(%i1) batch("temp/diffeq.add.max") read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.add.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([40],convfloat)),fixnum) (%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a], completearray([40],convfloat),[arr_b], completearray([40],convfloat),[jjj_ats],fixnum), convfloat) (%i25) mode_declare(att([mmm_att],fixnum,[arr_a], completearray([40],convfloat),[arr_b], completearray([40],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,40,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,[40],convfloat) (%i173) completearray(array_norms,[40],convfloat) (%i174) completearray(array_fact_1,[40],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,[40],convfloat) (%i184) completearray(array_x,[40],convfloat) (%i185) completearray(array_tmp0,[40],convfloat) (%i186) completearray(array_tmp1_g,[40],convfloat) (%i187) completearray(array_tmp1,[40],convfloat) (%i188) completearray(array_tmp2,[40],convfloat) (%i189) completearray(array_tmp3_g,[40],convfloat) (%i190) completearray(array_tmp3,[40],convfloat) (%i191) completearray(array_tmp4,[40],convfloat) (%i192) completearray(array_m1,[40],convfloat) (%i193) completearray(array_y_higher,[2,40],convfloat) (%i194) completearray(array_y_higher_work,[2,40],convfloat) (%i195) completearray(array_y_higher_work2,[2,40],convfloat) (%i196) completearray(array_y_set_initial,[2,40],convfloat) (%i197) completearray(array_given_rad_poles,[2,3],convfloat) (%i198) completearray(array_given_ord_poles,[2,3],convfloat) (%i199) completearray(array_rad_test_poles,[2,4],convfloat) (%i200) completearray(array_ord_test_poles,[2,4],convfloat) (%i201) completearray(array_fact_2,[40,40],convfloat) (%i202) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%i203) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%i204) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%i205) omniout_float(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (if vallen = 4 then printf(true,"~a = ~g ~s ~%",prelabel, value,postlabel) else printf(true,"~a = ~g ~s ~%",prelabel, value,postlabel)) (%i206) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%i207) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%i208) logitem_time(fd,secs_in):=( block(mode_declare( [[days_int,hours_int,minutes_int,sec_int, years_int],fixnum,[secs,secs_temp],convfloat]), secs:secs_in,printf(fd,"~%"), if secs >= 0 then (years_int :truncate(secs/glob_sec_in_year), sec_temp :mod(truncate(secs), truncate(glob_sec_in_year)), days_int :truncate(sec_temp/glob_sec_in_day), sec_temp :mod(sec_temp, truncate(glob_sec_in_day)), hours_int :truncate(sec_temp/glob_sec_in_hour), sec_temp :mod(sec_temp, truncate(glob_sec_in_hour)), minutes_int :truncate(sec_temp/glob_sec_in_minute), sec_int :mod(sec_temp, truncate(glob_sec_in_minute)), if truncate(years_int) > 0.1 then printf(fd, "~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int,days_int, hours_int,minutes_int, sec_int) elseif days_int > 0.1 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,hours_int, minutes_int,sec_int) elseif hours_int > 0.1 then printf(fd, "~d Hours ~d Minutes ~d Seconds~%", hours_int,minutes_int, sec_int) elseif minutes_int > 0.1 then printf(fd, "~d Minutes ~d Seconds~%", minutes_int,sec_int) else printf(fd,"~d Seconds~%", sec_int)) else printf(fd," 0.0 Seconds~%"), printf(fd,"~%")),0) (%i209) omniout_timestr(secs_in):=( block(mode_declare( [[days_int,hours_int,minutes_int,sec_int, years_int],fixnum,[secs,secs_temp], convfloat]),secs:secs_in, if secs >= 0 then ( years_int:truncate(secs/glob_sec_in_year), sec_temp :mod(truncate(secs), truncate(glob_sec_in_year)), days_int:truncate(sec_temp/glob_sec_in_day), sec_temp :mod(sec_temp,truncate(glob_sec_in_day)), hours_int :truncate(sec_temp/glob_sec_in_hour), sec_temp :mod(sec_temp,truncate(glob_sec_in_hour)), minutes_int :truncate(sec_temp/glob_sec_in_minute), sec_int :mod(sec_temp, truncate(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int,days_int, hours_int,minutes_int, sec_int) elseif days_int > 0.1 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,hours_int, minutes_int,sec_int) elseif hours_int > 0.1 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,minutes_int, sec_int) elseif minutes_int > 0.1 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int,sec_int) else printf(true,"= ~d Seconds~%", sec_int)) else printf(true,"= 0.0 Seconds~%")),0) (%i210) zero_ats_ar(arr_a):=( block(mode_declare([iii],fixnum),iii:1, while iii <= ats_max_terms do (arr_a[iii]:glob__0,iii:1+iii)),0) (%i211) ats(mmm_ats,arr_a,arr_b,jjj_ats):=block( mode_declare([[iii_ats,lll_ats,ma_ats],fixnum,[ret_ats], convfloat]),ret_ats:glob__0, if jjj_ats <= mmm_ats then (ma_ats:1+mmm_ats,iii_ats:jjj_ats, while iii_ats <= mmm_ats do (lll_ats:ma_ats-iii_ats, if lll_ats <= ats_max_terms and iii_ats <= ats_max_terms then ret_ats :c(arr_a[iii_ats])*c(arr_b[lll_ats])+ret_ats, iii_ats:1+iii_ats)),ret_ats) (%i212) att(mmm_att,arr_aa,arr_bb,jjj_att):=block( mode_declare([[al_att,iii_att,lll_att,ma_att],convfloat,[ret_att], fixnum]),ret_att:glob__0, if jjj_att < mmm_att then (ma_att:2+mmm_att,iii_att:jjj_att, while iii_att < mmm_att and iii_att <= ats_max_terms do (lll_att:ma_att-iii_att,al_att:lll_att-1, if lll_att <= ats_max_terms and iii_att <= ats_max_terms then ret_att :c(arr_aa[iii_att])*c(arr_bb[lll_att]) *c(al_att) +ret_att,iii_att:1+iii_att), ret_att:ret_att/c(mmm_att)),ret_att) (%i213) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%i214) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%i215) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%i216) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), printf(file,"~d",glob_min_good_digits), printf(file,"")),0) (%i217) log_revs(file,revs):=printf(file,revs) (%i218) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%i219) logitem_h_reason(file):=(printf(file,""), if glob_h_reason = 1 then printf(file,"Max H") elseif glob_h_reason = 2 then printf(file,"Display_interval") elseif glob_h_reason = 3 then printf(file,"Optimal") elseif glob_h_reason = 4 then printf(file,"Pole Accuracy") elseif glob_h_reason = 5 then printf(file,"Min H (Pole)") elseif glob_h_reason = 6 then printf(file,"Pole") elseif glob_h_reason = 7 then printf(file,"Opt Iter") else printf(file,"Impossible"), printf(file,""),0) (%i220) logstart(file):=(printf(file,""),0) (%i221) logend(file):=(printf(file,"~%"),0) (%i222) chk_data():=( block(mode_declare([[errflag],boolean]),errflag:false, if glob_max_iter < 2 then (omniout_str(always,"Illegal max_iter"), errflag:true),if errflag then quit()),0) (%i223) comp_expect_sec(t_end2,t_start2,t2,clock_sec2):=block( mode_declare([[ms2,rrr,sec_left,sub1,sub2], convfloat]),ms2:c(clock_sec2), sub1:c(t_end2-t_start2),sub2:c(t2-t_start2), if sub1 = glob__0 then sec_left:glob__0 else (if sub2 > glob__0 then (rrr:sub1/sub2, sec_left:rrr*c(ms2)-c(ms2)) else sec_left:glob__0),sec_left) (%i224) comp_percent(t_end2,t_start2,t2):=block( mode_declare([[rrr,sub1,sub2],convfloat]), sub1:t_end2-t_start2,sub2:t2-t_start2, if sub2 > glob_small_float then rrr:glob__100*sub2/sub1 else rrr:0.0,rrr) (%i225) comp_rad_from_ratio(term1,term2,last_no):=( if abs(term2) > glob__0 then ret:abs(term1*glob_h/term2) else ret:glob_larger_float,ret) (%i226) comp_ord_from_ratio(term1,term2,last_no):=( if abs(term2) > glob__0 then ret :abs(term2)*c(last_no) *log(abs(term1*glob_h/term2)) /log(c(last_no)) +glob__1 else ret:glob_larger_float,ret) (%i227) c(in_val):=(ret:in_val,ret) (%i228) comp_rad_from_three_terms(term1,term2,term3,last_no):=( temp:abs( term1*term3-term1*term3*c(last_no) +glob__m2*term2*term2 +term2*term2*c(last_no)), if abs(temp) > glob__0 then ret:abs(term2*glob_h*term1/temp) else ret:glob_larger_float,ret) (%i229) comp_ord_from_three_terms(term1,term2,term3,last_no):=( ret:abs( (-term1*term3*c(last_no*last_no) +term2*term2*c(last_no*last_no) +glob__4*term2*term2 -glob__4*term2*term2*c(last_no) -glob__3*term1*term3 +glob__4*term1*term3*c(last_no)) /(term1*term3-term1*term3*c(last_no) -glob__2*term2*term2 +term2*term2*c(last_no))), ret) (%i230) comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):= ( if term5 # glob__0 and term4 # glob__0 and term3 # glob__0 and term2 # glob__0 and term1 # glob__0 then (rm0:term6/term5,rm1:term5/term4, rm2:term4/term3,rm3:term3/term2, rm4:term2/term1, nr1 :c(last_no-3)*rm2 -glob__2*c(last_no-2)*rm1 +c(last_no-1)*rm0, nr2 :c(last_no-4)*rm3 -glob__2*c(last_no-3)*rm2 +c(last_no-2)*rm1, dr1 :(-glob__1)/rm3+glob__2/rm2 +glob__m1/rm1, dr2 :(-glob__1)/rm4+glob__2/rm3 +glob__m1/rm2, ds1 :glob__5/rm3-glob__8/rm2 +glob__3/rm1, ds2 :glob__5/rm4-glob__8/rm3 +glob__3/rm2, if abs(nr1*dr2-nr2*dr1) = glob__0 or abs(dr1) = glob__0 then (rad_c:glob_larger_float, ord_no:glob_larger_float) else (if abs(nr1*dr2-nr2*dr1) > glob__0 then ( rcs :(dr1*dr2-ds2*dr1+ds1*dr2) /(nr1*dr2-nr2*dr1), ord_no :(rcs*nr1-ds1)/(glob__2*dr1) -c(last_no)/glob__2, if abs(rcs) # glob__0 then (if rcs > glob__0 then rad_c :sqrt(rcs) *abs(glob_h) else ( rad_c :glob_larger_float, ord_no :glob_larger_float)) else ( rad_c:glob_larger_float, ord_no:glob_larger_float)) else (rad_c:glob_larger_float, ord_no:glob_larger_float))) else (rad_c:glob_larger_float, ord_no:glob_larger_float), glob_six_term_ord_save:ord_no,rad_c) (%i231) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%i232) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret) (%i233) factorial_1(nnn):=block(mode_declare([[ret],convfloat]), if nnn <= ats_max_terms then (if array_fact_1[nnn] = 0 then (ret:factorial_2(nnn), array_fact_1[nnn]:ret) else ret:array_fact_1[nnn]) else ret:factorial_2(nnn),ret) (%i234) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret) (%i235) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret) (%i236) factorial_3(mmm,nnn):=block(mode_declare([[ret],convfloat]), if nnn <= ats_max_terms and mmm <= ats_max_terms then (if array_fact_2[mmm,nnn] = 0 then (ret:factorial_1(mmm)/factorial_1(nnn), array_fact_2[mmm,nnn]:ret) else ret:array_fact_2[mmm,nnn]) else ret:factorial_2(mmm)/factorial_2(nnn),ret) (%i237) log10(x):=log(x)/glob_log_10 (%i238) c(x):=x (%i239) expt(x,y):=if y = 0.0 then 1.0 elseif x <= 0.0 and y < 0.0 then print("expt error x = ",x,"y = ",y) else x^y (%i240) estimated_needed_step_error(x_start,x_end,estimated_h, estimated_answer):=block( [desired_abs_gbl_error,range, estimated_steps,step_error], omniout_float(always, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32,""), desired_abs_gbl_error :expt(glob__10, c(-glob_desired_digits_correct)) *c(abs(c(estimated_answer))), omniout_float(always,"estimated_h",32, estimated_h,32,""), omniout_float(always,"estimated_answer", 32,estimated_answer,32,""), omniout_float(always, "desired_abs_gbl_error",32, desired_abs_gbl_error,32, ""),range:x_end-x_start, omniout_float(always,"range",32,range,32, ""), estimated_steps:range/estimated_h, omniout_float(always,"estimated_steps",32, estimated_steps,32,""), step_error :c( abs(desired_abs_gbl_error) /sqrt(c(estimated_steps)) /c(ats_max_terms)), omniout_float(always,"step_error",32, step_error,32,""), step_error) (%i241) exact_soln_y(x):=block(-c(cos(x))-c(cos(x))+c(2.0)) (%o241) exact_soln_y(x) := block(- c(cos(x)) - c(cos(x)) + c(2.0)) (%i242) display_poles():=( block(mode_declare([[rad_given],convfloat]), if glob_type_given_pole = 1 or glob_type_given_pole = 2 then (rad_given :sqrt( array_given_rad_poles[1,2] *array_given_rad_poles[1,2] +(array_x[1] -array_given_rad_poles[1,1]) *(array_x[1] -array_given_rad_poles[1,1])), omniout_float(always, "Radius of convergence (given) for eq 1 ", 4,rad_given,4," "), omniout_float(always, "Order of pole (given) ", 4, array_given_ord_poles[ 1,1],4," "), if rad_given < glob_least_given_sing then glob_least_given_sing :rad_given) elseif glob_type_given_pole = 3 then omniout_str(always, "NO POLE (given) for Equation 1") elseif glob_type_given_pole = 5 then omniout_str(always, "SOME POLE (given) for Equation 1") else omniout_str(always, "NO info (given) for Equation 1"), if array_rad_test_poles[1,1] < glob_large_float then (omniout_float(always, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1,1], 4," "), if array_rad_test_poles[1,1] < glob_least_ratio_sing then glob_least_ratio_sing :array_rad_test_poles[1,1], omniout_float(always, "Order of pole (ratio test) ", 4, array_ord_test_poles[1,1], 4," ")) else omniout_str(always, "NO POLE (ratio test) for Equation 1"), if array_rad_test_poles[1,2] > glob__small and array_rad_test_poles[1,2] < glob_large_float then (omniout_float(always, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1,2], 4," "), if array_rad_test_poles[1,2] < glob_least_3_sing then glob_least_3_sing :array_rad_test_poles[1,2], omniout_float(always, "Order of pole (three term test) ", 4, array_ord_test_poles[1,2], 4," ")) else omniout_str(always, "NO REAL POLE (three term test) for Equation 1"), if array_rad_test_poles[1,3] > glob__small and array_rad_test_poles[1,3] < glob_large_float then (omniout_float(always, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1,3], 4," "), if array_rad_test_poles[1,3] < glob_least_6_sing then glob_least_6_sing :array_rad_test_poles[1,3], omniout_float(always, "Order of pole (six term test) ", 4, array_ord_test_poles[1,3], 4," ")) else omniout_str(always, "NO COMPLEX POLE (six term test) for Equation 1")), 0) (%i243) my_check_sign(x0,xf):=block([ret], if xf > x0 then ret:glob__1 else ret:glob__m1,ret) (%i244) est_size_answer():=block([min_size], min_size:glob_estimated_size_answer, if abs(array_y[1]) < min_size then (min_size:abs(array_y[1]), omniout_float(always,"min_size",32,min_size, 32,"")), if min_size < glob__1 then (min_size:glob__1, omniout_float(always,"min_size",32,min_size, 32,"")),min_size) (%i245) test_suggested_h():=block( [max_estimated_step_error,hn_div_ho,hn_div_ho_2, hn_div_ho_3,no_terms,est_tmp], max_estimated_step_error:glob__small, no_terms:ats_max_terms,hn_div_ho:glob__0_5, hn_div_ho_2:glob__0_25,hn_div_ho_3:glob__0_125, omniout_float(always,"hn_div_ho",32,hn_div_ho,32,""), omniout_float(always,"hn_div_ho_2",32,hn_div_ho_2,32, ""), omniout_float(always,"hn_div_ho_3",32,hn_div_ho_3,32, ""), est_tmp:abs(array_y[no_terms]*hn_div_ho_3 +array_y[no_terms-1]*hn_div_ho_2 +array_y[no_terms-2]*hn_div_ho +array_y[no_terms-3]), if est_tmp >= max_estimated_step_error then max_estimated_step_error:est_tmp, omniout_float(always,"max_estimated_step_error",32, max_estimated_step_error,32,""), max_estimated_step_error) (%i246) track_estimated_error():=block( [hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms, est_tmp],no_terms:ats_max_terms, hn_div_ho:glob__0_5,hn_div_ho_2:glob__0_25, hn_div_ho_3:glob__0_125, est_tmp:c(abs(array_y[no_terms]))*c(hn_div_ho_3) +c(abs(array_y[no_terms-1])) *c(hn_div_ho_2) +c(abs(array_y[no_terms-2])) *c(hn_div_ho) +c(abs(array_y[no_terms-3])), if glob_prec*c(abs(array_y[1])) > c(est_tmp) then est_tmp :c(glob_prec)*c(abs(array_y[1])), if c(est_tmp) >= c(array_max_est_error[1]) then array_max_est_error[1]:c(est_tmp)) (%i247) reached_interval():=block(mode_declare([[ret],boolean]), if glob_check_sign*array_x[1] >= glob_check_sign*glob_next_display -glob_h/glob__10 then ret:true else ret:false, return(ret)) (%i248) display_alot(iter):=( block(mode_declare( [[abserr,est_rel_err],convfloat, [closed_form_val_y],convfloat,[ind_var], convfloat,[numeric_val],convfloat,[relerr], convfloat,[term_no],fixnum]), if reached_interval() then (if iter >= 0 then (ind_var:array_x[1], omniout_float(always, "x[1] ", 33,ind_var,20, " "), closed_form_val_y :exact_soln_y(ind_var), omniout_float(always, "y[1] (closed_form) ", 33, closed_form_val_y, 20," "), term_no:1, numeric_val:array_y[term_no], abserr :abs( numeric_val -closed_form_val_y), omniout_float(always, "y[1] (numeric) ", 33,numeric_val, 20," "), if c(abs(closed_form_val_y)) > c(glob_prec) then ( relerr :abserr*glob__100 /abs(closed_form_val_y), if c(relerr) > c(glob_prec) then glob_good_digits :3 -floor(log10(c(relerr))) else glob_good_digits:16) else (relerr:glob__m1, glob_good_digits:-16), if glob_good_digits < glob_min_good_digits then glob_min_good_digits :glob_good_digits, if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits then glob_min_apfp_est_good_digits :glob_apfp_est_good_digits, if c(abs(numeric_val)) > c(glob_prec) then ( est_rel_err :c(array_max_est_error[1]) *glob__100 *c(sqrt(glob_iter))*c(22) *c(ats_max_terms) /c(abs(numeric_val)), if est_rel_err > glob_prec then glob_est_digits :3 -floor( log10(est_rel_err)) else glob_est_digits:16) else (relerr:glob__m1, glob_est_digits:-16), array_est_digits[1] :glob_est_digits, if glob_iter = 1 then array_1st_rel_error[1] :relerr else array_last_rel_error[ 1] :relerr, array_est_rel_error[1] :est_rel_err, omniout_float(always, "absolute error ", 4,abserr,20," "), omniout_float(always, "relative error ", 4,relerr,20,"%"), omniout_int(info, "Desired digits ", 32, glob_desired_digits_correct, 4," "), omniout_int(info, "Estimated correct digits ", 32,glob_est_digits, 4," "), omniout_int(info, "Correct digits ", 32, glob_good_digits,4, " "), omniout_float(always, "h ", 4,glob_h,20, " ")))),0) (%i249) prog_report(x_start,x_end):=( block(mode_declare([[clock_sec],convfloat,[opt_clock_sec], convfloat,[clock_sec1],convfloat, [expect_sec],convfloat,[left_sec], convfloat,[percent_done],convfloat, [total_clock_sec],convfloat]), clock_sec1:elapsed_time_seconds(), total_clock_sec:clock_sec1-glob_orig_start_sec, glob_clock_sec:clock_sec1-glob_clock_start_sec, left_sec:-clock_sec1+glob_orig_start_sec +glob_max_sec, expect_sec:comp_expect_sec(x_end,x_start, glob_h+array_x[1], clock_sec1 -glob_orig_start_sec), opt_clock_sec:clock_sec1 -glob_optimal_clock_start_sec, glob_optimal_expect_sec :comp_expect_sec(x_end,x_start,glob_h+array_x[1], opt_clock_sec), glob_total_exp_sec :c(total_clock_sec)+glob_optimal_expect_sec, percent_done:comp_percent(x_end,x_start, glob_h+array_x[1]), glob_percent_done:percent_done, omniout_str_noeol(info, "Total Elapsed Time "), omniout_timestr(total_clock_sec), omniout_str_noeol(info, "Elapsed Time(since restart) "), omniout_timestr(glob_clock_sec), if c(percent_done) < glob__100 then (omniout_str_noeol(info, "Expected Time Remaining "), omniout_timestr(expect_sec), omniout_str_noeol(info, "Optimized Time Remaining "), omniout_timestr(glob_optimal_expect_sec), omniout_str_noeol(info, "Expected Total Time "), omniout_timestr(glob_total_exp_sec)), omniout_str_noeol(info, "Time to Timeout "), omniout_timestr(left_sec), omniout_float(info, "Percent Done ",33, percent_done,4,"%")),0) (%i250) check_for_pole():=( block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc], convfloat,[m,n],fixnum,[nr1,nr2], convfloat,[ord_no],fixnum, [term1,term2,term3,part1,part2, part3,part4,part5,part6,part7, part8,part9,part10,part11,part12, part13,part14,rad_c,rcs,rm0,rm1, rm2,rm3,rm4],convfloat, [found_sing],fixnum, [h_new,ratio,term,local_test, tmp_rad,tmp_ord,tmp_ratio, prev_tmp_rad],convfloat,[last_no], fixnum),tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,1]:glob_larger_float, array_ord_test_poles[1,1]:glob_larger_float, found_sing:1,last_no:-10-1+ats_max_terms,cnt:0, while last_no < ats_max_terms-3 and found_sing = 1 do (tmp_rad :comp_rad_from_ratio( array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,1] then ( array_rad_test_poles[1,1]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_ratio( array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,1]:rad_c, array_ord_test_poles[1,1] :tmp_ord)), tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,2]:glob_larger_float, array_ord_test_poles[1,2]:glob_larger_float, found_sing:1,last_no:-10-1+ats_max_terms,cnt:0, while last_no < ats_max_terms-4 and found_sing = 1 do (tmp_rad :comp_rad_from_three_terms( array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,2] then ( array_rad_test_poles[1,2]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_three_terms( array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,2]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,2] :tmp_ord)), tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,3]:glob_larger_float, array_ord_test_poles[1,3]:glob_larger_float, found_sing:1,last_no:-10-1+ats_max_terms,cnt:0, while last_no < ats_max_terms-7 and found_sing = 1 do (tmp_rad :comp_rad_from_six_terms( array_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,3] then ( array_rad_test_poles[1,3]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_six_terms( array_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,3]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,3] :tmp_ord)), if abs(glob_min_pole_est)*glob_ratio_of_radius < abs(glob_h) then (h_new :glob_check_sign*glob_min_pole_est *glob_ratio_of_radius, omniout_str(always, "SETTING H FOR POLE"), glob_h_reason:6, if glob_check_sign*glob_min_h > glob_check_sign*h_new then ( omniout_str(always, "SETTING H FOR MIN H"), h_new:glob_min_h,glob_h_reason:5), term:1,ratio:c(1.0), while term <= ats_max_terms do ( array_y[term] :array_y[term]*ratio, array_y_higher[1,term] :array_y_higher[1,term]*ratio, array_x[term] :array_x[term]*ratio, ratio:ratio*h_new/abs(glob_h), term:1+term),glob_h:h_new), if reached_interval() then display_poles()),0) (%i251) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]),array_tmp1[1]:sin(array_x[1]), array_tmp1_g[1]:cos(array_x[1]), array_tmp2[1]:array_tmp1[1]+array_const_0D0[1], array_tmp3[1]:sin(array_x[1]), array_tmp3_g[1]:cos(array_x[1]), array_tmp4[1]:array_tmp3[1]+array_tmp2[1], if not array_y_set_initial[1,2] then (if 1 <= ats_max_terms then ( temporary :c(array_tmp4[1])*expt(glob_h,c(1)) *c(factorial_3(0,1)), if 2 <= ats_max_terms then (array_y[2]:temporary, array_y_higher[1,2]:temporary), temporary:c(temporary)*c(1)/c(glob_h), array_y_higher[2,1]:c(temporary),0)), kkk:2,array_tmp1[2]:array_tmp1_g[1]*array_x[2]/c(1), array_tmp1_g[2]:neg(array_tmp1[1])*array_x[2]/c(1), array_tmp2[2]:array_tmp1[2], array_tmp3[2]:array_tmp3_g[1]*array_x[2]/c(1), array_tmp3_g[2]:neg(array_tmp3[1])*array_x[2]/c(1), array_tmp4[2]:array_tmp3[2]+array_tmp2[2], if not array_y_set_initial[1,3] then (if 2 <= ats_max_terms then ( temporary :c(array_tmp4[2])*expt(glob_h,c(1)) *c(factorial_3(1,2)), if 3 <= ats_max_terms then (array_y[3]:temporary, array_y_higher[1,3]:temporary), temporary:c(temporary)*c(2)/c(glob_h), array_y_higher[2,2]:c(temporary),0)), kkk:3,array_tmp1[3]:array_tmp1_g[2]*array_x[2]/c(2), array_tmp1_g[3]:neg(array_tmp1[2])*array_x[2]/c(2), array_tmp2[3]:array_tmp1[3], array_tmp3[3]:array_tmp3_g[2]*array_x[2]/c(2), array_tmp3_g[3]:neg(array_tmp3[2])*array_x[2]/c(2), array_tmp4[3]:array_tmp3[3]+array_tmp2[3], if not array_y_set_initial[1,4] then (if 3 <= ats_max_terms then ( temporary :c(array_tmp4[3])*expt(glob_h,c(1)) *c(factorial_3(2,3)), if 4 <= ats_max_terms then (array_y[4]:temporary, array_y_higher[1,4]:temporary), temporary:c(temporary)*c(3)/c(glob_h), array_y_higher[2,3]:c(temporary),0)), kkk:4,array_tmp1[4]:array_tmp1_g[3]*array_x[2]/c(3), array_tmp1_g[4]:neg(array_tmp1[3])*array_x[2]/c(3), array_tmp2[4]:array_tmp1[4], array_tmp3[4]:array_tmp3_g[3]*array_x[2]/c(3), array_tmp3_g[4]:neg(array_tmp3[3])*array_x[2]/c(3), array_tmp4[4]:array_tmp3[4]+array_tmp2[4], if not array_y_set_initial[1,5] then (if 4 <= ats_max_terms then ( temporary :c(array_tmp4[4])*expt(glob_h,c(1)) *c(factorial_3(3,4)), if 5 <= ats_max_terms then (array_y[5]:temporary, array_y_higher[1,5]:temporary), temporary:c(temporary)*c(4)/c(glob_h), array_y_higher[2,4]:c(temporary),0)), kkk:5,array_tmp1[5]:array_tmp1_g[4]*array_x[2]/c(4), array_tmp1_g[5]:neg(array_tmp1[4])*array_x[2]/c(4), array_tmp2[5]:array_tmp1[5], array_tmp3[5]:array_tmp3_g[4]*array_x[2]/c(4), array_tmp3_g[5]:neg(array_tmp3[4])*array_x[2]/c(4), array_tmp4[5]:array_tmp3[5]+array_tmp2[5], if not array_y_set_initial[1,6] then (if 5 <= ats_max_terms then ( temporary :c(array_tmp4[5])*expt(glob_h,c(1)) *c(factorial_3(4,5)), if 6 <= ats_max_terms then (array_y[6]:temporary, array_y_higher[1,6]:temporary), temporary:c(temporary)*c(5)/c(glob_h), array_y_higher[2,5]:c(temporary),0)), kkk:6, while kkk <= ats_max_terms do (array_tmp1[kkk] :array_tmp1_g[kkk-1]*array_x[2]/c(kkk-1), array_tmp1_g[kkk] :neg(array_tmp1[kkk-1])*array_x[2]/c(kkk-1), array_tmp2[kkk]:array_tmp1[kkk], array_tmp3[kkk] :array_tmp3_g[kkk-1]*array_x[2]/c(kkk-1), array_tmp3_g[kkk] :neg(array_tmp3[kkk-1])*array_x[2]/c(kkk-1), array_tmp4[kkk]:array_tmp3[kkk]+array_tmp2[kkk], order_d:1, if order_d+kkk <= ats_max_terms then (if not array_y_set_initial[1,order_d+kkk] then ( temporary :c(array_tmp4[kkk])*expt(glob_h,c(order_d)) *c( factorial_3( kkk-1, -1+order_d+kkk)), array_y[order_d+kkk]:c(temporary), array_y_higher[1,order_d+kkk]:c(temporary), term:-1+order_d+kkk,adj2:-1+order_d+kkk, adj3:2, while term >= 1 and term <= ats_max_terms and adj3 < 1+order_d do ( if adj3 <= 1+order_d then ( if adj2 > 0 then temporary :c(temporary)*c(adj2) /c(glob_h) else temporary:c(temporary), array_y_higher[adj3,term] :c(temporary)),term:term-1, adj2:adj2-1,adj3:1+adj3))), kkk:1+kkk)),0) (%i252) exact_soln_y(x):=block(-c(cos(x))-c(cos(x))+c(2.0)) (%o252) exact_soln_y(x) := block(- c(cos(x)) - c(cos(x)) + c(2.0)) (%i253) main_prog():=block( mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat, [niii,done_once,term,ord,order_diff,term_no, html_log_file,iiif,jjjf,rows,r_order, sub_iter,calc_term,iii],fixnum,[temp_sum], convfloat,[current_iter],fixnum, [x_start,x_end],convfloat,[it,opt_iter], fixnum,[tmp],convfloat,[subiter],fixnum, [est_needed_step_err,estimated_step_error, min_value,est_answer,last_min_pole_est], convfloat,[repeat_it],fixnum],[found_h], boolean),max_terms:40,Digits:32, glob_html_log:true,term:1, while term <= 40 do (array_y_init[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_norms[term]:c(0.0),term:1+term), term:1, while term <= 40 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 <= 40 do (array_y[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_x[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp0[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp1_g[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp1[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp2[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp3_g[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp3[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp4[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_m1[term]:c(0.0),term:1+term), ord:1, while ord <= 2 do (term:1, while term <= 40 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 <= 40 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 <= 40 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 <= 40 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 <= 40 do (term:1, while term <= 40 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_g), zero_ats_ar(array_tmp1),zero_ats_ar(array_tmp2), zero_ats_ar(array_tmp3_g),zero_ats_ar(array_tmp3), zero_ats_ar(array_tmp4),zero_ats_ar(array_m1), zero_ats_ar(array_const_1),array_const_1[1]:c(1), zero_ats_ar(array_const_0D0),array_const_0D0[1]:c(0.0), zero_ats_ar(array_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, array_y_set_initial[1,31]:false, array_y_set_initial[1,32]:false, array_y_set_initial[1,33]:false, array_y_set_initial[1,34]:false, array_y_set_initial[1,35]:false, array_y_set_initial[1,36]:false, array_y_set_initial[1,37]:false, array_y_set_initial[1,38]:false, array_y_set_initial[1,39]:false, array_y_set_initial[1,40]: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/addpostode.ode#################"), omniout_str(always, "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ; "), omniout_str(always,"!"), omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(always,"max_terms:40,"), omniout_str(always,"Digits:32,"),omniout_str(always,"!"), omniout_str(always,"/* END FIRST INPUT BLOCK */"), omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(always,"x_start:c(-5.0),"), 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," (c(2.0) - c(cos(x)) - c(cos(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(-5.0),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 ) = sin ( x ) + sin ( 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, "2015-04-24T20:19:27-05:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "add"), logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) + sin ( 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, "add diffeq.max"), logitem_str(html_log_file, "add maxima results"), logitem_str(html_log_file,"OK"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i254) main():=(glob_iolevel:2,compile(all),main_prog()) (%i255) main() warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable secs in translation. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable sec_temp in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable years_int in translation. warning: encountered undefined variable days_int in translation. warning: encountered undefined variable hours_int in translation. warning: encountered undefined variable minutes_int in translation. warning: encountered undefined variable sec_int in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable iii in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_ats in translation. warning: encountered undefined variable ma_ats in translation. warning: encountered undefined variable ret_ats in translation. warning: encountered undefined variable lll_ats in translation. warning: encountered undefined variable ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_att in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable ma_att in translation. warning: encountered undefined variable lll_att in translation. warning: encountered undefined variable ret_att in translation. warning: encountered undefined variable al_att in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_h_reason in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable errflag in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable sub1 in translation. warning: encountered undefined variable sub2 in translation. warning: encountered undefined variable rrr in translation. warning: encountered undefined variable ms2 in translation. warning: encountered undefined variable sec_left in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ret in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__m2 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temp in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm0 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm1 in translation. warning: encountered undefined variable rm2 in translation. warning: encountered undefined variable rm3 in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable rm4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__8 in translation. warning: encountered undefined variable glob__5 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable nr1 in translation. warning: encountered undefined variable dr2 in translation. warning: encountered undefined variable nr2 in translation. warning: encountered undefined variable dr1 in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable ds1 in translation. warning: encountered undefined variable ds2 in translation. warning: encountered undefined variable rcs in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable ord_no in translation. warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any. warning: encountered undefined variable rad_c in translation. warning: encountered undefined variable glob_six_term_ord_save in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_2 in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob_log_10 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob__10 in translation. warning: encountered undefined variable ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_x in translation. warning: encountered undefined variable array_given_rad_poles in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable rad_given in translation. warning: encountered undefined variable array_given_ord_poles in translation. warning: variable glob_least_given_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable array_rad_test_poles in translation. warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable array_ord_test_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: variable glob_least_3_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob__small in translation. warning: variable glob_least_6_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_estimated_size_answer in translation. warning: encountered undefined variable array_y in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob__small in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable array_max_est_error in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_next_display in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__10 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable always in translation. warning: encountered undefined variable ind_var in translation. warning: encountered undefined variable closed_form_val_y in translation. warning: encountered undefined variable term_no in translation. warning: encountered undefined variable numeric_val in translation. warning: encountered undefined variable abserr in translation. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable relerr in translation. warning: variable glob_good_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_apfp_est_good_digits in translation. warning: encountered undefined variable glob_min_apfp_est_good_digits in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable est_rel_err in translation. warning: variable glob_est_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_est_digits in translation. warning: encountered undefined variable array_est_digits in translation. warning: encountered undefined variable array_1st_rel_error in translation. warning: encountered undefined variable array_last_rel_error in translation. warning: encountered undefined variable array_est_rel_error in translation. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable clock_sec1 in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_clock_start_sec in translation. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_optimal_clock_start_sec in translation. warning: encountered undefined variable opt_clock_sec in translation. warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_optimal_expect_sec in translation. warning: encountered undefined variable total_clock_sec in translation. warning: variable glob_total_exp_sec (declared type convfloat) assigned type any. warning: encountered undefined variable percent_done in translation. warning: variable glob_percent_done (declared type convfloat) assigned type any. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable expect_sec in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable left_sec in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable last_no in translation. warning: encountered undefined variable found_sing in translation. warning: encountered undefined variable array_y_higher in translation. warning: variable tmp_rad (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_rad in translation. warning: encountered undefined variable prev_tmp_rad in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable cnt in translation. warning: encountered undefined variable tmp_ratio in translation. warning: encountered undefined variable glob_upper_ratio_limit in translation. warning: encountered undefined variable glob_lower_ratio_limit in translation. warning: variable tmp_ord (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_ord in translation. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_ratio_of_radius in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable h_new in translation. warning: variable ratio (declared type convfloat) assigned type any. warning: encountered undefined variable term in translation. warning: encountered undefined variable ratio in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_tmp1_g in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable array_tmp3_g in translation. warning: encountered undefined variable array_tmp4 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temporary in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable array_y_set_initial in translation. warning: encountered undefined variable kkk in translation. warning: encountered undefined variable order_d in translation. warning: encountered undefined variable adj3 in translation. warning: encountered undefined variable adj2 in translation. modedeclare: [found_h] is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: variable term (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable array_y_init in translation. warning: variable term (declared type [found_h]) assigned type any. warning: encountered undefined variable array_norms in translation. warning: encountered undefined variable array_fact_1 in translation. warning: encountered undefined variable array_type_pole in translation. warning: encountered undefined variable array_type_real_pole in translation. warning: encountered undefined variable array_type_complex_pole in translation. warning: encountered undefined variable array_tmp0 in translation. warning: encountered undefined variable array_m1 in translation. warning: variable ord (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable ord in translation. warning: variable ord (declared type [found_h]) assigned type any. warning: encountered undefined variable array_y_higher_work in translation. warning: encountered undefined variable array_y_higher_work2 in translation. warning: encountered undefined variable array_const_1 in translation. warning: encountered undefined variable glob__m1 in translation. warning: variable iiif (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable iiif in translation. warning: encountered undefined variable ats_max_terms in translation. warning: variable jjjf (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable jjjf in translation. warning: variable jjjf (declared type [found_h]) assigned type any. warning: variable iiif (declared type [found_h]) assigned type any. warning: variable glob_orig_start_sec (declared type convfloat) assigned type any. warning: variable opt_iter (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob__0 in translation. warning: variable glob_large_float (declared type convfloat) assigned type any. warning: variable glob_larger_float (declared type convfloat) assigned type any. warning: variable glob_almost_1 (declared type convfloat) assigned type any. warning: variable x_start (declared type [found_h]) assigned type any. warning: variable x_end (declared type [found_h]) assigned type any. warning: encountered undefined variable x_start in translation. warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_h (declared type convfloat) assigned type any. warning: variable glob_display_interval (declared type convfloat) assigned type any. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_max_minutes in translation. warning: encountered undefined variable glob_max_hours in translation. warning: encountered undefined variable x_end in translation. warning: variable glob_check_sign (declared type convfloat) assigned type any. warning: encountered undefined variable glob_larger_float in translation. warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_max_h in translation. warning: encountered undefined variable glob_display_interval in translation. warning: encountered undefined variable glob__10 in translation. warning: variable display_max (declared type [found_h]) assigned type any. warning: encountered undefined variable display_max in translation. warning: variable min_value (declared type [found_h]) assigned type convfloat. warning: variable est_answer (declared type [found_h]) assigned type any. warning: encountered undefined variable est_answer in translation. warning: variable est_needed_step_err (declared type [found_h]) assigned type any. warning: encountered undefined variable est_needed_step_err in translation. warning: encountered undefined variable glob_small_float in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable opt_iter in translation. warning: encountered undefined variable found_h in translation. warning: variable glob_next_display (declared type convfloat) assigned type any. warning: variable order_diff (declared type [found_h]) assigned type fixnum. warning: variable term_no (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable order_diff in translation. warning: variable term_no (declared type [found_h]) assigned type any. warning: variable r_order (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable r_order in translation. warning: encountered undefined variable rows in translation. warning: variable it (declared type [found_h]) assigned type any. warning: encountered undefined variable it in translation. warning: variable r_order (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_look_poles in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type any. warning: encountered undefined variable estimated_step_error in translation. warning: encountered undefined variable glob__2 in translation. warning: variable opt_iter (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_optimize in translation. warning: variable html_log_file (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_html_log in translation. warning: variable current_iter (declared type [found_h]) assigned type fixnum. warning: variable glob_clock_start_sec (declared type convfloat) assigned type any. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable debugl in translation. warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable info in translation. warning: encountered undefined variable current_iter in translation. warning: encountered undefined variable glob_next_display in translation. warning: variable calc_term (declared type [found_h]) assigned type fixnum. warning: variable iii (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable calc_term in translation. warning: variable iii (declared type [found_h]) assigned type any. warning: variable temp_sum (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable temp_sum in translation. warning: variable temp_sum (declared type [found_h]) assigned type any. warning: encountered undefined variable html_log_file in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob_percent_done in translation. warning: encountered undefined variable glob__100 in translation. WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : |$Digits| 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/addpostode.ode#################" "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "max_terms:40," "Digits:32," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:c(-5.0)," "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(" " (c(2.0) - c(cos(x)) - c(cos(x))) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = -5. " " y[1] (closed_form) = 1.4326756290735476 " " y[1] (numeric) = 1.4326756290735476 " " 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] = -4.989999999999997 " " y[1] (closed_form) = 1.4518821609091521 " " y[1] (numeric) = 1.4518821609091455 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 4.5880708001672010000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.979999999999993 " " y[1] (closed_form) = 1.471143504071902 " " y[1] (numeric) = 1.4711435040718892 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 8.7541338081606870000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.96999999999999 " " y[1] (closed_form) = 1.490457732443533 " " y[1] (numeric) = 1.4904577324435135 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.3110016344688954000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.959999999999987 " " y[1] (closed_form) = 1.5098229146173026 " " y[1] (numeric) = 1.509822914617276 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 1.7647998538793935000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.949999999999983 " " y[1] (closed_form) = 1.5292371140911305 " " y[1] (numeric) = 1.5292371140910976 " " absolute error = 3.286260152890463400000000000000E-14 " " relative error = 2.1489539605135613000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.93999999999998 " " y[1] (closed_form) = 1.5486983894612485 " " y[1] (numeric) = 1.548698389461209 " " absolute error = 3.95239396766555730000000000000E-14 " " relative error = 2.5520746935369976000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.929999999999977 " " y[1] (closed_form) = 1.5682047946163369 " " y[1] (numeric) = 1.5682047946162907 " " absolute error = 4.61852778244065100000000000000E-14 " " relative error = 2.9451050005051027000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.919999999999973 " " y[1] (closed_form) = 1.5877543789321353 " " y[1] (numeric) = 1.5877543789320832 " " absolute error = 5.21804821573823600000000000000E-14 " " relative error = 3.286432892251067700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.90999999999997 " " y[1] (closed_form) = 1.6073451874665041 " " y[1] (numeric) = 1.6073451874664453 " " absolute error = 5.8841820305133300000000000000E-14 " " relative error = 3.660807943680083000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.899999999999967 " " y[1] (closed_form) = 1.6269752611549149 " " y[1] (numeric) = 1.6269752611548491 " " absolute error = 6.57252030578092700000000000000E-14 " " relative error = 4.0397174208508846000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.889999999999963 " " y[1] (closed_form) = 1.646642637006357 " " y[1] (numeric) = 1.6466426370062848 " " absolute error = 7.21644966006351800000000000000E-14 " " relative error = 4.3825232615033144000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.87999999999996 " " y[1] (closed_form) = 1.6663453482996355 " " y[1] (numeric) = 1.6663453482995567 " " absolute error = 7.88258347483861100000000000000E-14 " " relative error = 4.73046207551281000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.869999999999957 " " y[1] (closed_form) = 1.6860814247800393 " " y[1] (numeric) = 1.686081424779954 " " absolute error = 8.52651282912120200000000000000E-14 " " relative error = 5.056999444871735000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.859999999999953 " " y[1] (closed_form) = 1.705848892856367 " " y[1] (numeric) = 1.7058488928562752 " " absolute error = 9.19264664389629600000000000000E-14 " " relative error = 5.388898560940896000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.84999999999995 " " y[1] (closed_form) = 1.725645775798284 " " y[1] (numeric) = 1.7256457757981856 " " absolute error = 9.83657599817888700000000000000E-14 " " relative error = 5.7002289439317210000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.839999999999947 " " y[1] (closed_form) = 1.7454700939339935 " " y[1] (numeric) = 1.7454700939338883 " " absolute error = 1.05249142734464840000000000000E-13 " " relative error = 6.029845088737735000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.829999999999943 " " y[1] (closed_form) = 1.7653198648482018 " " y[1] (numeric) = 1.7653198648480903 " " absolute error = 1.11466391672365720000000000000E-13 " " relative error = 6.314231992282634000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.81999999999994 " " y[1] (closed_form) = 1.7851931035803594 " " y[1] (numeric) = 1.7851931035802413 " " absolute error = 1.18127729820116660000000000000E-13 " " relative error = 6.617084145306257000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.8099999999999365 " " y[1] (closed_form) = 1.805087822823154 " " y[1] (numeric) = 1.8050878228230285 " " absolute error = 1.2545520178264270000000000000E-13 " " relative error = 6.950088532890938000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.799999999999933 " " y[1] (closed_form) = 1.82500203312124 " " y[1] (numeric) = 1.8250020331211076 " " absolute error = 1.32338584535318660000000000000E-13 " " relative error = 7.251421211240209000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.78999999999993 " " y[1] (closed_form) = 1.8449337430701824 " " y[1] (numeric) = 1.8449337430700437 " " absolute error = 1.38777878078144570000000000000E-13 " " relative error = 7.522106341185033000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.7799999999999265 " " y[1] (closed_form) = 1.8648809595155966 " " y[1] (numeric) = 1.8648809595154512 " " absolute error = 1.4543921622589550000000000000E-13 " " relative error = 7.798847185595880000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.769999999999923 " " y[1] (closed_form) = 1.8848416877524605 " " y[1] (numeric) = 1.8848416877523084 " " absolute error = 1.52100554373646450000000000000E-13 " " relative error = 8.069672660679292000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.75999999999992 " " y[1] (closed_form) = 1.904813931724584 " " y[1] (numeric) = 1.9048139317244255 " " absolute error = 1.58539847916472350000000000000E-13 " " relative error = 8.32311467676705000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.7499999999999165 " " y[1] (closed_form) = 1.9247956942242137 " " y[1] (numeric) = 1.9247956942240485 " " absolute error = 1.6520118606422330000000000000E-13 " " relative error = 8.582790711759537000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.739999999999913 " " y[1] (closed_form) = 1.944784977091751 " " y[1] (numeric) = 1.9447849770915788 " " absolute error = 1.72084568816899260000000000000E-13 " " relative error = 8.848513889398512000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.72999999999991 " " y[1] (closed_form) = 1.9647797814155665 " " y[1] (numeric) = 1.964779781415388 " " absolute error = 1.78523862359725170000000000000E-13 " " relative error = 9.086202130556532000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.7199999999999065 " " y[1] (closed_form) = 1.984778107731891 " " y[1] (numeric) = 1.984778107731705 " " absolute error = 1.8585133432225120000000000000E-13 " " relative error = 9.36383435499665000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.709999999999903 " " y[1] (closed_form) = 2.004777956224757 " " y[1] (numeric) = 2.004777956224565 " " absolute error = 1.91846538655227050000000000000E-13 " " relative error = 9.56946568868392900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.6999999999999 " " y[1] (closed_form) = 2.0247773269259817 " " y[1] (numeric) = 2.0247773269257836 " " absolute error = 1.98063787593127930000000000000E-13 " " relative error = 9.782003431154008000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.6899999999998965 " " y[1] (closed_form) = 2.044774219915162 " " y[1] (numeric) = 2.044774219914957 " " absolute error = 2.05169214950728930000000000000E-13 " " relative error = 1.0033832241842400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.679999999999893 " " y[1] (closed_form) = 2.0647666355196623 " " y[1] (numeric) = 2.06476663551945 " " absolute error = 2.12274642308329930000000000000E-13 " " relative error = 1.028080552332755300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.66999999999989 " " y[1] (closed_form) = 2.0847525745145834 " " y[1] (numeric) = 2.084752574514364 " " absolute error = 2.19380069665930930000000000000E-13 " " relative error = 1.052307464913488200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.6599999999998865 " " y[1] (closed_form) = 2.1047300383226792 " " y[1] (numeric) = 2.104730038322454 " " absolute error = 2.25153229393981750000000000000E-13 " " relative error = 1.069748734015374700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.649999999999883 " " y[1] (closed_form) = 2.124697029214217 " " y[1] (numeric) = 2.1246970292139853 " " absolute error = 2.3181456754173269000000000000E-13 " " relative error = 1.091047638107092200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.63999999999988 " " y[1] (closed_form) = 2.1446515505067483 " " y[1] (numeric) = 2.1446515505065094 " " absolute error = 2.3891999489933370000000000000E-13 " " relative error = 1.114027100779520800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.629999999999876 " " y[1] (closed_form) = 2.1645916067647706 " " y[1] (numeric) = 2.1645916067645254 " " absolute error = 2.45137243837234560000000000000E-13 " " relative error = 1.132487269520647300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.619999999999873 " " y[1] (closed_form) = 2.1845152039992763 " " y[1] (numeric) = 2.1845152039990245 " " absolute error = 2.5179858198498550000000000000E-13 " " relative error = 1.152652000425577900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.60999999999987 " " y[1] (closed_form) = 2.204420349867144 " " y[1] (numeric) = 2.204420349866886 " " absolute error = 2.5801583092288640000000000000E-13 " " relative error = 1.17044750987912300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.599999999999866 " " y[1] (closed_form) = 2.224305053870374 " " y[1] (numeric) = 2.2243050538701103 " " absolute error = 2.6378899065093720000000000000E-13 " " relative error = 1.185938907938614100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.589999999999863 " " y[1] (closed_form) = 2.2441673275551386 " " y[1] (numeric) = 2.2441673275548673 " " absolute error = 2.71338507218388260000000000000E-13 " " relative error = 1.209083226044433700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.57999999999986 " " y[1] (closed_form) = 2.2640051847106184 " " y[1] (numeric) = 2.264005184710341 " " absolute error = 2.77555756156289140000000000000E-13 " " relative error = 1.22595017904857800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.569999999999856 " " y[1] (closed_form) = 2.2838166415676318 " " y[1] (numeric) = 2.2838166415673467 " " absolute error = 2.8510527272374020000000000000E-13 " " relative error = 1.248371990704303800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.559999999999853 " " y[1] (closed_form) = 2.3035997169970006 " " y[1] (numeric) = 2.3035997169967093 " " absolute error = 2.9132252166164110000000000000E-13 " " relative error = 1.264640377892616300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.54999999999985 " " y[1] (closed_form) = 2.3233524327076696 " " y[1] (numeric) = 2.323352432707371 " " absolute error = 2.9842794901924210000000000000E-13 " " relative error = 1.284471287343391700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.539999999999846 " " y[1] (closed_form) = 2.3430728134445262 " " y[1] (numeric) = 2.343072813444222 " " absolute error = 3.0420110874729290000000000000E-13 " " relative error = 1.298299852235876900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.529999999999843 " " y[1] (closed_form) = 2.362758887185932 " " y[1] (numeric) = 2.3627588871856218 " " absolute error = 3.10418357685193770000000000000E-13 " " relative error = 1.313796170098866800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.51999999999984 " " y[1] (closed_form) = 2.382408685340917 " " y[1] (numeric) = 2.3824086853406006 " " absolute error = 3.16635606623094650000000000000E-13 " " relative error = 1.329056633193833300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.509999999999836 " " y[1] (closed_form) = 2.4020202429460404 " " y[1] (numeric) = 2.4020202429457176 " " absolute error = 3.2285285556099550000000000000E-13 " " relative error = 1.344088820687962000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.499999999999833 " " y[1] (closed_form) = 2.4215915988618857 " " y[1] (numeric) = 2.421591598861556 " " absolute error = 3.29514193708746460000000000000E-13 " " relative error = 1.36073396465206410000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.48999999999983 " " y[1] (closed_form) = 2.4411207959691694 " " y[1] (numeric) = 2.441120795968833 " " absolute error = 3.36619621066347460000000000000E-13 " " relative error = 1.378955198047474300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.479999999999826 " " y[1] (closed_form) = 2.4606058813644562 " " y[1] (numeric) = 2.4606058813641125 " " absolute error = 3.43725048423948460000000000000E-13 " " relative error = 1.39691224436700900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.469999999999823 " " y[1] (closed_form) = 2.4800449065554426 " " y[1] (numeric) = 2.4800449065550922 " " absolute error = 3.5038638657169940000000000000E-13 " " relative error = 1.412822750287833800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.45999999999982 " " y[1] (closed_form) = 2.49943592765581 " " y[1] (numeric) = 2.4994359276554534 " " absolute error = 3.5660363550960030000000000000E-13 " " relative error = 1.426736455069102000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.449999999999816 " " y[1] (closed_form) = 2.518777005579607 " " y[1] (numeric) = 2.5187770055792438 " " absolute error = 3.6326497365735120000000000000E-13 " " relative error = 1.442227608290233300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.439999999999813 " " y[1] (closed_form) = 2.5380662062351593 " " y[1] (numeric) = 2.538066206234789 " " absolute error = 3.7037040101495220000000000000E-13 " " relative error = 1.459262174111451400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.42999999999981 " " y[1] (closed_form) = 2.557301600718474 " " y[1] (numeric) = 2.557301600718098 " " absolute error = 3.75699471533153000000000000000E-13 " " relative error = 1.46912460942268300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.419999999999806 " " y[1] (closed_form) = 2.5764812655061338 " " y[1] (numeric) = 2.576481265505751 " " absolute error = 3.828048988907540000000000000E-13 " " relative error = 1.485766281384368300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.409999999999803 " " y[1] (closed_form) = 2.5956032826476427 " " y[1] (numeric) = 2.5956032826472533 " " absolute error = 3.8946623703850490000000000000E-13 " " relative error = 1.50048445246698200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.3999999999998 " " y[1] (closed_form) = 2.6146657399572204 " " y[1] (numeric) = 2.614665739956825 " " absolute error = 3.95239396766555730000000000000E-13 " " relative error = 1.511624949707806300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.389999999999796 " " y[1] (closed_form) = 2.6336667312050226 " " y[1] (numeric) = 2.6336667312046202 " " absolute error = 4.02344824124156730000000000000E-13 " " relative error = 1.52769832020494700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.379999999999793 " " y[1] (closed_form) = 2.6526043563077586 " " y[1] (numeric) = 2.6526043563073505 " " absolute error = 4.08117983852207540000000000000E-13 " " relative error = 1.538555807924101600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.36999999999979 " " y[1] (closed_form) = 2.6714767215186983 " " y[1] (numeric) = 2.671476721518285 " " absolute error = 4.1344705437040830000000000000E-13 " " relative error = 1.54763487564798690000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.359999999999786 " " y[1] (closed_form) = 2.690281939617048 " " y[1] (numeric) = 2.6902819396166286 " " absolute error = 4.1922021409845910000000000000E-13 " " relative error = 1.55827613427808100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.349999999999783 " " y[1] (closed_form) = 2.709018130096669 " " y[1] (numeric) = 2.7090181300962435 " " absolute error = 4.25437463036360000000000000E-13 " " relative error = 1.570448932437298000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.33999999999978 " " y[1] (closed_form) = 2.7276834193541273 " " y[1] (numeric) = 2.7276834193536943 " " absolute error = 4.32986979603811050000000000000E-13 " " relative error = 1.58737988628583400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.329999999999776 " " y[1] (closed_form) = 2.7462759408760506 " " y[1] (numeric) = 2.746275940875612 " " absolute error = 4.38760139331861860000000000000E-13 " " relative error = 1.597654965407078500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.319999999999773 " " y[1] (closed_form) = 2.764793835425781 " " y[1] (numeric) = 2.7647938354253365 " " absolute error = 4.4453329905991270000000000000E-13 " " relative error = 1.607835251091892200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.30999999999977 " " y[1] (closed_form) = 2.7832352512292946 " " y[1] (numeric) = 2.7832352512288434 " " absolute error = 4.5119463720766360000000000000E-13 " " relative error = 1.62111570341882100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.299999999999766 " " y[1] (closed_form) = 2.8015983441603787 " " y[1] (numeric) = 2.801598344159922 " " absolute error = 4.5652370772586437000000000000E-13 " " relative error = 1.629511627451656000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.289999999999763 " " y[1] (closed_form) = 2.8198812779250435 " " y[1] (numeric) = 2.819881277924581 " " absolute error = 4.6229686745391520000000000000E-13 " " relative error = 1.639419613417511200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.2799999999997596 " " y[1] (closed_form) = 2.8380822242451487 " " y[1] (numeric) = 2.83808222424468 " " absolute error = 4.6851411639181606000000000000E-13 " " relative error = 1.650812342184440600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.269999999999756 " " y[1] (closed_form) = 2.8561993630412275 " " y[1] (numeric) = 2.856199363040753 " " absolute error = 4.7428727611986690000000000000E-13 " " relative error = 1.660553819376441300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.259999999999753 " " y[1] (closed_form) = 2.8742308826144995 " " y[1] (numeric) = 2.874230882614019 " " absolute error = 4.8050452505776775000000000000E-13 " " relative error = 1.67176731682976120000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.2499999999997495 " " y[1] (closed_form) = 2.8921749798280336 " " y[1] (numeric) = 2.8921749798275473 " " absolute error = 4.8627768478581856000000000000E-13 " " relative error = 1.681356377734559700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.239999999999746 " " y[1] (closed_form) = 2.910029860287062 " " y[1] (numeric) = 2.910029860286569 " " absolute error = 4.9293902293356950000000000000E-13 " " relative error = 1.69393115053789600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.229999999999743 " " y[1] (closed_form) = 2.9277937385184165 " " y[1] (numeric) = 2.927793738517918 " " absolute error = 4.9871218266162030000000000000E-13 " " relative error = 1.7033719831438301000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.2199999999997395 " " y[1] (closed_form) = 2.9454648381490784 " " y[1] (numeric) = 2.945464838148573 " " absolute error = 5.0537352080937130000000000000E-13 " " relative error = 1.715768303406217000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.209999999999736 " " y[1] (closed_form) = 2.9630413920838095 " " y[1] (numeric) = 2.9630413920832988 " " absolute error = 5.107025913275720000000000000E-13 " " relative error = 1.72357562297977800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.199999999999733 " " y[1] (closed_form) = 2.9805216426818646 " " y[1] (numeric) = 2.980521642681348 " " absolute error = 5.1647575105562280000000000000E-13 " " relative error = 1.732836774809994300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.1899999999997295 " " y[1] (closed_form) = 2.99790384193275 " " y[1] (numeric) = 2.997903841932228 " " absolute error = 5.2224891078367360000000000000E-13 " " relative error = 1.74204690450304620000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.179999999999726 " " y[1] (closed_form) = 3.015186251631026 " " y[1] (numeric) = 3.015186251630498 " " absolute error = 5.2802207051172450000000000000E-13 " " relative error = 1.751208802527862700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.169999999999723 " " y[1] (closed_form) = 3.0323671435501245 " " y[1] (numeric) = 3.0323671435495907 " " absolute error = 5.3379523023977530000000000000E-13 " " relative error = 1.760325201304080400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.1599999999997195 " " y[1] (closed_form) = 3.049444799615171 " " y[1] (numeric) = 3.049444799614631 " " absolute error = 5.3956838996782610000000000000E-13 " " relative error = 1.76939877723288420000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.149999999999716 " " y[1] (closed_form) = 3.066417512074789 " " y[1] (numeric) = 3.0664175120742443 " " absolute error = 5.4489746048602680000000000000E-13 " " relative error = 1.776983918009717200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.139999999999713 " " y[1] (closed_form) = 3.0832835836718795 " " y[1] (numeric) = 3.0832835836713284 " " absolute error = 5.5111470942392770000000000000E-13 " " relative error = 1.787427897785534800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.1299999999997095 " " y[1] (closed_form) = 3.1000413278133356 " " y[1] (numeric) = 3.100041327812778 " " absolute error = 5.5777604757167860000000000000E-13 " " relative error = 1.799253585967884600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.119999999999706 " " y[1] (closed_form) = 3.116689068738708 " " y[1] (numeric) = 3.1166890687381454 " " absolute error = 5.6266102888002930000000000000E-13 " " relative error = 1.805316528118515500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.109999999999703 " " y[1] (closed_form) = 3.1332251416877774 " " y[1] (numeric) = 3.13322514168721 " " absolute error = 5.67546010188380000000000000E-13 " " relative error = 1.811379599369164500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.099999999999700 " " y[1] (closed_form) = 3.14964789306703 " " y[1] (numeric) = 3.149647893066456 " " absolute error = 5.7376325912628090000000000000E-13 " " relative error = 1.82167429060639500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.089999999999696 " " y[1] (closed_form) = 3.1659556806150118 " " y[1] (numeric) = 3.1659556806144327 " " absolute error = 5.7909232964448170000000000000E-13 " " relative error = 1.829123298188395400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.079999999999693 " " y[1] (closed_form) = 3.182146873566559 " " y[1] (numeric) = 3.182146873565974 " " absolute error = 5.8486548937253250000000000000E-13 " " relative error = 1.837958814003495800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.069999999999690 " " y[1] (closed_form) = 3.1982198528158676 " " y[1] (numeric) = 3.1982198528152783 " " absolute error = 5.8930638147103310000000000000E-13 " " relative error = 1.842607477257009700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.059999999999686 " " y[1] (closed_form) = 3.214173011078408 " " y[1] (numeric) = 3.214173011077813 " " absolute error = 5.9507954119908390000000000000E-13 " " relative error = 1.851423489488591100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.049999999999683 " " y[1] (closed_form) = 3.2300047530516487 " " y[1] (numeric) = 3.230004753051048 " " absolute error = 6.0085270092713470000000000000E-13 " " relative error = 1.86022234289116820000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.039999999999680 " " y[1] (closed_form) = 3.2457134955745843 " " y[1] (numeric) = 3.2457134955739777 " " absolute error = 6.0662586065518550000000000000E-13 " " relative error = 1.86900618764502290000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.029999999999676 " " y[1] (closed_form) = 3.261297667786054 " " y[1] (numeric) = 3.261297667785442 " " absolute error = 6.1195493117338630000000000000E-13 " " relative error = 1.876415444128454700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.019999999999673 " " y[1] (closed_form) = 3.2767557112818224 " " y[1] (numeric) = 3.276755711281205 " " absolute error = 6.172840016915870000000000000E-13 " " relative error = 1.883826736202174600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.009999999999670 " " y[1] (closed_form) = 3.2920860802704217 " " y[1] (numeric) = 3.2920860802698 " " absolute error = 6.2172489379008770000000000000E-13 " " relative error = 1.8885438552658300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.9999999999996665 " " y[1] (closed_form) = 3.307287241727728 " " y[1] (numeric) = 3.3072872417271024 " " absolute error = 6.2572169667873820000000000000E-13 " " relative error = 1.891948448819525700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.9899999999996676 " " y[1] (closed_form) = 3.3223576755502586 " " y[1] (numeric) = 3.3223576755496342 " " absolute error = 6.243894290491880000000000000E-13 " " relative error = 1.879356439085911300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.9799999999996687 " " y[1] (closed_form) = 3.337295874707195 " " y[1] (numeric) = 3.3372958747065726 " " absolute error = 6.2216898299993770000000000000E-13 " " relative error = 1.864290750230604100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.96999999999967 " " y[1] (closed_form) = 3.3521003453910705 " " y[1] (numeric) = 3.3521003453904483 " " absolute error = 6.2216898299993770000000000000E-13 " " relative error = 1.856057154898066700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.959999999999671 " " y[1] (closed_form) = 3.3667696071671527 " " y[1] (numeric) = 3.3667696071665327 " " absolute error = 6.1994853695068740000000000000E-13 " " relative error = 1.841374995280181400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.949999999999672 " " y[1] (closed_form) = 3.38130219312149 " " y[1] (numeric) = 3.381302193120872 " " absolute error = 6.1817218011128720000000000000E-13 " " relative error = 1.828207432535374800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.939999999999673 " " y[1] (closed_form) = 3.3956966500075954 " " y[1] (numeric) = 3.39569665000698 " " absolute error = 6.1550764485218680000000000000E-13 " " relative error = 1.81261080800845400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.929999999999674 " " y[1] (closed_form) = 3.409951538391778 " " y[1] (numeric) = 3.409951538391163 " " absolute error = 6.1461946643248670000000000000E-13 " " relative error = 1.802428742791920300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.9199999999996753 " " y[1] (closed_form) = 3.424065432797076 " " y[1] (numeric) = 3.424065432796463 " " absolute error = 6.1328719880293650000000000000E-13 " " relative error = 1.791108291706767800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.9099999999996764 " " y[1] (closed_form) = 3.4380369218458124 " " y[1] (numeric) = 3.4380369218452005 " " absolute error = 6.1195493117338630000000000000E-13 " " relative error = 1.779954506261788900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.8999999999996775 " " y[1] (closed_form) = 3.451864608400724 " " y[1] (numeric) = 3.4518646084001134 " " absolute error = 6.1062266354383610000000000000E-13 " " relative error = 1.76896469826127500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.8899999999996786 " " y[1] (closed_form) = 3.465547109704678 " " y[1] (numeric) = 3.46554710970407 " " absolute error = 6.0795812828473570000000000000E-13 " " relative error = 1.754291917089373400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.8799999999996797 " " y[1] (closed_form) = 3.479083057518948 " " y[1] (numeric) = 3.4790830575183405 " " absolute error = 6.0751403907488570000000000000E-13 " " relative error = 1.746190099606660700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.869999999999681 " " y[1] (closed_form) = 3.4924710982600304 " " y[1] (numeric) = 3.492471098259425 " " absolute error = 6.0529359302563530000000000000E-13 " " relative error = 1.73313844551840700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.859999999999682 " " y[1] (closed_form) = 3.505709893135009 " " y[1] (numeric) = 3.505709893134405 " " absolute error = 6.0396132539608520000000000000E-13 " " relative error = 1.72279322535724120000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.849999999999683 " " y[1] (closed_form) = 3.518798118275429 " " y[1] (numeric) = 3.5187981182748254 " " absolute error = 6.0351723618623510000000000000E-13 " " relative error = 1.715123220771813700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.839999999999684 " " y[1] (closed_form) = 3.5317344648696807 " " y[1] (numeric) = 3.5317344648690785 " " absolute error = 6.0218496855668490000000000000E-13 " " relative error = 1.705068641333728800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.829999999999685 " " y[1] (closed_form) = 3.544517639293888 " " y[1] (numeric) = 3.5445176392932867 " " absolute error = 6.0129679013698480000000000000E-13 " " relative error = 1.69641359227872400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.8199999999996863 " " y[1] (closed_form) = 3.5571463632412588 " " y[1] (numeric) = 3.557146363240659 " " absolute error = 5.9996452250743460000000000000E-13 " " relative error = 1.686645589586449300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.8099999999996874 " " y[1] (closed_form) = 3.569619373849923 " " y[1] (numeric) = 3.5696193738493243 " " absolute error = 5.9863225487788440000000000000E-13 " " relative error = 1.677019850528894700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.7999999999996885 " " y[1] (closed_form) = 3.581935423829215 " " y[1] (numeric) = 3.581935423828617 " " absolute error = 5.9774407645818430000000000000E-13 " " relative error = 1.66877401664370320000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.7899999999996896 " " y[1] (closed_form) = 3.5940932815843984 " " y[1] (numeric) = 3.5940932815838025 " " absolute error = 5.959677196187840000000000000E-13 " " relative error = 1.658186565920351500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.7799999999996907 " " y[1] (closed_form) = 3.6060917313398306 " " y[1] (numeric) = 3.6060917313392364 " " absolute error = 5.9419136277938380000000000000E-13 " " relative error = 1.64774333834989300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.769999999999692 " " y[1] (closed_form) = 3.6179295732605334 " " y[1] (numeric) = 3.617929573259941 " " absolute error = 5.9241500593998350000000000000E-13 " " relative error = 1.637442061665368400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.759999999999693 " " y[1] (closed_form) = 3.6296056235721803 " " y[1] (numeric) = 3.6296056235715897 " " absolute error = 5.9063864910058330000000000000E-13 " " relative error = 1.627280510215016700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.749999999999694 " " y[1] (closed_form) = 3.6411187146794717 " " y[1] (numeric) = 3.641118714678881 " " absolute error = 5.9063864910058330000000000000E-13 " " relative error = 1.6221351056733600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.739999999999695 " " y[1] (closed_form) = 3.652467695282888 " " y[1] (numeric) = 3.652467695282299 " " absolute error = 5.888622922611830000000000000E-13 " " relative error = 1.612231349839700300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.7299999999996962 " " y[1] (closed_form) = 3.663651430493829 " " y[1] (numeric) = 3.663651430493241 " " absolute error = 5.8797411384148290000000000000E-13 " " relative error = 1.604885521989271300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.7199999999996973 " " y[1] (closed_form) = 3.6746688019480906 " " y[1] (numeric) = 3.6746688019475053 " " absolute error = 5.8530957858238250000000000000E-13 " " relative error = 1.592822673630032400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.7099999999996984 " " y[1] (closed_form) = 3.685518707917712 " " y[1] (numeric) = 3.6855187079171268 " " absolute error = 5.8530957858238250000000000000E-13 " " relative error = 1.58813351652494400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.6999999999996995 " " y[1] (closed_form) = 3.6962000634211343 " " y[1] (numeric) = 3.696200063420551 " " absolute error = 5.8308913253313220000000000000E-13 " " relative error = 1.5775367202213500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.6899999999997006 " " y[1] (closed_form) = 3.7067118003317105 " " y[1] (numeric) = 3.706711800331129 " " absolute error = 5.817568649035820000000000000E-13 " " relative error = 1.569468834484302200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.6799999999997017 " " y[1] (closed_form) = 3.71705286748451 " " y[1] (numeric) = 3.717052867483928 " " absolute error = 5.817568649035820000000000000E-13 " " relative error = 1.56510247672985600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.669999999999703 " " y[1] (closed_form) = 3.7272222307814316 " " y[1] (numeric) = 3.7272222307808516 " " absolute error = 5.7998050806418180000000000000E-13 " " relative error = 1.55606634687458900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.659999999999704 " " y[1] (closed_form) = 3.7372188732946228 " " y[1] (numeric) = 3.737218873294045 " " absolute error = 5.7776006201493150000000000000E-13 " " relative error = 1.545962603751904800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.649999999999705 " " y[1] (closed_form) = 3.7470417953681627 " " y[1] (numeric) = 3.747041795367586 " " absolute error = 5.7687188359523130000000000000E-13 " " relative error = 1.539539495685158800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.639999999999706 " " y[1] (closed_form) = 3.7566900147180284 " " y[1] (numeric) = 3.756690014717453 " " absolute error = 5.7553961596568120000000000000E-13 " " relative error = 1.532039145393475600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.6299999999997072 " " y[1] (closed_form) = 3.766162566530327 " " y[1] (numeric) = 3.7661625665297516 " " absolute error = 5.7553961596568120000000000000E-13 " " relative error = 1.528185801325914700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.6199999999997083 " " y[1] (closed_form) = 3.7754585035577684 " " y[1] (numeric) = 3.7754585035571946 " " absolute error = 5.7376325912628090000000000000E-13 " " relative error = 1.519718091420155800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.6099999999997094 " " y[1] (closed_form) = 3.784576896214399 " " y[1] (numeric) = 3.7845768962138258 " " absolute error = 5.7331916991643080000000000000E-13 " " relative error = 1.514883131295086400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.5999999999997105 " " y[1] (closed_form) = 3.7935168326685504 " " y[1] (numeric) = 3.7935168326679776 " " absolute error = 5.7287508070658080000000000000E-13 " " relative error = 1.51014245086027930000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.5899999999997116 " " y[1] (closed_form) = 3.802277418934027 " " y[1] (numeric) = 3.802277418933455 " " absolute error = 5.7198690228688060000000000000E-13 " " relative error = 1.504327115740118300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.5799999999997127 " " y[1] (closed_form) = 3.8108577789595035 " " y[1] (numeric) = 3.8108577789589324 " " absolute error = 5.7109872386718050000000000000E-13 " " relative error = 1.49860938663292300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.569999999999714 " " y[1] (closed_form) = 3.819257054716127 " " y[1] (numeric) = 3.819257054715557 " " absolute error = 5.7021054544748040000000000000E-13 " " relative error = 1.492988131666519400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.559999999999715 " " y[1] (closed_form) = 3.8274744062833213 " " y[1] (numeric) = 3.827474406282752 " " absolute error = 5.6932236702778030000000000000E-13 " " relative error = 1.487462244275650500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.549999999999716 " " y[1] (closed_form) = 3.8355090119327775 " " y[1] (numeric) = 3.8355090119322095 " " absolute error = 5.6799009939823010000000000000E-13 " " relative error = 1.480872806271964200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.539999999999717 " " y[1] (closed_form) = 3.843360068210626 " " y[1] (numeric) = 3.843360068210059 " " absolute error = 5.67101920978530000000000000E-13 " " relative error = 1.475536798306172300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.5299999999997183 " " y[1] (closed_form) = 3.851026790017782 " " y[1] (numeric) = 3.8510267900172157 " " absolute error = 5.6621374255882980000000000000E-13 " " relative error = 1.470292920388163200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.5199999999997194 " " y[1] (closed_form) = 3.8585084106884544 " " y[1] (numeric) = 3.8585084106878877 " " absolute error = 5.6665783176867990000000000000E-13 " " relative error = 1.468592967684043400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.5099999999997205 " " y[1] (closed_form) = 3.8658041820668085 " " y[1] (numeric) = 3.865804182066243 " " absolute error = 5.6532556413912970000000000000E-13 " " relative error = 1.462375064835500200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.4999999999997216 " " y[1] (closed_form) = 3.8729133745817883 " " y[1] (numeric) = 3.8729133745812234 " " absolute error = 5.6488147492927960000000000000E-13 " " relative error = 1.458544047580918600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.4899999999997227 " " y[1] (closed_form) = 3.8798352773200655 " " y[1] (numeric) = 3.8798352773195015 " " absolute error = 5.6399329650957950000000000000E-13 " " relative error = 1.453652684191141500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.4799999999997238 " " y[1] (closed_form) = 3.886569198097135 " " y[1] (numeric) = 3.8865691980965718 " " absolute error = 5.6310511808987940000000000000E-13 " " relative error = 1.448848815982938800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.469999999999725 " " y[1] (closed_form) = 3.8931144635265307 " " y[1] (numeric) = 3.893114463525968 " " absolute error = 5.6266102888002930000000000000E-13 " " relative error = 1.445272247069637200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.459999999999726 " " y[1] (closed_form) = 3.899470419087164 " " y[1] (numeric) = 3.899470419086602 " " absolute error = 5.6221693967017930000000000000E-13 " " relative error = 1.441777675548542600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.449999999999727 " " y[1] (closed_form) = 3.9056364291887746 " " y[1] (numeric) = 3.9056364291882137 " " absolute error = 5.6088467204062910000000000000E-13 " " relative error = 1.436090333060336400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.439999999999728 " " y[1] (closed_form) = 3.911611877235493 " " y[1] (numeric) = 3.911611877234932 " " absolute error = 5.6088467204062910000000000000E-13 " " relative error = 1.433896535862425000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.4299999999997293 " " y[1] (closed_form) = 3.9173961656874914 " " y[1] (numeric) = 3.9173961656869314 " " absolute error = 5.599964936209290000000000000E-13 " " relative error = 1.429512027723780800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.4199999999997304 " " y[1] (closed_form) = 3.922988716120746 " " y[1] (numeric) = 3.9229887161201864 " " absolute error = 5.5955240441107890000000000000E-13 " " relative error = 1.426342120515690000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.4099999999997315 " " y[1] (closed_form) = 3.9283889692848737 " " y[1] (numeric) = 3.9283889692843146 " " absolute error = 5.5910831520122880000000000000E-13 " " relative error = 1.423250904054465800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.3999999999997326 " " y[1] (closed_form) = 3.933596385159059 " " y[1] (numeric) = 3.9335963851585003 " " absolute error = 5.5866422599137880000000000000E-13 " " relative error = 1.420237795873377500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.3899999999997337 " " y[1] (closed_form) = 3.938610443006053 " " y[1] (numeric) = 3.938610443005495 " " absolute error = 5.5777604757167860000000000000E-13 " " relative error = 1.416174703345297300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.3799999999997348 " " y[1] (closed_form) = 3.94343064142425 " " y[1] (numeric) = 3.943430641423692 " " absolute error = 5.5777604757167860000000000000E-13 " " relative error = 1.414443661598740500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.369999999999736 " " y[1] (closed_form) = 3.9480564983978237 " " y[1] (numeric) = 3.9480564983972672 " " absolute error = 5.5644377994212850000000000000E-13 " " relative error = 1.409411897139620800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.359999999999737 " " y[1] (closed_form) = 3.952487551344934 " " y[1] (numeric) = 3.952487551344377 " " absolute error = 5.5688786915197850000000000000E-13 " " relative error = 1.408955403192815600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.349999999999738 " " y[1] (closed_form) = 3.956723357163977 " " y[1] (numeric) = 3.956723357163421 " " absolute error = 5.5599969073227840000000000000E-13 " " relative error = 1.405202336740562800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.339999999999739 " " y[1] (closed_form) = 3.9607634922779003 " " y[1] (numeric) = 3.960763492277345 " " absolute error = 5.5511151231257830000000000000E-13 " " relative error = 1.40152653243459520000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.3299999999997403 " " y[1] (closed_form) = 3.9646075526765605 " " y[1] (numeric) = 3.9646075526760054 " " absolute error = 5.5511151231257830000000000000E-13 " " relative error = 1.40016762046930700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.3199999999997414 " " y[1] (closed_form) = 3.968255153957121 " " y[1] (numeric) = 3.968255153956566 " " absolute error = 5.5511151231257830000000000000E-13 " " relative error = 1.398880593046100700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.3099999999997425 " " y[1] (closed_form) = 3.971705931362493 " " y[1] (numeric) = 3.971705931361938 " " absolute error = 5.5511151231257830000000000000E-13 " " relative error = 1.397665189482312500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.2999999999997436 " " y[1] (closed_form) = 3.97495953981781 " " y[1] (numeric) = 3.9749595398172564 " " absolute error = 5.5377924468302810000000000000E-13 " " relative error = 1.393169513137762000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.2899999999997447 " " y[1] (closed_form) = 3.978015653964942 " " y[1] (numeric) = 3.978015653964387 " " absolute error = 5.5466742310272820000000000000E-13 " " relative error = 1.394331926647608000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.279999999999746 " " y[1] (closed_form) = 3.9808739681950165 " " y[1] (numeric) = 3.980873968194463 " " absolute error = 5.533351554731780000000000000E-13 " " relative error = 1.389984108751043700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.269999999999747 " " y[1] (closed_form) = 3.9835341966789946 " " y[1] (numeric) = 3.9835341966784417 " " absolute error = 5.528910662633280000000000000E-13 " " relative error = 1.387941056773816500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.259999999999748 " " y[1] (closed_form) = 3.9859960733962447 " " y[1] (numeric) = 3.9859960733956923 " " absolute error = 5.5244697705347790000000000000E-13 " " relative error = 1.385969697112041400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.249999999999749 " " y[1] (closed_form) = 3.9882593521611467 " " y[1] (numeric) = 3.9882593521605947 " " absolute error = 5.5200288784362780000000000000E-13 " " relative error = 1.384069688307783000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.23999999999975 " " y[1] (closed_form) = 3.9903238066477096 " " y[1] (numeric) = 3.990323806647158 " " absolute error = 5.5155879863377780000000000000E-13 " " relative error = 1.38224070366145300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.2299999999997513 " " y[1] (closed_form) = 3.9921892304122055 " " y[1] (numeric) = 3.992189230411654 " " absolute error = 5.5155879863377780000000000000E-13 " " relative error = 1.381594826297418700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.2199999999997524 " " y[1] (closed_form) = 3.9938554369138126 " " y[1] (numeric) = 3.993855436913261 " " absolute error = 5.5155879863377780000000000000E-13 " " relative error = 1.381018435309180600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.2099999999997535 " " y[1] (closed_form) = 3.9953222595332694 " " y[1] (numeric) = 3.9953222595327174 " " absolute error = 5.5200288784362780000000000000E-13 " " relative error = 1.381622937990770500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.1999999999997546 " " y[1] (closed_form) = 3.996589551589535 " " y[1] (numeric) = 3.9965895515889835 " " absolute error = 5.5155879863377780000000000000E-13 " " relative error = 1.380073664092952000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.1899999999997557 " " y[1] (closed_form) = 3.997657186354461 " " y[1] (numeric) = 3.9976571863539103 " " absolute error = 5.5067062021407760000000000000E-13 " " relative error = 1.37748334723079300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.179999999999757 " " y[1] (closed_form) = 3.9985250570654607 " " y[1] (numeric) = 3.99852505706491 " " absolute error = 5.5067062021407760000000000000E-13 " " relative error = 1.377184367623340000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.169999999999758 " " y[1] (closed_form) = 3.9991930769361854 " " y[1] (numeric) = 3.999193076935635 " " absolute error = 5.5022653100422760000000000000E-13 " " relative error = 1.375843877549819700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.159999999999759 " " y[1] (closed_form) = 3.999661179165205 " " y[1] (numeric) = 3.9996611791646552 " " absolute error = 5.4978244179437750000000000000E-13 " " relative error = 1.374572537939641500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.14999999999976 " " y[1] (closed_form) = 3.999929316942688 " " y[1] (numeric) = 3.9999293169421377 " " absolute error = 5.5022653100422760000000000000E-13 " " relative error = 1.37559063524849620000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.139999999999761 " " y[1] (closed_form) = 3.9999974634550783 " " y[1] (numeric) = 3.9999974634545272 " " absolute error = 5.5111470942392770000000000000E-13 " " relative error = 1.377787647264884200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.1299999999997623 " " y[1] (closed_form) = 3.999865611887782 " " y[1] (numeric) = 3.9998656118872304 " " absolute error = 5.5155879863377780000000000000E-13 " " relative error = 1.378943324982019300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.1199999999997634 " " y[1] (closed_form) = 3.9995337754258466 " " y[1] (numeric) = 3.9995337754252946 " " absolute error = 5.5200288784362780000000000000E-13 " " relative error = 1.380168086678687500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.1099999999997645 " " y[1] (closed_form) = 3.9990019872526403 " " y[1] (numeric) = 3.999001987252089 " " absolute error = 5.5111470942392770000000000000E-13 " " relative error = 1.378130621541775500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.0999999999997656 " " y[1] (closed_form) = 3.9982703005465394 " " y[1] (numeric) = 3.9982703005459874 " " absolute error = 5.5200288784362780000000000000E-13 " " relative error = 1.380604227203379200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.0899999999997667 " " y[1] (closed_form) = 3.997338788475603 " " y[1] (numeric) = 3.99733878847505 " " absolute error = 5.528910662633280000000000000E-13 " " relative error = 1.383147877926490500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.079999999999768 " " y[1] (closed_form) = 3.9962075441902627 " " y[1] (numeric) = 3.99620754418971 " " absolute error = 5.528910662633280000000000000E-13 " " relative error = 1.383539418684918000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.069999999999769 " " y[1] (closed_form) = 3.994876680814004 " " y[1] (numeric) = 3.994876680813451 " " absolute error = 5.528910662633280000000000000E-13 " " relative error = 1.384000334525144200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.05999999999977 " " y[1] (closed_form) = 3.993346331432056 " " y[1] (numeric) = 3.9933463314315025 " " absolute error = 5.533351554731780000000000000E-13 " " relative error = 1.385642790653587300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.049999999999771 " " y[1] (closed_form) = 3.9916166490780807 " " y[1] (numeric) = 