_val],convfloat,[relerr],
convfloat,[term_no],fixnum]),
if reached_interval()
then (if iter >= 0
then (ind_var:array_x[1],
omniout_float(always,
"x[1] ",
33,ind_var,20,
" "),
closed_form_val_y
:exact_soln_y(ind_var),
omniout_float(always,
"y[1] (closed_form) ",
33,
closed_form_val_y,
20," "),
term_no:1,
numeric_val:array_y[term_no],
abserr
:abs(
numeric_val
-closed_form_val_y),
omniout_float(always,
"y[1] (numeric) ",
33,numeric_val,
20," "),
if
c(abs(closed_form_val_y))
> c(glob_prec)
then (
relerr
:abserr*glob__100
/abs(closed_form_val_y),
if c(relerr) > c(glob_prec)
then glob_good_digits
:3
-floor(log10(c(relerr)))
else glob_good_digits:16)
else (relerr:glob__m1,
glob_good_digits:-16),
if
glob_good_digits
< glob_min_good_digits
then glob_min_good_digits
:glob_good_digits,
if
glob_apfp_est_good_digits
< glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits
:glob_apfp_est_good_digits,
if
c(abs(numeric_val))
> c(glob_prec)
then (
est_rel_err
:c(array_max_est_error[1])
*glob__100
*c(sqrt(glob_iter))*c(25)
*c(ats_max_terms)
/c(abs(numeric_val)),
if est_rel_err > glob_prec
then glob_est_digits
:3
-floor(
log10(est_rel_err))
else glob_est_digits:16)
else (relerr:glob__m1,
glob_est_digits:-16),
array_est_digits[1]
:glob_est_digits,
if glob_iter = 1
then array_1st_rel_error[1]
:relerr
else array_last_rel_error[
1]
:relerr,
array_est_rel_error[1]
:est_rel_err,
omniout_float(always,
"absolute error ",
4,abserr,20," "),
omniout_float(always,
"relative error ",
4,relerr,20,"%"),
omniout_int(info,
"Desired digits ",
32,
glob_desired_digits_correct,
4," "),
omniout_int(info,
"Estimated correct digits ",
32,glob_est_digits,
4," "),
omniout_int(info,
"Correct digits ",
32,
glob_good_digits,4,
" "),
omniout_float(always,
"h ",
4,glob_h,20,
" ")))),0)
(%i248) 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)
(%i249) 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)
(%i250) 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]:exp(array_x[1]),
array_tmp4[1]:array_tmp2[1]/array_tmp3[1],
array_tmp5[1]:array_tmp4[1]+array_const_0D0[1],
if not array_y_set_initial[1,2]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp5[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]:array_tmp3[1]*array_x[2]/c(1),
array_tmp4[2]:(array_tmp2[2]
-array_tmp4[1]*array_tmp3[2])
/array_tmp3[1],
array_tmp5[2]:array_tmp4[2],
if not array_y_set_initial[1,3]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp5[2])*expt(glob_h,c(1))
*c(factorial_3(1,2)),
if 3 <= ats_max_terms
then (array_y[3]:temporary,
array_y_higher[1,3]:temporary),
temporary:c(temporary)*c(2)/c(glob_h),
array_y_higher[2,2]:c(temporary),0)),
kkk:3,array_tmp3[3]:array_tmp3[2]*array_x[2]/c(2),
array_tmp4[3]:neg(ats(3,array_tmp3,array_tmp4,2))
/array_tmp3[1],
array_tmp5[3]:array_tmp4[3],
if not array_y_set_initial[1,4]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp5[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]:array_tmp3[3]*array_x[2]/c(3),
array_tmp4[4]:neg(ats(4,array_tmp3,array_tmp4,2))
/array_tmp3[1],
array_tmp5[4]:array_tmp4[4],
if not array_y_set_initial[1,5]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp5[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]:array_tmp3[4]*array_x[2]/c(4),
array_tmp4[5]:neg(ats(5,array_tmp3,array_tmp4,2))
/array_tmp3[1],
array_tmp5[5]:array_tmp4[5],
if not array_y_set_initial[1,6]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp5[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_tmp3[kkk-1]*array_x[2]/c(kkk-1),
array_tmp4[kkk]
:neg(ats(kkk,array_tmp3,array_tmp4,2))
/array_tmp3[1],array_tmp5[kkk]:array_tmp4[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_tmp5[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)
(%i251) exact_soln_y(x):=block(neg(c(0.1)*(c(2.0)*c(x)+c(5.0)))/exp(c(x)))
neg(c(0.1) (c(2.0) c(x) + c(5.0)))
(%o251) exact_soln_y(x) := block(----------------------------------)
exp(c(x))
(%i252) 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_tmp5[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_tmp5),
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_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_lin_exppostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / exp ( x ) ; "),
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(1.0),"),
omniout_str(always,""),omniout_str(always,"x_end:c(5.0),"),
omniout_str(always,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(always,"glob_look_poles:true,"),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),
omniout_str(always,"glob_type_given_pole:3,"),
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,
" (neg (c(0.1) * (c(5.0) + c(2.0)*c(x)))/exp(c(x))) "),
omniout_str(always,"));"),
omniout_str(always,"/* END USER DEF BLOCK */"),
omniout_str(always,
"#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false,
glob_small_float:glob__0,glob_smallish_float:glob__0,
glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100),
glob_almost_1:c(0.99),x_start:c(1.0),x_end:c(5.0),
array_y_init[1+0]:exact_soln_y(x_start),
glob_look_poles:true,glob_type_given_pole:3,
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 ) = ( 0.2 * x + 0.3 ) / exp ( x ) ; "),
omniout_int(info,
"Iterations ",32,
glob_iter,4," "),
prog_report(x_start,x_end),
if glob_html_log
then (logstart(html_log_file),
logitem_str(html_log_file,
"2015-04-24T20:50:41-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"div_lin_exp"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / exp ( x ) ; "),
logitem_float(html_log_file,x_start),
logitem_float(html_log_file,x_end),
logitem_float(html_log_file,array_x[1]),
logitem_float(html_log_file,glob_h),
logitem_h_reason(html_log_file),
logitem_str(html_log_file,"16"),
logitem_float(html_log_file,
glob_desired_digits_correct),
if array_est_digits[1] # -16
then (
logitem_integer(html_log_file,
array_est_digits[
1]),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_min_good_digits # -16
then (
logitem_integer(html_log_file,
glob_min_good_digits),
0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_good_digits # -16
then (
logitem_integer(html_log_file,
glob_good_digits),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
logitem_str(html_log_file,"NA"),
logitem_str(html_log_file,"NA"),
logitem_integer(html_log_file,
ats_max_terms),
if glob_type_given_pole = 0
then (
logitem_str(html_log_file,
"Not Given"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 4
then (
logitem_str(html_log_file,
"No Solution"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 5
then (
logitem_str(html_log_file,
"Some Pole"),
logitem_str(html_log_file,"????"),0)
elseif glob_type_given_pole = 3
then (
logitem_str(html_log_file,
"No Pole"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 1
then (
logitem_str(html_log_file,
"Real Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0) elseif glob_type_given_pole = 2
then (
logitem_str(html_log_file,
"Complex Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0),
if
glob_least_ratio_sing
< glob_large_float
then (
logitem_float(html_log_file,
glob_least_ratio_sing),
0)
else (
logitem_str(html_log_file,"NONE"),0),
if glob_least_3_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_3_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
if glob_least_6_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_6_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
logitem_integer(html_log_file,
glob_iter),
logitem_time(html_log_file,
glob_clock_sec),
if c(glob_percent_done) < glob__100
then (
logitem_time(html_log_file,
glob_total_exp_sec),0)
else (
logitem_str(html_log_file,"Done"),
0),
log_revs(html_log_file,
" 308.maple.seems.ok | "),
logitem_str(html_log_file,
"div_lin_exp diffeq.max"),
logitem_str(html_log_file,
"div_lin_exp maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i253) main():=(glob_iolevel:2,compile(all),main_prog())
(%i254) 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_tmp3 in translation.
warning: encountered undefined variable array_tmp4 in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp5 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temporary in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable array_y_set_initial in translation.
warning: encountered undefined variable kkk in translation.
warning: encountered undefined variable order_d in translation.
warning: encountered undefined variable adj3 in translation.
warning: encountered undefined variable adj2 in translation.
modedeclare: [found_h]
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: variable term (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable array_y_init in translation.
warning: variable term (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_norms in translation.
warning: encountered undefined variable array_fact_1 in translation.
warning: encountered undefined variable array_type_pole in translation.
warning: encountered undefined variable array_type_real_pole in translation.
warning: encountered undefined variable array_type_complex_pole in translation.
warning: encountered undefined variable array_tmp0 in translation.
warning: encountered undefined variable array_m1 in translation.
warning: variable ord (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable ord in translation.
warning: variable ord (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_y_higher_work in translation.
warning: encountered undefined variable array_y_higher_work2 in translation.
warning: encountered undefined variable array_const_1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: variable iiif (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable iiif in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: variable jjjf (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable jjjf in translation.
warning: variable jjjf (declared type [found_h]) assigned type any.
warning: variable iiif (declared type [found_h]) assigned type any.
warning: variable glob_orig_start_sec (declared type convfloat) assigned type any.
warning: variable opt_iter (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__0 in translation.
warning: variable glob_large_float (declared type convfloat) assigned type any.
warning: variable glob_larger_float (declared type convfloat) assigned type any.
warning: variable glob_almost_1 (declared type convfloat) assigned type any.
warning: variable x_start (declared type [found_h]) assigned type any.
warning: variable x_end (declared type [found_h]) assigned type any.
warning: encountered undefined variable x_start in translation.
warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_h (declared type convfloat) assigned type any.
warning: variable glob_display_interval (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_max_minutes in translation.
warning: encountered undefined variable glob_max_hours in translation.
warning: encountered undefined variable x_end in translation.
warning: variable glob_check_sign (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_larger_float in translation.
warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_max_h in translation.
warning: encountered undefined variable glob_display_interval in translation.
warning: encountered undefined variable glob__10 in translation.
warning: variable display_max (declared type [found_h]) assigned type any.
warning: encountered undefined variable display_max in translation.
warning: variable min_value (declared type [found_h]) assigned type convfloat.
warning: variable est_answer (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_answer in translation.
warning: variable est_needed_step_err (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_needed_step_err in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable opt_iter in translation.
warning: encountered undefined variable found_h in translation.
warning: variable glob_next_display (declared type convfloat) assigned type any.
warning: variable order_diff (declared type [found_h]) assigned type fixnum.
warning: variable term_no (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable order_diff in translation.
warning: variable term_no (declared type [found_h]) assigned type any.
warning: variable r_order (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable r_order in translation.
warning: encountered undefined variable rows in translation.
warning: variable it (declared type [found_h]) assigned type any.
warning: encountered undefined variable it in translation.
warning: variable r_order (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_look_poles in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type any.
warning: encountered undefined variable estimated_step_error in translation.
warning: encountered undefined variable glob__2 in translation.
warning: variable opt_iter (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_optimize in translation.
warning: variable html_log_file (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_html_log in translation.
warning: variable current_iter (declared type [found_h]) assigned type fixnum.
warning: variable glob_clock_start_sec (declared type convfloat) assigned type any.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable debugl in translation.
warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable current_iter in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: variable calc_term (declared type [found_h]) assigned type fixnum.
warning: variable iii (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable calc_term in translation.
warning: variable iii (declared type [found_h]) assigned type any.
warning: variable temp_sum (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable temp_sum in translation.
warning: variable temp_sum (declared type [found_h]) assigned type any.
warning: encountered undefined variable html_log_file in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob_percent_done in translation.
warning: encountered undefined variable glob__100 in translation.
WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB__PI is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $LAST_MIN_POLE_EST is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H is neither declared nor
bound,
it will be treated as if it were declared SPECIAL.
