(%i1) batch("temp/diffeq.lin_ln.max") read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.lin_ln.max (%i2) load("stringproc") (%i3) keepfloat:true (%i4) alias(convfloat,float) (%i5) alias(int_trunc,truncate) (%i6) alias(elapsed_time_seconds,elapsed_real_time) (%i7) alias(ln,log) (%i8) alias(arcsin,asin) (%i9) alias(arccos,acos) (%i10) alias(arctan,atan) (%i11) alias(float_abs,abs) (%i12) mode_declare(display_poles(),fixnum) (%i13) mode_declare(est_size_answer(),convfloat) (%i14) mode_declare(test_suggested_h(),convfloat) (%i15) mode_declare(reached_interval(),boolean) (%i16) mode_declare(display_alot([iter],fixnum),fixnum) (%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum) (%i18) mode_declare(check_for_pole(),fixnum) (%i19) mode_declare(atomall(),fixnum) (%i20) mode_declare(log10([x],convfloat),convfloat) (%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum) (%i22) mode_declare(omniout_timestr(secs_in,number),fixnum) (%i23) mode_declare(zero_ats_ar(ar,array([30],convfloat)),fixnum) (%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a], completearray([30],convfloat),[arr_b], completearray([30],convfloat),[jjj_ats],fixnum), convfloat) (%i25) mode_declare(att([mmm_att],fixnum,[arr_a], completearray([30],convfloat),[arr_b], completearray([30],convfloat),[jjj_att],fixnum), convfloat) (%i26) mode_declare(logitem_ditto([file],fixnum),fixnum) (%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum) (%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum) (%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum) (%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum) (%i31) mode_declare(logstart([file],fixnum),fixnum) (%i32) mode_declare(logend([file],fixnum),fixnum) (%i33) mode_declare(chk_data(),fixnum) (%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat, [t2],convfloat,[clock_sec2],convfloat), convfloat) (%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2], convfloat),convfloat) (%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i42) mode_declare(neg([nnn],convfloat),convfloat) (%i43) mode_declare(factorial_2([nnn],fixnum),convfloat) (%i44) mode_declare(factorial_1([nnn],fixnum),convfloat) (%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat) (%i46) mode_declare(convfloat([mmm],fixnum),convfloat) (%i47) mode_declare(elaped_time_seconds(),convfloat) (%i48) mode_declare(Si([x],convfloat),convfloat) (%i49) mode_declare(Ci([x],convfloat),convfloat) (%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end], convfloat,[estimated_h], convfloat,[estimated_answer], convfloat),convfloat) (%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat) (%i52) mode_declare(main_prog(),fixnum) (%i53) define_variable(always,1,fixnum) (%i54) define_variable(info,2,fixnum) (%i55) define_variable(debugl,3,fixnum) (%i56) define_variable(debugmassive,4,fixnum) (%i57) define_variable(glob_iolevel,5,fixnum) (%i58) define_variable(glob_yes_pole,4,fixnum) (%i59) define_variable(glob_no_pole,3,fixnum) (%i60) define_variable(glob_not_given,0,fixnum) (%i61) define_variable(glob_no_sing_tests,4,fixnum) (%i62) define_variable(glob_ratio_test,1,fixnum) (%i63) define_variable(glob_three_term_test,2,fixnum) (%i64) define_variable(glob_six_term_test,3,fixnum) (%i65) define_variable(ats_max_terms,30,fixnum) (%i66) define_variable(glob_log_10,0.0,convfloat) (%i67) define_variable(max_unchanged,10,fixnum) (%i68) define_variable(glob__small,1.0E-51,convfloat) (%i69) define_variable(glob_small_float,1.0E-51,convfloat) (%i70) define_variable(glob_smallish_float,1.0E-61,convfloat) (%i71) define_variable(glob_large_float,1.0E+100,convfloat) (%i72) define_variable(glob_larger_float,1.1E+100,convfloat) (%i73) define_variable(glob__m2,-2.0,convfloat) (%i74) define_variable(glob__m1,-1.0,convfloat) (%i75) define_variable(glob__0,0.0,convfloat) (%i76) define_variable(glob__1,1.0,convfloat) (%i77) define_variable(glob__2,2.0,convfloat) (%i78) define_variable(glob__3,3.0,convfloat) (%i79) define_variable(glob__4,4.0,convfloat) (%i80) define_variable(glob__5,5.0,convfloat) (%i81) define_variable(glob__8,8.0,convfloat) (%i82) define_variable(glob__10,10.0,convfloat) (%i83) define_variable(glob__100,100.0,convfloat) (%i84) define_variable(glob__pi,0.0,convfloat) (%i85) define_variable(glob__0_5,0.5,convfloat) (%i86) define_variable(glob__0_8,0.8,convfloat) (%i87) define_variable(glob__m0_8,-0.8,convfloat) (%i88) define_variable(glob__0_25,0.25,convfloat) (%i89) define_variable(glob__0_125,0.125,convfloat) (%i90) define_variable(glob_prec,1.0E-16,convfloat) (%i91) define_variable(glob_check_sign,1.0,convfloat) (%i92) define_variable(glob_desired_digits_correct,8.0,convfloat) (%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat) (%i94) define_variable(glob_ratio_of_radius,0.1,convfloat) (%i95) define_variable(glob_percent_done,0.0,convfloat) (%i96) define_variable(glob_total_exp_sec,0.1,convfloat) (%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat) (%i98) define_variable(glob_estimated_size_answer,100.0,convfloat) (%i99) define_variable(glob_almost_1,0.999,convfloat) (%i100) define_variable(glob_clock_sec,0.0,convfloat) (%i101) define_variable(glob_clock_start_sec,0.0,convfloat) (%i102) define_variable(glob_disp_incr,0.1,convfloat) (%i103) define_variable(glob_h,0.1,convfloat) (%i104) define_variable(glob_diff_rc_fm,0.1,convfloat) (%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat) (%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat) (%i107) define_variable(glob_diff_ord_fm,0.1,convfloat) (%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat) (%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat) (%i110) define_variable(glob_six_term_ord_save,0.1,convfloat) (%i111) define_variable(glob_guess_error_rc,0.1,convfloat) (%i112) define_variable(glob_guess_error_ord,0.1,convfloat) (%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat) (%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat) (%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat) (%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat) (%i117) define_variable(glob_last_good_h,0.1,convfloat) (%i118) define_variable(glob_max_h,0.1,convfloat) (%i119) define_variable(glob_min_h,1.0E-6,convfloat) (%i120) define_variable(glob_display_interval,0.1,convfloat) (%i121) define_variable(glob_abserr,1.0E-11,convfloat) (%i122) define_variable(glob_relerr,1.0E-11,convfloat) (%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat) (%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat) (%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat) (%i126) define_variable(glob_max_hours,0.0,convfloat) (%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat) (%i128) define_variable(glob_optimal_start,0.0,convfloat) (%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat) (%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat) (%i131) define_variable(glob_max_sec,10000.0,convfloat) (%i132) define_variable(glob_orig_start_sec,0.0,convfloat) (%i133) define_variable(glob_normmax,0.0,convfloat) (%i134) define_variable(glob_max_minutes,0.0,convfloat) (%i135) define_variable(glob_next_display,0.0,convfloat) (%i136) define_variable(glob_est_digits,1,fixnum) (%i137) define_variable(glob_subiter_method,3,fixnum) (%i138) define_variable(glob_html_log,true,boolean) (%i139) define_variable(glob_min_good_digits,99999,fixnum) (%i140) define_variable(glob_good_digits,0,fixnum) (%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum) (%i142) define_variable(glob_apfp_est_good_digits,0,fixnum) (%i143) define_variable(glob_max_opt_iter,10,fixnum) (%i144) define_variable(glob_dump,false,boolean) (%i145) define_variable(glob_djd_debug,true,boolean) (%i146) define_variable(glob_display_flag,true,boolean) (%i147) define_variable(glob_djd_debug2,true,boolean) (%i148) define_variable(glob_h_reason,0,fixnum) (%i149) define_variable(glob_sec_in_minute,60,fixnum) (%i150) define_variable(glob_min_in_hour,60,fixnum) (%i151) define_variable(glob_hours_in_day,24,fixnum) (%i152) define_variable(glob_days_in_year,365,fixnum) (%i153) define_variable(glob_sec_in_hour,3600,fixnum) (%i154) define_variable(glob_sec_in_day,86400,fixnum) (%i155) define_variable(glob_sec_in_year,31536000,fixnum) (%i156) define_variable(glob_not_yet_finished,true,boolean) (%i157) define_variable(glob_initial_pass,true,boolean) (%i158) define_variable(glob_not_yet_start_msg,true,boolean) (%i159) define_variable(glob_reached_optimal_h,false,boolean) (%i160) define_variable(glob_optimal_done,false,boolean) (%i161) define_variable(glob_type_given_pole,0,fixnum) (%i162) define_variable(glob_optimize,false,boolean) (%i163) define_variable(glob_look_poles,false,boolean) (%i164) define_variable(glob_dump_closed_form,false,boolean) (%i165) define_variable(glob_max_iter,1000,fixnum) (%i166) define_variable(glob_no_eqs,0,fixnum) (%i167) define_variable(glob_unchanged_h_cnt,0,fixnum) (%i168) define_variable(glob_warned,false,boolean) (%i169) define_variable(glob_warned2,false,boolean) (%i170) define_variable(glob_start,0,fixnum) (%i171) define_variable(glob_iter,0,fixnum) (%i172) completearray(array_y_init,[30],convfloat) (%i173) completearray(array_norms,[30],convfloat) (%i174) completearray(array_fact_1,[30],convfloat) (%i175) completearray(array_1st_rel_error,[2],convfloat) (%i176) completearray(array_last_rel_error,[2],convfloat) (%i177) completearray(array_est_rel_error,[2],convfloat) (%i178) completearray(array_max_est_error,[2],convfloat) (%i179) completearray(array_type_pole,[2],convfloat) (%i180) completearray(array_type_real_pole,[2],convfloat) (%i181) completearray(array_type_complex_pole,[2],convfloat) (%i182) completearray(array_est_digits,[2],convfloat) (%i183) completearray(array_y,[30],convfloat) (%i184) completearray(array_x,[30],convfloat) (%i185) completearray(array_tmp0,[30],convfloat) (%i186) completearray(array_tmp1,[30],convfloat) (%i187) completearray(array_tmp2,[30],convfloat) (%i188) completearray(array_tmp3,[30],convfloat) (%i189) completearray(array_tmp4,[30],convfloat) (%i190) completearray(array_m1,[30],convfloat) (%i191) completearray(array_y_higher,[2,30],convfloat) (%i192) completearray(array_y_higher_work,[2,30],convfloat) (%i193) completearray(array_y_higher_work2,[2,30],convfloat) (%i194) completearray(array_y_set_initial,[2,30],convfloat) (%i195) completearray(array_given_rad_poles,[2,3],convfloat) (%i196) completearray(array_given_ord_poles,[2,3],convfloat) (%i197) completearray(array_rad_test_poles,[2,4],convfloat) (%i198) completearray(array_ord_test_poles,[2,4],convfloat) (%i199) completearray(array_fact_2,[30,30],convfloat) (%i200) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%i201) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%i202) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%i203) omniout_float(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (if vallen = 4 then printf(true,"~a = ~g ~s ~%",prelabel, value,postlabel) else printf(true,"~a = ~g ~s ~%",prelabel, value,postlabel)) (%i204) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%i205) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%i206) logitem_time(fd,secs_in):=( block(mode_declare( [[days_int,hours_int,minutes_int,sec_int, years_int],fixnum,[secs,secs_temp],convfloat]), secs:secs_in,printf(fd,"~%"), if secs >= 0 then (years_int :truncate(secs/glob_sec_in_year), sec_temp :mod(truncate(secs), truncate(glob_sec_in_year)), days_int :truncate(sec_temp/glob_sec_in_day), sec_temp :mod(sec_temp, truncate(glob_sec_in_day)), hours_int :truncate(sec_temp/glob_sec_in_hour), sec_temp :mod(sec_temp, truncate(glob_sec_in_hour)), minutes_int :truncate(sec_temp/glob_sec_in_minute), sec_int :mod(sec_temp, truncate(glob_sec_in_minute)), if truncate(years_int) > 0.1 then printf(fd, "~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int,days_int, hours_int,minutes_int, sec_int) elseif days_int > 0.1 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,hours_int, minutes_int,sec_int) elseif hours_int > 0.1 then printf(fd, "~d Hours ~d Minutes ~d Seconds~%", hours_int,minutes_int, sec_int) elseif minutes_int > 0.1 then printf(fd, "~d Minutes ~d Seconds~%", minutes_int,sec_int) else printf(fd,"~d Seconds~%", sec_int)) else printf(fd," 0.0 Seconds~%"), printf(fd,"~%")),0) (%i207) omniout_timestr(secs_in):=( block(mode_declare( [[days_int,hours_int,minutes_int,sec_int, years_int],fixnum,[secs,secs_temp], convfloat]),secs:secs_in, if secs >= 0 then ( years_int:truncate(secs/glob_sec_in_year), sec_temp :mod(truncate(secs), truncate(glob_sec_in_year)), days_int:truncate(sec_temp/glob_sec_in_day), sec_temp :mod(sec_temp,truncate(glob_sec_in_day)), hours_int :truncate(sec_temp/glob_sec_in_hour), sec_temp :mod(sec_temp,truncate(glob_sec_in_hour)), minutes_int :truncate(sec_temp/glob_sec_in_minute), sec_int :mod(sec_temp, truncate(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int,days_int, hours_int,minutes_int, sec_int) elseif days_int > 0.1 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,hours_int, minutes_int,sec_int) elseif hours_int > 0.1 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,minutes_int, sec_int) elseif minutes_int > 0.1 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int,sec_int) else printf(true,"= ~d Seconds~%", sec_int)) else printf(true,"= 0.0 Seconds~%")),0) (%i208) zero_ats_ar(arr_a):=( block(mode_declare([iii],fixnum),iii:1, while iii <= ats_max_terms do (arr_a[iii]:glob__0,iii:1+iii)),0) (%i209) ats(mmm_ats,arr_a,arr_b,jjj_ats):=block( mode_declare([[iii_ats,lll_ats,ma_ats],fixnum,[ret_ats], convfloat]),ret_ats:glob__0, if jjj_ats <= mmm_ats then (ma_ats:1+mmm_ats,iii_ats:jjj_ats, while iii_ats <= mmm_ats do (lll_ats:ma_ats-iii_ats, if lll_ats <= ats_max_terms and iii_ats <= ats_max_terms then ret_ats :c(arr_a[iii_ats])*c(arr_b[lll_ats])+ret_ats, iii_ats:1+iii_ats)),ret_ats) (%i210) att(mmm_att,arr_aa,arr_bb,jjj_att):=block( mode_declare([[al_att,iii_att,lll_att,ma_att],convfloat,[ret_att], fixnum]),ret_att:glob__0, if jjj_att < mmm_att then (ma_att:2+mmm_att,iii_att:jjj_att, while iii_att < mmm_att and iii_att <= ats_max_terms do (lll_att:ma_att-iii_att,al_att:lll_att-1, if lll_att <= ats_max_terms and iii_att <= ats_max_terms then ret_att :c(arr_aa[iii_att])*c(arr_bb[lll_att]) *c(al_att) +ret_att,iii_att:1+iii_att), ret_att:ret_att/c(mmm_att)),ret_att) (%i211) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%i212) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%i213) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%i214) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), printf(file,"~d",glob_min_good_digits), printf(file,"")),0) (%i215) log_revs(file,revs):=printf(file,revs) (%i216) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%i217) logitem_h_reason(file):=(printf(file,""), if glob_h_reason = 1 then printf(file,"Max H") elseif glob_h_reason = 2 then printf(file,"Display_interval") elseif glob_h_reason = 3 then printf(file,"Optimal") elseif glob_h_reason = 4 then printf(file,"Pole Accuracy") elseif glob_h_reason = 5 then printf(file,"Min H (Pole)") elseif glob_h_reason = 6 then printf(file,"Pole") elseif glob_h_reason = 7 then printf(file,"Opt Iter") else printf(file,"Impossible"), printf(file,""),0) (%i218) logstart(file):=(printf(file,""),0) (%i219) logend(file):=(printf(file,"~%"),0) (%i220) chk_data():=( block(mode_declare([[errflag],boolean]),errflag:false, if glob_max_iter < 2 then (omniout_str(always,"Illegal max_iter"), errflag:true),if errflag then quit()),0) (%i221) comp_expect_sec(t_end2,t_start2,t2,clock_sec2):=block( mode_declare([[ms2,rrr,sec_left,sub1,sub2], convfloat]),ms2:c(clock_sec2), sub1:c(t_end2-t_start2),sub2:c(t2-t_start2), if sub1 = glob__0 then sec_left:glob__0 else (if sub2 > glob__0 then (rrr:sub1/sub2, sec_left:rrr*c(ms2)-c(ms2)) else sec_left:glob__0),sec_left) (%i222) comp_percent(t_end2,t_start2,t2):=block( mode_declare([[rrr,sub1,sub2],convfloat]), sub1:t_end2-t_start2,sub2:t2-t_start2, if sub2 > glob_small_float then rrr:glob__100*sub2/sub1 else rrr:0.0,rrr) (%i223) comp_rad_from_ratio(term1,term2,last_no):=( if abs(term2) > glob__0 then ret:abs(term1*glob_h/term2) else ret:glob_larger_float,ret) (%i224) comp_ord_from_ratio(term1,term2,last_no):=( if abs(term2) > glob__0 then ret :abs(term2)*c(last_no) *log(abs(term1*glob_h/term2)) /log(c(last_no)) +glob__1 else ret:glob_larger_float,ret) (%i225) c(in_val):=(ret:in_val,ret) (%i226) comp_rad_from_three_terms(term1,term2,term3,last_no):=( temp:abs( term1*term3-term1*term3*c(last_no) +glob__m2*term2*term2 +term2*term2*c(last_no)), if abs(temp) > glob__0 then ret:abs(term2*glob_h*term1/temp) else ret:glob_larger_float,ret) (%i227) comp_ord_from_three_terms(term1,term2,term3,last_no):=( ret:abs( (-term1*term3*c(last_no*last_no) +term2*term2*c(last_no*last_no) +glob__4*term2*term2 -glob__4*term2*term2*c(last_no) -glob__3*term1*term3 +glob__4*term1*term3*c(last_no)) /(term1*term3-term1*term3*c(last_no) -glob__2*term2*term2 +term2*term2*c(last_no))), ret) (%i228) comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):= ( if term5 # glob__0 and term4 # glob__0 and term3 # glob__0 and term2 # glob__0 and term1 # glob__0 then (rm0:term6/term5,rm1:term5/term4, rm2:term4/term3,rm3:term3/term2, rm4:term2/term1, nr1 :c(last_no-3)*rm2 -glob__2*c(last_no-2)*rm1 +c(last_no-1)*rm0, nr2 :c(last_no-4)*rm3 -glob__2*c(last_no-3)*rm2 +c(last_no-2)*rm1, dr1 :(-glob__1)/rm3+glob__2/rm2 +glob__m1/rm1, dr2 :(-glob__1)/rm4+glob__2/rm3 +glob__m1/rm2, ds1 :glob__5/rm3-glob__8/rm2 +glob__3/rm1, ds2 :glob__5/rm4-glob__8/rm3 +glob__3/rm2, if abs(nr1*dr2-nr2*dr1) = glob__0 or abs(dr1) = glob__0 then (rad_c:glob_larger_float, ord_no:glob_larger_float) else (if abs(nr1*dr2-nr2*dr1) > glob__0 then ( rcs :(dr1*dr2-ds2*dr1+ds1*dr2) /(nr1*dr2-nr2*dr1), ord_no :(rcs*nr1-ds1)/(glob__2*dr1) -c(last_no)/glob__2, if abs(rcs) # glob__0 then (if rcs > glob__0 then rad_c :sqrt(rcs) *abs(glob_h) else ( rad_c :glob_larger_float, ord_no :glob_larger_float)) else ( rad_c:glob_larger_float, ord_no:glob_larger_float)) else (rad_c:glob_larger_float, ord_no:glob_larger_float))) else (rad_c:glob_larger_float, ord_no:glob_larger_float), glob_six_term_ord_save:ord_no,rad_c) (%i229) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%i230) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret) (%i231) factorial_1(nnn):=block(mode_declare([[ret],convfloat]), if nnn <= ats_max_terms then (if array_fact_1[nnn] = 0 then (ret:factorial_2(nnn), array_fact_1[nnn]:ret) else ret:array_fact_1[nnn]) else ret:factorial_2(nnn),ret) (%i232) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret) (%i233) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret) (%i234) factorial_3(mmm,nnn):=block(mode_declare([[ret],convfloat]), if nnn <= ats_max_terms and mmm <= ats_max_terms then (if array_fact_2[mmm,nnn] = 0 then (ret:factorial_1(mmm)/factorial_1(nnn), array_fact_2[mmm,nnn]:ret) else ret:array_fact_2[mmm,nnn]) else ret:factorial_2(mmm)/factorial_2(nnn),ret) (%i235) log10(x):=log(x)/glob_log_10 (%i236) c(x):=x (%i237) expt(x,y):=if y = 0.0 then 1.0 elseif x <= 0.0 and y < 0.0 then print("expt error x = ",x,"y = ",y) else x^y (%i238) estimated_needed_step_error(x_start,x_end,estimated_h, estimated_answer):=block( [desired_abs_gbl_error,range, estimated_steps,step_error], omniout_float(always, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32,""), desired_abs_gbl_error :expt(glob__10, c(-glob_desired_digits_correct)) *c(abs(c(estimated_answer))), omniout_float(always,"estimated_h",32, estimated_h,32,""), omniout_float(always,"estimated_answer", 32,estimated_answer,32,""), omniout_float(always, "desired_abs_gbl_error",32, desired_abs_gbl_error,32, ""),range:x_end-x_start, omniout_float(always,"range",32,range,32, ""), estimated_steps:range/estimated_h, omniout_float(always,"estimated_steps",32, estimated_steps,32,""), step_error :c( abs(desired_abs_gbl_error) /sqrt(c(estimated_steps)) /c(ats_max_terms)), omniout_float(always,"step_error",32, step_error,32,""), step_error) (%i239) exact_soln_y(x):=block( -c(2.0)-c(x) +c(10.0)*(c(0.2)+c(0.1)*c(x)) *log(c(0.2)+c(0.1)*c(x))) (%o239) exact_soln_y(x) := block(- c(2.0) - c(x) + c(10.0) (c(0.2) + c(0.1) c(x)) log(c(0.2) + c(0.1) c(x))) (%i240) display_poles():=( block(mode_declare([[rad_given],convfloat]), if glob_type_given_pole = 1 or glob_type_given_pole = 2 then (rad_given :sqrt( array_given_rad_poles[1,2] *array_given_rad_poles[1,2] +(array_x[1] -array_given_rad_poles[1,1]) *(array_x[1] -array_given_rad_poles[1,1])), omniout_float(always, "Radius of convergence (given) for eq 1 ", 4,rad_given,4," "), omniout_float(always, "Order of pole (given) ", 4, array_given_ord_poles[ 1,1],4," "), if rad_given < glob_least_given_sing then glob_least_given_sing :rad_given) elseif glob_type_given_pole = 3 then omniout_str(always, "NO POLE (given) for Equation 1") elseif glob_type_given_pole = 5 then omniout_str(always, "SOME POLE (given) for Equation 1") else omniout_str(always, "NO info (given) for Equation 1"), if array_rad_test_poles[1,1] < glob_large_float then (omniout_float(always, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1,1], 4," "), if array_rad_test_poles[1,1] < glob_least_ratio_sing then glob_least_ratio_sing :array_rad_test_poles[1,1], omniout_float(always, "Order of pole (ratio test) ", 4, array_ord_test_poles[1,1], 4," ")) else omniout_str(always, "NO POLE (ratio test) for Equation 1"), if array_rad_test_poles[1,2] > glob__small and array_rad_test_poles[1,2] < glob_large_float then (omniout_float(always, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1,2], 4," "), if array_rad_test_poles[1,2] < glob_least_3_sing then glob_least_3_sing :array_rad_test_poles[1,2], omniout_float(always, "Order of pole (three term test) ", 4, array_ord_test_poles[1,2], 4," ")) else omniout_str(always, "NO REAL POLE (three term test) for Equation 1"), if array_rad_test_poles[1,3] > glob__small and array_rad_test_poles[1,3] < glob_large_float then (omniout_float(always, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1,3], 4," "), if array_rad_test_poles[1,3] < glob_least_6_sing then glob_least_6_sing :array_rad_test_poles[1,3], omniout_float(always, "Order of pole (six term test) ", 4, array_ord_test_poles[1,3], 4," ")) else omniout_str(always, "NO COMPLEX POLE (six term test) for Equation 1")), 0) (%i241) my_check_sign(x0,xf):=block([ret], if xf > x0 then ret:glob__1 else ret:glob__m1,ret) (%i242) est_size_answer():=block([min_size], min_size:glob_estimated_size_answer, if abs(array_y[1]) < min_size then (min_size:abs(array_y[1]), omniout_float(always,"min_size",32,min_size, 32,"")), if min_size < glob__1 then (min_size:glob__1, omniout_float(always,"min_size",32,min_size, 32,"")),min_size) (%i243) test_suggested_h():=block( [max_estimated_step_error,hn_div_ho,hn_div_ho_2, hn_div_ho_3,no_terms,est_tmp], max_estimated_step_error:glob__small, no_terms:ats_max_terms,hn_div_ho:glob__0_5, hn_div_ho_2:glob__0_25,hn_div_ho_3:glob__0_125, omniout_float(always,"hn_div_ho",32,hn_div_ho,32,""), omniout_float(always,"hn_div_ho_2",32,hn_div_ho_2,32, ""), omniout_float(always,"hn_div_ho_3",32,hn_div_ho_3,32, ""), est_tmp:abs(array_y[no_terms]*hn_div_ho_3 +array_y[no_terms-1]*hn_div_ho_2 +array_y[no_terms-2]*hn_div_ho +array_y[no_terms-3]), if est_tmp >= max_estimated_step_error then max_estimated_step_error:est_tmp, omniout_float(always,"max_estimated_step_error",32, max_estimated_step_error,32,""), max_estimated_step_error) (%i244) track_estimated_error():=block( [hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms, est_tmp],no_terms:ats_max_terms, hn_div_ho:glob__0_5,hn_div_ho_2:glob__0_25, hn_div_ho_3:glob__0_125, est_tmp:c(abs(array_y[no_terms]))*c(hn_div_ho_3) +c(abs(array_y[no_terms-1])) *c(hn_div_ho_2) +c(abs(array_y[no_terms-2])) *c(hn_div_ho) +c(abs(array_y[no_terms-3])), if glob_prec*c(abs(array_y[1])) > c(est_tmp) then est_tmp :c(glob_prec)*c(abs(array_y[1])), if c(est_tmp) >= c(array_max_est_error[1]) then array_max_est_error[1]:c(est_tmp)) (%i245) reached_interval():=block(mode_declare([[ret],boolean]), if glob_check_sign*array_x[1] >= glob_check_sign*glob_next_display -glob_h/glob__10 then ret:true else ret:false, return(ret)) (%i246) display_alot(iter):=( block(mode_declare( [[abserr,est_rel_err],convfloat, [closed_form_val_y],convfloat,[ind_var], convfloat,[numeric_val],convfloat,[relerr], convfloat,[term_no],fixnum]), if reached_interval() then (if iter >= 0 then (ind_var:array_x[1], omniout_float(always, "x[1] ", 33,ind_var,20, " "), closed_form_val_y :exact_soln_y(ind_var), omniout_float(always, "y[1] (closed_form) ", 33, closed_form_val_y, 20," "), term_no:1, numeric_val:array_y[term_no], abserr :abs( numeric_val -closed_form_val_y), omniout_float(always, "y[1] (numeric) ", 33,numeric_val, 20," "), if c(abs(closed_form_val_y)) > c(glob_prec) then ( relerr :abserr*glob__100 /abs(closed_form_val_y), if c(relerr) > c(glob_prec) then glob_good_digits :3 -floor(log10(c(relerr))) else glob_good_digits:16) else (relerr:glob__m1, glob_good_digits:-16), if glob_good_digits < glob_min_good_digits then glob_min_good_digits :glob_good_digits, if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits then glob_min_apfp_est_good_digits :glob_apfp_est_good_digits, if c(abs(numeric_val)) > c(glob_prec) then ( est_rel_err :c(array_max_est_error[1]) *glob__100 *c(sqrt(glob_iter))*c(21) *c(ats_max_terms) /c(abs(numeric_val)), if est_rel_err > glob_prec then glob_est_digits :3 -floor( log10(est_rel_err)) else glob_est_digits:16) else (relerr:glob__m1, glob_est_digits:-16), array_est_digits[1] :glob_est_digits, if glob_iter = 1 then array_1st_rel_error[1] :relerr else array_last_rel_error[ 1] :relerr, array_est_rel_error[1] :est_rel_err, omniout_float(always, "absolute error ", 4,abserr,20," "), omniout_float(always, "relative error ", 4,relerr,20,"%"), omniout_int(info, "Desired digits ", 32, glob_desired_digits_correct, 4," "), omniout_int(info, "Estimated correct digits ", 32,glob_est_digits, 4," "), omniout_int(info, "Correct digits ", 32, glob_good_digits,4, " "), omniout_float(always, "h ", 4,glob_h,20, " ")))),0) (%i247) prog_report(x_start,x_end):=( block(mode_declare([[clock_sec],convfloat,[opt_clock_sec], convfloat,[clock_sec1],convfloat, [expect_sec],convfloat,[left_sec], convfloat,[percent_done],convfloat, [total_clock_sec],convfloat]), clock_sec1:elapsed_time_seconds(), total_clock_sec:clock_sec1-glob_orig_start_sec, glob_clock_sec:clock_sec1-glob_clock_start_sec, left_sec:-clock_sec1+glob_orig_start_sec +glob_max_sec, expect_sec:comp_expect_sec(x_end,x_start, glob_h+array_x[1], clock_sec1 -glob_orig_start_sec), opt_clock_sec:clock_sec1 -glob_optimal_clock_start_sec, glob_optimal_expect_sec :comp_expect_sec(x_end,x_start,glob_h+array_x[1], opt_clock_sec), glob_total_exp_sec :c(total_clock_sec)+glob_optimal_expect_sec, percent_done:comp_percent(x_end,x_start, glob_h+array_x[1]), glob_percent_done:percent_done, omniout_str_noeol(info, "Total Elapsed Time "), omniout_timestr(total_clock_sec), omniout_str_noeol(info, "Elapsed Time(since restart) "), omniout_timestr(glob_clock_sec), if c(percent_done) < glob__100 then (omniout_str_noeol(info, "Expected Time Remaining "), omniout_timestr(expect_sec), omniout_str_noeol(info, "Optimized Time Remaining "), omniout_timestr(glob_optimal_expect_sec), omniout_str_noeol(info, "Expected Total Time "), omniout_timestr(glob_total_exp_sec)), omniout_str_noeol(info, "Time to Timeout "), omniout_timestr(left_sec), omniout_float(info, "Percent Done ",33, percent_done,4,"%")),0) (%i248) check_for_pole():=( block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc], convfloat,[m,n],fixnum,[nr1,nr2], convfloat,[ord_no],fixnum, [term1,term2,term3,part1,part2, part3,part4,part5,part6,part7, part8,part9,part10,part11,part12, part13,part14,rad_c,rcs,rm0,rm1, rm2,rm3,rm4],convfloat, [found_sing],fixnum, [h_new,ratio,term,local_test, tmp_rad,tmp_ord,tmp_ratio, prev_tmp_rad],convfloat,[last_no], fixnum),tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,1]:glob_larger_float, array_ord_test_poles[1,1]:glob_larger_float, found_sing:1,last_no:-10-1+ats_max_terms,cnt:0, while last_no < ats_max_terms-3 and found_sing = 1 do (tmp_rad :comp_rad_from_ratio( array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,1] then ( array_rad_test_poles[1,1]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_ratio( array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,1]:rad_c, array_ord_test_poles[1,1] :tmp_ord)), tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,2]:glob_larger_float, array_ord_test_poles[1,2]:glob_larger_float, found_sing:1,last_no:-10-1+ats_max_terms,cnt:0, while last_no < ats_max_terms-4 and found_sing = 1 do (tmp_rad :comp_rad_from_three_terms( array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,2] then ( array_rad_test_poles[1,2]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_three_terms( array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,2]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,2] :tmp_ord)), tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,3]:glob_larger_float, array_ord_test_poles[1,3]:glob_larger_float, found_sing:1,last_no:-10-1+ats_max_terms,cnt:0, while last_no < ats_max_terms-7 and found_sing = 1 do (tmp_rad :comp_rad_from_six_terms( array_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,3] then ( array_rad_test_poles[1,3]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_six_terms( array_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,3]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,3] :tmp_ord)), if abs(glob_min_pole_est)*glob_ratio_of_radius < abs(glob_h) then (h_new :glob_check_sign*glob_min_pole_est *glob_ratio_of_radius, omniout_str(always, "SETTING H FOR POLE"), glob_h_reason:6, if glob_check_sign*glob_min_h > glob_check_sign*h_new then ( omniout_str(always, "SETTING H FOR MIN H"), h_new:glob_min_h,glob_h_reason:5), term:1,ratio:c(1.0), while term <= ats_max_terms do ( array_y[term] :array_y[term]*ratio, array_y_higher[1,term] :array_y_higher[1,term]*ratio, array_x[term] :array_x[term]*ratio, ratio:ratio*h_new/abs(glob_h), term:1+term),glob_h:h_new), if reached_interval() then display_poles()),0) (%i249) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:array_const_0D1[1]*array_x[1], array_tmp2[1]:array_const_0D2[1]+array_tmp1[1], array_tmp3[1]:log(array_tmp2[1]), array_tmp4[1]:array_tmp3[1]+array_const_0D0[1], if not array_y_set_initial[1,2] then (if 1 <= ats_max_terms then ( temporary :c(array_tmp4[1])*expt(glob_h,c(1)) *c(factorial_3(0,1)), if 2 <= ats_max_terms then (array_y[2]:temporary, array_y_higher[1,2]:temporary), temporary:c(temporary)*c(1)/c(glob_h), array_y_higher[2,1]:c(temporary),0)), kkk:2,array_tmp1[2]:array_const_0D1[1]*array_x[2], array_tmp2[2]:array_tmp1[2], array_tmp3[2]:array_tmp2[2]/array_tmp2[1], array_tmp4[2]:array_tmp3[2], if not array_y_set_initial[1,3] then (if 2 <= ats_max_terms then ( temporary :c(array_tmp4[2])*expt(glob_h,c(1)) *c(factorial_3(1,2)), if 3 <= ats_max_terms then (array_y[3]:temporary, array_y_higher[1,3]:temporary), temporary:c(temporary)*c(2)/c(glob_h), array_y_higher[2,2]:c(temporary),0)), kkk:3, array_tmp3[3]:neg(array_tmp2[2])*array_tmp3[2]*c(1) /array_tmp2[1] /c(2),array_tmp4[3]:array_tmp3[3], if not array_y_set_initial[1,4] then (if 3 <= ats_max_terms then ( temporary :c(array_tmp4[3])*expt(glob_h,c(1)) *c(factorial_3(2,3)), if 4 <= ats_max_terms then (array_y[4]:temporary, array_y_higher[1,4]:temporary), temporary:c(temporary)*c(3)/c(glob_h), array_y_higher[2,3]:c(temporary),0)), kkk:4, array_tmp3[4]:neg(array_tmp2[2])*array_tmp3[3]*c(2) /array_tmp2[1] /c(3),array_tmp4[4]:array_tmp3[4], if not array_y_set_initial[1,5] then (if 4 <= ats_max_terms then ( temporary :c(array_tmp4[4])*expt(glob_h,c(1)) *c(factorial_3(3,4)), if 5 <= ats_max_terms then (array_y[5]:temporary, array_y_higher[1,5]:temporary), temporary:c(temporary)*c(4)/c(glob_h), array_y_higher[2,4]:c(temporary),0)), kkk:5, array_tmp3[5]:neg(array_tmp2[2])*array_tmp3[4]*c(3) /array_tmp2[1] /c(4),array_tmp4[5]:array_tmp3[5], if not array_y_set_initial[1,6] then (if 5 <= ats_max_terms then ( temporary :c(array_tmp4[5])*expt(glob_h,c(1)) *c(factorial_3(4,5)), if 6 <= ats_max_terms then (array_y[6]:temporary, array_y_higher[1,6]:temporary), temporary:c(temporary)*c(5)/c(glob_h), array_y_higher[2,5]:c(temporary),0)), kkk:6, while kkk <= ats_max_terms do (array_tmp3[kkk] :neg(array_tmp2[2])*array_tmp3[kkk-1]*c(kkk-2) /array_tmp2[1] /c(kkk-1),array_tmp4[kkk]:array_tmp3[kkk], order_d:1, if order_d+kkk <= ats_max_terms then (if not array_y_set_initial[1,order_d+kkk] then ( temporary :c(array_tmp4[kkk])*expt(glob_h,c(order_d)) *c( factorial_3( kkk-1, -1+order_d+kkk)), array_y[order_d+kkk]:c(temporary), array_y_higher[1,order_d+kkk]:c(temporary), term:-1+order_d+kkk,adj2:-1+order_d+kkk, adj3:2, while term >= 1 and term <= ats_max_terms and adj3 < 1+order_d do ( if adj3 <= 1+order_d then ( if adj2 > 0 then temporary :c(temporary)*c(adj2) /c(glob_h) else temporary:c(temporary), array_y_higher[adj3,term] :c(temporary)),term:term-1, adj2:adj2-1,adj3:1+adj3))), kkk:1+kkk)),0) (%i250) exact_soln_y(x):=block( -c(2.0)-c(x) +c(10.0)*(c(0.2)+c(0.1)*c(x)) *log(c(0.2)+c(0.1)*c(x))) (%o250) exact_soln_y(x) := block(- c(2.0) - c(x) + c(10.0) (c(0.2) + c(0.1) c(x)) log(c(0.2) + c(0.1) c(x))) (%i251) main_prog():=block( mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat, [niii,done_once,term,ord,order_diff,term_no, html_log_file,iiif,jjjf,rows,r_order, sub_iter,calc_term,iii],fixnum,[temp_sum], convfloat,[current_iter],fixnum, [x_start,x_end],convfloat,[it,opt_iter], fixnum,[tmp],convfloat,[subiter],fixnum, [est_needed_step_err,estimated_step_error, min_value,est_answer,last_min_pole_est], convfloat,[repeat_it],fixnum],[found_h], boolean),Digits:32,max_terms:30, glob_html_log:true,term:1, while term <= 30 do (array_y_init[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_norms[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_fact_1[term]:c(0.0),term:1+term), term:1, while term <= 2 do (array_1st_rel_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_last_rel_error[term]:c(0.0),term:1+term), term:1, while term <= 2 do (array_est_rel_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_max_est_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_type_pole[term]:0,term:1+term), term:1, while term <= 2 do (array_type_real_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_type_complex_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_est_digits[term]:0,term:1+term), term:1, while term <= 30 do (array_y[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_x[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp0[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp1[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp2[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp3[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp4[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_m1[term]:c(0.0),term:1+term), ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_higher[ord,term]:c(0.0),term:1+term), ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_higher_work[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_higher_work2[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_set_initial[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_rad_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_ord_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 