(%i1) batch("temp/diffeq.mult.max") read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.mult.max (%i2) load("stringproc") (%i3) keepfloat:true (%i4) alias(convfloat,float) (%i5) alias(int_trunc,truncate) (%i6) alias(elapsed_time_seconds,elapsed_real_time) (%i7) alias(ln,log) (%i8) alias(arcsin,asin) (%i9) alias(arccos,acos) (%i10) alias(arctan,atan) (%i11) alias(float_abs,abs) (%i12) mode_declare(display_poles(),fixnum) (%i13) mode_declare(est_size_answer(),convfloat) (%i14) mode_declare(test_suggested_h(),convfloat) (%i15) mode_declare(reached_interval(),boolean) (%i16) mode_declare(display_alot([iter],fixnum),fixnum) (%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum) (%i18) mode_declare(check_for_pole(),fixnum) (%i19) mode_declare(atomall(),fixnum) (%i20) mode_declare(log10([x],convfloat),convfloat) (%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum) (%i22) mode_declare(omniout_timestr(secs_in,number),fixnum) (%i23) mode_declare(zero_ats_ar(ar,array([30],convfloat)),fixnum) (%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a], completearray([30],convfloat),[arr_b], completearray([30],convfloat),[jjj_ats],fixnum), convfloat) (%i25) mode_declare(att([mmm_att],fixnum,[arr_a], completearray([30],convfloat),[arr_b], completearray([30],convfloat),[jjj_att],fixnum), convfloat) (%i26) mode_declare(logitem_ditto([file],fixnum),fixnum) (%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum) (%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum) (%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum) (%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum) (%i31) mode_declare(logstart([file],fixnum),fixnum) (%i32) mode_declare(logend([file],fixnum),fixnum) (%i33) mode_declare(chk_data(),fixnum) (%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat, [t2],convfloat,[clock_sec2],convfloat), convfloat) (%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2], convfloat),convfloat) (%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i42) mode_declare(neg([nnn],convfloat),convfloat) (%i43) mode_declare(factorial_2([nnn],fixnum),convfloat) (%i44) mode_declare(factorial_1([nnn],fixnum),convfloat) (%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat) (%i46) mode_declare(convfloat([mmm],fixnum),convfloat) (%i47) mode_declare(elaped_time_seconds(),convfloat) (%i48) mode_declare(Si([x],convfloat),convfloat) (%i49) mode_declare(Ci([x],convfloat),convfloat) (%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end], convfloat,[estimated_h], convfloat,[estimated_answer], convfloat),convfloat) (%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat) (%i52) mode_declare(main_prog(),fixnum) (%i53) define_variable(always,1,fixnum) (%i54) define_variable(info,2,fixnum) (%i55) define_variable(debugl,3,fixnum) (%i56) define_variable(debugmassive,4,fixnum) (%i57) define_variable(glob_iolevel,5,fixnum) (%i58) define_variable(glob_yes_pole,4,fixnum) (%i59) define_variable(glob_no_pole,3,fixnum) (%i60) define_variable(glob_not_given,0,fixnum) (%i61) define_variable(glob_no_sing_tests,4,fixnum) (%i62) define_variable(glob_ratio_test,1,fixnum) (%i63) define_variable(glob_three_term_test,2,fixnum) (%i64) define_variable(glob_six_term_test,3,fixnum) (%i65) define_variable(ats_max_terms,30,fixnum) (%i66) define_variable(glob_log_10,0.0,convfloat) (%i67) define_variable(max_unchanged,10,fixnum) (%i68) define_variable(glob__small,1.0E-51,convfloat) (%i69) define_variable(glob_small_float,1.0E-51,convfloat) (%i70) define_variable(glob_smallish_float,1.0E-61,convfloat) (%i71) define_variable(glob_large_float,1.0E+100,convfloat) (%i72) define_variable(glob_larger_float,1.1E+100,convfloat) (%i73) define_variable(glob__m2,-2.0,convfloat) (%i74) define_variable(glob__m1,-1.0,convfloat) (%i75) define_variable(glob__0,0.0,convfloat) (%i76) define_variable(glob__1,1.0,convfloat) (%i77) define_variable(glob__2,2.0,convfloat) (%i78) define_variable(glob__3,3.0,convfloat) (%i79) define_variable(glob__4,4.0,convfloat) (%i80) define_variable(glob__5,5.0,convfloat) (%i81) define_variable(glob__8,8.0,convfloat) (%i82) define_variable(glob__10,10.0,convfloat) (%i83) define_variable(glob__100,100.0,convfloat) (%i84) define_variable(glob__pi,0.0,convfloat) (%i85) define_variable(glob__0_5,0.5,convfloat) (%i86) define_variable(glob__0_8,0.8,convfloat) (%i87) define_variable(glob__m0_8,-0.8,convfloat) (%i88) define_variable(glob__0_25,0.25,convfloat) (%i89) define_variable(glob__0_125,0.125,convfloat) (%i90) define_variable(glob_prec,1.0E-16,convfloat) (%i91) define_variable(glob_check_sign,1.0,convfloat) (%i92) define_variable(glob_desired_digits_correct,8.0,convfloat) (%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat) (%i94) define_variable(glob_ratio_of_radius,0.1,convfloat) (%i95) define_variable(glob_percent_done,0.0,convfloat) (%i96) define_variable(glob_total_exp_sec,0.1,convfloat) (%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat) (%i98) define_variable(glob_estimated_size_answer,100.0,convfloat) (%i99) define_variable(glob_almost_1,0.999,convfloat) (%i100) define_variable(glob_clock_sec,0.0,convfloat) (%i101) define_variable(glob_clock_start_sec,0.0,convfloat) (%i102) define_variable(glob_disp_incr,0.1,convfloat) (%i103) define_variable(glob_h,0.1,convfloat) (%i104) define_variable(glob_diff_rc_fm,0.1,convfloat) (%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat) (%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat) (%i107) define_variable(glob_diff_ord_fm,0.1,convfloat) (%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat) (%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat) (%i110) define_variable(glob_six_term_ord_save,0.1,convfloat) (%i111) define_variable(glob_guess_error_rc,0.1,convfloat) (%i112) define_variable(glob_guess_error_ord,0.1,convfloat) (%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat) (%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat) (%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat) (%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat) (%i117) define_variable(glob_last_good_h,0.1,convfloat) (%i118) define_variable(glob_max_h,0.1,convfloat) (%i119) define_variable(glob_min_h,1.0E-6,convfloat) (%i120) define_variable(glob_display_interval,0.1,convfloat) (%i121) define_variable(glob_abserr,1.0E-11,convfloat) (%i122) define_variable(glob_relerr,1.0E-11,convfloat) (%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat) (%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat) (%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat) (%i126) define_variable(glob_max_hours,0.0,convfloat) (%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat) (%i128) define_variable(glob_optimal_start,0.0,convfloat) (%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat) (%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat) (%i131) define_variable(glob_max_sec,10000.0,convfloat) (%i132) define_variable(glob_orig_start_sec,0.0,convfloat) (%i133) define_variable(glob_normmax,0.0,convfloat) (%i134) define_variable(glob_max_minutes,0.0,convfloat) (%i135) define_variable(glob_next_display,0.0,convfloat) (%i136) define_variable(glob_est_digits,1,fixnum) (%i137) define_variable(glob_subiter_method,3,fixnum) (%i138) define_variable(glob_html_log,true,boolean) (%i139) define_variable(glob_min_good_digits,99999,fixnum) (%i140) define_variable(glob_good_digits,0,fixnum) (%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum) (%i142) define_variable(glob_apfp_est_good_digits,0,fixnum) (%i143) define_variable(glob_max_opt_iter,10,fixnum) (%i144) define_variable(glob_dump,false,boolean) (%i145) define_variable(glob_djd_debug,true,boolean) (%i146) define_variable(glob_display_flag,true,boolean) (%i147) define_variable(glob_djd_debug2,true,boolean) (%i148) define_variable(glob_h_reason,0,fixnum) (%i149) define_variable(glob_sec_in_minute,60,fixnum) (%i150) define_variable(glob_min_in_hour,60,fixnum) (%i151) define_variable(glob_hours_in_day,24,fixnum) (%i152) define_variable(glob_days_in_year,365,fixnum) (%i153) define_variable(glob_sec_in_hour,3600,fixnum) (%i154) define_variable(glob_sec_in_day,86400,fixnum) (%i155) define_variable(glob_sec_in_year,31536000,fixnum) (%i156) define_variable(glob_not_yet_finished,true,boolean) (%i157) define_variable(glob_initial_pass,true,boolean) (%i158) define_variable(glob_not_yet_start_msg,true,boolean) (%i159) define_variable(glob_reached_optimal_h,false,boolean) (%i160) define_variable(glob_optimal_done,false,boolean) (%i161) define_variable(glob_type_given_pole,0,fixnum) (%i162) define_variable(glob_optimize,false,boolean) (%i163) define_variable(glob_look_poles,false,boolean) (%i164) define_variable(glob_dump_closed_form,false,boolean) (%i165) define_variable(glob_max_iter,1000,fixnum) (%i166) define_variable(glob_no_eqs,0,fixnum) (%i167) define_variable(glob_unchanged_h_cnt,0,fixnum) (%i168) define_variable(glob_warned,false,boolean) (%i169) define_variable(glob_warned2,false,boolean) (%i170) define_variable(glob_start,0,fixnum) (%i171) define_variable(glob_iter,0,fixnum) (%i172) completearray(array_y_init,[30],convfloat) (%i173) completearray(array_norms,[30],convfloat) (%i174) completearray(array_fact_1,[30],convfloat) (%i175) completearray(array_1st_rel_error,[2],convfloat) (%i176) completearray(array_last_rel_error,[2],convfloat) (%i177) completearray(array_est_rel_error,[2],convfloat) (%i178) completearray(array_max_est_error,[2],convfloat) (%i179) completearray(array_type_pole,[2],convfloat) (%i180) completearray(array_type_real_pole,[2],convfloat) (%i181) completearray(array_type_complex_pole,[2],convfloat) (%i182) completearray(array_est_digits,[2],convfloat) (%i183) completearray(array_y,[30],convfloat) (%i184) completearray(array_x,[30],convfloat) (%i185) completearray(array_tmp0,[30],convfloat) (%i186) completearray(array_tmp1,[30],convfloat) (%i187) completearray(array_tmp2,[30],convfloat) (%i188) completearray(array_m1,[30],convfloat) (%i189) completearray(array_y_higher,[2,30],convfloat) (%i190) completearray(array_y_higher_work,[2,30],convfloat) (%i191) completearray(array_y_higher_work2,[2,30],convfloat) (%i192) completearray(array_y_set_initial,[2,30],convfloat) (%i193) completearray(array_given_rad_poles,[2,3],convfloat) (%i194) completearray(array_given_ord_poles,[2,3],convfloat) (%i195) completearray(array_rad_test_poles,[2,4],convfloat) (%i196) completearray(array_ord_test_poles,[2,4],convfloat) (%i197) completearray(array_fact_2,[30,30],convfloat) (%i198) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%i199) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%i200) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%i201) 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)) (%i202) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%i203) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%i204) 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) (%i205) 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) (%i206) 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) (%i207) 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) (%i208) 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) (%i209) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%i210) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%i211) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%i212) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), printf(file,"~d",glob_min_good_digits), printf(file,"")),0) (%i213) log_revs(file,revs):=printf(file,revs) (%i214) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%i215) 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) (%i216) logstart(file):=(printf(file,""),0) (%i217) logend(file):=(printf(file,"~%"),0) (%i218) 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) (%i219) 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) (%i220) 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) (%i221) 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) (%i222) 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) (%i223) c(in_val):=(ret:in_val,ret) (%i224) 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) (%i225) 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) (%i226) 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) (%i227) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%i228) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret) (%i229) 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) (%i230) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret) (%i231) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret) (%i232) 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) (%i233) log10(x):=log(x)/glob_log_10 (%i234) c(x):=x (%i235) 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 (%i236) 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) (%i237) exact_soln_y(x):=block(c(x)*c(x)*c(x)/c(3.0)+c(1.0)) c(x) c(x) c(x) (%o237) exact_soln_y(x) := block(-------------- + c(1.0)) c(3.0) (%i238) 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) (%i239) my_check_sign(x0,xf):=block([ret], if xf > x0 then ret:glob__1 else ret:glob__m1,ret) (%i240) 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) (%i241) 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) (%i242) 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)) (%i243) 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)) (%i244) 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(16) *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) (%i245) 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) (%i246) 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) (%i247) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:array_x[1]*array_x[1], array_tmp2[1]:array_tmp1[1]+array_const_0D0[1], if not array_y_set_initial[1,2] then (if 1 <= ats_max_terms then ( temporary :c(array_tmp2[1])*expt(glob_h,c(1)) *c(factorial_3(0,1)), if 2 <= ats_max_terms then (array_y[2]:temporary, array_y_higher[1,2]:temporary), temporary:c(temporary)*c(1)/c(glob_h), array_y_higher[2,1]:c(temporary),0)), kkk:2, array_tmp1[2]:array_x[2]*array_x[1] +array_x[1]*array_x[2], array_tmp2[2]:array_tmp1[2], if not array_y_set_initial[1,3] then (if 2 <= ats_max_terms then ( temporary :c(array_tmp2[2])*expt(glob_h,c(1)) *c(factorial_3(1,2)), if 3 <= ats_max_terms then (array_y[3]:temporary, array_y_higher[1,3]:temporary), temporary:c(temporary)*c(2)/c(glob_h), array_y_higher[2,2]:c(temporary),0)), kkk:3,array_tmp1[3]:array_x[2]*array_x[2], array_tmp2[3]:array_tmp1[3], if not array_y_set_initial[1,4] then (if 3 <= ats_max_terms then ( temporary :c(array_tmp2[3])*expt(glob_h,c(1)) *c(factorial_3(2,3)), if 4 <= ats_max_terms then (array_y[4]:temporary, array_y_higher[1,4]:temporary), temporary:c(temporary)*c(3)/c(glob_h), array_y_higher[2,3]:c(temporary),0)), kkk:4,array_tmp2[4]:array_tmp1[4], if not array_y_set_initial[1,5] then (if 4 <= ats_max_terms then ( temporary :c(array_tmp2[4])*expt(glob_h,c(1)) *c(factorial_3(3,4)), if 5 <= ats_max_terms then (array_y[5]:temporary, array_y_higher[1,5]:temporary), temporary:c(temporary)*c(4)/c(glob_h), array_y_higher[2,4]:c(temporary),0)), kkk:5,array_tmp2[5]:array_tmp1[5], if not array_y_set_initial[1,6] then (if 5 <= ats_max_terms then ( temporary :c(array_tmp2[5])*expt(glob_h,c(1)) *c(factorial_3(4,5)), if 6 <= ats_max_terms then (array_y[6]:temporary, array_y_higher[1,6]:temporary), temporary:c(temporary)*c(5)/c(glob_h), array_y_higher[2,5]:c(temporary),0)), kkk:6, while kkk <= ats_max_terms do (array_tmp2[kkk]:array_tmp1[kkk],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_tmp2[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) (%i248) exact_soln_y(x):=block(c(x)*c(x)*c(x)/c(3.0)+c(1.0)) c(x) c(x) c(x) (%o248) exact_soln_y(x) := block(-------------- + c(1.0)) c(3.0) (%i249) main_prog():=block( mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat, [niii,done_once,term,ord,order_diff,term_no, html_log_file,iiif,jjjf,rows,r_order, sub_iter,calc_term,iii],fixnum,[temp_sum], convfloat,[current_iter],fixnum, [x_start,x_end],convfloat,[it,opt_iter], fixnum,[tmp],convfloat,[subiter],fixnum, [est_needed_step_err,estimated_step_error, min_value,est_answer,last_min_pole_est], convfloat,[repeat_it],fixnum],[found_h], boolean),Digits:32,max_terms:30, glob_html_log:true,term:1, while term <= 30 do (array_y_init[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_norms[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_fact_1[term]:c(0.0),term:1+term), term:1, while term <= 2 do (array_1st_rel_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_last_rel_error[term]:c(0.0),term:1+term), term:1, while term <= 2 do (array_est_rel_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_max_est_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_type_pole[term]:0,term:1+term), term:1, while term <= 2 do (array_type_real_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_type_complex_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_est_digits[term]:0,term:1+term), term:1, while term <= 30 do (array_y[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_x[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp0[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp1[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp2[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_m1[term]:c(0.0),term:1+term), ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_higher[ord,term]:c(0.0),term:1+term), ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_higher_work[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_higher_work2[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_set_initial[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_rad_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_ord_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 4 do (array_rad_test_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 4 do (array_ord_test_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 30 do (term:1, while term <= 30 do (array_fact_2[ord,term]:c(0.0),term:1+term), ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x), zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2),zero_ats_ar(array_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,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/multpostode.ode#################"), omniout_str(always, "diff ( y , x , 1 ) = x * x ; "), omniout_str(always,"!"), omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(always,"Digits:32,"), omniout_str(always,"max_terms:30,"),omniout_str(always,"!"), omniout_str(always,"/* END FIRST INPUT BLOCK */"), omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(always,"x_start:c(0.1),"), omniout_str(always,"x_end:c(10.0),"), 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,""), 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(1.0) + c(x) * c(x) * c(x) / c(3.0)) "), omniout_str(always,"));"),omniout_str(always,""), omniout_str(always,"/* END USER DEF BLOCK */"), omniout_str(always, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false, glob_small_float:glob__0,glob_smallish_float:glob__0, glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100), glob_almost_1:c(0.99),x_start:c(0.1),x_end:c(10.0), 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 ) = x * 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, "2015-04-24T22:10:01-05:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "mult"), logitem_str(html_log_file, "diff ( y , x , 1 ) = x * 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, "mult diffeq.max"), logitem_str(html_log_file, "mult maxima results"), logitem_str(html_log_file,"OK"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i250) main():=(glob_iolevel:2,compile(all),main_prog()) (%i251) main() warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable secs in translation. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable sec_temp in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable years_int in translation. warning: encountered undefined variable days_int in translation. warning: encountered undefined variable hours_int in translation. warning: encountered undefined variable minutes_int in translation. warning: encountered undefined variable sec_int in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable iii in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_ats in translation. warning: encountered undefined variable ma_ats in translation. warning: encountered undefined variable ret_ats in translation. warning: encountered undefined variable lll_ats in translation. warning: encountered undefined variable ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_att in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable ma_att in translation. warning: encountered undefined variable lll_att in translation. warning: encountered undefined variable ret_att in translation. warning: encountered undefined variable al_att in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_h_reason in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable errflag in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable sub1 in translation. warning: encountered undefined variable sub2 in translation. warning: encountered undefined variable rrr in translation. warning: encountered undefined variable ms2 in translation. warning: encountered undefined variable sec_left in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ret in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__m2 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temp in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm0 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm1 in translation. warning: encountered undefined variable rm2 in translation. warning: encountered undefined variable rm3 in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable rm4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__8 in translation. warning: encountered undefined variable glob__5 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable nr1 in translation. warning: encountered undefined variable dr2 in translation. warning: encountered undefined variable nr2 in translation. warning: encountered undefined variable dr1 in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable ds1 in translation. warning: encountered undefined variable ds2 in translation. warning: encountered undefined variable rcs in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable ord_no in translation. warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any. warning: encountered undefined variable rad_c in translation. warning: encountered undefined variable glob_six_term_ord_save in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_2 in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob_log_10 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob__10 in translation. warning: encountered undefined variable ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_x in translation. warning: encountered undefined variable array_given_rad_poles in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable rad_given in translation. warning: encountered undefined variable array_given_ord_poles in translation. warning: variable glob_least_given_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable array_rad_test_poles in translation. warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable array_ord_test_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: variable glob_least_3_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob__small in translation. warning: variable glob_least_6_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_estimated_size_answer in translation. warning: encountered undefined variable array_y in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob__small in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable array_max_est_error in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_next_display in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__10 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable always in translation. warning: encountered undefined variable ind_var in translation. warning: encountered undefined variable closed_form_val_y in translation. warning: encountered undefined variable term_no in translation. warning: encountered undefined variable numeric_val in translation. warning: encountered undefined variable abserr in translation. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable relerr in translation. warning: variable glob_good_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_apfp_est_good_digits in translation. warning: encountered undefined variable glob_min_apfp_est_good_digits in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable est_rel_err in translation. warning: variable glob_est_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_est_digits in translation. warning: encountered undefined variable array_est_digits in translation. warning: encountered undefined variable array_1st_rel_error in translation. warning: encountered undefined variable array_last_rel_error in translation. warning: encountered undefined variable array_est_rel_error in translation. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable clock_sec1 in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_clock_start_sec in translation. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_optimal_clock_start_sec in translation. warning: encountered undefined variable opt_clock_sec in translation. warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_optimal_expect_sec in translation. warning: encountered undefined variable total_clock_sec in translation. warning: variable glob_total_exp_sec (declared type convfloat) assigned type any. warning: encountered undefined variable percent_done in translation. warning: variable glob_percent_done (declared type convfloat) assigned type any. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable expect_sec in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable left_sec in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable last_no in translation. warning: encountered undefined variable found_sing in translation. warning: encountered undefined variable array_y_higher in translation. warning: variable tmp_rad (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_rad in translation. warning: encountered undefined variable prev_tmp_rad in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable cnt in translation. warning: encountered undefined variable tmp_ratio in translation. warning: encountered undefined variable glob_upper_ratio_limit in translation. warning: encountered undefined variable glob_lower_ratio_limit in translation. warning: variable tmp_ord (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_ord in translation. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_ratio_of_radius in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable h_new in translation. warning: variable ratio (declared type convfloat) assigned type any. warning: encountered undefined variable term in translation. warning: encountered undefined variable ratio in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temporary in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable array_y_set_initial in translation. warning: encountered undefined variable kkk in translation. warning: encountered undefined variable order_d in translation. warning: encountered undefined variable adj3 in translation. warning: encountered undefined variable adj2 in translation. modedeclare: [found_h] is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: variable term (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable array_y_init in translation. warning: variable term (declared type [found_h]) assigned type any. warning: encountered undefined variable array_norms in translation. warning: encountered undefined variable array_fact_1 in translation. warning: encountered undefined variable array_type_pole in translation. warning: encountered undefined variable array_type_real_pole in translation. warning: encountered undefined variable array_type_complex_pole in translation. warning: encountered undefined variable array_tmp0 in translation. warning: encountered undefined variable array_m1 in translation. warning: variable ord (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable ord in translation. warning: variable ord (declared type [found_h]) assigned type any. warning: encountered undefined variable array_y_higher_work in translation. warning: encountered undefined variable array_y_higher_work2 in translation. warning: encountered undefined variable array_const_1 in translation. warning: encountered undefined variable glob__m1 in translation. warning: variable iiif (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable iiif in translation. warning: encountered undefined variable ats_max_terms in translation. warning: variable jjjf (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable jjjf in translation. warning: variable jjjf (declared type [found_h]) assigned type any. warning: variable iiif (declared type [found_h]) assigned type any. warning: variable glob_orig_start_sec (declared type convfloat) assigned type any. warning: variable opt_iter (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob__0 in translation. warning: variable glob_large_float (declared type convfloat) assigned type any. warning: variable glob_larger_float (declared type convfloat) assigned type any. warning: variable glob_almost_1 (declared type convfloat) assigned type any. warning: variable x_start (declared type [found_h]) assigned type any. warning: variable x_end (declared type [found_h]) assigned type any. warning: encountered undefined variable x_start in translation. warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_h (declared type convfloat) assigned type any. warning: variable glob_display_interval (declared type convfloat) assigned type any. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_max_minutes in translation. warning: encountered undefined variable glob_max_hours in translation. warning: encountered undefined variable x_end in translation. warning: variable glob_check_sign (declared type convfloat) assigned type any. warning: encountered undefined variable glob_larger_float in translation. warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_max_h in translation. warning: encountered undefined variable glob_display_interval in translation. warning: encountered undefined variable glob__10 in translation. warning: variable display_max (declared type [found_h]) assigned type any. warning: encountered undefined variable display_max in translation. warning: variable min_value (declared type [found_h]) assigned type convfloat. warning: variable est_answer (declared type [found_h]) assigned type any. warning: encountered undefined variable est_answer in translation. warning: variable est_needed_step_err (declared type [found_h]) assigned type any. warning: encountered undefined variable est_needed_step_err in translation. warning: encountered undefined variable glob_small_float in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable opt_iter in translation. warning: encountered undefined variable found_h in translation. warning: variable glob_next_display (declared type convfloat) assigned type any. warning: variable order_diff (declared type [found_h]) assigned type fixnum. warning: variable term_no (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable order_diff in translation. warning: variable term_no (declared type [found_h]) assigned type any. warning: variable r_order (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable r_order in translation. warning: encountered undefined variable rows in translation. warning: variable it (declared type [found_h]) assigned type any. warning: encountered undefined variable it in translation. warning: variable r_order (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_look_poles in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type any. warning: encountered undefined variable estimated_step_error in translation. warning: encountered undefined variable glob__2 in translation. warning: variable opt_iter (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_optimize in translation. warning: variable html_log_file (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_html_log in translation. warning: variable current_iter (declared type [found_h]) assigned type fixnum. warning: variable glob_clock_start_sec (declared type convfloat) assigned type any. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable debugl in translation. warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable info in translation. warning: encountered undefined variable current_iter in translation. warning: encountered undefined variable glob_next_display in translation. warning: variable calc_term (declared type [found_h]) assigned type fixnum. warning: variable iii (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable calc_term in translation. warning: variable iii (declared type [found_h]) assigned type any. warning: variable temp_sum (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable temp_sum in translation. warning: variable temp_sum (declared type [found_h]) assigned type any. warning: encountered undefined variable html_log_file in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob_percent_done in translation. warning: encountered undefined variable glob__100 in translation. WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB__PI is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $LAST_MIN_POLE_EST is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. "##############ECHO OF PROBLEM#################" "##############temp/multpostode.ode#################" "diff ( y , x , 1 ) = x * x ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:c(0.1)," "x_end:c(10.0)," "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(1.0) + c(x) * c(x) * c(x) / c(3.0)) " "));" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (closed_form) = 1.0003333333333333 " " y[1] (numeric) = 1.0003333333333333 " " 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] = 0.11000000000000001 " " y[1] (closed_form) = 1.0004436666666667 " " y[1] (numeric) = 1.0004436666666667 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12000000000000002 " " y[1] (closed_form) = 1.000576 " " y[1] (numeric) = 1.0005760000000001 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.219167808592563700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.13000000000000003 " " y[1] (closed_form) = 1.0007323333333333 " " y[1] (numeric) = 1.0007323333333333 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.14000000000000004 " " y[1] (closed_form) = 1.0009146666666666 " " y[1] (numeric) = 1.0009146666666666 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000005 " " y[1] (closed_form) = 1.001125 " " y[1] (numeric) = 1.001125 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000006 " " y[1] (closed_form) = 1.0013653333333334 " " y[1] (numeric) = 1.0013653333333332 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.217418533812147700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000007 " " y[1] (closed_form) = 1.0016376666666666 " " y[1] (numeric) = 1.0016376666666666 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000008 " " y[1] (closed_form) = 1.001944 " " y[1] (numeric) = 1.0019440000000002 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.216137877217003400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000009 " " y[1] (closed_form) = 1.0022863333333334 " " y[1] (numeric) = 1.002286333333334 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.64614284981531100000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2000000000000001 " " y[1] (closed_form) = 1.0026666666666666 " " y[1] (numeric) = 1.0026666666666675 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.85816243051986700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2100000000000001 " " y[1] (closed_form) = 1.003087 " " y[1] (numeric) = 1.003087000000001 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.85445050828218400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2200000000000001 " " y[1] (closed_form) = 1.0035493333333334 " " y[1] (numeric) = 1.0035493333333343 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.85037127920758400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.23000000000000012 " " y[1] (closed_form) = 1.0040556666666667 " " y[1] (numeric) = 1.0040556666666673 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.63443110665936400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.24000000000000013 " " y[1] (closed_form) = 1.004608 " " y[1] (numeric) = 1.0046080000000006 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.63078349739494300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (closed_form) = 1.0052083333333333 " " y[1] (numeric) = 1.0052083333333337 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.417882294881452000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (closed_form) = 1.0058586666666667 " " y[1] (numeric) = 1.0058586666666671 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.415025933233124300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (closed_form) = 1.006561 " " y[1] (numeric) = 1.0065610000000003 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.205972662610922700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (closed_form) = 1.0073173333333334 " " y[1] (numeric) = 1.0073173333333336 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.20431633187785200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (closed_form) = 1.0081296666666666 " " y[1] (numeric) = 1.008129666666667 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.405080264311859000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (closed_form) = 1.0090000000000001 " " y[1] (numeric) = 1.0090000000000006 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.401280573340561000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (closed_form) = 1.0099303333333334 " " y[1] (numeric) = 1.0099303333333338 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.397226176822717000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (closed_form) = 1.0109226666666666 " " y[1] (numeric) = 1.0109226666666673 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.58936471344092900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (closed_form) = 1.011979 " " y[1] (numeric) = 1.0119790000000004 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.38832436098044200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (closed_form) = 1.0131013333333334 " " y[1] (numeric) = 1.0131013333333336 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.191731445012061500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (closed_form) = 1.0142916666666666 " " y[1] (numeric) = 1.0142916666666668 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.1891593140536300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y[1] (closed_form) = 1.015552 " " y[1] (numeric) = 1.0155520000000002 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.186442495559374000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y[1] (closed_form) = 1.0168843333333333 " " y[1] (numeric) = 1.0168843333333337 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.36715558783705600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y[1] (closed_form) = 1.0182906666666667 " " y[1] (numeric) = 1.0182906666666671 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.361124228937211500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (closed_form) = 1.019773 " " y[1] (numeric) = 1.0197730000000005 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.35478493596185230000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y[1] (closed_form) = 1.0213333333333334 " " y[1] (numeric) = 1.0213333333333339 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.34813195022907200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (closed_form) = 1.0229736666666667 " " y[1] (numeric) = 1.0229736666666671 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.34115974164922370000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y[1] (closed_form) = 1.024696 " " y[1] (numeric) = 1.0246960000000005 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.33386301742236300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y[1] (closed_form) = 1.0265023333333334 " " y[1] (numeric) = 1.026502333333334 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.48935509588152200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y[1] (closed_form) = 1.0283946666666668 " " y[1] (numeric) = 1.0283946666666672 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.31827608839598400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y[1] (closed_form) = 1.030375 " " y[1] (numeric) = 1.030375000000001 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.61995312095232500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000003 " " y[1] (closed_form) = 1.0324453333333334 " " y[1] (numeric) = 1.0324453333333345 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.07533347169163090000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000003 " " y[1] (closed_form) = 1.0346076666666668 " " y[1] (numeric) = 1.0346076666666677 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.58468817036401700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000003 " " y[1] (closed_form) = 1.036864 " " y[1] (numeric) = 1.0368640000000011 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.07075086474711880000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4900000000000003 " " y[1] (closed_form) = 1.0392163333333335 " " y[1] (numeric) = 1.0392163333333344 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.54661720771124300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000003 " " y[1] (closed_form) = 1.0416666666666667 " " y[1] (numeric) = 1.0416666666666679 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.06581410364015030000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000003 " " y[1] (closed_form) = 1.0442170000000002 " " y[1] (numeric) = 1.0442170000000013 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.06321102282873810000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000004 " " y[1] (closed_form) = 1.0468693333333334 " " y[1] (numeric) = 1.0468693333333345 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.06051728642207800000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000004 " " y[1] (closed_form) = 1.0496256666666668 " " y[1] (numeric) = 1.049625666666668 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.05773235152578820000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000004 " " y[1] (closed_form) = 1.052488 " " y[1] (numeric) = 1.0524880000000012 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.05485575571897870000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000004 " " y[1] (closed_form) = 1.0554583333333334 " " y[1] (numeric) = 1.055458333333335 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.4726419654733430000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000004 " " y[1] (closed_form) = 1.0585386666666667 " " y[1] (numeric) = 1.0585386666666683 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.46835659709034640000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5700000000000004 " " y[1] (closed_form) = 1.0617310000000002 " " y[1] (numeric) = 1.061731000000002 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.67307617409706430000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5800000000000004 " " y[1] (closed_form) = 1.0650373333333334 " " y[1] (numeric) = 1.0650373333333354 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.87636750541947980000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5900000000000004 " " y[1] (closed_form) = 1.0684596666666668 " " y[1] (numeric) = 1.0684596666666686 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.66253991125565830000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6000000000000004 " " y[1] (closed_form) = 1.072 " " y[1] (numeric) = 1.0720000000000018 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.6570492904853080000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000004 " " y[1] (closed_form) = 1.0756603333333334 " " y[1] (numeric) = 1.0756603333333357 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 2.0642632069265170000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000004 " " y[1] (closed_form) = 1.0794426666666668 " " y[1] (numeric) = 1.079442666666669 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 2.05703009323050000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6300000000000004 " " y[1] (closed_form) = 1.0833490000000001 " " y[1] (numeric) = 1.0833490000000023 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 2.04961286644498920000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6400000000000005 " " y[1] (closed_form) = 1.0873813333333335 " " y[1] (numeric) = 1.0873813333333355 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.83781106320746230000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000005 " " y[1] (closed_form) = 1.0915416666666669 " " y[1] (numeric) = 1.0915416666666689 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.83080637721138860000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000005 " " y[1] (closed_form) = 1.0958320000000001 " " y[1] (numeric) = 1.0958320000000026 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 2.22889152185311630000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000005 " " y[1] (closed_form) = 1.1002543333333334 " " y[1] (numeric) = 1.1002543333333363 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 2.62355691459102650000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6800000000000005 " " y[1] (closed_form) = 1.1048106666666668 " " y[1] (numeric) = 1.1048106666666695 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 2.41175736213659730000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000005 " " y[1] (closed_form) = 1.1095030000000001 " " y[1] (numeric) = 1.109503000000003 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 2.60168729965165160000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000005 " " y[1] (closed_form) = 1.1143333333333336 " " y[1] (numeric) = 1.1143333333333363 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 2.39114740571376740000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000005 " " y[1] (closed_form) = 1.119303666666667 " " y[1] (numeric) = 1.1193036666666696 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 2.3805293759426993000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000005 " " y[1] (closed_form) = 1.1244160000000003 " " y[1] (numeric) = 1.124416000000003 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 2.3697059265435347000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000005 " " y[1] (closed_form) = 1.1296723333333336 " " y[1] (numeric) = 1.129672333333336 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 2.16212310605878670000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000005 " " y[1] (closed_form) = 1.135074666666667 " " y[1] (numeric) = 1.1350746666666693 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 2.15183258502995160000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000006 " " y[1] (closed_form) = 1.1406250000000004 " " y[1] (numeric) = 1.1406250000000027 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.94669242673999960000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000006 " " y[1] (closed_form) = 1.1463253333333336 " " y[1] (numeric) = 1.1463253333333359 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.93701210701992030000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000006 " " y[1] (closed_form) = 1.152177666666667 " " y[1] (numeric) = 1.1521776666666694 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 2.11989064259650700000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000006 " " y[1] (closed_form) = 1.1581840000000003 " " y[1] (numeric) = 1.1581840000000025 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.9171790054519080000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000006 " " y[1] (closed_form) = 1.1643463333333337 " " y[1] (numeric) = 1.1643463333333357 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.71632905701191520000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000006 " " y[1] (closed_form) = 1.170666666666667 " " y[1] (numeric) = 1.170666666666669 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.707062737179910000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000006 " " y[1] (closed_form) = 1.1771470000000004 " " y[1] (numeric) = 1.1771470000000024 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.69766515509556680000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000006 " " y[1] (closed_form) = 1.1837893333333338 " " y[1] (numeric) = 1.1837893333333354 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.31299733044439650000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000006 " " y[1] (closed_form) = 1.190595666666667 " " y[1] (numeric) = 1.1905956666666688 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.49199000897890870000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000006 " " y[1] (closed_form) = 1.1975680000000004 " " y[1] (numeric) = 1.1975680000000022 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.48330352798358850000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000006 " " y[1] (closed_form) = 1.204708333333334 " " y[1] (numeric) = 1.2047083333333357 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.47451195467803360000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000007 " " y[1] (closed_form) = 1.2120186666666672 " " y[1] (numeric) = 1.212018666666669 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.4656183838204770000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8700000000000007 " " y[1] (closed_form) = 1.2195010000000006 " " y[1] (numeric) = 1.2195010000000022 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.27454773261786450000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000007 " " y[1] (closed_form) = 1.2271573333333339 " " y[1] (numeric) = 1.2271573333333354 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.26659572677061130000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000007 " " y[1] (closed_form) = 1.2349896666666673 " " y[1] (numeric) = 1.2349896666666689 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.25856294706532100000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000007 " " y[1] (closed_form) = 1.2430000000000005 " " y[1] (numeric) = 1.243000000000002 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.2504523205753970000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000007 " " y[1] (closed_form) = 1.2511903333333338 " " y[1] (numeric) = 1.2511903333333356 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.419733506626289800000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000007 " " y[1] (closed_form) = 1.2595626666666673 " " y[1] (numeric) = 1.2595626666666688 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.2340094507473640000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000007 " " y[1] (closed_form) = 1.2681190000000007 " " y[1] (numeric) = 1.268119000000002 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.0505856544615980000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000007 " " y[1] (closed_form) = 1.276861333333334 " " y[1] (numeric) = 1.2768613333333354 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.04339257111985040000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000007 " " y[1] (closed_form) = 1.2857916666666673 " " y[1] (numeric) = 1.2857916666666689 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.20883676163858960000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9600000000000007 " " y[1] (closed_form) = 1.2949120000000007 " " y[1] (numeric) = 1.2949120000000023 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.20032267403129960000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000008 " " y[1] (closed_form) = 1.3042243333333339 " " y[1] (numeric) = 1.3042243333333357 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.36200252824622670000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000008 " " y[1] (closed_form) = 1.3137306666666673 " " y[1] (numeric) = 1.3137306666666688 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.18312853152692260000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000008 " " y[1] (closed_form) = 1.3234330000000007 " " y[1] (numeric) = 1.323433000000002 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.0066755397139010000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0000000000000007 " " y[1] (closed_form) = 1.333333333333334 " " y[1] (numeric) = 1.3333333333333355 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.16573417585641380000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0099999999999996 " " y[1] (closed_form) = 1.3434336666666662 " " y[1] (numeric) = 1.3434336666666689 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.98337686870065780000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0199999999999985 " " y[1] (closed_form) = 1.3537359999999983 " " y[1] (numeric) = 1.353736000000002 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 2.7884006067102723000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0299999999999974 " " y[1] (closed_form) = 1.3642423333333304 " " y[1] (numeric) = 1.364242333333335 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 3.41796804680033650000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0399999999999963 " " y[1] (closed_form) = 1.3749546666666626 " " y[1] (numeric) = 1.374954666666668 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 4.03730774381346860000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0499999999999952 " " y[1] (closed_form) = 1.3858749999999946 " " y[1] (numeric) = 1.3858750000000015 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 4.9668135673679070000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.059999999999994 " " y[1] (closed_form) = 1.3970053333333268 " " y[1] (numeric) = 1.3970053333333348 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.7219579528934020000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.069999999999993 " " y[1] (closed_form) = 1.4083476666666586 " " y[1] (numeric) = 1.408347666666668 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 6.7795177552818290000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0799999999999919 " " y[1] (closed_form) = 1.4199039999999905 " " y[1] (numeric) = 1.419904000000001 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 7.3498605761210190000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0899999999999908 " " y[1] (closed_form) = 1.4316763333333222 " " y[1] (numeric) = 1.4316763333333338 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 8.0648951074149090000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0999999999999897 " " y[1] (closed_form) = 1.4436666666666542 " " y[1] (numeric) = 1.443666666666667 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 8.9207483853511380000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1099999999999886 " " y[1] (closed_form) = 1.4558769999999859 " " y[1] (numeric) = 1.4558770000000003 " " absolute error = 1.443289932012703500000000000000E-14 " " relative error = 9.9135430535183790000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1199999999999875 " " y[1] (closed_form) = 1.4683093333333175 " " y[1] (numeric) = 1.4683093333333335 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.0888176756534336000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1299999999999863 " " y[1] (closed_form) = 1.4809656666666493 " " y[1] (numeric) = 1.4809656666666664 " " absolute error = 1.70974345792274100000000000000E-14 " " relative error = 1.1544787947522267000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1399999999999852 " " y[1] (closed_form) = 1.4938479999999807 " " y[1] (numeric) = 1.4938479999999994 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 1.248570591767226000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1499999999999841 " " y[1] (closed_form) = 1.5069583333333123 " " y[1] (numeric) = 1.5069583333333323 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 1.3261159251197896000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.159999999999983 " " y[1] (closed_form) = 1.5202986666666438 " " y[1] (numeric) = 1.5202986666666651 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.4021114758681183000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.169999999999982 " " y[1] (closed_form) = 1.5338709999999753 " " y[1] (numeric) = 1.5338709999999982 " " absolute error = 2.287059430727822500000000000000E-14 " " relative error = 1.4910376627029648000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1799999999999808 " " y[1] (closed_form) = 1.5476773333333065 " " y[1] (numeric) = 1.5476773333333311 " " absolute error = 2.464695114667847500000000000000E-14 " " relative error = 1.5925122514778428000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1899999999999797 " " y[1] (closed_form) = 1.561719666666638 " " y[1] (numeric) = 1.5617196666666642 " " absolute error = 2.620126338115369400000000000000E-14 " " relative error = 1.6777187314979605000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1999999999999786 " " y[1] (closed_form) = 1.5759999999999692 " " y[1] (numeric) = 1.5759999999999974 " " absolute error = 2.819966482547897600000000000000E-14 " " relative error = 1.789318834104031100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2099999999999775 " " y[1] (closed_form) = 1.5905203333333002 " " y[1] (numeric) = 1.5905203333333302 " " absolute error = 2.997602166487922700000000000000E-14 " " relative error = 1.884667617046907000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2199999999999764 " " y[1] (closed_form) = 1.6052826666666316 " " y[1] (numeric) = 1.6052826666666629 " " absolute error = 3.130828929442941400000000000000E-14 " " relative error = 1.9503287454938423000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2299999999999753 " " y[1] (closed_form) = 1.6202889999999626 " " y[1] (numeric) = 1.6202889999999956 " " absolute error = 3.308464613382966500000000000000E-14 " " relative error = 2.041897842534907700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2399999999999742 " " y[1] (closed_form) = 1.6355413333332938 " " y[1] (numeric) = 1.6355413333333289 " " absolute error = 3.508304757815494700000000000000E-14 " " relative error = 2.145041941963912000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2499999999999731 " " y[1] (closed_form) = 1.6510416666666248 " " y[1] (numeric) = 1.6510416666666619 " " absolute error = 3.70814490224802300000000000000E-14 " " relative error = 2.2459426537275660000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.259999999999972 " " y[1] (closed_form) = 1.6667919999999556 " " y[1] (numeric) = 1.6667919999999943 " " absolute error = 3.86357612569554500000000000000E-14 " " relative error = 2.3179713639708177000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.269999999999971 " " y[1] (closed_form) = 1.6827943333332862 " " y[1] (numeric) = 1.6827943333333268 " " absolute error = 4.06341627012807300000000000000E-14 " " relative error = 2.4146838325033107000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2799999999999698 " " y[1] (closed_form) = 1.6990506666666172 " " y[1] (numeric) = 1.6990506666666596 " " absolute error = 4.24105195406809800000000000000E-14 " " relative error = 2.4961303610731378000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2899999999999687 " " y[1] (closed_form) = 1.715562999999948 " " y[1] (numeric) = 1.715562999999992 " " absolute error = 4.3964831775156200000000000000E-14 " " relative error = 2.562705757536012000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2999999999999676 " " y[1] (closed_form) = 1.7323333333332784 " " y[1] (numeric) = 1.7323333333333242 " " absolute error = 4.57411886145564500000000000000E-14 " " relative error = 2.640438057411462000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3099999999999665 " " y[1] (closed_form) = 1.7493636666666093 " " y[1] (numeric) = 1.7493636666666565 " " absolute error = 4.72955008490316700000000000000E-14 " " relative error = 2.703583122836469000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3199999999999654 " " y[1] (closed_form) = 1.7666559999999396 " " y[1] (numeric) = 1.7666559999999891 " " absolute error = 4.95159468982819800000000000000E-14 " " relative error = 2.802806369677157000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3299999999999643 " " y[1] (closed_form) = 1.78421233333327 " " y[1] (numeric) = 1.7842123333333215 " " absolute error = 5.151434834260726000000000000000E-14 " " relative error = 2.8872319387215545000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3399999999999632 " " y[1] (closed_form) = 1.8020346666666005 " " y[1] (numeric) = 1.8020346666666538 " " absolute error = 5.329070518200751000000000000000E-14 " " relative error = 2.957251942360495400000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3499999999999621 " " y[1] (closed_form) = 1.8201249999999307 " " y[1] (numeric) = 1.8201249999999862 " " absolute error = 5.55111512312578300000000000000E-14 " " relative error = 3.0498537864849906000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.359999999999961 " " y[1] (closed_form) = 1.8384853333332611 " " y[1] (numeric) = 1.8384853333333184 " " absolute error = 5.72875080706580800000000000000E-14 " " relative error = 3.1160165943120743000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.36999999999996 " " y[1] (closed_form) = 1.8571176666665914 " " y[1] (numeric) = 1.8571176666666507 " " absolute error = 5.92859095149833600000000000000E-14 " " relative error = 3.192361506171971000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3799999999999588 " " y[1] (closed_form) = 1.8760239999999215 " " y[1] (numeric) = 1.876023999999983 " " absolute error = 6.15063555642336700000000000000E-14 " " relative error = 3.2785484388385355000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3899999999999577 " " y[1] (closed_form) = 1.8952063333332516 " " y[1] (numeric) = 1.8952063333333151 " " absolute error = 6.35047570085589500000000000000E-14 " " relative error = 3.3508096660308240000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3999999999999566 " " y[1] (closed_form) = 1.9146666666665815 " " y[1] (numeric) = 1.9146666666666474 " " absolute error = 6.5947247662734300000000000000E-14 " " relative error = 3.4443200380956074000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4099999999999555 " " y[1] (closed_form) = 1.9344069999999114 " " y[1] (numeric) = 1.9344069999999796 " " absolute error = 6.81676937119846100000000000000E-14 " " relative error = 3.523958180051444000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4199999999999544 " " y[1] (closed_form) = 1.9544293333332414 " " y[1] (numeric) = 1.9544293333333116 " " absolute error = 7.01660951563098900000000000000E-14 " " relative error = 3.590106531845947000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4299999999999533 " " y[1] (closed_form) = 1.9747356666665712 " " y[1] (numeric) = 1.9747356666666436 " " absolute error = 7.23865412055602100000000000000E-14 " " relative error = 3.665631933804662000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4399999999999522 " " y[1] (closed_form) = 1.9953279999999007 " " y[1] (numeric) = 1.9953279999999756 " " absolute error = 7.48290318597355500000000000000E-14 " " relative error = 3.7502120884255250000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.449999999999951 " " y[1] (closed_form) = 2.0162083333332306 " " y[1] (numeric) = 2.016208333333308 " " absolute error = 7.7271522513910900000000000000E-14 " " relative error = 3.8325167710305150000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.45999999999995 " " y[1] (closed_form) = 2.03737866666656 " " y[1] (numeric) = 2.0373786666666405 " " absolute error = 8.03801469828613300000000000000E-14 " " relative error = 3.9452728301300330000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.469999999999949 " " y[1] (closed_form) = 2.0588409999998896 " " y[1] (numeric) = 2.058840999999972 " " absolute error = 8.26005930321116500000000000000E-14 " " relative error = 4.01199475977582000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4799999999999478 " " y[1] (closed_form) = 2.080597333333219 " " y[1] (numeric) = 2.0805973333333045 " " absolute error = 8.57092175010620800000000000000E-14 " " relative error = 4.119452434544445500000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4899999999999467 " " y[1] (closed_form) = 2.102649666666548 " " y[1] (numeric) = 2.102649666666636 " " absolute error = 8.7929663550312400000000000000E-14 " " relative error = 4.181850402578589000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4999999999999456 " " y[1] (closed_form) = 2.1249999999998774 " " y[1] (numeric) = 2.124999999999968 " " absolute error = 9.05941988094127700000000000000E-14 " " relative error = 4.263256414560846500000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5099999999999445 " " y[1] (closed_form) = 2.147650333333207 " " y[1] (numeric) = 2.1476503333333 " " absolute error = 9.32587340685131500000000000000E-14 " " relative error = 4.3423611665765566000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5199999999999434 " " y[1] (closed_form) = 2.170602666666536 " " y[1] (numeric) = 2.170602666666632 " " absolute error = 9.59232693276135300000000000000E-14 " " relative error = 4.419199828724340600000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5299999999999423 " " y[1] (closed_form) = 2.193858999999865 " " y[1] (numeric) = 2.1938589999999634 " " absolute error = 9.8587804586713900000000000000E-14 " " relative error = 4.4938076962430120000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5399999999999412 " " y[1] (closed_form) = 2.217421333333194 " " y[1] (numeric) = 2.217421333333295 " " absolute error = 1.01252339845814280000000000000E-13 " " relative error = 4.566220155084975000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.54999999999994 " " y[1] (closed_form) = 2.2412916666665224 " " y[1] (numeric) = 2.2412916666666267 " " absolute error = 1.04360964314764710000000000000E-13 " " relative error = 4.656286634482561500000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.559999999999939 " " y[1] (closed_form) = 2.2654719999998516 " " y[1] (numeric) = 2.265471999999959 " " absolute error = 1.07469588783715150000000000000E-13 " " relative error = 4.743805652143226500000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.569999999999938 " " y[1] (closed_form) = 2.28996433333318 " " y[1] (numeric) = 2.2899643333332906 " " absolute error = 1.10578213252665590000000000000E-13 " " relative error = 4.8288181454648416000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5799999999999368 " " y[1] (closed_form) = 2.314770666666509 " " y[1] (numeric) = 2.314770666666622 " " absolute error = 1.13242748511765970000000000000E-13 " " relative error = 4.892180039366334000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5899999999999357 " " y[1] (closed_form) = 2.3398929999998375 " " y[1] (numeric) = 2.3398929999999534 " " absolute error = 1.15907283770866340000000000000E-13 " " relative error = 4.953529232784336700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5999999999999346 " " y[1] (closed_form) = 2.365333333333166 " " y[1] (numeric) = 2.3653333333332847 " " absolute error = 1.18571819029966720000000000000E-13 " " relative error = 5.0129010300158580000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6099999999999335 " " y[1] (closed_form) = 2.391093666666494 " " y[1] (numeric) = 2.3910936666666167 " " absolute error = 1.22568621918617280000000000000E-13 " " relative error = 5.126048537006683000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6199999999999324 " " y[1] (closed_form) = 2.417175999999823 " " y[1] (numeric) = 2.4171759999999485 " " absolute error = 1.25677246387567720000000000000E-13 " " relative error = 5.199341975411677000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6299999999999313 " " y[1] (closed_form) = 2.4435823333331506 " " y[1] (numeric) = 2.443582333333279 " " absolute error = 1.2834178164666810000000000000E-13 " " relative error = 5.252197967547279000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6399999999999302 " " y[1] (closed_form) = 2.4703146666664786 " " y[1] (numeric) = 2.4703146666666105 " " absolute error = 1.3189449532546860000000000000E-13 " " relative error = 5.339177923574053000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.649999999999929 " " y[1] (closed_form) = 2.4973749999998067 " " y[1] (numeric) = 2.4973749999999413 " " absolute error = 1.34559030584568970000000000000E-13 " " relative error = 5.388018642958281000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.659999999999928 " " y[1] (closed_form) = 2.524765333333135 " " y[1] (numeric) = 