"##############ECHO OF PROBLEM#################"
"##############temp/div_lin_exppostode.ode#################"
"diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / exp ( x ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:c(1.0),"
""
"x_end:c(5.0),"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
""
""
""
""
""
""
""
"glob_type_given_pole:3,"
"/* 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("
""
" (neg (c(0.1) * (c(5.0) + c(2.0)*c(x)))/exp(c(x))) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1. " "
y[1] (closed_form) = -0.2575156088200097 " "
y[1] (numeric) = -0.2575156088200097 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 15
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.009999999999999 " "
y[1] (closed_form) = -0.2556817236592096 " "
y[1] (numeric) = -0.25568172365920944 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 6.51331081902986700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0199999999999978 " "
y[1] (closed_form) = -0.25385883788184754 " "
y[1] (numeric) = -0.2538588378818472 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 1.31201619831949640000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0299999999999967 " "
y[1] (closed_form) = -0.2520469141618187 " "
y[1] (numeric) = -0.2520469141618181 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 2.2024134441740740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0399999999999956 " "
y[1] (closed_form) = -0.2502459148268172 " "
y[1] (numeric) = -0.2502459148268164 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 3.10556964646332370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0499999999999945 " "
y[1] (closed_form) = -0.24845580186892133 " "
y[1] (numeric) = -0.24845580186892038 " "
absolute error = 9.436895709313831000000000000000E-16 " "
relative error = 3.7982190950374690000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0599999999999934 " "
y[1] (closed_form) = -0.2466765369550021 " "
y[1] (numeric) = -0.24667653695500094 " "
absolute error = 1.1657341758564144000000000000000E-15 " "
relative error = 4.7257602617838906000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0699999999999923 " "
y[1] (closed_form) = -0.24490808143695794 " "
y[1] (numeric) = -0.24490808143695658 " "
absolute error = 1.3600232051658168000000000000000E-15 " "
relative error = 5.5531985599907690000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0799999999999912 " "
y[1] (closed_form) = -0.243150396361778 " "
y[1] (numeric) = -0.24315039636177643 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 6.3923902972487580000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.08999999999999 " "
y[1] (closed_form) = -0.24140344248143628 " "
y[1] (numeric) = -0.24140344248143455 " "
absolute error = 1.7208456881689926000000000000000E-15 " "
relative error = 7.1285051715918430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.099999999999989 " "
y[1] (closed_form) = -0.2396671802626192 " "
y[1] (numeric) = -0.2396671802626173 " "
absolute error = 1.915134717478395000000000000000E-15 " "
relative error = 7.9908092354566660000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1099999999999879 " "
y[1] (closed_form) = -0.23794156989628862 " "
y[1] (numeric) = -0.2379415698962865 " "
absolute error = 2.1094237467877974000000000000000E-15 " "
relative error = 8.8653014591238940000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1199999999999868 " "
y[1] (closed_form) = -0.23622657130708286 " "
y[1] (numeric) = -0.23622657130708058 " "
absolute error = 2.275957200481571000000000000000E-15 " "
relative error = 9.634636729849240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1299999999999857 " "
y[1] (closed_form) = -0.2345221441625581 " "
y[1] (numeric) = -0.23452214416255562 " "
absolute error = 2.4702462297909733000000000000000E-15 " "
relative error = 1.0533104405180312000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1399999999999846 " "
y[1] (closed_form) = -0.23282824788227185 " "
y[1] (numeric) = -0.2328282478822692 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.1444209555052277000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1499999999999835 " "
y[1] (closed_form) = -0.23114484164671165 " "
y[1] (numeric) = -0.23114484164670882 " "
absolute error = 2.831068712794149000000000000000E-15 " "
relative error = 1.224802895286426100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1599999999999824 " "
y[1] (closed_form) = -0.22947188440607003 " "
y[1] (numeric) = -0.22947188440606706 " "
absolute error = 2.9698465908722940000000000000000E-15 " "
relative error = 1.2942093531671606000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1699999999999813 " "
y[1] (closed_form) = -0.22780933488886912 " "
y[1] (numeric) = -0.22780933488886593 " "
absolute error = 3.191891195797325000000000000000E-15 " "
relative error = 1.401123969460868200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1799999999999802 " "
y[1] (closed_form) = -0.22615715161043587 " "
y[1] (numeric) = -0.22615715161043254 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 1.4727233033128537000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.189999999999979 " "
y[1] (closed_form) = -0.22451529288123104 " "
y[1] (numeric) = -0.2245152928812275 " "
absolute error = 3.524958103184872000000000000000E-15 " "
relative error = 1.5700302896736665000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.199999999999978 " "
y[1] (closed_form) = -0.22288371681503316 " "
y[1] (numeric) = -0.22288371681502947 " "
absolute error = 3.6914915568786455000000000000000E-15 " "
relative error = 1.6562410254231996000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2099999999999769 " "
y[1] (closed_form) = -0.22126238133698017 " "
y[1] (numeric) = -0.22126238133697634 " "
absolute error = 3.83026943495679000000000000000E-15 " "
relative error = 1.7310983511125336000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2199999999999758 " "
y[1] (closed_form) = -0.2196512441914705 " "
y[1] (numeric) = -0.21965124419146648 " "
absolute error = 4.0245584642661925000000000000000E-15 " "
relative error = 1.8322493364790482000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2299999999999747 " "
y[1] (closed_form) = -0.2180502629499252 " "
y[1] (numeric) = -0.218050262949921 " "
absolute error = 4.191091917959966000000000000000E-15 " "
relative error = 1.922076066894008700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2399999999999736 " "
y[1] (closed_form) = -0.21645939501841407 " "
y[1] (numeric) = -0.21645939501840972 " "
absolute error = 4.3576253716537394000000000000000E-15 " "
relative error = 2.0131375546360733000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2499999999999725 " "
y[1] (closed_form) = -0.21487859764514697 " "
y[1] (numeric) = -0.21487859764514242 " "
absolute error = 4.551914400963142000000000000000E-15 " "
relative error = 2.1183656496494016000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2599999999999714 " "
y[1] (closed_form) = -0.21330782792783182 " "
y[1] (numeric) = -0.21330782792782713 " "
absolute error = 4.690692279041286400000000000000E-15 " "
relative error = 2.199024913716848300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2699999999999703 " "
y[1] (closed_form) = -0.21174704282090298 " "
y[1] (numeric) = -0.21174704282089812 " "
absolute error = 4.85722573273506000000000000000E-15 " "
relative error = 2.2938812594626565000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2799999999999692 " "
y[1] (closed_form) = -0.21019619914261953 " "
y[1] (numeric) = -0.21019619914261453 " "
absolute error = 4.9960036108132044000000000000000E-15 " "
relative error = 2.3768287110764466000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.289999999999968 " "
y[1] (closed_form) = -0.20865525358203718 " "
y[1] (numeric) = -0.208655253582032 " "
absolute error = 5.190292640122607000000000000000E-15 " "
relative error = 2.4874967445197513000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.299999999999967 " "
y[1] (closed_form) = -0.20712416270585465 " "
y[1] (numeric) = -0.20712416270584927 " "
absolute error = 5.384581669432009000000000000000E-15 " "
relative error = 2.5996878389697440000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3099999999999659 " "
y[1] (closed_form) = -0.2056028829651366 " "
y[1] (numeric) = -0.20560288296513107 " "
absolute error = 5.523359547510154000000000000000E-15 " "
relative error = 2.6864212543394794000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3199999999999648 " "
y[1] (closed_form) = -0.204091370701915 " "
y[1] (numeric) = -0.20409137070190936 " "
absolute error = 5.6343818499726690000000000000000E-15 " "
relative error = 2.760715374978763000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3299999999999637 " "
y[1] (closed_form) = -0.2025895821556706 " "
y[1] (numeric) = -0.20258958215566478 " "
absolute error = 5.828670879282072000000000000000E-15 " "
relative error = 2.8770832227707044000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3399999999999626 " "
y[1] (closed_form) = -0.20109747346969595 " "
y[1] (numeric) = -0.20109747346968992 " "
absolute error = 6.022959908591474000000000000000E-15 " "
relative error = 2.9950450419254493000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3499999999999615 " "
y[1] (closed_form) = -0.19961500069734217 " "
y[1] (numeric) = -0.19961500069733595 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 3.114620101786597700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3599999999999604 " "
y[1] (closed_form) = -0.19814211980815097 " "
y[1] (numeric) = -0.19814211980814458 " "
absolute error = 6.38378239159465000000000000000E-15 " "
relative error = 3.2218199733482616000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3699999999999593 " "
y[1] (closed_form) = -0.1966787866938734 " "
y[1] (numeric) = -0.19667878669386685 " "
absolute error = 6.5503158452884240000000000000000E-15 " "
relative error = 3.3304638265253590000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3799999999999581 " "
y[1] (closed_form) = -0.19522495717437716 " "
y[1] (numeric) = -0.1952249571743704 " "
absolute error = 6.744604874597826000000000000000E-15 " "
relative error = 3.454786197531839000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.389999999999957 " "
y[1] (closed_form) = -0.19378058700344403 " "
y[1] (numeric) = -0.19378058700343714 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 3.5521529060873540000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.399999999999956 " "
y[1] (closed_form) = -0.19234563187445938 " "
y[1] (numeric) = -0.1923456318744523 " "
absolute error = 7.077671781985373000000000000000E-15 " "
relative error = 3.679663381492773000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4099999999999548 " "
y[1] (closed_form) = -0.1909200474259942 " "
y[1] (numeric) = -0.190920047425987 " "
absolute error = 7.188694084447889000000000000000E-15 " "
relative error = 3.765290330359059000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4199999999999537 " "
y[1] (closed_form) = -0.18950378924728312 " "
y[1] (numeric) = -0.18950378924727573 " "
absolute error = 7.382983113757291000000000000000E-15 " "
relative error = 3.895955401779988000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4299999999999526 " "
y[1] (closed_form) = -0.18809681288359772 " "
y[1] (numeric) = -0.18809681288359018 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 4.013633432546795000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4399999999999515 " "
y[1] (closed_form) = -0.18669907384151874 " "
y[1] (numeric) = -0.18669907384151102 " "
absolute error = 7.716050021144838000000000000000E-15 " "
relative error = 4.132880716748857400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4499999999999504 " "
y[1] (closed_form) = -0.18531052759410702 " "
y[1] (numeric) = -0.1853105275940992 " "
absolute error = 7.827072323607354000000000000000E-15 " "
relative error = 4.2237602068411895000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4599999999999493 " "
y[1] (closed_form) = -0.183931129585976 " "
y[1] (numeric) = -0.183931129585968 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 4.345977646793404700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4699999999999482 " "
y[1] (closed_form) = -0.18256083523826583 " "
y[1] (numeric) = -0.18256083523825772 " "
absolute error = 8.104628079763643000000000000000E-15 " "
relative error = 4.439412248079408500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4799999999999471 " "
y[1] (closed_form) = -0.18119959995352214 " "
y[1] (numeric) = -0.18119959995351387 " "
absolute error = 8.271161533457416000000000000000E-15 " "
relative error = 4.564668760625838000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.489999999999946 " "
y[1] (closed_form) = -0.17984737912047938 " "
y[1] (numeric) = -0.179847379120471 " "
absolute error = 8.382183835919932000000000000000E-15 " "
relative error = 4.660720593712252000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.499999999999945 " "
y[1] (closed_form) = -0.17850412811875127 " "
y[1] (numeric) = -0.17850412811874275 " "
absolute error = 8.520961713998076000000000000000E-15 " "
relative error = 4.773537622799087000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5099999999999438 " "
y[1] (closed_form) = -0.17716980232342877 " "
y[1] (numeric) = -0.17716980232342014 " "
absolute error = 8.631984016460592000000000000000E-15 " "
relative error = 4.8721531001669505000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5199999999999427 " "
y[1] (closed_form) = -0.17584435710958823 " "
y[1] (numeric) = -0.1758443571095794 " "
absolute error = 8.826273045769994000000000000000E-15 " "
relative error = 5.019366666551238000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5299999999999416 " "
y[1] (closed_form) = -0.17452774785670935 " "
y[1] (numeric) = -0.1745277478567004 " "
absolute error = 8.965050923848139000000000000000E-15 " "
relative error = 5.136748187003833000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5399999999999405 " "
y[1] (closed_form) = -0.17321992995300595 " "
y[1] (numeric) = -0.1732199299529968 " "
absolute error = 9.159339953157541000000000000000E-15 " "
relative error = 5.2876940636348500000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5499999999999394 " "
y[1] (closed_form) = -0.17192085879966973 " "
y[1] (numeric) = -0.1719208587996604 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 5.4245153682708510000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5599999999999383 " "
y[1] (closed_form) = -0.17063048981502893 " "
y[1] (numeric) = -0.17063048981501944 " "
absolute error = 9.492406860545088000000000000000E-15 " "
relative error = 5.563136383676377000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5699999999999372 " "
y[1] (closed_form) = -0.1693487784386227 " "
y[1] (numeric) = -0.16934877843861312 " "
absolute error = 9.575673587391975000000000000000E-15 " "