3.9916166490775273 " " absolute error = 5.533351554731780000000000000E-13 " " relative error = 1.386243229547052000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.039999999999772 " " y[1] (closed_form) = 3.989687806718873 " " y[1] (numeric) = 3.9896878067183192 " " absolute error = 5.5377924468302810000000000000E-13 " " relative error = 1.388026511123077500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.0299999999997733 " " y[1] (closed_form) = 3.987559997237061 " " y[1] (numeric) = 3.9875599972365077 " " absolute error = 5.533351554731780000000000000E-13 " " relative error = 1.387653492001570700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.0199999999997744 " " y[1] (closed_form) = 3.9852334334118193 " " y[1] (numeric) = 3.9852334334112665 " " absolute error = 5.528910662633280000000000000E-13 " " relative error = 1.387349261972816200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.0099999999997755 " " y[1] (closed_form) = 3.982708347897593 " " y[1] (numeric) = 3.9827083478970398 " " absolute error = 5.533351554731780000000000000E-13 " " relative error = 1.389343901531917600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.9999999999997766 " " y[1] (closed_form) = 3.979984993200828 " " y[1] (numeric) = 3.979984993200274 " " absolute error = 5.5422333389287810000000000000E-13 " " relative error = 1.39252619002252700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.9899999999997777 " " y[1] (closed_form) = 3.977063641654725 " " y[1] (numeric) = 3.977063641654171 " " absolute error = 5.5422333389287810000000000000E-13 " " relative error = 1.39354906994217500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.979999999999779 " " y[1] (closed_form) = 3.9739445853920037 " " y[1] (numeric) = 3.97394458539145 " " absolute error = 5.5377924468302810000000000000E-13 " " relative error = 1.39352533177913300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.96999999999978 " " y[1] (closed_form) = 3.9706281363156926 " " y[1] (numeric) = 3.970628136315138 " " absolute error = 5.5466742310272820000000000000E-13 " " relative error = 1.396926138788203700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.959999999999781 " " y[1] (closed_form) = 3.967114626067934 " " y[1] (numeric) = 3.967114626067379 " " absolute error = 5.5511151231257830000000000000E-13 " " relative error = 1.399282765022561400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.949999999999782 " " y[1] (closed_form) = 3.963404405996825 " " y[1] (numeric) = 3.96340440599627 " " absolute error = 5.5511151231257830000000000000E-13 " " relative error = 1.400592660876763800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.9399999999997832 " " y[1] (closed_form) = 3.9594978471212823 " " y[1] (numeric) = 3.9594978471207267 " " absolute error = 5.5555560152242830000000000000E-13 " " relative error = 1.403096107064031300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.9299999999997843 " " y[1] (closed_form) = 3.9553953400939355 " " y[1] (numeric) = 3.955395340093381 " " absolute error = 5.5466742310272820000000000000E-13 " " relative error = 1.402305902220018200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.9199999999997854 " " y[1] (closed_form) = 3.9510972951620715 " " y[1] (numeric) = 3.9510972951615155 " " absolute error = 5.5599969073227840000000000000E-13 " " relative error = 1.40720323797916400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.9099999999997865 " " y[1] (closed_form) = 3.946604142126599 " " y[1] (numeric) = 3.946604142126044 " " absolute error = 5.5511151231257830000000000000E-13 " " relative error = 1.40655483124654200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.8999999999997876 " " y[1] (closed_form) = 3.9419163302990796 " " y[1] (numeric) = 3.9419163302985236 " " absolute error = 5.5599969073227840000000000000E-13 " " relative error = 1.410480700614195600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.8899999999997887 " " y[1] (closed_form) = 3.9370343284567877 " " y[1] (numeric) = 3.9370343284562317 " " absolute error = 5.5599969073227840000000000000E-13 " " relative error = 1.41222972508399600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.87999999999979 " " y[1] (closed_form) = 3.9319586247958407 " " y[1] (numeric) = 3.9319586247952842 " " absolute error = 5.5644377994212850000000000000E-13 " " relative error = 1.415182185369564200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.869999999999791 " " y[1] (closed_form) = 3.9266897268823744 " " y[1] (numeric) = 3.926689726881817 " " absolute error = 5.5733195836182860000000000000E-13 " " relative error = 1.41934300167975500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.859999999999792 " " y[1] (closed_form) = 3.921228161601789 " " y[1] (numeric) = 3.921228161601231 " " absolute error = 5.5777604757167860000000000000E-13 " " relative error = 1.42245241690764500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.849999999999793 " " y[1] (closed_form) = 3.9155744751060615 " " y[1] (numeric) = 3.9155744751055033 " " absolute error = 5.5822013678152870000000000000E-13 " " relative error = 1.425640452839064300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.8399999999997942 " " y[1] (closed_form) = 3.9097292327591306 " " y[1] (numeric) = 3.909729232758571 " " absolute error = 5.5955240441107890000000000000E-13 " " relative error = 1.43117942726739080000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.8299999999997953 " " y[1] (closed_form) = 3.903693019080359 " " y[1] (numeric) = 3.9036930190797987 " " absolute error = 5.604405828307790000000000000E-13 " " relative error = 1.435667661600114600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.8199999999997964 " " y[1] (closed_form) = 3.8974664376860852 " " y[1] (numeric) = 3.8974664376855244 " " absolute error = 5.6088467204062910000000000000E-13 " " relative error = 1.439100710700731000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.8099999999997975 " " y[1] (closed_form) = 3.8910501112292604 " " y[1] (numeric) = 3.891050111228698 " " absolute error = 5.6221693967017930000000000000E-13 " " relative error = 1.444897710383287000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.7999999999997986 " " y[1] (closed_form) = 3.8844446813371816 " " y[1] (numeric) = 3.8844446813366194 " " absolute error = 5.6221693967017930000000000000E-13 " " relative error = 1.44735473353849310000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.7899999999997998 " " y[1] (closed_form) = 3.877650808547335 " " y[1] (numeric) = 3.8776508085467714 " " absolute error = 5.6354920729972950000000000000E-13 " " relative error = 1.453326344026447000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.779999999999801 " " y[1] (closed_form) = 3.870669172241337 " " y[1] (numeric) = 3.870669172240773 " " absolute error = 5.6399329650957950000000000000E-13 " " relative error = 1.45709506912727330000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.769999999999802 " " y[1] (closed_form) = 3.8635004705770006 " " y[1] (numeric) = 3.8635004705764358 " " absolute error = 5.6488147492927960000000000000E-13 " " relative error = 1.462097595771527000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.759999999999803 " " y[1] (closed_form) = 3.8561454204185184 " " y[1] (numeric) = 3.8561454204179535 " " absolute error = 5.6488147492927960000000000000E-13 " " relative error = 1.464886339447155600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.749999999999804 " " y[1] (closed_form) = 3.848604757264778 " " y[1] (numeric) = 3.8486047572642113 " " absolute error = 5.6665783176867990000000000000E-13 " " relative error = 1.472372112774205400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.7399999999998053 " " y[1] (closed_form) = 3.8408792351758088 " " y[1] (numeric) = 3.840879235175242 " " absolute error = 5.6665783176867990000000000000E-13 " " relative error = 1.475333633453180200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.7299999999998064 " " y[1] (closed_form) = 3.832969626697384 " " y[1] (numeric) = 3.832969626696816 " " absolute error = 5.6799009939823010000000000000E-13 " " relative error = 1.4818539010642500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.7199999999998075 " " y[1] (closed_form) = 3.824876722783758 " " y[1] (numeric) = 3.8248767227831895 " " absolute error = 5.6843418860808010000000000000E-13 " " relative error = 1.486150351518707000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.7099999999998086 " " y[1] (closed_form) = 3.81660133271858 " " y[1] (numeric) = 3.8166013327180104 " " absolute error = 5.6976645623763030000000000000E-13 " " relative error = 1.492863431538403500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.6999999999998097 " " y[1] (closed_form) = 3.8081442840339594 " " y[1] (numeric) = 3.808144284033389 " " absolute error = 5.7065463465733050000000000000E-13 " " relative error = 1.498511064955861400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.6899999999998108 " " y[1] (closed_form) = 3.7995064224277177 " " y[1] (numeric) = 3.7995064224271453 " " absolute error = 5.7243099149673070000000000000E-13 " " relative error = 1.506593035657964300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.679999999999812 " " y[1] (closed_form) = 3.7906886116788163 " " y[1] (numeric) = 3.7906886116782434 " " absolute error = 5.7287508070658080000000000000E-13 " " relative error = 1.511269163448554800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.669999999999813 " " y[1] (closed_form) = 3.781691733560983 " " y[1] (numeric) = 3.7816917335604088 " " absolute error = 5.742073483361310000000000000E-13 " " relative error = 1.518387506946357600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.659999999999814 " " y[1] (closed_form) = 3.772516687754532 " " y[1] (numeric) = 3.7725166877539564 " " absolute error = 5.7553961596568120000000000000E-13 " " relative error = 1.5256118490711100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.649999999999815 " " y[1] (closed_form) = 3.7631643917563977 " " y[1] (numeric) = 3.7631643917558213 " " absolute error = 5.7642779438538130000000000000E-13 " " relative error = 1.531763522338025800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.6399999999998163 " " y[1] (closed_form) = 3.753635780788386 " " y[1] (numeric) = 3.753635780787809 " " absolute error = 5.7687188359523130000000000000E-13 " " relative error = 1.536834997544885600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.6299999999998174 " " y[1] (closed_form) = 3.743931807703654 " " y[1] (numeric) = 3.7439318077030763 " " absolute error = 5.7776006201493150000000000000E-13 " " relative error = 1.543190666096296600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.6199999999998185 " " y[1] (closed_form) = 3.7340534428914243 " " y[1] (numeric) = 3.734053442890845 " " absolute error = 5.7909232964448170000000000000E-13 " " relative error = 1.550841032409187300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.6099999999998196 " " y[1] (closed_form) = 3.724001674179944 " " y[1] (numeric) = 3.7240016741793642 " " absolute error = 5.7998050806418180000000000000E-13 " " relative error = 1.557412049745918500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.5999999999998207 " " y[1] (closed_form) = 3.71377750673771 " " y[1] (numeric) = 3.713777506737128 " " absolute error = 5.817568649035820000000000000E-13 " " relative error = 1.566482816614973300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.589999999999822 " " y[1] (closed_form) = 3.7033819629729443 " " y[1] (numeric) = 3.703381962972362 " " absolute error = 5.8220095411343210000000000000E-13 " " relative error = 1.572079142617149300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.579999999999823 " " y[1] (closed_form) = 3.6928160824313627 " " y[1] (numeric) = 3.6928160824307787 " " absolute error = 5.8397731095283230000000000000E-13 " " relative error = 1.58138747751645330000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.569999999999824 " " y[1] (closed_form) = 3.6820809216922123 " " y[1] (numeric) = 3.6820809216916284 " " absolute error = 5.8397731095283230000000000000E-13 " " relative error = 1.58599803581841900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.559999999999825 " " y[1] (closed_form) = 3.6711775542626235 " " y[1] (numeric) = 3.6711775542620373 " " absolute error = 5.8619775700208270000000000000E-13 " " relative error = 1.596756758118237600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.549999999999826 " " y[1] (closed_form) = 3.66010707047025 " " y[1] (numeric) = 3.6601070704696634 " " absolute error = 5.8664184621193270000000000000E-13 " " relative error = 1.60279968568395210000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.5399999999998273 " " y[1] (closed_form) = 3.6488705773542494 " " y[1] (numeric) = 3.648870577353661 " " absolute error = 5.884182030513330000000000000E-13 " " relative error = 1.612603655232923100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.5299999999998284 " " y[1] (closed_form) = 3.637469198554566 " " y[1] (numeric) = 3.637469198553977 " " absolute error = 5.888622922611830000000000000E-13 " " relative error = 1.618879116543946000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.5199999999998295 " " y[1] (closed_form) = 3.625904074199582 " " y[1] (numeric) = 3.625904074198991 " " absolute error = 5.9063864910058330000000000000E-13 " " relative error = 1.628941739808620300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.5099999999998306 " " y[1] (closed_form) = 3.614176360792092 " " y[1] (numeric) = 3.614176360791501 " " absolute error = 5.9063864910058330000000000000E-13 " " relative error = 1.63422752555201100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.4999999999998317 " " y[1] (closed_form) = 3.6022872310936656 " " y[1] (numeric) = 3.6022872310930736 " " absolute error = 5.9197091673013350000000000000E-13 " " relative error = 1.643319587678768500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.489999999999833 " " y[1] (closed_form) = 3.5902378740073653 " " y[1] (numeric) = 3.5902378740067715 " " absolute error = 5.9374727356953370000000000000E-13 " " relative error = 1.653782547023277500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.479999999999834 " " y[1] (closed_form) = 3.5780294944588587 " " y[1] (numeric) = 3.5780294944582622 " " absolute error = 5.9641180882863410000000000000E-13 " " relative error = 1.666872253994193300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.469999999999835 " " y[1] (closed_form) = 3.565663313275925 " " y[1] (numeric) = 3.565663313275328 " " absolute error = 5.9685589803848420000000000000E-13 " " relative error = 1.67389864269076900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.459999999999836 " " y[1] (closed_form) = 3.5531405670663796 " " y[1] (numeric) = 3.5531405670657814 " " absolute error = 5.9818816566803430000000000000E-13 " " relative error = 1.683547707660559300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.449999999999837 " " y[1] (closed_form) = 3.540462508094407 " " y[1] (numeric) = 3.540462508093807 " " absolute error = 6.0040861171728470000000000000E-13 " " relative error = 1.695847958690697200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.4399999999998383 " " y[1] (closed_form) = 3.5276304041553397 " " y[1] (numeric) = 3.527630404154739 " " absolute error = 6.0085270092713470000000000000E-13 " " relative error = 1.70327566124661400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.4299999999998394 " " y[1] (closed_form) = 3.5146455384488773 " " y[1] (numeric) = 3.514645538448276 " " absolute error = 6.0129679013698480000000000000E-13 " " relative error = 1.71083195605083900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.4199999999998405 " " y[1] (closed_form) = 3.501509209450771 " " y[1] (numeric) = 3.501509209450168 " " absolute error = 6.030731469763850000000000000E-13 " " relative error = 1.72232346369004720000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.4099999999998416 " " y[1] (closed_form) = 3.488222730782973 " " y[1] (numeric) = 3.4882227307823683 " " absolute error = 6.0484950381578530000000000000E-13 " " relative error = 1.733976154900004300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.3999999999998427 " " y[1] (closed_form) = 3.4747874310822784 " " y[1] (numeric) = 3.474787431081672 " " absolute error = 6.0618177144533550000000000000E-13 " " relative error = 1.744514688936037700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.389999999999844 " " y[1] (closed_form) = 3.461204653867461 " " y[1] (numeric) = 3.461204653866853 " " absolute error = 6.0795812828473570000000000000E-13 " " relative error = 1.75649286616270700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.379999999999845 " " y[1] (closed_form) = 3.4474757574049235 " " y[1] (numeric) = 3.4474757574043142 " " absolute error = 6.0929039591428590000000000000E-13 " " relative error = 1.76735222751189770000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.369999999999846 " " y[1] (closed_form) = 3.433602114572871 " " y[1] (numeric) = 3.4336021145722606 " " absolute error = 6.101785743339860000000000000E-13 " " relative error = 1.777080028417591700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.359999999999847 " " y[1] (closed_form) = 3.4195851127240253 " " y[1] (numeric) = 3.419585112723414 " " absolute error = 6.1151084196353620000000000000E-13 " " relative error = 1.7882603351153600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.349999999999848 " " y[1] (closed_form) = 3.405426153546892 " " y[1] (numeric) = 3.405426153546278 " " absolute error = 6.1373128801278650000000000000E-13 " " relative error = 1.802215817757669100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.3399999999998493 " " y[1] (closed_form) = 3.3911266529255872 " " y[1] (numeric) = 3.391126652924973 " " absolute error = 6.1417537722263660000000000000E-13 " " relative error = 1.811124856374138300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.3299999999998504 " " y[1] (closed_form) = 3.3766880407982596 " " y[1] (numeric) = 3.3766880407976436 " " absolute error = 6.1595173406203680000000000000E-13 " " relative error = 1.824129817797512400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.3199999999998515 " " y[1] (closed_form) = 3.362111761014088 " " y[1] (numeric) = 3.36211176101347 " " absolute error = 6.1772809090143710000000000000E-13 " " relative error = 1.837321703770836100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.3099999999998526 " " y[1] (closed_form) = 3.3473992711889036 " " y[1] (numeric) = 3.347399271188285 " " absolute error = 6.1861626932113720000000000000E-13 " " relative error = 1.848050439173997400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.2999999999998537 " " y[1] (closed_form) = 3.3325520425594304 " " y[1] (numeric) = 3.3325520425588095 " " absolute error = 6.2083671537038750000000000000E-13 " " relative error = 1.862946797054605700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.289999999999855 " " y[1] (closed_form) = 3.317571559836157 " " y[1] (numeric) = 3.3175715598355344 " " absolute error = 6.2261307220978780000000000000E-13 " " relative error = 1.87671331568967400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.279999999999856 " " y[1] (closed_form) = 3.3024593210548723 " " y[1] (numeric) = 3.3024593210542483 " " absolute error = 6.239453398393380000000000000E-13 " " relative error = 1.88933542908875900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.269999999999857 " " y[1] (closed_form) = 3.287216837426862 " " y[1] (numeric) = 3.287216837426236 " " absolute error = 6.2616578588858830000000000000E-13 " " relative error = 1.90485087189664300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.259999999999858 " " y[1] (closed_form) = 3.2718456331877857 " " y[1] (numeric) = 3.2718456331871577 " " absolute error = 6.2794214272798850000000000000E-13 " " relative error = 1.919229123643524400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.2499999999998592 " " y[1] (closed_form) = 3.2563472454452587 " " y[1] (numeric) = 3.256347245444629 " " absolute error = 6.2971849956738880000000000000E-13 " " relative error = 1.933818638194047300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.2399999999998603 " " y[1] (closed_form) = 3.2407232240251407 " " y[1] (numeric) = 3.240723224024508 " " absolute error = 6.3282712403633920000000000000E-13 " " relative error = 1.95273425186349710000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.2299999999998614 " " y[1] (closed_form) = 3.224975131316551 " " y[1] (numeric) = 3.2249751313159174 " " absolute error = 6.3371530245603940000000000000E-13 " " relative error = 1.965023842516682700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.2199999999998625 " " y[1] (closed_form) = 3.2091045421156403 " " y[1] (numeric) = 3.209104542115004 " " absolute error = 6.3637983771513970000000000000E-13 " " relative error = 1.983044894185961300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.2099999999998636 " " y[1] (closed_form) = 3.1931130434681005 " " y[1] (numeric) = 3.1931130434674637 " " absolute error = 6.3682392692498980000000000000E-13 " " relative error = 1.99436699626933100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.1999999999998647 " " y[1] (closed_form) = 3.177002234510473 " " y[1] (numeric) = 3.177002234509833 " " absolute error = 6.3993255139394020000000000000E-13 " " relative error = 2.014265348770029600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.189999999999866 " " y[1] (closed_form) = 3.160773726310225 " " y[1] (numeric) = 3.1607737263095848 " " absolute error = 6.4037664060379030000000000000E-13 " " relative error = 2.026012287033729700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.179999999999867 " " y[1] (closed_form) = 3.144429141704655 " " y[1] (numeric) = 3.144429141704013 " " absolute error = 6.4170890823334050000000000000E-13 " " relative error = 2.040780311193331500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.169999999999868 " " y[1] (closed_form) = 3.127970115138602 " " y[1] (numeric) = 3.1279701151379573 " " absolute error = 6.4481753270229090000000000000E-13 " " relative error = 2.06145682013243500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.159999999999869 " " y[1] (closed_form) = 3.1113982925010077 " " y[1] (numeric) = 3.111398292500361 " " absolute error = 6.4659388954169120000000000000E-13 " " relative error = 2.078145671996063600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.1499999999998702 " " y[1] (closed_form) = 3.094715330960325 " " y[1] (numeric) = 3.0947153309596764 " " absolute error = 6.4837024638109140000000000000E-13 " " relative error = 2.09508848809009800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.1399999999998713 " " y[1] (closed_form) = 3.077922898798806 " " y[1] (numeric) = 3.0779228987981546 " " absolute error = 6.5147887085004190000000000000E-13 " " relative error = 2.116618551765181700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.1299999999998724 " " y[1] (closed_form) = 3.061022675245674 " " y[1] (numeric) = 3.06102267524502 " " absolute error = 6.5414340610914220000000000000E-13 " " relative error = 2.137009344619250400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.1199999999998735 " " y[1] (closed_form) = 3.0440163503091986 " " y[1] (numeric) = 3.044016350308543 " " absolute error = 6.5547567373869240000000000000E-13 " " relative error = 2.153325075511213500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.1099999999998746 " " y[1] (closed_form) = 3.0269056246077035 " " y[1] (numeric) = 3.0269056246070463 " " absolute error = 6.5725203057809270000000000000E-13 " " relative error = 2.171366114737305600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.0999999999998757 " " y[1] (closed_form) = 3.0096922091995006 " " y[1] (numeric) = 3.0096922091988407 " " absolute error = 6.599165658371930000000000000E-13 " " relative error = 2.19263805056236500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.089999999999877 " " y[1] (closed_form) = 2.9923778254117845 " " y[1] (numeric) = 2.992377825411123 " " absolute error = 6.6169292267659330000000000000E-13 " " relative error = 2.211261282106102600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.079999999999878 " " y[1] (closed_form) = 2.974964204668505 " " y[1] (numeric) = 2.9749642046678417 " " absolute error = 6.6346927951599350000000000000E-13 " " relative error = 2.230175672281484700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.069999999999879 " " y[1] (closed_form) = 2.9574530883172274 " " y[1] (numeric) = 2.9574530883165617 " " absolute error = 6.6568972556524390000000000000E-13 " " relative error = 2.2508885371501100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.05999999999988 " " y[1] (closed_form) = 2.939846227454993 " " y[1] (numeric) = 2.939846227454325 " " absolute error = 6.6791017161449420000000000000E-13 " " relative error = 2.271922134487625600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.0499999999998813 " " y[1] (closed_form) = 2.9221453827532153 " " y[1] (numeric) = 2.922145382752545 " " absolute error = 6.7013061766374450000000000000E-13 " " relative error = 2.29328294758679770000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.0399999999998824 " " y[1] (closed_form) = 2.9043523242816143 " " y[1] (numeric) = 2.9043523242809415 " " absolute error = 6.7279515292284490000000000000E-13 " " relative error = 2.31650666931140800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.0299999999998835 " " y[1] (closed_form) = 2.886468831331209 " " y[1] (numeric) = 2.886468831330535 " " absolute error = 6.7412742055239500000000000000E-13 " " relative error = 2.335474449732736500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.0199999999998846 " " y[1] (closed_form) = 2.868496692236393 " " y[1] (numeric) = 2.8684966922357162 " " absolute error = 6.7679195581149540000000000000E-13 " " relative error = 2.359395977841765300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.0099999999998857 " " y[1] (closed_form) = 2.850437704196098 " " y[1] (numeric) = 2.8504377041954188 " " absolute error = 6.7945649107059580000000000000E-13 " " relative error = 2.38369177502239520000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9999999999998868 " " y[1] (closed_form) = 2.832293673094079 " " y[1] (numeric) = 2.832293673093398 " " absolute error = 6.8123284790999600000000000000E-13 " " relative error = 2.405233801782276600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9899999999998879 " " y[1] (closed_form) = 2.8140664133183257 " " y[1] (numeric) = 2.814066413317643 " " absolute error = 6.8256511553954620000000000000E-13 " " relative error = 2.42554728740275400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.979999999999889 " " y[1] (closed_form) = 2.7957577475796285 " " y[1] (numeric) = 2.7957577475789437 " " absolute error = 6.8478556158879660000000000000E-13 " " relative error = 2.449373741990471300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.96999999999989 " " y[1] (closed_form) = 2.7773695067293014 " " y[1] (numeric) = 2.777369506728615 " " absolute error = 6.8656191842819680000000000000E-13 " " relative error = 2.47198623288951200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9599999999998912 " " y[1] (closed_form) = 2.7589035295761075 " " y[1] (numeric) = 2.758903529575419 " " absolute error = 6.8833827526759700000000000000E-13 " " relative error = 2.494970439844835800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9499999999998923 " " y[1] (closed_form) = 2.740361662702374 " " y[1] (numeric) = 2.7403616627016834 " " absolute error = 6.9055872131684740000000000000E-13 " " relative error = 2.519954685966017000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9399999999998934 " " y[1] (closed_form) = 2.721745760279336 " " y[1] (numeric) = 2.721745760278644 " " absolute error = 6.9189098894639760000000000000E-13 " " relative error = 2.542085300705632700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9299999999998945 " " y[1] (closed_form) = 2.703057683881722 " " y[1] (numeric) = 2.7030576838810285 " " absolute error = 6.9366734578579780000000000000E-13 " " relative error = 2.566232122688768500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9199999999998956 " " y[1] (closed_form) = 2.6842993023016 " " y[1] (numeric) = 2.6842993023009045 " " absolute error = 6.9544370262519810000000000000E-13 " " relative error = 2.59078301003507100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9099999999998967 " " y[1] (closed_form) = 2.6654724913614958 " " y[1] (numeric) = 2.6654724913607977 " " absolute error = 6.9810823788429840000000000000E-13 " " relative error = 2.61907875675622500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8999999999998978 " " y[1] (closed_form) = 2.6465791337268136 " " y[1] (numeric) = 2.6465791337261133 " " absolute error = 7.0032868393354870000000000000E-13 " " relative error = 2.64616566725277600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8899999999998989 " " y[1] (closed_form) = 2.627621118717572 " " y[1] (numeric) = 2.6276211187168705 " " absolute error = 7.0166095156309890000000000000E-13 " " relative error = 2.670327721774245500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8799999999999 " " y[1] (closed_form) = 2.608600342119476 " " y[1] (numeric) = 2.6086003421187725 " " absolute error = 7.0343730840249920000000000000E-13 " " relative error = 2.696608204194896300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.869999999999901 " " y[1] (closed_form) = 2.589518705994333 " " y[1] (numeric) = 2.5895187059936275 " " absolute error = 7.0565775445174950000000000000E-13 " " relative error = 2.72505370522430100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8599999999999022 " " y[1] (closed_form) = 2.570378118489854 " " y[1] (numeric) = 2.5703781184891463 " " absolute error = 7.0787820050099980000000000000E-13 " " relative error = 2.753984697461133000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8499999999999033 " " y[1] (closed_form) = 2.5511804936488396 " " y[1] (numeric) = 2.55118049364813 " " absolute error = 7.0965455734040010000000000000E-13 " " relative error = 2.781671305135345000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8399999999999044 " " y[1] (closed_form) = 2.5319277512177765 " " y[1] (numeric) = 2.5319277512170633 " " absolute error = 7.1320727101920060000000000000E-13 " " relative error = 2.8168547490194800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8299999999999055 " " y[1] (closed_form) = 2.512621816454862 " " y[1] (numeric) = 2.512621816454147 " " absolute error = 7.1498362785860080000000000000E-13 " " relative error = 2.845568016548522500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8199999999999066 " " y[1] (closed_form) = 2.493264619937487 " " y[1] (numeric) = 2.4932646199367694 " " absolute error = 7.1764816311770120000000000000E-13 " " relative error = 2.878347357833580500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8099999999999077 " " y[1] (closed_form) = 2.4738580973691695 " " y[1] (numeric) = 2.4738580973684496 " " absolute error = 7.1986860916695150000000000000E-13 " " relative error = 2.909902592765921000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7999999999999088 " " y[1] (closed_form) = 2.454404189385997 " " y[1] (numeric) = 2.4544041893852735 " " absolute error = 7.234213228457520000000000000E-13 " " relative error = 2.947441688594598700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7899999999999099 " " y[1] (closed_form) = 2.4349048413625534 " " y[1] (numeric) = 2.4349048413618286 " " absolute error = 7.2475359047530220000000000000E-13 " " relative error = 2.97651710310673100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.779999999999911 " " y[1] (closed_form) = 2.4153620032173935 " " y[1] (numeric) = 2.415362003216666 " " absolute error = 7.2741812573440260000000000000E-13 " " relative error = 3.01163189934031460000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.769999999999912 " " y[1] (closed_form) = 2.3957776292180455 " " y[1] (numeric) = 2.3957776292173167 " " absolute error = 7.2875039336395280000000000000E-13 " " relative error = 3.04181149567628500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7599999999999132 " " y[1] (closed_form) = 2.37615367778559 " " y[1] (numeric) = 2.376153677784859 " " absolute error = 7.3097083941320310000000000000E-13 " " relative error = 3.076277625672836000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7499999999999143 " " y[1] (closed_form) = 2.3564921112988158 " " y[1] (numeric) = 2.3564921112980817 " " absolute error = 7.3407946388215350000000000000E-13 " " relative error = 3.115136521622194300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7399999999999154 " " y[1] (closed_form) = 2.336794895897987 " " y[1] (numeric) = 2.3367948958972504 " " absolute error = 7.3674399914125390000000000000E-13 " " relative error = 3.15279702311287700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7299999999999165 " " y[1] (closed_form) = 2.31706400128823 " " y[1] (numeric) = 2.317064001287492 " " absolute error = 7.3807626677080410000000000000E-13 " " relative error = 3.185394388590267500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7199999999999176 " " y[1] (closed_form) = 2.2973014005425645 " " y[1] (numeric) = 2.297301400541824 " " absolute error = 7.4029671282005440000000000000E-13 " " relative error = 3.22246228834063730000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7099999999999187 " " y[1] (closed_form) = 2.2775090699045943 " " y[1] (numeric) = 2.277509069903852 " " absolute error = 7.4251715886930470000000000000E-13 " " relative error = 3.260216034618948500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6999999999999198 " " y[1] (closed_form) = 2.25768898859089 " " y[1] (numeric) = 2.2576889885901466 " " absolute error = 7.4340533728900480000000000000E-13 " " relative error = 3.292771241060057000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.689999999999921 " " y[1] (closed_form) = 2.2378431385930675 " " y[1] (numeric) = 2.237843138592321 " " absolute error = 7.4651396175795530000000000000E-13 " " relative error = 3.335863666598583600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.679999999999922 " " y[1] (closed_form) = 2.2179735044795876 " " y[1] (numeric) = 2.217973504478838 " " absolute error = 7.4962258622690570000000000000E-13 " " relative error = 3.37976348551013400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.669999999999923 " " y[1] (closed_form) = 2.1980820731973028 " " y[1] (numeric) = 2.198082073196552 " " absolute error = 7.5095485385645590000000000000E-13 " " relative error = 3.416409528167101000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6599999999999242 " " y[1] (closed_form) = 2.178170833872767 " " y[1] (numeric) = 2.1781708338720134 " " absolute error = 7.5361938911555630000000000000E-13 " " relative error = 3.45987273998903100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6499999999999253 " " y[1] (closed_form) = 2.158241777613319 " " y[1] (numeric) = 2.158241777612563 " " absolute error = 7.5583983516480660000000000000E-13 " " relative error = 3.50210918445220900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6399999999999264 " " y[1] (closed_form) = 2.1382968973079777 " " y[1] (numeric) = 2.13829689730722 " " absolute error = 7.5761619200420680000000000000E-13 " " relative error = 3.54308231451868300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6299999999999275 " " y[1] (closed_form) = 2.1183381874281517 " " y[1] (numeric) = 2.1183381874273923 " " absolute error = 7.5939254884360710000000000000E-13 " " relative error = 3.584850395231633500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6199999999999286 " " y[1] (closed_form) = 2.0983676438281984 " " y[1] (numeric) = 2.098367643827437 " " absolute error = 7.6161299489285740000000000000E-13 " " relative error = 3.629549841434810400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6099999999999297 " " y[1] (closed_form) = 2.078387263545835 " " y[1] (numeric) = 2.0783872635450713 " " absolute error = 7.6383344094210770000000000000E-13 " " relative error = 3.67512568201062100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5999999999999308 " " y[1] (closed_form) = 2.0583990446024387 " " y[1] (numeric) = 2.058399044601673 " " absolute error = 7.656097977815080000000000000E-13 " " relative error = 3.719443029227496600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.589999999999932 " " y[1] (closed_form) = 2.0384049858032487 " " y[1] (numeric) = 2.038404985802481 " " absolute error = 7.6783024383075830000000000000E-13 " " relative error = 3.76681890585245540000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.579999999999933 " " y[1] (closed_form) = 2.018407086537483 " " y[1] (numeric) = 2.0184070865367123 " " absolute error = 7.7049477908985860000000000000E-13 " " relative error = 3.81734083391284300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5699999999999341 " " y[1] (closed_form) = 1.9984073465784018 " " y[1] (numeric) = 1.9984073465776295 " " absolute error = 7.7227113592925890000000000000E-13 " " relative error = 3.86443303089088700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5599999999999352 " " y[1] (closed_form) = 1.9784077658833357 " " y[1] (numeric) = 1.9784077658825614 " " absolute error = 7.7426953737358420000000000000E-13 " " relative error = 3.91359936371803500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5499999999999363 " " y[1] (closed_form) = 1.9584103443936876 " " y[1] (numeric) = 1.9584103443929113 " " absolute error = 7.7626793881790950000000000000E-13 " " relative error = 3.963765515435110000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5399999999999374 " " y[1] (closed_form) = 1.9384170818349427 " " y[1] (numeric) = 1.938417081834164 " " absolute error = 7.7871042947208480000000000000E-13 " " relative error = 4.01724910892212500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5299999999999385 " " y[1] (closed_form) = 1.9184299775166949 " " y[1] (numeric) = 1.9184299775159142 " " absolute error = 7.8070883091641010000000000000E-13 " " relative error = 4.069519555397043700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5199999999999396 " " y[1] (closed_form) = 1.8984510301327209 " " y[1] (numeric) = 1.898451030131938 " " absolute error = 7.8292927696566040000000000000E-13 " " relative error = 4.12404251960571100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5099999999999407 " " y[1] (closed_form) = 1.8784822375611099 " " y[1] (numeric) = 1.878482237560325 " " absolute error = 7.8492767840998570000000000000E-13 " " relative error = 4.17852063072515900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4999999999999418 " " y[1] (closed_form) = 1.858525596664478 " " y[1] (numeric) = 1.858525596663691 " " absolute error = 7.869260798543110000000000000E-13 " " relative error = 4.234141737227715700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.489999999999943 " " y[1] (closed_form) = 1.838583103090285 " " y[1] (numeric) = 1.8385831030894957 " " absolute error = 7.8936857050848630000000000000E-13 " " relative error = 4.293352686542794600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.479999999999944 " " y[1] (closed_form) = 1.818656751071269 " " y[1] (numeric) = 1.8186567510704774 " " absolute error = 7.9158901655773660000000000000E-13 " " relative error = 4.352602634287397500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4699999999999451 " " y[1] (closed_form) = 1.7987485332260276 " " y[1] (numeric) = 1.7987485332252338 " " absolute error = 7.9380946260698690000000000000E-13 " " relative error = 4.41312083342356900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4599999999999462 " " y[1] (closed_form) = 1.7788604403597539 " " y[1] (numeric) = 1.7788604403589583 " " absolute error = 7.9558581944638720000000000000E-13 " " relative error = 4.47244652472843400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4499999999999473 " " y[1] (closed_form) = 1.7589944612651625 " " y[1] (numeric) = 1.7589944612643644 " " absolute error = 7.9802831010056250000000000000E-13 " " relative error = 4.53684379157497760000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4399999999999484 " " y[1] (closed_form) = 1.739152582523607 " " y[1] (numeric) = 1.739152582522807 " " absolute error = 8.0002671154488780000000000000E-13 " " relative error = 4.60009500939822400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4299999999999495 " " y[1] (closed_form) = 1.7193367883064266 " " y[1] (numeric) = 1.7193367883056248 " " absolute error = 8.0180306838428800000000000000E-13 " " relative error = 4.663443915337125400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4199999999999506 " " y[1] (closed_form) = 1.6995490601765306 " " y[1] (numeric) = 1.6995490601757264 " " absolute error = 8.0424555903846340000000000000E-13 " " relative error = 4.73211146346623900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4099999999999517 " " y[1] (closed_form) = 1.6797913768902424 " " y[1] (numeric) = 1.679791376889436 " " absolute error = 8.0646600508771370000000000000E-13 " " relative error = 4.800989076278656700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3999999999999528 " " y[1] (closed_form) = 1.6600657141994253 " " y[1] (numeric) = 1.660065714198617 " " absolute error = 8.082423619271140000000000000E-13 " " relative error = 4.86873715307645400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.389999999999954 " " y[1] (closed_form) = 1.6403740446539103 " " y[1] (numeric) = 1.6403740446531005 " " absolute error = 8.0979667416158920000000000000E-13 " " relative error = 4.936658665142692500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.379999999999955 " " y[1] (closed_form) = 1.6207183374042429 " " y[1] (numeric) = 1.6207183374034309 " " absolute error = 8.1201712021083950000000000000E-13 " " relative error = 5.01022973252325500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3699999999999561 " " y[1] (closed_form) = 1.6011005580047684 " " y[1] (numeric) = 1.601100558003954 " " absolute error = 8.1445961086501480000000000000E-13 " " relative error = 5.08687356826584300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3599999999999572 " " y[1] (closed_form) = 1.5815226682170778 " " y[1] (numeric) = 1.581522668216261 " " absolute error = 8.1668005691426520000000000000E-13 " " relative error = 5.163884611498776000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3499999999999583 " " y[1] (closed_form) = 1.5619866258138355 " " y[1] (numeric) = 1.5619866258130164 " " absolute error = 8.1912254756844050000000000000E-13 " " relative error = 5.24410730560293000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3399999999999594 " " y[1] (closed_form) = 1.5424943843830023 " " y[1] (numeric) = 1.542494384382181 " " absolute error = 8.2134299361769080000000000000E-13 " " relative error = 5.32477136988883100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3299999999999605 " " y[1] (closed_form) = 1.523047893132477 " " y[1] (numeric) = 1.523047893131654 " " absolute error = 8.228973058521660000000000000E-13 " " relative error = 5.402964079873417000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3199999999999616 " " y[1] (closed_form) = 1.5036490966951797 " " y[1] (numeric) = 1.5036490966943545 " " absolute error = 8.2511775190141630000000000000E-13 " " relative error = 5.48743555737116500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3099999999999627 " " y[1] (closed_form) = 1.4842999349345884 " " y[1] (numeric) = 1.4842999349337616 " " absolute error = 8.2689410874081660000000000000E-13 " " relative error = 5.57093677146362600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2999999999999639 " " y[1] (closed_form) = 1.4650023427507555 " " y[1] (numeric) = 1.4650023427499261 " " absolute error = 8.2933659939499190000000000000E-13 " " relative error = 5.66099162570478500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.289999999999965 " " y[1] (closed_form) = 1.4457582498868176 " " y[1] (numeric) = 1.4457582498859858 " " absolute error = 8.3177909004916730000000000000E-13 " " relative error = 5.75323772224217800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.279999999999966 " " y[1] (closed_form) = 1.426569580736024 " " y[1] (numeric) = 1.4265695807351897 " " absolute error = 8.3422158070334260000000000000E-13 " " relative error = 5.8477454725547600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2699999999999672 " " y[1] (closed_form) = 1.4074382541492998 " " y[1] (numeric) = 1.4074382541484634 " " absolute error = 8.3644202675259290000000000000E-13 " " relative error = 5.94301046093254600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2599999999999683 " " y[1] (closed_form) = 1.388366183243361 " " y[1] (numeric) = 1.388366183242522 " " absolute error = 8.3888451740676830000000000000E-13 " " relative error = 6.04224251160490600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2499999999999694 " " y[1] (closed_form) = 1.3693552752094043 " " y[1] (numeric) = 1.3693552752085636 " " absolute error = 8.4066087424616850000000000000E-13 " " relative error = 6.13909983380765300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2399999999999705 " " y[1] (closed_form) = 1.3504074311223917 " " y[1] (numeric) = 1.3504074311215488 " " absolute error = 8.4288132029541880000000000000E-13 " " relative error = 6.24168159082816800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2299999999999716 " " y[1] (closed_form) = 1.3315245457509413 " " y[1] (numeric) = 1.3315245457500964 " " absolute error = 8.4487972173974410000000000000E-13 " " relative error = 6.34520576008801000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2199999999999727 " " y[1] (closed_form) = 1.3127085073678546 " " y[1] (numeric) = 1.312708507367008 " " absolute error = 8.4665607857914440000000000000E-13 " " relative error = 6.44968836437874700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2099999999999738 " " y[1] (closed_form) = 1.2939611975612904 " " y[1] (numeric) = 1.2939611975604417 " " absolute error = 8.4865448002346970000000000000E-13 " " relative error = 6.55857750311923100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1999999999999749 " " y[1] (closed_form) = 1.2752844910466061 " " y[1] (numeric) = 1.2752844910457553 " " absolute error = 8.50874926072720000000000000E-13 " " relative error = 6.67204009808368500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.189999999999976 " " y[1] (closed_form) = 1.2566802554788894 " " y[1] (numeric) = 1.2566802554780367 " " absolute error = 8.5265128291212020000000000000E-13 " " relative error = 6.7849501032161610000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.179999999999977 " " y[1] (closed_form) = 1.238150351266194 " " y[1] (numeric) = 1.2381503512653396 " " absolute error = 8.5442763975152050000000000000E-13 " " relative error = 6.90083913377515400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1699999999999782 " " y[1] (closed_form) = 1.2196966313834992 " " y[1] (numeric) = 1.219696631382643 " " absolute error = 8.5620399659092070000000000000E-13 " " relative error = 7.01981111171661200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1599999999999793 " " y[1] (closed_form) = 1.201320941187416 " " y[1] (numeric) = 1.2013209411865569 " " absolute error = 8.5909057645494610000000000000E-13 " " relative error = 7.15121619045281400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1499999999999804 " " y[1] (closed_form) = 1.1830251182316496 " " y[1] (numeric) = 1.1830251182307887 " " absolute error = 8.6086693329434640000000000000E-13 " " relative error = 7.27682717828632800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1399999999999815 " " y[1] (closed_form) = 1.1648109920832503 " " y[1] (numeric) = 1.164810992082387 " " absolute error = 8.6330942394852170000000000000E-13 " " relative error = 7.41158376608812100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1299999999999826 " " y[1] (closed_form) = 1.1466803841396538 " " y[1] (numeric) = 1.1466803841387887 " " absolute error = 8.650857807879220000000000000E-13 " " relative error = 7.54426248807761500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1199999999999837 " " y[1] (closed_form) = 1.1286351074465464 " " y[1] (numeric) = 1.128635107445679 " " absolute error = 8.6730622683717230000000000000E-13 " " relative error = 7.68455828739359800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1099999999999848 " " y[1] (closed_form) = 1.110676966516559 " " y[1] (numeric) = 1.1106769665156897 " " absolute error = 8.6930462828149760000000000000E-13 " " relative error = 7.82679982108494800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0999999999999859 " " y[1] (closed_form) = 1.0928077571488202 " " y[1] (numeric) = 1.0928077571479489 " " absolute error = 8.7130302972582290000000000000E-13 " " relative error = 7.97306776078427400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.089999999999987 " " y[1] (closed_form) = 1.0750292662493752 " " y[1] (numeric) = 1.0750292662485024 " " absolute error = 8.7285734196029810000000000000E-13 " " relative error = 8.11938213557267700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.079999999999988 " " y[1] (closed_form) = 1.057343271652499 " " y[1] (numeric) = 1.0573432716516242 " " absolute error = 8.7485574340462340000000000000E-13 " " relative error = 8.27409382420649700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0699999999999892 " " y[1] (closed_form) = 1.0397515419429126 " " y[1] (numeric) = 1.0397515419420365 " " absolute error = 8.7618801103417350000000000000E-13 " " relative error = 8.42689792406463700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0599999999999903 " " y[1] (closed_form) = 1.0222558362789278 " " y[1] (numeric) = 1.0222558362780498 " " absolute error = 8.7796436787357380000000000000E-13 " " relative error = 8.58849944128875200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0499999999999914 " " y[1] (closed_form) = 1.0048579042165313 " " y[1] (numeric) = 1.0048579042156511 " " absolute error = 8.8018481392282410000000000000E-13 " " relative error = 8.75929631671741200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0399999999999925 " " y[1] (closed_form) = 0.9875594855344304 " " y[1] (numeric) = 0.9875594855335483 " " absolute error = 8.8207219306468690000000000000E-13 " " relative error = 8.93183859792853100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0299999999999936 " " y[1] (closed_form) = 0.9703623100600782 " " y[1] (numeric) = 0.9703623100591946 " " absolute error = 8.8362650529916210000000000000E-13 " " relative error = 9.10615031249981200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0199999999999947 " " y[1] (closed_form) = 0.953268097496692 " " y[1] (numeric) = 0.9532680974958061 " " absolute error = 8.8584695134841240000000000000E-13 " " relative error = 9.29273678280717300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0099999999999958 " " y[1] (closed_form) = 0.9362785572512821 " " y[1] (numeric) = 0.9362785572503944 " " absolute error = 8.8762330818781270000000000000E-13 " " relative error = 9.48033361773967100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9999999999999968 " " y[1] (closed_form) = 0.9193953882637151 " " y[1] (numeric) = 0.919395388262826 " " absolute error = 8.8917762042228790000000000000E-13 " " relative error = 9.67133000418357800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9899999999999968 " " y[1] (closed_form) = 0.9026202788368193 " " y[1] (numeric) = 0.9026202788359303 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 9.84861072435614200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9799999999999968 " " y[1] (closed_form) = 0.88595490646756 " " y[1] (numeric) = 0.8859549064666709 " " absolute error = 8.8917762042228790000000000000E-13 " " relative error = 1.0036375598026510000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9699999999999968 " " y[1] (closed_form) = 0.869400937679286 " " y[1] (numeric) = 0.8694009376783969 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 1.02261978287374920000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9599999999999967 " " y[1] (closed_form) = 0.8529600278550813 " " y[1] (numeric) = 0.8529600278541921 " " absolute error = 8.8917762042228790000000000000E-13 " " relative error = 1.0424610666202990000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9499999999999967 " " y[1] (closed_form) = 0.8366338210722278 " " y[1] (numeric) = 0.8366338210713385 " " absolute error = 8.8928864272475040000000000000E-13 " " relative error = 1.0629365205258380000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9399999999999967 " " y[1] (closed_form) = 0.8204239499377984 " " y[1] (numeric) = 0.8204239499369091 " " absolute error = 8.8928864272475040000000000000E-13 " " relative error = 1.08393793573697230000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9299999999999967 " " y[1] (closed_form) = 0.8043320354253982 " " y[1] (numeric) = 0.8043320354245092 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 1.10534774068723060000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9199999999999967 " " y[1] (closed_form) = 0.7883596867130692 " " y[1] (numeric) = 0.78835968671218 " " absolute error = 8.8917762042228790000000000000E-13 " " relative error = 1.12788316730090780000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9099999999999967 " " y[1] (closed_form) = 0.7725085010223718 " " y[1] (numeric) = 0.7725085010214827 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 1.15088260769065390000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8999999999999967 " " y[1] (closed_form) = 0.7567800634586659 " " y[1] (numeric) = 0.7567800634577769 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 1.17465511942085680000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8899999999999967 " " y[1] (closed_form) = 0.741175946852601 " " y[1] (numeric) = 0.7411759468517122 " " absolute error = 8.8884455351490030000000000000E-13 " " relative error = 1.19923556247254540000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8799999999999967 " " y[1] (closed_form) = 0.7256977116028346 " " y[1] (numeric) = 0.7256977116019455 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 1.22511974876723940000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8699999999999967 " " y[1] (closed_form) = 0.7103469055199926 " " y[1] (numeric) = 0.7103469055191036 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 1.25143865470438540000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8599999999999967 " " y[1] (closed_form) = 0.6951250636718913 " " y[1] (numeric) = 0.6951250636710022 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 1.2790023617095140000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8499999999999966 " " y[1] (closed_form) = 0.6800337082300308 " " y[1] (numeric) = 0.6800337082291416 " " absolute error = 8.8928864272475040000000000000E-13 " " relative error = 1.3077125912469270000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8399999999999966 " " y[1] (closed_form) = 0.6650743483173787 " " y[1] (numeric) = 0.6650743483164898 " " absolute error = 8.8884455351490030000000000000E-13 " " relative error = 1.33645893239403180000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8299999999999966 " " y[1] (closed_form) = 0.6502484798574608 " " y[1] (numeric) = 0.6502484798565719 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 1.36710135179743650000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8199999999999966 " " y[1] (closed_form) = 0.6355575854247678 " " y[1] (numeric) = 0.6355575854238789 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 1.39870185834260700000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8099999999999966 " " y[1] (closed_form) = 0.621003134096501 " " y[1] (numeric) = 0.6210031340956118 " " absolute error = 8.8917762042228790000000000000E-13 " " relative error = 1.4318407937118620000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7999999999999966 " " y[1] (closed_form) = 0.6065865813056642 " " y[1] (numeric) = 0.6065865813047749 " " absolute error = 8.8928864272475040000000000000E-13 " " relative error = 1.46605393217003940000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7899999999999966 " " y[1] (closed_form) = 0.5923093686955231 " " y[1] (numeric) = 0.5923093686946338 " " absolute error = 8.8928864272475040000000000000E-13 " " relative error = 1.50139216045709650000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7799999999999966 " " y[1] (closed_form) = 0.5781729239754405 " " y[1] (numeric) = 0.5781729239745514 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 1.5377174565815380000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7699999999999966 " " y[1] (closed_form) = 0.5641786607781086 " " y[1] (numeric) = 0.5641786607772195 " " absolute error = 8.8917762042228790000000000000E-13 " " relative error = 1.57605681008201270000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7599999999999966 " " y[1] (closed_form) = 0.5503279785181849 " " y[1] (numeric) = 0.5503279785172959 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 1.61552134876683770000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7499999999999966 " " y[1] (closed_form) = 0.5366222622523535 " " y[1] (numeric) = 0.5366222622514644 " " absolute error = 8.8917762042228790000000000000E-13 " " relative error = 1.65698981009502120000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7399999999999965 " " y[1] (closed_form) = 0.5230628825408195 " " y[1] (numeric) = 0.5230628825399304 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 1.69973176800677170000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7299999999999965 " " y[1] (closed_form) = 0.5096511953102548 " " y[1] (numeric) = 0.5096511953093655 " " absolute error = 8.8928864272475040000000000000E-13 " " relative error = 1.7448966095005190000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7199999999999965 " " y[1] (closed_form) = 0.49638854171820546 " " y[1] (numeric) = 0.49638854171731644 " " absolute error = 8.8901108696859410000000000000E-13 " " relative error = 1.79095811497050300000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7099999999999965 " " y[1] (closed_form) = 0.48327624801897917 " " y[1] (numeric) = 0.4832762480180901 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 1.83966541241006750000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6999999999999965 " " y[1] (closed_form) = 0.47031562543101846 " " y[1] (numeric) = 0.4703156254301296 " " absolute error = 8.8884455351490030000000000000E-13 " " relative error = 1.88988948155894870000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6899999999999965 " " y[1] (closed_form) = 0.45750797000578214 " " y[1] (numeric) = 0.4575079700048933 " " absolute error = 8.8884455351490030000000000000E-13 " " relative error = 1.94279578015584500000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6799999999999965 " " y[1] (closed_form) = 0.4448545624981398 " " y[1] (numeric) = 0.44485456249725075 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 1.99855564732696900000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6699999999999965 " " y[1] (closed_form) = 0.4323566682382971 " " y[1] (numeric) = 0.43235666823740804 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 2.05632678626760240000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6599999999999965 " " y[1] (closed_form) = 0.4200155370052654 " " y[1] (numeric) = 0.42001553700437644 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 2.11648260003824280000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6499999999999965 " " y[1] (closed_form) = 0.40783240290188416 " " y[1] (numeric) = 0.40783240290099493 " " absolute error = 8.8923313157351910000000000000E-13 " " relative error = 2.18038862347936040000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6399999999999965 " " y[1] (closed_form) = 0.39580848423141035 " " y[1] (numeric) = 0.39580848423052134 " " absolute error = 8.8901108696859410000000000000E-13 " " relative error = 2.2460637464477182000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6299999999999965 " " y[1] (closed_form) = 0.38394498337569205 " " y[1] (numeric) = 0.3839449833748029 " " absolute error = 8.8917762042228790000000000000E-13 " " relative error = 2.3158985243263960000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6199999999999964 " " y[1] (closed_form) = 0.3722430866749279 " " y[1] (numeric) = 0.3722430866740389 " " absolute error = 8.8901108696859410000000000000E-13 " " relative error = 2.3882541242329340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6099999999999964 " " y[1] (closed_form) = 0.36070396430903695 " " y[1] (numeric) = 0.3607039643081478 " " absolute error = 8.8917762042228790000000000000E-13 " " relative error = 2.46511740486576840000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5999999999999964 " " y[1] (closed_form) = 0.34932877018063924 " " y[1] (numeric) = 0.3493287701797503 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 2.5447534005220370000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5899999999999964 " " y[1] (closed_form) = 0.3381186417996691 " " y[1] (numeric) = 