2.524765333333272 " " absolute error = 1.37223565843669350000000000000E-13 " " relative error = 5.435101790728015000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6699999999999269 " " y[1] (closed_form) = 2.5524876666664627 " " y[1] (numeric) = 2.5524876666666025 " " absolute error = 1.39888101102769720000000000000E-13 " " relative error = 5.4804613918257620000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6799999999999258 " " y[1] (closed_form) = 2.58054399999979 " " y[1] (numeric) = 2.580543999999933 " " absolute error = 1.42996725571720160000000000000E-13 " " relative error = 5.541340336445796000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6899999999999247 " " y[1] (closed_form) = 2.608936333333118 " " y[1] (numeric) = 2.608936333333264 " " absolute error = 1.4610535004067060000000000000E-13 " " relative error = 5.600188405288132000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6999999999999236 " " y[1] (closed_form) = 2.637666666666446 " " y[1] (numeric) = 2.6376666666665947 " " absolute error = 1.48769885299770980000000000000E-13 " " relative error = 5.640207960310253000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7099999999999225 " " y[1] (closed_form) = 2.666736999999773 " " y[1] (numeric) = 2.666736999999925 " " absolute error = 1.51878509768721410000000000000E-13 " " relative error = 5.6952939029508480000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7199999999999214 " " y[1] (closed_form) = 2.696149333333101 " " y[1] (numeric) = 2.6961493333332553 " " absolute error = 1.5454304502782180000000000000E-13 " " relative error = 5.731991292810504000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7299999999999203 " " y[1] (closed_form) = 2.725905666666428 " " y[1] (numeric) = 2.725905666666585 " " absolute error = 1.57207580286922170000000000000E-13 " " relative error = 5.767168769239727000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7399999999999192 " " y[1] (closed_form) = 2.756007999999755 " " y[1] (numeric) = 2.756007999999916 " " absolute error = 1.61204383175572730000000000000E-13 " " relative error = 5.849198666171762000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.749999999999918 " " y[1] (closed_form) = 2.786458333333082 " " y[1] (numeric) = 2.7864583333332464 " " absolute error = 1.64313007644523170000000000000E-13 " " relative error = 5.896840648177811000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.759999999999917 " " y[1] (closed_form) = 2.817258666666409 " " y[1] (numeric) = 2.817258666666577 " " absolute error = 1.67865721323323670000000000000E-13 " " relative error = 5.9584774131498170000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7699999999999159 " " y[1] (closed_form) = 2.8484109999997362 " " y[1] (numeric) = 2.848410999999908 " " absolute error = 1.71862524211974230000000000000E-13 " " relative error = 6.0336280196920380000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7799999999999148 " " y[1] (closed_form) = 2.879917333333063 " " y[1] (numeric) = 2.8799173333332386 " " absolute error = 1.75415237890774730000000000000E-13 " " relative error = 6.090981704942151000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7899999999999137 " " y[1] (closed_form) = 2.9117796666663898 " " y[1] (numeric) = 2.9117796666665687 " " absolute error = 1.78967951569575230000000000000E-13 " " relative error = 6.146342514111666000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7999999999999126 " " y[1] (closed_form) = 2.9439999999997166 " " y[1] (numeric) = 2.943999999999899 " " absolute error = 1.82520665248375740000000000000E-13 " " relative error = 6.199750857622055000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8099999999999115 " " y[1] (closed_form) = 2.976580333333043 " " y[1] (numeric) = 2.9765803333332292 " " absolute error = 1.86073378927176240000000000000E-13 " " relative error = 6.251246668650111000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8199999999999104 " " y[1] (closed_form) = 3.0095226666663697 " " y[1] (numeric) = 3.0095226666665593 " " absolute error = 1.89626092605976740000000000000E-13 " " relative error = 6.3008693938837960000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8299999999999093 " " y[1] (closed_form) = 3.042828999999696 " " y[1] (numeric) = 3.0428289999998896 " " absolute error = 1.9362289549462730000000000000E-13 " " relative error = 6.363252601268314000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8399999999999082 " " y[1] (closed_form) = 3.0765013333330224 " " y[1] (numeric) = 3.0765013333332196 " " absolute error = 1.9717560917342780000000000000E-13 " " relative error = 6.409085770159948000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.849999999999907 " " y[1] (closed_form) = 3.1105416666663483 " " y[1] (numeric) = 3.1105416666665495 " " absolute error = 2.01172412062078370000000000000E-13 " " relative error = 6.467439874473062000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.859999999999906 " " y[1] (closed_form) = 3.1449519999996745 " " y[1] (numeric) = 3.144951999999879 " " absolute error = 2.04725125740878870000000000000E-13 " " relative error = 6.5096423010875860000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8699999999999048 " " y[1] (closed_form) = 3.179734333333 " " y[1] (numeric) = 3.1797343333332093 " " absolute error = 2.0916601783937950000000000000E-13 " " relative error = 6.578097284628541000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8799999999999037 " " y[1] (closed_form) = 3.214890666666326 " " y[1] (numeric) = 3.2148906666665398 " " absolute error = 2.13606909937880120000000000000E-13 " " relative error = 6.64429780311563000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8899999999999026 " " y[1] (closed_form) = 3.2504229999996523 " " y[1] (numeric) = 3.2504229999998695 " " absolute error = 2.17159623616680620000000000000E-13 " " relative error = 6.680965019528345000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8999999999999015 " " y[1] (closed_form) = 3.286333333332978 " " y[1] (numeric) = 3.2863333333331988 " " absolute error = 2.20712337295481120000000000000E-13 " " relative error = 6.716066658753574000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9099999999999004 " " y[1] (closed_form) = 3.3226236666663036 " " y[1] (numeric) = 3.322623666666528 " " absolute error = 2.24265050974281620000000000000E-13 " " relative error = 6.749637439358098000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9199999999998993 " " y[1] (closed_form) = 3.359295999999629 " " y[1] (numeric) = 3.359295999999857 " " absolute error = 2.2826185386293218000000000000E-13 " " relative error = 6.79493125532723000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9299999999998982 " " y[1] (closed_form) = 3.3963523333329544 " " y[1] (numeric) = 3.396352333333187 " " absolute error = 2.3270274596143280000000000000E-13 " " relative error = 6.85154904800686000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9399999999998971 " " y[1] (closed_form) = 3.4337946666662793 " " y[1] (numeric) = 3.4337946666665164 " " absolute error = 2.37143638059933440000000000000E-13 " " relative error = 6.9061682797173720000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.949999999999896 " " y[1] (closed_form) = 3.4716249999996047 " " y[1] (numeric) = 3.471624999999845 " " absolute error = 2.4025226252888388000000000000E-13 " " relative error = 6.920455479175062000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.959999999999895 " " y[1] (closed_form) = 3.5098453333329296 " " y[1] (numeric) = 3.509845333333174 " " absolute error = 2.44249065417534440000000000000E-13 " " relative error = 6.9589694764582930000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9699999999998938 " " y[1] (closed_form) = 3.5484576666662546 " " y[1] (numeric) = 3.548457666666503 " " absolute error = 2.482458683061850000000000000E-13 " " relative error = 6.995880791764097000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9799999999998927 " " y[1] (closed_form) = 3.5874639999995797 " " y[1] (numeric) = 3.587463999999833 " " absolute error = 2.5313084961453570000000000000E-13 " " relative error = 7.055982990061095000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9899999999998916 " " y[1] (closed_form) = 3.626866333332904 " " y[1] (numeric) = 3.6268663333331626 " " absolute error = 2.58459920132736440000000000000E-13 " " relative error = 7.1262598722579630000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9999999999998905 " " y[1] (closed_form) = 3.6666666666662286 " " y[1] (numeric) = 3.666666666666491 " " absolute error = 2.624567230213870000000000000E-13 " " relative error = 7.157910627856864000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0099999999998897 " " y[1] (closed_form) = 3.706866999999554 " " y[1] (numeric) = 3.70686699999982 " " absolute error = 2.6600943670018750000000000000E-13 " " relative error = 7.1761257336780490000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0199999999998886 " " y[1] (closed_form) = 3.7474693333328783 " " y[1] (numeric) = 3.7474693333331492 " " absolute error = 2.7089441800853820000000000000E-13 " " relative error = 7.2287294147811860000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0299999999998875 " " y[1] (closed_form) = 3.788475666666203 " " y[1] (numeric) = 3.788475666666478 " " absolute error = 2.74891220897188760000000000000E-13 " " relative error = 7.25598486261596000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0399999999998863 " " y[1] (closed_form) = 3.829887999999527 " " y[1] (numeric) = 3.829887999999807 " " absolute error = 2.79776202205539450000000000000E-13 " " relative error = 7.305075297386607000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0499999999998852 " " y[1] (closed_form) = 3.871708333332851 " " y[1] (numeric) = 3.871708333333136 " " absolute error = 2.8510527272374020000000000000E-13 " " relative error = 7.363810705191095000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.059999999999884 " " y[1] (closed_form) = 3.913938666666175 " " y[1] (numeric) = 3.9139386666664646 " " absolute error = 2.89546164822240800000000000000E-13 " " relative error = 7.397820698832545000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.069999999999883 " " y[1] (closed_form) = 3.956580999999498 " " y[1] (numeric) = 3.956580999999793 " " absolute error = 2.9487523534044160000000000000E-13 " " relative error = 7.452778935663873000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.079999999999882 " " y[1] (closed_form) = 3.999637333332823 " " y[1] (numeric) = 3.999637333333121 " " absolute error = 2.979838598093920000000000000E-13 " " relative error = 7.450271986562533000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.089999999999881 " " y[1] (closed_form) = 4.043109666666146 " " y[1] (numeric) = 4.04310966666645 " " absolute error = 3.04645197957142950000000000000E-13 " " relative error = 7.534922944802195000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0999999999998797 " " y[1] (closed_form) = 4.0869999999994695 " " y[1] (numeric) = 4.0869999999997795 " " absolute error = 3.0997426847534370000000000000E-13 " " relative error = 7.584396096779641000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1099999999998786 " " y[1] (closed_form) = 4.131310333332793 " " y[1] (numeric) = 4.131310333333109 " " absolute error = 3.15303338993544460000000000000E-13 " " relative error = 7.632041980714247000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999998775 " " y[1] (closed_form) = 4.176042666666116 " " y[1] (numeric) = 4.1760426666664365 " " absolute error = 3.2063240951174520000000000000E-13 " " relative error = 7.6779007089915000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999998764 " " y[1] (closed_form) = 4.221198999999439 " " y[1] (numeric) = 4.221198999999765 " " absolute error = 3.25961480029945960000000000000E-13 " " relative error = 7.722011685068372000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999998753 " " y[1] (closed_form) = 4.266781333332762 " " y[1] (numeric) = 4.266781333333093 " " absolute error = 3.3040237212844660000000000000E-13 " " relative error = 7.743597487579025000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1499999999998742 " " y[1] (closed_form) = 4.312791666666085 " " y[1] (numeric) = 4.3127916666664206 " " absolute error = 3.35731442646647340000000000000E-13 " " relative error = 7.78455043960372000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.159999999999873 " " y[1] (closed_form) = 4.359231999999407 " " y[1] (numeric) = 4.359231999999748 " " absolute error = 3.4106051316484810000000000000E-13 " " relative error = 7.823866983103778000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.169999999999872 " " y[1] (closed_form) = 4.40610433333273 " " y[1] (numeric) = 4.406104333333077 " " absolute error = 3.46389583683048840000000000000E-13 " " relative error = 7.861583781903853000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.179999999999871 " " y[1] (closed_form) = 4.453410666666053 " " y[1] (numeric) = 4.453410666666403 " " absolute error = 3.49942297361849340000000000000E-13 " " relative error = 7.857849265534407000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.18999999999987 " " y[1] (closed_form) = 4.501152999999375 " " y[1] (numeric) = 4.501152999999731 " " absolute error = 3.5615954629975020000000000000E-13 " " relative error = 7.91262919300454100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1999999999998687 " " y[1] (closed_form) = 4.549333333332697 " " y[1] (numeric) = 4.549333333333059 " " absolute error = 3.61488616817950970000000000000E-13 " " relative error = 7.945969009774358000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2099999999998676 " " y[1] (closed_form) = 4.59795366666602 " " y[1] (numeric) = 4.597953666666386 " " absolute error = 3.6592950891645160000000000000E-13 " " relative error = 7.958529716585582000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999998665 " " y[1] (closed_form) = 4.647015999999342 " " y[1] (numeric) = 4.647015999999713 " " absolute error = 3.71258579434652350000000000000E-13 " " relative error = 7.989182293211491000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999998654 " " y[1] (closed_form) = 4.696522333332664 " " y[1] (numeric) = 4.696522333333041 " " absolute error = 3.7747582837255320000000000000E-13 " " relative error = 8.037347670924316000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2399999999998643 " " y[1] (closed_form) = 4.746474666665986 " " y[1] (numeric) = 4.746474666666370 " " absolute error = 3.8369307731045410000000000000E-13 " " relative error = 8.083748555640504000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.249999999999863 " " y[1] (closed_form) = 4.796874999999307 " " y[1] (numeric) = 4.796874999999698 " " absolute error = 3.9079850466805510000000000000E-13 " " relative error = 8.146939510996462000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.259999999999862 " " y[1] (closed_form) = 4.84772533333263 " " y[1] (numeric) = 4.847725333333025 " " absolute error = 3.95239396766555730000000000000E-13 " " relative error = 8.153089739819137000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.269999999999861 " " y[1] (closed_form) = 4.89902766666595 " " y[1] (numeric) = 4.899027666666352 " " absolute error = 4.0145664570445660000000000000E-13 " " relative error = 8.194618871741732000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.27999999999986 " " y[1] (closed_form) = 4.950783999999271 " " y[1] (numeric) = 4.950783999999679 " " absolute error = 4.0767389464235750000000000000E-13 " " relative error = 8.234532038610805000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999859 " " y[1] (closed_form) = 5.002996333332592 " " y[1] (numeric) = 5.002996333333006 " " absolute error = 4.13891143580258360000000000000E-13 " " relative error = 8.272865219242674000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2999999999998577 " " y[1] (closed_form) = 5.055666666665914 " " y[1] (numeric) = 5.055666666666330 " " absolute error = 4.16555678839358730000000000000E-13 " " relative error = 8.239381792828259000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999998566 " " y[1] (closed_form) = 5.108796999999234 " " y[1] (numeric) = 5.108796999999657 " " absolute error = 4.2277292777725960000000000000E-13 " " relative error = 8.275391012352281000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999998555 " " y[1] (closed_form) = 5.1623893333325555 " " y[1] (numeric) = 5.162389333332984 " " absolute error = 4.2899017671516050000000000000E-13 " " relative error = 8.309915215910846000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999998544 " " y[1] (closed_form) = 5.2164456666658765 " " y[1] (numeric) = 5.216445666666310 " " absolute error = 4.34319247233361240000000000000E-13 " " relative error = 8.325961295997913000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3399999999998533 " " y[1] (closed_form) = 5.270967999999197 " " y[1] (numeric) = 5.2709679999996375 " " absolute error = 4.4053649617126210000000000000E-13 " " relative error = 8.357791133835933000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.349999999999852 " " y[1] (closed_form) = 5.325958333332517 " " y[1] (numeric) = 5.325958333332965 " " absolute error = 4.4764192352886310000000000000E-13 " " relative error = 8.404908478673134000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.359999999999851 " " y[1] (closed_form) = 5.381418666665837 " " y[1] (numeric) = 5.381418666666292 " " absolute error = 4.5474735088646410000000000000E-13 " " relative error = 8.450324701612777000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.36999999999985 " " y[1] (closed_form) = 5.437350999999157 " " y[1] (numeric) = 5.437350999999619 " " absolute error = 4.6185277824406510000000000000E-13 " " relative error = 8.494076954828494000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.379999999999849 " " y[1] (closed_form) = 5.493757333332478 " " y[1] (numeric) = 5.493757333332945 " " absolute error = 4.6718184876226587000000000000E-13 " " relative error = 8.50386757943813900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999848 " " y[1] (closed_form) = 5.550639666665797 " " y[1] (numeric) = 5.550639666666271 " " absolute error = 4.7428727611986690000000000000E-13 " " relative error = 8.544731861593992000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3999999999998467 " " y[1] (closed_form) = 5.607999999999117 " " y[1] (numeric) = 5.607999999999596 " " absolute error = 4.7961634663806760000000000000E-13 " " relative error = 8.552359961450484000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999998456 " " y[1] (closed_form) = 5.6658403333324365 " " y[1] (numeric) = 5.665840333332922 " " absolute error = 4.8583359557596850000000000000E-13 " " relative error = 8.574784444908973000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999998445 " " y[1] (closed_form) = 5.724162666665755 " " y[1] (numeric) = 5.724162666666247 " " absolute error = 4.9205084451386940000000000000E-13 " " relative error = 8.596031824519796000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4299999999998434 " " y[1] (closed_form) = 5.782968999999076 " " y[1] (numeric) = 5.782968999999573 " " absolute error = 4.9737991503207013000000000000E-13 " " relative error = 8.60077090214645000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4399999999998423 " " y[1] (closed_form) = 5.842261333332394 " " y[1] (numeric) = 5.842261333332899 " " absolute error = 5.0448534238967110000000000000E-13 " " relative error = 8.635104005214286000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.449999999999841 " " y[1] (closed_form) = 5.902041666665713 " " y[1] (numeric) = 5.902041666666223 " " absolute error = 5.0981441290787190000000000000E-13 " " relative error = 8.637933137396594000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.45999999999984 " " y[1] (closed_form) = 5.962311999999033 " " y[1] (numeric) = 5.962311999999549 " " absolute error = 5.1603166184577280000000000000E-13 " " relative error = 8.654891958788076000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.469999999999839 " " y[1] (closed_form) = 6.02307433333235 " " y[1] (numeric) = 6.0230743333328745 " " absolute error = 5.2402526762307390000000000000E-13 " " relative error = 8.700295540486043000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999838 " " y[1] (closed_form) = 6.084330666665669 " " y[1] (numeric) = 6.084330666666200 " " absolute error = 5.3024251656097480000000000000E-13 " " relative error = 8.714886576859209000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999837 " " y[1] (closed_form) = 6.146082999998988 " " y[1] (numeric) = 6.146082999999526 " " absolute error = 5.3734794391857580000000000000E-13 " " relative error = 8.742933408459733000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4999999999998357 " " y[1] (closed_form) = 6.208333333332306 " " y[1] (numeric) = 6.208333333332850 " " absolute error = 5.4445337127617680000000000000E-13 " " relative error = 8.769718731966712000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5099999999998346 " " y[1] (closed_form) = 6.271083666665625 " " y[1] (numeric) = 6.271083666666177 " " absolute error = 5.5244697705347790000000000000E-13 " " relative error = 8.809434005641602000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999998335 " " y[1] (closed_form) = 6.334335999998943 " " y[1] (numeric) = 6.334335999999503 " " absolute error = 5.604405828307790000000000000E-13 " " relative error = 8.847661109718092000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5299999999998324 " " y[1] (closed_form) = 6.39809233333226 " " y[1] (numeric) = 6.398092333332829 " " absolute error = 5.6932236702778030000000000000E-13 " " relative error = 8.898314331316711000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5399999999998313 " " y[1] (closed_form) = 6.462354666665577 " " y[1] (numeric) = 6.462354666666154 " " absolute error = 5.7642779438538130000000000000E-13 " " relative error = 8.919779617772114000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.54999999999983 " " y[1] (closed_form) = 6.527124999998895 " " y[1] (numeric) = 6.527124999999478 " " absolute error = 5.8264504332328220000000000000E-13 " " relative error = 8.926518847476964000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.559999999999829 " " y[1] (closed_form) = 6.592405333332213 " " y[1] (numeric) = 6.592405333332802 " " absolute error = 5.888622922611830000000000000E-13 " " relative error = 8.932434558958396000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999828 " " y[1] (closed_form) = 6.65819766666553 " " y[1] (numeric) = 6.658197666666126 " " absolute error = 5.959677196187840000000000000E-13 " " relative error = 8.95088655301591000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999827 " " y[1] (closed_form) = 6.724503999998847 " " y[1] (numeric) = 6.72450399999945 " " absolute error = 6.030731469763850000000000000E-13 " " relative error = 8.968291891513313000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5899999999998258 " " y[1] (closed_form) = 6.791326333332165 " " y[1] (numeric) = 6.791326333332775 " " absolute error = 6.101785743339860000000000000E-13 " " relative error = 8.984674633277442000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5999999999998247 " " y[1] (closed_form) = 6.858666666665481 " " y[1] (numeric) = 6.8586666666661005 " " absolute error = 6.1906035853098730000000000000E-13 " " relative error = 9.025957793513233000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6099999999998236 " " y[1] (closed_form) = 6.9265269999987975 " " y[1] (numeric) = 6.926526999999424 " " absolute error = 6.2616578588858830000000000000E-13 " " relative error = 9.040111817779631000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6199999999998225 " " y[1] (closed_form) = 6.994909333332115 " " y[1] (numeric) = 6.994909333332746 " " absolute error = 6.314948564067890000000000000E-13 " " relative error = 9.027920539264065000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6299999999998214 " " y[1] (closed_form) = 7.063815666665431 " " y[1] (numeric) = 7.063815666666070 " " absolute error = 6.3948846218409020000000000000E-13 " " relative error = 9.053017410998908000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999998203 " " y[1] (closed_form) = 7.133247999998748 " " y[1] (numeric) = 7.133247999999395 " " absolute error = 6.4748206796139130000000000000E-13 " " relative error = 9.07696000421554100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.649999999999819 " " y[1] (closed_form) = 7.2032083333320625 " " y[1] (numeric) = 7.203208333332719 " " absolute error = 6.5636385215839250000000000000E-13 " " relative error = 9.112104242787763000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.659999999999818 " " y[1] (closed_form) = 7.273698666665380 " " y[1] (numeric) = 7.273698666666042 " " absolute error = 6.6258110109629340000000000000E-13 " " relative error = 9.109273444785873000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.669999999999817 " " y[1] (closed_form) = 7.344720999998694 " " y[1] (numeric) = 7.344720999999365 " " absolute error = 6.7057470687359460000000000000E-13 " " relative error = 9.13002286776739100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.679999999999816 " " y[1] (closed_form) = 7.41627733333201 " " y[1] (numeric) = 7.416277333332689 " " absolute error = 6.7856831265089570000000000000E-13 " " relative error = 9.14971598487979000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6899999999998148 " " y[1] (closed_form) = 7.488369666665325 " " y[1] (numeric) = 7.488369666666011 " " absolute error = 6.8567374000849670000000000000E-13 " " relative error = 9.156515643996468000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6999999999998137 " " y[1] (closed_form) = 7.560999999998641 " " y[1] (numeric) = 7.560999999999334 " " absolute error = 6.9277916736609770000000000000E-13 " " relative error = 9.162533624735116000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7099999999998126 " " y[1] (closed_form) = 7.634170333331956 " " y[1] (numeric) = 7.634170333332657 " " absolute error = 7.0077277314339880000000000000E-13 " " relative error = 9.179422812767456000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7199999999998115 " " y[1] (closed_form) = 7.707882666665272 " " y[1] (numeric) = 7.70788266666598 " " absolute error = 7.0787820050099980000000000000E-13 " " relative error = 9.183821694152168000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999998104 " " y[1] (closed_form) = 7.782138999998587 " " y[1] (numeric) = 7.782138999999303 " " absolute error = 7.1587180627830090000000000000E-13 " " relative error = 9.198907990186642000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999998093 " " y[1] (closed_form) = 7.856941333331900 " " y[1] (numeric) = 7.8569413333326255 " " absolute error = 7.2475359047530220000000000000E-13 " " relative error = 9.224373197247168000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.749999999999808 " " y[1] (closed_form) = 7.932291666665216 " " y[1] (numeric) = 7.9322916666659475 " " absolute error = 7.3185901783290320000000000000E-13 " " relative error = 9.226325109910907000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999807 " " y[1] (closed_form) = 8.00819199999853 " " y[1] (numeric) = 8.008191999999271 " " absolute error = 7.4074080202990440000000000000E-13 " " relative error = 9.249788242215475000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.769999999999806 " " y[1] (closed_form) = 8.084644333331845 " " y[1] (numeric) = 8.084644333332596 " " absolute error = 7.5139894306630600000000000000E-13 " " relative error = 9.294149650695137000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.779999999999805 " " y[1] (closed_form) = 8.161650666665158 " " y[1] (numeric) = 8.16165066666592 " " absolute error = 7.6205708410270740000000000000E-13 " " relative error = 9.337046085728673000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7899999999998037 " " y[1] (closed_form) = 8.239212999998472 " " y[1] (numeric) = 8.239212999999243 " " absolute error = 7.7093886829970870000000000000E-13 " " relative error = 9.356947906309155000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7999999999998026 " " y[1] (closed_form) = 8.317333333331785 " " y[1] (numeric) = 8.317333333332565 " " absolute error = 7.79820652496710000000000000E-13 " " relative error = 9.375849460927241000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8099999999998015 " " y[1] (closed_form) = 8.396013666665098 " " y[1] (numeric) = 8.396013666665887 " " absolute error = 7.8870243669371120000000000000E-13 " " relative error = 9.393772664105063000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8199999999998004 " " y[1] (closed_form) = 8.475255999998414 " " y[1] (numeric) = 8.475255999999208 " " absolute error = 7.940315072119120000000000000E-13 " " relative error = 9.368820330761226000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999997993 " " y[1] (closed_form) = 8.555062333331726 " " y[1] (numeric) = 8.55506233333253 " " absolute error = 8.0468964824831350000000000000E-13 " " relative error = 9.406005671205099000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8399999999997982 " " y[1] (closed_form) = 8.635434666665038 " " y[1] (numeric) = 8.635434666665853 " " absolute error = 8.153477892847150000000000000E-13 " " relative error = 9.441884754593346000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.849999999999797 " " y[1] (closed_form) = 8.716374999998353 " " y[1] (numeric) = 8.716374999999177 " " absolute error = 8.2422957348171620000000000000E-13 " " relative error = 9.456105014778183000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.859999999999796 " " y[1] (closed_form) = 8.797885333331664 " " y[1] (numeric) = 8.797885333332498 " " absolute error = 8.3488771451811770000000000000E-13 " " relative error = 9.489640781689466000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.869999999999795 " " y[1] (closed_form) = 8.879967666664976 " " y[1] (numeric) = 8.87996766666582 " " absolute error = 8.437694987151190000000000000E-13 " " relative error = 9.501943367233128000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.879999999999794 " " y[1] (closed_form) = 8.96262399999829 " " y[1] (numeric) = 8.962623999999142 " " absolute error = 8.5265128291212020000000000000E-13 " " relative error = 9.513411283484424000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8899999999997927 " " y[1] (closed_form) = 9.045856333331603 " " y[1] (numeric) = 9.045856333332463 " " absolute error = 8.5975671026972120000000000000E-13 " " relative error = 9.504425878418429000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8999999999997916 " " y[1] (closed_form) = 9.129666666664914 " " y[1] (numeric) = 9.129666666665788 " " absolute error = 8.7396756498492320000000000000E-13 " " relative error = 9.572831045146859000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9099999999997905 " " y[1] (closed_form) = 9.214056999998226 " " y[1] (numeric) = 9.214056999999109 " " absolute error = 8.8284934918192450000000000000E-13 " " relative error = 9.5815485966940990000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999997894 " " y[1] (closed_form) = 9.299029333331536 " " y[1] (numeric) = 9.299029333332431 " " absolute error = 8.9528384705772620000000000000E-13 " " relative error = 9.62771290384752100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9299999999997883 " " y[1] (closed_form) = 9.384585666664849 " " y[1] (numeric) = 9.384585666665751 " " absolute error = 9.0238927441532720000000000000E-13 " " relative error = 9.615653865473465000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9399999999997872 " " y[1] (closed_form) = 9.47072799999816 " " y[1] (numeric) = 9.47072799999907 " " absolute error = 9.0949470177292820000000000000E-13 " " relative error = 9.603218483025854000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.949999999999786 " " y[1] (closed_form) = 9.557458333331471 " " y[1] (numeric) = 9.557458333332393 " " absolute error = 9.21929199648730000000000000E-13 " " relative error = 9.646175452667345000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.959999999999785 " " y[1] (closed_form) = 9.644778666664783 " " y[1] (numeric) = 9.644778666665715 " " absolute error = 9.3258734068513150000000000000E-13 " " relative error = 9.66934932274215900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.969999999999784 " " y[1] (closed_form) = 9.732690999998093 " " y[1] (numeric) = 9.732690999999038 " " absolute error = 9.4502183856093320000000000000E-13 " " relative error = 9.709769256633324000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.979999999999783 " " y[1] (closed_form) = 9.821197333331403 " " y[1] (numeric) = 9.821197333332357 " " absolute error = 9.5390362275793450000000000000E-13 " " relative error = 9.712701928109668000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9899999999997817 " " y[1] (closed_form) = 9.910299666664717 " " y[1] (numeric) = 9.910299666665678 " " absolute error = 9.6100905011553550000000000000E-13 " " relative error = 9.697073574354995000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9999999999997806 " " y[1] (closed_form) = 9.999999999998025 " " y[1] (numeric) = 9.999999999998998 " " absolute error = 9.7344354799133730000000000000E-13 " " relative error = 9.734435479915295000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0099999999997795 " " y[1] (closed_form) = 10.090300333331335 " " y[1] (numeric) = 10.090300333332317 " " absolute error = 9.8232533218833850000000000000E-13 " " relative error = 9.73534285142552900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0199999999997784 " " y[1] (closed_form) = 10.181202666664646 " " y[1] (numeric) = 10.181202666665637 " " absolute error = 9.9120711638533980000000000000E-13 " " relative error = 9.735658436804877000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0299999999997773 " " y[1] (closed_form) = 10.272708999997956 " " y[1] (numeric) = 10.272708999998954 " " absolute error = 9.9831254374294080000000000000E-13 " " relative error = 9.718103995188994000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.039999999999776 " " y[1] (closed_form) = 10.364821333331264 " " y[1] (numeric) = 10.364821333332271 " " absolute error = 1.007194327939942000000000000E-12 " " relative error = 9.717430677758039000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.049999999999775 " " y[1] (closed_form) = 10.457541666664575 " " y[1] (numeric) = 10.457541666665591 " " absolute error = 1.0160761121369433000000000000E-12 " " relative error = 9.716204290879196000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.059999999999774 " " y[1] (closed_form) = 10.550871999997883 " " y[1] (numeric) = 10.550871999998911 " " absolute error = 1.028510610012745000000000000E-12 " " relative error = 9.748110014157612000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.069999999999773 " " y[1] (closed_form) = 10.644814333331194 " " y[1] (numeric) = 10.64481433333223 " " absolute error = 1.035616037370346000000000000E-12 " " relative error = 9.728831381563982000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.079999999999772 " " y[1] (closed_form) = 10.739370666664502 " " y[1] (numeric) = 10.739370666665549 " " absolute error = 1.0462741784067475000000000000E-12 " " relative error = 9.742416114329961000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0899999999997707 " " y[1] (closed_form) = 10.83454299999781 " " y[1] (numeric) = 10.83454299999887 " " absolute error = 1.0604850331219495000000000000E-12 " " relative error = 9.787999670333708000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0999999999997696 " " y[1] (closed_form) = 10.930333333331118 " " y[1] (numeric) = 10.930333333332188 " " absolute error = 1.0693668173189508000000000000E-12 " " relative error = 9.783478551912117000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1099999999997685 " " y[1] (closed_form) = 11.026743666664427 " " y[1] (numeric) = 11.026743666665508 " " absolute error = 1.0818013151947525000000000000E-12 " " relative error = 9.810705208149596000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1199999999997674 " " y[1] (closed_form) = 11.123775999997735 " " y[1] (numeric) = 11.123775999998829 " " absolute error = 1.0942358130705543000000000000E-12 " " relative error = 9.8369098143542010000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1299999999997663 " " y[1] (closed_form) = 11.221432333331043 " " y[1] (numeric) = 11.22143233333215 " " absolute error = 1.106670310946356000000000000E-12 " " relative error = 9.86211276843163000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.139999999999765 " " y[1] (closed_form) = 11.319714666664352 " " y[1] (numeric) = 11.319714666665467 " " absolute error = 1.1155520951433573000000000000E-12 " " relative error = 9.854948892206342000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.149999999999764 " " y[1] (closed_form) = 11.41862499999766 " " y[1] (numeric) = 11.418624999998787 " " absolute error = 1.127986593019159000000000000E-12 " " relative error = 9.878480053591306000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.159999999999763 " " y[1] (closed_form) = 11.518165333330966 " " y[1] (numeric) = 11.518165333332105 " " absolute error = 1.1386447340555605000000000000E-12 " " relative error = 9.885643252233758000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.169999999999762 " " y[1] (closed_form) = 11.618337666664273 " " y[1] (numeric) = 11.618337666665424 " " absolute error = 1.1510792319313623000000000000E-12 " " relative error = 9.907434823779291000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.179999999999761 " " y[1] (closed_form) = 11.71914399999758 " " y[1] (numeric) = 11.71914399999874 " " absolute error = 1.1599610161283636000000000000E-12 " " relative error = 9.89800122029905000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1899999999997597 " " y[1] (closed_form) = 11.820586333330887 " " y[1] (numeric) = 11.820586333332056 " " absolute error = 1.1688428003253648000000000000E-12 " " relative error = 9.888196468135774000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1999999999997586 " " y[1] (closed_form) = 11.922666666664194 " " y[1] (numeric) = 11.922666666665373 " " absolute error = 1.1795009413617663000000000000E-12 " " relative error = 9.892928942311655000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2099999999997575 " " y[1] (closed_form) = 12.025386999997501 " " y[1] (numeric) = 12.02538699999869 " " absolute error = 1.1883827255587676000000000000E-12 " " relative error = 9.882282587321426000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2199999999997564 " " y[1] (closed_form) = 12.128749333330806 " " y[1] (numeric) = 12.128749333332006 " " absolute error = 1.2008172234345693000000000000E-12 " " relative error = 9.900585711130366000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2299999999997553 " " y[1] (closed_form) = 12.232755666664113 " " y[1] (numeric) = 12.232755666665325 " " absolute error = 1.2114753644709708000000000000E-12 " " relative error = 9.903536026411467000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.239999999999754 " " y[1] (closed_form) = 12.337407999997419 " " y[1] (numeric) = 12.337407999998645 " " absolute error = 1.2256862191861728000000000000E-12 " " relative error = 9.934714157029007000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.249999999999753 " " y[1] (closed_form) = 12.442708333330724 " " y[1] (numeric) = 12.442708333331963 " " absolute error = 1.2381207170619746000000000000E-12 " " relative error = 9.950572527247759000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.259999999999752 " " y[1] (closed_form) = 12.548658666664029 " " y[1] (numeric) = 12.548658666665277 " " absolute error = 1.248778858098376100000000000E-12 " " relative error = 9.9514927552838990000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.269999999999751 " " y[1] (closed_form) = 12.655260999997335 " " y[1] (numeric) = 12.655260999998596 " " absolute error = 1.2612133559741778000000000000E-12 " " relative error = 9.965921334806478000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.27999999999975 " " y[1] (closed_form) = 12.762517333330642 " " y[1] (numeric) = 12.762517333331916 " " absolute error = 1.2736478538499796000000000000E-12 " " relative error = 9.979597446059608000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2899999999997487 " " y[1] (closed_form) = 12.870429666663945 " " y[1] (numeric) = 12.870429666665233 " " absolute error = 1.2878587085651816000000000000E-12 " " relative error = 1.000633810929327500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2999999999997476 " " y[1] (closed_form) = 12.978999999997251 " " y[1] (numeric) = 12.97899999999855 " " absolute error = 1.298516849601583000000000000E-12 " " relative error = 1.00047526743343700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3099999999997465 " " y[1] (closed_form) = 13.088230333330557 " " y[1] (numeric) = 13.088230333331866 " " absolute error = 1.3091749906379846000000000000E-12 " " relative error = 1.00026891130119600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3199999999997454 " " y[1] (closed_form) = 13.19812266666386 " " y[1] (numeric) = 13.198122666665183 " " absolute error = 1.3233858453531866000000000000E-12 " " relative error = 1.002707641667725100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3299999999997443 " " y[1] (closed_form) = 13.308678999997165 " " y[1] (numeric) = 13.3086789999985 " " absolute error = 1.3358203432289883000000000000E-12 " " relative error = 1.003721213224297300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.339999999999743 " " y[1] (closed_form) = 13.419901333330467 " " y[1] (numeric) = 13.419901333331815 " " absolute error = 1.3482548411047900000000000000E-12 " " relative error = 1.004668221931098900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.349999999999742 " " y[1] (closed_form) = 13.531791666663771 " " y[1] (numeric) = 13.531791666665132 " " absolute error = 1.3606893389805919000000000000E-12 " " relative error = 1.005550020647093300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.359999999999741 " " y[1] (closed_form) = 13.644351999997074 " " y[1] (numeric) = 13.644351999998447 " " absolute error = 1.3731238368563936000000000000E-12 " " relative error = 1.006367936606068400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.36999999999974 " " y[1] (closed_form) = 13.757584333330378 " " y[1] (numeric) = 13.757584333331762 " " absolute error = 1.3837819778927950000000000000E-12 " " relative error = 1.005832088225197100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3799999999997388 " " y[1] (closed_form) = 13.871490666663682 " " y[1] (numeric) = 13.871490666665077 " " absolute error = 1.3944401189291966000000000000E-12 " " relative error = 1.005256141850962400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3899999999997377 " " y[1] (closed_form) = 13.986072999996985 " " y[1] (numeric) = 13.986072999998393 " " absolute error = 1.4086509736443986000000000000E-12 " " relative error = 1.007181196354904200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3999999999997366 " " y[1] (closed_form) = 14.101333333330288 " " y[1] (numeric) = 14.101333333331707 " " absolute error = 1.4193091146808000000000000000E-12 " " relative error = 1.006507031023855800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4099999999997355 " " y[1] (closed_form) = 14.217273666663589 " " y[1] (numeric) = 14.217273666665022 " " absolute error = 1.4335199693960020000000000000E-12 " " relative error = 1.008294559847500300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4199999999997344 " " y[1] (closed_form) = 14.333895999996892 " " y[1] (numeric) = 14.333895999998338 " " absolute error = 1.4459544672718040000000000000E-12 " " relative error = 1.008765842358642400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4299999999997333 " " y[1] (closed_form) = 14.451202333330194 " " y[1] (numeric) = 14.451202333331652 " " absolute error = 1.4583889651476056000000000000E-12 " " relative error = 1.009181749385643400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.439999999999732 " " y[1] (closed_form) = 14.569194666663495 " " y[1] (numeric) = 14.569194666664968 " " absolute error = 1.4725998198628076000000000000E-12 " " relative error = 1.010762676699170800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.449999999999731 " " y[1] (closed_form) = 14.687874999996797 " " y[1] (numeric) = 14.68787499999828 " " absolute error = 1.4832579608992090000000000000E-12 " " relative error = 1.009851977157711800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.45999999999973 " " y[1] (closed_form) = 14.807245333330101 " " y[1] (numeric) = 14.807245333331595 " " absolute error = 1.4939161019356106000000000000E-12 " " relative error = 1.008908860700043300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.469999999999729 " " y[1] (closed_form) = 14.927307666663399 " " y[1] (numeric) = 14.927307666664905 " " absolute error = 1.5063505998114124000000000000E-12 " " relative error = 1.009124105598418800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4799999999997278 " " y[1] (closed_form) = 15.048063999996701 " " y[1] (numeric) = 15.04806399999822 " " absolute error = 1.5187850976872141000000000000E-12 " " relative error = 1.009289366185276300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4899999999997267 " " y[1] (closed_form) = 15.169516333330003 " " y[1] (numeric) = 15.169516333331533 " " absolute error = 1.5294432387236157000000000000E-12 " " relative error = 1.008234676120272200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4999999999997256 " " y[1] (closed_form) = 15.291666666663305 " " y[1] (numeric) = 15.291666666664847 " " absolute error = 1.5418777365994174000000000000E-12 " " relative error = 1.008312416305017800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5099999999997245 " " y[1] (closed_form) = 15.414516999996604 " " y[1] (numeric) = 15.414516999998161 " " absolute error = 1.5578649481540197000000000000E-12 " " relative error = 1.01064791595764100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5199999999997234 " " y[1] (closed_form) = 15.538069333329904 " " y[1] (numeric) = 15.538069333331473 " " absolute error = 1.5685230891904212000000000000E-12 " " relative error = 1.009471032431206900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5299999999997222 " " y[1] (closed_form) = 15.662325666663204 " " y[1] (numeric) = 15.662325666664785 " " absolute error = 1.580957587066223000000000000E-12 " " relative error = 1.00940155422208090000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.539999999999721 " " y[1] (closed_form) = 15.787287999996504 " " y[1] (numeric) = 15.787287999998098 " " absolute error = 1.5933920849420247000000000000E-12 " " relative error = 1.009288032841598600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.54999999999972 " " y[1] (closed_form) = 15.912958333329806 " " y[1] (numeric) = 15.91295833333141 " " absolute error = 1.6040502259784262000000000000E-12 " " relative error = 1.00801509837346300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.559999999999719 " " y[1] (closed_form) = 16.039338666663102 " " y[1] (numeric) = 16.039338666664726 " " absolute error = 1.623590151211829000000000000E-12 " " relative error = 1.012255046765970000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.569999999999718 " " y[1] (closed_form) = 16.1664309999964 " " y[1] (numeric) = 16.166430999998042 " " absolute error = 1.6413537196058314000000000000E-12 " " relative error = 1.015285142160441400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5799999999997167 " " y[1] (closed_form) = 16.2942373333297 " " y[1] (numeric) = 16.294237333331356 " " absolute error = 1.6555645743210334000000000000E-12 " " relative error = 1.01604299756613490000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5899999999997156 " " y[1] (closed_form) = 16.422759666663 " " y[1] (numeric) = 16.42275966666467 " " absolute error = 1.6697754290362354000000000000E-12 " " relative error = 1.016744726786544400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5999999999997145 " " y[1] (closed_form) = 16.551999999996298 " " y[1] (numeric) = 16.55199999999798 " " absolute error = 1.6839862837514374000000000000E-12 " " relative error = 1.017391423243000400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6099999999997134 " " y[1] (closed_form) = 16.6819603333296 " " y[1] (numeric) = 16.681960333331297 " " absolute error = 1.6981971384666394000000000000E-12 " " relative error = 1.017984160454895200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6199999999997123 " " y[1] (closed_form) = 16.812642666662896 " " y[1] (numeric) = 16.81264266666461 " " absolute error = 1.7124079931818414000000000000E-12 " " relative error = 1.018523992410369500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6299999999997112 " " y[1] (closed_form) = 16.944048999996195 " " y[1] (numeric) = 16.944048999997925 " " absolute error = 1.730171561575844000000000000E-12 " " relative error = 1.02110868634541400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.63999999999971 " " y[1] (closed_form) = 17.076181333329494 " " y[1] (numeric) = 17.076181333331238 " " absolute error = 1.744382416291046000000000000E-12 " " relative error = 1.021529569310873800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.649999999999709 " " y[1] (closed_form) = 17.209041666662788 " " y[1] (numeric) = 17.20904166666455 " " absolute error = 1.7621459846850485000000000000E-12 " " relative error = 1.023965203186568600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.659999999999708 " " y[1] (closed_form) = 17.342631999996087 " " y[1] (numeric) = 17.342631999997863 " " absolute error = 1.7763568394002505000000000000E-12 " " relative error = 1.02427177109025400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.669999999999707 " " y[1] (closed_form) = 17.476954333329385 " " y[1] (numeric) = 17.476954333331175 " " absolute error = 1.7905676941154525000000000000E-12 " " relative error = 1.024530739146439600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6799999999997057 " " y[1] (closed_form) = 17.61201066666268 " " y[1] (numeric) = 17.612010666664485 " " absolute error = 1.8047785488306545000000000000E-12 " " relative error = 1.024743047792307500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6899999999997046 " " y[1] (closed_form) = 17.747802999995976 " " y[1] (numeric) = 17.7478029999978 " " absolute error = 1.822542117224657000000000000E-12 " " relative error = 1.026911396990979700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6999999999997035 " " y[1] (closed_form) = 17.884333333329273 " " y[1] (numeric) = 17.884333333331103 " " absolute error = 1.829647544582258000000000000E-12 " " relative error = 1.023044868646304900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7099999999997024 " " y[1] (closed_form) = 18.02160366666257 " " y[1] (numeric) = 18.021603666664415 " " absolute error = 1.84385839929746000000000000E-12 " " relative error = 1.023137803606422900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7199999999997013 " " y[1] (closed_form) = 18.159615999995864 " " y[1] (numeric) = 18.15961599999772 " " absolute error = 1.8545165403338615000000000000E-12 " " relative error = 1.02123114295714400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7299999999997 " " y[1] (closed_form) = 18.298372333329162 " " y[1] (numeric) = 18.298372333331027 " " absolute error = 1.865174681370263000000000000E-12 " " relative error = 1.01931179855433500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.739999999999699 " " y[1] (closed_form) = 18.43787466666246 " " y[1] (numeric) = 18.437874666664342 " " absolute error = 1.8829382497642655000000000000E-12 " " relative error = 1.021233891544348200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.749999999999698 " " y[1] (closed_form) = 18.57812499999575 " " y[1] (numeric) = 18.57812499999765 " " absolute error = 1.900701818158268000000000000E-12 " " relative error = 1.023085923987863500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.759999999999697 " " y[1] (closed_form) = 18.719125333329046 " " y[1] (numeric) = 18.719125333330965 " " absolute error = 1.9184653865522705000000000000E-12 " " relative error = 1.024869139123973500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.769999999999696 " " y[1] (closed_form) = 18.86087766666234 " " y[1] (numeric) = 18.860877666664276 " " absolute error = 1.936228954946273000000000000E-12 " " relative error = 1.026584758761606600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7799999999996947 " " y[1] (closed_form) = 19.003383999995634 " " y[1] (numeric) = 19.003383999997588 " " absolute error = 1.9539925233402755000000000000E-12 " " relative error = 1.028233983663501400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7899999999996936 " " y[1] (closed_form) = 19.14664633332893 " " y[1] (numeric) = 19.1466463333309 " " absolute error = 1.9682033780554775000000000000E-12 " " relative error = 1.027962466006064300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7999999999996925 " " y[1] (closed_form) = 19.290666666662226 " " y[1] (numeric) = 19.29066666666421 " " absolute error = 1.98596694644948000000000000E-12 " " relative error = 1.029496274424559600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8099999999996914 " " y[1] (closed_form) = 19.43544699999552 " " y[1] (numeric) = 19.435446999997524 " " absolute error = 2.0037305148434825000000000000E-12 " " relative error = 1.030967034019821800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8199999999996903 " " y[1] (closed_form) = 19.580989333328812 " " y[1] (numeric) = 19.580989333330834 " " absolute error = 2.021494083237485000000000000E-12 " " relative error = 1.032375866625236800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.829999999999689 " " y[1] (closed_form) = 19.727295666662105 " " y[1] (numeric) = 19.727295666664144 " " absolute error = 2.0392576516314875000000000000E-12 " " relative error = 1.033723874822693000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.839999999999688 " " y[1] (closed_form) = 19.8743679999954 " " y[1] (numeric) = 19.874367999997453 " " absolute error = 2.0534685063466895000000000000E-12 " " relative error = 1.033224556547994400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.849999999999687 " " y[1] (closed_form) = 20.02220833332869 " " y[1] (numeric) = 20.02220833333077 " " absolute error = 2.078337502098293000000000000E-12 " " relative error = 1.038016120648750500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.859999999999686 " " y[1] (closed_form) = 20.170818666661987 " " y[1] (numeric) = 20.17081866666408 " " absolute error = 2.092548356813495000000000000E-12 " " relative error = 1.037413697180286600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.869999999999685 " " y[1] (closed_form) = 20.32020099999528 " " y[1] (numeric) = 20.320200999997393 " " absolute error = 2.113864638886298000000000000E-12 " " relative error = 1.040277425841796100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8799999999996837 " " y[1] (closed_form) = 20.47035733332857 " " y[1] (numeric) = 20.4703573333307 " " absolute error = 2.1280754936015000000000000E-12 " " relative error = 1.039588835186916300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8899999999996826 " " y[1] (closed_form) = 20.621289666661863 " " y[1] (numeric) = 20.621289666664005 " " absolute error = 2.142286348316702000000000000E-12 " " relative error = 1.038871177771245500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8999999999996815 " " y[1] (closed_form) = 20.772999999995154 " " y[1] (numeric) = 20.77299999999731 " " absolute error = 2.156497203031904000000000000E-12 " " relative error = 1.03812506765147400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9099999999996804 " " y[1] (closed_form) = 20.925490333328447 " " y[1] (numeric) = 20.925490333330625 " " absolute error = 2.177813485104707000000000000E-12 " " relative error = 1.04074669238983600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9199999999996793 " " y[1] (closed_form) = 21.07876266666174 " " y[1] (numeric) = 21.07876266666393 " " absolute error = 2.192024339819909000000000000E-12 " " relative error = 1.039920784006370500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.929999999999678 " " y[1] (closed_form) = 21.23281899999503 " " y[1] (numeric) = 21.23281899999724 " " absolute error = 2.2097879082139116000000000000E-12 " " relative error = 1.040741650091035500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.939999999999677 " " y[1] (closed_form) = 21.38766133332832 " " y[1] (numeric) = 21.387661333330545 " " absolute error = 2.2239987629291136000000000000E-12 " " relative error = 1.039851308784034100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.949999999999676 " " y[1] (closed_form) = 21.54329166666161 " " y[1] (numeric) = 21.54329166666385 " " absolute error = 2.241762331323116000000000000E-12 " " relative error = 1.040584867906819700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.959999999999675 " " y[1] (closed_form) = 21.699711999994904 " " y[1] (numeric) = 21.699711999997156 " " absolute error = 2.2524204723595176000000000000E-12 " " relative error = 1.03799556065999690000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.969999999999674 " " y[1] (closed_form) = 21.85692433332819 " " y[1] (numeric) = 21.856924333330465 " " absolute error = 2.2737367544323206000000000000E-12 " " relative error = 1.040282118269151200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9799999999996727 " " y[1] (closed_form) = 22.01493066666148 " " y[1] (numeric) = 22.014930666663773 " " absolute error = 2.291500322826323000000000000E-12 " " relative error = 1.040884642119940300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9899999999996716 " " y[1] (closed_form) = 22.17373299999477 " " y[1] (numeric) = 22.17373299999708 " " absolute error = 2.3092638912203256000000000000E-12 " " relative error = 1.041441191350536600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9999999999996705 " " y[1] (closed_form) = 22.33333333332806 " " y[1] (numeric) = 22.33333333333039 " " absolute error = 2.3305801732931286000000000000E-12 " " relative error = 1.043543361176274100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.009999999999674 " " y[1] (closed_form) = 22.49373366666142 " " y[1] (numeric) = 22.493733666663697 " " absolute error = 2.277289468111121000000000000E-12 " " relative error = 1.012410612599345400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.019999999999677 " " y[1] (closed_form) = 22.654935999994784 " " y[1] (numeric) = 22.654935999997 " " absolute error = 2.2168933355715126000000000000E-12 " " relative error = 9.785476046244505000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0299999999996805 " " y[1] (closed_form) = 22.816942333328143 " " y[1] (numeric) = 22.81694233333031 " " absolute error = 2.1671553440683056000000000000E-12 " " relative error = 9.498009472122807000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.039999999999684 " " y[1] (closed_form) = 22.979754666661506 " " y[1] (numeric) = 22.979754666663617 " " absolute error = 2.1103119252074976000000000000E-12 " " relative error = 9.183352719901267000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.049999999999687 " " y[1] (closed_form) = 23.14337499999487 " " y[1] (numeric) = 23.143374999996926 " " absolute error = 2.05702122002549000000000000E-12 " " relative error = 8.888164410013432000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0599999999996905 " " y[1] (closed_form) = 23.307805333328233 " " y[1] (numeric) = 23.307805333330236 " " absolute error = 2.0037305148434825000000000000E-12 " " relative error = 8.596821906601021000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.069999999999694 " " y[1] (closed_form) = 23.473047666661593 " " y[1] (numeric) = 23.473047666663543 " " absolute error = 1.950439809661475000000000000E-12 " " relative error = 8.309273841895078000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.079999999999697 " " y[1] (closed_form) = 23.639103999994962 " " y[1] (numeric) = 23.639103999996856 " " absolute error = 1.893596390800667000000000000E-12 " " relative error = 8.010440627534235000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0899999999997005 " " y[1] (closed_form) = 23.80597633332832 " " y[1] (numeric) = 23.805976333330165 " " absolute error = 1.84385839929746000000000000E-12 " " relative error = 7.745359289112885000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.099999999999704 " " y[1] (closed_form) = 23.97366666666169 " " y[1] (numeric) = 23.973666666663476 " " absolute error = 1.787014980436652000000000000E-12 " " relative error = 7.454074528039195000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.109999999999707 " " y[1] (closed_form) = 24.14217699999505 " " y[1] (numeric) = 24.142176999996785 " " absolute error = 1.7337242752546445000000000000E-12 " " relative error = 7.181308774494529000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.119999999999710 " " y[1] (closed_form) = 24.31150933332842 " " y[1] (numeric) = 24.311509333330093 " " absolute error = 1.673328142715036000000000000E-12 " " relative error = 6.882864077966093000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.129999999999714 " " y[1] (closed_form) = 24.481665666661787 " " y[1] (numeric) = 24.481665666663407 " " absolute error = 1.6200374375330284000000000000E-12 " " relative error = 6.6173497326169860000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.139999999999717 " " y[1] (closed_form) = 24.652647999995153 " " y[1] (numeric) = 24.652647999996717 " " absolute error = 1.5631940186722204000000000000E-12 " " relative error = 6.340876723151718000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.149999999999720 " " y[1] (closed_form) = 24.824458333328522 " " y[1] (numeric) = 24.82445833333003 " " absolute error = 1.5063505998114124000000000000E-12 " " relative error = 6.068009942392316000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.159999999999724 " " y[1] (closed_form) = 24.997098666661888 " " y[1] (numeric) = 24.99709866666334 " " absolute error = 1.4530598946294050000000000000E-12 " " relative error = 5.812914186586465000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.169999999999727 " " y[1] (closed_form) = 25.170570999995256 " " y[1] (numeric) = 25.170570999996656 " " absolute error = 1.3997691894473974000000000000E-12 " " relative error = 5.561134030084821000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.179999999999730 " " y[1] (closed_form) = 25.344877333328625 " " y[1] (numeric) = 25.34487733332997 " " absolute error = 1.3429257705865894000000000000E-12 " " relative error = 5.298608286498337000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.189999999999734 " " y[1] (closed_form) = 25.520019666661995 " " y[1] (numeric) = 25.52001966666328 " " absolute error = 1.2860823517257813000000000000E-12 " " relative error = 5.039503764199098000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.199999999999737 " " y[1] (closed_form) = 25.695999999995365 " " y[1] (numeric) = 25.695999999996594 " " absolute error = 1.2292389328649733000000000000E-12 " " relative error = 4.783775423665921300000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.209999999999740 " " y[1] (closed_form) = 25.872820333328733 " " y[1] (numeric) = 25.872820333329912 " " absolute error = 1.1795009413617663000000000000E-12 " " relative error = 4.558841773590342500000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.219999999999744 " " y[1] (closed_form) = 26.050482666662106 " " y[1] (numeric) = 26.050482666663225 " " absolute error = 1.1191048088221578000000000000E-12 " " relative error = 4.295908153188744000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.229999999999747 " " y[1] (closed_form) = 26.22898899999548 " " y[1] (numeric) = 26.228988999996538 " " absolute error = 1.0587086762825493000000000000E-12 " " relative error = 4.036406726476311500000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.239999999999750 " " y[1] (closed_form) = 26.40834133332885 " " y[1] (numeric) = 26.40834133332985 " " absolute error = 1.0018652574217413000000000000E-12 " " relative error = 3.793745486610057000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.249999999999754 " " y[1] (closed_form) = 26.588541666662216 " " y[1] (numeric) = 26.588541666663165 " " absolute error = 9.4857455223973370000000000000E-13 " " relative error = 3.5676065431941106000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.259999999999757 " " y[1] (closed_form) = 26.769591999995598 " " y[1] (numeric) = 26.76959199999648 " " absolute error = 8.8107299234252420000000000000E-13 " " relative error = 3.2913202126602040000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.269999999999760 " " y[1] (closed_form) = 26.951494333328966 " " y[1] (numeric) = 26.95149433332979 " " absolute error = 8.2422957348171620000000000000E-13 " " relative error = 3.0581961923441514000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.279999999999764 " " y[1] (closed_form) = 27.134250666662343 " " y[1] (numeric) = 27.13425066666311 " " absolute error = 7.6738615462090820000000000000E-13 " " relative error = 2.8281088873544370000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.289999999999767 " " y[1] (closed_form) = 27.317862999995715 " " y[1] (numeric) = 27.31786299999642 " " absolute error = 7.0699002208129970000000000000E-13 " " relative error = 2.588013645435628000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.299999999999770 " " y[1] (closed_form) = 27.50233333332909 " " y[1] (numeric) = 27.50233333332973 " " absolute error = 6.3948846218409020000000000000E-13 " " relative error = 2.3252152987656394000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.309999999999774 " " y[1] (closed_form) = 27.687663666662466 " " y[1] (numeric) = 27.687663666663045 " " absolute error = 5.7909232964448170000000000000E-13 " " relative error = 2.0915174953592855000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.319999999999777 " " y[1] (closed_form) = 27.873855999995843 " " y[1] (numeric) = 27.87385599999635 " " absolute error = 5.0803805606847160000000000000E-13 " " relative error = 1.822632850182434000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.329999999999780 " " y[1] (closed_form) = 28.06091233332922 " " y[1] (numeric) = 28.060912333329664 " " absolute error = 4.4408920985006260000000000000E-13 " " relative error = 1.5825900618441321000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.339999999999784 " " y[1] (closed_form) = 28.248834666662596 " " y[1] (numeric) = 28.248834666662983 " " absolute error = 3.8724579098925460000000000000E-13 " " relative error = 1.3708381091070510000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.349999999999787 " " y[1] (closed_form) = 28.437624999995975 " " y[1] (numeric) = 28.4376249999963 " " absolute error = 3.2329694477084560000000000000E-13 " " relative error = 1.1368633800146508000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.359999999999790 " " y[1] (closed_form) = 28.627285333329358 " " y[1] (numeric) = 28.627285333329617 " " absolute error = 2.59348098552436570000000000000E-13 " " relative error = 9.0594723017795250000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.369999999999794 " " y[1] (closed_form) = 28.817817666662734 " " y[1] (numeric) = 28.817817666662933 " " absolute error = 1.98951966012828050000000000000E-13 " " relative error = 6.9037832189139470000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.379999999999797 " " y[1] (closed_form) = 29.00922399999611 " " y[1] (numeric) = 29.009223999996244 " " absolute error = 1.35003119794419040000000000000E-13 " " relative error = 4.6537997636350825000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.389999999999800 " " y[1] (closed_form) = 29.201506333329494 " " y[1] (numeric) = 29.201506333329558 " " absolute error = 6.39488462184090200000000000000E-14 " " relative error = 2.18991600941559060000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.399999999999804 " " y[1] (closed_form) = 29.394666666662875 " " y[1] (numeric) = 29.394666666662875 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.409999999999807 " " y[1] (closed_form) = 29.588706999996255 " " y[1] (numeric) = 29.588706999996187 " " absolute error = 6.75015598972095200000000000000E-14 " " relative error = 2.281328477693130000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.419999999999810 " " y[1] (closed_form) = 29.783629333329635 " " y[1] (numeric) = 29.783629333329504 " " absolute error = 1.31450406115618530000000000000E-13 " " relative error = 4.41351202180446770000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.429999999999814 " " y[1] (closed_form) = 29.979435666663015 " " y[1] (numeric) = 29.979435666662827 " " absolute error = 1.88293824976426550000000000000E-13 " " relative error = 6.2807661581771650000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.439999999999817 " " y[1] (closed_form) = 30.1761279999964 " " y[1] (numeric) = 30.17612799999614 " " absolute error = 2.59348098552436570000000000000E-13 " " relative error = 