relative error = 5.654409601107633000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5799999999999361 " "
y[1] (closed_form) = -0.16807568013519303 " "
y[1] (numeric) = -0.16807568013518334 " "
absolute error = 9.686695889854491000000000000000E-15 " "
relative error = 5.763294179183401000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.589999999999935 " "
y[1] (closed_form) = -0.16681115039859482 " "
y[1] (numeric) = -0.1668111503985849 " "
absolute error = 9.908740494779522000000000000000E-15 " "
relative error = 5.9400948144669060000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.599999999999934 " "
y[1] (closed_form) = -0.16555514475562572 " "
y[1] (numeric) = -0.1655551447556157 " "
absolute error = 1.001976279724203800000000000000E-14 " "
relative error = 6.052220734083564000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6099999999999328 " "
y[1] (closed_form) = -0.16430761876977718 " "
y[1] (numeric) = -0.16430761876976702 " "
absolute error = 1.015854067532018200000000000000E-14 " "
relative error = 6.182635200595306000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6199999999999317 " "
y[1] (closed_form) = -0.16306852804490696 " "
y[1] (numeric) = -0.16306852804489663 " "
absolute error = 1.032507412901395600000000000000E-14 " "
relative error = 6.331739332417696000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6299999999999306 " "
y[1] (closed_form) = -0.16183782822883563 " "
y[1] (numeric) = -0.16183782822882517 " "
absolute error = 1.0463852007092100000000000000E-14 " "
relative error = 6.465640401634908000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6399999999999295 " "
y[1] (closed_form) = -0.1606154750168671 " "
y[1] (numeric) = -0.1606154750168565 " "
absolute error = 1.060262988517024500000000000000E-14 " "
relative error = 6.6012505233737940000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6499999999999284 " "
y[1] (closed_form) = -0.1594014241552346 " "
y[1] (numeric) = -0.1594014241552239 " "
absolute error = 1.068589661201713200000000000000E-14 " "
relative error = 6.703764830614418000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6599999999999273 " "
y[1] (closed_form) = -0.15819563144447382 " "
y[1] (numeric) = -0.158195631444463 " "
absolute error = 1.082467449009527600000000000000E-14 " "
relative error = 6.8425874919907030000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6699999999999262 " "
y[1] (closed_form) = -0.1569980527427236 " "
y[1] (numeric) = -0.1569980527427127 " "
absolute error = 1.090794121694216300000000000000E-14 " "
relative error = 6.94781943239593000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.679999999999925 " "
y[1] (closed_form) = -0.15580864396895563 " "
y[1] (numeric) = -0.1558086439689446 " "
absolute error = 1.104671909502030800000000000000E-14 " "
relative error = 7.08992698583612000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.689999999999924 " "
y[1] (closed_form) = -0.15462736110613395 " "
y[1] (numeric) = -0.1546273611061228 " "
absolute error = 1.115774139748282300000000000000E-14 " "
relative error = 7.2158907179592310000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.699999999999923 " "
y[1] (closed_form) = -0.15345416020430613 " "
y[1] (numeric) = -0.15345416020429484 " "
absolute error = 1.129651927556096800000000000000E-14 " "
relative error = 7.361494312386828000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7099999999999218 " "
y[1] (closed_form) = -0.1522889973836259 " "
y[1] (numeric) = -0.15228899738361443 " "
absolute error = 1.146305272925474100000000000000E-14 " "
relative error = 7.527170659859665000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7199999999999207 " "
y[1] (closed_form) = -0.1511318288373094 " "
y[1] (numeric) = -0.15113182883729787 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 7.639899248841239000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7299999999999196 " "
y[1] (closed_form) = -0.14998261083452585 " "
y[1] (numeric) = -0.14998261083451414 " "
absolute error = 1.171285290979540200000000000000E-14 " "
relative error = 7.809473941427824000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7399999999999185 " "
y[1] (closed_form) = -0.14884129972322263 " "
y[1] (numeric) = -0.14884129972321078 " "
absolute error = 1.185163078787354600000000000000E-14 " "
relative error = 7.962595603446226000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7499999999999174 " "
y[1] (closed_form) = -0.14770785193288768 " "
y[1] (numeric) = -0.14770785193287572 " "
absolute error = 1.196265309033606200000000000000E-14 " "
relative error = 8.098860645384915000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7599999999999163 " "
y[1] (closed_form) = -0.14658222397724846 " "
y[1] (numeric) = -0.14658222397723636 " "
absolute error = 1.210143096841420600000000000000E-14 " "
relative error = 8.255728859928139000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7699999999999152 " "
y[1] (closed_form) = -0.14546437245690913 " "
y[1] (numeric) = -0.1454643724568969 " "
absolute error = 1.224020884649235100000000000000E-14 " "
relative error = 8.414575087874706000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.779999999999914 " "
y[1] (closed_form) = -0.14435425406192726 " "
y[1] (numeric) = -0.144354254061915 " "
absolute error = 1.22679644221079800000000000000E-14 " "
relative error = 8.498512566761687000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.789999999999913 " "
y[1] (closed_form) = -0.1432518255743305 " "
y[1] (numeric) = -0.14325182557431812 " "
absolute error = 1.237898672457049500000000000000E-14 " "
relative error = 8.641416383309745000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.799999999999912 " "
y[1] (closed_form) = -0.14215704387057404 " "
y[1] (numeric) = -0.1421570438705616 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 8.747014947161297000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8099999999999108 " "
y[1] (closed_form) = -0.14106986592394058 " "
y[1] (numeric) = -0.141069865923928 " "
absolute error = 1.257327575387989800000000000000E-14 " "
relative error = 8.912800527264216000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8199999999999097 " "
y[1] (closed_form) = -0.1399902488068827 " "
y[1] (numeric) = -0.13999024880686997 " "
absolute error = 1.273980920757367000000000000000E-14 " "
relative error = 9.10049758190537000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8299999999999086 " "
y[1] (closed_form) = -0.13891814969330937 " "
y[1] (numeric) = -0.13891814969329655 " "
absolute error = 1.282307593442055800000000000000E-14 " "
relative error = 9.230669975615251000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8399999999999075 " "
y[1] (closed_form) = -0.13785352586081698 " "
y[1] (numeric) = -0.13785352586080402 " "
absolute error = 1.296185381249870300000000000000E-14 " "
relative error = 9.402627703251903000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8499999999999064 " "
y[1] (closed_form) = -0.1367963346928659 " "
y[1] (numeric) = -0.1367963346928528 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 9.576741745303546000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8599999999999053 " "
y[1] (closed_form) = -0.13574653368090359 " "
y[1] (numeric) = -0.13574653368089035 " "
absolute error = 1.323940956865499200000000000000E-14 " "
relative error = 9.753036935570365000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8699999999999042 " "
y[1] (closed_form) = -0.13470408042643484 " "
y[1] (numeric) = -0.1347040804264215 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 9.89032867699781000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.879999999999903 " "
y[1] (closed_form) = -0.13366893264304028 " "
y[1] (numeric) = -0.13366893264302684 " "
absolute error = 1.343369859796439400000000000000E-14 " "
relative error = 1.004997820536112800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.889999999999902 " "
y[1] (closed_form) = -0.13264104815834366 " "
y[1] (numeric) = -0.13264104815833008 " "
absolute error = 1.357247647604254000000000000000E-14 " "
relative error = 1.023248584392973700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8999999999999009 " "
y[1] (closed_form) = -0.13162038491592895 " "
y[1] (numeric) = -0.13162038491591527 " "
absolute error = 1.368349877850505400000000000000E-14 " "
relative error = 1.039618504933353300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9099999999998998 " "
y[1] (closed_form) = -0.13060690097720803 " "
y[1] (numeric) = -0.13060690097719424 " "
absolute error = 1.37945210809675700000000000000E-14 " "
relative error = 1.056186233480482400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9199999999998987 " "
y[1] (closed_form) = -0.1296005545232397 " "
y[1] (numeric) = -0.12960055452322583 " "
absolute error = 1.387778780781445700000000000000E-14 " "
relative error = 1.070812378763851700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9299999999998976 " "
y[1] (closed_form) = -0.12860130385650084 " "
y[1] (numeric) = -0.12860130385648683 " "
absolute error = 1.401656568589260000000000000000E-14 " "
relative error = 1.089924072739800500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9399999999998965 " "
y[1] (closed_form) = -0.12760910740261044 " "
y[1] (numeric) = -0.1276091074025963 " "
absolute error = 1.415534356397074600000000000000E-14 " "
relative error = 1.109273769881504200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9499999999998954 " "
y[1] (closed_form) = -0.12662392371200734 " "
y[1] (numeric) = -0.1266239237119931 " "
absolute error = 1.423861029081763300000000000000E-14 " "
relative error = 1.124480261976547000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9599999999998943 " "
y[1] (closed_form) = -0.12564571146158243 " "
y[1] (numeric) = -0.1256457114615681 " "
absolute error = 1.43218770176645200000000000000E-14 " "
relative error = 1.139861985822221400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9699999999998932 " "
y[1] (closed_form) = -0.12467442945626588 " "
y[1] (numeric) = -0.12467442945625141 " "
absolute error = 1.446065489574266400000000000000E-14 " "
relative error = 1.159873356454000800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.979999999999892 " "
y[1] (closed_form) = -0.12371003663057033 " "
y[1] (numeric) = -0.12371003663055578 " "
absolute error = 1.45439216225895500000000000000E-14 " "
relative error = 1.17564605255282590000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.989999999999891 " "
y[1] (closed_form) = -0.12275249205009083 " "
y[1] (numeric) = -0.12275249205007618 " "
absolute error = 1.464106613724425200000000000000E-14 " "
relative error = 1.192730664178269100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9999999999998899 " "
y[1] (closed_form) = -0.12180175491296184 " "
y[1] (numeric) = -0.12180175491294712 " "
absolute error = 1.47243328640911400000000000000E-14 " "
relative error = 1.208876906134314600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0099999999998888 " "
y[1] (closed_form) = -0.12085778455127254 " "
y[1] (numeric) = -0.12085778455125772 " "
absolute error = 1.48214773787458400000000000000E-14 " "
relative error = 1.226356865118439800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0199999999998877 " "
y[1] (closed_form) = -0.11992054043244053 " "
y[1] (numeric) = -0.11992054043242562 " "
absolute error = 1.49186218934005400000000000000E-14 " "
relative error = 1.244042249943430200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0299999999998866 " "
y[1] (closed_form) = -0.11898998216054525 " "
y[1] (numeric) = -0.11898998216053024 " "
absolute error = 1.501576640805524200000000000000E-14 " "
relative error = 1.261935344085981200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0399999999998855 " "
y[1] (closed_form) = -0.11806606947762129 " "
y[1] (numeric) = -0.11806606947760616 " "
absolute error = 1.512678871051775800000000000000E-14 " "
relative error = 1.281213881129916700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0499999999998844 " "
y[1] (closed_form) = -0.11714876226491241 " "
y[1] (numeric) = -0.11714876226489719 " "
absolute error = 1.52239332251724600000000000000E-14 " "
relative error = 1.299538546616998700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0599999999998833 " "
y[1] (closed_form) = -0.11623802054408712 " "
y[1] (numeric) = -0.11623802054407181 " "
absolute error = 1.530719995201934600000000000000E-14 " "
relative error = 1.316884086667114400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.069999999999882 " "
y[1] (closed_form) = -0.11533380447841604 " "
y[1] (numeric) = -0.11533380447840065 " "
absolute error = 1.539046667886623300000000000000E-14 " "
relative error = 1.334428075833261600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.079999999999881 " "
y[1] (closed_form) = -0.11443607437391214 " "
y[1] (numeric) = -0.11443607437389666 " "
absolute error = 1.54737334057131200000000000000E-14 " "
relative error = 1.35217268596209800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.08999999999988 " "
y[1] (closed_form) = -0.1135447906804342 " "
y[1] (numeric) = -0.11354479068041859 " "
absolute error = 1.561251128379126400000000000000E-14 " "
relative error = 1.375009033019564000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.099999999999879 " "
y[1] (closed_form) = -0.11265991399275406 " "
y[1] (numeric) = -0.11265991399273836 " "
absolute error = 1.56957780106381500000000000000E-14 " "
relative error = 1.393199892878282700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1099999999998778 " "
y[1] (closed_form) = -0.11178140505158861 " "
y[1] (numeric) = -0.11178140505157283 " "
absolute error = 1.577904473748503700000000000000E-14 " "
relative error = 1.411598353966189400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999998766 " "
y[1] (closed_form) = -0.11090922474459675 " "
y[1] (numeric) = -0.11090922474458088 " "
absolute error = 1.586231146433192400000000000000E-14 " "
relative error = 1.430206684868627600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999998755 " "
y[1] (closed_form) = -0.11004333410734209 " "
y[1] (numeric) = -0.11004333410732611 " "
absolute error = 1.59733337667944400000000000000E-14 " "
relative error = 1.451549418814701300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999998744 " "
y[1] (closed_form) = -0.10918369432422186 " "
y[1] (numeric) = -0.10918369432420577 " "
absolute error = 1.608435606925695500000000000000E-14 " "
relative error = 1.473146349261120500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1499999999998733 " "
y[1] (closed_form) = -0.10833026672936295 " "
y[1] (numeric) = -0.10833026672934679 " "
absolute error = 1.616762279610384200000000000000E-14 " "
relative error = 1.49243819702712900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1599999999998722 " "
y[1] (closed_form) = -0.10748301280748505 " "
y[1] (numeric) = -0.10748301280746882 " "