4 do (array_rad_test_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 4 do (array_ord_test_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 30 do (term:1, while term <= 30 do (array_fact_2[ord,term]:c(0.0),term:1+term), ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x), zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2),zero_ats_ar(array_tmp3), zero_ats_ar(array_tmp4),zero_ats_ar(array_m1), zero_ats_ar(array_const_1),array_const_1[1]:c(1), zero_ats_ar(array_const_0D0),array_const_0D0[1]:c(0.0), zero_ats_ar(array_const_0D1),array_const_0D1[1]:c(0.1), zero_ats_ar(array_const_0D2),array_const_0D2[1]:c(0.2), 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/lin_lnpostode.ode#################"), omniout_str(always, "diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; "), 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(20.0),"), omniout_str(always,"x_end:c(30.0),"), omniout_str(always, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(always,"glob_look_poles:true,"), omniout_str(always,"glob_min_h:c(0.001),"), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""), omniout_str(always,"glob_type_given_pole:1,"), omniout_str(always,""), omniout_str(always,"array_given_rad_poles[1,1]:c(-2.0),"), omniout_str(always,""), omniout_str(always,"array_given_rad_poles[1,2]:c(0.0),"), omniout_str(always,""), omniout_str(always,"array_given_ord_poles[1,1]:c(1.0),"), omniout_str(always,""), omniout_str(always,"array_given_ord_poles[1,2]:c(0.0),"), omniout_str(always,"/* END SECOND INPUT BLOCK */"), omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"), omniout_str(always,"glob_desired_digits_correct:8,"), omniout_str(always,"glob_max_minutes:(3.0),"), omniout_str(always,"glob_subiter_method:3,"), omniout_str(always,"glob_max_iter:100000,"), omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"), omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"), omniout_str(always,"glob_look_poles:false,"), omniout_str(always,"glob_h:c(0.001),"), omniout_str(always,"glob_display_interval:c(0.01),"), omniout_str(always,"/* END OVERRIDE BLOCK */"), omniout_str(always,"!"), omniout_str(always,"/* BEGIN USER DEF BLOCK */"), omniout_str(always,"exact_soln_y (x) := (block("), omniout_str(always,""), omniout_str(always, " (c(10.0) * (c(0.1) * c(x) + c(0.2)) * ln(c(0.1) * c(x) + c(0.2)) - c(x) - c(2.0)) "), omniout_str(always,"));"),omniout_str(always,""), omniout_str(always,""), omniout_str(always,"/* END USER DEF BLOCK */"), omniout_str(always, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false, glob_small_float:glob__0,glob_smallish_float:glob__0, glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100), glob_almost_1:c(0.99),x_start:c(20.0),x_end:c(30.0), array_y_init[1+0]:exact_soln_y(x_start), glob_look_poles:true,glob_min_h:c(0.001), glob_type_given_pole:1,array_given_rad_poles[1,1]:c(-2.0), array_given_rad_poles[1,2]:c(0.0), array_given_ord_poles[1,1]:c(1.0), array_given_ord_poles[1,2]:c(0.0), glob_desired_digits_correct:8,glob_max_minutes:3.0, glob_subiter_method:3,glob_max_iter:100000, glob_upper_ratio_limit:c(1.000001), glob_lower_ratio_limit:c(0.999999),glob_look_poles:false, glob_h:c(0.001),glob_display_interval:c(0.01), glob_last_good_h:glob_h, glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes, glob_check_sign:c(my_check_sign(x_start,x_end)), glob__pi:3.141592654,glob_prec:1.0E-16, if glob_optimize then (omniout_str(always,"START of Optimize"), found_h:false,glob_min_pole_est:glob_larger_float, last_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float, glob_min_h:abs(glob_min_h)*glob_check_sign, glob_max_h:abs(glob_max_h)*glob_check_sign, glob_h:abs(glob_min_h)*glob_check_sign, glob_display_interval :c(abs(c(glob_display_interval)) *glob_check_sign), display_max:c(x_end)-c(x_start)/glob__10, if glob_display_interval > display_max then glob_display_interval:c(display_max), chk_data(),min_value:glob_larger_float, est_answer:est_size_answer(),opt_iter:1, est_needed_step_err :estimated_needed_step_error( x_start,x_end,glob_h,est_answer), omniout_float(always,"est_needed_step_err",32, est_needed_step_err,16,""), estimated_step_error:glob_small_float, while opt_iter <= 100 and not found_h do (omniout_int(always,"opt_iter",32,opt_iter, 4,""),array_x[1]:c(x_start), array_x[2]:c(glob_h), glob_next_display:c(x_start),order_diff:1, term_no:1, while term_no <= order_diff do ( array_y[term_no] :array_y_init[term_no] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no),rows:order_diff, r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < ats_max_terms then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h, c(term_no-1)) /c( factorial_1( term_no-1)), term_no:1+term_no), r_order:1+r_order),atomall(), if glob_check_sign*glob_min_h >= glob_check_sign*glob_h then ( omniout_str(always, "SETTING H FOR MIN H"), glob_h:glob_check_sign*abs(glob_min_h), glob_h_reason:1,found_h:true), if glob_check_sign*glob_display_interval <= glob_check_sign*glob_h then ( omniout_str(always, "SETTING H FOR DISPLAY INTERVAL"), glob_h_reason:2, glob_h:glob_display_interval, found_h:true), if glob_look_poles then check_for_pole(), if not found_h then (est_answer:est_size_answer(), est_needed_step_err :estimated_needed_step_error( x_start,x_end,glob_h, est_answer), omniout_float(always, "est_needed_step_err", 32, est_needed_step_err, 16,""), estimated_step_error :test_suggested_h(), omniout_float(always, "estimated_step_error", 32, estimated_step_error, 32,""), if estimated_step_error < est_needed_step_err then ( omniout_str(always, "Double H and LOOP"), glob_h:glob_h*glob__2) else ( omniout_str(always, "Found H for OPTIMAL"), found_h:true,glob_h_reason:3, glob_h:glob_h/glob__2)), opt_iter:1+opt_iter), if not found_h and opt_iter = 1 then (omniout_str(always, "Beginning glob_h too large."), found_h:false), if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then (omniout_str(always, "SETTING H FOR MAX H"), glob_h:glob_check_sign*abs(glob_max_h), glob_h_reason:1,found_h:true)) else (found_h:true,glob_h:glob_h*glob_check_sign), if glob_html_log then html_log_file:openw("entry.html"), if found_h then (omniout_str(always,"START of Soultion"), array_x[1]:c(x_start),array_x[2]:c(glob_h), glob_next_display:c(x_start), glob_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float,order_diff:1, term_no:1, while term_no <= order_diff do (array_y[term_no] :array_y_init[term_no] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no),rows:order_diff, r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < ats_max_terms then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no), r_order:1+r_order),current_iter:1, glob_clock_start_sec:elapsed_time_seconds(), glob_clock_sec:elapsed_time_seconds(),glob_iter:0, omniout_str(debugl," "), glob_reached_optimal_h:true, glob_optimal_clock_start_sec :elapsed_time_seconds(), while glob_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec-glob_orig_start_sec < glob_max_sec do (if reached_interval() then (omniout_str(info," "), omniout_str(info, "TOP MAIN SOLVE Loop")), glob_iter:1+glob_iter, glob_clock_sec:elapsed_time_seconds(), track_estimated_error(),atomall(), track_estimated_error(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display :glob_display_interval +glob_next_display, array_x[1]:glob_h+array_x[1], array_x[2]:glob_h,order_diff:2,ord:2, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[2,iii] :array_y_higher[2,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:2, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:1, calc_term:2,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:1, calc_term:2,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:1, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:1, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)), term_no:ats_max_terms, while term_no >= 1 do ( array_y[term_no] :array_y_higher_work2[1,term_no], ord:1, while ord <= order_diff do ( array_y_higher[ord,term_no] :array_y_higher_work2[ ord,term_no],ord:1+ord), term_no:term_no-1)), omniout_str(always,"Finished!"), if glob_iter >= glob_max_iter then omniout_str(always, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds()-glob_orig_start_sec >= glob_max_sec then omniout_str(always, "Maximum Time Reached before Solution Completed!"), glob_clock_sec:elapsed_time_seconds(), omniout_str(info, "diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; "), 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, "2015-04-24T21:27:40-05:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "lin_ln"), logitem_str(html_log_file, "diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; "), 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, "lin_ln diffeq.max"), logitem_str(html_log_file, "lin_ln maxima results"), logitem_str(html_log_file,"OK"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i252) main():=(glob_iolevel:2,compile(all),main_prog()) (%i253) main() warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable secs in translation. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable sec_temp in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable years_int in translation. warning: encountered undefined variable days_int in translation. warning: encountered undefined variable hours_int in translation. warning: encountered undefined variable minutes_int in translation. warning: encountered undefined variable sec_int in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable iii in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_ats in translation. warning: encountered undefined variable ma_ats in translation. warning: encountered undefined variable ret_ats in translation. warning: encountered undefined variable lll_ats in translation. warning: encountered undefined variable ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_att in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable ma_att in translation. warning: encountered undefined variable lll_att in translation. warning: encountered undefined variable ret_att in translation. warning: encountered undefined variable al_att in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_h_reason in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable errflag in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable sub1 in translation. warning: encountered undefined variable sub2 in translation. warning: encountered undefined variable rrr in translation. warning: encountered undefined variable ms2 in translation. warning: encountered undefined variable sec_left in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ret in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__m2 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temp in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm0 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm1 in translation. warning: encountered undefined variable rm2 in translation. warning: encountered undefined variable rm3 in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable rm4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__8 in translation. warning: encountered undefined variable glob__5 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable nr1 in translation. warning: encountered undefined variable dr2 in translation. warning: encountered undefined variable nr2 in translation. warning: encountered undefined variable dr1 in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable ds1 in translation. warning: encountered undefined variable ds2 in translation. warning: encountered undefined variable rcs in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable ord_no in translation. warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any. warning: encountered undefined variable rad_c in translation. warning: encountered undefined variable glob_six_term_ord_save in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_2 in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob_log_10 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob__10 in translation. warning: encountered undefined variable ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_x in translation. warning: encountered undefined variable array_given_rad_poles in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable rad_given in translation. warning: encountered undefined variable array_given_ord_poles in translation. warning: variable glob_least_given_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable array_rad_test_poles in translation. warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable array_ord_test_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: variable glob_least_3_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob__small in translation. warning: variable glob_least_6_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_estimated_size_answer in translation. warning: encountered undefined variable array_y in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob__small in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable array_max_est_error in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_next_display in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__10 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable always in translation. warning: encountered undefined variable ind_var in translation. warning: encountered undefined variable closed_form_val_y in translation. warning: encountered undefined variable term_no in translation. warning: encountered undefined variable numeric_val in translation. warning: encountered undefined variable abserr in translation. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable relerr in translation. warning: variable glob_good_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_apfp_est_good_digits in translation. warning: encountered undefined variable glob_min_apfp_est_good_digits in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable est_rel_err in translation. warning: variable glob_est_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_est_digits in translation. warning: encountered undefined variable array_est_digits in translation. warning: encountered undefined variable array_1st_rel_error in translation. warning: encountered undefined variable array_last_rel_error in translation. warning: encountered undefined variable array_est_rel_error in translation. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable clock_sec1 in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_clock_start_sec in translation. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_optimal_clock_start_sec in translation. warning: encountered undefined variable opt_clock_sec in translation. warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_optimal_expect_sec in translation. warning: encountered undefined variable total_clock_sec in translation. warning: variable glob_total_exp_sec (declared type convfloat) assigned type any. warning: encountered undefined variable percent_done in translation. warning: variable glob_percent_done (declared type convfloat) assigned type any. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable expect_sec in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable left_sec in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable last_no in translation. warning: encountered undefined variable found_sing in translation. warning: encountered undefined variable array_y_higher in translation. warning: variable tmp_rad (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_rad in translation. warning: encountered undefined variable prev_tmp_rad in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable cnt in translation. warning: encountered undefined variable tmp_ratio in translation. warning: encountered undefined variable glob_upper_ratio_limit in translation. warning: encountered undefined variable glob_lower_ratio_limit in translation. warning: variable tmp_ord (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_ord in translation. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_ratio_of_radius in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable h_new in translation. warning: variable ratio (declared type convfloat) assigned type any. warning: encountered undefined variable term in translation. warning: encountered undefined variable ratio in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_const_0D1 in translation. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_const_0D2 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp4 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temporary in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable array_y_set_initial in translation. warning: encountered undefined variable kkk in translation. warning: encountered undefined variable order_d in translation. warning: encountered undefined variable adj3 in translation. warning: encountered undefined variable adj2 in translation. modedeclare: [found_h] is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: variable term (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable array_y_init in translation. warning: variable term (declared type [found_h]) assigned type any. warning: encountered undefined variable array_norms in translation. warning: encountered undefined variable array_fact_1 in translation. warning: encountered undefined variable array_type_pole in translation. warning: encountered undefined variable array_type_real_pole in translation. warning: encountered undefined variable array_type_complex_pole in translation. warning: encountered undefined variable array_tmp0 in translation. warning: encountered undefined variable array_m1 in translation. warning: variable ord (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable ord in translation. warning: variable ord (declared type [found_h]) assigned type any. warning: encountered undefined variable array_y_higher_work in translation. warning: encountered undefined variable array_y_higher_work2 in translation. warning: encountered undefined variable array_const_1 in translation. warning: encountered undefined variable glob__m1 in translation. warning: variable iiif (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable iiif in translation. warning: encountered undefined variable ats_max_terms in translation. warning: variable jjjf (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable jjjf in translation. warning: variable jjjf (declared type [found_h]) assigned type any. warning: variable iiif (declared type [found_h]) assigned type any. warning: variable glob_orig_start_sec (declared type convfloat) assigned type any. warning: variable opt_iter (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob__0 in translation. warning: variable glob_large_float (declared type convfloat) assigned type any. warning: variable glob_larger_float (declared type convfloat) assigned type any. warning: variable glob_almost_1 (declared type convfloat) assigned type any. warning: variable x_start (declared type [found_h]) assigned type any. warning: variable x_end (declared type [found_h]) assigned type any. warning: encountered undefined variable x_start in translation. warning: variable glob_min_h (declared type convfloat) assigned type any. warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_h (declared type convfloat) assigned type any. warning: 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/lin_lnpostode.ode#################" "diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:c(20.0)," "x_end:c(30.0)," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_min_h:c(0.001)," "" "" "" "" "" "" "" "glob_type_given_pole:1," "" "array_given_rad_poles[1,1]:c(-2.0)," "" "array_given_rad_poles[1,2]:c(0.0)," "" "array_given_ord_poles[1,1]:c(1.0)," "" "array_given_ord_poles[1,2]:c(0.0)," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:8," "glob_max_minutes:(3.0)," "glob_subiter_method:3," "glob_max_iter:100000," "glob_upper_ratio_limit:c(1.000001)," "glob_lower_ratio_limit:c(0.999999)," "glob_look_poles:false," "glob_h:c(0.001)," "glob_display_interval:c(0.01)," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" "" " (c(10.0) * (c(0.1) * c(x) + c(0.2)) * ln(c(0.1) * c(x) + c(0.2)) - c(x) - c(2.0)) " "));" "" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 20. " " y[1] (closed_form) = -4.653938071986055 " " y[1] (numeric) = -4.653938071986055 " " 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] = 20.010000000000012 " " y[1] (closed_form) = -4.646051225999404 " " y[1] (numeric) = -4.646051225999413 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 1.91168451766063060000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.020000000000024 " " y[1] (closed_form) = -4.6381598366232275 " " y[1] (numeric) = -4.638159836623248 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 4.40435525567730000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.030000000000037 " " y[1] (closed_form) = -4.6302639059208275 " " y[1] (numeric) = -4.6302639059208595 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 6.9055293086681440000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.04000000000005 " " y[1] (closed_form) = -4.622363435953634 " " y[1] (numeric) = -4.622363435953676 " " absolute error = 4.174438572590588600000000000000E-14 " " relative error = 9.0309613911381360000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.05000000000006 " " y[1] (closed_form) = -4.614458428781205 " " y[1] (numeric) = -4.614458428781254 " " absolute error = 4.88498130835068900000000000000E-14 " " relative error = 1.0586250550838608000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.060000000000073 " " y[1] (closed_form) = -4.606548886461226 " " y[1] (numeric) = -4.606548886461285 " " absolute error = 5.86197757002082700000000000000E-14 " " relative error = 1.2725312841570702000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.070000000000086 " " y[1] (closed_form) = -4.598634811049525 " " y[1] (numeric) = -4.5986348110495925 " " absolute error = 6.75015598972095200000000000000E-14 " " relative error = 1.4678608472022580000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.080000000000098 " " y[1] (closed_form) = -4.5907162046000565 " " y[1] (numeric) = -4.5907162046001355 " " absolute error = 7.90478793533111500000000000000E-14 " " relative error = 1.721907341475442000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.09000000000011 " " y[1] (closed_form) = -4.582793069164932 " " y[1] (numeric) = -4.582793069165018 " " absolute error = 8.61533067109121500000000000000E-14 " " relative error = 1.8799301083566240000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.100000000000122 " " y[1] (closed_form) = -4.574865406794384 " " y[1] (numeric) = -4.574865406794480 " " absolute error = 9.68114477473136500000000000000E-14 " " relative error = 2.1161594744084417000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.110000000000134 " " y[1] (closed_form) = -4.5669332195368035 " " y[1] (numeric) = -4.566933219536911 " " absolute error = 1.07469588783715150000000000000E-13 " " relative error = 2.353211304338169200000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.120000000000147 " " y[1] (closed_form) = -4.558996509438728 " " y[1] (numeric) = -4.558996509438844 " " absolute error = 1.15463194561016280000000000000E-13 " " relative error = 2.5326449432888753000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.13000000000016 " " y[1] (closed_form) = -4.551055278544837 " " y[1] (numeric) = -4.551055278544962 " " absolute error = 1.25233157177717660000000000000E-13 " " relative error = 2.7517388718196356000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.14000000000017 " " y[1] (closed_form) = -4.543109528897965 " " y[1] (numeric) = -4.543109528898102 " " absolute error = 1.36779476633819290000000000000E-13 " " relative error = 3.010701717926626000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.150000000000183 " " y[1] (closed_form) = -4.535159262539110 " " y[1] (numeric) = -4.535159262539256 " " absolute error = 1.45661260830820540000000000000E-13 " " relative error = 3.21182239472818040000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.160000000000196 " " y[1] (closed_form) = -4.527204481507415 " " y[1] (numeric) = -4.527204481507571 " " absolute error = 1.56319401867222040000000000000E-13 " " relative error = 3.452890243985018000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.170000000000208 " " y[1] (closed_form) = -4.519245187840188 " " y[1] (numeric) = -4.519245187840353 " " absolute error = 1.6520118606422330000000000000E-13 " " relative error = 3.65550394363921000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.18000000000022 " " y[1] (closed_form) = -4.511281383572896 " " y[1] (numeric) = -4.511281383573071 " " absolute error = 1.74971148680924670000000000000E-13 " " relative error = 3.878524388171704000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.190000000000232 " " y[1] (closed_form) = -4.503313070739175 " " y[1] (numeric) = -4.503313070739361 " " absolute error = 1.8651746813702630000000000000E-13 " " relative error = 4.1417832872634660000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.200000000000244 " " y[1] (closed_form) = -4.495340251370827 " " y[1] (numeric) = -4.495340251371023 " " absolute error = 1.96287430753727680000000000000E-13 " " relative error = 4.3664643781718415000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.210000000000257 " " y[1] (closed_form) = -4.4873629274978235 " " y[1] (numeric) = -4.487362927498029 " " absolute error = 2.05169214950728930000000000000E-13 " " relative error = 4.572155590391088000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.22000000000027 " " y[1] (closed_form) = -4.479381101148306 " " y[1] (numeric) = -4.47938110114852 " " absolute error = 2.14050999147730180000000000000E-13 " " relative error = 4.778584235506495000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.23000000000028 " " y[1] (closed_form) = -4.471394774348589 " " y[1] (numeric) = -4.471394774348813 " " absolute error = 2.23820961764431560000000000000E-13 " " relative error = 5.0056184492687450000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.240000000000293 " " y[1] (closed_form) = -4.4634039491231725 " " y[1] (numeric) = -4.463403949123403 " " absolute error = 2.30926389122032560000000000000E-13 " " relative error = 5.173773016161748000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.250000000000306 " " y[1] (closed_form) = -4.455408627494723 " " y[1] (numeric) = -4.4554086274949665 " " absolute error = 2.4336088699783430000000000000E-13 " " relative error = 5.462145166574232000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.260000000000318 " " y[1] (closed_form) = -4.447408811484106 " " y[1] (numeric) = -4.447408811484355 " " absolute error = 2.48689957516035070000000000000E-13 " " relative error = 5.5917944146233520000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.27000000000033 " " y[1] (closed_form) = -4.4394045031103495 " " y[1] (numeric) = -4.43940450311061 " " absolute error = 2.6023627697213670000000000000E-13 " " relative error = 5.861963621242650000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.280000000000342 " " y[1] (closed_form) = -4.431395704390688 " " y[1] (numeric) = -4.431395704390956 " " absolute error = 2.6822988274943780000000000000E-13 " " relative error = 6.05294360157618000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.290000000000354 " " y[1] (closed_form) = -4.42338241734053 " " y[1] (numeric) = -4.423382417340812 " " absolute error = 2.8155255904493970000000000000E-13 " " relative error = 6.365096491345587000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.300000000000367 " " y[1] (closed_form) = -4.4153646439734935 " " y[1] (numeric) = -4.415364643973781 " " absolute error = 2.8776980798284060000000000000E-13 " " relative error = 6.517464154984707000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.31000000000038 " " y[1] (closed_form) = -4.407342386301370 " " y[1] (numeric) = -4.407342386301669 " " absolute error = 2.9931612743894220000000000000E-13 " " relative error = 6.791306442840888000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.32000000000039 " " y[1] (closed_form) = -4.399315646334166 " " y[1] (numeric) = -4.399315646334474 " " absolute error = 3.07309733216243330000000000000E-13 " " relative error = 6.985398591990472000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.330000000000403 " " y[1] (closed_form) = -4.39128442608007 " " y[1] (numeric) = -4.391284426080387 " " absolute error = 3.1707969583294470000000000000E-13 " " relative error = 7.220659494288089000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.340000000000416 " " y[1] (closed_form) = -4.383248727545485 " " y[1] (numeric) = -4.38324872754581 " " absolute error = 3.25073301610245840000000000000E-13 " " relative error = 7.416264095792692000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.350000000000428 " " y[1] (closed_form) = -4.37520855273501 " " y[1] (numeric) = -4.375208552735347 " " absolute error = 3.36619621066347460000000000000E-13 " " relative error = 7.693796010156392000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.36000000000044 " " y[1] (closed_form) = -4.367163903651456 " " y[1] (numeric) = -4.367163903651802 " " absolute error = 3.46389583683048840000000000000E-13 " " relative error = 7.931682696713694000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.370000000000452 " " y[1] (closed_form) = -4.3591147822958405 " " y[1] (numeric) = -4.359114782296197 " " absolute error = 3.5615954629975020000000000000E-13 " " relative error = 8.17045579405848000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.380000000000464 " " y[1] (closed_form) = -4.351061190667390 " " y[1] (numeric) = -4.351061190667756 " " absolute error = 3.65041330496751470000000000000E-13 " " relative error = 8.38970803903494000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.390000000000477 " " y[1] (closed_form) = -4.343003130763542 " " y[1] (numeric) = -4.343003130763918 " " absolute error = 3.7658764995285310000000000000E-13 " " relative error = 8.671134664520616000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.40000000000049 " " y[1] (closed_form) = -4.334940604579959 " " y[1] (numeric) = -4.334940604580345 " " absolute error = 3.8635761256955450000000000000E-13 " " relative error = 8.91263912961943000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.4100000000005 " " y[1] (closed_form) = -4.326873614110510 " " y[1] (numeric) = -4.326873614110908 " " absolute error = 3.970157536059560000000000000E-13 " " relative error = 9.17558008422605000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.420000000000513 " " y[1] (closed_form) = -4.3188021613473 " " y[1] (numeric) = -4.318802161347704 " " absolute error = 4.041211809635570000000000000E-13 " " relative error = 9.357251521738768000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.430000000000526 " " y[1] (closed_form) = -4.310726248280634 " " y[1] (numeric) = -4.3107262482810516 " " absolute error = 4.17443857259058860000000000000E-13 " " relative error = 9.683840569221012000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.440000000000538 " " y[1] (closed_form) = -4.302645876899067 " " y[1] (numeric) = -4.302645876899494 " " absolute error = 4.27213819875760240000000000000E-13 " " relative error = 9.92909554024592000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.45000000000055 " " y[1] (closed_form) = -4.294561049189369 " " y[1] (numeric) = -4.294561049189805 " " absolute error = 4.3609560407276150000000000000E-13 " " relative error = 1.015460250949460500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.460000000000562 " " y[1] (closed_form) = -4.286471767136536 " " y[1] (numeric) = -4.286471767136982 " " absolute error = 4.45865566689462870000000000000E-13 " " relative error = 1.040169143554890400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.470000000000574 " " y[1] (closed_form) = -4.278378032723808 " " y[1] (numeric) = -4.2783780327242615 " " absolute error = 4.538591724667640000000000000E-13 " " relative error = 1.060820640428113100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.480000000000587 " " y[1] (closed_form) = -4.270279847932649 " " y[1] (numeric) = -4.2702798479331125 " " absolute error = 4.6362913508346537000000000000E-13 " " relative error = 1.085711362237582600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.4900000000006 " " y[1] (closed_form) = -4.262177214742767 " " y[1] (numeric) = -4.26217721474324 " " absolute error = 4.7339909770016675000000000000E-13 " " relative error = 1.110697828477640200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.50000000000061 " " y[1] (closed_form) = -4.254070135132107 " " y[1] (numeric) = -4.254070135132592 " " absolute error = 4.8494541715626840000000000000E-13 " " relative error = 1.139956328296897700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.510000000000623 " " y[1] (closed_form) = -4.245958611076855 " " y[1] (numeric) = -4.245958611077352 " " absolute error = 4.9737991503207013000000000000E-13 " " relative error = 1.171419602947861200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.520000000000636 " " y[1] (closed_form) = -4.237842644551446 " " y[1] (numeric) = -4.237842644551952 " " absolute error = 5.0626169922907140000000000000E-13 " " relative error = 1.194621277125443200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.530000000000648 " " y[1] (closed_form) = -4.229722237528552 " " y[1] (numeric) = -4.229722237529070 " " absolute error = 5.1869619710487310000000000000E-13 " " relative error = 1.226312670138713400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.54000000000066 " " y[1] (closed_form) = -4.221597391979106 " " y[1] (numeric) = -4.221597391979634 " " absolute error = 5.2757798130187440000000000000E-13 " " relative error = 1.249711737799191600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.550000000000672 " " y[1] (closed_form) = -4.213468109872284 " " y[1] (numeric) = -4.213468109872819 " " absolute error = 5.3468340865947540000000000000E-13 " " relative error = 1.268986485044697200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.560000000000684 " " y[1] (closed_form) = -4.205334393175512 " " y[1] (numeric) = -4.20533439317606 " " absolute error = 5.4800608495497730000000000000E-13 " " relative error = 1.303121306701057700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.570000000000697 " " y[1] (closed_form) = -4.197196243854481 " " y[1] (numeric) = -4.19719624385504 " " absolute error = 5.5866422599137880000000000000E-13 " " relative error = 1.33104147038483800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.58000000000071 " " y[1] (closed_form) = -4.189053663873143 " " y[1] (numeric) = -4.1890536638737075 " " absolute error = 5.6488147492927960000000000000E-13 " " relative error = 1.348470371246087000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.59000000000072 " " y[1] (closed_form) = -4.1809066551936915 " " y[1] (numeric) = -4.180906655194268 " " absolute error = 5.7642779438538130000000000000E-13 " " relative error = 1.37871481457094800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.600000000000733 " " y[1] (closed_form) = -4.1727552197766045 " " y[1] (numeric) = -4.172755219777189 " " absolute error = 5.8442140016268240000000000000E-13 " " relative error = 