8.5944790051416640000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.449999999999820 " " y[1] (closed_form) = 30.37370833332978 " " y[1] (numeric) = 30.373708333329457 " " absolute error = 3.2329694477084560000000000000E-13 " " relative error = 1.0643973439887296000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.459999999999824 " " y[1] (closed_form) = 30.572178666663167 " " y[1] (numeric) = 30.572178666662776 " " absolute error = 3.9079850466805510000000000000E-13 " " relative error = 1.2782815020448432000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4699999999998274 " " y[1] (closed_form) = 30.77154099999655 " " y[1] (numeric) = 30.7715409999961 " " absolute error = 4.5119463720766360000000000000E-13 " " relative error = 1.4662724795216275000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.479999999999830 " " y[1] (closed_form) = 30.971797333329935 " " y[1] (numeric) = 30.971797333329416 " " absolute error = 5.1869619710487310000000000000E-13 " " relative error = 1.6747371536836330000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.489999999999834 " " y[1] (closed_form) = 31.17294966666332 " " y[1] (numeric) = 31.17294966666274 " " absolute error = 5.8264504332328220000000000000E-13 " " relative error = 1.8690725438355577000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4999999999998375 " " y[1] (closed_form) = 31.374999999996707 " " y[1] (numeric) = 31.374999999996053 " " absolute error = 6.5369931689929220000000000000E-13 " " relative error = 2.083503798882424800000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.509999999999840 " " y[1] (closed_form) = 31.577950333330094 " " y[1] (numeric) = 31.577950333329373 " " absolute error = 7.2120087679650170000000000000E-13 " " relative error = 2.2838748847966994000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.519999999999844 " " y[1] (closed_form) = 31.781802666663484 " " y[1] (numeric) = 31.781802666662692 " " absolute error = 7.9225515037251170000000000000E-13 " " relative error = 2.4927948822850207000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5299999999998475 " " y[1] (closed_form) = 31.986558999996873 " " y[1] (numeric) = 31.986558999996017 " " absolute error = 8.5620399659092070000000000000E-13 " " relative error = 2.6767618129571374000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.539999999999850 " " y[1] (closed_form) = 32.19222133333025 " " y[1] (numeric) = 32.19222133332934 " " absolute error = 9.0949470177292820000000000000E-13 " " relative error = 2.8252002008674126000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.549999999999854 " " y[1] (closed_form) = 32.39879166666364 " " y[1] (numeric) = 32.39879166666265 " " absolute error = 9.8765440270653930000000000000E-13 " " relative error = 3.0484297466030960000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5599999999998575 " " y[1] (closed_form) = 32.606271999997034 " " y[1] (numeric) = 32.606271999995975 " " absolute error = 1.0587086762825493000000000000E-12 " " relative error = 3.2469479377545696000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.569999999999860 " " y[1] (closed_form) = 32.81466433333042 " " y[1] (numeric) = 32.814664333329304 " " absolute error = 1.1155520951433573000000000000E-12 " " relative error = 3.399553577058144000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.579999999999864 " " y[1] (closed_form) = 33.023970666663814 " " y[1] (numeric) = 33.02397066666262 " " absolute error = 1.1937117960769683000000000000E-12 " " relative error = 3.6146828257752955000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5899999999998675 " " y[1] (closed_form) = 33.234192999997205 " " y[1] (numeric) = 33.23419299999595 " " absolute error = 1.2576606422953773000000000000E-12 " " relative error = 3.784237042540745000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.599999999999870 " " y[1] (closed_form) = 33.4453333333306 " " y[1] (numeric) = 33.44533333332928 " " absolute error = 1.3216094885137863000000000000E-12 " " relative error = 3.951551253330493000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.609999999999874 " " y[1] (closed_form) = 33.65739366666399 " " y[1] (numeric) = 33.65739366666260 " " absolute error = 1.3855583347321954000000000000E-12 " " relative error = 4.116653679291048000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.6199999999998775 " " y[1] (closed_form) = 33.87037599999738 " " y[1] (numeric) = 33.870375999995936 " " absolute error = 1.4424017535930034000000000000E-12 " " relative error = 4.2585938626518793000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.629999999999880 " " y[1] (closed_form) = 34.084282333330776 " " y[1] (numeric) = 34.084282333329256 " " absolute error = 1.5205614545266144000000000000E-12 " " relative error = 4.461180786076484600000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.639999999999884 " " y[1] (closed_form) = 34.299114666664174 " " y[1] (numeric) = 34.29911466666257 " " absolute error = 1.6058265828178264000000000000E-12 " " relative error = 4.68183099891657960000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.649999999999888 " " y[1] (closed_form) = 34.514874999997566 " " y[1] (numeric) = 34.5148749999959 " " absolute error = 1.6697754290362354000000000000E-12 " " relative error = 4.8378428982760424000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.659999999999891 " " y[1] (closed_form) = 34.73156533333096 " " y[1] (numeric) = 34.73156533332922 " " absolute error = 1.7408297026122455000000000000E-12 " " relative error = 5.0122408417383290000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.669999999999894 " " y[1] (closed_form) = 34.94918766666436 " " y[1] (numeric) = 34.94918766666254 " " absolute error = 1.8189894035458565000000000000E-12 " " relative error = 5.2046686203263780000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.679999999999898 " " y[1] (closed_form) = 35.167743999997754 " " y[1] (numeric) = 35.167743999995864 " " absolute error = 1.8900436771218665000000000000E-12 " " relative error = 5.3743671391659000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.689999999999901 " " y[1] (closed_form) = 35.38723633333115 " " y[1] (numeric) = 35.38723633332919 " " absolute error = 1.9610979506978765000000000000E-12 " " relative error = 5.5418228545039650000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.699999999999904 " " y[1] (closed_form) = 35.60766666666455 " " y[1] (numeric) = 35.60766666666252 " " absolute error = 2.0321522242738865000000000000E-12 " " relative error = 5.707063715512597000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.709999999999908 " " y[1] (closed_form) = 35.82903699999795 " " y[1] (numeric) = 35.82903699999584 " " absolute error = 2.1103119252074976000000000000E-12 " " relative error = 5.889948773135091000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.719999999999911 " " y[1] (closed_form) = 36.051349333331345 " " y[1] (numeric) = 36.05134933332917 " " absolute error = 2.1742607714259066000000000000E-12 " " relative error = 6.0310107988543160000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.729999999999914 " " y[1] (closed_form) = 36.27460566666474 " " y[1] (numeric) = 36.27460566666251 " " absolute error = 2.2311041902867146000000000000E-12 " " relative error = 6.150595297406725000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.739999999999918 " " y[1] (closed_form) = 36.49880799999815 " " y[1] (numeric) = 36.49880799999583 " " absolute error = 2.3163693185779266000000000000E-12 " " relative error = 6.3464245697504540000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.749999999999921 " " y[1] (closed_form) = 36.72395833333155 " " y[1] (numeric) = 36.723958333329165 " " absolute error = 2.3874235921539366000000000000E-12 " " relative error = 6.50099744282482000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.759999999999924 " " y[1] (closed_form) = 36.95005866666495 " " y[1] (numeric) = 36.95005866666249 " " absolute error = 2.4584778657299466000000000000E-12 " " relative error = 6.653515459632814000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.769999999999928 " " y[1] (closed_form) = 37.177110999998355 " " y[1] (numeric) = 37.177110999995826 " " absolute error = 2.5295321393059567000000000000E-12 " " relative error = 6.804004053209161000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.779999999999931 " " y[1] (closed_form) = 37.40511733333176 " " y[1] (numeric) = 37.40511733332916 " " absolute error = 2.6005864128819667000000000000E-12 " " relative error = 6.952488317860668000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.789999999999934 " " y[1] (closed_form) = 37.63407966666516 " " y[1] (numeric) = 37.634079666662494 " " absolute error = 2.6645352591003757000000000000E-12 " " relative error = 7.080112713532145000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.799999999999938 " " y[1] (closed_form) = 37.86399999999856 " " y[1] (numeric) = 37.863999999995826 " " absolute error = 2.7355895326763857000000000000E-12 " " relative error = 7.224776919175179000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.809999999999941 " " y[1] (closed_form) = 38.094880333331965 " " y[1] (numeric) = 38.09488033332915 " " absolute error = 2.8137492336099970000000000000E-12 " " relative error = 7.38616110351197000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.819999999999944 " " y[1] (closed_form) = 38.32672266666537 " " y[1] (numeric) = 38.32672266666248 " " absolute error = 2.8919089345436080000000000000E-12 " " relative error = 7.545411486640997000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.829999999999948 " " y[1] (closed_form) = 38.559528999998776 " " y[1] (numeric) = 38.559528999995806 " " absolute error = 2.9700686354772190000000000000E-12 " " relative error = 7.702554238868718000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.839999999999951 " " y[1] (closed_form) = 38.79330133333218 " " y[1] (numeric) = 38.79330133332913 " " absolute error = 3.0482283364108300000000000000E-12 " " relative error = 7.857615185206512000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.849999999999954 " " y[1] (closed_form) = 39.02804166666559 " " y[1] (numeric) = 39.02804166666247 " " absolute error = 3.11928260998684000000000000E-12 " " relative error = 7.992413856242917000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.859999999999958 " " y[1] (closed_form) = 39.263751999999 " " y[1] (numeric) = 39.2637519999958 " " absolute error = 3.204547738278052000000000000E-12 " " relative error = 8.161593263624254000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.869999999999961 " " y[1] (closed_form) = 39.50043433333241 " " y[1] (numeric) = 39.500434333329125 " " absolute error = 3.282707439211663000000000000E-12 " " relative error = 8.310560363741503000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.879999999999964 " " y[1] (closed_form) = 39.73809066666581 " " y[1] (numeric) = 39.73809066666245 " " absolute error = 3.360867140145274000000000000E-12 " " relative error = 8.457545603630443000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.889999999999968 " " y[1] (closed_form) = 39.976722999999225 " " y[1] (numeric) = 39.976722999995786 " " absolute error = 3.439026841078885000000000000E-12 " " relative error = 8.60257315508065100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.899999999999971 " " y[1] (closed_form) = 40.21633333333264 " " y[1] (numeric) = 40.21633333332911 " " absolute error = 3.531397396727698000000000000E-12 " " relative error = 8.781002901129124000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.909999999999974 " " y[1] (closed_form) = 40.45692366666604 " " y[1] (numeric) = 40.45692366666245 " " absolute error = 3.595346242946107000000000000E-12 " " relative error = 8.886850301740677000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.919999999999978 " " y[1] (closed_form) = 40.69849599999946 " " y[1] (numeric) = 40.69849599999578 " " absolute error = 3.680611371237319000000000000E-12 " " relative error = 9.043605373617167000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.929999999999981 " " y[1] (closed_form) = 40.94105233333287 " " y[1] (numeric) = 40.94105233332911 " " absolute error = 3.75877107217093000000000000E-12 " " relative error = 9.180934191842111000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.939999999999984 " " y[1] (closed_form) = 41.184594666666285 " " y[1] (numeric) = 41.18459466666244 " " absolute error = 3.844036200462142000000000000E-12 " " relative error = 9.333674961655998000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.949999999999988 " " y[1] (closed_form) = 41.429124999999694 " " y[1] (numeric) = 41.42912499999578 " " absolute error = 3.915090474038152000000000000E-12 " " relative error = 9.45009211282686000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.959999999999991 " " y[1] (closed_form) = 41.67464533333312 " " y[1] (numeric) = 41.67464533332912 " " absolute error = 4.000355602329364000000000000E-12 " " relative error = 9.599015349339308000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.969999999999994 " " y[1] (closed_form) = 41.921157666666524 " " y[1] (numeric) = 41.921157666662445 " " absolute error = 4.078515303262975000000000000E-12 " " relative error = 9.729014011714647000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.979999999999998 " " y[1] (closed_form) = 42.16866399999994 " " y[1] (numeric) = 42.168663999995786 " " absolute error = 4.156675004196586000000000000E-12 " " relative error = 9.857260368022549000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.990000000000001 " " y[1] (closed_form) = 42.41716633333336 " " y[1] (numeric) = 42.41716633332912 " " absolute error = 4.241940132487798000000000000E-12 " " relative error = 1.00005269073202700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.000000000000004 " " y[1] (closed_form) = 42.66666666666678 " " y[1] (numeric) = 42.66666666666245 " " absolute error = 4.32720526077901000000000000E-12 " " relative error = 1.014188732995077700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.010000000000008 " " y[1] (closed_form) = 42.91716700000019 " " y[1] (numeric) = 42.91716699999578 " " absolute error = 4.412470389070222000000000000E-12 " " relative error = 1.028136453897388600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.020000000000011 " " y[1] (closed_form) = 43.16866933333361 " " y[1] (numeric) = 43.16866933332911 " " absolute error = 4.497735517361434000000000000E-12 " " relative error = 1.041898114262329500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.0300000000000145 " " y[1] (closed_form) = 43.421175666667025 " " y[1] (numeric) = 43.421175666662464 " " absolute error = 4.561684363579843000000000000E-12 " " relative error = 1.050566755400336700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.040000000000018 " " y[1] (closed_form) = 43.674688000000444 " " y[1] (numeric) = 43.6746879999958 " " absolute error = 4.646949491871055000000000000E-12 " " relative error = 1.063991456990146800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.050000000000021 " " y[1] (closed_form) = 43.92920833333387 " " y[1] (numeric) = 43.929208333329136 " " absolute error = 4.732214620162267000000000000E-12 " " relative error = 1.077236490185374300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.0600000000000245 " " y[1] (closed_form) = 44.184738666667286 " " y[1] (numeric) = 44.184738666662476 " " absolute error = 4.810374321095878000000000000E-12 " " relative error = 1.08869588601296800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.070000000000028 " " y[1] (closed_form) = 44.441281000000714 " " y[1] (numeric) = 44.441280999995804 " " absolute error = 4.909850304102292300000000000E-12 " " relative error = 1.10479495496590500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.080000000000031 " " y[1] (closed_form) = 44.69883733333413 " " y[1] (numeric) = 44.69883733332914 " " absolute error = 4.995115432393504300000000000E-12 " " relative error = 1.117504555016333600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.0900000000000345 " " y[1] (closed_form) = 44.95740966666756 " " y[1] (numeric) = 44.95740966666247 " " absolute error = 5.087485988042317000000000000E-12 " " relative error = 1.131623468914912800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.100000000000038 " " y[1] (closed_form) = 45.21700000000098 " " y[1] (numeric) = 45.21699999999580 " " absolute error = 5.172751116333529000000000000E-12 " " relative error = 1.143983704432717200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.110000000000041 " " y[1] (closed_form) = 45.47761033333441 " " y[1] (numeric) = 45.47761033332914 " " absolute error = 5.272227099339943000000000000E-12 " " relative error = 1.159301700484354500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.1200000000000445 " " y[1] (closed_form) = 45.73924266666783 " " y[1] (numeric) = 45.73924266666248 " " absolute error = 5.350386800273554000000000000E-12 " " relative error = 1.169758502401399300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.130000000000048 " " y[1] (closed_form) = 46.00189900000126 " " y[1] (numeric) = 46.001898999995824 " " absolute error = 5.4356519285647660000000000000E-12 " " relative error = 1.18161468259486800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.140000000000051 " " y[1] (closed_form) = 46.26558133333468 " " y[1] (numeric) = 46.265581333329166 " " absolute error = 5.5138116294983770000000000000E-12 " " relative error = 1.191773986318774800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.1500000000000545 " " y[1] (closed_form) = 46.530291666668106 " " y[1] (numeric) = 46.53029166666250 " " absolute error = 5.5990767577895900000000000000E-12 " " relative error = 1.203318646248778800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.160000000000058 " " y[1] (closed_form) = 46.79603200000154 " " y[1] (numeric) = 46.796031999995854 " " absolute error = 5.6843418860808010000000000000E-12 " " relative error = 1.214705957565080400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.170000000000061 " " y[1] (closed_form) = 47.06280433333497 " " y[1] (numeric) = 47.0628043333292 " " absolute error = 5.7696070143720140000000000000E-12 " " relative error = 1.22593778592266210000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.1800000000000646 " " y[1] (closed_form) = 47.33061066666839 " " y[1] (numeric) = 47.33061066666254 " " absolute error = 5.8548721426632260000000000000E-12 " " relative error = 1.237015973425079500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.190000000000068 " " y[1] (closed_form) = 47.59945300000183 " " y[1] (numeric) = 47.599452999995876 " " absolute error = 5.9543481256696400000000000000E-12 " " relative error = 1.25092784693752900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.200000000000071 " " y[1] (closed_form) = 47.869333333335256 " " y[1] (numeric) = 47.869333333329195 " " absolute error = 6.0609295360336550000000000000E-12 " " relative error = 1.26614036878866300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.210000000000075 " " y[1] (closed_form) = 48.14025366666869 " " y[1] (numeric) = 48.14025366666253 " " absolute error = 6.160405519040069000000000000E-12 " " relative error = 1.279678657635617300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.220000000000078 " " y[1] (closed_form) = 48.41221600000212 " " y[1] (numeric) = 48.41221599999587 " " absolute error = 6.245670647331281000000000000E-12 " " relative error = 1.290102202165463200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.230000000000081 " " y[1] (closed_form) = 48.68522233333556 " " y[1] (numeric) = 48.68522233332922 " " absolute error = 6.338041202980094000000000000E-12 " " relative error = 1.301840866533402800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.240000000000085 " " y[1] (closed_form) = 48.95927466666899 " " y[1] (numeric) = 48.959274666662566 " " absolute error = 6.423306331271306000000000000E-12 " " relative error = 1.311969259145138500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.250000000000088 " " y[1] (closed_form) = 49.23437500000242 " " y[1] (numeric) = 49.23437499999591 " " absolute error = 6.515676886920119000000000000E-12 " " relative error = 1.323399938949117700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.260000000000091 " " y[1] (closed_form) = 49.51052533333585 " " y[1] (numeric) = 49.510525333329255 " " absolute error = 6.59383658785373000000000000E-12 " " relative error = 1.331805013875311200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.270000000000095 " " y[1] (closed_form) = 49.7877276666693 " " y[1] (numeric) = 49.7877276666626 " " absolute error = 6.700417998217745000000000000E-12 " " relative error = 1.345797109495997500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.280000000000098 " " y[1] (closed_form) = 50.06598400000272 " " y[1] (numeric) = 50.065983999995936 " " absolute error = 6.785683126508957000000000000E-12 " " relative error = 1.35534799965353500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.290000000000101 " " y[1] (closed_form) = 50.345296333336165 " " y[1] (numeric) = 50.34529633332927 " " absolute error = 6.892264536872972000000000000E-12 " " relative error = 1.368998702726724200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.300000000000105 " " y[1] (closed_form) = 50.6256666666696 " " y[1] (numeric) = 50.62566666666262 " " absolute error = 6.984635092521785000000000000E-12 " " relative error = 1.379662837530642400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.310000000000108 " " y[1] (closed_form) = 50.90709700000304 " " y[1] (numeric) = 50.907096999995964 " " absolute error = 7.077005648170598000000000000E-12 " " relative error = 1.390180557373007200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.320000000000111 " " y[1] (closed_form) = 51.18958933333648 " " y[1] (numeric) = 51.1895893333293 " " absolute error = 7.176481631177012000000000000E-12 " " relative error = 1.401941630053951700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.330000000000115 " " y[1] (closed_form) = 51.47314566666992 " " y[1] (numeric) = 51.47314566666267 " " absolute error = 7.254641332110623000000000000E-12 " " relative error = 1.409403143746113500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.340000000000118 " " y[1] (closed_form) = 51.75776800000336 " " y[1] (numeric) = 51.75776799999601 " " absolute error = 7.347011887759436000000000000E-12 " " relative error = 1.419499366309412700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.350000000000121 " " y[1] (closed_form) = 52.0434583333368 " " y[1] (numeric) = 52.043458333329355 " " absolute error = 7.44648787076585000000000000E-12 " " relative error = 1.430821107827100500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.360000000000125 " " y[1] (closed_form) = 52.33021866667025 " " y[1] (numeric) = 52.330218666662695 " " absolute error = 7.553069281129865000000000000E-12 " " relative error = 1.44334754823803290000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.370000000000128 " " y[1] (closed_form) = 52.61805100000369 " " y[1] (numeric) = 52.61805099999604 " " absolute error = 7.645439836778678000000000000E-12 " " relative error = 1.453007036839533000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.380000000000131 " " y[1] (closed_form) = 52.90695733333713 " " y[1] (numeric) = 52.906957333329395 " " absolute error = 7.737810392427491000000000000E-12 " " relative error = 1.462531731635194600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.390000000000135 " " y[1] (closed_form) = 53.19693966667058 " " y[1] (numeric) = 53.19693966666274 " " absolute error = 7.837286375433905000000000000E-12 " " relative error = 1.473258880029933400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.400000000000138 " " y[1] (closed_form) = 53.48800000000402 " " y[1] (numeric) = 53.48799999999609 " " absolute error = 7.929656931082718000000000000E-12 " " relative error = 1.48251139154242480000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.410000000000141 " " y[1] (closed_form) = 53.78014033333747 " " y[1] (numeric) = 53.780140333329435 " " absolute error = 8.036238341446733000000000000E-12 " " relative error = 1.494276194081478600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.420000000000145 " " y[1] (closed_form) = 54.07336266667091 " " y[1] (numeric) = 54.073362666662774 " " absolute error = 8.135714324453147000000000000E-12 " " relative error = 1.50456970368290780000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.430000000000148 " " y[1] (closed_form) = 54.36766900000436 " " y[1] (numeric) = 54.36766899999613 " " absolute error = 8.235190307459561000000000000E-12 " " relative error = 1.514721977037290200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.440000000000151 " " y[1] (closed_form) = 54.66306133333781 " " y[1] (numeric) = 54.66306133332948 " " absolute error = 8.327560863108374000000000000E-12 " " relative error = 1.523434776608381700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.450000000000155 " " y[1] (closed_form) = 54.95954166667126 " " y[1] (numeric) = 54.95954166666283 " " absolute error = 8.427036846114788000000000000E-12 " " relative error = 1.533316434337213500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.460000000000158 " " y[1] (closed_form) = 55.25711200000471 " " y[1] (numeric) = 55.257111999996155 " " absolute error = 8.554934538551606000000000000E-12 " " relative error = 1.548205150234937500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.470000000000161 " " y[1] (closed_form) = 55.55577433333816 " " y[1] (numeric) = 55.5557743333295 " " absolute error = 8.65441052155802000000000000E-12 " " relative error = 1.55778775931211200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.480000000000165 " " y[1] (closed_form) = 55.85553066667161 " " y[1] (numeric) = 55.85553066666286 " " absolute error = 8.753886504564434000000000000E-12 " " relative error = 1.567237192106346300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.490000000000168 " " y[1] (closed_form) = 56.156383000005064 " " y[1] (numeric) = 56.15638299999621 " " absolute error = 8.853362487570848000000000000E-12 " " relative error = 1.576554972846105600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.500000000000171 " " y[1] (closed_form) = 56.45833333333852 " " y[1] (numeric) = 56.45833333332957 " " absolute error = 8.952838470577262000000000000E-12 " " relative error = 1.585742607334572300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.510000000000175 " " y[1] (closed_form) = 56.761383666671975 " " y[1] (numeric) = 56.76138366666292 " " absolute error = 9.052314453583676000000000000E-12 " " relative error = 1.594801583193053000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.520000000000178 " " y[1] (closed_form) = 57.06553600000542 " " y[1] (numeric) = 57.06553599999627 " " absolute error = 9.15179043659009000000000000E-12 " " relative error = 1.603733370100864600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.530000000000181 " " y[1] (closed_form) = 57.370792333338876 " " y[1] (numeric) = 57.370792333329625 " " absolute error = 9.251266419596504000000000000E-12 " " relative error = 1.61253942003176410000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.540000000000185 " " y[1] (closed_form) = 57.67715466667234 " " y[1] (numeric) = 57.677154666662986 " " absolute error = 9.350742402602918000000000000E-12 " " relative error = 1.621221167486972300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.550000000000188 " " y[1] (closed_form) = 57.98462500000579 " " y[1] (numeric) = 57.98462499999634 " " absolute error = 9.450218385609332000000000000E-12 " " relative error = 1.629780029724843300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.5600000000001915 " " y[1] (closed_form) = 58.29320533333925 " " y[1] (numeric) = 58.2932053333297 " " absolute error = 9.549694368615746000000000000E-12 " " relative error = 1.638217406987235000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.570000000000195 " " y[1] (closed_form) = 58.60289766667271 " " y[1] (numeric) = 58.60289766666306 " " absolute error = 9.64917035162216000000000000E-12 " " relative error = 1.646534682722628200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.580000000000198 " " y[1] (closed_form) = 58.91370400000617 " " y[1] (numeric) = 58.913703999996414 " " absolute error = 9.755751761986176000000000000E-12 " " relative error = 1.65593929758433700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.5900000000002015 " " y[1] (closed_form) = 59.225626333339626 " " y[1] (numeric) = 59.22562633332978 " " absolute error = 9.848122317634989000000000000E-12 " " relative error = 1.662814380755856500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.600000000000205 " " y[1] (closed_form) = 59.538666666673095 " " y[1] (numeric) = 59.53866666666314 " " absolute error = 9.954703727999004000000000000E-12 " " relative error = 1.67197290186734600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.610000000000208 " " y[1] (closed_form) = 59.85282700000654 " " y[1] (numeric) = 59.852826999996495 " " absolute error = 1.004707428364781700000000000E-11 " " relative error = 1.67862986382359500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.6200000000002115 " " y[1] (closed_form) = 60.168109333340006 " " y[1] (numeric) = 60.16810933332985 " " absolute error = 1.015365569401183200000000000E-11 " " relative error = 1.687547740242113200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.630000000000215 " " y[1] (closed_form) = 60.484515666673474 " " y[1] (numeric) = 60.48451566666321 " " absolute error = 1.026023710437584700000000000E-11 " " relative error = 1.69634111991892200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.640000000000218 " " y[1] (closed_form) = 60.802048000006934 " " y[1] (numeric) = 60.80204799999657 " " absolute error = 1.036681851473986200000000000E-11 " " relative error = 1.705011402697928800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.6500000000002215 " " y[1] (closed_form) = 61.1207083333404 " " y[1] (numeric) = 61.12070833332993 " " absolute error = 1.047339992510387700000000000E-11 " " relative error = 1.71355997184849400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.660000000000225 " " y[1] (closed_form) = 61.440498666673875 " " y[1] (numeric) = 61.44049866666329 " " absolute error = 1.058708676282549300000000000E-11 " " relative error = 1.72314466721085800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.670000000000228 " " y[1] (closed_form) = 61.761421000007346 " " y[1] (numeric) = 61.761420999996645 " " absolute error = 1.070077360054710900000000000E-11 " " relative error = 1.732598348173666000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.6800000000002315 " " y[1] (closed_form) = 62.083477333340795 " " y[1] (numeric) = 62.083477333329995 " " absolute error = 1.080024958355352300000000000E-11 " " relative error = 1.73963348179813500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.690000000000235 " " y[1] (closed_form) = 62.40666966667426 " " y[1] (numeric) = 62.406669666663355 " " absolute error = 1.090683099391753800000000000E-11 " " relative error = 1.74770277795193520000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.700000000000238 " " y[1] (closed_form) = 62.73100000000774 " " y[1] (numeric) = 62.73099999999672 " " absolute error = 1.102051783163915400000000000E-11 " " relative error = 1.7567897581160502000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.7100000000002415 " " y[1] (closed_form) = 63.05647033334121 " " y[1] (numeric) = 63.056470333330076 " " absolute error = 1.11342046693607700000000000E-11 " " relative error = 1.76575133535083720000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.720000000000245 " " y[1] (closed_form) = 63.38308266667468 " " y[1] (numeric) = 63.38308266666343 " " absolute error = 1.125499693443998700000000000E-11 " " relative error = 1.77570993093360500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.730000000000248 " " y[1] (closed_form) = 63.71083900000815 " " y[1] (numeric) = 63.71083899999678 " " absolute error = 1.136868377216160300000000000E-11 " " relative error = 1.784419095808822700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.740000000000252 " " y[1] (closed_form) = 64.03974133334161 " " y[1] (numeric) = 64.03974133333014 " " absolute error = 1.146815975516801700000000000E-11 " " relative error = 1.790787957039614300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.750000000000255 " " y[1] (closed_form) = 64.3697916666751 " " y[1] (numeric) = 64.3697916666635 " " absolute error = 1.159605744760483500000000000E-11 " " relative error = 1.80147506265865900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.760000000000258 " " y[1] (closed_form) = 64.70099200000857 " " y[1] (numeric) = 64.70099199999686 " " absolute error = 1.170974428532645100000000000E-11 " " relative error = 1.809824536434449200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.770000000000262 " " y[1] (closed_form) = 65.03334433334203 " " y[1] (numeric) = 65.03334433333022 " " absolute error = 1.180922026833286500000000000E-11 " " relative error = 1.815871594701055600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.780000000000265 " " y[1] (closed_form) = 65.36685066667552 " " y[1] (numeric) = 65.36685066666357 " " absolute error = 1.195132881548488500000000000E-11 " " relative error = 1.828347043431565700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.790000000000268 " " y[1] (closed_form) = 65.70151300000899 " " y[1] (numeric) = 65.70151299999694 " " absolute error = 1.205080479849129900000000000E-11 " " relative error = 1.834174625246400600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.800000000000272 " " y[1] (closed_form) = 66.03733333334246 " " y[1] (numeric) = 66.0373333333303 " " absolute error = 1.216449163621291500000000000E-11 " " relative error = 1.842062818437737200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.810000000000275 " " y[1] (closed_form) = 66.37431366667595 " " y[1] (numeric) = 66.37431366666365 " " absolute error = 1.229238932864973300000000000E-11 " " relative error = 1.85197987739363720000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.820000000000278 " " y[1] (closed_form) = 66.71245600000942 " " y[1] (numeric) = 66.71245599999703 " " absolute error = 1.239186531165614700000000000E-11 " " relative error = 1.857503988708554800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.830000000000282 " " y[1] (closed_form) = 67.05176233334291 " " y[1] (numeric) = 67.05176233333042 " " absolute error = 1.249134129466256100000000000E-11 " " relative error = 