0.33811864179878 " " absolute error = 8.8912210927105660000000000000E-13 " " relative error = 2.62961576013265140000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5799999999999964 " " y[1] (closed_form) = 0.32707470016962226 " " y[1] (numeric) = 0.32707470016873313 " " absolute error = 8.8912210927105660000000000000E-13 " " relative error = 2.7184068618268376000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5699999999999964 " " y[1] (closed_form) = 0.3161980496754585 " " y[1] (numeric) = 0.31619804967456955 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 2.811388548189260300000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5599999999999964 " " y[1] (closed_form) = 0.3054897779731639 " " y[1] (numeric) = 0.3054897779722748 " " absolute error = 8.8912210927105660000000000000E-13 " " relative error = 2.91048072105758840000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5499999999999964 " " y[1] (closed_form) = 0.29495095588098463 " " y[1] (numeric) = 0.2949509558800957 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 3.01390979785827350000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5399999999999964 " " y[1] (closed_form) = 0.284582637272348 " " y[1] (numeric) = 0.28458263727145894 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 3.12410696113192940000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5299999999999964 " " y[1] (closed_form) = 0.2743858589704744 " " y[1] (numeric) = 0.2743858589695852 " " absolute error = 8.8923313157351910000000000000E-13 " " relative error = 3.2408125364405390000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5199999999999964 " " y[1] (closed_form) = 0.26436164064469647 " " y[1] (numeric) = 0.26436164064380746 " " absolute error = 8.8901108696859410000000000000E-13 " " relative error = 3.36285962214703400000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5099999999999963 " " y[1] (closed_form) = 0.254510984708494 " " y[1] (numeric) = 0.25451098470760486 " " absolute error = 8.8912210927105660000000000000E-13 " " relative error = 3.4934527886465060000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.49999999999999634 " " y[1] (closed_form) = 0.24483487621925104 " " y[1] (numeric) = 0.24483487621836203 " " absolute error = 8.8901108696859410000000000000E-13 " " relative error = 3.63106392641741000000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.4899999999999963 " " y[1] (closed_form) = 0.23533428277975343 " " y[1] (numeric) = 0.23533428277886453 " " absolute error = 8.8890006466613160000000000000E-13 " " relative error = 3.77718050326752760000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.4799999999999963 " " y[1] (closed_form) = 0.22601015444142813 " " y[1] (numeric) = 0.22601015444053918 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 3.93325502570611660000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.4699999999999963 " " y[1] (closed_form) = 0.21686342360933875 " " y[1] (numeric) = 0.21686342360844973 " " absolute error = 8.8901108696859410000000000000E-13 " " relative error = 4.09940538691334570000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.4599999999999963 " " y[1] (closed_form) = 0.2078950049489463 " " y[1] (numeric) = 0.2078950049480572 " " absolute error = 8.890943536954410000000000000E-13 " " relative error = 4.276650869576110000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.4499999999999963 " " y[1] (closed_form) = 0.1991057952946429 " " y[1] (numeric) = 0.19910579529375397 " " absolute error = 8.8892782024174720000000000000E-13 " " relative error = 4.46460043479038060000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.4399999999999963 " " y[1] (closed_form) = 0.19049667356006994 " " y[1] (numeric) = 0.19049667355918107 " " absolute error = 8.888723090905160000000000000E-13 " " relative error = 4.6660778504892110000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.4299999999999963 " " y[1] (closed_form) = 0.18206850065022673 " " y[1] (numeric) = 0.18206850064933774 " " absolute error = 8.8898333139297850000000000000E-13 " " relative error = 4.8826860671567320000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.41999999999999627 " " y[1] (closed_form) = 0.17382211937538028 " " y[1] (numeric) = 0.17382211937449152 " " absolute error = 8.8876128678805340000000000000E-13 " " relative error = 5.1130505713643680000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.40999999999999626 " " y[1] (closed_form) = 0.16575835436678688 " " y[1] (numeric) = 0.16575835436589792 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 5.3629609150818370000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.39999999999999625 " " y[1] (closed_form) = 0.15787801199422702 " " y[1] (numeric) = 0.157878011993338 " " absolute error = 8.8901108696859410000000000000E-13 " " relative error = 5.6310000090519360000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.38999999999999624 " " y[1] (closed_form) = 0.15018188028537116 " " y[1] (numeric) = 0.15018188028448215 " " absolute error = 8.8901108696859410000000000000E-13 " " relative error = 5.9195629011923520000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.37999999999999623 " " y[1] (closed_form) = 0.1426707288469765 " " y[1] (numeric) = 0.14267072884608778 " " absolute error = 8.8873353121243780000000000000E-13 " " relative error = 6.2292632721156240000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.3699999999999962 " " y[1] (closed_form) = 0.1353453087879285 " " y[1] (numeric) = 0.13534530878703946 " " absolute error = 8.8903884254420970000000000000E-13 " " relative error = 6.5686712787159670000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.3599999999999962 " " y[1] (closed_form) = 0.12820635264412772 " " y[1] (numeric) = 0.12820635264323868 " " absolute error = 8.8903884254420970000000000000E-13 " " relative error = 6.9344367436454860000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.3499999999999962 " " y[1] (closed_form) = 0.12125457430523945 " " y[1] (numeric) = 0.12125457430435062 " " absolute error = 8.8883067572709250000000000000E-13 " " relative error = 7.3302857300014110000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.3399999999999962 " " y[1] (closed_form) = 0.11449066894330506 " " y[1] (numeric) = 0.11449066894241607 " " absolute error = 8.8899720918078630000000000000E-13 " " relative error = 7.7648005499995050000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.3299999999999962 " " y[1] (closed_form) = 0.10791531294322354 " " y[1] (numeric) = 0.10791531294233467 " " absolute error = 8.888723090905160000000000000E-13 " " relative error = 8.2367579247828340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.3199999999999962 " " y[1] (closed_form) = 0.1015291638351159 " " y[1] (numeric) = 0.10152916383422694 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 8.7556672608969090000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.30999999999999617 " " y[1] (closed_form) = 9.5332860228570900E-2 " " y[1] (numeric) = 9.53328602276819700E-2 " " absolute error = 8.8892782024174720000000000000E-13 " " relative error = 9.3244639687768330000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.29999999999999616 " " y[1] (closed_form) = 8.9327021748785710E-2 " " y[1] (numeric) = 8.93270217478968200E-2 " " absolute error = 8.8888618687832380000000000000E-13 " " relative error = 9.9509215629973370000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.28999999999999615 " " y[1] (closed_form) = 8.35122489746034100E-2 " " y[1] (numeric) = 8.35122489737145900E-2 " " absolute error = 8.8881679793928470000000000000E-13 " " relative error = 1.0642951289811145000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.27999999999999614 " " y[1] (closed_form) = 7.78891233784558800E-2 " " y[1] (numeric) = 7.78891233775671000E-2 " " absolute error = 8.8877516457586130000000000000E-13 " " relative error = 1.141077375152095100000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.26999999999999613 " " y[1] (closed_form) = 7.24582072682169500E-2 " " y[1] (numeric) = 7.24582072673280500E-2 " " absolute error = 8.8890006466613160000000000000E-13 " " relative error = 1.2267762316775377000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.2599999999999961 " " y[1] (closed_form) = 6.72200437309715700E-2 " " y[1] (numeric) = 6.72200437300826800E-2 " " absolute error = 8.8888618687832380000000000000E-13 " " relative error = 1.3223528839639392000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.24999999999999611 " " y[1] (closed_form) = 6.217515657870853000E-2 " " y[1] (numeric) = 6.21751565778196700E-2 " " absolute error = 8.888723090905160000000000000E-13 " " relative error = 1.4296261690395234000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.2399999999999961 " " y[1] (closed_form) = 5.7324050295938900E-2 " " y[1] (numeric) = 5.732405029505010000E-2 " " absolute error = 8.887959812575730000000000000E-13 " " relative error = 1.5504765917082092000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.2299999999999961 " " y[1] (closed_form) = 5.266720998924856000E-2 " " y[1] (numeric) = 5.26672099883597100E-2 " " absolute error = 8.8885149240880420000000000000E-13 " " relative error = 1.6876752966224215000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.2199999999999961 " " y[1] (closed_form) = 4.820510133878741500E-2 " " y[1] (numeric) = 4.820510133789849000E-2 " " absolute error = 8.8892088134784330000000000000E-13 " " relative error = 1.8440390262857680000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.20999999999999608 " " y[1] (closed_form) = 4.393817055170190500E-2 " " y[1] (numeric) = 4.39381705508130600E-2 " " absolute error = 8.8884455351490030000000000000E-13 " " relative error = 2.022943928603035000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.19999999999999607 " " y[1] (closed_form) = 3.986684431751530400E-2 " " y[1] (numeric) = 3.98668443166263700E-2 " " absolute error = 8.8893475913565110000000000000E-13 " " relative error = 2.22975952662774980000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.18999999999999606 " " y[1] (closed_form) = 3.59915297654578300E-2 " " y[1] (numeric) = 3.599152976456907500E-2 " " absolute error = 8.8875434789414950000000000000E-13 " " relative error = 2.4693430751229536000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.17999999999999605 " " y[1] (closed_form) = 3.23126144237556600E-2 " " y[1] (numeric) = 3.23126144228669700E-2 " " absolute error = 8.8869189784901440000000000000E-13 " " relative error = 2.7502940065278775000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.16999999999999604 " " y[1] (closed_form) = 2.883046618087714600E-2 " " y[1] (numeric) = 2.88304661799884600E-2 " " absolute error = 8.8868495895511050000000000000E-13 " " relative error = 3.0824508815766677000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.15999999999999603 " " y[1] (closed_form) = 2.554543324874470000E-2 " " y[1] (numeric) = 2.554543324785606000E-2 " " absolute error = 8.8863985614473510000000000000E-13 " " relative error = 3.4786642586631517000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.14999999999999603 " " y[1] (closed_form) = 2.245784412791429500E-2 " " y[1] (numeric) = 2.245784412702545600E-2 " " absolute error = 8.8883761462099640000000000000E-13 " " relative error = 3.9578047187361287000000000E-9 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.13999999999999602 " " y[1] (closed_form) = 1.956800757472454400E-2 " " y[1] (numeric) = 1.956800757383576000E-2 " " absolute error = 8.8878210346976520000000000000E-13 " " relative error = 4.5420163502889305000000000E-9 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.129999999999996 " " y[1] (closed_form) = 1.687621257042293300E-2 " " y[1] (numeric) = 1.687621256953411300E-2 " " absolute error = 8.8882026738623670000000000000E-13 " " relative error = 5.266704621533231000000000E-9 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.119999999999996 " " y[1] (closed_form) = 1.438272829226672200E-2 " " y[1] (numeric) = 1.438272829137776400E-2 " " absolute error = 8.8895731054083880000000000000E-13 " " relative error = 6.180727970915029000000000E-9 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.10999999999999599 " " y[1] (closed_form) = 1.20878040866054800E-2 " " y[1] (numeric) = 1.20878040857166500E-2 " " absolute error = 8.8883067572709250000000000000E-13 " " relative error = 7.353119469499076000000000E-9 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -9.99999999999959800E-2 " " y[1] (closed_form) = 9.991669443947693000E-3 " " y[1] (numeric) = 9.991669443058895000E-3 " " absolute error = 8.887977159810490000000000000E-13 " " relative error = 8.895387512238259000000000E-9 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -8.99999999999959700E-2 " " y[1] (closed_form) = 8.094533976010787000E-3 " " y[1] (numeric) = 8.094533975122001000E-3 " " absolute error = 8.8878557291671710000000000000E-13 " " relative error = 1.098007094109123100000000E-8 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -7.99999999999959600E-2 " " y[1] (closed_form) = 6.396587394760789000E-3 " " y[1] (numeric) = 6.396587393871815000E-3 " " absolute error = 8.8897292305212260000000000000E-13 " " relative error = 1.38976124015791300000000E-8 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -6.99999999999959500E-2 " " y[1] (closed_form) = 4.897999493440497000E-3 " " y[1] (numeric) = 4.897999492551515000E-3 " " absolute error = 8.8898159666950250000000000000E-13 " " relative error = 1.814989156001435300000000E-8 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -5.999999999999595000E-2 " " y[1] (closed_form) = 3.5989201295912876000E-3 " " y[1] (numeric) = 3.5989201287024136000E-3 " " absolute error = 8.8887404381399190000000000000E-13 " " relative error = 2.469835427870240600000000E-8 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.99999999999959370E-2 " " y[1] (closed_form) = 2.4994792100669905000E-3 " " y[1] (numeric) = 2.4994792091783333000E-3 " " absolute error = 8.8865720337949480000000000000E-13 " " relative error = 3.555369453765840000000000E-8 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.99999999999959300E-2 " " y[1] (closed_form) = 1.5997866780437242000E-3 " " y[1] (numeric) = 1.5997866771550268000E-3 " " absolute error = 8.8869753570031130000000000000E-13 " " relative error = 5.55510023865833300000000E-8 "%" Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.99999999999959200E-2 " " y[1] (closed_form) = 8.9993250202458070000E-4 " " y[1] (numeric) = 8.9993250113595610000E-4 " " absolute error = 8.886245688941030000000000000E-13 " " relative error = 9.87434687484852200000000E-8 "%" Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.99999999999959100E-2 " " y[1] (closed_form) = 3.9998666684415430000E-4 " " y[1] (numeric) = 3.99986665955513600000E-4 " " absolute error = 8.8864072350647300000000000000E-13 " " relative error = 2.22167586364250400000000E-7 "%" Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -9.999999999995901000E-3 " " y[1] (closed_form) = 9.99991666694732800000E-5 " " y[1] (numeric) = 9.99991657805966900000E-5 " " absolute error = 8.8887659168909730000000000000E-13 " " relative error = 8.8888399903080840000000E-7 "%" Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.100886297209172000000000000000E-15 " " y[1] (closed_form) = 0.0 " " y[1] (numeric) = -8.8876573561685070000000000000E-13 " " absolute error = 8.8876573561685070000000000000E-13 " " relative error = -1. "%" Desired digits = 8 Estimated correct digits = 0 Correct digits = -16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.000000000000410300E-2 " " y[1] (closed_form) = 9.99991666694732800000E-5 " " y[1] (numeric) = 9.99991657807607100000E-5 " " absolute error = 8.8871256545292730000000000000E-13 " " relative error = 8.8871997142774630000000E-7 "%" Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.00000000000041120E-2 " " y[1] (closed_form) = 3.9998666684482040000E-4 " " y[1] (numeric) = 3.99986665955841540000E-4 " " absolute error = 8.8897888616407130000000000000E-13 " " relative error = 2.22252129846358400000000E-7 "%" Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.00000000000041230E-2 " " y[1] (closed_form) = 8.9993250202524690000E-4 " " y[1] (numeric) = 8.9993250113644810000E-4 " " absolute error = 8.8879880018322140000000000000E-13 " " relative error = 9.87628292325291400000000E-8 "%" Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.00000000000041300E-2 " " y[1] (closed_form) = 1.5997866780442793000E-3 " " y[1] (numeric) = 1.5997866771556826000E-3 " " absolute error = 8.8859670489827010000000000000E-13 " " relative error = 5.55446996211125700000000E-8 "%" Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.00000000000041400E-2 " " y[1] (closed_form) = 2.4994792100678787000E-3 " " y[1] (numeric) = 2.4994792091791526000E-3 " " absolute error = 8.8872615863766490000000000000E-13 " " relative error = 3.555645332267155500000000E-8 "%" Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.00000000000041500E-2 " " y[1] (closed_form) = 3.5989201295921760000E-3 " " y[1] (numeric) = 3.598920128703397300E-3 " " absolute error = 8.8877863402281320000000000000E-13 " " relative error = 2.469570321149439600000000E-8 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.00000000000041600E-2 " " y[1] (closed_form) = 4.897999493441496000E-3 " " y[1] (numeric) = 4.897999492552661000E-3 " " absolute error = 8.8883501253578250000000000000E-13 " " relative error = 1.814689882524380700000000E-8 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.00000000000041700E-2 " " y[1] (closed_form) = 6.396587394761788000E-3 " " y[1] (numeric) = 6.396587393873122000E-3 " " absolute error = 8.8866587699687470000000000000E-13 " " relative error = 1.389281224742758300000000E-8 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.00000000000041800E-2 " " y[1] (closed_form) = 8.094533976012452000E-3 " " y[1] (numeric) = 8.094533975123469000E-3 " " absolute error = 8.8898333139297850000000000000E-13 " " relative error = 1.098251405241381700000000E-8 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10000000000000418 " " y[1] (closed_form) = 9.991669443949358000E-3 " " y[1] (numeric) = 9.991669443060524000E-3 " " absolute error = 8.8883414517404450000000000000E-13 " " relative error = 8.895752107895188000000000E-9 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000419 " " y[1] (closed_form) = 1.208780408660725700E-2 " " y[1] (numeric) = 1.208780408571843900E-2 " " absolute error = 8.8881853266276070000000000000E-13 " " relative error = 7.353019012340972000000000E-9 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1200000000000042 " " y[1] (closed_form) = 1.43827282922686100E-2 " " y[1] (numeric) = 1.438272829137971500E-2 " " absolute error = 8.8889312577222770000000000000E-13 " " relative error = 6.180281708096018000000000E-9 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1300000000000042 " " y[1] (closed_form) = 1.687621257042504200E-2 " " y[1] (numeric) = 1.687621256953622300E-2 " " absolute error = 8.8882026738623670000000000000E-13 " " relative error = 5.266704621532573000000000E-9 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1400000000000042 " " y[1] (closed_form) = 1.956800757472698700E-2 " " y[1] (numeric) = 1.95680075738380420E-2 " " absolute error = 8.889451674765070000000000000E-13 " " relative error = 4.542849669705882300000000E-9 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1500000000000042 " " y[1] (closed_form) = 2.245784412791662600E-2 " " y[1] (numeric) = 2.245784412702789300E-2 " " absolute error = 8.8873353121243780000000000000E-13 " " relative error = 3.957341257470398000000000E-9 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000422 " " y[1] (closed_form) = 2.554543324874736000E-2 " " y[1] (numeric) = 2.554543324785864500E-2 " " absolute error = 8.887161839776780000000000000E-13 " " relative error = 3.4789630511404884000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000423 " " y[1] (closed_form) = 2.88304661808799200E-2 " " y[1] (numeric) = 2.88304661799912100E-2 " " absolute error = 8.8871271453072610000000000000E-13 " " relative error = 3.0825471532614745000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000424 " " y[1] (closed_form) = 3.23126144237586570E-2 " " y[1] (numeric) = 3.23126144228698800E-2 " " absolute error = 8.8877516457586130000000000000E-13 " " relative error = 2.7505516976130756000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000425 " " y[1] (closed_form) = 3.59915297654609400E-2 " " y[1] (numeric) = 3.59915297645721550E-2 " " absolute error = 8.8878210346976520000000000000E-13 " " relative error = 2.4694201920883052000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20000000000000426 " " y[1] (closed_form) = 3.986684431751852400E-2 " " y[1] (numeric) = 3.9866844316629600E-2 " " absolute error = 8.8892088134784330000000000000E-13 " " relative error = 2.229724716278154200000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.21000000000000427 " " y[1] (closed_form) = 4.393817055170512500E-2 " " y[1] (numeric) = 4.39381705508164600E-2 " " absolute error = 8.8866414227339870000000000000E-13 " " relative error = 2.0225333260692893000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.22000000000000428 " " y[1] (closed_form) = 4.82051013387909700E-2 " " y[1] (numeric) = 4.820510133790205700E-2 " " absolute error = 8.8891394245393940000000000000E-13 " " relative error = 1.8440246317636602000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.23000000000000428 " " y[1] (closed_form) = 5.26672099892522300E-2 " " y[1] (numeric) = 5.26672099883634300E-2 " " absolute error = 8.887959812575730000000000000E-13 " " relative error = 1.6875698967895758000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2400000000000043 " " y[1] (closed_form) = 5.7324050295942900E-2 " " y[1] (numeric) = 5.73240502950539900E-2 " " absolute error = 8.8891394245393940000000000000E-13 " " relative error = 1.5506823712993154000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000043 " " y[1] (closed_form) = 6.21751565787125300E-2 " " y[1] (numeric) = 6.21751565778237100E-2 " " absolute error = 8.8882373683318860000000000000E-13 " " relative error = 1.4295480473908500000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000043 " " y[1] (closed_form) = 6.7220043730975900E-2 " " y[1] (numeric) = 6.72200437300869200E-2 " " absolute error = 8.8898333139297850000000000000E-13 " " relative error = 1.3224974011484060000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2700000000000043 " " y[1] (closed_form) = 7.24582072682212800E-2 " " y[1] (numeric) = 7.24582072673324200E-2 " " absolute error = 8.8885843130270810000000000000E-13 " " relative error = 1.2267187732265958000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2800000000000043 " " y[1] (closed_form) = 7.78891233784603200E-2 " " y[1] (numeric) = 7.78891233775716300E-2 " " absolute error = 8.8869189784901440000000000000E-13 " " relative error = 1.1409704709743539000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2900000000000043 " " y[1] (closed_form) = 8.35122489746079600E-2 " " y[1] (numeric) = 8.35122489737192700E-2 " " absolute error = 8.8869189784901440000000000000E-13 " " relative error = 1.0641455699740794000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3000000000000043 " " y[1] (closed_form) = 8.93270217487903700E-2 " " y[1] (numeric) = 8.93270217479016400E-2 " " absolute error = 8.8873353121243780000000000000E-13 " " relative error = 9.9492126101749580000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3100000000000043 " " y[1] (closed_form) = 9.5332860228575900E-2 " " y[1] (numeric) = 9.53328602276869400E-2 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 9.3247551126227470000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.32000000000000434 " " y[1] (closed_form) = 0.1015291638351209 " " y[1] (numeric) = 0.10152916383423206 " " absolute error = 8.8883067572709250000000000000E-13 " " relative error = 8.7544370716035470000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.33000000000000435 " " y[1] (closed_form) = 0.10791531294322887 " " y[1] (numeric) = 0.10791531294233994 " " absolute error = 8.8892782024174720000000000000E-13 " " relative error = 8.2372723202812410000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.34000000000000435 " " y[1] (closed_form) = 0.1144906689433105 " " y[1] (numeric) = 0.11449066894242152 " " absolute error = 8.8898333139297850000000000000E-13 " " relative error = 7.764679336734019000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.35000000000000436 " " y[1] (closed_form) = 0.12125457430524511 " " y[1] (numeric) = 0.12125457430435621 " " absolute error = 8.8890006466613160000000000000E-13 " " relative error = 7.3308579883215210000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.36000000000000437 " " y[1] (closed_form) = 0.12820635264413316 " " y[1] (numeric) = 0.12820635264324443 " " absolute error = 8.8873353121243780000000000000E-13 " " relative error = 6.932055338001280000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000044 " " y[1] (closed_form) = 0.13534530878793438 " " y[1] (numeric) = 0.1353453087870454 " " absolute error = 8.8898333139297850000000000000E-13 " " relative error = 6.568261134088370000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000044 " " y[1] (closed_form) = 0.14267072884698273 " " y[1] (numeric) = 0.14267072884609383 " " absolute error = 8.8890006466613160000000000000E-13 " " relative error = 6.2304305294430440000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3900000000000044 " " y[1] (closed_form) = 0.15018188028537705 " " y[1] (numeric) = 0.15018188028448828 " " absolute error = 8.8876128678805340000000000000E-13 " " relative error = 5.9178995834865090000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4000000000000044 " " y[1] (closed_form) = 0.15787801199423335 " " y[1] (numeric) = 0.15787801199334428 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 5.63135161691990000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4100000000000044 " " y[1] (closed_form) = 0.1657583543667932 " " y[1] (numeric) = 0.1657583543659043 " " absolute error = 8.8890006466613160000000000000E-13 " " relative error = 5.3626260230549640000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4200000000000044 " " y[1] (closed_form) = 0.17382211937538716 " " y[1] (numeric) = 0.17382211937449807 " " absolute error = 8.890943536954410000000000000E-13 " " relative error = 5.1149667078638480000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000443 " " y[1] (closed_form) = 0.1820685006502334 " " y[1] (numeric) = 0.18206850064934446 " " absolute error = 8.8892782024174720000000000000E-13 " " relative error = 4.8823811755853430000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.44000000000000444 " " y[1] (closed_form) = 0.19049667356007705 " " y[1] (numeric) = 0.19049667355918798 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 4.6670977582159195000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.45000000000000445 " " y[1] (closed_form) = 0.19910579529465 " " y[1] (numeric) = 0.19910579529376107 " " absolute error = 8.8892782024174720000000000000E-13 " " relative error = 4.4646004347902220000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.46000000000000446 " " y[1] (closed_form) = 0.2078950049489534 " " y[1] (numeric) = 0.2078950049480645 " " absolute error = 8.8890006466613160000000000000E-13 " " relative error = 4.27571631595666400000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.47000000000000447 " " y[1] (closed_form) = 0.21686342360934596 " " y[1] (numeric) = 0.2168634236084572 " " absolute error = 8.8876128678805340000000000000E-13 " " relative error = 4.0982535090336525000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000045 " " y[1] (closed_form) = 0.22601015444143568 " " y[1] (numeric) = 0.2260101544405468 " " absolute error = 8.888723090905160000000000000E-13 " " relative error = 3.932886605415080000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4900000000000045 " " y[1] (closed_form) = 0.23533428277976132 " " y[1] (numeric) = 0.23533428277887228 " " absolute error = 8.8903884254420970000000000000E-13 " " relative error = 3.77777020858546400000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000044 " " y[1] (closed_form) = 0.24483487621925892 " " y[1] (numeric) = 0.24483487621836988 " " absolute error = 8.8903884254420970000000000000E-13 " " relative error = 3.6311772908858040000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000044 " " y[1] (closed_form) = 0.254510984708502 " " y[1] (numeric) = 0.2545109847076129 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 3.4932346795879810000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000045 " " y[1] (closed_form) = 0.2643616406447046 " " y[1] (numeric) = 0.26436164064381573 " " absolute error = 8.8884455351490030000000000000E-13 " " relative error = 3.36222967654178360000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000045 " " y[1] (closed_form) = 0.2743858589704824 " " y[1] (numeric) = 0.27438585896959355 " " absolute error = 8.8884455351490030000000000000E-13 " " relative error = 3.23939636266211360000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000045 " " y[1] (closed_form) = 0.2845826372723562 " " y[1] (numeric) = 0.28458263727146743 " " absolute error = 8.8878904236366910000000000000E-13 " " relative error = 3.1231316530146030000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000045 " " y[1] (closed_form) = 0.2949509558809932 " " y[1] (numeric) = 0.2949509558801043 " " absolute error = 8.8890006466613160000000000000E-13 " " relative error = 3.01372159317491730000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000045 " " y[1] (closed_form) = 0.30548977797317256 " " y[1] (numeric) = 0.3054897779722836 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 2.90993558512923200000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5700000000000045 " " y[1] (closed_form) = 0.3161980496754673 " " y[1] (numeric) = 0.31619804967457843 " " absolute error = 8.8884455351490030000000000000E-13 " " relative error = 2.81103743184745740000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5800000000000045 " " y[1] (closed_form) = 0.32707470016963114 " " y[1] (numeric) = 0.3270747001687421 " " absolute error = 8.8901108696859410000000000000E-13 " " relative error = 2.71806742162425060000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5900000000000045 " " y[1] (closed_form) = 0.338118641799678 " " y[1] (numeric) = 0.3381186417987891 " " absolute error = 8.8890006466613160000000000000E-13 " " relative error = 2.6289590539428760000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6000000000000045 " " y[1] (closed_form) = 0.34932877018064845 " " y[1] (numeric) = 0.34932877017975955 " " absolute error = 8.8890006466613160000000000000E-13 " " relative error = 2.5445944924789750000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000045 " " y[1] (closed_form) = 0.36070396430904605 " " y[1] (numeric) = 0.3607039643081571 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 2.4645018180496578000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000045 " " y[1] (closed_form) = 0.37224308667493744 " " y[1] (numeric) = 0.37224308667404843 " " absolute error = 8.8901108696859410000000000000E-13 " " relative error = 2.3882541242328730000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6300000000000046 " " y[1] (closed_form) = 0.3839449833757015 " " y[1] (numeric) = 0.38394498337481264 " " absolute error = 8.8884455351490030000000000000E-13 " " relative error = 2.31503103830149460000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6400000000000046 " " y[1] (closed_form) = 0.3958084842314201 " " y[1] (numeric) = 0.39580848423053117 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 2.24592349894554320000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000046 " " y[1] (closed_form) = 0.40783240290189393 " " y[1] (numeric) = 0.40783240290100486 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 2.179980285513740000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000046 " " y[1] (closed_form) = 0.4200155370052753 " " y[1] (numeric) = 0.42001553700438643 " " absolute error = 8.8884455351490030000000000000E-13 " " relative error = 2.11621827100109540000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000046 " " y[1] (closed_form) = 0.432356668238307 " " y[1] (numeric) = 0.4323566682374181 " " absolute error = 8.8890006466613160000000000000E-13 " " relative error = 2.05594161017122630000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6800000000000046 " " y[1] (closed_form) = 0.4448545624981498 " " y[1] (numeric) = 0.44485456249726085 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 1.99830607744089420000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000046 " " y[1] (closed_form) = 0.4575079700057927 " " y[1] (numeric) = 0.4575079700049036 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 1.94328111509963130000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000046 " " y[1] (closed_form) = 0.470315625431029 " " y[1] (numeric) = 0.47031562543014005 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 1.89012554069974580000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000046 " " y[1] (closed_form) = 0.4832762480189895 " " y[1] (numeric) = 0.48327624801810065 " " absolute error = 8.8884455351490030000000000000E-13 " " relative error = 1.83920595551382150000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000046 " " y[1] (closed_form) = 0.4963885417182161 " " y[1] (numeric) = 0.49638854171732705 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 1.7910699450119860000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000046 " " y[1] (closed_form) = 0.5096511953102655 " " y[1] (numeric) = 0.5096511953093763 " " absolute error = 8.8917762042228790000000000000E-13 " " relative error = 1.74467876972401540000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000047 " " y[1] (closed_form) = 0.5230628825408306 " " y[1] (numeric) = 0.5230628825399413 " " absolute error = 8.8928864272475040000000000000E-13 " " relative error = 1.70015627644030360000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000047 " " y[1] (closed_form) = 0.5366222622523646 " " y[1] (numeric) = 0.5366222622514755 " " absolute error = 8.8917762042228790000000000000E-13 " " relative error = 1.65698981009498670000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000047 " " y[1] (closed_form) = 0.550327978518196 " " y[1] (numeric) = 0.5503279785173072 " " absolute error = 8.8884455351490030000000000000E-13 " " relative error = 1.61511787190647380000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000047 " " y[1] (closed_form) = 0.5641786607781198 " " y[1] (numeric) = 0.5641786607772308 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 1.57586002436465300000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000047 " " y[1] (closed_form) = 0.578172923975452 " " y[1] (numeric) = 0.5781729239745629 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 1.53771745658150770000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000047 " " y[1] (closed_form) = 0.5923093686955346 " " y[1] (numeric) = 0.5923093686946456 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 1.5010172810162542000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000047 " " y[1] (closed_form) = 0.6065865813056758 " " y[1] (numeric) = 0.6065865813047869 " " absolute error = 8.8884455351490030000000000000E-13 " " relative error = 1.46532182034370930000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000047 " " y[1] (closed_form) = 0.6210031340965126 " " y[1] (numeric) = 0.6210031340956238 " " absolute error = 8.8884455351490030000000000000E-13 " " relative error = 1.43130445679322680000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000047 " " y[1] (closed_form) = 0.63555758542478 " " y[1] (numeric) = 0.6355575854238908 " " absolute error = 8.8917762042228790000000000000E-13 " " relative error = 1.39905122810862000000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000047 " " y[1] (closed_form) = 0.6502484798574728 " " y[1] (numeric) = 0.6502484798565838 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 1.36710135179741150000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000047 " " y[1] (closed_form) = 0.6650743483173908 " " y[1] (numeric) = 0.6650743483165019 " " absolute error = 8.8884455351490030000000000000E-13 " " relative error = 1.33645893239400760000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000048 " " y[1] (closed_form) = 0.6800337082300426 " " y[1] (numeric) = 0.6800337082291539 " " absolute error = 8.8873353121243780000000000000E-13 " " relative error = 1.30689629125236820000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000048 " " y[1] (closed_form) = 0.6951250636719034 " " y[1] (numeric) = 0.6951250636710146 " " absolute error = 8.8884455351490030000000000000E-13 " " relative error = 1.27868293055022370000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8700000000000048 " " y[1] (closed_form) = 0.710346905520005 " " y[1] (numeric) = 0.710346905519116 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 1.25159494777976080000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000048 " " y[1] (closed_form) = 0.725697711602847 " " y[1] (numeric) = 0.7256977116019581 " " absolute error = 8.8895557581736280000000000000E-13 " " relative error = 1.22496676178560420000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000048 " " y[1] (closed_form) = 0.7411759468526138 " " y[1] (numeric) = 0.7411759468517247 " " absolute error = 8.8906659811982540000000000000E-13 " " relative error = 1.1995351466749910000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000048 " " y[1] (closed_form) = 0.7567800634586784 " " y[1] (numeric) = 0.7567800634577896 " " absolute error = 8.8884455351490030000000000000E-13 " " relative error = 1.17450841589649370000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000048 " " y[1] (closed_form) = 0.7725085010223846 " " y[1] (numeric) = 0.7725085010214954 " " absolute error = 8.8917762042228790000000000000E-13 " " relative error = 1.15102632429998690000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000048 " " y[1] (closed_form) = 0.7883596867130819 " " y[1] (numeric) = 0.7883596867121927 " " absolute error = 8.8917762042228790000000000000E-13 " " relative error = 1.12788316730088960000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000048 " " y[1] (closed_form) = 0.8043320354254114 " " y[1] (numeric) = 0.8043320354245219 " " absolute error = 8.8951068732967540000000000000E-13 " " relative error = 1.10589986243580740000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000048 " " y[1] (closed_form) = 0.8204239499378114 " " y[1] (numeric) = 0.8204239499369219 " " absolute error = 8.8951068732967540000000000000E-13 " " relative error = 1.08420858191316930000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000048 " " y[1] (closed_form) = 0.8366338210722408 " " y[1] (numeric) = 0.8366338210713515 " " absolute error = 8.8928864272475040000000000000E-13 " " relative error = 1.06293652052582150000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9600000000000048 " " y[1] (closed_form) = 0.8529600278550946 " " y[1] (numeric) = 0.8529600278542053 " " absolute error = 8.8928864272475040000000000000E-13 " " relative error = 1.04259122782225780000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000049 " " y[1] (closed_form) = 0.8694009376792994 " " y[1] (numeric) = 0.8694009376784101 " " absolute error = 8.8928864272475040000000000000E-13 " " relative error = 1.02287518241990590000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000049 " " y[1] (closed_form) = 0.8859549064675737 " " y[1] (numeric) = 0.8859549064666841 " " absolute error = 8.8962170963213790000000000000E-13 " " relative error = 1.00413881467081020000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000049 " " y[1] (closed_form) = 0.9026202788368329 " " y[1] (numeric) = 0.9026202788359435 " " absolute error = 8.8939966502721290000000000000E-13 " " relative error = 9.85353072471785300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0000000000000049 " " y[1] (closed_form) = 0.9193953882637286 " " y[1] (numeric) = 0.9193953882628393 " " absolute error = 8.8928864272475040000000000000E-13 " " relative error = 9.67253756193149300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0100000000000038 " " y[1] (closed_form) = 0.9362785572512955 " " y[1] (numeric) = 0.9362785572504079 " " absolute error = 8.8762330818781270000000000000E-13 " " relative error = 9.48033361773953600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0200000000000027 " " y[1] (closed_form) = 0.9532680974967054 " " y[1] (numeric) = 0.9532680974958198 " " absolute error = 8.8562490674348740000000000000E-13 " " relative error = 9.29040748420250400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0300000000000016 " " y[1] (closed_form) = 0.970362310060092 " " y[1] (numeric) = 0.9703623100592083 " " absolute error = 8.8373752760162460000000000000E-13 " " relative error = 9.10729444496764300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0400000000000005 " " y[1] (closed_form) = 0.987559485534444 " " y[1] (numeric) = 0.9875594855335622 " " absolute error = 8.8173912615729930000000000000E-13 " " relative error = 8.92846597164851200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0499999999999994 " " y[1] (closed_form) = 1.004857904216545 " " y[1] (numeric) = 1.0048579042156651 " " absolute error = 8.7996276931789910000000000000E-13 " " relative error = 8.75708660523477100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0599999999999983 " " y[1] (closed_form) = 1.022255836278942 " " y[1] (numeric) = 1.022255836278064 " " absolute error = 8.7796436787357380000000000000E-13 " " relative error = 8.58849944128863300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0699999999999972 " " y[1] (closed_form) = 1.0397515419429268 " " y[1] (numeric) = 1.0397515419420507 " " absolute error = 8.7618801103417350000000000000E-13 " " relative error = 8.42689792406452100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.079999999999996 " " y[1] (closed_form) = 1.0573432716525133 " " y[1] (numeric) = 1.0573432716516387 " " absolute error = 8.7463369879969830000000000000E-13 " " relative error = 8.27199380039313500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.089999999999995 " " y[1] (closed_form) = 1.0750292662493894 " " y[1] (numeric) = 1.0750292662485168 " " absolute error = 8.726352973553730000000000000E-13 " " relative error = 8.1173166605953200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0999999999999939 " " y[1] (closed_form) = 1.0928077571488344 " " y[1] (numeric) = 1.0928077571479635 " " absolute error = 8.7085894051597280000000000000E-13 " " relative error = 7.96900401574809200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1099999999999928 " " y[1] (closed_form) = 1.1106769665165732 " " y[1] (numeric) = 1.1106769665157044 " " absolute error = 8.6886053907164750000000000000E-13 " " relative error = 7.82280145591443300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1199999999999917 " " y[1] (closed_form) = 1.1286351074465606 " " y[1] (numeric) = 1.1286351074456937 " " absolute error = 8.6686213762732220000000000000E-13 " " relative error = 7.68062354172663400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1299999999999906 " " y[1] (closed_form) = 1.1466803841396684 " " y[1] (numeric) = 1.1466803841388034 " " absolute error = 8.650857807879220000000000000E-13 " " relative error = 7.54426248807751900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1399999999999895 " " y[1] (closed_form) = 1.1648109920832646 " " y[1] (numeric) = 1.164810992082402 " " absolute error = 8.6264329013374660000000000000E-13 " " relative error = 7.40586495145370200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1499999999999884 " " y[1] (closed_form) = 1.1830251182316642 " " y[1] (numeric) = 1.1830251182308036 " " absolute error = 8.6064488868942140000000000000E-13 " " relative error = 7.27495025613553200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1599999999999873 " " y[1] (closed_form) = 1.2013209411874302 " " y[1] (numeric) = 1.2013209411865717 " " absolute error = 8.584244426401710000000000000E-13 " " relative error = 7.1456711791910700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1699999999999862 " " y[1] (closed_form) = 1.2196966313835143 " " y[1] (numeric) = 1.2196966313826578 " " absolute error = 8.5642604119584580000000000000E-13 " " relative error = 7.0216316021500600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.179999999999985 " " y[1] (closed_form) = 1.238150351266209 " " y[1] (numeric) = 1.2381503512653544 " " absolute error = 8.5464968435644550000000000000E-13 " " relative error = 6.90263249113831700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.189999999999984 " " y[1] (closed_form) = 1.2566802554789045 " " y[1] (numeric) = 1.2566802554780516 " " absolute error = 8.5287332751704530000000000000E-13 " " relative error = 6.78671701730545900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1999999999999829 " " y[1] (closed_form) = 1.2752844910466208 " " y[1] (numeric) = 1.2752844910457701 " " absolute error = 8.5065288146779490000000000000E-13 " " relative error = 6.67029896027095500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2099999999999818 " " y[1] (closed_form) = 1.2939611975613055 " " y[1] (numeric) = 1.2939611975604566 " " absolute error = 8.4887652462839470000000000000E-13 " " relative error = 6.56029350979186900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2199999999999807 " " y[1] (closed_form) = 1.3127085073678697 " " y[1] (numeric) = 1.312708507367023 " " absolute error = 8.4665607857914440000000000000E-13 " " relative error = 6.44968836437867200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2299999999999796 " " y[1] (closed_form) = 1.3315245457509564 " " y[1] (numeric) = 1.3315245457501115 " " absolute error = 8.4487972173974410000000000000E-13 " " relative error = 6.34520576008793600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2399999999999785 " " y[1] (closed_form) = 1.3504074311224068 " " y[1] (numeric) = 1.3504074311215644 " " absolute error = 8.4243723108556880000000000000E-13 " " relative error = 6.23839303361480500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2499999999999774 " " y[1] (closed_form) = 1.3693552752094198 " " y[1] (numeric) = 1.3693552752085791 " " absolute error = 8.4066087424616850000000000000E-13 " " relative error = 6.13909983380758300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2599999999999763 " " y[1] (closed_form) = 1.388366183243376 " " y[1] (numeric) = 1.3883661832425378 " " absolute error = 8.3821838359199320000000000000E-13 " " relative error = 6.03744454243204800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2699999999999751 " " y[1] (closed_form) = 1.407438254149315 " " y[1] (numeric) = 1.4074382541484791 " " absolute error = 8.3577589293781780000000000000E-13 " " relative error = 5.93827750861424700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.279999999999974 " " y[1] (closed_form) = 1.4265695807360395 " " y[1] (numeric) = 1.4265695807352055 " " absolute error = 8.3399953609841760000000000000E-13 " " relative error = 5.84618897921624700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.289999999999973 " " y[1] (closed_form) = 1.4457582498868327 " " y[1] (numeric) = 1.4457582498860015 " " absolute error = 8.3111295623439220000000000000E-13 " " relative error = 5.74863021739248500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2999999999999718 " " y[1] (closed_form) = 1.465002342750771 " " y[1] (numeric) = 1.465002342749942 " " absolute error = 8.2911455479006690000000000000E-13 " " relative error = 5.659475965296238000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3099999999999707 " " y[1] (closed_form) = 1.484299934934604 " " y[1] (numeric) = 1.4842999349337775 " " absolute error = 8.2645001953096650000000000000E-13 " " relative error = 5.56794486127481200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3199999999999696 " " y[1] (closed_form) = 1.5036490966951952 " " y[1] (numeric) = 1.5036490966943705 " " absolute error = 8.2467366269156630000000000000E-13 " " relative error = 5.48448214749093100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3299999999999685 " " y[1] (closed_form) = 1.5230478931324924 " " y[1] (numeric) = 1.5230478931316702 " " absolute error = 8.2223117203739090000000000000E-13 " " relative error = 5.398590390655981000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3399999999999674 " " y[1] (closed_form) = 1.5424943843830174 " " y[1] (numeric) = 1.5424943843821974 " " absolute error = 8.2001072598814060000000000000E-13 " " relative error = 5.31613427115416600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3499999999999663 " " y[1] (closed_form) = 1.561986625813851 " " y[1] (numeric) = 1.5619866258130328 " " absolute error = 8.1823436914874040000000000000E-13 " " relative error = 5.238421095458553000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3599999999999652 " " y[1] (closed_form) = 1.5815226682170933 " " y[1] (numeric) = 1.5815226682162775 " " absolute error = 8.157918784945650000000000000E-13 " " relative error = 5.15826864128502300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3699999999999641 " " y[1] (closed_form) = 1.601100558004784 " " y[1] (numeric) = 1.6011005580039703 " " absolute error = 8.1357143244531470000000000000E-13 " " relative error = 5.08132626884565700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.379999999999963 " " y[1] (closed_form) = 1.6207183374042589 " " y[1] (numeric) = 1.6207183374034473 " " absolute error = 8.1157303100098940000000000000E-13 " " relative error = 5.007489656103996000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.389999999999962 " " y[1] (closed_form) = 1.6403740446539263 " " y[1] (numeric) = 1.640374044653117 " " absolute error = 8.0935258495173910000000000000E-13 " " relative error = 4.93395142156428160000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3999999999999608 " " y[1] (closed_form) = 1.6600657141994408 " " y[1] (numeric) = 1.6600657141986335 " " absolute error = 8.0735418350741380000000000000E-13 " " relative error = 4.86338689246863200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4099999999999597 " " y[1] (closed_form) = 1.679791376890258 " " y[1] (numeric) = 1.6797913768894523 " " absolute error = 8.0557782666801360000000000000E-13 " " relative error = 4.79570164337522100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4199999999999586 " " y[1] (closed_form) = 1.6995490601765466 " " y[1] (numeric) = 1.6995490601757428 " " absolute error = 8.0380146982861330000000000000E-13 " " relative error = 4.72949848088007330000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4299999999999575 " " y[1] (closed_form) = 1.7193367883064425 " " y[1] (numeric) = 1.7193367883056414 " " absolute error = 8.011369345695130000000000000E-13 " " relative error = 4.659569550411573000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4399999999999564 " " y[1] (closed_form) = 1.7391525825236225 " " y[1] (numeric) = 1.7391525825228236 " " absolute error = 7.9891648852026260000000000000E-13 " " relative error = 4.5937113083027103000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4499999999999553 " " y[1] (closed_form) = 1.758994461265178 " " y[1] (numeric) = 1.758994461264381 " " absolute error = 7.9691808707593740000000000000E-13 " " relative error = 4.53053210015649800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4599999999999542 " " y[1] (closed_form) = 1.7788604403597699 " " y[1] (numeric) = 1.778860440358975 " " absolute error = 7.9491968563161210000000000000E-13 " " relative error = 4.468701802547488000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4699999999999531 " " y[1] (closed_form) = 1.7987485332260431 " " y[1] (numeric) = 1.7987485332252504 " " absolute error = 7.9269923958236180000000000000E-13 " " relative error = 4.406948636453708600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.479999999999952 " " y[1] (closed_form) = 1.818656751071285 " " y[1] (numeric) = 1.818656751070494 " " absolute error = 7.9092288274296150000000000000E-13 " " relative error = 4.348939855071970500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.489999999999951 " " y[1] (closed_form) = 1.838583103090301 " " y[1] (numeric) = 1.8385831030895123 " " absolute error = 7.8870243669371120000000000000E-13 " " relative error = 4.289729604106856700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4999999999999498 " " y[1] (closed_form) = 1.858525596664494 " " y[1] (numeric) = 1.8585255966637078 " " absolute error = 7.8625994603953590000000000000E-13 " " relative error = 4.23055753146817500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5099999999999487 " " y[1] (closed_form) = 1.8784822375611259 " " y[1] (numeric) = 1.8784822375603416 " " absolute error = 7.8426154459521060000000000000E-13 " " relative error = 4.174974502891410400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5199999999999476 " " y[1] (closed_form) = 1.8984510301327369 " " y[1] (numeric) = 1.8984510301319548 " " absolute error = 7.8204109854596030000000000000E-13 " " relative error = 4.1193640822606903000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5299999999999465 " " y[1] (closed_form) = 1.9184299775167108 " " y[1] (numeric) = 1.918429977515931 " " absolute error = 7.79820652496710000000000000E-13 " " relative error = 4.06488984031692200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5399999999999454 " " y[1] (closed_form) = 1.9384170818349586 " " y[1] (numeric) = 1.9384170818341808 " " absolute error = 7.7782225105238470000000000000E-13 " " relative error = 4.01266713103908900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5499999999999443 " " y[1] (closed_form) = 1.9584103443937035 " " y[1] (numeric) = 1.9584103443929282 " " absolute error = 7.7537976039820930000000000000E-13 " " relative error = 3.95923031461650140000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5599999999999432 " " y[1] (closed_form) = 1.9784077658833517 " " y[1] (numeric) = 1.9784077658825783 " " absolute error = 7.733813589538840000000000000E-13 " " relative error = 3.90911000396610400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.569999999999942 " " y[1] (closed_form) = 1.9984073465784178 " " y[1] (numeric) = 1.9984073465776464 " " absolute error = 7.7138295750955880000000000000E-13 " " relative error = 3.85998859957298270000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.579999999999941 " " y[1] (closed_form) = 2.018407086537499 " " y[1] (numeric) = 2.018407086536729 " " absolute error = 7.6960660067015850000000000000E-13 " " relative error = 3.812940441020694600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.58999999999994 " " y[1] (closed_form) = 2.0384049858032647 " " y[1] (numeric) = 2.0384049858024977 " " absolute error = 7.6694206541105810000000000000E-13 " " relative error = 3.76246168328926500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5999999999999388 " " y[1] (closed_form) = 2.0583990446024547 " " y[1] (numeric) = 2.05839904460169 " " absolute error = 7.6472161936180780000000000000E-13 " " relative error = 3.71512813012163500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6099999999999377 " " y[1] (closed_form) = 2.078387263545851 " " y[1] (numeric) = 2.078387263545088 " " absolute error = 7.6294526252240760000000000000E-13 " " relative error = 3.67085228005476700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6199999999999366 " " y[1] (closed_form) = 2.0983676438282144 " " y[1] (numeric) = 2.0983676438274537 " " absolute error = 7.6072481647315730000000000000E-13 " " relative error = 3.62531713024943600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6299999999999355 " " y[1] (closed_form) = 2.1183381874281677 " " y[1] (numeric) = 2.118338187427409 " " absolute error = 7.5850437042390700000000000000E-13 " " relative error = 3.580657587751803000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6399999999999344 " " y[1] (closed_form) = 2.1382968973079928 " " y[1] (numeric) = 2.138296897307237 " " absolute error = 7.5583983516480660000000000000E-13 " " relative error = 3.534774970287664600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6499999999999333 " " y[1] (closed_form) = 2.158241777613335 " " y[1] (numeric) = 2.15824177761258 " " absolute error = 7.5495165674510640000000000000E-13 " " relative error = 3.497993897513931300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6599999999999322 " " y[1] (closed_form) = 2.178170833872783 " " y[1] (numeric) = 2.1781708338720303 " " absolute error = 7.5273121069585610000000000000E-13 " " relative error = 3.455795105646060000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.669999999999931 " " y[1] (closed_form) = 2.1980820731973187 " " y[1] (numeric) = 2.1980820731965687 " " absolute error = 7.5006667543675580000000000000E-13 " " relative error = 3.41236883091318200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.67999999999993 " " y[1] (closed_form) = 2.2179735044796036 " " y[1] (numeric) = 2.217973504478855 " " absolute error = 7.4873440780720560000000000000E-13 " " relative error = 3.37575902640405500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.689999999999929 " " y[1] (closed_form) = 2.2378431385930835 " " y[1] (numeric) = 2.237843138592338 " " absolute error = 7.4562578333825510000000000000E-13 " " relative error = 3.33189476277155400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6999999999999278 " " y[1] (closed_form) = 2.257688988590906 " " y[1] (numeric) = 2.2576889885901634 " " absolute error = 7.4251715886930470000000000000E-13 " " relative error = 3.288837225240367500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7099999999999267 " " y[1] (closed_form) = 2.2775090699046103 " " y[1] (numeric) = 2.2775090699038687 " " absolute error = 7.4162898044960460000000000000E-13 " " relative error = 3.256316254673209400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7199999999999256 " " y[1] (closed_form) = 2.2973014005425805 " " y[1] (numeric) = 2.297301400541841 " " absolute error = 7.3940853440035430000000000000E-13 " " relative error = 3.21859610683090800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7299999999999245 " " y[1] (closed_form) = 2.317064001288246 " " y[1] (numeric) = 2.317064001287509 " " absolute error = 7.3718808835110390000000000000E-13 " " relative error = 3.18156118234645460000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7399999999999234 " " y[1] (closed_form) = 2.336794895898003 " " y[1] (numeric) = 2.3367948958972673 " " absolute error = 7.3585582072155380000000000000E-13 " " relative error = 3.14899618281977160000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7499999999999223 " " y[1] (closed_form) = 2.356492111298831 " " y[1] (numeric) = 2.356492111298098 " " absolute error = 7.3274719625260330000000000000E-13 " " relative error = 3.109482916319775000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7599999999999212 " " y[1] (closed_form) = 2.376153677785606 " " y[1] (numeric) = 2.3761536777848753 " " absolute error = 7.305267502033530000000000000E-13 " " relative error = 3.07440868422343900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.76999999999992 " " y[1] (closed_form) = 2.3957776292180615 " " y[1] (numeric) = 2.395777629217333 " " absolute error = 7.2830630415410270000000000000E-13 " " relative error = 3.03995786283307370000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.779999999999919 " " y[1] (closed_form) = 2.4153620032174095 " " y[1] (numeric) = 2.4153620032166825 " " absolute error = 7.2697403652455250000000000000E-13 " " relative error = 3.00979329622714400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7899999999999179 " " y[1] (closed_form) = 2.4349048413625685 " " y[1] (numeric) = 2.434904841361845 " " absolute error = 7.234213228457520000000000000E-13 " " relative error = 2.97104556431423700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7999999999999168 " " y[1] (closed_form) = 2.454404189386012 " " y[1] (numeric) = 2.45440418938529 " " absolute error = 7.2208905521620180000000000000E-13 " " relative error = 2.942013619186487600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8099999999999157 " " y[1] (closed_form) = 2.4738580973691855 " " y[1] (numeric) = 2.473858097368466 " " absolute error = 7.1942451995710140000000000000E-13 " " relative error = 2.908107464701271700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8199999999999146 " " y[1] (closed_form) = 2.493264619937502 " " y[1] (numeric) = 2.4932646199367854 " " absolute error = 7.1675998469800110000000000000E-13 " " relative error = 2.874785046747135300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8299999999999135 " " y[1] (closed_form) = 2.512621816454878 " " y[1] (numeric) = 2.512621816454163 " " absolute error = 7.1498362785860080000000000000E-13 " " relative error = 2.845568016548505000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8399999999999124 " " y[1] (closed_form) = 2.5319277512177916 " " y[1] (numeric) = 2.5319277512170792 " " absolute error = 7.1231909259950040000000000000E-13 " " relative error = 2.813346835259787300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8499999999999113 " " y[1] (closed_form) = 2.5511804936488556 " " y[1] (numeric) = 2.5511804936481455 " " absolute error = 7.1009864655025010000000000000E-13 " " relative error = 2.783412025601620000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8599999999999102 " " y[1] (closed_form) = 2.5703781184898693 " " y[1] (numeric) = 2.570378118489162 " " absolute error = 7.0743411129114970000000000000E-13 " " relative error = 2.752256978077515000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.869999999999909 " " y[1] (closed_form) = 2.5895187059943483 " " y[1] (numeric) = 2.589518705993643 " " absolute error = 7.0521366524189940000000000000E-13 " " relative error = 2.723338756385251000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.879999999999908 " " y[1] (closed_form) = 2.608600342119491 " " y[1] (numeric) = 2.608600342118788 " " absolute error = 7.0299321919264910000000000000E-13 " " relative error = 2.694905800025565500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8899999999999069 " " y[1] (closed_form) = 2.627621118717588 " " y[1] (numeric) = 2.627621118716886 " " absolute error = 7.021050407729490000000000000E-13 " " relative error = 2.672017802610795500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8999999999999058 " " y[1] (closed_form) = 2.6465791337268287 " " y[1] (numeric) = 2.646579133726129 " " absolute error = 6.9988459472369870000000000000E-13 " " relative error = 2.644487692828377000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9099999999999047 " " y[1] (closed_form) = 2.665472491361511 " " y[1] (numeric) = 2.6654724913608128 " " absolute error = 6.9810823788429840000000000000E-13 " " relative error = 2.619078756756210000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9199999999999036 " " y[1] (closed_form) = 2.684299302301615 " " y[1] (numeric) = 2.6842993023009196 " " absolute error = 6.9544370262519810000000000000E-13 " " relative error = 2.590783010035057000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9299999999999025 " " y[1] (closed_form) = 2.7030576838817373 " " y[1] (numeric) = 2.7030576838810436 " " absolute error = 6.9366734578579780000000000000E-13 " " relative error = 2.566232122688754000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9399999999999014 " " y[1] (closed_form) = 2.721745760279351 " " y[1] (numeric) = 2.721745760278659 " " absolute error = 6.9189098894639760000000000000E-13 " " relative error = 2.542085300705618000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9499999999999003 " " y[1] (closed_form) = 2.740361662702389 " " y[1] (numeric) = 2.7403616627016985 " " absolute error = 6.9055872131684740000000000000E-13 " " relative error = 2.519954685966003000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9599999999998992 " " y[1] (closed_form) = 2.7589035295761226 " " y[1] (numeric) = 2.758903529575434 " " absolute error = 6.8878236447744710000000000000E-13 " " relative error = 2.49658009819310900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.969999999999898 " " y[1] (closed_form) = 2.7773695067293165 " " y[1] (numeric) = 2.777369506728629 " " absolute error = 6.8745009684789690000000000000E-13 " " relative error = 2.475184145221826500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.979999999999897 " " y[1] (closed_form) = 2.7957577475796427 " " y[1] (numeric) = 2.795757747578958 " " absolute error = 6.8478556158879660000000000000E-13 " " relative error = 2.449373741990458500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9899999999998959 " " y[1] (closed_form) = 2.814066413318341 " " y[1] (numeric) = 2.8140664133176574 " " absolute error = 6.8345329395924640000000000000E-13 " " relative error = 2.428703497275744300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9999999999998948 " " y[1] (closed_form) = 2.8322936730940933 " " y[1] (numeric) = 2.832293673093412 " " absolute error = 6.8123284790999600000000000000E-13 " " relative error = 2.405233801782264100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0099999999998936 " " y[1] (closed_form) = 2.8504377041961124 " " y[1] (numeric) = 2.850437704195433 " " absolute error = 6.7945649107059580000000000000E-13 " " relative error = 2.383691775022383500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0199999999998925 " " y[1] (closed_form) = 2.8684966922364072 " " y[1] (numeric) = 2.8684966922357304 " " absolute error = 6.7679195581149540000000000000E-13 " " relative error = 2.359395977841753600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0299999999998914 " " y[1] (closed_form) = 2.8864688313312232 " " y[1] (numeric) = 2.886468831330549 " " absolute error = 6.7412742055239500000000000000E-13 " " relative error = 2.335474449732724800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0399999999998903 " " y[1] (closed_form) = 2.9043523242816285 " " y[1] (numeric) = 2.9043523242809557 " " absolute error = 6.7279515292284490000000000000E-13 " " relative error = 2.316506669311396700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0499999999998892 " " y[1] (closed_form) = 2.9221453827532295 " " y[1] (numeric) = 2.922145382752559 " " absolute error = 6.7057470687359460000000000000E-13 " " relative error = 2.29480268446391520000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.059999999999888 " " y[1] (closed_form) = 2.939846227455007 " " y[1] (numeric) = 2.9398462274543387 " " absolute error = 6.6835426082434420000000000000E-13 " " relative error = 2.273432721013205500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.069999999999887 " " y[1] (closed_form) = 2.9574530883172416 " " y[1] (numeric) = 2.9574530883165755 " " absolute error = 6.6613381477509390000000000000E-13 " " relative error = 2.252390130570479400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.079999999999886 " " y[1] (closed_form) = 2.9749642046685194 " " y[1] (numeric) = 2.9749642046678555 " " absolute error = 6.6391336872584360000000000000E-13 " " relative error = 2.23166842708219800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.089999999999885 " " y[1] (closed_form) = 2.992377825411798 " " y[1] (numeric) = 2.9923778254111366 " " absolute error = 6.6124883346674320000000000000E-13 " " relative error = 2.209777214131524700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0999999999998837 " " y[1] (closed_form) = 3.009692209199514 " " y[1] (numeric) = 3.0096922091988545 " " absolute error = 6.594724766273430000000000000E-13 " " relative error = 2.191162520245691600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1099999999998826 " " y[1] (closed_form) = 3.0269056246077177 " " y[1] (numeric) = 3.02690562460706 " " absolute error = 6.5769611978794270000000000000E-13 " " relative error = 2.1728332540040100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999998815 " " y[1] (closed_form) = 3.044016350309212 " " y[1] (numeric) = 3.044016350308557 " " absolute error = 6.5503158452884240000000000000E-13 " " relative error = 2.151866183183622500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999998804 " " y[1] (closed_form) = 3.0610226752456873 " " y[1] (numeric) = 3.0610226752450336 " " absolute error = 6.5369931689929220000000000000E-13 " " relative error = 2.13555855755568400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999998793 " " y[1] (closed_form) = 3.0779228987988194 " " y[1] (numeric) = 3.077922898798168 " " absolute error = 6.5147887085004190000000000000E-13 " " relative error = 2.116618551765172600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1499999999998782 " " y[1] (closed_form) = 3.094715330960338 " " y[1] (numeric) = 3.0947153309596898 " " absolute error = 6.4837024638109140000000000000E-13 " " relative error = 2.09508848809008900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.159999999999877 " " y[1] (closed_form) = 3.111398292501021 " " y[1] (numeric) = 3.1113982925003745 " " absolute error = 6.4659388954169120000000000000E-13 " " relative error = 2.078145671996054500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.169999999999876 " " y[1] (closed_form) = 3.1279701151386154 " " y[1] (numeric) = 3.1279701151379706 " " absolute error = 6.4481753270229090000000000000E-13 " " relative error = 2.061456820132426300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.179999999999875 " " y[1] (closed_form) = 3.144429141704668 " " y[1] (numeric) = 3.144429141704026 " " absolute error = 6.4215299744319050000000000000E-13 " " relative error = 2.04219261590695100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.189999999999874 " " y[1] (closed_form) = 3.1607737263102385 " " y[1] (numeric) = 3.1607737263095976 " " absolute error = 6.4082072981364040000000000000E-13 " " relative error = 2.02741728861973600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1999999999998727 " " y[1] (closed_form) = 3.1770022345104856 " " y[1] (numeric) = 3.177002234509846 " " absolute error = 6.3948846218409020000000000000E-13 " " relative error = 2.012867524100507800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2099999999998716 " " y[1] (closed_form) = 3.193113043468114 " " y[1] (numeric) = 3.1931130434674766 " " absolute error = 6.3726801613483990000000000000E-13 " " relative error = 1.995757768233248400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999998705 " " y[1] (closed_form) = 3.2091045421156528 " " y[1] (numeric) = 3.209104542115017 " " absolute error = 6.3593574850528970000000000000E-13 " " relative error = 1.981661052668726700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999998694 " " y[1] (closed_form) = 3.2249751313165635 " " y[1] (numeric) = 3.22497513131593 " " absolute error = 6.3371530245603940000000000000E-13 " " relative error = 1.965023842516675200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2399999999998683 " " y[1] (closed_form) = 3.240723224025153 " " y[1] (numeric) = 3.2407232240245203 " " absolute error = 6.3282712403633920000000000000E-13 " " relative error = 1.952734251863489400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.249999999999867 " " y[1] (closed_form) = 3.256347245445271 " " y[1] (numeric) = 3.2563472454446414 " " absolute error = 6.2971849956738880000000000000E-13 " " relative error = 1.9338186381940400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.259999999999866 " " y[1] (closed_form) = 3.271845633187798 " " y[1] (numeric) = 3.27184563318717 " " absolute error = 6.2794214272798850000000000000E-13 " " relative error = 1.91922912364351700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.269999999999865 " " y[1] (closed_form) = 3.2872168374268744 " " y[1] (numeric) = 3.287216837426248 " " absolute error = 6.2660987509843840000000000000E-13 " " relative error = 1.906201829961810500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.279999999999864 " " y[1] (closed_form) = 3.3024593210548847 " " y[1] (numeric) = 3.3024593210542603 " " absolute error = 6.243894290491880000000000000E-13 " " relative error = 1.89068015181408230000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999863 " " y[1] (closed_form) = 3.3175715598361695 " " y[1] (numeric) = 3.3175715598355464 " " absolute error = 6.2305716141963790000000000000E-13 " " relative error = 1.878051912919117500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2999999999998617 " " y[1] (closed_form) = 3.332552042559442 " " y[1] (numeric) = 3.332552042558821 " " absolute error = 6.2083671537038750000000000000E-13 " " relative error = 1.862946797054599300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999998606 " " y[1] (closed_form) = 3.347399271188916 " " y[1] (numeric) = 3.3473992711882965 " " absolute error = 6.1950444774083730000000000000E-13 " " relative error = 1.85070377792370180000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999998595 " " y[1] (closed_form) = 3.3621117610140994 " " y[1] (numeric) = 3.3621117610134816 " " absolute error = 6.1772809090143710000000000000E-13 " " relative error = 1.8373217037708300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999998584 " " y[1] (closed_form) = 3.376688040798271 " " y[1] (numeric) = 3.376688040797655 " " absolute error = 6.1595173406203680000000000000E-13 " " relative error = 1.824129817797506300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3399999999998573 " " y[1] (closed_form) = 3.3911266529255997 " " y[1] (numeric) = 3.3911266529249846 " " absolute error = 6.1506355564233670000000000000E-13 " " relative error = 1.813743981256812600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.349999999999856 " " y[1] (closed_form) = 3.4054261535469035 " " y[1] (numeric) = 3.4054261535462897 " " absolute error = 6.1373128801278650000000000000E-13 " " relative error = 1.80221581775766300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.359999999999855 " " y[1] (closed_form) = 3.419585112724037 " " y[1] (numeric) = 3.419585112723425 " " absolute error = 6.1195493117338630000000000000E-13 " " relative error = 1.789558999120521600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.369999999999854 " " y[1] (closed_form) = 3.4336021145728823 " " y[1] (numeric) = 3.4336021145722717 " " absolute error = 6.1062266354383610000000000000E-13 " " relative error = 1.77837339088368320000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.379999999999853 " " y[1] (closed_form) = 3.447475757404934 " " y[1] (numeric) = 3.4474757574043253 " " absolute error = 6.0884630670443580000000000000E-13 " " relative error = 1.766064069911665300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999852 " " y[1] (closed_form) = 3.4612046538674717 " " y[1] (numeric) = 3.461204653866864 " " absolute error = 6.0751403907488570000000000000E-13 " " relative error = 1.75520981805009200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3999999999998507 " " y[1] (closed_form) = 3.474787431082289 " " y[1] (numeric) = 3.4747874310816833 " " absolute error = 6.0573768223548540000000000000E-13 " " relative error = 1.74323665619688500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999998496 " " y[1] (closed_form) = 3.488222730782984 " " y[1] (numeric) = 3.4882227307823794 " " absolute error = 6.0440541460593520000000000000E-13 " " relative error = 1.73270304465411080000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999998485 " " y[1] (closed_form) = 3.5015092094507816 " " y[1] (numeric) = 3.501509209450179 " " absolute error = 6.026290577665350000000000000E-13 " " relative error = 1.721055184261698300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4299999999998474 " " y[1] (closed_form) = 3.514645538448888 " " y[1] (numeric) = 3.514645538448287 " " absolute error = 6.0085270092713470000000000000E-13 " " relative error = 1.709568416940013800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4399999999998463 " " y[1] (closed_form) = 3.5276304041553495 " " y[1] (numeric) = 3.52763040415475 " " absolute error = 5.9952043329758450000000000000E-13 " " relative error = 1.699498996809255800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.449999999999845 " " y[1] (closed_form) = 3.540462508094417 " " y[1] (numeric) = 3.540462508093818 " " absolute error = 5.9907634408773450000000000000E-13 " " relative error = 1.69208498245099400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.459999999999844 " " y[1] (closed_form) = 3.5531405670663894 " " y[1] (numeric) = 3.5531405670657925 " " absolute error = 5.9685589803848420000000000000E-13 " " relative error = 1.67979815820028600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.469999999999843 " " y[1] (closed_form) = 3.5656633132759348 " " y[1] (numeric) = 3.5656633132753393 " " absolute error = 5.955236304089340000000000000E-13 " " relative error = 1.670162261791901500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999842 " " y[1] (closed_form) = 3.5780294944588675 " " y[1] (numeric) = 3.5780294944582733 " " absolute error = 5.9419136277938380000000000000E-13 " " relative error = 1.660666474939854800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999841 " " y[1] (closed_form) = 3.590237874007375 " " y[1] (numeric) = 3.590237874006782 " " absolute error = 5.9285909514983360000000000000E-13 " " relative error = 1.651308676347097400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4999999999998397 " " y[1] (closed_form) = 3.6022872310936753 " " y[1] (numeric) = 3.6022872310930842 " " absolute error = 5.9108273831043330000000000000E-13 " " relative error = 1.640853991898300600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5099999999998386 " " y[1] (closed_form) = 3.6141763607921016 " " y[1] (numeric) = 3.6141763607915114 " " absolute error = 5.9019455989073320000000000000E-13 " " relative error = 1.632998783051591300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999998375 " " y[1] (closed_form) = 3.6259040741995907 " " y[1] (numeric) = 3.6259040741990014 " " absolute error = 5.8930638147103310000000000000E-13 " " relative error = 1.625267435132356500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5299999999998364 " " y[1] (closed_form) = 3.6374691985545757 " " y[1] (numeric) = 3.6374691985539873 " " absolute error = 5.884182030513330000000000000E-13 " " relative error = 1.617658242398734600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5399999999998353 " " y[1] (closed_form) = 3.6488705773542582 " " y[1] (numeric) = 3.648870577353671 " " absolute error = 5.8708593542178280000000000000E-13 " " relative error = 1.608952477145599300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.549999999999834 " " y[1] (closed_form) = 3.660107070470259 " " y[1] (numeric) = 3.6601070704696737 " " absolute error = 5.8530957858238250000000000000E-13 " " relative error = 1.59915971667785300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.559999999999833 " " y[1] (closed_form) = 3.6711775542626324 " " y[1] (numeric) = 3.6711775542620475 " " absolute error = 5.8486548937253250000000000000E-13 " " relative error = 1.593127765486146700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999832 " " y[1] (closed_form) = 3.6820809216922212 " " y[1] (numeric) = 3.6820809216916386 " " absolute error = 5.8264504332328220000000000000E-13 " " relative error = 1.582379789348867800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999831 " " y[1] (closed_form) = 3.6928160824313707 " " y[1] (numeric) = 3.692816082430789 " " absolute error = 5.817568649035820000000000000E-13 " " relative error = 1.575374597373801500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5899999999998298 " " y[1] (closed_form) = 3.703381962972953 " " y[1] (numeric) = 3.7033819629723723 " " absolute error = 5.8086868648388190000000000000E-13 " " relative error = 1.568481707508181700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5999999999998287 " " y[1] (closed_form) = 3.713777506737718 " " y[1] (numeric) = 3.7137775067371384 " " absolute error = 5.7953641885433170000000000000E-13 " " relative error = 1.56050387456682100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6099999999998276 " " y[1] (closed_form) = 3.724001674179952 " " y[1] (numeric) = 3.7240016741793744 " " absolute error = 5.7776006201493150000000000000E-13 " " relative error = 1.551449522756075700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6199999999998265 " " y[1] (closed_form) = 3.7340534428914314 " " y[1] (numeric) = 3.7340534428908554 " " absolute error = 5.7598370517553120000000000000E-13 " " relative error = 1.54251596551741700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6299999999998254 " " y[1] (closed_form) = 3.743931807703662 " " y[1] (numeric) = 3.7439318077030865 " " absolute error = 5.7553961596568120000000000000E-13 " " relative error = 1.537259879524055500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999998243 " " y[1] (closed_form) = 3.753635780788394 " " y[1] (numeric) = 3.7536357807878193 " " absolute error = 5.746514375459810000000000000E-13 " " relative error = 1.530919543358797400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.649999999999823 " " y[1] (closed_form) = 3.763164391756405 " " y[1] (numeric) = 3.7631643917558315 " " absolute error = 5.7331916991643080000000000000E-13 " " relative error = 1.523502856192902300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.659999999999822 " " y[1] (closed_form) = 3.772516687754539 " " y[1] (numeric) = 3.7725166877539666 " " absolute error = 5.7243099149673070000000000000E-13 " " relative error = 1.517371661614704500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.669999999999821 " " y[1] (closed_form) = 3.78169173356099 " " y[1] (numeric) = 3.781691733560419 " " absolute error = 5.7109872386718050000000000000E-13 " " relative error = 1.510167311626459400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.67999999999982 " " y[1] (closed_form) = 3.7906886116788234 " " y[1] (numeric) = 3.790688611678253 " " absolute error = 5.7021054544748040000000000000E-13 " " relative error = 1.504240004548791000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6899999999998188 " " y[1] (closed_form) = 3.799506422427725 " " y[1] (numeric) = 3.799506422427155 " " absolute error = 5.6976645623763030000000000000E-13 " " relative error = 1.499580189875224500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6999999999998177 " " y[1] (closed_form) = 3.8081442840339665 " " y[1] (numeric) = 3.8081442840333977 " " absolute error = 5.6887827781793020000000000000E-13 " " relative error = 1.493846439072727400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7099999999998166 " " y[1] (closed_form) = 3.8166013327185873 " " y[1] (numeric) = 3.816601332718019 " " absolute error = 5.6843418860808010000000000000E-13 " " relative error = 1.48937271423940200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7199999999998155 " " y[1] (closed_form) = 3.824876722783765 " " y[1] (numeric) = 3.824876722783198 " " absolute error = 5.67101920978530000000000000E-13 " " relative error = 1.482667186632332000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999998144 " " y[1] (closed_form) = 3.8329696266973903 " " y[1] (numeric) = 3.832969626696824 " " absolute error = 5.6621374255882980000000000000E-13 " " relative error = 1.477219486987424400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999998133 " " y[1] (closed_form) = 3.840879235175815 " " y[1] (numeric) = 3.84087923517525 " " absolute error = 5.6488147492927960000000000000E-13 " " relative error = 1.470708763128873700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.749999999999812 " " y[1] (closed_form) = 3.848604757264784 " " y[1] (numeric) = 3.8486047572642192 " " absolute error = 5.6488147492927960000000000000E-13 " " relative error = 1.467756526213782000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999811 " " y[1] (closed_form) = 3.8561454204185246 " " y[1] (numeric) = 3.8561454204179615 " " absolute error = 5.6310511808987940000000000000E-13 " " relative error = 1.460279778631281600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.76999999999981 " " y[1] (closed_form) = 3.863500470577007 " " y[1] (numeric) = 3.8635004705764437 " " absolute error = 5.6310511808987940000000000000E-13 " " relative error = 1.457499804589853500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.779999999999809 " " y[1] (closed_form) = 3.8706691722413424 " " y[1] (numeric) = 3.8706691722407807 " " absolute error = 5.6177285046032920000000000000E-13 " " relative error = 1.451358474366927200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7899999999998077 " " y[1] (closed_form) = 3.8776508085473402 " " y[1] (numeric) = 3.877650808546779 " " absolute error = 5.6132876125047910000000000000E-13 " " relative error = 1.447600077895529500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7999999999998066 " " y[1] (closed_form) = 3.884444681337187 " " y[1] (numeric) = 3.884444681336627 " " absolute error = 5.599964936209290000000000000E-13 " " relative error = 1.44163848261614300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8099999999998055 " " y[1] (closed_form) = 3.8910501112292657 " " y[1] (numeric) = 3.8910501112287057 " " absolute error = 5.599964936209290000000000000E-13 " " relative error = 1.439191163343856700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8199999999998044 " " y[1] (closed_form) = 3.8974664376860906 " " y[1] (numeric) = 3.897466437685532 " " absolute error = 5.5866422599137880000000000000E-13 " " relative error = 1.433403558243481200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999998033 " " y[1] (closed_form) = 3.9036930190803645 " " y[1] (numeric) = 3.9036930190798063 " " absolute error = 5.5822013678152870000000000000E-13 " " relative error = 1.429979596379826700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8399999999998022 " " y[1] (closed_form) = 3.909729232759135 " " y[1] (numeric) = 3.9097292327585786 " " absolute error = 5.5644377994212850000000000000E-13 " " relative error = 1.423228430449237000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.849999999999801 " " y[1] (closed_form) = 3.915574475106066 " " y[1] (numeric) = 3.915574475105511 " " absolute error = 5.5511151231257830000000000000E-13 " " relative error = 1.417701325416729200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8599999999998 " " y[1] (closed_form) = 3.9212281616017934 " " y[1] (numeric) = 3.9212281616012388 " " absolute error = 5.5466742310272820000000000000E-13 " " relative error = 1.414524736240164400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.869999999999799 " " y[1] (closed_form) = 3.926689726882379 " " y[1] (numeric) = 3.9266897268818246 " " absolute error = 5.5422333389287810000000000000E-13 " " relative error = 1.41142634748711700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.879999999999798 " " y[1] (closed_form) = 3.931958624795845 " " y[1] (numeric) = 3.931958624795292 " " absolute error = 5.533351554731780000000000000E-13 " " relative error = 1.407276139641241200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8899999999997967 " " y[1] (closed_form) = 3.937034328456792 " " y[1] (numeric) = 3.9370343284562392 " " absolute error = 5.528910662633280000000000000E-13 " " relative error = 1.404333871988476500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8999999999997956 " " y[1] (closed_form) = 3.941916330299083 " " y[1] (numeric) = 3.941916330298531 " " absolute error = 5.5200288784362780000000000000E-13 " " relative error = 1.400341462350993000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9099999999997945 " " y[1] (closed_form) = 3.9466041421266027 " " y[1] (numeric) = 3.946604142126051 " " absolute error = 5.5155879863377780000000000000E-13 " " relative error = 1.397552880326563000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999997934 " " y[1] (closed_form) = 3.951097295162075 " " y[1] (numeric) = 3.9510972951615226 " " absolute error = 5.5244697705347790000000000000E-13 " " relative error = 1.398211523998465200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9299999999997923 " " y[1] (closed_form) = 3.955395340093939 " " y[1] (numeric) = 3.955395340093388 " " absolute error = 5.5111470942392770000000000000E-13 " " relative error = 1.393323958891145900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9399999999997912 " " y[1] (closed_form) = 3.959497847121285 " " y[1] (numeric) = 3.959497847120734 " " absolute error = 5.5111470942392770000000000000E-13 " " relative error = 1.391880310844493500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.94999999999979 " " y[1] (closed_form) = 3.963404405996828 " " y[1] (numeric) = 3.963404405996277 " " absolute error = 5.5067062021407760000000000000E-13 " " relative error = 1.389387919589748800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.959999999999789 " " y[1] (closed_form) = 3.9671146260679366 " " y[1] (numeric) = 3.967114626067386 " " absolute error = 5.5067062021407760000000000000E-13 " " relative error = 1.388088502902379600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.969999999999788 " " y[1] (closed_form) = 3.9706281363156952 " " y[1] (numeric) = 3.970628136315145 " " absolute error = 5.5022653100422760000000000000E-13 " " relative error = 1.385741782192620700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.979999999999787 " " y[1] (closed_form) = 3.9739445853920063 " " y[1] (numeric) = 3.973944585391457 " " absolute error = 5.4933835258452750000000000000E-13 " " relative error = 1.38235030907039790000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9899999999997857 " " y[1] (closed_form) = 3.977063641654727 " " y[1] (numeric) = 3.977063641654178 " " absolute error = 5.4889426337467740000000000000E-13 " " relative error = 1.380149559654268700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9999999999997846 " " y[1] (closed_form) = 3.97998499320083 " " y[1] (numeric) = 3.979984993200281 " " absolute error = 5.4889426337467740000000000000E-13 " " relative error = 1.379136515118463000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0099999999997835 " " y[1] (closed_form) = 3.982708347897595 " " y[1] (numeric) = 3.9827083478970464 " " absolute error = 5.4845017416482730000000000000E-13 " " relative error = 1.377078425675696300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0199999999997824 " " y[1] (closed_form) = 3.985233433411821 " " y[1] (numeric) = 3.985233433411273 " " absolute error = 5.4800608495497730000000000000E-13 " " relative error = 1.375091557650164000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0299999999997813 " " y[1] (closed_form) = 3.987559997237063 " " y[1] (numeric) = 3.9875599972365143 " " absolute error = 5.4845017416482730000000000000E-13 " " relative error = 1.375402939503963800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.03999999999978 " " y[1] (closed_form) = 3.989687806718875 " " y[1] (numeric) = 3.989687806718326 " " absolute error = 5.4889426337467740000000000000E-13 " " relative error = 1.375782492179730000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.049999999999779 " " y[1] (closed_form) = 3.9916166490780824 " " y[1] (numeric) = 3.9916166490775336 " " absolute error = 5.4889426337467740000000000000E-13 " " relative error = 1.375117681958391000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ; " Iterations = 8051 "Total Elapsed Time "= 3 Minutes 0 Seconds "Elapsed Time(since restart) "= 3 Minutes 0 Seconds "Expected Time Remaining "= 43 Seconds "Optimized Time Remaining "= 43 Seconds "Expected Total Time "= 3 Minutes 43 Seconds "Time to Timeout "= 0.0 Seconds Percent Done = 80.51999999999781 "%" (%o255) temp/diffeq.add.max