1.400564781257335200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.610000000000746 " " y[1] (closed_form) = -4.16459935958061 " " y[1] (numeric) = -4.164599359581206 " " absolute error = 5.959677196187840000000000000E-13 " " relative error = 1.431032539175149400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.620000000000758 " " y[1] (closed_form) = -4.156439076562712 " " y[1] (numeric) = -4.156439076563317 " " absolute error = 6.0484950381578530000000000000E-13 " " relative error = 1.455210801059023400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.63000000000077 " " y[1] (closed_form) = -4.1482743726781806 " " y[1] (numeric) = -4.148274372678795 " " absolute error = 6.1461946643248670000000000000E-13 " " relative error = 1.48162684339435390000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.640000000000782 " " y[1] (closed_form) = -4.1401052498805555 " " y[1] (numeric) = -4.140105249881183 " " absolute error = 6.2705396430828840000000000000E-13 " " relative error = 1.514584597399738500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.650000000000794 " " y[1] (closed_form) = -4.131931710121659 " " y[1] (numeric) = -4.131931710122295 " " absolute error = 6.3593574850528970000000000000E-13 " " relative error = 1.539076134650263500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.660000000000807 " " y[1] (closed_form) = -4.123753755351583 " " y[1] (numeric) = -4.123753755352225 " " absolute error = 6.4215299744319050000000000000E-13 " " relative error = 1.557205001898669000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.67000000000082 " " y[1] (closed_form) = -4.115571387518692 " " y[1] (numeric) = -4.115571387519348 " " absolute error = 6.5636385215839250000000000000E-13 " " relative error = 1.594830438730693600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.68000000000083 " " y[1] (closed_form) = -4.1073846085696495 " " y[1] (numeric) = -4.107384608570315 " " absolute error = 6.6524563635539380000000000000E-13 " " relative error = 1.619633172329235600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.690000000000843 " " y[1] (closed_form) = -4.099193420449389 " " y[1] (numeric) = -4.099193420450063 " " absolute error = 6.7412742055239500000000000000E-13 " " relative error = 1.644536745178741500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.700000000000855 " " y[1] (closed_form) = -4.09099782510113 " " y[1] (numeric) = -4.090997825101816 " " absolute error = 6.8567374000849670000000000000E-13 " " relative error = 1.676055009859475400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.710000000000868 " " y[1] (closed_form) = -4.082797824466386 " " y[1] (numeric) = -4.082797824467082 " " absolute error = 6.9633188104489820000000000000E-13 " " relative error = 1.70552623711145300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.72000000000088 " " y[1] (closed_form) = -4.074593420484955 " " y[1] (numeric) = -4.074593420485663 " " absolute error = 7.0787820050099980000000000000E-13 " " relative error = 1.737297755751906800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.730000000000892 " " y[1] (closed_form) = -4.0663846150949325 " " y[1] (numeric) = -4.066384615095651 " " absolute error = 7.1853634153740130000000000000E-13 " " relative error = 1.76701519789865400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.740000000000904 " " y[1] (closed_form) = -4.058171410232706 " " y[1] (numeric) = -4.0581714102334345 " " absolute error = 7.2830630415410270000000000000E-13 " " relative error = 1.79466619452710500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.750000000000917 " " y[1] (closed_form) = -4.049953807832956 " " y[1] (numeric) = -4.049953807833696 " " absolute error = 7.3985262361020430000000000000E-13 " " relative error = 1.82681743722426200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.76000000000093 " " y[1] (closed_form) = -4.041731809828672 " " y[1] (numeric) = -4.041731809829420 " " absolute error = 7.4873440780720560000000000000E-13 " " relative error = 1.852508882421231900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.77000000000094 " " y[1] (closed_form) = -4.033505418151133 " " y[1] (numeric) = -4.033505418151893 " " absolute error = 7.5939254884360710000000000000E-13 " " relative error = 1.88271111630660800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.780000000000953 " " y[1] (closed_form) = -4.025274634729932 " " y[1] (numeric) = -4.025274634730701 " " absolute error = 7.6916251146030850000000000000E-13 " " relative error = 1.910832381035570700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.790000000000965 " " y[1] (closed_form) = -4.017039461492963 " " y[1] (numeric) = -4.017039461493742 " " absolute error = 7.7893247407700980000000000000E-13 " " relative error = 1.939071003767320600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.800000000000978 " " y[1] (closed_form) = -4.0087999003664265 " " y[1] (numeric) = -4.008799900367217 " " absolute error = 7.9047879353311150000000000000E-13 " " relative error = 1.97185894327341520000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.81000000000099 " " y[1] (closed_form) = -4.000555953274837 " " y[1] (numeric) = -4.000555953275638 " " absolute error = 8.011369345695130000000000000E-13 " " relative error = 2.002564003419839400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.820000000001002 " " y[1] (closed_form) = -3.99230762214102 " " y[1] (numeric) = -3.9923076221418317 " " absolute error = 8.1179507560591450000000000000E-13 " " relative error = 2.03339810565639700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.830000000001014 " " y[1] (closed_form) = -3.984054908886119 " " y[1] (numeric) = -3.984054908886939 " " absolute error = 8.2023277059306570000000000000E-13 " " relative error = 2.058788820313699800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.840000000001027 " " y[1] (closed_form) = -3.975797815429587 " " y[1] (numeric) = -3.975797815430417 " " absolute error = 8.300027332097670000000000000E-13 " " relative error = 2.08763818418690100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.85000000000104 " " y[1] (closed_form) = -3.9675363436892006 " " y[1] (numeric) = -3.9675363436900417 " " absolute error = 8.4110496345601860000000000000E-13 " " relative error = 2.119967885849080900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.86000000000105 " " y[1] (closed_form) = -3.9592704955810625 " " y[1] (numeric) = -3.959270495581912 " " absolute error = 8.4954265844316980000000000000E-13 " " relative error = 2.145705021648163500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.870000000001063 " " y[1] (closed_form) = -3.951000273019588 " " y[1] (numeric) = -3.95100027302045 " " absolute error = 8.6197715631897150000000000000E-13 " " relative error = 2.181668177056838600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.880000000001075 " " y[1] (closed_form) = -3.9427256779175295 " " y[1] (numeric) = -3.9427256779184017 " " absolute error = 8.721912081455230000000000000E-13 " " relative error = 2.212152909928537800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.890000000001088 " " y[1] (closed_form) = -3.934446712185963 " " y[1] (numeric) = -3.9344467121868445 " " absolute error = 8.8151708155237430000000000000E-13 " " relative error = 2.240510918147895800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.9000000000011 " " y[1] (closed_form) = -3.926163377734291 " " y[1] (numeric) = -3.926163377735182 " " absolute error = 8.9128704416907570000000000000E-13 " " relative error = 2.270122148313194500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.910000000001112 " " y[1] (closed_form) = -3.9178756764702527 " " y[1] (numeric) = -3.917875676471154 " " absolute error = 9.0150109599562710000000000000E-13 " " relative error = 2.300994647200801700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.920000000001124 " " y[1] (closed_form) = -3.909583610299922 " " y[1] (numeric) = -3.909583610300834 " " absolute error = 9.1171514782217860000000000000E-13 " " relative error = 2.33200063919911080000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.930000000001137 " " y[1] (closed_form) = -3.9012871811277066 " " y[1] (numeric) = -3.9012871811286303 " " absolute error = 9.2370555648813020000000000000E-13 " " relative error = 2.367694336773033300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.94000000000115 " " y[1] (closed_form) = -3.892986390856361 " " y[1] (numeric) = -3.8929863908572906 " " absolute error = 9.294787162161811000000000000E-13 " " relative error = 2.38757247751826500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.95000000000116 " " y[1] (closed_form) = -3.8846812413869642 " " y[1] (numeric) = -3.8846812413879057 " " absolute error = 9.4146912488213270000000000000E-13 " " relative error = 2.42354279896076080000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.960000000001173 " " y[1] (closed_form) = -3.8763717346189566 " " y[1] (numeric) = -3.8763717346199074 " " absolute error = 9.507949982889841000000000000E-13 " " relative error = 2.452796231583414500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.970000000001185 " " y[1] (closed_form) = -3.868057872450116 " " y[1] (numeric) = -3.868057872451075 " " absolute error = 9.5878860406628520000000000000E-13 " " relative error = 2.478733865113984500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.980000000001198 " " y[1] (closed_form) = -3.859739656776565 " " y[1] (numeric) = -3.8597396567775335 " " absolute error = 9.6855856668298660000000000000E-13 " " relative error = 2.509388333957921500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 20.99000000000121 " " y[1] (closed_form) = -3.8514170894927773 " " y[1] (numeric) = -3.8514170894937587 " " absolute error = 9.8143715376863840000000000000E-13 " " relative error = 2.548249464972622300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.000000000001222 " " y[1] (closed_form) = -3.843090172491589 " " y[1] (numeric) = -3.8430901724925794 " " absolute error = 9.9031893796563960000000000000E-13 " " relative error = 2.57688186723858900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.010000000001234 " " y[1] (closed_form) = -3.834758907664174 " " y[1] (numeric) = -3.8347589076651754 " " absolute error = 1.0014211682118912000000000000E-12 " " relative error = 2.61143188483230200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.020000000001247 " " y[1] (closed_form) = -3.8264232969000744 " " y[1] (numeric) = -3.8264232969010856 " " absolute error = 1.0111911308285926000000000000E-12 " " relative error = 2.642653601988560500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.03000000000126 " " y[1] (closed_form) = -3.818083342087185 " " y[1] (numeric) = -3.8180833420882054 " " absolute error = 1.0205170042354439000000000000E-12 " " relative error = 2.672851566612400000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.04000000000127 " " y[1] (closed_form) = -3.809739045111762 " " y[1] (numeric) = -3.809739045112793 " " absolute error = 1.0311751452718454000000000000E-12 " " relative error = 2.706681830596602300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.050000000001283 " " y[1] (closed_form) = -3.801390407858424 " " y[1] (numeric) = -3.8013904078594662 " " absolute error = 1.042277375518097000000000000E-12 " " relative error = 2.741831971174150000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.060000000001295 " " y[1] (closed_form) = -3.793037432210159 " " y[1] (numeric) = -3.793037432211208 " " absolute error = 1.048938713665847900000000000E-12 " " relative error = 2.76543201171269070000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.070000000001308 " " y[1] (closed_form) = -3.7846801200483107 " " y[1] (numeric) = -3.7846801200493716 " " absolute error = 1.0609291223317996000000000000E-12 " " relative error = 2.803220057388250400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.08000000000132 " " y[1] (closed_form) = -3.776318473252605 " " y[1] (numeric) = -3.776318473253676 " " absolute error = 1.071143174158351000000000000E-12 " " relative error = 2.836474682273706400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.090000000001332 " " y[1] (closed_form) = -3.767952493701131 " " y[1] (numeric) = -3.767952493702212 " " absolute error = 1.0813572259849025000000000000E-12 " " relative error = 2.869880200964854400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.100000000001344 " " y[1] (closed_form) = -3.75958218327035 " " y[1] (numeric) = -3.7595821832714442 " " absolute error = 1.0942358130705543000000000000E-12 " " relative error = 2.91052505233097670000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.110000000001357 " " y[1] (closed_form) = -3.751207543835111 " " y[1] (numeric) = -3.7512075438362125 " " absolute error = 1.1013412404281553000000000000E-12 " " relative error = 2.93596455956734450000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.12000000000137 " " y[1] (closed_form) = -3.7428285772686216 " " y[1] (numeric) = -3.7428285772697336 " " absolute error = 1.1119993814645568000000000000E-12 " " relative error = 2.97101338869239100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.13000000000138 " " y[1] (closed_form) = -3.734445285442483 " " y[1] (numeric) = -3.7344452854436048 " " absolute error = 1.1217693440812582000000000000E-12 " " relative error = 3.003844636455406700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.140000000001393 " " y[1] (closed_form) = -3.7260576702266697 " " y[1] (numeric) = -3.726057670227803 " " absolute error = 1.1333156635373598000000000000E-12 " " relative error = 3.04159453191827800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.150000000001405 " " y[1] (closed_form) = -3.71766573348955 " " y[1] (numeric) = -3.7176657334906915 " " absolute error = 1.141309269314660900000000000E-12 " " relative error = 3.06996204374561200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.160000000001418 " " y[1] (closed_form) = -3.709269477097866 " " y[1] (numeric) = -3.709269477099018 " " absolute error = 1.1519674103510624000000000000E-12 " " relative error = 3.10564497258463470000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.17000000000143 " " y[1] (closed_form) = -3.7008689029167563 " " y[1] (numeric) = -3.700868902917919 " " absolute error = 1.162625551387463900000000000E-12 " " relative error = 3.141493475954166000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.180000000001442 " " y[1] (closed_form) = -3.6924640128097472 " " y[1] (numeric) = -3.6924640128109187 " " absolute error = 1.1715073355844652000000000000E-12 " " relative error = 3.172698045316945700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.190000000001454 " " y[1] (closed_form) = -3.6840548086387557 " " y[1] (numeric) = -3.684054808639937 " " absolute error = 1.1812772982011666000000000000E-12 " " relative error = 3.20645962006641300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.200000000001467 " " y[1] (closed_form) = -3.6756412922640926 " " y[1] (numeric) = -3.675641292265286 " " absolute error = 1.1932677068671182000000000000E-12 " " relative error = 3.246420452884015000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.21000000000148 " " y[1] (closed_form) = -3.6672234655444704 " " y[1] (numeric) = -3.6672234655456744 " " absolute error = 1.2039258479035198000000000000E-12 " " relative error = 3.28293560295697300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.22000000000149 " " y[1] (closed_form) = -3.6588013303369955 " " y[1] (numeric) = -3.658801330338208 " " absolute error = 1.212363542890671000000000000E-12 " " relative error = 3.31355390312762800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.230000000001503 " " y[1] (closed_form) = -3.6503748884971685 " " y[1] (numeric) = -3.6503748884983955 " " absolute error = 1.227018486815723000000000000E-12 " " relative error = 3.36134924301124900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.240000000001515 " " y[1] (closed_form) = -3.641944141878909 " " y[1] (numeric) = -3.6419441418801455 " " absolute error = 1.2363443602225743000000000000E-12 " " relative error = 3.394737294308786700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.250000000001528 " " y[1] (closed_form) = -3.6335090923345277 " " y[1] (numeric) = -3.633509092335773 " " absolute error = 1.2452261444195756000000000000E-12 " " relative error = 3.427062139590019000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.26000000000154 " " y[1] (closed_form) = -3.625069741714743 " " y[1] (numeric) = -3.6250697417159987 " " absolute error = 1.255884285455977000000000000E-12 " " relative error = 3.46444172095269600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.270000000001552 " " y[1] (closed_form) = -3.6166260918686888 " " y[1] (numeric) = -3.616626091869953 " " absolute error = 1.2643219804431283000000000000E-12 " " relative error = 3.495860363573997700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.280000000001564 " " y[1] (closed_form) = -3.608178144643901 " " y[1] (numeric) = -3.6081781446451764 " " absolute error = 1.2754242106893798000000000000E-12 " " relative error = 3.534814966336022000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.290000000001577 " " y[1] (closed_form) = -3.5997259018863375 " " y[1] (numeric) = -3.5997259018876213 " " absolute error = 1.283861905676531000000000000E-12 " " relative error = 3.56655462296103900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.30000000000159 " " y[1] (closed_form) = -3.591269365440361 " " y[1] (numeric) = -3.591269365441656 " " absolute error = 1.2949641359227826000000000000E-12 " " relative error = 3.60586746397953400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.3100000000016 " " y[1] (closed_form) = -3.582808537148761 " " y[1] (numeric) = -3.5828085371500658 " " absolute error = 1.304734098539484000000000000E-12 " " relative error = 3.64165175172270300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.320000000001613 " " y[1] (closed_form) = -3.5743434188527345 " " y[1] (numeric) = -3.5743434188540544 " " absolute error = 1.319833131674386000000000000E-12 " " relative error = 3.69251909235407460000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.330000000001625 " " y[1] (closed_form) = -3.565874012391916 " " y[1] (numeric) = -3.5658740123932446 " " absolute error = 1.3287149158713873000000000000E-12 " " relative error = 3.72619703122969400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.340000000001638 " " y[1] (closed_form) = -3.5574003196043478 " " y[1] (numeric) = -3.5574003196056863 " " absolute error = 1.3384848784880887000000000000E-12 " " relative error = 3.7625365666941700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.35000000000165 " " y[1] (closed_form) = -3.5489223423265024 " " y[1] (numeric) = -3.548922342327851 " " absolute error = 1.3486989303146402000000000000E-12 " " relative error = 3.80030555819516300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.360000000001662 " " y[1] (closed_form) = -3.540440082393282 " " y[1] (numeric) = -3.5404400823946394 " " absolute error = 1.3575807145116414000000000000E-12 " " relative error = 3.83449707640282470000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.370000000001674 " " y[1] (closed_form) = -3.531953541638007 " " y[1] (numeric) = -3.5319535416393784 " " absolute error = 1.3713474800169934000000000000E-12 " " relative error = 3.882688330552066500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.380000000001687 " " y[1] (closed_form) = -3.52346272189245 " " y[1] (numeric) = -3.523462721893829 " " absolute error = 1.3788969965844444000000000000E-12 " " relative error = 3.91347122254734500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.3900000000017 " " y[1] (closed_form) = -3.5149676249867916 " " y[1] (numeric) = -3.514967624988183 " " absolute error = 1.3913314944602462000000000000E-12 " " relative error = 3.95830529012475500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.40000000000171 " " y[1] (closed_form) = -3.5064682527496664 " " y[1] (numeric) = -3.5064682527510693 " " absolute error = 1.4028778139163478000000000000E-12 " " relative error = 4.0008285054805600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.410000000001723 " " y[1] (closed_form) = -3.4979646070081394 " " y[1] (numeric) = -3.497964607009552 " " absolute error = 1.4126477765330492000000000000E-12 " " relative error = 4.0384850484273700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.420000000001735 " " y[1] (closed_form) = -3.489456689587712 " " y[1] (numeric) = -3.489456689589135 " " absolute error = 1.4228618283596006000000000000E-12 " " relative error = 4.07760277582844900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.430000000001748 " " y[1] (closed_form) = -3.4809445023123295 " " y[1] (numeric) = -3.480944502313762 " " absolute error = 1.432631790976302000000000000E-12 " " relative error = 4.115640999230611400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.44000000000176 " " y[1] (closed_form) = -3.4724280470043816 " " y[1] (numeric) = -3.472428047005824 " " absolute error = 1.4424017535930034000000000000E-12 " " relative error = 4.153870819115589000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.450000000001772 " " y[1] (closed_form) = -3.4639073254846977 " " y[1] (numeric) = -3.463907325486151 " " absolute error = 1.453503983839255000000000000E-12 " " relative error = 4.19613992887603900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.460000000001784 " " y[1] (closed_form) = -3.4553823395725622 " " y[1] (numeric) = -3.455382339574026 " " absolute error = 1.4637180356658064000000000000E-12 " " relative error = 4.23605231439271400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.470000000001797 " " y[1] (closed_form) = -3.4468530910857 " " y[1] (numeric) = -3.446853091087176 " " absolute error = 1.4761525335416080000000000000E-12 " " relative error = 4.282609367249375400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.48000000000181 " " y[1] (closed_form) = -3.4383195818402967 " " y[1] (numeric) = -3.4383195818417827 " " absolute error = 1.4859224961583095000000000000E-12 " " relative error = 4.32165324016506100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.49000000000182 " " y[1] (closed_form) = -3.4297818136509832 " " y[1] (numeric) = -3.4297818136524776 " " absolute error = 1.4943601911454607000000000000E-12 " " relative error = 4.35701240585541100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.500000000001833 " " y[1] (closed_form) = -3.421239788330844 " " y[1] (numeric) = -3.4212397883323504 " " absolute error = 1.5063505998114124000000000000E-12 " " relative error = 4.40293780327607900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.510000000001845 " " y[1] (closed_form) = -3.4126935076914293 " " y[1] (numeric) = -3.4126935076929454 " " absolute error = 1.5161205624281138000000000000E-12 " " relative error = 4.44259221934558500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.520000000001858 " " y[1] (closed_form) = -3.40414297354274 " " y[1] (numeric) = -3.4041429735442676 " " absolute error = 1.5276668818842154000000000000E-12 " " relative error = 4.48766956545996850000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.53000000000187 " " y[1] (closed_form) = -3.395588187693246 " " y[1] (numeric) = -3.3955881876947815 " " absolute error = 1.5356604876615165000000000000E-12 " " relative error = 4.52251687418181900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.540000000001882 " " y[1] (closed_form) = -3.387029151949868 " " y[1] (numeric) = -3.3870291519514146 " " absolute error = 1.546762717907768000000000000E-12 " " relative error = 4.566723959306099300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.550000000001894 " " y[1] (closed_form) = -3.3784658681180026 " " y[1] (numeric) = -3.3784658681195605 " " absolute error = 1.5578649481540197000000000000E-12 " " relative error = 4.61116083147478700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.560000000001907 " " y[1] (closed_form) = -3.3698983380015086 " " y[1] (numeric) = -3.369898338003077 " " absolute error = 1.5685230891904212000000000000E-12 " " relative error = 4.65451159609942800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.57000000000192 " " y[1] (closed_form) = -3.361326563402713 " " y[1] (numeric) = -3.3613265634042935 " " absolute error = 1.5805134978563729000000000000E-12 " " relative error = 4.70205279982198300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.58000000000193 " " y[1] (closed_form) = -3.352750546122415 " " y[1] (numeric) = -3.3527505461240072 " " absolute error = 1.5920598173124745000000000000E-12 " " relative error = 4.74851855338224550000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.590000000001943 " " y[1] (closed_form) = -3.344170287959887 " " y[1] (numeric) = -3.344170287961491 " " absolute error = 1.6040502259784262000000000000E-12 " " relative error = 4.7965566578757500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.600000000001955 " " y[1] (closed_form) = -3.3355857907128765 " " y[1] (numeric) = -3.33558579071449 " " absolute error = 1.6133760993852775000000000000E-12 " " relative error = 4.83685985195562600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.610000000001968 " " y[1] (closed_form) = -3.3269970561776034 " " y[1] (numeric) = -3.326997056179227 " " absolute error = 1.623590151211829000000000000E-12 " " relative error = 4.88004685245251200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.62000000000198 " " y[1] (closed_form) = -3.3184040861487674 " " y[1] (numeric) = -3.3184040861504025 " " absolute error = 1.6351364706679306000000000000E-12 " " relative error = 4.927478475249881000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.630000000001992 " " y[1] (closed_form) = -3.3098068824195543 " " y[1] (numeric) = -3.3098068824211966 " " absolute error = 1.6422418980255316000000000000E-12 " " relative error = 4.96174537175718850000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.640000000002004 " " y[1] (closed_form) = -3.301205446781619 " " y[1] (numeric) = -3.3012054467832734 " " absolute error = 1.6542323066914832000000000000E-12 " " relative error = 5.01099472104716200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.650000000002017 " " y[1] (closed_form) = -3.292599781025114 " " y[1] (numeric) = -3.292599781026781 " " absolute error = 1.667110893777135000000000000E-12 " " relative error = 5.063205383735094000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.66000000000203 " " y[1] (closed_form) = -3.283989886938677 " " y[1] (numeric) = -3.2839898869403537 " " absolute error = 1.6764367671839864000000000000E-12 " " relative error = 5.104877983490852000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.67000000000204 " " y[1] (closed_form) = -3.2753757663094234 " " y[1] (numeric) = -3.275375766311112 " " absolute error = 1.688427175849938000000000000E-12 " " relative error = 5.15491136381093100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.680000000002053 " " y[1] (closed_form) = -3.2667574209229677 " " y[1] (numeric) = -3.2667574209246677 " " absolute error = 1.6999734953060397000000000000E-12 " " relative error = 5.20385592275088700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.690000000002065 " " y[1] (closed_form) = -3.2581348525634155 " " y[1] (numeric) = -3.2581348525651257 " " absolute error = 1.7101875471325910000000000000E-12 " " relative error = 5.24897717412482100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.700000000002078 " " y[1] (closed_form) = -3.249508063013362 " " y[1] (numeric) = -3.2495080630150825 " " absolute error = 1.7204015989591426000000000000E-12 " " relative error = 5.294344761107516000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.71000000000209 " " y[1] (closed_form) = -3.2408770540539003 " " y[1] (numeric) = -3.240877054055631 " " absolute error = 1.730615650785694000000000000E-12 " " relative error = 5.3399608251751700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.720000000002102 " " y[1] (closed_form) = -3.2322418274646196 " " y[1] (numeric) = -3.2322418274663622 " " absolute error = 1.7426060594516457000000000000E-12 " " relative error = 5.39132327490035300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.730000000002114 " " y[1] (closed_form) = -3.2236023850236144 " " y[1] (numeric) = -3.223602385025367 " " absolute error = 1.752376022068347000000000000E-12 " " relative error = 5.436079927877054000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.740000000002127 " " y[1] (closed_form) = -3.2149587285074723 " " y[1] (numeric) = -3.214958728509236 " " absolute error = 1.7634782523145986000000000000E-12 " " relative error = 5.485228275802110000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.75000000000214 " " y[1] (closed_form) = -3.206310859691289 " " y[1] (numeric) = -3.2063108596930645 " " absolute error = 1.7754686609805503000000000000E-12 " " relative error = 5.53741897986615200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.76000000000215 " " y[1] (closed_form) = -3.197658780348668 " " y[1] (numeric) = -3.1976587803504533 " " absolute error = 1.7852386235972517000000000000E-12 " " relative error = 5.582955362743839000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.770000000002163 " " y[1] (closed_form) = -3.1890024922517135 " " y[1] (numeric) = -3.1890024922535085 " " absolute error = 1.795008586213953000000000000E-12 " " relative error = 5.62874626337002500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.780000000002175 " " y[1] (closed_form) = -3.180341997171041 " " y[1] (numeric) = -3.1803419971728473 " " absolute error = 1.8061108164602047000000000000E-12 " " relative error = 5.67898300895553200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.790000000002188 " " y[1] (closed_form) = -3.171677296875778 " " y[1] (numeric) = -3.1716772968775966 " " absolute error = 1.8185453143360064000000000000E-12 " " relative error = 5.733702215314723000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.8000000000022 " " y[1] (closed_form) = -3.1630083931335697 " " y[1] (numeric) = -3.163008393135395 " " absolute error = 1.8252066524837574000000000000E-12 " " relative error = 5.77047679179737500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.810000000002212 " " y[1] (closed_form) = -3.154335287710559 " " y[1] (numeric) = -3.154335287712398 " " absolute error = 1.8389734179891093000000000000E-12 " " relative error = 5.82998714548145100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.820000000002224 " " y[1] (closed_form) = -3.145657982371425 " " y[1] (numeric) = -3.1456579823732755 " " absolute error = 1.850519737445211000000000000E-12 " " relative error = 5.88277475750925400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.830000000002237 " " y[1] (closed_form) = -3.136976478879358 " " y[1] (numeric) = -3.136976478881217 " " absolute error = 1.858957432432362000000000000E-12 " " relative error = 5.9259527285217310000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.84000000000225 " " y[1] (closed_form) = -3.1282907789960603 " " y[1] (numeric) = -3.1282907789979317 " " absolute error = 1.871391930308164000000000000E-12 " " relative error = 5.98215467332207700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.85000000000226 " " y[1] (closed_form) = -3.1196008844817698 " " y[1] (numeric) = -3.1196008844836505 " " absolute error = 1.880717803715015200000000000E-12 " " relative error = 6.0287128814154100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.860000000002273 " " y[1] (closed_form) = -3.1109067970952395 " " y[1] (numeric) = -3.110906797097129 " " absolute error = 1.8895995879120164000000000000E-12 " " relative error = 6.07411186242030900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.870000000002285 " " y[1] (closed_form) = -3.1022085185937485 " " y[1] (numeric) = -3.102208518595649 " " absolute error = 1.900701818158268000000000000E-12 " " relative error = 6.12693120648082200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.880000000002298 " " y[1] (closed_form) = -3.0935060507331045 " " y[1] (numeric) = -3.0935060507350185 " " absolute error = 1.91402449445377000000000000E-12 " " relative error = 6.18723371819551200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.89000000000231 " " y[1] (closed_form) = -3.084799395267652 " " y[1] (numeric) = -3.0847993952695747 " " absolute error = 1.922906278650771000000000000E-12 " " relative error = 6.23348889915070400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.900000000002322 " " y[1] (closed_form) = -3.076088553950253 " " y[1] (numeric) = -3.0760885539521885 " " absolute error = 1.935340776526573000000000000E-12 " " relative error = 6.29156392146528400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.910000000002334 " " y[1] (closed_form) = -3.0673735285323183 " " y[1] (numeric) = -3.0673735285342616 " " absolute error = 1.943334382303874000000000000E-12 " " relative error = 6.33549961955146700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.920000000002346 " " y[1] (closed_form) = -3.0586543207637753 " " y[1] (numeric) = -3.0586543207657315 " " absolute error = 1.956212969389525800000000000E-12 " " relative error = 6.39566542747151900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.93000000000236 " " y[1] (closed_form) = -3.0499309323931065 " " y[1] (numeric) = -3.0499309323950734 " " absolute error = 1.9668711104259273000000000000E-12 " " relative error = 6.44890377528200600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.94000000000237 " " y[1] (closed_form) = -3.04120336516732 " " y[1] (numeric) = -3.041203365169299 " " absolute error = 1.979305608301729000000000000E-12 " " relative error = 6.50829744229495900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.950000000002383 " " y[1] (closed_form) = -3.032471620831977 " " y[1] (numeric) = -3.032471620833964 " " absolute error = 1.98685512486918010000000000E-12 " " relative error = 6.55193312023172200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.960000000002395 " " y[1] (closed_form) = -3.023735701131166 " " y[1] (numeric) = -3.023735701133162 " " absolute error = 1.9961809982760315000000000000E-12 " " relative error = 6.60170463155648600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.970000000002408 " " y[1] (closed_form) = -3.014995607807524 " " y[1] (numeric) = -3.0149956078095346 " " absolute error = 2.0103918529912335000000000000E-12 " " relative error = 6.66797605868875900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.98000000000242 " " y[1] (closed_form) = -3.0062513426022477 " " y[1] (numeric) = -3.0062513426042674 " " absolute error = 2.0197177263980848000000000000E-12 " " relative error = 6.71839276302756600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 21.990000000002432 " " y[1] (closed_form) = -2.9975029072550647 " " y[1] (numeric) = -2.997502907257095 " " absolute error = 2.0303758674344863000000000000E-12 " " relative error = 6.77355762531614700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.000000000002444 " " y[1] (closed_form) = -2.9887503035042577 " " y[1] (numeric) = -2.9887503035063006 " " absolute error = 2.042810365310288000000000000E-12 " " relative error = 6.83499843702275200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.010000000002456 " " y[1] (closed_form) = -2.9799935330866667 " " y[1] (numeric) = -2.979993533088719 " " absolute error = 2.0521362387171393000000000000E-12 " " relative error = 