absolute error = 1.623701173514291400000000000000E-14 " "
relative error = 1.51065841113193820000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.169999999999871 " "
y[1] (closed_form) = -0.10664189419473208 " "
y[1] (numeric) = -0.10664189419471574 " "
absolute error = 1.633415624979761600000000000000E-14 " "
relative error = 1.53168286939566500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.17999999999987 " "
y[1] (closed_form) = -0.10580687267947189 " "
y[1] (numeric) = -0.10580687267945549 " "
absolute error = 1.640354518883668800000000000000E-14 " "
relative error = 1.550328893901730400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.189999999999869 " "
y[1] (closed_form) = -0.10497791020306531 " "
y[1] (numeric) = -0.10497791020304884 " "
absolute error = 1.64729341278757600000000000000E-14 " "
relative error = 1.569180992078346700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.199999999999868 " "
y[1] (closed_form) = -0.10415496886060469 " "
y[1] (numeric) = -0.10415496886058814 " "
absolute error = 1.654232306691483200000000000000E-14 " "
relative error = 1.588241372243524300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2099999999998667 " "
y[1] (closed_form) = -0.10333801090162259 " "
y[1] (numeric) = -0.10333801090160595 " "
absolute error = 1.663946758156953400000000000000E-14 " "
relative error = 1.61019816777877100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999998656 " "
y[1] (closed_form) = -0.1025269987307712 " "
y[1] (numeric) = -0.10252699873075444 " "
absolute error = 1.676436767183986400000000000000E-14 " "
relative error = 1.635117371948235000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999998645 " "
y[1] (closed_form) = -0.10172189490847289 " "
y[1] (numeric) = -0.10172189490845605 " "
absolute error = 1.683375661087893600000000000000E-14 " "
relative error = 1.654880360420495400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2399999999998634 " "
y[1] (closed_form) = -0.10092266215154255 " "
y[1] (numeric) = -0.10092266215152564 " "
absolute error = 1.691702333772582300000000000000E-14 " "
relative error = 1.676236335534204400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2499999999998623 " "
y[1] (closed_form) = -0.10012926333378201 " "
y[1] (numeric) = -0.10012926333376498 " "
absolute error = 1.70280456401883380000000000000E-14 " "
relative error = 1.700606303616272500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2599999999998612 " "
y[1] (closed_form) = -9.93416614865471700E-2 " "
y[1] (numeric) = -9.93416614865301000E-2 " "
absolute error = 1.708355679141959600000000000000E-14 " "
relative error = 1.719676974975201700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.26999999999986 " "
y[1] (closed_form) = -9.85598197992885000E-2 " "
y[1] (numeric) = -9.85598197992713100E-2 " "
absolute error = 1.718070130607429700000000000000E-14 " "
relative error = 1.743174991701671700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.279999999999859 " "
y[1] (closed_form) = -9.77837016200647200E-2 " "
y[1] (numeric) = -9.77837016200474600E-2 " "
absolute error = 1.726396803292118400000000000000E-14 " "
relative error = 1.76552613031563800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999858 " "
y[1] (closed_form) = -9.70132704560312300E-2 " "
y[1] (numeric) = -9.70132704560138800E-2 " "
absolute error = 1.73472347597680700000000000000E-14 " "
relative error = 1.788130085525800300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.299999999999857 " "
y[1] (closed_form) = -9.62484899739025000E-2 " "
y[1] (numeric) = -9.62484899738850900E-2 " "
absolute error = 1.74027459109993300000000000000E-14 " "
relative error = 1.808105863865296600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999998557 " "
y[1] (closed_form) = -9.54893240003900500E-2 " "
y[1] (numeric) = -9.54893240003725600E-2 " "
absolute error = 1.74998904256540300000000000000E-14 " "
relative error = 1.832654132684251600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3199999999998546 " "
y[1] (closed_form) = -9.47357365226154400E-2 " "
y[1] (numeric) = -9.47357365225978600E-2 " "
absolute error = 1.758315715250091700000000000000E-14 " "
relative error = 1.856021581497225600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3299999999998535 " "
y[1] (closed_form) = -9.39876916884995800E-2 " "
y[1] (numeric) = -9.39876916884819200E-2 " "
absolute error = 1.76525460915399900000000000000E-14 " "
relative error = 1.878176362714094600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3399999999998524 " "
y[1] (closed_form) = -9.32451538071281700E-2 " "
y[1] (numeric) = -9.32451538071104500E-2 " "
absolute error = 1.77219350305790600000000000000E-14 " "
relative error = 1.90057437915066190000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3499999999998513 " "
y[1] (closed_form) = -9.25080873490940500E-2 " "
y[1] (numeric) = -9.25080873490762500E-2 " "
absolute error = 1.779132396961813400000000000000E-14 " "
relative error = 1.923218226583772200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.35999999999985 " "
y[1] (closed_form) = -9.1776456946816800E-2 " "
y[1] (numeric) = -9.17764569467989100E-2 " "
absolute error = 1.788846848427283500000000000000E-14 " "
relative error = 1.9491347867829500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.369999999999849 " "
y[1] (closed_form) = -9.10502273948398800E-2 " "
y[1] (numeric) = -9.1050227394821890E-2 " "
absolute error = 1.798561299892753600000000000000E-14 " "
relative error = 1.975350695274248600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.379999999999848 " "
y[1] (closed_form) = -9.03293636501059600E-2 " "
y[1] (numeric) = -9.0329363650087900E-2 " "
absolute error = 1.806887972577442300000000000000E-14 " "
relative error = 2.000332892387560500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.389999999999847 " "
y[1] (closed_form) = -8.96138308322106600E-2 " "
y[1] (numeric) = -8.96138308321925400E-2 " "
absolute error = 1.81243908770056800000000000000E-14 " "
relative error = 2.0224992848415402000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.399999999999846 " "
y[1] (closed_form) = -8.89035942236351900E-2 " "
y[1] (numeric) = -8.89035942236169800E-2 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 2.048022665771147300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4099999999998447 " "
y[1] (closed_form) = -8.8198619269958100E-2 " "
y[1] (numeric) = -8.81986192699398400E-2 " "
absolute error = 1.826316875508382500000000000000E-14 " "
relative error = 2.070686469499478700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4199999999998436 " "
y[1] (closed_form) = -8.74988715800470600E-2 " "
y[1] (numeric) = -8.74988715800287400E-2 " "
absolute error = 1.831867990631508300000000000000E-14 " "
relative error = 2.093590417284011400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4299999999998425 " "
y[1] (closed_form) = -8.68043169262302500E-2 " "
y[1] (numeric) = -8.68043169262118400E-2 " "
absolute error = 1.84019466331619700000000000000E-14 " "
relative error = 2.119934501506494400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4399999999998414 " "
y[1] (closed_form) = -8.61149212444484200E-2 " "
y[1] (numeric) = -8.61149212444299600E-2 " "
absolute error = 1.845745778439322700000000000000E-14 " "
relative error = 2.143351874177452700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4499999999998403 " "
y[1] (closed_form) = -8.54306506343877000E-2 " "
y[1] (numeric) = -8.54306506343691500E-2 " "
absolute error = 1.854072451124011400000000000000E-14 " "
relative error = 2.17026610163461300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.459999999999839 " "
y[1] (closed_form) = -8.47514713595935300E-2 " "
y[1] (numeric) = -8.47514713595749400E-2 " "
absolute error = 1.859623566247137200000000000000E-14 " "
relative error = 2.194208001837404400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.469999999999838 " "
y[1] (closed_form) = -8.4077349847566200E-2 " "
y[1] (numeric) = -8.40773498475475100E-2 " "
absolute error = 1.86795023893182600000000000000E-14 " "
relative error = 2.221704468942532800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.479999999999837 " "
y[1] (closed_form) = -8.34082526898380500E-2 " "
y[1] (numeric) = -8.34082526898192800E-2 " "
absolute error = 1.876276911616514600000000000000E-14 " "
relative error = 2.24950991191919390000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.489999999999836 " "
y[1] (closed_form) = -8.2744146642033200E-2 " "
y[1] (numeric) = -8.27441466420143700E-2 " "
absolute error = 1.881828026739640300000000000000E-14 " "
relative error = 2.27427329075104680000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.499999999999835 " "
y[1] (closed_form) = -8.20849986239096600E-2 " "
y[1] (numeric) = -8.20849986238907500E-2 " "
absolute error = 1.89015469942432900000000000000E-14 " "
relative error = 2.30267982105291300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5099999999998337 " "
y[1] (closed_form) = -8.14307757193843100E-2 " "
y[1] (numeric) = -8.14307757193653600E-2 " "
absolute error = 1.895705814547454800000000000000E-14 " "
relative error = 2.327996752824974500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5199999999998326 " "
y[1] (closed_form) = -8.07814451765413900E-2 " "
y[1] (numeric) = -8.07814451765223600E-2 " "
absolute error = 1.90264470845136200000000000000E-14 " "
relative error = 2.35529917085945200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5299999999998315 " "
y[1] (closed_form) = -8.01369744076242400E-2 " "
y[1] (numeric) = -8.01369744076051300E-2 " "
absolute error = 1.910971381136050700000000000000E-14 " "
relative error = 2.384631308159596300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5399999999998304 " "
y[1] (closed_form) = -7.94973309890111500E-2 " "
y[1] (numeric) = -7.94973309889919900E-2 " "
absolute error = 1.916522496259176500000000000000E-14 " "
relative error = 2.410801057615501200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5499999999998293 " "
y[1] (closed_form) = -7.88624826611754700E-2 " "
y[1] (numeric) = -7.88624826611562400E-2 " "
absolute error = 1.923461390163083700000000000000E-14 " "
relative error = 2.439006895619856800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.559999999999828 " "
y[1] (closed_form) = -7.82323973286301200E-2 " "
y[1] (numeric) = -7.82323973286108300E-2 " "
absolute error = 1.929012505286209500000000000000E-14 " "
relative error = 2.465746380215122800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.569999999999827 " "
y[1] (closed_form) = -7.76070430598570400E-2 " "
y[1] (numeric) = -7.76070430598376800E-2 " "
absolute error = 1.935951399190116700000000000000E-14 " "
relative error = 2.49455632228759080000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.579999999999826 " "
y[1] (closed_form) = -7.69863880872217600E-2 " "
y[1] (numeric) = -7.69863880872023300E-2 " "
absolute error = 1.94289029309402400000000000000E-14 " "
relative error = 2.523680278249741400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.589999999999825 " "
y[1] (closed_form) = -7.6370400806873610E-2 " "
y[1] (numeric) = -7.63704008068540900E-2 " "
absolute error = 1.951216965778712600000000000000E-14 " "
relative error = 2.554938752662793700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.599999999999824 " "
y[1] (closed_form) = -7.57590497786312800E-2 " "
y[1] (numeric) = -7.57590497786117100E-2 " "
absolute error = 1.956768080901838400000000000000E-14 " "
relative error = 2.582883611422708000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6099999999998227 " "
y[1] (closed_form) = -7.51523037258550600E-2 " "
y[1] (numeric) = -7.51523037258354100E-2 " "
absolute error = 1.96509475358652700000000000000E-14 " "
relative error = 2.614816387738310700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6199999999998216 " "
y[1] (closed_form) = -7.45501315353047400E-2 " "
y[1] (numeric) = -7.45501315352850500E-2 " "
absolute error = 1.969258089928871400000000000000E-14 " "
relative error = 2.641521952240002400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6299999999998205 " "
y[1] (closed_form) = -7.3952502256984700E-2 " "
y[1] (numeric) = -7.39525022569649500E-2 " "
absolute error = 1.974809205051997200000000000000E-14 " "
relative error = 2.670375098586308400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6399999999998194 " "
y[1] (closed_form) = -7.33593851039755400E-2 " "
y[1] (numeric) = -7.33593851039557300E-2 " "
absolute error = 1.98036032017512300000000000000E-14 " "
relative error = 2.699532333004523000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6499999999998183 " "
y[1] (closed_form) = -7.27707494522531400E-2 " "
y[1] (numeric) = -7.27707494522332500E-2 " "
absolute error = 1.988686992859811700000000000000E-14 " "
relative error = 2.732810927232023300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.659999999999817 " "
y[1] (closed_form) = -7.21865648404949700E-2 " "
y[1] (numeric) = -7.21865648404750300E-2 " "
absolute error = 1.994238107982937400000000000000E-14 " "
relative error = 2.76261671737594100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.669999999999816 " "
y[1] (closed_form) = -7.16068009698743600E-2 " "
y[1] (numeric) = -7.16068009698543700E-2 " "
absolute error = 1.999789223106063200000000000000E-14 " "
relative error = 2.79273643846677800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.679999999999815 " "
y[1] (closed_form) = -7.10314277038425300E-2 " "
y[1] (numeric) = -7.10314277038224700E-2 " "
absolute error = 2.006728117009970400000000000000E-14 " "
relative error = 2.825127104831392500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.689999999999814 " "
y[1] (closed_form) = -7.04604150678989600E-2 " "
y[1] (numeric) = -7.04604150678788200E-2 " "
absolute error = 2.013667010913877700000000000000E-14 " "
relative error = 2.8578699245149400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6999999999998128 " "
y[1] (closed_form) = -6.98937332493503200E-2 " "
y[1] (numeric) = -6.98937332493301400E-2 " "
absolute error = 2.01783034725622200000000000000E-14 " "
relative error = 2.88699752244952300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7099999999998117 " "
y[1] (closed_form) = -6.93313525970581200E-2 " "
y[1] (numeric) = -6.93313525970378300E-2 " "
absolute error = 2.02754479872169200000000000000E-14 " "
relative error = 2.92442700563687800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7199999999998106 " "
y[1] (closed_form) = -6.87732436211752200E-2 " "
y[1] (numeric) = -6.87732436211548800E-2 " "
absolute error = 2.034483692625599400000000000000E-14 " "
relative error = 2.958248855953601300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7299999999998095 " "
y[1] (closed_form) = -6.8219376992871890E-2 " "
y[1] (numeric) = -6.82193769928514800E-2 " "
absolute error = 2.041422586529506600000000000000E-14 " "
relative error = 2.992438038158587400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7399999999998084 " "