1.86294004213681600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.840000000000285 " " y[1] (closed_form) = 67.39223466667639 " " y[1] (numeric) = 67.3922346666638 " " absolute error = 1.259081727766897500000000000E-11 " " relative error = 1.868289030619545400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.850000000000288 " " y[1] (closed_form) = 67.73387500000986 " " y[1] (numeric) = 67.73387499999717 " " absolute error = 1.26902932606753900000000000E-11 " " relative error = 1.87355193552318420000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.860000000000292 " " y[1] (closed_form) = 68.07668533334333 " " y[1] (numeric) = 68.07668533333054 " " absolute error = 1.278976924368180300000000000E-11 " " relative error = 1.878729726786138600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.870000000000295 " " y[1] (closed_form) = 68.42066766667682 " " y[1] (numeric) = 68.42066766666395 " " absolute error = 1.287503437197301500000000000E-11 " " relative error = 1.881746380303680200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.880000000000298 " " y[1] (closed_form) = 68.76582400001031 " " y[1] (numeric) = 68.76582399999731 " " absolute error = 1.300293206440983300000000000E-11 " " relative error = 1.8909003496283097000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.890000000000302 " " y[1] (closed_form) = 69.11215633334379 " " y[1] (numeric) = 69.11215633333066 " " absolute error = 1.313082975684665100000000000E-11 " " relative error = 1.89993055541685720000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.900000000000305 " " y[1] (closed_form) = 69.45966666667728 " " y[1] (numeric) = 69.45966666666403 " " absolute error = 1.324451659456826700000000000E-11 " " relative error = 1.906792420718917400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.910000000000308 " " y[1] (closed_form) = 69.80835700001077 " " y[1] (numeric) = 69.8083569999974 " " absolute error = 1.337241428700508500000000000E-11 " " relative error = 1.915589316477255600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.920000000000312 " " y[1] (closed_form) = 70.15822933334425 " " y[1] (numeric) = 70.15822933333075 " " absolute error = 1.350031197944190400000000000E-11 " " relative error = 1.924266348755409900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.930000000000315 " " y[1] (closed_form) = 70.50928566667773 " " y[1] (numeric) = 70.50928566666413 " " absolute error = 1.359978796244831800000000000E-11 " " relative error = 1.92879389343686100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.940000000000318 " " y[1] (closed_form) = 70.86152800001122 " " y[1] (numeric) = 70.8615279999975 " " absolute error = 1.371347480016993400000000000E-11 " " relative error = 1.93524966046001200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.950000000000322 " " y[1] (closed_form) = 71.21495833334471 " " y[1] (numeric) = 71.21495833333084 " " absolute error = 1.386979420203715600000000000E-11 " " relative error = 1.947595635331988400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.960000000000325 " " y[1] (closed_form) = 71.56957866667821 " " y[1] (numeric) = 71.56957866666421 " " absolute error = 1.399769189447397400000000000E-11 " " relative error = 1.95581588647679220000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.970000000000328 " " y[1] (closed_form) = 71.9253910000117 " " y[1] (numeric) = 71.92539099999756 " " absolute error = 1.413980044162599400000000000E-11 " " relative error = 1.965898307264494800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.980000000000332 " " y[1] (closed_form) = 72.28239733334519 " " y[1] (numeric) = 72.28239733333092 " " absolute error = 1.426769813406281200000000000E-11 " " relative error = 1.97388280693906400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.990000000000335 " " y[1] (closed_form) = 72.64059966667868 " " y[1] (numeric) = 72.6405996666643 " " absolute error = 1.438138497178442800000000000E-11 " " relative error = 1.979799869188219600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.000000000000338 " " y[1] (closed_form) = 73.0000000000122 " " y[1] (numeric) = 72.99999999999768 " " absolute error = 1.450928266422124600000000000E-11 " " relative error = 1.987572967701208600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.010000000000342 " " y[1] (closed_form) = 73.36060033334567 " " y[1] (numeric) = 73.36060033333106 " " absolute error = 1.46087586472276600000000000E-11 " " relative error = 1.991363017866052700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.020000000000345 " " y[1] (closed_form) = 73.72240266667917 " " y[1] (numeric) = 73.72240266666444 " " absolute error = 1.473665633966447800000000000E-11 " " relative error = 1.998938695242105400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.030000000000348 " " y[1] (closed_form) = 74.08540900001266 " " y[1] (numeric) = 74.08540899999781 " " absolute error = 1.485034317738609400000000000E-11 " " relative error = 2.004489598941616000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.040000000000352 " " y[1] (closed_form) = 74.44962133334616 " " y[1] (numeric) = 74.44962133333122 " " absolute error = 1.493560830567730600000000000E-11 " " relative error = 2.00613623524067700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.050000000000355 " " y[1] (closed_form) = 74.81504166667966 " " y[1] (numeric) = 74.8150416666646 " " absolute error = 1.506350599811412400000000000E-11 " " relative error = 2.01343281545253100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.060000000000358 " " y[1] (closed_form) = 75.18167200001317 " " y[1] (numeric) = 75.18167199999797 " " absolute error = 1.519140369055094200000000000E-11 " " relative error = 2.020625943321436300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.070000000000362 " " y[1] (closed_form) = 75.54951433334666 " " y[1] (numeric) = 75.54951433333135 " " absolute error = 1.53193013829877600000000000E-11 " " relative error = 2.02771672566874500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.080000000000365 " " y[1] (closed_form) = 75.91857066668015 " " y[1] (numeric) = 75.91857066666468 " " absolute error = 1.547562078485498200000000000E-11 " " relative error = 2.038449966715070000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.0900000000003685 " " y[1] (closed_form) = 76.28884300001366 " " y[1] (numeric) = 76.28884299999805 " " absolute error = 1.5603518477291800000000000E-11 " " relative error = 2.045321158860543600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.100000000000372 " " y[1] (closed_form) = 76.66033333334715 " " y[1] (numeric) = 76.66033333333141 " " absolute error = 1.57456270244438200000000000E-11 " " relative error = 2.053947111862412200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.110000000000375 " " y[1] (closed_form) = 77.03304366668067 " " y[1] (numeric) = 77.03304366666478 " " absolute error = 1.58877355715958400000000000E-11 " " relative error = 2.062457202176967700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.1200000000003785 " " y[1] (closed_form) = 77.40697600001417 " " y[1] (numeric) = 77.40697599999817 " " absolute error = 1.600142240931745600000000000E-11 " " relative error = 2.067180922984838700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.130000000000382 " " y[1] (closed_form) = 77.78213233334768 " " y[1] (numeric) = 77.78213233333156 " " absolute error = 1.611510924703907200000000000E-11 " " relative error = 2.07182662182301890000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.140000000000385 " " y[1] (closed_form) = 78.15851466668119 " " y[1] (numeric) = 78.15851466666494 " " absolute error = 1.62430069394758900000000000E-11 " " relative error = 2.078213360213746500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.1500000000003885 " " y[1] (closed_form) = 78.53612500001469 " " y[1] (numeric) = 78.53612499999834 " " absolute error = 1.635669377719750600000000000E-11 " " relative error = 2.082696819736706600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.160000000000392 " " y[1] (closed_form) = 78.9149653333482 " " y[1] (numeric) = 78.91496533333171 " " absolute error = 1.649880232434952600000000000E-11 " " relative error = 2.090706402094482700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.170000000000395 " " y[1] (closed_form) = 79.29503766668171 " " y[1] (numeric) = 79.29503766666508 " " absolute error = 1.662670001678634400000000000E-11 " " relative error = 2.096814694341531700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.1800000000003985 " " y[1] (closed_form) = 79.6763440000152 " " y[1] (numeric) = 79.67634399999847 " " absolute error = 1.67403868545079600000000000E-11 " " relative error = 2.101048569008734000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.190000000000402 " " y[1] (closed_form) = 80.05888633334872 " " y[1] (numeric) = 80.05888633333186 " " absolute error = 1.68682845469447780000000000E-11 " " relative error = 2.106984660854350500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.200000000000405 " " y[1] (closed_form) = 80.44266666668223 " " y[1] (numeric) = 80.44266666666525 " " absolute error = 1.698197138466639400000000000E-11 " " relative error = 2.11106519566686520000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.2100000000004085 " " y[1] (closed_form) = 80.82768700001576 " " y[1] (numeric) = 80.82768699999862 " " absolute error = 1.713829078653361600000000000E-11 " " relative error = 2.12034903170373700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.220000000000412 " " y[1] (closed_form) = 81.21394933334926 " " y[1] (numeric) = 81.21394933333201 " " absolute error = 1.725197762425523300000000000E-11 " " relative error = 2.124262859504970600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.230000000000415 " " y[1] (closed_form) = 81.60145566668277 " " y[1] (numeric) = 81.60145566666542 " " absolute error = 1.735145360726164700000000000E-11 " " relative error = 2.126365695991635200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.2400000000004185 " " y[1] (closed_form) = 81.9902080000163 " " y[1] (numeric) = 81.99020799999879 " " absolute error = 1.75077730091288690000000000E-11 " " relative error = 2.135349261356355000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.250000000000422 " " y[1] (closed_form) = 82.3802083333498 " " y[1] (numeric) = 82.38020833333219 " " absolute error = 1.760724899213528300000000000E-11 " " relative error = 2.137315424220331800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.260000000000425 " " y[1] (closed_form) = 82.77145866668333 " " y[1] (numeric) = 82.77145866666557 " " absolute error = 1.776356839400250500000000000E-11 " " relative error = 2.146098266255707700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.270000000000429 " " y[1] (closed_form) = 83.16396100001684 " " y[1] (numeric) = 83.16396099999895 " " absolute error = 1.789146608643932300000000000E-11 " " relative error = 2.151348477309263700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.280000000000432 " " y[1] (closed_form) = 83.55771733335035 " " y[1] (numeric) = 83.55771733333235 " " absolute error = 1.80051529241609400000000000E-11 " " relative error = 2.154816275357315200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.290000000000435 " " y[1] (closed_form) = 83.95272966668388 " " y[1] (numeric) = 83.95272966666573 " " absolute error = 1.81472614713129600000000000E-11 " " relative error = 2.161604696281196300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.300000000000439 " " y[1] (closed_form) = 84.3490000000174 " " y[1] (numeric) = 84.34899999999912 " " absolute error = 1.827515916374977700000000000E-11 " " relative error = 2.166612427384557700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.310000000000442 " " y[1] (closed_form) = 84.74653033335092 " " y[1] (numeric) = 84.74653033333252 " " absolute error = 1.840305685618659500000000000E-11 " " relative error = 2.171541039355602600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.320000000000445 " " y[1] (closed_form) = 85.14532266668445 " " y[1] (numeric) = 85.1453226666659 " " absolute error = 1.854516540333861500000000000E-11 " " relative error = 2.17806038224046120000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.330000000000449 " " y[1] (closed_form) = 85.54537900001796 " " y[1] (numeric) = 85.54537899999929 " " absolute error = 1.867306309577543300000000000E-11 " " relative error = 2.1828254563898200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.340000000000452 " " y[1] (closed_form) = 85.9467013333515 " " y[1] (numeric) = 85.94670133333267 " " absolute error = 1.882938249764265500000000000E-11 " " relative error = 2.190820846586224700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.350000000000455 " " y[1] (closed_form) = 86.34929166668502 " " y[1] (numeric) = 86.34929166666605 " " absolute error = 1.897149104479467500000000000E-11 " " relative error = 2.197063887683770300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.360000000000459 " " y[1] (closed_form) = 86.75315200001855 " " y[1] (numeric) = 86.75315199999946 " " absolute error = 1.90851778825162900000000000E-11 " " relative error = 2.199940571901319600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.370000000000462 " " y[1] (closed_form) = 87.15828433335207 " " y[1] (numeric) = 87.15828433333284 " " absolute error = 1.92272864296683100000000000E-11 " " relative error = 2.206019379194087700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.380000000000465 " " y[1] (closed_form) = 87.5646906666856 " " y[1] (numeric) = 87.56469066666624 " " absolute error = 1.93693949768203300000000000E-11 " " relative error = 2.21200975294366100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.390000000000469 " " y[1] (closed_form) = 87.97237300001912 " " y[1] (numeric) = 87.97237299999964 " " absolute error = 1.948308181454194700000000000E-11 " " relative error = 2.214681854101822600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.400000000000472 " " y[1] (closed_form) = 88.38133333335266 " " y[1] (numeric) = 88.38133333333303 " " absolute error = 1.962519036169396700000000000E-11 " " relative error = 2.220513045178055300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.410000000000475 " " y[1] (closed_form) = 88.79157366668619 " " y[1] (numeric) = 88.79157366666644 " " absolute error = 1.975308805413078500000000000E-11 " " relative error = 2.224657953274001600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.420000000000479 " " y[1] (closed_form) = 89.20309600001971 " " y[1] (numeric) = 89.20309599999982 " " absolute error = 1.989519660128280500000000000E-11 " " relative error = 2.2303257951134800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.430000000000482 " " y[1] (closed_form) = 89.61590233335326 " " y[1] (numeric) = 89.61590233333321 " " absolute error = 2.005151600315002700000000000E-11 " " relative error = 2.237495297270164200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.440000000000485 " " y[1] (closed_form) = 90.02999466668679 " " y[1] (numeric) = 90.0299946666666 " " absolute error = 2.019362455030204700000000000E-11 " " relative error = 2.242988531218270000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.450000000000489 " " y[1] (closed_form) = 90.44537500002032 " " y[1] (numeric) = 90.44537499999998 " " absolute error = 2.033573309745406700000000000E-11 " " relative error = 2.248399445239681600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.460000000000492 " " y[1] (closed_form) = 90.86204533335388 " " y[1] (numeric) = 90.8620453333334 " " absolute error = 2.047784164460608700000000000E-11 " " relative error = 2.253728888610988200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.470000000000495 " " y[1] (closed_form) = 91.2800076666874 " " y[1] (numeric) = 91.28000766666682 " " absolute error = 2.0577317627612500000000000E-11 " " relative error = 2.25430717564698300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.480000000000499 " " y[1] (closed_form) = 91.69926400002092 " " y[1] (numeric) = 91.69926400000021 " " absolute error = 2.07052153200493200000000000E-11 " " relative error = 2.25794781952062300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.490000000000502 " " y[1] (closed_form) = 92.11981633335446 " " y[1] (numeric) = 92.11981633333362 " " absolute error = 2.08473238672013400000000000E-11 " " relative error = 2.26306615633720100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.500000000000505 " " y[1] (closed_form) = 92.54166666668802 " " y[1] (numeric) = 92.54166666666703 " " absolute error = 2.09894324143533600000000000E-11 " " relative error = 2.26810615913716500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.510000000000509 " " y[1] (closed_form) = 92.96481700002154 " " y[1] (numeric) = 92.96481700000041 " " absolute error = 2.11315409615053800000000000E-11 " " relative error = 2.273068634287795400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.520000000000512 " " y[1] (closed_form) = 93.38926933335509 " " y[1] (numeric) = 93.38926933333381 " " absolute error = 2.1273649508657400000000000E-11 " " relative error = 2.277954379610855300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.530000000000515 " " y[1] (closed_form) = 93.81502566668863 " " y[1] (numeric) = 93.81502566666722 " " absolute error = 2.140154720109421800000000000E-11 " " relative error = 2.281249410636080300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.540000000000519 " " y[1] (closed_form) = 94.24208800002219 " " y[1] (numeric) = 94.24208800000063 " " absolute error = 2.15578666029614400000000000E-11 " " relative error = 2.287498829923670700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.550000000000522 " " y[1] (closed_form) = 94.67045833335573 " " y[1] (numeric) = 94.67045833333403 " " absolute error = 2.16999751501134600000000000E-11 " " relative error = 2.292159088709914700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.560000000000525 " " y[1] (closed_form) = 95.10013866668926 " " y[1] (numeric) = 95.10013866666742 " " absolute error = 2.18420836972654800000000000E-11 " " relative error = 2.296745725452460400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.570000000000529 " " y[1] (closed_form) = 95.53113100002281 " " y[1] (numeric) = 95.53113100000081 " " absolute error = 2.199840309913270200000000000E-11 " " relative error = 2.302747059398621300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.580000000000532 " " y[1] (closed_form) = 95.96343733335637 " " y[1] (numeric) = 95.96343733333421 " " absolute error = 2.215472250099992400000000000E-11 " " relative error = 2.308662873760886000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.590000000000535 " " y[1] (closed_form) = 96.39705966668993 " " y[1] (numeric) = 96.39705966666762 " " absolute error = 2.231104190286714600000000000E-11 " " relative error = 2.314494029175948300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.600000000000539 " " y[1] (closed_form) = 96.83200000002347 " " y[1] (numeric) = 96.83200000000105 " " absolute error = 2.242472874058876200000000000E-11 " " relative error = 2.31583864224464300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.610000000000542 " " y[1] (closed_form) = 97.268260333357 " " y[1] (numeric) = 97.26826033333444 " " absolute error = 2.256683728774078200000000000E-11 " " relative error = 2.320061776616534300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.6200000000005454 " " y[1] (closed_form) = 97.70584266669057 " " y[1] (numeric) = 97.70584266666785 " " absolute error = 2.272315668960800400000000000E-11 " " relative error = 2.325670202459108300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.630000000000549 " " y[1] (closed_form) = 98.1447490000241 " " y[1] (numeric) = 98.14474900000126 " " absolute error = 2.285105438204482200000000000E-11 " " relative error = 2.32830127081370500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.640000000000552 " " y[1] (closed_form) = 98.58498133335766 " " y[1] (numeric) = 98.58498133333467 " " absolute error = 2.299316292919684200000000000E-11 " " relative error = 2.332319042740110500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.6500000000005555 " " y[1] (closed_form) = 99.02654166669123 " " y[1] (numeric) = 99.02654166666808 " " absolute error = 2.314948233106406400000000000E-11 " " relative error = 2.337704815440472300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.660000000000559 " " y[1] (closed_form) = 99.46943200002478 " " y[1] (numeric) = 99.46943200000146 " " absolute error = 2.332001258764648800000000000E-11 " " relative error = 2.34444010775498100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.670000000000562 " " y[1] (closed_form) = 99.91365433335832 " " y[1] (numeric) = 99.91365433333488 " " absolute error = 2.344791028008330600000000000E-11 " " relative error = 2.346817403139934700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.6800000000005655 " " y[1] (closed_form) = 100.35921066669188 " " y[1] (numeric) = 100.35921066666826 " " absolute error = 2.36184405366657300000000000E-11 " " relative error = 2.3533904242338200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.690000000000569 " " y[1] (closed_form) = 100.80610300002547 " " y[1] (numeric) = 100.80610300000167 " " absolute error = 2.380318164796335600000000000E-11 " " relative error = 2.36128378536340600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.700000000000572 " " y[1] (closed_form) = 101.25433333335901 " " y[1] (numeric) = 101.2543333333351 " " absolute error = 2.391686848568497200000000000E-11 " " relative error = 2.362058758210734000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.7100000000005755 " " y[1] (closed_form) = 101.70390366669257 " " y[1] (numeric) = 101.70390366666852 " " absolute error = 2.40447661781217900000000000E-11 " " relative error = 2.364193045816815600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.720000000000579 " " y[1] (closed_form) = 102.15481600002614 " " y[1] (numeric) = 102.15481600000193 " " absolute error = 2.421529643470421400000000000E-11 " " relative error = 2.370450790562631500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.730000000000582 " " y[1] (closed_form) = 102.60707233335968 " " y[1] (numeric) = 102.60707233333532 " " absolute error = 2.435740498185623400000000000E-11 " " relative error = 2.373852447784648200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.7400000000005855 " " y[1] (closed_form) = 103.06067466669327 " " y[1] (numeric) = 103.06067466666873 " " absolute error = 2.45421460931538600000000000E-11 " " relative error = 2.381329849870009700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.750000000000589 " " y[1] (closed_form) = 103.51562500002683 " " y[1] (numeric) = 103.51562500000215 " " absolute error = 2.46842546403058800000000000E-11 " " relative error = 2.38459214638364780000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.760000000000592 " " y[1] (closed_form) = 103.9719253333604 " " y[1] (numeric) = 103.97192533333555 " " absolute error = 2.485478489688830500000000000E-11 " " relative error = 2.39052848326099080000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.7700000000005955 " " y[1] (closed_form) = 104.42957766669396 " " y[1] (numeric) = 104.42957766666896 " " absolute error = 2.499689344404032500000000000E-11 " " relative error = 2.393660302239511700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.780000000000599 " " y[1] (closed_form) = 104.88858400002752 " " y[1] (numeric) = 104.88858400000238 " " absolute error = 2.513900199119234500000000000E-11 " " relative error = 2.39673385153009100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.790000000000602 " " y[1] (closed_form) = 105.3489463333611 " " y[1] (numeric) = 105.34894633333577 " " absolute error = 2.53237431024899700000000000E-11 " " relative error = 2.403796524206017700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.800000000000606 " " y[1] (closed_form) = 105.81066666669467 " " y[1] (numeric) = 105.81066666666919 " " absolute error = 2.548006250435719000000000000E-11 " " relative error = 2.408080707460222600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.810000000000609 " " y[1] (closed_form) = 106.27374700002824 " " y[1] (numeric) = 106.27374700000264 " " absolute error = 2.55937493420788100000000000E-11 " " relative error = 2.40828521291076800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.820000000000612 " " y[1] (closed_form) = 106.7381893333618 " " y[1] (numeric) = 106.73818933333605 " " absolute error = 2.57500687439460300000000000E-11 " " relative error = 2.41245133581235120000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.830000000000616 " " y[1] (closed_form) = 107.20399566669539 " " y[1] (numeric) = 107.20399566666948 " " absolute error = 2.590638814581325300000000000E-11 " " relative error = 2.416550613128077600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.840000000000619 " " y[1] (closed_form) = 107.67116800002896 " " y[1] (numeric) = 107.6711680000029 " " absolute error = 2.606270754768047500000000000E-11 " " relative error = 2.42058371166489680000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.850000000000622 " " y[1] (closed_form) = 108.13970833336253 " " y[1] (numeric) = 108.13970833333634 " " absolute error = 2.619060524011729300000000000E-11 " " relative error = 2.421923051556552400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.860000000000626 " " y[1] (closed_form) = 108.60961866669612 " " y[1] (numeric) = 108.60961866666977 " " absolute error = 2.634692464198451500000000000E-11 " " relative error = 2.425837137209606600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.870000000000629 " " y[1] (closed_form) = 109.08090100002967 " " y[1] (numeric) = 109.0809010000032 " " absolute error = 2.647482233442133300000000000E-11 " " relative error = 2.42708137645600600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.880000000000632 " " y[1] (closed_form) = 109.55355733336326 " " y[1] (numeric) = 109.55355733333661 " " absolute error = 2.664535259100375700000000000E-11 " " relative error = 2.432175936553474800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.890000000000636 " " y[1] (closed_form) = 110.02758966669684 " " y[1] (numeric) = 110.02758966667004 " " absolute error = 2.68016719928709800000000000E-11 " " relative error = 2.43590467391501100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.900000000000639 " " y[1] (closed_form) = 110.50300000003041 " " y[1] (numeric) = 110.50300000000348 " " absolute error = 2.692956968530779700000000000E-11 " " relative error = 2.436998967023554800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.910000000000642 " " y[1] (closed_form) = 110.97979033336401 " " y[1] (numeric) = 110.9797903333369 " " absolute error = 2.711431079660542300000000000E-11 " " relative error = 2.443175529090363700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.920000000000646 " " y[1] (closed_form) = 111.45796266669757 " " y[1] (numeric) = 111.45796266667033 " " absolute error = 2.72422084890422400000000000E-11 " " relative error = 2.444168889979353200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.930000000000649 " " y[1] (closed_form) = 111.93751900003117 " " y[1] (numeric) = 111.93751900000375 " " absolute error = 2.742694960033986700000000000E-11 " " relative error = 2.450201670123868800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.940000000000652 " " y[1] (closed_form) = 112.41846133336475 " " y[1] (numeric) = 112.41846133333719 " " absolute error = 2.755484729277668500000000000E-11 " " relative error = 2.451096284894504800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.950000000000656 " " y[1] (closed_form) = 112.90079166669832 " " y[1] (numeric) = 112.9007916666706 " " absolute error = 2.77253775493591100000000000E-11 " " relative error = 2.45572924158131480000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.960000000000659 " " y[1] (closed_form) = 113.38451200003192 " " y[1] (numeric) = 113.38451200000404 " " absolute error = 2.78816969512263300000000000E-11 " " relative error = 2.459039286707736800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.970000000000662 " " y[1] (closed_form) = 113.8696243333655 " " y[1] (numeric) = 113.86962433333746 " " absolute error = 2.803801635309355300000000000E-11 " " relative error = 2.46229110855843900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.980000000000666 " " y[1] (closed_form) = 114.35613066669909 " " y[1] (numeric) = 114.3561306666709 " " absolute error = 2.819433575496077500000000000E-11 " " relative error = 2.46548528623582290000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.990000000000669 " " y[1] (closed_form) = 114.84403300003268 " " y[1] (numeric) = 114.84403300000432 " " absolute error = 2.8364866011543200000000000E-11 " " relative error = 2.469859797725418600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.000000000000672 " " y[1] (closed_form) = 115.33333333336628 " " y[1] (numeric) = 115.33333333333775 " " absolute error = 2.853539626812562300000000000E-11 " " relative error = 2.47416730648417400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.010000000000676 " " y[1] (closed_form) = 115.82403366669986 " " y[1] (numeric) = 115.82403366667118 " " absolute error = 2.867750481527764400000000000E-11 " " relative error = 2.475954593137486600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.020000000000679 " " y[1] (closed_form) = 116.31613600003347 " " y[1] (numeric) = 116.31613600000462 " " absolute error = 2.884803507186007000000000000E-11 " " relative error = 2.480140422808729300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.030000000000682 " " y[1] (closed_form) = 116.80964233336705 " " y[1] (numeric) = 116.80964233333806 " " absolute error = 2.899014361901209000000000000E-11 " " relative error = 2.48182795871218600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.040000000000686 " " y[1] (closed_form) = 117.30455466670065 " " y[1] (numeric) = 117.30455466667148 " " absolute error = 2.917488473030971400000000000E-11 " " relative error = 2.487105876937582600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.050000000000689 " " y[1] (closed_form) = 117.80087500003424 " " y[1] (numeric) = 117.80087500000491 " " absolute error = 2.933120413217693600000000000E-11 " " relative error = 2.489896966569086500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.060000000000692 " " y[1] (closed_form) = 118.29860533336785 " " y[1] (numeric) = 118.29860533333834 " " absolute error = 2.95017343887593600000000000E-11 " " relative error = 2.493836195754200200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.070000000000696 " " y[1] (closed_form) = 118.79774766670144 " " y[1] (numeric) = 118.79774766667181 " " absolute error = 2.96296320811961800000000000E-11 " " relative error = 2.49412406069557600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.080000000000699 " " y[1] (closed_form) = 119.29830400003505 " " y[1] (numeric) = 119.29830400000523 " " absolute error = 2.981437319249380400000000000E-11 " " relative error = 2.4991447650827500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.090000000000702 " " y[1] (closed_form) = 119.80027633336864 " " y[1] (numeric) = 119.80027633333869 " " absolute error = 2.995648173964582400000000000E-11 " " relative error = 2.500535278924217500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.100000000000706 " " y[1] (closed_form) = 120.30366666670224 " " y[1] (numeric) = 120.3036666666721 " " absolute error = 3.01412228509434500000000000E-11 " " relative error = 2.50542844504056700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.110000000000709 " " y[1] (closed_form) = 120.80847700003585 " " y[1] (numeric) = 120.80847700000557 " " absolute error = 3.02833313980954700000000000E-11 " " relative error = 2.506722388205132600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.120000000000712 " " y[1] (closed_form) = 121.31470933336945 " " y[1] (numeric) = 121.314709333339 " " absolute error = 3.045386165467789400000000000E-11 " " relative error = 2.51031897302671900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.130000000000716 " " y[1] (closed_form) = 121.82236566670305 " " y[1] (numeric) = 121.82236566667241 " " absolute error = 3.06386027659755200000000000E-11 " " relative error = 2.515022803760063600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.140000000000719 " " y[1] (closed_form) = 122.33144800003666 " " y[1] (numeric) = 122.33144800000585 " " absolute error = 3.080913302255794400000000000E-11 " " relative error = 2.518496553931799400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.1500000000007224 " " y[1] (closed_form) = 122.84195833337027 " " y[1] (numeric) = 122.84195833333928 " " absolute error = 3.09938741338555700000000000E-11 " " relative error = 2.523069035560630600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.160000000000726 " " y[1] (closed_form) = 123.35389866670387 " " y[1] (numeric) = 123.3538986666727 " " absolute error = 3.116440439043799400000000000E-11 " " relative error = 2.52642232854290800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.170000000000730 " " y[1] (closed_form) = 123.86727100003748 " " y[1] (numeric) = 123.86727100000614 " " absolute error = 3.13349346470204200000000000E-11 " " relative error = 2.5297186572400500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.1800000000007325 " " y[1] (closed_form) = 124.38207733337107 " " y[1] (numeric) = 124.38207733333957 " " absolute error = 3.15054649036028400000000000E-11 " " relative error = 2.53295857241243300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.190000000000736 " " y[1] (closed_form) = 124.89831966670471 " " y[1] (numeric) = 124.898319666673 " " absolute error = 3.17044168696156700000000000E-11 " " relative error = 2.53841820724409700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.200000000000740 " " y[1] (closed_form) = 125.41600000003831 " " y[1] (numeric) = 125.41600000000643 " " absolute error = 3.187494712619809400000000000E-11 " " relative error = 2.541537533184630000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.2100000000007425 " " y[1] (closed_form) = 125.93512033337193 " " y[1] (numeric) = 125.93512033333988 " " absolute error = 3.20454773827805200000000000E-11 " " relative error = 2.544602117181500300000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.220000000000746 " " y[1] (closed_form) = 126.45568266670554 " " y[1] (numeric) = 126.45568266667334 " " absolute error = 3.22017967846477400000000000E-11 " " relative error = 2.546488706997913000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.230000000000750 " " y[1] (closed_form) = 126.97768900003916 " " y[1] (numeric) = 126.97768900000678 " " absolute error = 3.238653789594536600000000000E-11 " " relative error = 2.550569170930129000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.2400000000007525 " " y[1] (closed_form) = 127.50114133337276 " " y[1] (numeric) = 127.50114133334019 " " absolute error = 3.25712790072429900000000000E-11 " " relative error = 2.554587250484292600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.250000000000756 " " y[1] (closed_form) = 128.02604166670636 " " y[1] (numeric) = 128.02604166667365 " " absolute error = 3.27133875543950100000000000E-11 " " relative error = 2.555213543160122000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.260000000000760 " " y[1] (closed_form) = 128.55239200004002 " " y[1] (numeric) = 128.55239200000705 " " absolute error = 3.29691829392686500000000000E-11 " " relative error = 2.5646495118704900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.2700000000007625 " " y[1] (closed_form) = 129.08019433337364 " " y[1] (numeric) = 129.0801943333405 " " absolute error = 3.31397131958510700000000000E-11 " " relative error = 2.567373977626776000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.280000000000766 " " y[1] (closed_form) = 129.60945066670723 " " y[1] (numeric) = 129.6094506666739 " " absolute error = 3.3338665161863900000000000E-11 " " relative error = 2.572240295007098000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.290000000000770 " " y[1] (closed_form) = 130.14016300004087 " " y[1] (numeric) = 130.1401630000073 " " absolute error = 3.35660388373071330000000000E-11 " " relative error = 2.579222129704616400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.3000000000007725 " " y[1] (closed_form) = 130.6723333333745 " " y[1] (numeric) = 130.67233333334073 " " absolute error = 3.37649908033199600000000000E-11 " " relative error = 2.583943359852454700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.310000000000776 " " y[1] (closed_form) = 131.2059636667081 " " y[1] (numeric) = 131.2059636666742 " " absolute error = 3.39070993504719800000000000E-11 " " relative error = 2.584265105251118400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.320000000000780 " " y[1] (closed_form) = 131.74105600004174 " " y[1] (numeric) = 131.74105600000766 " " absolute error = 3.407762960705440500000000000E-11 " " relative error = 2.58671295355668100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.330000000000783 " " y[1] (closed_form) = 132.27761233337537 " " y[1] (numeric) = 132.27761233334112 " " absolute error = 3.42481598636368300000000000E-11 " " relative error = 2.58911234180143830000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.340000000000786 " " y[1] (closed_form) = 132.815634666709 " " y[1] (numeric) = 132.81563466667455 " " absolute error = 3.44471118296496570000000000E-11 " " relative error = 2.593603675959696400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.350000000000790 " " y[1] (closed_form) = 133.35512500004262 " " y[1] (numeric) = 133.35512500000803 " " absolute error = 3.45892203768016770000000000E-11 " " relative error = 2.59376760936564100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.360000000000793 " " y[1] (closed_form) = 133.89608533337628 " " y[1] (numeric) = 133.8960853333415 " " absolute error = 3.478817234281450500000000000E-11 " " relative error = 2.598147082209195700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.370000000000796 " " y[1] (closed_form) = 134.4385176667099 " " y[1] (numeric) = 134.4385176666749 " " absolute error = 3.50155460182577370000000000E-11 " " relative error = 2.604576919322013600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.380000000000800 " " y[1] (closed_form) = 134.98242400004352 " " y[1] (numeric) = 134.9824240000084 " " absolute error = 3.51292328559793530000000000E-11 " " relative error = 2.602504223510464500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.390000000000803 " " y[1] (closed_form) = 135.52780633337716 " " y[1] (numeric) = 135.52780633334186 " " absolute error = 3.52997631125617800000000000E-11 " " relative error = 2.604614069066380000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.400000000000806 " " y[1] (closed_form) = 136.07466666671078 " " y[1] (numeric) = 136.0746666666753 " " absolute error = 3.5470293369144200000000000E-11 " " relative error = 2.606678688842354000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.410000000000810 " " y[1] (closed_form) = 136.62300700004442 " " y[1] (numeric) = 136.6230070000088 " " absolute error = 3.56124019162962200000000000E-11 " " relative error = 2.6066182188688497000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.420000000000813 " " y[1] (closed_form) = 137.17282933337808 " " y[1] (numeric) = 137.17282933334224 " " absolute error = 3.583977559173945300000000000E-11 " " relative error = 2.61274596185781300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.430000000000816 " " y[1] (closed_form) = 137.7241356667117 " " y[1] (numeric) = 137.7241356666757 " " absolute error = 3.60103058483218800000000000E-11 " " relative error = 2.614669220757772000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.440000000000820 " " y[1] (closed_form) = 138.27692800004536 " " y[1] (numeric) = 138.27692800000915 " " absolute error = 3.620925781433470500000000000E-11 " " relative error = 2.618604443853629000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.450000000000823 " " y[1] (closed_form) = 138.83120833337898 " " y[1] (numeric) = 138.83120833334263 " " absolute error = 3.635136636148672600000000000E-11 " " relative error = 2.61838579364628500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.460000000000826 " " y[1] (closed_form) = 139.38697866671262 " " y[1] (numeric) = 139.3869786666761 " " absolute error = 3.65218966180691500000000000E-11 " " relative error = 2.620179945602841300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.470000000000830 " " y[1] (closed_form) = 139.94424100004628 " " y[1] (numeric) = 139.94424100000953 " " absolute error = 3.67492702935123800000000000E-11 " " relative error = 2.625993755148540000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.480000000000833 " " y[1] (closed_form) = 140.5029973333799 " " y[1] (numeric) = 140.502997333343 " " absolute error = 3.691980055009480600000000000E-11 " " relative error = 2.627687754055023600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.490000000000836 " " y[1] (closed_form) = 141.06324966671355 " " y[1] (numeric) = 141.06324966667646 " " absolute error = 3.70903308066772300000000000E-11 " " relative error = 2.629340447941585500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.500000000000840 " " y[1] (closed_form) = 141.6250000000472 " " y[1] (numeric) = 141.6250000000099 " " absolute error = 3.73177044821204600000000000E-11 " " relative error = 2.634965894588386400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.510000000000843 " " y[1] (closed_form) = 142.18825033338084 " " y[1] (numeric) = 142.18825033334335 " " absolute error = 3.748823473870288600000000000E-11 " " relative error = 2.636521277307113400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.520000000000846 " " y[1] (closed_form) = 142.7530026667145 " " y[1] (numeric) = 142.75300266667682 " " absolute error = 3.768718670471571400000000000E-11 " " relative error = 2.64002760016922400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.530000000000850 " " y[1] (closed_form) = 143.31925900004816 " " y[1] (numeric) = 143.31925900001025 " " absolute error = 3.791456038015894600000000000E-11 " " relative error = 2.645461652864547000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.540000000000853 " " y[1] (closed_form) = 143.8870213333818 " " y[1] (numeric) = 143.8870213333437 " " absolute error = 3.80850906367413700000000000E-11 " " relative error = 2.646874630096024400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.550000000000856 " " y[1] (closed_form) = 144.45629166671546 " " y[1] (numeric) = 144.45629166667715 " " absolute error = 3.8312464312184600000000000E-11 " " relative error = 2.652183845379182000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.560000000000860 " " y[1] (closed_form) = 145.0270720000491 " " y[1] (numeric) = 145.0270720000106 " " absolute error = 3.848299456876702600000000000E-11 " " relative error = 2.6535042070458403000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.570000000000863 " " y[1] (closed_form) = 145.59936433338277 " " y[1] (numeric) = 145.59936433334406 " " absolute error = 3.87103682442102600000000000E-11 " " relative error = 2.658690745075925600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.580000000000866 " " y[1] (closed_form) = 146.1731706667164 " " y[1] (numeric) = 146.17317066667755 " " absolute error = 3.88524767913622800000000000E-11 " " relative error = 2.65797592089920900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.590000000000870 " " y[1] (closed_form) = 146.74849300005008 " " y[1] (numeric) = 146.74849300001105 " " absolute error = 3.9023007047944700000000000E-11 " " relative error = 2.659175999029263500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.600000000000873 " " y[1] (closed_form) = 147.32533333338372 " " y[1] (numeric) = 147.3253333333445 " " absolute error = 3.92219590139575300000000000E-11 " " relative error = 2.66226847253770160000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.610000000000876 " " y[1] (closed_form) = 147.9036936667174 " " y[1] (numeric) = 147.90369366667795 " " absolute error = 3.94493326894007600000000000E-11 " " relative error = 2.667231068501570400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.620000000000880 " " y[1] (closed_form) = 148.48357600005104 " " y[1] (numeric) = 148.48357600001142 " " absolute error = 3.961986294598318600000000000E-11 " " relative error = 2.66829935089720400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.630000000000883 " " y[1] (closed_form) = 149.0649823333847 " " y[1] (numeric) = 149.06498233334491 " " absolute error = 3.97903932025656100000000000E-11 " " relative error = 2.669332030883964600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.640000000000886 " " y[1] (closed_form) = 149.64791466671838 " " y[1] (numeric) = 149.6479146666784 " " absolute error = 3.99893451685784400000000000E-11 " " relative error = 2.672228694775928300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.650000000000890 " " y[1] (closed_form) = 150.23237500005206 " " y[1] (numeric) = 150.23237500001187 " " absolute error = 4.018829713459126700000000000E-11 " " relative error = 2.675075670911635000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.660000000000893 " " y[1] (closed_form) = 150.8183653333857 " " y[1] (numeric) = 150.81836533334533 " " absolute error = 4.038724910060409500000000000E-11 " " relative error = 2.677873414907237500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.670000000000896 " " y[1] (closed_form) = 151.40588766671937 " " y[1] (numeric) = 151.40588766667872 " " absolute error = 4.06430444854777300000000000E-11 " " relative error = 2.684376751249119600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.680000000000900 " " y[1] (closed_form) = 151.99494400005307 " " y[1] (numeric) = 151.9949440000122 " " absolute error = 4.08704181609209600000000000E-11 " " relative error = 2.688932742454031600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.690000000000903 " " y[1] (closed_form) = 152.5855363333867 " " y[1] (numeric) = 152.5855363333457 " " absolute error = 4.10125267080729800000000000E-11 " " relative error = 2.68783842122912800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.700000000000906 " " y[1] (closed_form) = 153.17766666672037 " " y[1] (numeric) = 153.17766666667913 " " absolute error = 4.123990038351621500000000000E-11 " " relative error = 2.692291982306065000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.7100000000009095 " " y[1] (closed_form) = 153.77133700005405 " " y[1] (numeric) = 153.77133700001266 " " absolute error = 4.138200893066823500000000000E-11 " " relative error = 2.691139307103357400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.720000000000913 " " y[1] (closed_form) = 154.36654933338772 " " y[1] (numeric) = 154.36654933334611 " " absolute error = 4.16093826061114670000000000E-11 " " relative error = 2.69549217662740300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.730000000000916 " " y[1] (closed_form) = 154.9633056667214 " " y[1] (numeric) = 154.9633056666796 " " absolute error = 4.180833457212429500000000000E-11 " " relative error = 2.697950614324220500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.7400000000009195 " " y[1] (closed_form) = 155.56160800005506 " " y[1] (numeric) = 155.56160800001308 " " absolute error = 4.19788648287067200000000000E-11 " " relative error = 2.698536314222970700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.750000000000923 " " y[1] (closed_form) = 156.16145833338874 " " y[1] (numeric) = 156.1614583333466 " " absolute error = 4.21493950852891430000000000E-11 " " relative error = 2.699090770227343700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.760000000000926 " " y[1] (closed_form) = 156.76285866672242 " " y[1] (numeric) = 156.7628586666801 " " absolute error = 4.23199253418715670000000000E-11 " " relative error = 2.699614290132566500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.7700000000009295 " " y[1] (closed_form) = 157.3658110000561 " " y[1] (numeric) = 157.36581100001354 " " absolute error = 4.2575720726745203000000000E-11 " " relative error = 2.705525454110869000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.780000000000933 " " y[1] (closed_form) = 157.9703173333898 " " y[1] (numeric) = 157.970317333347 " " absolute error = 4.280309440218843500000000000E-11 " " relative error = 2.709565640224314000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.790000000000936 " " y[1] (closed_form) = 158.57637966672348 " " y[1] (numeric) = 158.5763796666805 " " absolute error = 4.29736246587708600000000000E-11 " " relative error = 2.709963788370474000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.8000000000009395 " " y[1] (closed_form) = 159.18400000005715 " " y[1] (numeric) = 159.184000000014 " " absolute error = 4.314415491535328300000000000E-11 " " relative error = 2.710332377333010700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.810000000000943 " " y[1] (closed_form) = 159.79318033339084 " " y[1] (numeric) = 159.7931803333475 " " absolute error = 4.33431068813661100000000000E-11 " " relative error = 2.712450355574343400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.820000000000946 " " y[1] (closed_form) = 160.40392266672453 " " y[1] (numeric) = 160.40392266668098 " " absolute error = 4.35420588473789400000000000E-11 " " relative error = 2.714525812304941500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.8300000000009495 " " y[1] (closed_form) = 161.01622900005822 " " y[1] (numeric) = 161.01622900001448 " " absolute error = 4.37410108133917700000000000E-11 " " relative error = 2.716559137239262000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.840000000000953 " " y[1] (closed_form) = 161.63010133339188 " " y[1] (numeric) = 161.63010133334794 " " absolute error = 4.393996277940459500000000000E-11 " " relative error = 2.718550716538271600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.850000000000956 " " y[1] (closed_form) = 162.2455416667256 " " y[1] (numeric) = 162.24554166668142 " " absolute error = 4.41673364548478300000000000E-11 " " relative error = 2.722252704211346000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.8600000000009596 " " y[1] (closed_form) = 162.86255200005928 " " y[1] (numeric) = 162.8625520000149 " " absolute error = 4.43947101302910600000000000E-11 " " relative error = 2.725900434758931000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.870000000000963 " " y[1] (closed_form) = 163.48113433339296 " " y[1] (numeric) = 163.48113433334836 " " absolute error = 4.45936620963038900000000000E-11 " " relative error = 2.727755852572103500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.880000000000966 " " y[1] (closed_form) = 164.10129066672664 " " y[1] (numeric) = 164.1012906666818 " " absolute error = 4.484945748117752400000000000E-11 " " relative error = 2.733035023610040000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.89000000000097 " " y[1] (closed_form) = 164.72302300006032 " " y[1] (numeric) = 164.72302300001522 " " absolute error = 4.51052528660511600000000000E-11 " " relative error = 2.738248245118391000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.900000000000973 " " y[1] (closed_form) = 165.34633333339406 " " y[1] (numeric) = 165.34633333334872 " " absolute error = 4.53326265414943900000000000E-11 " " relative error = 2.741677158941801500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.910000000000976 " " y[1] (closed_form) = 165.97122366672772 " " y[1] (numeric) = 165.97122366668222 " " absolute error = 4.550315679807681600000000000E-11 " " relative error = 2.741629289270513500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.92000000000098 " " y[1] (closed_form) = 166.59769600006143 " " y[1] (numeric) = 166.59769600001567 " " absolute error = 4.57589521829504500000000000E-11 " " relative error = 2.74667377050241900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.930000000000983 " " y[1] (closed_form) = 167.22575233339512 " " y[1] (numeric) = 167.2257523333492 " " absolute error = 4.592948243953287600000000000E-11 " " relative error = 2.74655558720190700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.940000000000986 " " y[1] (closed_form) = 167.85539466672884 " " y[1] (numeric) = 167.85539466668266 " " absolute error = 4.61852778244065100000000000E-11 " " relative error = 2.751492015857208700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.95000000000099 " " y[1] (closed_form) = 168.48662500006253 " " y[1] (numeric) = 168.48662500001618 " " absolute error = 4.635580808098893600000000000E-11 " " relative error = 2.751304922926181000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.960000000000993 " " y[1] (closed_form) = 169.11944533339624 " " y[1] (numeric) = 169.11944533334966 " " absolute error = 4.65831817564321700000000000E-11 " " relative error = 2.754454501940903000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.970000000000996 " " y[1] (closed_form) = 169.75385766672994 " " y[1] (numeric) = 169.7538576666832 " " absolute error = 4.67537120130145900000000000E-11 " " relative error = 2.754206158001077000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.980000000001 " " y[1] (closed_form) = 170.38986400006365 " " y[1] (numeric) = 170.38986400001667 " " absolute error = 4.698108568845782400000000000E-11 " " relative error = 2.757269979888022000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.990000000001003 " " y[1] (closed_form) = 171.02746633339734 " " y[1] (numeric) = 171.02746633335016 " " absolute error = 4.71800376544706500000000000E-11 " " relative error = 2.75862343434936200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.000000000001005 " " y[1] (closed_form) = 171.666666666731 " " y[1] (numeric) = 171.66666666668365 " " absolute error = 4.735056791105307600000000000E-11 " " relative error = 2.75828550938069900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.010000000001 " " y[1] (closed_form) = 172.30746700006412 " " y[1] (numeric) = 172.30746700001717 " " absolute error = 4.69526639790274200000000000E-11 " " relative error = 2.724934954734721000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.020000000000994 " " y[1] (closed_form) = 172.9498693333973 " " y[1] (numeric) = 172.94986933335068 " " absolute error = 4.66116034658625700000000000E-11 " " relative error = 2.695093303366936600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.030000000000989 " " y[1] (closed_form) = 173.5938756667304 " " y[1] (numeric) = 173.59387566668417 " " absolute error = 4.62421212432673200000000000E-11 " " relative error = 2.663810636502178500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.040000000000983 " " y[1] (closed_form) = 174.23948800006355 " " y[1] (numeric) = 174.23948800001764 " " absolute error = 4.59010607301024700000000000E-11 " " relative error = 2.634366139212124000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.050000000000978 " " y[1] (closed_form) = 174.88670833339668 " " y[1] (numeric) = 174.88670833335115 " " absolute error = 4.55315785075072200000000000E-11 " " relative error = 2.60348993593656800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.060000000000972 " " y[1] (closed_form) = 175.5355386667298 " " y[1] (numeric) = 175.53553866668466 " " absolute error = 4.513367457548156400000000000E-11 " " relative error = 2.57119868251704630000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.070000000000967 " " y[1] (closed_form) = 176.18598100006295 " " y[1] (numeric) = 176.18598100001813 " " absolute error = 4.48210357717471200000000000E-11 " " relative error = 2.543961529591341500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.080000000000961 " " y[1] (closed_form) = 176.83803733339607 " " y[1] (numeric) = 176.83803733335162 " " absolute error = 4.44515535491518700000000000E-11 " " relative error = 2.513687338960142000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.090000000000956 " " y[1] (closed_form) = 177.4917096667292 " " y[1] (numeric) = 177.49170966668513 " " absolute error = 4.408207132655661600000000000E-11 " " relative error = 2.483612976027341500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.10000000000095 " " y[1] (closed_form) = 178.1470000000623 " " y[1] (numeric) = 178.14700000001864 " " absolute error = 4.365574568510055500000000000E-11 " " relative error = 2.450546216612420600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.110000000000944 " " y[1] (closed_form) = 178.80391033339544 " " y[1] (numeric) = 178.80391033335215 " " absolute error = 4.328626346250530300000000000E-11 " " relative error = 2.420879016672191400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.120000000000939 " " y[1] (closed_form) = 179.46244266672855 " " y[1] (numeric) = 179.4624426666856 " " absolute error = 4.294520294934045500000000000E-11 " " relative error = 2.39299110784377400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.130000000000933 " " y[1] (closed_form) = 180.12259900006168 " " y[1] (numeric) = 180.1225990000191 " " absolute error = 4.2575720726745203000000000E-11 " " relative error = 2.36370788358048420000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.140000000000928 " " y[1] (closed_form) = 180.78438133339478 " " y[1] (numeric) = 180.7843813333526 " " absolute error = 4.21778167947195470000000000E-11 " " relative error = 2.333045392728757500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.150000000000922 " " y[1] (closed_form) = 181.4477916667279 " " y[1] (numeric) = 181.4477916666861 " " absolute error = 4.180833457212429500000000000E-11 " " relative error = 2.304152295714640400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.160000000000917 " " y[1] (closed_form) = 182.11283200006102 " " y[1] (numeric) = 182.1128320000196 " " absolute error = 4.14104306400986400000000000E-11 " " relative error = 2.27388867579000480000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.170000000000911 " " y[1] (closed_form) = 182.77950433339413 " " y[1] (numeric) = 182.7795043333531 " " absolute error = 4.104094841750338700000000000E-11 " " relative error = 2.245380222863704300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.180000000000906 " " y[1] (closed_form) = 183.44781066672726 " " y[1] (numeric) = 183.4478106666866 " " absolute error = 4.067146619490813500000000000E-11 " " relative error = 2.2170592304749100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.1900000000009 " " y[1] (closed_form) = 184.1177530000604 " " y[1] (numeric) = 184.1177530000201 " " absolute error = 4.03019839723128800000000000E-11 " " relative error = 2.18892438755211530000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.200000000000895 " " y[1] (closed_form) = 184.78933333339347 " " y[1] (numeric) = 184.78933333335357 " " absolute error = 3.990408004028722600000000000E-11 " " relative error = 2.1594363332808300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.210000000000889 " " y[1] (closed_form) = 185.46255366672656 " " y[1] (numeric) = 185.46255366668706 " " absolute error = 3.95061761082615700000000000E-11 " " relative error = 2.130143003382428400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.220000000000883 " " y[1] (closed_form) = 186.13741600005966 " " y[1] (numeric) = 186.13741600002055 " " absolute error = 3.910827217623591400000000000E-11 " " relative error = 2.101043036732785600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.230000000000878 " " y[1] (closed_form) = 186.81392233339278 " " y[1] (numeric) = 186.81392233335401 " " absolute error = 3.876721166307106600000000000E-11 " " relative error = 2.075177865699224200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.240000000000872 " " y[1] (closed_form) = 187.4920746667259 " " y[1] (numeric) = 187.4920746666875 " " absolute error = 3.839772944047581400000000000E-11 " " relative error = 2.047965467805996600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.250000000000867 " " y[1] (closed_form) = 188.171875000059 " " y[1] (numeric) = 188.17187500002098 " " absolute error = 3.80282472178805600000000000E-11 " " relative error = 2.02093151369558500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.260000000000861 " " y[1] (closed_form) = 188.8533253333921 " " y[1] (numeric) = 188.85332533335446 " " absolute error = 3.763034328585490600000000000E-11 " " relative error = 1.992569800898354000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.270000000000856 " " y[1] (closed_form) = 189.53642766672516 " " y[1] (numeric) = 189.53642766668793 " " absolute error = 3.72324393538292500000000000E-11 " " relative error = 1.964394908787538400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.28000000000085 " " y[1] (closed_form) = 190.22118400005826 " " y[1] (numeric) = 190.22118400002142 " " absolute error = 3.683453542180359400000000000E-11 " " relative error = 1.93640553839641320000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.290000000000845 " " y[1] (closed_form) = 190.90759633339138 " " y[1] (numeric) = 190.9075963333549 " " absolute error = 3.649347490863874600000000000E-11 " " relative error = 1.911577936632148600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.30000000000084 " " y[1] (closed_form) = 191.59566666672447 " " y[1] (numeric) = 191.59566666668835 " " absolute error = 3.612399268604349300000000000E-11 " " relative error = 1.885428481473968300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.310000000000834 " " y[1] (closed_form) = 192.28539700005754 " " y[1] (numeric) = 192.28539700002182 " " absolute error = 3.57260887540178400000000000E-11 " " relative error = 1.857972020309329500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.320000000000828 " " y[1] (closed_form) = 192.97678933339063 " " y[1] (numeric) = 192.9767893333553 " " absolute error = 3.53281848219921800000000000E-11 " " relative error = 1.830696061636640500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.330000000000823 " " y[1] (closed_form) = 193.66984566672375 " " y[1] (numeric) = 193.66984566668876 " " absolute error = 3.49871243088273330000000000E-11 " " relative error = 1.80653442400294130000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.340000000000817 " " y[1] (closed_form) = 194.3645680000568 " " y[1] (numeric) = 194.36456800002222 " " absolute error = 3.45892203768016770000000000E-11 " " relative error = 1.779605240436187300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.350000000000811 " " y[1] (closed_form) = 195.0609583333899 " " y[1] (numeric) = 195.0609583333557 " " absolute error = 3.41913164447760200000000000E-11 " " relative error = 1.752852889522755200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.360000000000806 " " y[1] (closed_form) = 195.75901866672297 " " y[1] (numeric) = 195.75901866668917 " " absolute error = 3.379341251275036500000000000E-11 " " relative error = 1.726276150284712000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.3700000000008 " " y[1] (closed_form) = 196.45875100005608 " " y[1] (numeric) = 196.45875100002263 " " absolute error = 3.345235199958551700000000000E-11 " " relative error = 1.702767213437897000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.380000000000795 " " y[1] (closed_form) = 197.16015733338912 " " y[1] (numeric) = 197.1601573333561 " " absolute error = 3.302602635812945700000000000E-11 " " relative error = 1.675086224560264600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.39000000000079 " " y[1] (closed_form) = 197.86323966672222 " " y[1] (numeric) = 197.8632396666896 " " absolute error = 3.2628122426103800000000000E-11 " " relative error = 1.64902396630430710000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.400000000000784 " " y[1] (closed_form) = 198.56800000005526 " " y[1] (numeric) = 198.56800000002306 " " absolute error = 3.22017967846477400000000000E-11 " " relative error = 1.621701219966902300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.410000000000778 " " y[1] (closed_form) = 199.27444033338833 " " y[1] (numeric) = 199.27444033335655 " " absolute error = 3.17754711431916800000000000E-11 " " relative error = 1.594558293077173700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.420000000000773 " " y[1] (closed_form) = 199.98256266672144 " " y[1] (numeric) = 199.98256266669003 " " absolute error = 3.14059889205964300000000000E-11 " " relative error = 1.570436367141454500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.430000000000767 " " y[1] (closed_form) = 200.69236900005447 " " y[1] (numeric) = 200.69236900002352 " " absolute error = 3.095124156970996400000000000E-11 " " relative error = 1.542223141015469400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.440000000000762 " " y[1] (closed_form) = 201.40386133338757 " " y[1] (numeric) = 201.40386133335699 " " absolute error = 3.05817593471147100000000000E-11 " " relative error = 1.51842964403210500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.450000000000756 " " y[1] (closed_form) = 202.11704166672064 " " y[1] (numeric) = 202.11704166669045 " " absolute error = 3.018385541508905600000000000E-11 " " relative error = 1.49338497962287100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.46000000000075 " " y[1] (closed_form) = 202.83191200005368 " " y[1] (numeric) = 202.83191200002392 " " absolute error = 2.975752977363299600000000000E-11 " " relative error = 1.467102956344715500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.470000000000745 " " y[1] (closed_form) = 203.54847433338676 " " y[1] (numeric) = 203.54847433335738 " " absolute error = 2.938804755103774400000000000E-11 " " relative error = 1.443786186424754200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.48000000000074 " " y[1] (closed_form) = 204.26673066671984 " " y[1] (numeric) = 204.26673066669085 " " absolute error = 2.899014361901209000000000000E-11 " " relative error = 1.41922982388709200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.490000000000734 " " y[1] (closed_form) = 204.9866830000529 " " y[1] (numeric) = 204.98668300002433 " " absolute error = 2.856381797755603000000000000E-11 " " relative error = 1.393447494223254400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.500000000000728 " " y[1] (closed_form) = 205.70833333338592 " " y[1] (numeric) = 205.70833333335779 " " absolute error = 2.813749233609997000000000000E-11 " " relative error = 1.36783434487791480000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.510000000000723 " " y[1] (closed_form) = 206.43168366671898 " " y[1] (numeric) = 206.43168366669124 " " absolute error = 2.77395884040743100000000000E-11 " " relative error = 1.343766030066367300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.520000000000717 " " y[1] (closed_form) = 207.15673600005204 " " y[1] (numeric) = 207.15673600002472 " " absolute error = 2.73132627626182500000000000E-11 " " relative error = 1.31848296560394700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.530000000000712 " " y[1] (closed_form) = 207.8834923333851 " " y[1] (numeric) = 207.8834923333582 " " absolute error = 2.691535883059259500000000000E-11 " " relative error = 1.294732858702803000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.540000000000706 " " y[1] (closed_form) = 208.61195466671813 " " y[1] (numeric) = 208.61195466669164 " " absolute error = 2.648903318913653500000000000E-11 " " relative error = 1.26977541778254520000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.5500000000007 " " y[1] (closed_form) = 209.34212500005123 " " y[1] (numeric) = 209.3421250000251 " " absolute error = 2.611955096654128300000000000E-11 " " relative error = 1.247696848712837500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.560000000000695 " " y[1] (closed_form) = 210.07400533338424 " " y[1] (numeric) = 210.07400533335857 " " absolute error = 2.56648036156548200000000000E-11 " " relative error = 1.221702969623736500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.57000000000069 " " y[1] (closed_form) = 210.80759766671727 " " y[1] (numeric) = 210.80759766669203 " " absolute error = 2.52384779741987600000000000E-11 " " relative error = 1.197228100578248800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.580000000000684 " " y[1] (closed_form) = 211.54290400005033 " " y[1] (numeric) = 211.5429040000255 " " absolute error = 2.484057404217310200000000000E-11 " " relative error = 1.174257021741896600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.590000000000678 " " y[1] (closed_form) = 212.2799263333834 " " y[1] (numeric) = 212.2799263333589 " " absolute error = 2.449951352900825400000000000E-11 " " relative error = 1.154113530759946900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.600000000000673 " " y[1] (closed_form) = 213.01866666671643 " " y[1] (numeric) = 213.01866666669235 " " absolute error = 2.407318788755219400000000000E-11 " " relative error = 1.13009757615357200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.610000000000667 " " y[1] (closed_form) = 213.75912700004943 " " y[1] (numeric) = 213.75912700002584 " " absolute error = 2.359001882723532600000000000E-11 " " relative error = 1.103579489601390100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.620000000000662 " " y[1] (closed_form) = 214.5013093333825 " " y[1] (numeric) = 214.50130933335933 " " absolute error = 2.316369318577926600000000000E-11 " " relative error = 