y[1] (closed_form) = -6.76697235440510700E-2 " "
y[1] (numeric) = -6.76697235440305700E-2 " "
absolute error = 2.049749259214195300000000000000E-14 " "
relative error = 3.029049258461750000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7499999999998073 " "
y[1] (closed_form) = -6.71242542670534200E-2 " "
y[1] (numeric) = -6.71242542670328600E-2 " "
absolute error = 2.05530037433732100000000000000E-14 " "
relative error = 3.06193401592265200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.759999999999806 " "
y[1] (closed_form) = -6.6582940314352500E-2 " "
y[1] (numeric) = -6.65829403143318800E-2 " "
absolute error = 2.060851489460446800000000000000E-14 " "
relative error = 3.095164436612021000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.769999999999805 " "
y[1] (closed_form) = -6.60457529982398500E-2 " "
y[1] (numeric) = -6.60457529982191900E-2 " "
absolute error = 2.066402604583572600000000000000E-14 " "
relative error = 3.12874410658720600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.779999999999804 " "
y[1] (closed_form) = -6.55126637905007900E-2 " "
y[1] (numeric) = -6.55126637904800300E-2 " "
absolute error = 2.076117056049042700000000000000E-14 " "
relative error = 3.169031658807431300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.789999999999803 " "
y[1] (closed_form) = -6.49836443220805200E-2 " "
y[1] (numeric) = -6.49836443220597200E-2 " "
absolute error = 2.08028039239138700000000000000E-14 " "
relative error = 3.201236886747727600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7999999999998018 " "
y[1] (closed_form) = -6.4458666382741400E-2 " "
y[1] (numeric) = -6.44586663827205600E-2 " "
absolute error = 2.084443728733731400000000000000E-14 " "
relative error = 3.233768003136711600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8099999999998007 " "
y[1] (closed_form) = -6.39377019207110400E-2 " "
y[1] (numeric) = -6.39377019206901500E-2 " "
absolute error = 2.089994843856857200000000000000E-14 " "
relative error = 3.26879881677426200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8199999999997996 " "
y[1] (closed_form) = -6.3420723042321800E-2 " "
y[1] (numeric) = -6.34207230423008300E-2 " "
absolute error = 2.096933737760764400000000000000E-14 " "
relative error = 3.30638573193409100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8299999999997985 " "
y[1] (closed_form) = -6.2907702011641700E-2 " "
y[1] (numeric) = -6.29077020116206700E-2 " "
absolute error = 2.102484852883890200000000000000E-14 " "
relative error = 3.34217398768564900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8399999999997974 " "
y[1] (closed_form) = -6.23986112500971600E-2 " "
y[1] (numeric) = -6.23986112500760300E-2 " "
absolute error = 2.11289319373975100000000000000E-14 " "
relative error = 3.38612214504447200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8499999999997963 " "
y[1] (closed_form) = -6.189342333608740000E-2 " "
y[1] (numeric) = -6.189342333606622000E-2 " "
absolute error = 2.11775041947248600000000000000E-14 " "
relative error = 3.42160815370139100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.859999999999795 " "
y[1] (closed_form) = -6.13921110045912300E-2 " "
y[1] (numeric) = -6.13921110045699900E-2 " "
absolute error = 2.123995423986002600000000000000E-14 " "
relative error = 3.4597204579382500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.869999999999794 " "
y[1] (closed_form) = -6.08946471467657900E-2 " "
y[1] (numeric) = -6.08946471467444800E-2 " "
absolute error = 2.13024042849951900000000000000E-14 " "
relative error = 3.4982392185725303000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.879999999999793 " "
y[1] (closed_form) = -6.04010048095380700E-2 " "
y[1] (numeric) = -6.04010048095167100E-2 " "
absolute error = 2.13579154362264500000000000000E-14 " "
relative error = 3.53601988966477700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.889999999999792 " "
y[1] (closed_form) = -5.9911157195188900E-2 " "
y[1] (numeric) = -5.99111571951675000E-2 " "
absolute error = 2.1406487693553800000000000000E-14 " "
relative error = 3.57303859510041730000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8999999999997907 " "
y[1] (closed_form) = -5.942507766092994000E-2 " "
y[1] (numeric) = -5.94250776609084500E-2 " "
absolute error = 2.147587663259287200000000000000E-14 " "
relative error = 3.61394170237871900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9099999999997896 " "
y[1] (closed_form) = -5.894273971847355000E-2 " "
y[1] (numeric) = -5.89427397184520100E-2 " "
absolute error = 2.153832667772803700000000000000E-14 " "
relative error = 3.654110206040795400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9199999999997885 " "
y[1] (closed_form) = -5.846411703359600E-2 " "
y[1] (numeric) = -5.84641170335744100E-2 " "
absolute error = 2.158689893505538700000000000000E-14 " "
relative error = 3.692333012170632700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9299999999997874 " "
y[1] (closed_form) = -5.79891834256940900E-2 " "
y[1] (numeric) = -5.79891834256724500E-2 " "
absolute error = 2.164241008628664500000000000000E-14 " "
relative error = 3.732146032719825000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9399999999997863 " "
y[1] (closed_form) = -5.75179128673352200E-2 " "
y[1] (numeric) = -5.75179128673135400E-2 " "
absolute error = 2.169098234361399600000000000000E-14 " "
relative error = 3.771169929904121000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9499999999997852 " "
y[1] (closed_form) = -5.705027948380131000E-2 " "
y[1] (numeric) = -5.70502794837795600E-2 " "
absolute error = 2.174649349484525400000000000000E-14 " "
relative error = 3.81181191251129400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.959999999999784 " "
y[1] (closed_form) = -5.658625755262658000E-2 " "
y[1] (numeric) = -5.658625755260480000E-2 " "
absolute error = 2.178812685826869700000000000000E-14 " "
relative error = 3.85042725930500300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.969999999999783 " "
y[1] (closed_form) = -5.61258215031294700E-2 " "
y[1] (numeric) = -5.612582150310762000E-2 " "
absolute error = 2.184363800949995500000000000000E-14 " "
relative error = 3.891905262942475500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.979999999999782 " "
y[1] (closed_form) = -5.56689459159386700E-2 " "
y[1] (numeric) = -5.56689459159167800E-2 " "
absolute error = 2.189221026682730600000000000000E-14 " "
relative error = 3.93257136570989200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.989999999999781 " "
y[1] (closed_form) = -5.52156055225137700E-2 " "
y[1] (numeric) = -5.521560552249182000E-2 " "
absolute error = 2.19546603119624700000000000000E-14 " "
relative error = 3.976169436919534400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9999999999997797 " "
y[1] (closed_form) = -5.4765775204660200E-2 " "
y[1] (numeric) = -5.4765775204638200E-2 " "
absolute error = 2.20032325692898200000000000000E-14 " "
relative error = 4.01769763818069600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0099999999997786 " "
y[1] (closed_form) = -5.43194299940391400E-2 " "
y[1] (numeric) = -5.43194299940170800E-2 " "
absolute error = 2.206568261442498600000000000000E-14 " "
relative error = 4.062208056462745500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0199999999997775 " "
y[1] (closed_form) = -5.38765450716721200E-2 " "
y[1] (numeric) = -5.38765450716500E-2 " "
absolute error = 2.211425487175233700000000000000E-14 " "
relative error = 4.104616367351262600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0299999999997764 " "
y[1] (closed_form) = -5.34370957674407500E-2 " "
y[1] (numeric) = -5.343709576741859000E-2 " "
absolute error = 2.216282712907968700000000000000E-14 " "
relative error = 4.147461012015461000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0399999999997753 " "
y[1] (closed_form) = -5.30010575595815500E-2 " "
y[1] (numeric) = -5.30010575595593500E-2 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 4.18943725180234600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0499999999997742 " "
y[1] (closed_form) = -5.25684060741761400E-2 " "
y[1] (numeric) = -5.256840607415390000E-2 " "
absolute error = 2.22530327498304810000000000000E-14 " "
relative error = 4.233157215843781000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.059999999999773 " "
y[1] (closed_form) = -5.21391170846369000E-2 " "
y[1] (numeric) = -5.21391170846146200E-2 " "
absolute error = 2.22807883254461100000000000000E-14 " "
relative error = 4.273334412103283500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.069999999999772 " "
y[1] (closed_form) = -5.1713166511188090E-2 " "
y[1] (numeric) = -5.17131665111657600E-2 " "
absolute error = 2.23293605827734600000000000000E-14 " "
relative error = 4.31792560564677900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.079999999999771 " "
y[1] (closed_form) = -5.12905304203429700E-2 " "
y[1] (numeric) = -5.1290530420320600E-2 " "
absolute error = 2.23779328401008120000000000000E-14 " "
relative error = 4.36297551550085370000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.08999999999977 " "
y[1] (closed_form) = -5.08711850243765200E-2 " "
y[1] (numeric) = -5.087118502435409000E-2 " "
absolute error = 2.242650509742816200000000000000E-14 " "
relative error = 4.40848883050037100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0999999999997687 " "
y[1] (closed_form) = -5.04551066807943300E-2 " "
y[1] (numeric) = -5.04551066807718400E-2 " "
absolute error = 2.247507735475551300000000000000E-14 " "
relative error = 4.45447028720893100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1099999999997676 " "
y[1] (closed_form) = -5.00422718917975700E-2 " "
y[1] (numeric) = -5.004227189177506000E-2 " "
absolute error = 2.252364961208286300000000000000E-14 " "
relative error = 4.500924670403445600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1199999999997665 " "
y[1] (closed_form) = -4.96326573037443100E-2 " "
y[1] (numeric) = -4.96326573037217500E-2 " "
absolute error = 2.2558344081602400000000000000E-14 " "
relative error = 4.54506071346306600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1299999999997654 " "
y[1] (closed_form) = -4.92262397066070500E-2 " "
y[1] (numeric) = -4.92262397065844500E-2 " "
absolute error = 2.259997744502584300000000000000E-14 " "
relative error = 4.59104282182100530000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1399999999997643 " "
y[1] (closed_form) = -4.882299603342700000E-2 " "
y[1] (numeric) = -4.882299603340435300E-2 " "
absolute error = 2.264854970235319300000000000000E-14 " "
relative error = 4.63891025590619340000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.149999999999763 " "
y[1] (closed_form) = -4.842290335976484600E-2 " "
y[1] (numeric) = -4.842290335974215300E-2 " "
absolute error = 2.269018306577663700000000000000E-14 " "
relative error = 4.685836967931621000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.159999999999762 " "
y[1] (closed_form) = -4.802593890314829600E-2 " "
y[1] (numeric) = -4.802593890312556500E-2 " "
absolute error = 2.27318164292000800000000000000E-14 " "
relative error = 4.733237277264331600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.169999999999761 " "
y[1] (closed_form) = -4.763208002251663000E-2 " "
y[1] (numeric) = -4.763208002249385600E-2 " "
absolute error = 2.27803886865274300000000000000E-14 " "
relative error = 4.782572727405288700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.17999999999976 " "
y[1] (closed_form) = -4.72413042176620600E-2 " "
y[1] (numeric) = -4.72413042176392350E-2 " "
absolute error = 2.282202204995087400000000000000E-14 " "
relative error = 4.83094665312360840000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.189999999999759 " "
y[1] (closed_form) = -4.685358912866839400E-2 " "
y[1] (numeric) = -4.685358912864552300E-2 " "
absolute error = 2.287059430727822500000000000000E-14 " "
relative error = 4.881289722431178500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1999999999997577 " "
y[1] (closed_form) = -4.64689125353467700E-2 " "
y[1] (numeric) = -4.646891253532386000E-2 " "
absolute error = 2.291222767070166800000000000000E-14 " "
relative error = 4.93065716854755100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2099999999997566 " "
y[1] (closed_form) = -4.60872523566688230E-2 " "
y[1] (numeric) = -4.60872523566458700E-2 " "
absolute error = 2.29538610341251110000000000000E-14 " "
relative error = 4.98052278241397200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2199999999997555 " "
y[1] (closed_form) = -4.57085866501972860E-2 " "
y[1] (numeric) = -4.570858665017430400E-2 " "
absolute error = 2.29816166097407400000000000000E-14 " "
relative error = 5.02785544117049200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2299999999997544 " "
y[1] (closed_form) = -4.53328936115141250E-2 " "
y[1] (numeric) = -4.5332893611491100E-2 " "
absolute error = 2.302324997316418400000000000000E-14 " "
relative error = 5.0787073444869400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2399999999997533 " "
y[1] (closed_form) = -4.496015157364631000E-2 " "
y[1] (numeric) = -4.49601515736232500E-2 " "
absolute error = 2.306488333658762700000000000000E-14 " "
relative error = 5.13007241508217200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.249999999999752 " "
y[1] (closed_form) = -4.45903390064894430E-2 " "
y[1] (numeric) = -4.45903390064663300E-2 " "
absolute error = 2.311345559391497800000000000000E-14 " "
relative error = 5.183511968938198000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.259999999999751 " "
y[1] (closed_form) = -4.42234345162290700E-2 " "
y[1] (numeric) = -4.42234345162059200E-2 " "
absolute error = 2.31550889573384200000000000000E-14 " "
relative error = 5.235931856183850000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.26999999999975 " "
y[1] (closed_form) = -4.385941684476022400E-2 " "
y[1] (numeric) = -4.38594168447370300E-2 " "
absolute error = 2.319672232076186400000000000000E-14 " "
relative error = 5.28888069872573300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.279999999999749 " "
y[1] (closed_form) = -4.34982648691047300E-2 " "
y[1] (numeric) = -4.3498264869081504E-2 " "
absolute error = 2.322447789637749300000000000000E-14 " "
relative error = 5.33917340525300300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.289999999999748 " "
y[1] (closed_form) = -4.31399576008269060E-2 " "
y[1] (numeric) = -4.313995760080363600E-2 " "
absolute error = 2.327305015370484400000000000000E-14 " "
relative error = 5.39477817040291700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2999999999997467 " "
y[1] (closed_form) = -4.278447418544737400E-2 " "
y[1] (numeric) = -4.27844741854240700E-2 " "
absolute error = 2.33077446232243800000000000000E-14 " "
relative error = 5.44771089676082200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3099999999997456 " "
y[1] (closed_form) = -4.24317939018552860E-2 " "
y[1] (numeric) = -4.24317939018319400E-2 " "
absolute error = 2.334937798664782300000000000000E-14 " "
relative error = 5.502802460026771000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3199999999997445 " "
y[1] (closed_form) = -4.20818961617189300E-2 " "
y[1] (numeric) = -4.208189616169555000E-2 " "
absolute error = 2.33840724561673600000000000000E-14 " "
relative error = 5.55680104487292300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3299999999997434 " "
y[1] (closed_form) = -4.17347605088949500E-2 " "
y[1] (numeric) = -4.17347605088715300E-2 " "
absolute error = 2.341876692568689600000000000000E-14 " "
relative error = 5.61133372759995600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3399999999997423 " "
y[1] (closed_form) = -4.13903666188360440E-2 " "
y[1] (numeric) = -4.139036661881257400E-2 " "
absolute error = 2.346733918301424600000000000000E-14 " "
relative error = 5.66975871441898900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.349999999999741 " "
y[1] (closed_form) = -4.10486942979974900E-2 " "
y[1] (numeric) = -4.104869429797397600E-2 " "
absolute error = 2.351591144034159700000000000000E-14 " "
relative error = 5.72878427499429400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.35999999999974 " "
y[1] (closed_form) = -4.07097234832423600E-2 " "
y[1] (numeric) = -4.070972348321882000E-2 " "
absolute error = 2.354366701595722600000000000000E-14 " "
relative error = 5.783303103409355000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.369999999999739 " "
y[1] (closed_form) = -4.037343424124570400E-2 " "
y[1] (numeric) = -4.03734342412221100E-2 " "
absolute error = 2.359223927328457600000000000000E-14 " "
relative error = 5.84350569047768200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.379999999999738 " "
y[1] (closed_form) = -4.003980676789753400E-2 " "
y[1] (numeric) = -4.003980676787389000E-2 " "
absolute error = 2.364081153061192700000000000000E-14 " "
relative error = 5.90432707821314200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.389999999999737 " "
y[1] (closed_form) = -3.97088213877049730E-2 " "
y[1] (numeric) = -3.97088213876812870E-2 " "
absolute error = 2.36824448940353700000000000000E-14 " "
relative error = 5.96402614492309200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3999999999997357 " "
y[1] (closed_form) = -3.938045855319341500E-2 " "
y[1] (numeric) = -3.93804585531696900E-2 " "
absolute error = 2.372407825745881400000000000000E-14 " "
relative error = 6.02432757998827200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4099999999997346 " "
y[1] (closed_form) = -3.90546988443069800E-2 " "
y[1] (numeric) = -3.90546988442832200E-2 " "
absolute error = 2.37587727269783500000000000000E-14 " "
relative error = 6.08346074353142300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4199999999997335 " "
y[1] (closed_form) = -3.87315229678080400E-2 " "
y[1] (numeric) = -3.87315229677842540E-2 " "
absolute error = 2.37865283025939800000000000000E-14 " "
relative error = 6.14138729384958800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4299999999997324 " "
y[1] (closed_form) = -3.84109117566762900E-2 " "
y[1] (numeric) = -3.841091175665247700E-2 " "
absolute error = 2.381428387820960800000000000000E-14 " "
relative error = 6.19987466818472200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4399999999997313 " "
y[1] (closed_form) = -3.80928461695071100E-2 " "
y[1] (numeric) = -3.80928461694832470E-2 " "
absolute error = 2.386285613553695800000000000000E-14 " "
relative error = 6.26439306460615900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.44999999999973 " "
y[1] (closed_form) = -3.77773072899093300E-2 " "
y[1] (numeric) = -3.77773072898854370E-2 " "
absolute error = 2.389061171115258700000000000000E-14 " "
relative error = 6.32406421342105300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.459999999999729 " "
y[1] (closed_form) = -3.746427632590275700E-2 " "
y[1] (numeric) = -3.74642763258788300E-2 " "
absolute error = 2.392530618067212300000000000000E-14 " "
relative error = 6.38616530919888600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.469999999999728 " "
y[1] (closed_form) = -3.715373460931508700E-2 " "
y[1] (numeric) = -3.71537346092911170E-2 " "
absolute error = 2.396693954409556700000000000000E-14 " "
relative error = 6.45074843649409000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.479999999999727 " "
y[1] (closed_form) = -3.684566359517866000E-2 " "
y[1] (numeric) = -3.68456635951546650E-2 " "
absolute error = 2.400163401361510300000000000000E-14 " "
relative error = 6.51410007899973600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4899999999997258 " "
y[1] (closed_form) = -3.65400448611268900E-2 " "
y[1] (numeric) = -3.65400448611028500E-2 " "
absolute error = 2.404326737703854600000000000000E-14 " "
relative error = 6.5799775201198400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4999999999997247 " "
y[1] (closed_form) = -3.62368601067905140E-2 " "
y[1] (numeric) = -3.62368601067664330E-2 " "
absolute error = 2.40849007404619900000000000000E-14 " "
relative error = 6.64651977833715800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5099999999997236 " "
y[1] (closed_form) = -3.59360911531937170E-2 " "
y[1] (numeric) = -3.593609115316958600E-2 " "
absolute error = 2.41334729977893400000000000000E-14 " "
relative error = 6.71566445413041100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5199999999997225 " "
y[1] (closed_form) = -3.563771994215022600E-2 " "
y[1] (numeric) = -3.56377199421260600E-2 " "
absolute error = 2.41612285734049700000000000000E-14 " "
relative error = 6.77967855761402800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5299999999997214 " "
y[1] (closed_form) = -3.53417285356593670E-2 " "
y[1] (numeric) = -3.53417285356351700E-2 " "
absolute error = 2.419592304292450500000000000000E-14 " "
relative error = 6.84627607235201200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5399999999997203 " "
y[1] (closed_form) = -3.504809911530222000E-2 " "
y[1] (numeric) = -3.504809911527800000E-2 " "
absolute error = 2.42306175124440410000000000000E-14 " "
relative error = 6.91353258067704900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.549999999999719 " "
y[1] (closed_form) = -3.47568139816378600E-2 " "
y[1] (numeric) = -3.4756813981613600E-2 " "
absolute error = 2.42583730880596700000000000000E-14 " "
relative error = 6.97945821526548700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.559999999999718 " "
y[1] (closed_form) = -3.44678555535997400E-2 " "
y[1] (numeric) = -3.44678555535754500E-2 " "
absolute error = 2.429306755757920700000000000000E-14 " "
relative error = 7.04803567480486800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.569999999999717 " "
y[1] (closed_form) = -3.41812063678924100E-2 " "
y[1] (numeric) = -3.41812063678680830E-2 " "
absolute error = 2.432776202709874300000000000000E-14 " "
relative error = 7.11729181388713300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.579999999999716 " "
y[1] (closed_form) = -3.38968490783884250E-2 " "
y[1] (numeric) = -3.38968490783640700E-2 " "
absolute error = 2.435551760271437200000000000000E-14 " "
relative error = 7.18518631227074500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5899999999997148 " "
y[1] (closed_form) = -3.36147664555256460E-2 " "
y[1] (numeric) = -3.36147664555012600E-2 " "
absolute error = 2.439021207223390800000000000000E-14 " "
relative error = 7.25580292354659700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5999999999997137 " "
y[1] (closed_form) = -3.33349413857049140E-2 " "
y[1] (numeric) = -3.333494138568049400E-2 " "
absolute error = 2.441796764784953700000000000000E-14 " "
relative error = 7.32503692306498000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6099999999997125 " "
y[1] (closed_form) = -3.30573568706881600E-2 " "
y[1] (numeric) = -3.30573568706637200E-2 " "
absolute error = 2.443878432956125800000000000000E-14 " "
relative error = 7.39284281715548800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6199999999997114 " "
y[1] (closed_form) = -3.278199602699704600E-2 " "
y[1] (numeric) = -3.27819960269725930E-2 " "
absolute error = 2.445266211736907300000000000000E-14 " "
relative error = 7.459174266640600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6299999999997103 " "
y[1] (closed_form) = -3.25088420853121500E-2 " "
y[1] (numeric) = -3.25088420852876500E-2 " "
absolute error = 2.450123437469642300000000000000E-14 " "
relative error = 7.5367908553612710000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6399999999997092 " "
y[1] (closed_form) = -3.223787838987266500E-2 " "
y[1] (numeric) = -3.22378783898481400E-2 " "
absolute error = 2.452898995031205200000000000000E-14 " "
relative error = 7.60874821030954800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.649999999999708 " "
y[1] (closed_form) = -3.19690883978768900E-2 " "
y[1] (numeric) = -3.196908839785233500E-2 " "
absolute error = 2.45567455259276800000000000000E-14 " "
relative error = 7.68140311675528700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.659999999999707 " "
y[1] (closed_form) = -3.17024556788832400E-2 " "
y[1] (numeric) = -3.17024556788586430E-2 " "
absolute error = 2.459837888935112500000000000000E-14 " "
relative error = 7.75913990339111600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.669999999999706 " "
y[1] (closed_form) = -3.14379639142121200E-2 " "
y[1] (numeric) = -3.1437963914187506E-2 " "
absolute error = 2.461919557106284600000000000000E-14 " "
relative error = 7.83104008842419800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.679999999999705 " "
y[1] (closed_form) = -3.117559689634855600E-2 " "
y[1] (numeric) = -3.117559689632390000E-2 " "
absolute error = 2.465735948753433600000000000000E-14 " "
relative error = 7.90918601158277600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6899999999997037 " "
y[1] (closed_form) = -3.091533852834556000E-2 " "
y[1] (numeric) = -3.091533852832088000E-2 " "
absolute error = 2.468511506314996500000000000000E-14 " "
relative error = 7.98474680796936800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6999999999997026 " "
y[1] (closed_form) = -3.065717282322849600E-2 " "
y[1] (numeric) = -3.06571728232037800E-2 " "
absolute error = 2.471634008571754700000000000000E-14 " "
relative error = 8.06217201704598700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7099999999997015 " "
y[1] (closed_form) = -3.04010839034002300E-2 " "
y[1] (numeric) = -3.040108390337549000E-2 " "
absolute error = 2.473368732047731600000000000000E-14 " "
relative error = 8.13579127608373100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7199999999997004 " "
y[1] (closed_form) = -3.014705600004733400E-2 " "
y[1] (numeric) = -3.014705600002257600E-2 " "
absolute error = 2.476144289609294400000000000000E-14 " "
relative error = 8.21355255917993100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7299999999996993 " "
y[1] (closed_form) = -2.989507345254718300E-2 " "
y[1] (numeric) = -2.989507345252239700E-2 " "
absolute error = 2.478919847170857300000000000000E-14 " "
relative error = 8.2920680931113200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7399999999996982 " "
y[1] (closed_form) = -2.964512070787616000E-2 " "
y[1] (numeric) = -2.964512070785133600E-2 " "
absolute error = 2.482042349427615600000000000000E-14 " "
relative error = 8.37251557814768200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.749999999999697 " "
y[1] (closed_form) = -2.93971823200188700E-2 " "
y[1] (numeric) = -2.93971823199940200E-2 " "
absolute error = 2.484817906989178500000000000000E-14 " "
relative error = 8.45257167826274600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.759999999999696 " "
y[1] (closed_form) = -2.915124294937850300E-2 " "
y[1] (numeric) = -2.91512429493536230E-2 " "
absolute error = 2.48828735394113200000000000000E-14 " "
relative error = 8.53578476314740300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.769999999999695 " "
y[1] (closed_form) = -2.890728736218828300E-2 " "
y[1] (numeric) = -2.89072873621633800E-2 " "
absolute error = 2.490369022112304300000000000000E-14 " "
relative error = 8.61502150274325600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.779999999999694 " "
y[1] (closed_form) = -2.866530042992416000E-2 " "
y[1] (numeric) = -2.866530042989924000E-2 " "
absolute error = 2.492797634978671800000000000000E-14 " "
relative error = 8.6962201602338710000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7899999999996927 " "
y[1] (closed_form) = -2.842526712871865600E-2 " "
y[1] (numeric) = -2.842526712869370400E-2 " "
absolute error = 2.495573192540234700000000000000E-14 " "
relative error = 8.77941861105292300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7999999999996916 " "
y[1] (closed_form) = -2.818717253877597000E-2 " "
y[1] (numeric) = -2.818717253875098000E-2 " "
absolute error = 2.498348750101797600000000000000E-14 " "
relative error = 8.86342447673642700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8099999999996905 " "
y[1] (closed_form) = -2.795100184378837600E-2 " "
y[1] (numeric) = -2.79510018437633730E-2 " "
absolute error = 2.500430418272970000000000000000E-14 " "
relative error = 8.9457631330973100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8199999999996894 " "
y[1] (closed_form) = -2.771674033035393400E-2 " "
y[1] (numeric) = -2.771674033032890400E-2 " "
absolute error = 2.503205975834532600000000000000E-14 " "
relative error = 9.03138661328493700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8299999999996883 " "
y[1] (closed_form) = -2.74843733873955100E-2 " "
y[1] (numeric) = -2.74843733873704530E-2 " "
absolute error = 2.505981533396095500000000000000E-14 " "
relative error = 9.11784124773007500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.839999999999687 " "
y[1] (closed_form) = -2.725388650558120400E-2 " "
y[1] (numeric) = -2.72538865055561200E-2 " "
absolute error = 2.50841014626246300000000000000E-14 " "
relative error = 9.20386215649932000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.849999999999686 " "
y[1] (closed_form) = -2.702526527674615000E-2 " "
y[1] (numeric) = -2.702526527672105000E-2 " "
absolute error = 2.5101448697384400000000000000E-14 " "
relative error = 9.28814146330800300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.859999999999685 " "
y[1] (closed_form) = -2.67984953933158200E-2 " "
y[1] (numeric) = -2.679849539329068300E-2 " "
absolute error = 2.513614316690393500000000000000E-14 " "
relative error = 9.37968449272472500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.869999999999684 " "
y[1] (closed_form) = -2.657356264773063600E-2 " "
y[1] (numeric) = -2.657356264770548000E-2 " "
absolute error = 2.515695984861565600000000000000E-14 " "
relative error = 9.46691272905556200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.879999999999683 " "