1.079885864462382500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.630000000000656 " " y[1] (closed_form) = 215.24521566671552 " " y[1] (numeric) = 215.2452156666928 " " absolute error = 2.273736754432320600000000000E-11 " " relative error = 1.056347174727898200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.64000000000065 " " y[1] (closed_form) = 215.99084800004857 " " y[1] (numeric) = 215.99084800002623 " " absolute error = 2.23394636122975500000000000E-11 " " relative error = 1.03427824924751100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.650000000000645 " " y[1] (closed_form) = 216.73820833338158 " " y[1] (numeric) = 216.73820833335967 " " absolute error = 2.19131379708414900000000000E-11 " " relative error = 1.011041760441943900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.66000000000064 " " y[1] (closed_form) = 217.48729866671465 " " y[1] (numeric) = 217.48729866669316 " " absolute error = 2.14868123293854300000000000E-11 " " relative error = 9.879571111098582000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.670000000000634 " " y[1] (closed_form) = 218.23812100004764 " " y[1] (numeric) = 218.23812100002658 " " absolute error = 2.10604866879293700000000000E-11 " " relative error = 9.650232778500127000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.680000000000629 " " y[1] (closed_form) = 218.9906773333807 " " y[1] (numeric) = 218.99067733336 " " absolute error = 2.069100446533411700000000000E-11 " " relative error = 9.448349453632287000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.690000000000623 " " y[1] (closed_form) = 219.7449696667137 " " y[1] (numeric) = 219.7449696666934 " " absolute error = 2.02931005333084600000000000E-11 " " relative error = 9.234841900630046000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.700000000000617 " " y[1] (closed_form) = 220.50100000004673 " " y[1] (numeric) = 220.5010000000268 " " absolute error = 1.99236183107132100000000000E-11 " " relative error = 9.035613584840425000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.710000000000612 " " y[1] (closed_form) = 221.25877033337977 " " y[1] (numeric) = 221.25877033336022 " " absolute error = 1.955413608811795700000000000E-11 " " relative error = 8.837677285585077000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.720000000000606 " " y[1] (closed_form) = 222.01828266671274 " " y[1] (numeric) = 222.01828266669366 " " absolute error = 1.90709670278010900000000000E-11 " " relative error = 8.589818279258495000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.7300000000006 " " y[1] (closed_form) = 222.77953900004576 " " y[1] (numeric) = 222.77953900002714 " " absolute error = 1.861621967691462500000000000E-11 " " relative error = 8.356341771993164000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.740000000000595 " " y[1] (closed_form) = 223.54254133337878 " " y[1] (numeric) = 223.54254133336053 " " absolute error = 1.824673745431937300000000000E-11 " " relative error = 8.162534677060512000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.75000000000059 " " y[1] (closed_form) = 224.3072916667118 " " y[1] (numeric) = 224.30729166669394 " " absolute error = 1.784883352229371700000000000E-11 " " relative error = 7.95731310813315000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.760000000000584 " " y[1] (closed_form) = 225.07379200004482 " " y[1] (numeric) = 225.07379200002737 " " absolute error = 1.74509295902680600000000000E-11 " " relative error = 7.753425858779943000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.770000000000579 " " y[1] (closed_form) = 225.84204433337783 " " y[1] (numeric) = 225.8420443333608 " " absolute error = 1.702460394881200000000000E-11 " " relative error = 7.538279242496162000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.780000000000573 " " y[1] (closed_form) = 226.61205066671084 " " y[1] (numeric) = 226.61205066669424 " " absolute error = 1.65982783073559400000000000E-11 " " relative error = 7.324534709660177000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.790000000000568 " " y[1] (closed_form) = 227.38381300004383 " " y[1] (numeric) = 227.3838130000277 " " absolute error = 1.614353095646947600000000000E-11 " " relative error = 7.099683457443984000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.800000000000562 " " y[1] (closed_form) = 228.1573333333768 " " y[1] (numeric) = 228.15733333336112 " " absolute error = 1.568878360558301200000000000E-11 " " relative error = 6.8763003916508000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.810000000000556 " " y[1] (closed_form) = 228.93261366670984 " " y[1] (numeric) = 228.93261366669455 " " absolute error = 1.529087967355735600000000000E-11 " " relative error = 6.679205478262913000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.820000000000551 " " y[1] (closed_form) = 229.70965600004286 " " y[1] (numeric) = 229.70965600002802 " " absolute error = 1.483613232267089200000000000E-11 " " relative error = 6.458645483613508000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.830000000000545 " " y[1] (closed_form) = 230.48846233337582 " " y[1] (numeric) = 230.4884623333615 " " absolute error = 1.43245415529236200000000000E-11 " " relative error = 6.21486273451934100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.84000000000054 " " y[1] (closed_form) = 231.26903466670888 " " y[1] (numeric) = 231.26903466669492 " " absolute error = 1.395505933032836800000000000E-11 " " relative error = 6.034123569737543000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.850000000000534 " " y[1] (closed_form) = 232.05137500004184 " " y[1] (numeric) = 232.05137500002837 " " absolute error = 1.3471890270011500000000000E-11 " " relative error = 5.805563647278138000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.860000000000529 " " y[1] (closed_form) = 232.8354853333748 " " y[1] (numeric) = 232.8354853333618 " " absolute error = 1.301714291912503500000000000E-11 " " relative error = 5.590704054619096000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.870000000000523 " " y[1] (closed_form) = 233.6213676667078 " " y[1] (numeric) = 233.62136766669525 " " absolute error = 1.256239556823857000000000000E-11 " " relative error = 5.377245965857246000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.880000000000518 " " y[1] (closed_form) = 234.4090240000408 " " y[1] (numeric) = 234.4090240000287 " " absolute error = 1.210764821735210700000000000E-11 " " relative error = 5.165180081697708000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.890000000000512 " " y[1] (closed_form) = 235.1984563333738 " " y[1] (numeric) = 235.19845633336212 " " absolute error = 1.168132257589604700000000000E-11 " " relative error = 4.966581310949918000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.900000000000507 " " y[1] (closed_form) = 235.98966666670677 " " y[1] (numeric) = 235.98966666669554 " " absolute error = 1.122657522500958300000000000E-11 " " relative error = 4.757231697295083000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.910000000000501 " " y[1] (closed_form) = 236.7826570000398 " " y[1] (numeric) = 236.78265700002896 " " absolute error = 1.082867129298392700000000000E-11 " " relative error = 4.573253560957426000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.920000000000496 " " y[1] (closed_form) = 237.57742933337275 " " y[1] (numeric) = 237.57742933336237 " " absolute error = 1.037392394209746300000000000E-11 " " relative error = 4.36654440247377000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.93000000000049 " " y[1] (closed_form) = 238.37398566670575 " " y[1] (numeric) = 238.3739856666958 " " absolute error = 9.947598300641403000000000000E-12 " " relative error = 4.173105665376642400000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.940000000000484 " " y[1] (closed_form) = 239.1723280000387 " " y[1] (numeric) = 239.17232800002924 " " absolute error = 9.464429240324534000000000000E-12 " " relative error = 3.957158973810299000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.950000000000479 " " y[1] (closed_form) = 239.97245833337172 " " y[1] (numeric) = 239.97245833336265 " " absolute error = 9.066525308298878000000000000E-12 " " relative error = 3.7781524476878037000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.960000000000473 " " y[1] (closed_form) = 240.77437866670465 " " y[1] (numeric) = 240.774378666696 " " absolute error = 8.640199666842818000000000000E-12 " " relative error = 3.588504605302351000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.970000000000468 " " y[1] (closed_form) = 241.57809100003763 " " y[1] (numeric) = 241.57809100002945 " " absolute error = 8.185452315956354000000000000E-12 " " relative error = 3.3883256060480590000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.980000000000462 " " y[1] (closed_form) = 242.38359733337057 " " y[1] (numeric) = 242.38359733336284 " " absolute error = 7.73070496506989000000000000E-12 " " relative error = 3.189450544558591000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.990000000000457 " " y[1] (closed_form) = 243.19089966670356 " " y[1] (numeric) = 243.19089966669628 " " absolute error = 7.275957614183426000000000000E-12 " " relative error = 2.991870840625708000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.000000000000451 " " y[1] (closed_form) = 244.00000000003655 " " y[1] (numeric) = 244.0000000000297 " " absolute error = 6.849631972727366000000000000E-12 " " relative error = 2.807226218330467000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.010000000000446 " " y[1] (closed_form) = 244.8109003333695 " " y[1] (numeric) = 244.81090033336312 " " absolute error = 6.366462912410498000000000000E-12 " " relative error = 2.600563497679642700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.02000000000044 " " y[1] (closed_form) = 245.62360266670248 " " y[1] (numeric) = 245.62360266669654 " " absolute error = 5.9401372709544380000000000000E-12 " " relative error = 2.418390255033785000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.030000000000435 " " y[1] (closed_form) = 246.43810900003544 " " y[1] (numeric) = 246.43810900002993 " " absolute error = 5.5138116294983770000000000000E-12 " " relative error = 2.2374021825892135000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.040000000000429 " " y[1] (closed_form) = 247.25442133336838 " " y[1] (numeric) = 247.25442133336335 " " absolute error = 5.030642569181509000000000000E-12 " " relative error = 2.0346016633606684000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.050000000000423 " " y[1] (closed_form) = 248.07254166670134 " " y[1] (numeric) = 248.0725416666968 " " absolute error = 4.547473508864641000000000000E-12 " " relative error = 1.8331224722865191000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.060000000000418 " " y[1] (closed_form) = 248.89247200003433 " " y[1] (numeric) = 248.8924720000302 " " absolute error = 4.121147867408581000000000000E-12 " " relative error = 1.6557945020562990000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.070000000000412 " " y[1] (closed_form) = 249.71421433336724 " " y[1] (numeric) = 249.7142143333636 " " absolute error = 3.637978807091713000000000000E-12 " " relative error = 1.4568569181388405000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.080000000000407 " " y[1] (closed_form) = 250.53777066670017 " " y[1] (numeric) = 250.53777066669696 " " absolute error = 3.211653165635653000000000000E-12 " " relative error = 1.2819037852413220000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.090000000000401 " " y[1] (closed_form) = 251.36314300003315 " " y[1] (numeric) = 251.36314300003033 " " absolute error = 2.8137492336099970000000000000E-12 " " relative error = 1.1193961055816468000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.100000000000396 " " y[1] (closed_form) = 252.1903333333661 " " y[1] (numeric) = 252.19033333336375 " " absolute error = 2.3590018827235326000000000000E-12 " " relative error = 9.3540535497259050000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.11000000000039 " " y[1] (closed_form) = 253.01934366669906 " " y[1] (numeric) = 253.01934366669715 " " absolute error = 1.9042545318370685000000000000E-12 " " relative error = 7.5261223282024310000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.120000000000385 " " y[1] (closed_form) = 253.85017600003198 " " y[1] (numeric) = 253.85017600003056 " " absolute error = 1.4210854715202004000000000000E-12 " " relative error = 5.5981267923959250000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.13000000000038 " " y[1] (closed_form) = 254.6828323333649 " " y[1] (numeric) = 254.68283233336393 " " absolute error = 9.6633812063373630000000000000E-13 " " relative error = 3.7942805637125010000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.140000000000374 " " y[1] (closed_form) = 255.51731466669787 " " y[1] (numeric) = 255.51731466669736 " " absolute error = 5.1159076974727210000000000000E-13 " " relative error = 2.00217652731127740000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.150000000000368 " " y[1] (closed_form) = 256.3536250000308 " " y[1] (numeric) = 256.35362500003066 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 4.434766144680122300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.160000000000363 " " y[1] (closed_form) = 257.1917653333637 " " y[1] (numeric) = 257.191765333364 " " absolute error = 2.84217094304040100000000000000E-13 " " relative error = 1.10507851577458930000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.170000000000357 " " y[1] (closed_form) = 258.0317376666967 " " y[1] (numeric) = 258.0317376666974 " " absolute error = 6.8212102632969620000000000000E-13 " " relative error = 2.6435547522095970000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.180000000000351 " " y[1] (closed_form) = 258.8735440000296 " " y[1] (numeric) = 258.87354400003073 " " absolute error = 1.1368683772161603000000000000E-12 " " relative error = 4.39159737858740130000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.190000000000346 " " y[1] (closed_form) = 259.7171863333625 " " y[1] (numeric) = 259.7171863333641 " " absolute error = 1.5916157281026244000000000000E-12 " " relative error = 6.1282649430049290000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.20000000000034 " " y[1] (closed_form) = 260.56266666669546 " " y[1] (numeric) = 260.56266666669757 " " absolute error = 2.1032064978498966000000000000E-12 " " relative error = 8.0717875847511940000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.210000000000335 " " y[1] (closed_form) = 261.4099870000284 " " y[1] (numeric) = 261.409987000031 " " absolute error = 2.5579538487363607000000000000E-12 " " relative error = 9.785218530063591000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.22000000000033 " " y[1] (closed_form) = 262.25914933336134 " " y[1] (numeric) = 262.2591493333644 " " absolute error = 3.069544618483633000000000000E-12 " " relative error = 1.1704242259178119000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.230000000000324 " " y[1] (closed_form) = 263.11015566669425 " " y[1] (numeric) = 263.11015566669784 " " absolute error = 3.581135388230905000000000000E-12 " " relative error = 1.36107835866566000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.240000000000318 " " y[1] (closed_form) = 263.9630080000272 " " y[1] (numeric) = 263.96300800003127 " " absolute error = 4.092726157978177000000000000E-12 " " relative error = 1.5504923167028603000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.250000000000313 " " y[1] (closed_form) = 264.8177083333601 " " y[1] (numeric) = 264.8177083333646 " " absolute error = 4.490630090003833000000000000E-12 " " relative error = 1.6957438829396182000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.260000000000307 " " y[1] (closed_form) = 265.674258666693 " " y[1] (numeric) = 265.67425866669794 " " absolute error = 4.945377440890297300000000000E-12 " " relative error = 1.8614439598736665000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.270000000000302 " " y[1] (closed_form) = 266.5326610000259 " " y[1] (numeric) = 266.5326610000313 " " absolute error = 5.4001247917767610000000000000E-12 " " relative error = 2.0260649376011136000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.280000000000296 " " y[1] (closed_form) = 267.3929173333588 " " y[1] (numeric) = 267.39291733336466 " " absolute error = 5.8548721426632260000000000000E-12 " " relative error = 2.1896137717679168000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.29000000000029 " " y[1] (closed_form) = 268.2550296666917 " " y[1] (numeric) = 268.255029666698 " " absolute error = 6.30961949354969000000000000E-12 " " relative error = 2.3520973684591956000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.300000000000285 " " y[1] (closed_form) = 269.1190000000246 " " y[1] (numeric) = 269.1190000000313 " " absolute error = 6.707523425575346000000000000E-12 " " relative error = 2.4924005460687400000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.31000000000028 " " y[1] (closed_form) = 269.98483033335754 " " y[1] (numeric) = 269.98483033336464 " " absolute error = 7.105427357601002000000000000E-12 " " relative error = 2.6317876263002404000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.320000000000274 " " y[1] (closed_form) = 270.85252266669045 " " y[1] (numeric) = 270.852522666698 " " absolute error = 7.560174708487466000000000000E-12 " " relative error = 2.7912513548160570000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.330000000000268 " " y[1] (closed_form) = 271.7220790000233 " " y[1] (numeric) = 271.7220790000314 " " absolute error = 8.071765478234738000000000000E-12 " " relative error = 2.9705960987564960000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.340000000000263 " " y[1] (closed_form) = 272.59350133335624 " " y[1] (numeric) = 272.5935013333648 " " absolute error = 8.58335624798201000000000000E-12 " " relative error = 3.1487750830440275000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.350000000000257 " " y[1] (closed_form) = 273.4667916666891 " " y[1] (numeric) = 273.46679166669827 " " absolute error = 9.15179043659009000000000000E-12 " " relative error = 3.3465820039109584000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.360000000000252 " " y[1] (closed_form) = 274.34195200002205 " " y[1] (numeric) = 274.34195200003165 " " absolute error = 9.606537787476555000000000000E-12 " " relative error = 3.5016656101782720000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.370000000000246 " " y[1] (closed_form) = 275.2189843333549 " " y[1] (numeric) = 275.2189843333651 " " absolute error = 1.017497197608463500000000000E-11 " " relative error = 3.6970458272458234000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.38000000000024 " " y[1] (closed_form) = 276.0978906666878 " " y[1] (numeric) = 276.0978906666984 " " absolute error = 1.05728759081102910000000000E-11 " " relative error = 3.829393945234491600000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.390000000000235 " " y[1] (closed_form) = 276.9786730000207 " " y[1] (numeric) = 276.97867300003173 " " absolute error = 1.102762325899675500000000000E-11 " " relative error = 3.981397968137399000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.40000000000023 " " y[1] (closed_form) = 277.8613333333536 " " y[1] (numeric) = 277.8613333333651 " " absolute error = 1.148237060988321900000000000E-11 " " relative error = 4.132410390512190600000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.410000000000224 " " y[1] (closed_form) = 278.74587366668646 " " y[1] (numeric) = 278.7458736666985 " " absolute error = 1.205080479849129900000000000E-11 " " relative error = 4.323222668724124300000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.420000000000218 " " y[1] (closed_form) = 279.6322960000193 " " y[1] (numeric) = 279.6322960000319 " " absolute error = 1.256239556823857000000000000E-11 " " relative error = 4.492469485083261400000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.430000000000213 " " y[1] (closed_form) = 280.52060233335226 " " y[1] (numeric) = 280.5206023333652 " " absolute error = 1.296029950026422700000000000E-11 " " relative error = 4.62008829029358000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.440000000000207 " " y[1] (closed_form) = 281.4107946666851 " " y[1] (numeric) = 281.4107946666986 " " absolute error = 1.352873368887230800000000000E-11 " " relative error = 4.807467924212472000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.450000000000202 " " y[1] (closed_form) = 282.30287500001805 " " y[1] (numeric) = 282.302875000032 " " absolute error = 1.392663762089796400000000000E-11 " " relative error = 4.933225572320889000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.460000000000196 " " y[1] (closed_form) = 283.1968453333509 " " y[1] (numeric) = 283.19684533336533 " " absolute error = 1.443822839064523600000000000E-11 " " relative error = 5.098301280033682000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.47000000000019 " " y[1] (closed_form) = 284.09270766668374 " " y[1] (numeric) = 284.0927076666988 " " absolute error = 1.506350599811412400000000000E-11 " " relative error = 5.302320542415198000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.480000000000185 " " y[1] (closed_form) = 284.99046400001663 " " y[1] (numeric) = 284.99046400003226 " " absolute error = 1.563194018672220400000000000E-11 " " relative error = 5.4850748222653830000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.49000000000018 " " y[1] (closed_form) = 285.8901163333495 " " y[1] (numeric) = 285.8901163333656 " " absolute error = 1.608668753760866800000000000E-11 " " relative error = 5.6268778172280350000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.500000000000174 " " y[1] (closed_form) = 286.7916666666824 " " y[1] (numeric) = 286.79166666669903 " " absolute error = 1.665512172621674800000000000E-11 " " relative error = 5.8073938897164030000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.510000000000169 " " y[1] (closed_form) = 287.6951170000152 " " y[1] (numeric) = 287.6951170000323 " " absolute error = 1.710986907710321200000000000E-11 " " relative error = 5.947222620779590000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.520000000000163 " " y[1] (closed_form) = 288.6004693333481 " " y[1] (numeric) = 288.60046933336565 " " absolute error = 1.756461642798967700000000000E-11 " " relative error = 6.0861357809164410000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.530000000000157 " " y[1] (closed_form) = 289.507725666681 " " y[1] (numeric) = 289.50772566669906 " " absolute error = 1.80762071977369500000000000E-11 " " relative error = 6.24377368725166000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.540000000000152 " " y[1] (closed_form) = 290.41688800001384 " " y[1] (numeric) = 290.41688800003243 " " absolute error = 1.85877979674842200000000000E-11 " " relative error = 6.400384666157339000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.550000000000146 " " y[1] (closed_form) = 291.3279583333467 " " y[1] (numeric) = 291.32795833336576 " " absolute error = 1.904254531837068500000000000E-11 " " relative error = 6.536463382131555000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.56000000000014 " " y[1] (closed_form) = 292.24093866667954 " " y[1] (numeric) = 292.24093866669915 " " absolute error = 1.961097950697876500000000000E-11 " " relative error = 6.710551778423627000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.570000000000135 " " y[1] (closed_form) = 293.15583100001237 " " y[1] (numeric) = 293.15583100003244 " " absolute error = 2.00657268578652300000000000E-11 " " relative error = 6.844730595812157000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.58000000000013 " " y[1] (closed_form) = 294.0726373333452 " " y[1] (numeric) = 294.07263733336583 " " absolute error = 2.06341610464733100000000000E-11 " " relative error = 7.016688541165941000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.590000000000124 " " y[1] (closed_form) = 294.9913596666781 " " y[1] (numeric) = 294.9913596666991 " " absolute error = 2.103206497849896600000000000E-11 " " relative error = 7.129722376365156000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.600000000000119 " " y[1] (closed_form) = 295.91200000001095 " " y[1] (numeric) = 295.9120000000325 " " absolute error = 2.154365574824623800000000000E-11 " " relative error = 7.280426528239963000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.610000000000113 " " y[1] (closed_form) = 296.83456033334375 " " y[1] (numeric) = 296.83456033336586 " " absolute error = 2.211208993685431800000000000E-11 " " relative error = 7.449297653218867000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.620000000000108 " " y[1] (closed_form) = 297.7590426666766 " " y[1] (numeric) = 297.75904266669914 " " absolute error = 2.256683728774078200000000000E-11 " " relative error = 7.578892343834879000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.630000000000102 " " y[1] (closed_form) = 298.68544900000944 " " y[1] (numeric) = 298.6854490000325 " " absolute error = 2.307842805748805400000000000E-11 " " relative error = 7.726666342385942000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.640000000000096 " " y[1] (closed_form) = 299.6137813333423 " " y[1] (numeric) = 299.6137813333659 " " absolute error = 2.364686224609613400000000000E-11 " " relative error = 7.892448117994701000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.650000000000091 " " y[1] (closed_form) = 300.54404166667507 " " y[1] (numeric) = 300.54404166669934 " " absolute error = 2.427213985356502200000000000E-11 " " relative error = 8.076067560335988000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.660000000000085 " " y[1] (closed_form) = 301.47623200000794 " " y[1] (numeric) = 301.4762320000327 " " absolute error = 2.478373062331229400000000000E-11 " " relative error = 8.220790892501152000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.67000000000008 " " y[1] (closed_form) = 302.4103543333408 " " y[1] (numeric) = 302.4103543333661 " " absolute error = 2.529532139305956700000000000E-11 " " relative error = 8.36456855084302000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.680000000000074 " " y[1] (closed_form) = 303.3464106666736 " " y[1] (numeric) = 303.3464106666994 " " absolute error = 2.58069121628068400000000000E-11 " " relative error = 8.507406468430007000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.690000000000069 " " y[1] (closed_form) = 304.2844030000065 " " y[1] (numeric) = 304.2844030000326 " " absolute error = 2.614797267597168700000000000E-11 " " relative error = 8.59326748863008000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.700000000000063 " " y[1] (closed_form) = 305.22433333333925 " " y[1] (numeric) = 305.224333333366 " " absolute error = 2.677325028344057500000000000E-11 " " relative error = 8.771663121039952000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.710000000000058 " " y[1] (closed_form) = 306.16620366667206 " " y[1] (numeric) = 306.16620366669935 " " absolute error = 2.728484105318784700000000000E-11 " " relative error = 8.911774299848353000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.720000000000052 " " y[1] (closed_form) = 307.1100160000049 " " y[1] (numeric) = 307.11001600003266 " " absolute error = 2.77395884040743100000000000E-11 " " relative error = 9.03245969160246000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.730000000000047 " " y[1] (closed_form) = 308.0557723333377 " " y[1] (numeric) = 308.055772333366 " " absolute error = 2.83080225926823900000000000E-11 " " relative error = 9.18925244551209000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.740000000000041 " " y[1] (closed_form) = 309.00347466667057 " " y[1] (numeric) = 309.0034746666993 " " absolute error = 2.870592652470805000000000000E-11 " " relative error = 9.289839396037153000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.750000000000036 " " y[1] (closed_form) = 309.95312500000335 " " y[1] (numeric) = 309.9531250000326 " " absolute error = 2.92743607133161300000000000E-11 " " relative error = 9.444770306257053000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.76000000000003 " " y[1] (closed_form) = 310.90472533333616 " " y[1] (numeric) = 310.90472533336595 " " absolute error = 2.9785951483063400000000000E-11 " " relative error = 9.580411314472118000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.770000000000024 " " y[1] (closed_form) = 311.858277666669 " " y[1] (numeric) = 311.8582776666992 " " absolute error = 3.024069883394986400000000000E-11 " " relative error = 9.696936396946552000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.780000000000019 " " y[1] (closed_form) = 312.81378400000176 " " y[1] (numeric) = 312.8137840000325 " " absolute error = 3.075228960369713600000000000E-11 " " relative error = 9.83086141872091000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.790000000000013 " " y[1] (closed_form) = 313.7712463333346 " " y[1] (numeric) = 313.7712463333658 " " absolute error = 3.1207036954583600000000000E-11 " " relative error = 9.945792458443065000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.800000000000008 " " y[1] (closed_form) = 314.7306666666674 " " y[1] (numeric) = 314.73066666669916 " " absolute error = 3.17754711431916800000000000E-11 " " relative error = 1.009608357511764800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.810000000000002 " " y[1] (closed_form) = 315.69204700000023 " " y[1] (numeric) = 315.6920470000326 " " absolute error = 3.23439053317997600000000000E-11 " " relative error = 1.024539757626511800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.819999999999997 " " y[1] (closed_form) = 316.655389333333 " " y[1] (numeric) = 316.655389333366 " " absolute error = 3.29691829392686500000000000E-11 " " relative error = 1.041169171593130400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.829999999999991 " " y[1] (closed_form) = 317.6206956666658 " " y[1] (numeric) = 317.62069566669936 " " absolute error = 3.35376171278767300000000000E-11 " " relative error = 1.055901507220220200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.839999999999986 " " y[1] (closed_form) = 318.5879679999986 " " y[1] (numeric) = 318.58796800003273 " " absolute error = 3.41060513164848100000000000E-11 " " relative error = 1.070537959439979800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.84999999999998 " " y[1] (closed_form) = 319.5572083333314 " " y[1] (numeric) = 319.5572083333661 " " absolute error = 3.46744855050928900000000000E-11 " " relative error = 1.085079122011974600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.859999999999975 " " y[1] (closed_form) = 320.52841866666415 " " y[1] (numeric) = 320.52841866669934 " " absolute error = 3.51860762748401600000000000E-11 " " relative error = 1.097752156305122400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.869999999999969 " " y[1] (closed_form) = 321.501600999997 " " y[1] (numeric) = 321.5016010000327 " " absolute error = 3.569766704458743300000000000E-11 " " relative error = 1.110341812717373400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.879999999999963 " " y[1] (closed_form) = 322.4767573333297 " " y[1] (numeric) = 322.476757333366 " " absolute error = 3.626610123319551300000000000E-11 " " relative error = 1.124611321854395900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.889999999999958 " " y[1] (closed_form) = 323.4538896666625 " " y[1] (numeric) = 323.4538896666993 " " absolute error = 3.677769200294278600000000000E-11 " " relative error = 1.137030444767390800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.899999999999952 " " y[1] (closed_form) = 324.43299999999533 " " y[1] (numeric) = 324.43300000003256 " " absolute error = 3.72324393538292500000000000E-11 " " relative error = 1.147615666526826300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.909999999999947 " " y[1] (closed_form) = 325.4140903333281 " " y[1] (numeric) = 325.4140903333659 " " absolute error = 3.78008735424373300000000000E-11 " " relative error = 1.16162374848972110000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.919999999999941 " " y[1] (closed_form) = 326.3971626666609 " " y[1] (numeric) = 326.3971626666993 " " absolute error = 3.83693077310454100000000000E-11 " " relative error = 1.175540480118412300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.929999999999936 " " y[1] (closed_form) = 327.38221899999365 " " y[1] (numeric) = 327.38221900003253 " " absolute error = 3.88808985007926800000000000E-11 " " relative error = 1.187630122966251700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.93999999999993 " " y[1] (closed_form) = 328.36926133332645 " " y[1] (numeric) = 328.36926133336584 " " absolute error = 3.939248927053995400000000000E-11 " " relative error = 1.19963997575743800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.949999999999925 " " y[1] (closed_form) = 329.35829166665917 " " y[1] (numeric) = 329.35829166669913 " " absolute error = 3.996092345914803400000000000E-11 " " relative error = 1.213296415187632600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.95999999999992 " " y[1] (closed_form) = 330.349311999992 " " y[1] (numeric) = 330.3493120000324 " " absolute error = 4.0415670810034500000000000E-11 " " relative error = 1.223422278840268400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.969999999999914 " " y[1] (closed_form) = 331.3423243333247 " " y[1] (numeric) = 331.34232433336575 " " absolute error = 4.104094841750338700000000000E-11 " " relative error = 1.238626803867558200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.979999999999908 " " y[1] (closed_form) = 332.33733066665746 " " y[1] (numeric) = 332.337330666699 " " absolute error = 4.15525391872506600000000000E-11 " " relative error = 1.250312118229320600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.989999999999903 " " y[1] (closed_form) = 333.33433299999024 " " y[1] (numeric) = 333.3343330000324 " " absolute error = 4.21778167947195470000000000E-11 " " relative error = 1.265330709114827000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.999999999999897 " " y[1] (closed_form) = 334.333333333323 " " y[1] (numeric) = 334.3333333333657 " " absolute error = 4.26894075644668200000000000E-11 " " relative error = 1.276851671918289300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " "Finished!" "diff ( y , x , 1 ) = x * x ; " Iterations = 9901 "Total Elapsed Time "= 2 Minutes 0 Seconds "Elapsed Time(since restart) "= 2 Minutes 0 Seconds "Time to Timeout "= 59 Seconds Percent Done = 100.02020202020097 "%" (%o251) temp/diffeq.mult.max