y[1] (closed_form) = -2.63504529318722800E-2 " "
y[1] (numeric) = -2.6350452931847100E-2 " "
absolute error = 2.518124597727933000000000000000E-14 " "
relative error = 9.55628582263239500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8899999999996817 " "
y[1] (closed_form) = -2.612915223649134300E-2 " "
y[1] (numeric) = -2.61291522364661300E-2 " "
absolute error = 2.521247099984691400000000000000E-14 " "
relative error = 9.64917298948405400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8999999999996806 " "
y[1] (closed_form) = -2.590964665063660300E-2 " "
y[1] (numeric) = -2.590964665061136000E-2 " "
absolute error = 2.524022657546254300000000000000E-14 " "
relative error = 9.74163288129689200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9099999999996795 " "
y[1] (closed_form) = -2.56919223610858600E-2 " "
y[1] (numeric) = -2.5691922361060600E-2 " "
absolute error = 2.526104325717426500000000000000E-14 " "
relative error = 9.83229004904505600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9199999999996784 " "
y[1] (closed_form) = -2.54759656517783700E-2 " "
y[1] (numeric) = -2.54759656517530900E-2 " "
absolute error = 2.528185993888598700000000000000E-14 " "
relative error = 9.92380830012665900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9299999999996773 " "
y[1] (closed_form) = -2.526176290324886000E-2 " "
y[1] (numeric) = -2.52617629032235500E-2 " "
absolute error = 2.530614606754966000000000000000E-14 " "
relative error = 1.00175693060182650000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.939999999999676 " "
y[1] (closed_form) = -2.50493005920632400E-2 " "
y[1] (numeric) = -2.504930059203791000E-2 " "
absolute error = 2.532696274926138400000000000000E-14 " "
relative error = 1.01108462714069240000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.949999999999675 " "
y[1] (closed_form) = -2.483856529025595400E-2 " "
y[1] (numeric) = -2.483856529023060200E-2 " "
absolute error = 2.53512488779250600000000000000E-14 " "
relative error = 1.02064062805874820000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.959999999999674 " "
y[1] (closed_form) = -2.462954366476902400E-2 " "
y[1] (numeric) = -2.46295436647436500E-2 " "
absolute error = 2.537553500658873400000000000000E-14 " "
relative error = 1.03028847598531840000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.969999999999673 " "
y[1] (closed_form) = -2.442222247689278300E-2 " "
y[1] (numeric) = -2.44222224768673900E-2 " "
absolute error = 2.539288224134850000000000000000E-14 " "
relative error = 1.03974493989538080000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.979999999999672 " "
y[1] (closed_form) = -2.421658858170839300E-2 " "
y[1] (numeric) = -2.42165885816829800E-2 " "
absolute error = 2.541369892306022400000000000000E-14 " "
relative error = 1.04943348388286410000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9899999999996707 " "
y[1] (closed_form) = -2.401262892753207300E-2 " "
y[1] (numeric) = -2.40126289275066320E-2 " "
absolute error = 2.544145449867585300000000000000E-14 " "
relative error = 1.05950308795658500000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9999999999996696 " "
y[1] (closed_form) = -2.38103305553610920E-2 " "
y[1] (numeric) = -2.381033055533563200E-2 " "
absolute error = 2.54588017334356200000000000000E-14 " "
relative error = 1.06923344361984770000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.009999999999673 " "
y[1] (closed_form) = -2.360968059832153000E-2 " "
y[1] (numeric) = -2.360968059829614300E-2 " "
absolute error = 2.53894127943965500000000000000E-14 " "
relative error = 1.07538146010334180000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.019999999999676 " "
y[1] (closed_form) = -2.341066628111814200E-2 " "
y[1] (numeric) = -2.341066628109282300E-2 " "
absolute error = 2.532002385535747600000000000000E-14 " "
relative error = 1.08155930084652590000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.02999999999968 " "
y[1] (closed_form) = -2.32132749194855380E-2 " "
y[1] (numeric) = -2.321327491946028600E-2 " "
absolute error = 2.525410436327036000000000000000E-14 " "
relative error = 1.08791648101628770000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.039999999999683 " "
y[1] (closed_form) = -2.30174939196415820E-2 " "
y[1] (numeric) = -2.301749391961639700E-2 " "
absolute error = 2.518471542423128500000000000000E-14 " "
relative error = 1.09415540684645720000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.049999999999686 " "
y[1] (closed_form) = -2.28233107777425730E-2 " "
y[1] (numeric) = -2.28233107777174480E-2 " "
absolute error = 2.51222653790961200000000000000E-14 " "
relative error = 1.10072835723708860000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.05999999999969 " "
y[1] (closed_form) = -2.263071307934026400E-2 " "
y[1] (numeric) = -2.263071307931520700E-2 " "
absolute error = 2.505634588700900000000000000000E-14 " "
relative error = 1.10718322481332320000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.069999999999693 " "
y[1] (closed_form) = -2.24396884988408700E-2 " "
y[1] (numeric) = -2.243968849881587700E-2 " "
absolute error = 2.499389584187383700000000000000E-14 " "
relative error = 1.11382543671071480000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.079999999999696 " "
y[1] (closed_form) = -2.22502247989658790E-2 " "
y[1] (numeric) = -2.225022479894094900E-2 " "
absolute error = 2.49314457967386720000000000000E-14 " "
relative error = 1.1205030970247730000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0899999999997 " "
y[1] (closed_form) = -2.206230983021489600E-2 " "
y[1] (numeric) = -2.206230983019002400E-2 " "
absolute error = 2.48724651985554600000000000000E-14 " "
relative error = 1.12737357919305380000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.099999999999703 " "
y[1] (closed_form) = -2.18759315303303610E-2 " "
y[1] (numeric) = -2.18759315303055500E-2 " "
absolute error = 2.481001515342029500000000000000E-14 " "
relative error = 1.13412382549387280000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.109999999999706 " "
y[1] (closed_form) = -2.169107792376429600E-2 " "
y[1] (numeric) = -2.169107792373954300E-2 " "
absolute error = 2.475450400218903700000000000000E-14 " "
relative error = 1.14122977609464550000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.11999999999971 " "
y[1] (closed_form) = -2.150773712114693600E-2 " "
y[1] (numeric) = -2.150773712112224700E-2 " "
absolute error = 2.46885845101019190000000000000E-14 " "
relative error = 1.14789316844622850000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.129999999999713 " "
y[1] (closed_form) = -2.13258973187574600E-2 " "
y[1] (numeric) = -2.13258973187328300E-2 " "
absolute error = 2.462960391191870700000000000000E-14 " "
relative error = 1.15491524430512120000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.139999999999716 " "
y[1] (closed_form) = -2.114554679799662600E-2 " "
y[1] (numeric) = -2.114554679797205300E-2 " "
absolute error = 2.457062331373549600000000000000E-14 " "
relative error = 1.16197625667752280000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.14999999999972 " "
y[1] (closed_form) = -2.09666739248614700E-2 " "
y[1] (numeric) = -2.096667392483696500E-2 " "
absolute error = 2.450470382164837700000000000000E-14 " "
relative error = 1.16874540565977150000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.159999999999723 " "
y[1] (closed_form) = -2.07892671494220300E-2 " "
y[1] (numeric) = -2.078926714939758300E-2 " "
absolute error = 2.444572322346516600000000000000E-14 " "
relative error = 1.1758819129006569000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.169999999999726 " "
y[1] (closed_form) = -2.06133150053000900E-2 " "
y[1] (numeric) = -2.061331500527570400E-2 " "
absolute error = 2.438674262528195400000000000000E-14 " "
relative error = 1.18305777692775950000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.17999999999973 " "
y[1] (closed_form) = -2.043880610914998700E-2 " "
y[1] (numeric) = -2.04388061091256600E-2 " "
absolute error = 2.432776202709874300000000000000E-14 " "
relative error = 1.19027314497629850000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.189999999999733 " "
y[1] (closed_form) = -2.02657291601414690E-2 " "
y[1] (numeric) = -2.0265729160117202E-2 " "
absolute error = 2.42687814289155300000000000000E-14 " "
relative error = 1.19752816378535450000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.199999999999736 " "
y[1] (closed_form) = -2.009407293944463800E-2 " "
y[1] (numeric) = -2.009407293942042400E-2 " "
absolute error = 2.421327027768427300000000000000E-14 " "
relative error = 1.20499563979155540000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.20999999999974 " "
y[1] (closed_form) = -1.99238263097169400E-2 " "
y[1] (numeric) = -1.992382630969278800E-2 " "
absolute error = 2.415428967950106200000000000000E-14 " "
relative error = 1.21233187360807820000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.219999999999743 " "
y[1] (closed_form) = -1.975497821459231100E-2 " "
y[1] (numeric) = -1.975497821456821400E-2 " "
absolute error = 2.409877852826980400000000000000E-14 " "
relative error = 1.21988383214054270000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.229999999999746 " "
y[1] (closed_form) = -1.958751767817234500E-2 " "
y[1] (numeric) = -1.9587517678148300E-2 " "
absolute error = 2.404326737703854600000000000000E-14 " "
relative error = 1.22747903905309740000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.23999999999975 " "
y[1] (closed_form) = -1.942143380451959400E-2 " "
y[1] (numeric) = -1.942143380449560800E-2 " "
absolute error = 2.39877562258072890000000000000E-14 " "
relative error = 1.23511767808950620000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.249999999999753 " "
y[1] (closed_form) = -1.925671577715304700E-2 " "
y[1] (numeric) = -1.925671577712911600E-2 " "
absolute error = 2.39322450745760300000000000000E-14 " "
relative error = 1.24279993284058450000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.259999999999756 " "
y[1] (closed_form) = -1.90933528585456370E-2 " "
y[1] (numeric) = -1.909335285852176400E-2 " "
absolute error = 2.38732644763928200000000000000E-14 " "
relative error = 1.25034427705073450000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.26999999999976 " "
y[1] (closed_form) = -1.89313343896239380E-2 " "
y[1] (numeric) = -1.893133438960012400E-2 " "
absolute error = 2.381428387820960800000000000000E-14 " "
relative error = 1.25792949340443550000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.279999999999763 " "
y[1] (closed_form) = -1.87706497892700E-2 " "
y[1] (numeric) = -1.877064978924623800E-2 " "
absolute error = 2.376224217393030400000000000000E-14 " "
relative error = 1.26592539100663840000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.2899999999997664 " "
y[1] (closed_form) = -1.861128855382530600E-2 " "
y[1] (numeric) = -1.8611288553801597E-2 " "
absolute error = 2.370673102269904600000000000000E-14 " "
relative error = 1.27378235817134980000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.29999999999977 " "
y[1] (closed_form) = -1.845324025659689200E-2 " "
y[1] (numeric) = -1.84532402565732420E-2 " "
absolute error = 2.365121987146778800000000000000E-14 " "
relative error = 1.28168384211074570000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.309999999999773 " "
y[1] (closed_form) = -1.829649454736565500E-2 " "
y[1] (numeric) = -1.82964945473420510E-2 " "
absolute error = 2.36061170610923900000000000000E-14 " "
relative error = 1.29019889574919780000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3199999999997765 " "
y[1] (closed_form) = -1.814104115189676700E-2 " "
y[1] (numeric) = -1.81410411518732080E-2 " "
absolute error = 2.35575448037650400000000000000E-14 " "
relative error = 1.298577331174950000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.32999999999978 " "
y[1] (closed_form) = -1.798686987145232700E-2 " "
y[1] (numeric) = -1.798686987142881800E-2 " "
absolute error = 2.35089725464376900000000000000E-14 " "
relative error = 1.30700742899962340000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.339999999999783 " "
y[1] (closed_form) = -1.783397058230612500E-2 " "
y[1] (numeric) = -1.783397058228266800E-2 " "
absolute error = 2.345693084215838600000000000000E-14 " "
relative error = 1.31529491617705440000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3499999999997865 " "
y[1] (closed_form) = -1.76823332352606500E-2 " "
y[1] (numeric) = -1.768233323523724400E-2 " "
absolute error = 2.34048891378790800000000000000E-14 " "
relative error = 1.3236312666705650000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.35999999999979 " "
y[1] (closed_form) = -1.753194785516622000E-2 " "
y[1] (numeric) = -1.75319478551428680E-2 " "
absolute error = 2.334937798664782300000000000000E-14 " "
relative error = 1.33181881326251800000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.369999999999793 " "
y[1] (closed_form) = -1.738280454044236500E-2 " "
y[1] (numeric) = -1.738280454041907200E-2 " "
absolute error = 2.329386683541656600000000000000E-14 " "
relative error = 1.34005227874602640000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3799999999997965 " "
y[1] (closed_form) = -1.72348934626013500E-2 " "
y[1] (numeric) = -1.723489346257810500E-2 " "
absolute error = 2.324529457808921500000000000000E-14 " "
relative error = 1.34873445133444320000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3899999999998 " "
y[1] (closed_form) = -1.708820486577393400E-2 " "
y[1] (numeric) = -1.70882048657507420E-2 " "
absolute error = 2.31932528738099100000000000000E-14 " "
relative error = 1.35726678466172950000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.399999999999803 " "
y[1] (closed_form) = -1.694272906623730500E-2 " "
y[1] (numeric) = -1.694272906621416300E-2 " "
absolute error = 2.314121116953060700000000000000E-14 " "
relative error = 1.3658490954474010000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4099999999998065 " "
y[1] (closed_form) = -1.679845645194522600E-2 " "
y[1] (numeric) = -1.679845645192213400E-2 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 1.37468814341743740000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.41999999999981 " "
y[1] (closed_form) = -1.66553774820604130E-2 " "
y[1] (numeric) = -1.665537748203737600E-2 " "
absolute error = 2.303712776097199800000000000000E-14 " "
relative error = 1.3831645536575440000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.429999999999813 " "
y[1] (closed_form) = -1.651348268648908700E-2 " "
y[1] (numeric) = -1.651348268646609700E-2 " "
absolute error = 2.2992024950596600000000000000E-14 " "
relative error = 1.3923183490184110000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4399999999998165 " "
y[1] (closed_form) = -1.637276266541774800E-2 " "
y[1] (numeric) = -1.6372762665394802E-2 " "
absolute error = 2.294692214022120400000000000000E-14 " "
relative error = 1.40153024930174290000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.44999999999982 " "
y[1] (closed_form) = -1.623320808885217500E-2 " "
y[1] (numeric) = -1.623320808882927300E-2 " "
absolute error = 2.290181932984580700000000000000E-14 " "
relative error = 1.41080057647835880000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.459999999999823 " "
y[1] (closed_form) = -1.60948096961586400E-2 " "
y[1] (numeric) = -1.609480969613578000E-2 " "
absolute error = 2.28567165194704100000000000000E-14 " "
relative error = 1.42012965365633630000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.469999999999827 " "
y[1] (closed_form) = -1.59575582956073300E-2 " "
y[1] (numeric) = -1.595755829558451500E-2 " "
absolute error = 2.281508315604696700000000000000E-14 " "
relative error = 1.42973522223179500000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.47999999999983 " "
y[1] (closed_form) = -1.582144476391798600E-2 " "
y[1] (numeric) = -1.58214447638952180E-2 " "
absolute error = 2.276651089871961600000000000000E-14 " "
relative error = 1.43896535609948750000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.489999999999833 " "
y[1] (closed_form) = -1.568646004580778700E-2 " "
y[1] (numeric) = -1.568646004578506000E-2 " "
absolute error = 2.272487753529617300000000000000E-14 " "
relative error = 1.44869380784031030000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.499999999999837 " "
y[1] (closed_form) = -1.55525951535414100E-2 " "
y[1] (numeric) = -1.555259515351873000E-2 " "
absolute error = 2.2678040001444800000000000000E-14 " "
relative error = 1.45815150317732600000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.50999999999984 " "
y[1] (closed_form) = -1.541984116648336400E-2 " "
y[1] (numeric) = -1.541984116646072700E-2 " "
absolute error = 2.263640663802135600000000000000E-14 " "
relative error = 1.46800517551529300000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.519999999999843 " "
y[1] (closed_form) = -1.5288189230652500E-2 " "
y[1] (numeric) = -1.52881892306299100E-2 " "
absolute error = 2.258956910416998200000000000000E-14 " "
relative error = 1.4775830389957740000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.529999999999847 " "
y[1] (closed_form) = -1.515763055827877300E-2 " "
y[1] (numeric) = -1.51576305582562300E-2 " "
absolute error = 2.254446629379458500000000000000E-14 " "
relative error = 1.48733446214529080000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.53999999999985 " "
y[1] (closed_form) = -1.502815642736222000E-2 " "
y[1] (numeric) = -1.502815642733971700E-2 " "
absolute error = 2.250109820689516500000000000000E-14 " "
relative error = 1.49726270921207200000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.549999999999853 " "
y[1] (closed_form) = -1.489975818123411800E-2 " "
y[1] (numeric) = -1.489975818121166400E-2 " "
absolute error = 2.245599539651976800000000000000E-14 " "
relative error = 1.50713824502216040000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.559999999999857 " "
y[1] (closed_form) = -1.477242722812046300E-2 " "
y[1] (numeric) = -1.477242722809804800E-2 " "
absolute error = 2.2416096756572300000000000000E-14 " "
relative error = 1.51742813895210940000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.56999999999986 " "
y[1] (closed_form) = -1.464615504070753400E-2 " "
y[1] (numeric) = -1.464615504068516000E-2 " "
absolute error = 2.23727286696728800000000000000E-14 " "
relative error = 1.52754962701747350000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.579999999999863 " "
y[1] (closed_form) = -1.452093315570980300E-2 " "
y[1] (numeric) = -1.452093315568747000E-2 " "
absolute error = 2.233283002972541500000000000000E-14 " "
relative error = 1.53797485259711990000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.589999999999867 " "
y[1] (closed_form) = -1.439675317343997500E-2 " "
y[1] (numeric) = -1.439675317341768400E-2 " "
absolute error = 2.228946194282599400000000000000E-14 " "
relative error = 1.54822838693567250000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.59999999999987 " "
y[1] (closed_form) = -1.427360675738128200E-2 " "
y[1] (numeric) = -1.427360675735903400E-2 " "
absolute error = 2.22478285794025500000000000000E-14 " "
relative error = 1.5586690146061072000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.609999999999873 " "
y[1] (closed_form) = -1.415148563376199800E-2 " "
y[1] (numeric) = -1.415148563373979400E-2 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 1.5690550848971432000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.619999999999877 " "
y[1] (closed_form) = -1.403038159113214600E-2 " "
y[1] (numeric) = -1.403038159110997800E-2 " "
absolute error = 2.21662965760316400000000000000E-14 " "
relative error = 1.57987838264083830000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.62999999999988 " "
y[1] (closed_form) = -1.391028647994241600E-2 " "
y[1] (numeric) = -1.391028647992029000E-2 " "
absolute error = 2.212639793608417400000000000000E-14 " "
relative error = 1.5906500536842840000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.639999999999883 " "
y[1] (closed_form) = -1.379119221212532800E-2 " "
y[1] (numeric) = -1.379119221210323700E-2 " "
absolute error = 2.208823401961268500000000000000E-14 " "
relative error = 1.6016188941368340000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.649999999999887 " "
y[1] (closed_form) = -1.367309076067855000E-2 " "
y[1] (numeric) = -1.367309076065650300E-2 " "
absolute error = 2.204486593271326500000000000000E-14 " "
relative error = 1.61228110882657930000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.65999999999989 " "
y[1] (closed_form) = -1.355597415925047000E-2 " "
y[1] (numeric) = -1.35559741592284600E-2 " "
absolute error = 2.200843673971775200000000000000E-14 " "
relative error = 1.62352306674318940000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.669999999999893 " "
y[1] (closed_form) = -1.343983450172791800E-2 " "
y[1] (numeric) = -1.343983450170595000E-2 " "
absolute error = 2.197027282324626200000000000000E-14 " "
relative error = 1.6347130480231442000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.679999999999897 " "
y[1] (closed_form) = -1.332466394182615400E-2 " "
y[1] (numeric) = -1.332466394180422000E-2 " "
absolute error = 2.193210890677477200000000000000E-14 " "
relative error = 1.64597839033897330000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.6899999999999 " "
y[1] (closed_form) = -1.32104546926809700E-2 " "
y[1] (numeric) = -1.321045469265907700E-2 " "
absolute error = 2.189221026682730600000000000000E-14 " "
relative error = 1.65718824795306360000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.699999999999903 " "
y[1] (closed_form) = -1.309719902644306800E-2 " "
y[1] (numeric) = -1.30971990264212080E-2 " "
absolute error = 2.18575157973077700000000000000E-14 " "
relative error = 1.6688694852370908000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.709999999999907 " "
y[1] (closed_form) = -1.298488927387456400E-2 " "
y[1] (numeric) = -1.298488927385274300E-2 " "
absolute error = 2.182108660431225600000000000000E-14 " "
relative error = 1.68049847357697620000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.71999999999991 " "
y[1] (closed_form) = -1.287351782394771000E-2 " "
y[1] (numeric) = -1.287351782392592600E-2 " "
absolute error = 2.178465741131674300000000000000E-14 " "
relative error = 1.69220703379089300000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.729999999999913 " "
y[1] (closed_form) = -1.276307712344580000E-2 " "
y[1] (numeric) = -1.276307712342405500E-2 " "
absolute error = 2.17482282183212300000000000000E-14 " "
relative error = 1.7039956750217930000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.739999999999917 " "
y[1] (closed_form) = -1.265355967656624000E-2 " "
y[1] (numeric) = -1.265355967654452600E-2 " "
absolute error = 2.171353374880169400000000000000E-14 " "
relative error = 1.71600200289994900000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.74999999999992 " "
y[1] (closed_form) = -1.254495804452578400E-2 " "
y[1] (numeric) = -1.25449580445041120E-2 " "
absolute error = 2.167363510885422800000000000000E-14 " "
relative error = 1.72767697045522640000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.759999999999923 " "
y[1] (closed_form) = -1.243726484516800300E-2 " "
y[1] (numeric) = -1.243726484514636500E-2 " "
absolute error = 2.163894063933469200000000000000E-14 " "
relative error = 1.73984721791476730000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.769999999999927 " "
y[1] (closed_form) = -1.233047275257282600E-2 " "
y[1] (numeric) = -1.23304727525512190E-2 " "
absolute error = 2.160598089329113200000000000000E-14 " "
relative error = 1.75224270203126780000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.77999999999993 " "
y[1] (closed_form) = -1.222457449666832500E-2 " "
y[1] (numeric) = -1.22245744966467500E-2 " "
absolute error = 2.15747558707235500000000000000E-14 " "
relative error = 1.76486763417438500000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.789999999999933 " "
y[1] (closed_form) = -1.211956286284460400E-2 " "
y[1] (numeric) = -1.211956286282306900E-2 " "
absolute error = 2.15365919542520600000000000000E-14 " "
relative error = 1.77701062307103450000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.799999999999937 " "
y[1] (closed_form) = -1.201543069156989900E-2 " "
y[1] (numeric) = -1.201543069154839500E-2 " "
absolute error = 2.1503632208208500000000000000E-14 " "
relative error = 1.78966803273190870000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.80999999999994 " "
y[1] (closed_form) = -1.191217087800875700E-2 " "
y[1] (numeric) = -1.191217087798728800E-2 " "
absolute error = 2.146893773868896500000000000000E-14 " "
relative error = 1.80226912109891780000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.819999999999943 " "
y[1] (closed_form) = -1.180977637164241600E-2 " "
y[1] (numeric) = -1.180977637162098400E-2 " "
absolute error = 2.143250854569345200000000000000E-14 " "
relative error = 1.81481070184843630000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.829999999999947 " "
y[1] (closed_form) = -1.170824017589130700E-2 " "
y[1] (numeric) = -1.170824017586990500E-2 " "
absolute error = 2.14012835231258700000000000000E-14 " "
relative error = 1.8278821754266470000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.83999999999995 " "
y[1] (closed_form) = -1.160755534773967300E-2 " "
y[1] (numeric) = -1.160755534771830400E-2 " "
absolute error = 2.13683237770823100000000000000E-14 " "
relative error = 1.84089785806994620000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.8499999999999535 " "
y[1] (closed_form) = -1.150771499736234800E-2 " "
y[1] (numeric) = -1.150771499734101500E-2 " "
absolute error = 2.133362930756277400000000000000E-14 " "
relative error = 1.85385450651607160000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.859999999999957 " "
y[1] (closed_form) = -1.140871228775364200E-2 " "
y[1] (numeric) = -1.14087122877323400E-2 " "
absolute error = 2.13024042849951900000000000000E-14 " "
relative error = 1.8672049700001330000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.86999999999996 " "
y[1] (closed_form) = -1.131054043435834200E-2 " "
y[1] (numeric) = -1.131054043433707300E-2 " "
absolute error = 2.126944453895163200000000000000E-14 " "
relative error = 1.88049763513871120000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.8799999999999635 " "
y[1] (closed_form) = -1.121319270470484500E-2 " "
y[1] (numeric) = -1.121319270468360600E-2 " "
absolute error = 2.123995423986002600000000000000E-14 " "
relative error = 1.89419327743722280000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.889999999999967 " "
y[1] (closed_form) = -1.11166624180403710E-2 " "
y[1] (numeric) = -1.111666241801916300E-2 " "
absolute error = 2.120699449381646700000000000000E-14 " "
relative error = 1.90767639569600270000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.89999999999997 " "
y[1] (closed_form) = -1.102094294496831000E-2 " "
y[1] (numeric) = -1.102094294494713700E-2 " "
absolute error = 2.11723000242969300000000000000E-14 " "
relative error = 1.92109696330142940000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9099999999999735 " "
y[1] (closed_form) = -1.092602770708764500E-2 " "
y[1] (numeric) = -1.092602770706650600E-2 " "
absolute error = 2.11393402782533700000000000000E-14 " "
relative error = 1.93476905284986760000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.919999999999977 " "
y[1] (closed_form) = -1.083191017663447400E-2 " "
y[1] (numeric) = -1.083191017661336600E-2 " "
absolute error = 2.11081152556857900000000000000E-14 " "
relative error = 1.94869740530327930000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.92999999999998 " "
y[1] (closed_form) = -1.073858387612560600E-2 " "
y[1] (numeric) = -1.07385838761045310E-2 " "
absolute error = 2.10751555096422300000000000000E-14 " "
relative error = 1.96256375633450640000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9399999999999835 " "
y[1] (closed_form) = -1.06460423780042500E-2 " "
y[1] (numeric) = -1.064604237798320900E-2 " "
absolute error = 2.10421957635986700000000000000E-14 " "
relative error = 1.97652752229071280000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.949999999999987 " "
y[1] (closed_form) = -1.05542793042877810E-2 " "
y[1] (numeric) = -1.055427930426676700E-2 " "
absolute error = 2.101270546450706400000000000000E-14 " "
relative error = 1.99091807774789940000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.95999999999999 " "
y[1] (closed_form) = -1.046328832621754200E-2 " "
y[1] (numeric) = -1.04632883261965600E-2 " "
absolute error = 2.098148044193948200000000000000E-14 " "
relative error = 2.00524727865587230000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9699999999999935 " "
y[1] (closed_form) = -1.037306316391075000E-2 " "
y[1] (numeric) = -1.037306316388979800E-2 " "
absolute error = 2.095372486632385300000000000000E-14 " "
relative error = 2.0200132338174331000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.979999999999997 " "
y[1] (closed_form) = -1.028359758601442200E-2 " "
y[1] (numeric) = -1.028359758599349500E-2 " "
absolute error = 2.092596929070822400000000000000E-14 " "
relative error = 2.03488799670334340000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.99 " "
y[1] (closed_form) = -1.019488540936135700E-2 " "
y[1] (numeric) = -1.019488540934046200E-2 " "
absolute error = 2.08947442681406410000000000000E-14 " "
relative error = 2.04953203779556400000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
"Finished!"
"diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / exp ( x ) ; "
Iterations = 4000
"Total Elapsed Time "= 1 Minutes 22 Seconds
"Elapsed Time(since restart) "= 1 Minutes 22 Seconds
"Time to Timeout "= 1 Minutes 37 Seconds
Percent Done = 100.02500000000009 "%"
(%o254) temp/diffeq.div_lin_exp.max