6.8863781613362910000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.02000000000247 " " y[1] (closed_form) = -2.9712325977376786 " " y[1] (numeric) = -2.971232597739739 " " absolute error = 2.0605739337042905000000000000E-12 " " relative error = 6.93508120257306300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.03000000000248 " " y[1] (closed_form) = -2.962467499191227 " " y[1] (numeric) = -2.962467499193303 " " absolute error = 2.0756729668391927000000000000E-12 " " relative error = 7.00656789451990500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.040000000002493 " " y[1] (closed_form) = -2.9536982391798254 " " y[1] (numeric) = -2.953698239181911 " " absolute error = 2.085442929455894000000000000E-12 " " relative error = 7.06044680459630800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.050000000002505 " " y[1] (closed_form) = -2.9449248194345223 " " y[1] (numeric) = -2.944924819436622 " " absolute error = 2.099653784171096000000000000E-12 " " relative error = 7.1297364547807610000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.060000000002518 " " y[1] (closed_form) = -2.936147241684946 " " y[1] (numeric) = -2.9361472416870553 " " absolute error = 2.1094237467877974000000000000E-12 " " relative error = 7.18432548899447400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.07000000000253 " " y[1] (closed_form) = -2.9273655076592746 " " y[1] (numeric) = -2.9273655076613916 " " absolute error = 2.1169732633552485000000000000E-12 " " relative error = 7.23166703240957100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.080000000002542 " " y[1] (closed_form) = -2.918579619084248 " " y[1] (numeric) = -2.9185796190863766 " " absolute error = 2.12851958281135000000000000E-12 " " relative error = 7.29299817244392300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.090000000002554 " " y[1] (closed_form) = -2.909789577685185 " " y[1] (numeric) = -2.9097895776873224 " " absolute error = 2.1374013670083514000000000000E-12 " " relative error = 7.34555303723615200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.100000000002566 " " y[1] (closed_form) = -2.900995385185958 " " y[1] (numeric) = -2.900995385188108 " " absolute error = 2.150279954094003200000000000E-12 " " relative error = 7.41221432158937300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.11000000000258 " " y[1] (closed_form) = -2.892197043309018 " " y[1] (numeric) = -2.8921970433111808 " " absolute error = 2.162714451969805000000000000E-12 " " relative error = 7.47775625098973800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.12000000000259 " " y[1] (closed_form) = -2.883394553775389 " " y[1] (numeric) = -2.8833945537775603 " " absolute error = 2.171152146956956000000000000E-12 " " relative error = 7.52984756842987600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.130000000002603 " " y[1] (closed_form) = -2.8745879183046554 " " y[1] (numeric) = -2.87458791830684 " " absolute error = 2.184474823252458000000000000E-12 " " relative error = 7.59926252156794300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.140000000002615 " " y[1] (closed_form) = -2.865777138614991 " " y[1] (numeric) = -2.8657771386171853 " " absolute error = 2.1942447858691594000000000000E-12 " " relative error = 7.65671815963198700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.150000000002628 " " y[1] (closed_form) = -2.8569622164231383 " " y[1] (numeric) = -2.8569622164253414 " " absolute error = 2.2031265700661606000000000000E-12 " " relative error = 7.71143054465883900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.16000000000264 " " y[1] (closed_form) = -2.848143153444415 " " y[1] (numeric) = -2.8481431534466295 " " absolute error = 2.2146728895222623000000000000E-12 " " relative error = 7.77584822885021700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.170000000002652 " " y[1] (closed_form) = -2.8393199513927243 " " y[1] (numeric) = -2.8393199513949523 " " absolute error = 2.227995565817764100000000000E-12 " " relative error = 7.84693378682068800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.180000000002664 " " y[1] (closed_form) = -2.8304926119805565 " " y[1] (numeric) = -2.8304926119827925 " " absolute error = 2.2359891715950653000000000000E-12 " " relative error = 7.89964673333132500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.190000000002676 " " y[1] (closed_form) = -2.8216611369189692 " " y[1] (numeric) = -2.8216611369212186 " " absolute error = 2.249311847890567200000000000E-12 " " relative error = 7.97158743996679100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.20000000000269 " " y[1] (closed_form) = -2.8128255279176244 " " y[1] (numeric) = -2.812825527919882 " " absolute error = 2.2577495428777183000000000000E-12 " " relative error = 8.02662490250208600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.2100000000027 " " y[1] (closed_form) = -2.803985786684752 " " y[1] (numeric) = -2.803985786687022 " " absolute error = 2.27018404075352000000000000E-12 " " relative error = 8.09627513639302700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.220000000002713 " " y[1] (closed_form) = -2.795141914927189 " " y[1] (numeric) = -2.7951419149294687 " " absolute error = 2.2795099141603714000000000000E-12 " " relative error = 8.15525645401711500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.230000000002725 " " y[1] (closed_form) = -2.786293914350349 " " y[1] (numeric) = -2.786293914352641 " " absolute error = 2.291944412036173200000000000E-12 " " relative error = 8.22578120790448600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.240000000002738 " " y[1] (closed_form) = -2.777441786658244 " " y[1] (numeric) = -2.7774417866605488 " " absolute error = 2.304822999121825000000000000E-12 " " relative error = 8.29836654072572600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.25000000000275 " " y[1] (closed_form) = -2.768585533553484 " " y[1] (numeric) = -2.7685855335557976 " " absolute error = 2.3137047833188262000000000000E-12 " " relative error = 8.35699224487813500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.260000000002762 " " y[1] (closed_form) = -2.7597251567372645 " " y[1] (numeric) = -2.75972515673959 " " absolute error = 2.325695191984778000000000000E-12 " " relative error = 8.42727105018810400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.270000000002774 " " y[1] (closed_form) = -2.7508606579093886 " " y[1] (numeric) = -2.750860657911724 " " absolute error = 2.3354651546014793000000000000E-12 " " relative error = 8.48994349418045900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.280000000002786 " " y[1] (closed_form) = -2.7419920387682524 " " y[1] (numeric) = -2.741992038770598 " " absolute error = 2.3456792064280307000000000000E-12 " " relative error = 8.55465359951135400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.2900000000028 " " y[1] (closed_form) = -2.733119301010852 " " y[1] (numeric) = -2.73311930101321 " " absolute error = 2.3581137043038325000000000000E-12 " " relative error = 8.62792086474848500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.30000000000281 " " y[1] (closed_form) = -2.724242446332795 " " y[1] (numeric) = -2.724242446335163 " " absolute error = 2.367883666920534000000000000E-12 " " relative error = 8.69189770575680900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.310000000002823 " " y[1] (closed_form) = -2.7153614764282814 " " y[1] (numeric) = -2.715361476430662 " " absolute error = 2.3807622540061857000000000000E-12 " " relative error = 8.76775440276843300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.320000000002835 " " y[1] (closed_form) = -2.7064763929901297 " " y[1] (numeric) = -2.7064763929925193 " " absolute error = 2.389644038203187000000000000E-12 " " relative error = 8.82935481865812700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.330000000002848 " " y[1] (closed_form) = -2.6975871977097547 " " y[1] (numeric) = -2.6975871977121555 " " absolute error = 2.4007462684494385000000000000E-12 " " relative error = 8.89960580509748200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.34000000000286 " " y[1] (closed_form) = -2.6886938922771897 " " y[1] (numeric) = -2.6886938922796007 " " absolute error = 2.41096032027599000000000000E-12 " " relative error = 8.96703164016200800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.350000000002872 " " y[1] (closed_form) = -2.679796478381075 " " y[1] (numeric) = -2.679796478383496 " " absolute error = 2.4211743721025414000000000000E-12 " " relative error = 9.03491885161826400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.360000000002884 " " y[1] (closed_form) = -2.6708949577086614 " " y[1] (numeric) = -2.670894957711095 " " absolute error = 2.433608869978343000000000000E-12 " " relative error = 9.1115858486105210000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.370000000002896 " " y[1] (closed_form) = -2.661989331945822 " " y[1] (numeric) = -2.661989331948266 " " absolute error = 2.4438229218048946000000000000E-12 " " relative error = 9.1804384505874200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.38000000000291 " " y[1] (closed_form) = -2.6530796027770407 " " y[1] (numeric) = -2.6530796027794956 " " absolute error = 2.454925152051146100000000000E-12 " " relative error = 9.25311532108391600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.39000000000292 " " y[1] (closed_form) = -2.6441657718854223 " " y[1] (numeric) = -2.644165771887887 " " absolute error = 2.4646951146678475000000000000E-12 " " relative error = 9.32125792139876600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.400000000002933 " " y[1] (closed_form) = -2.6352478409526867 " " y[1] (numeric) = -2.635247840955163 " " absolute error = 2.476241434123949100000000000E-12 " " relative error = 9.39661687846690700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.410000000002945 " " y[1] (closed_form) = -2.626325811659182 " " y[1] (numeric) = -2.626325811661668 " " absolute error = 2.4860113967406505000000000000E-12 " " relative error = 9.46573873547742400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.420000000002958 " " y[1] (closed_form) = -2.6173996856838713 " " y[1] (numeric) = -2.6173996856863706 " " absolute error = 2.4993340730361524000000000000E-12 " " relative error = 9.54892020009977700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.43000000000297 " " y[1] (closed_form) = -2.6084694647043527 " " y[1] (numeric) = -2.608469464706864 " " absolute error = 2.511324481702104000000000000E-12 " " relative error = 9.62757860762131100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.440000000002982 " " y[1] (closed_form) = -2.5995351503968465 " " y[1] (numeric) = -2.599535150399367 " " absolute error = 2.5206503551089554000000000000E-12 " " relative error = 9.69654268658052700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.450000000002994 " " y[1] (closed_form) = -2.5905967444361977 " " y[1] (numeric) = -2.590596744438729 " " absolute error = 2.531308496145357000000000000E-12 " " relative error = 9.77114057439401300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.460000000003006 " " y[1] (closed_form) = -2.5816542484958838 " " y[1] (numeric) = -2.5816542484984266 " " absolute error = 2.5428548156014585000000000000E-12 " " relative error = 9.84971096374725500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.47000000000302 " " y[1] (closed_form) = -2.5727076642480142 " " y[1] (numeric) = -2.5727076642505695 " " absolute error = 2.5552893134772603000000000000E-12 " " relative error = 9.93229564706161400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.48000000000303 " " y[1] (closed_form) = -2.5637569933633344 " " y[1] (numeric) = -2.5637569933659012 " " absolute error = 2.566835632933362000000000000E-12 " " relative error = 1.00120083127144930000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.490000000003043 " " y[1] (closed_form) = -2.554802237511222 " " y[1] (numeric) = -2.554802237513799 " " absolute error = 2.5770496847599134000000000000E-12 " " relative error = 1.00870808977776850000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.500000000003055 " " y[1] (closed_form) = -2.545843398359686 " " y[1] (numeric) = -2.545843398362276 " " absolute error = 2.589928271845565000000000000E-12 " " relative error = 1.01731641212271070000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.510000000003068 " " y[1] (closed_form) = -2.5368804775753873 " " y[1] (numeric) = -2.536880477577987 " " absolute error = 2.5996982344622666000000000000E-12 " " relative error = 1.02476181177716230000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.52000000000308 " " y[1] (closed_form) = -2.527913476823617 " " y[1] (numeric) = -2.527913476826225 " " absolute error = 2.6081359294494180000000000000E-12 " " relative error = 1.03173465126923660000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.530000000003092 " " y[1] (closed_form) = -2.5189423977683028 " " y[1] (numeric) = -2.518942397770924 " " absolute error = 2.6214586057449196000000000000E-12 " " relative error = 1.04069811523576040000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.540000000003104 " " y[1] (closed_form) = -2.5099672420720296 " " y[1] (numeric) = -2.5099672420746617 " " absolute error = 2.632116746781321000000000000E-12 " " relative error = 1.04866577645390090000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.550000000003116 " " y[1] (closed_form) = -2.500988011396018 " " y[1] (numeric) = -2.500988011398662 " " absolute error = 2.644107155447273000000000000E-12 " " relative error = 1.05722504202303930000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.56000000000313 " " y[1] (closed_form) = -2.4920047074001417 " " y[1] (numeric) = -2.492004707402794 " " absolute error = 2.652100761224574000000000000E-12 " " relative error = 1.0642438809802480000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.57000000000314 " " y[1] (closed_form) = -2.4830173317429107 " " y[1] (numeric) = -2.483017331745575 " " absolute error = 2.6640911698905256000000000000E-12 " " relative error = 1.07292491914283720000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.580000000003153 " " y[1] (closed_form) = -2.474025886081499 " " y[1] (numeric) = -2.474025886084174 " " absolute error = 2.675193400136777000000000000E-12 " " relative error = 1.08131180647179830000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.590000000003165 " " y[1] (closed_form) = -2.4650303720717233 " " y[1] (numeric) = -2.465030372074411 " " absolute error = 2.687627898012579000000000000E-12 " " relative error = 1.09030214331751820000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.600000000003178 " " y[1] (closed_form) = -2.456030791368061 " " y[1] (numeric) = -2.456030791370757 " " absolute error = 2.69606559299973000000000000E-12 " " relative error = 1.09773281445627340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.61000000000319 " " y[1] (closed_form) = -2.4470271456236325 " " y[1] (numeric) = -2.4470271456263406 " " absolute error = 2.708056001665682000000000000E-12 " " relative error = 1.10667182687731290000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.620000000003202 " " y[1] (closed_form) = -2.4380194364902295 " " y[1] (numeric) = -2.4380194364929464 " " absolute error = 2.716937785862683000000000000E-12 " " relative error = 1.11440366110205600000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.630000000003214 " " y[1] (closed_form) = -2.429007665618286 " " y[1] (numeric) = -2.4290076656210164 " " absolute error = 2.730260462158185000000000000E-12 " " relative error = 1.12402299128323950000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.640000000003226 " " y[1] (closed_form) = -2.419991834656912 " " y[1] (numeric) = -2.4199918346596534 " " absolute error = 2.7413626924044365000000000000E-12 " " relative error = 1.13279832317826220000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.65000000000324 " " y[1] (closed_form) = -2.41097194525387 " " y[1] (numeric) = -2.4109719452566205 " " absolute error = 2.750688565811288000000000000E-12 " " relative error = 1.14090442704079110000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.66000000000325 " " y[1] (closed_form) = -2.401947999055583 " " y[1] (numeric) = -2.401947999058344 " " absolute error = 2.7609026176378393000000000000E-12 " " relative error = 1.14944312646376740000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.670000000003263 " " y[1] (closed_form) = -2.3929199977071427 " " y[1] (numeric) = -2.3929199977099156 " " absolute error = 2.772893026303791000000000000E-12 " " relative error = 1.15879052745630120000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.680000000003275 " " y[1] (closed_form) = -2.3838879428523114 " " y[1] (numeric) = -2.383887942855094 " " absolute error = 2.7826629889204924000000000000E-12 " " relative error = 1.16727927470913280000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.690000000003288 " " y[1] (closed_form) = -2.3748518361335087 " " y[1] (numeric) = -2.3748518361363042 " " absolute error = 2.795541576006144000000000000E-12 " " relative error = 1.17714357311551680000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.7000000000033 " " y[1] (closed_form) = -2.3658116791918324 " " y[1] (numeric) = -2.365811679194641 " " absolute error = 2.808420163091796000000000000E-12 " " relative error = 1.18708525610591270000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.710000000003312 " " y[1] (closed_form) = -2.356767473667052 " " y[1] (numeric) = -2.356767473669871 " " absolute error = 2.8190783041281975000000000000E-12 " " relative error = 1.19616310714854080000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.720000000003324 " " y[1] (closed_form) = -2.347719221197604 " " y[1] (numeric) = -2.3477192212004345 " " absolute error = 2.830624623584299000000000000E-12 " " relative error = 1.2056912930756510000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.730000000003336 " " y[1] (closed_form) = -2.338666923420604 " " y[1] (numeric) = -2.3386669234234434 " " absolute error = 2.8395064077813004000000000000E-12 " " relative error = 1.2141559703714260000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.74000000000335 " " y[1] (closed_form) = -2.3296105819718385 " " y[1] (numeric) = -2.329610581974689 " " absolute error = 2.850608638027552000000000000E-12 " " relative error = 1.22364169363221570000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.75000000000336 " " y[1] (closed_form) = -2.3205501984857726 " " y[1] (numeric) = -2.3205501984886374 " " absolute error = 2.864819492742754000000000000E-12 " " relative error = 1.23454321074895650000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.760000000003373 " " y[1] (closed_form) = -2.311485774595564 " " y[1] (numeric) = -2.3114857745984363 " " absolute error = 2.872369009310205000000000000E-12 " " relative error = 1.2426505241256688000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.770000000003385 " " y[1] (closed_form) = -2.302417311933027 " " y[1] (numeric) = -2.302417311935911 " " absolute error = 2.8839153287663066000000000000E-12 " " relative error = 1.25255978306776820000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.780000000003398 " " y[1] (closed_form) = -2.2933448121286766 " " y[1] (numeric) = -2.2933448121315725 " " absolute error = 2.8959057374322583000000000000E-12 " " relative error = 1.26274327441597670000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.79000000000341 " " y[1] (closed_form) = -2.2842682768117086 " " y[1] (numeric) = -2.284268276814615 " " absolute error = 2.90656387846866000000000000E-12 " " relative error = 1.27242667070854160000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.800000000003422 " " y[1] (closed_form) = -2.275187707609998 " " y[1] (numeric) = -2.2751877076129166 " " absolute error = 2.9185542871346115000000000000E-12 " " relative error = 1.28277516504361170000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.810000000003434 " " y[1] (closed_form) = -2.2661031061501156 " " y[1] (numeric) = -2.266103106153044 " " absolute error = 2.928324249751313000000000000E-12 " " relative error = 1.29222904368470920000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.820000000003446 " " y[1] (closed_form) = -2.257014474057314 " " y[1] (numeric) = -2.2570144740602527 " " absolute error = 2.9385383015778643000000000000E-12 " " relative error = 1.3019581111925310000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.83000000000346 " " y[1] (closed_form) = -2.247921812955539 " " y[1] (numeric) = -2.247921812958489 " " absolute error = 2.949640531824116000000000000E-12 " " relative error = 1.31216331227551270000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.84000000000347 " " y[1] (closed_form) = -2.2388251244674287 " " y[1] (numeric) = -2.2388251244703907 " " absolute error = 2.9620750296999176000000000000E-12 " " relative error = 1.32304886046181740000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.850000000003483 " " y[1] (closed_form) = -2.2297244102143168 " " y[1] (numeric) = -2.229724410217288 " " absolute error = 2.971400903106769000000000000E-12 " " relative error = 1.33263146310586580000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.860000000003495 " " y[1] (closed_form) = -2.220619671816223 " " y[1] (numeric) = -2.2206196718192084 " " absolute error = 2.985167668612121000000000000E-12 " " relative error = 1.34429488601737060000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.870000000003508 " " y[1] (closed_form) = -2.2115109108918745 " " y[1] (numeric) = -2.211510910894873 " " absolute error = 2.9984903449076230000000000000E-12 " " relative error = 1.35585600330516530000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.88000000000352 " " y[1] (closed_form) = -2.2023981290586967 " " y[1] (numeric) = -2.202398129061704 " " absolute error = 3.007372129104624000000000000E-12 " " relative error = 1.36549885755214120000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.890000000003532 " " y[1] (closed_form) = -2.1932813279328016 " " y[1] (numeric) = -2.193281327935822 " " absolute error = 3.020250716190276000000000000E-12 " " relative error = 1.37704665503941750000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.900000000003544 " " y[1] (closed_form) = -2.1841605091290184 " " y[1] (numeric) = -2.18416050913205 " " absolute error = 3.0317970356463775000000000000E-12 " " relative error = 1.38808344120065260000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.910000000003556 " " y[1] (closed_form) = -2.1750356742608723 " " y[1] (numeric) = -2.175035674263913 " " absolute error = 3.0406788198433790000000000000E-12 " " relative error = 1.39799032072274950000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.92000000000357 " " y[1] (closed_form) = -2.1659068249405884 " " y[1] (numeric) = -2.165906824943641 " " absolute error = 3.0526692285093304000000000000E-12 " " relative error = 1.4094185370107350000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.93000000000358 " " y[1] (closed_form) = -2.1567739627791056 " " y[1] (numeric) = -2.156773962782169 " " absolute error = 3.063327369545732000000000000E-12 " " relative error = 1.42032842681320660000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.940000000003593 " " y[1] (closed_form) = -2.147637089386066 " " y[1] (numeric) = -2.147637089389142 " " absolute error = 3.0757618674215337000000000000E-12 " " relative error = 1.43216090028543200000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.950000000003605 " " y[1] (closed_form) = -2.138496206369826 " " y[1] (numeric) = -2.138496206372911 " " absolute error = 3.085087740828385000000000000E-12 " " relative error = 1.44264354158730620000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.960000000003618 " " y[1] (closed_form) = -2.1293513153374484 " " y[1] (numeric) = -2.129351315340542 " " absolute error = 3.093525435815536000000000000E-12 " " relative error = 1.45280180566413060000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.97000000000363 " " y[1] (closed_form) = -2.1202024178947028 " " y[1] (numeric) = -2.120202417897809 " " absolute error = 3.106404022901188000000000000E-12 " " relative error = 1.4651450242122419000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.980000000003642 " " y[1] (closed_form) = -2.1110495156460836 " " y[1] (numeric) = -2.1110495156492024 " " absolute error = 3.1188385207769900000000000000E-12 " " relative error = 1.47738766791667300000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 22.990000000003654 " " y[1] (closed_form) = -2.1018926101947955 " " y[1] (numeric) = -2.1018926101979263 " " absolute error = 3.1308289294429414000000000000E-12 " " relative error = 1.4895284917305018000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.000000000003666 " " y[1] (closed_form) = -2.092731703142764 " " y[1] (numeric) = -2.092731703145904 " " absolute error = 3.1397107136399427000000000000E-12 " " relative error = 1.50029299452236340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.01000000000368 " " y[1] (closed_form) = -2.083566796090622 " " y[1] (numeric) = -2.0835667960937747 " " absolute error = 3.1525893007255945000000000000E-12 " " relative error = 1.51307330614059020000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.02000000000369 " " y[1] (closed_form) = -2.0743978906377336 " " y[1] (numeric) = -2.074397890640898 " " absolute error = 3.1645797093915460000000000000E-12 " " relative error = 1.52554132631645580000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.030000000003703 " " y[1] (closed_form) = -2.0652249883821803 " " y[1] (numeric) = -2.0652249883853577 " " absolute error = 3.177458296477198000000000000E-12 " " relative error = 1.53855309438527540000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.040000000003715 " " y[1] (closed_form) = -2.056048090920772 " " y[1] (numeric) = -2.0560480909239573 " " absolute error = 3.185451902254499000000000000E-12 " " relative error = 1.54930807130485930000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.050000000003728 " " y[1] (closed_form) = -2.0468671998490287 " " y[1] (numeric) = -2.046867199852228 " " absolute error = 3.199218667759851000000000000E-12 " " relative error = 1.5629830152126220000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.06000000000374 " " y[1] (closed_form) = -2.0376823167612166 " " y[1] (numeric) = -2.0376823167644242 " " absolute error = 3.2076563627470020000000000000E-12 " " relative error = 1.57416901366911530000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.070000000003752 " " y[1] (closed_form) = -2.0284934432503086 " " y[1] (numeric) = -2.02849344325353 " " absolute error = 3.2214231282523540000000000000E-12 " " relative error = 1.58808653731243140000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.080000000003764 " " y[1] (closed_form) = -2.019300580908027 " " y[1] (numeric) = -2.019300580911258 " " absolute error = 3.2311930908690556000000000000E-12 " " relative error = 1.60015458888050850000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.090000000003776 " " y[1] (closed_form) = -2.010103731324808 " " y[1] (numeric) = -2.0101037313280496 " " absolute error = 3.241851231905457000000000000E-12 " " relative error = 1.6127780777606120000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.10000000000379 " " y[1] (closed_form) = -2.00090289608983 " " y[1] (numeric) = -2.0009028960930824 " " absolute error = 3.2525093729418586000000000000E-12 " " relative error = 1.6255208482620130000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.1100000000038 " " y[1] (closed_form) = -1.9916980767910033 " " y[1] (numeric) = -1.9916980767942645 " " absolute error = 3.261169112533935000000000000E-12 " " relative error = 1.63738126302169550000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.120000000003813 " " y[1] (closed_form) = -1.9824892750149665 " " y[1] (numeric) = -1.982489275018241 " " absolute error = 3.2744917888294367000000000000E-12 " " relative error = 1.65170718959108450000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.130000000003825 " " y[1] (closed_form) = -1.9732764923471038 " " y[1] (numeric) = -1.9732764923503923 " " absolute error = 3.2884805989397137000000000000E-12 " " relative error = 1.6665077659888640000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.140000000003837 " " y[1] (closed_form) = -1.9640597303715381 " " y[1] (numeric) = -1.9640597303748382 " " absolute error = 3.3000269183958153000000000000E-12 " " relative error = 1.68020700560443460000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.15000000000385 " " y[1] (closed_form) = -1.9548389906711279 " " y[1] (numeric) = -1.9548389906744381 " " absolute error = 3.3102409702223670000000000000E-12 " " relative error = 1.69335734862026050000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.160000000003862 " " y[1] (closed_form) = -1.94561427482747 " " y[1] (numeric) = -1.9456142748307919 " " absolute error = 3.3217872896784684000000000000E-12 " " relative error = 1.70732057872726740000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.170000000003874 " " y[1] (closed_form) = -1.9363855844209112 " " y[1] (numeric) = -1.936385584424243 " " absolute error = 3.3317792969000950000000000000E-12 " " relative error = 1.7206176929356170000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.180000000003886 " " y[1] (closed_form) = -1.9271529210305367 " " y[1] (numeric) = -1.927152921033879 " " absolute error = 3.3422153933315710000000000000E-12 " " relative error = 1.73427617334297260000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.1900000000039 " " y[1] (closed_form) = -1.9179162862341776 " " y[1] (numeric) = -1.9179162862375327 " " absolute error = 3.355093980417223000000000000E-12 " " relative error = 1.74934328703414830000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.20000000000391 " " y[1] (closed_form) = -1.9086756816084183 " " y[1] (numeric) = -1.9086756816117845 " " absolute error = 3.3661962106634746000000000000E-12 " " relative error = 1.76362922370699530000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.210000000003923 " " y[1] (closed_form) = -1.8994311087285851 " " y[1] (numeric) = -1.8994311087319642 " " absolute error = 3.3790747977491264000000000000E-12 " " relative error = 1.77899307967582160000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.220000000003935 " " y[1] (closed_form) = -1.8901825691687613 " " y[1] (numeric) = -1.8901825691721508 " " absolute error = 3.389510894180603000000000000E-12 " " relative error = 1.79321878715197100000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.230000000003947 " " y[1] (closed_form) = -1.8809300645017757 " " y[1] (numeric) = -1.8809300645051756 " " absolute error = 3.3999469906120794000000000000E-12 " " relative error = 1.80758820052815930000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.24000000000396 " " y[1] (closed_form) = -1.8716735962992104 " " y[1] (numeric) = -1.8716735963026232 " " absolute error = 3.4128255776977310000000000000E-12 " " relative error = 1.8234085176206910000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.250000000003972 " " y[1] (closed_form) = -1.862413166131411 " " y[1] (numeric) = -1.8624131661348324 " " absolute error = 3.4214853172898074000000000000E-12 " " relative error = 1.83712474734963770000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.260000000003984 " " y[1] (closed_form) = -1.8531487755674654 " " y[1] (numeric) = -1.8531487755708984 " " absolute error = 3.433031636745909000000000000E-12 " " relative error = 1.85253967841554260000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.270000000003996 " " y[1] (closed_form) = -1.8438804261752288 " " y[1] (numeric) = -1.843880426178674 " " absolute error = 3.4452440900167860000000000000E-12 " " relative error = 1.86847478887949060000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.28000000000401 " " y[1] (closed_form) = -1.834608119521313 " " y[1] (numeric) = -1.8346081195247712 " " absolute error = 3.4581226771024376000000000000E-12 " " relative error = 1.884938064050830000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.29000000000402 " " y[1] (closed_form) = -1.825331857171097 " " y[1] (numeric) = -1.825331857174563 " " absolute error = 3.4658942382748137000000000000E-12 " " relative error = 1.89877485820373670000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.300000000004033 " " y[1] (closed_form) = -1.8160516406887055 " " y[1] (numeric) = -1.8160516406921836 " " absolute error = 3.4781066915456904000000000000E-12 " " relative error = 1.91520252707498980000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.310000000004045 " " y[1] (closed_form) = -1.8067674716370412 " " y[1] (numeric) = -1.8067674716405313 " " absolute error = 3.490097100211642000000000000E-12 " " relative error = 1.93168028260404860000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.320000000004057 " " y[1] (closed_form) = -1.797479351577767 " " y[1] (numeric) = -1.7974793515812693 " " absolute error = 3.502309553482519000000000000E-12 " " relative error = 1.94845607011190940000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.33000000000407 " " y[1] (closed_form) = -1.7881872820713163 " " y[1] (numeric) = -1.7881872820748268 " " absolute error = 3.510525203864745000000000000E-12 " " relative error = 1.9631753558824040000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.340000000004082 " " y[1] (closed_form) = -1.7788912646768793 " " y[1] (numeric) = -1.778891264680402 " " absolute error = 3.5227376571356217000000000000E-12 " " relative error = 1.98029959845550050000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.350000000004094 " " y[1] (closed_form) = -1.7695913009524276 " " y[1] (numeric) = -1.7695913009559614 " " absolute error = 3.5338398873818730000000000000E-12 " " relative error = 1.9969808200796950000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.360000000004106 " " y[1] (closed_form) = -1.7602873924546998 " " y[1] (numeric) = -1.760287392458243 " " absolute error = 3.5431657607887246000000000000E-12 " " relative error = 2.01283368612202700000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.37000000000412 " " y[1] (closed_form) = -1.7509795407391984 " " y[1] (numeric) = -1.7509795407427569 " " absolute error = 3.5584868385285520000000000000E-12 " " relative error = 2.03228350516665160000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.38000000000413 " " y[1] (closed_form) = -1.7416677473602178 " " y[1] (numeric) = -1.7416677473637867 " " absolute error = 3.5689229349600280000000000000E-12 " " relative error = 2.04914108352142020000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.390000000004143 " " y[1] (closed_form) = -1.7323520138708126 " " y[1] (numeric) = -1.732352013874392 " " absolute error = 3.5793590313915047000000000000E-12 " " relative error = 2.06618458761951730000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.400000000004155 " " y[1] (closed_form) = -1.7230323418228153 " " y[1] (numeric) = -1.7230323418264077 " " absolute error = 3.5924596630820815000000000000E-12 " " relative error = 2.08496357026100780000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.410000000004167 " " y[1] (closed_form) = -1.7137087327668468 " " y[1] (numeric) = -1.7137087327704477 " " absolute error = 3.6008973580692330000000000000E-12 " " relative error = 2.1012306754459080000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.42000000000418 " " y[1] (closed_form) = -1.7043811882522917 " " y[1] (numeric) = -1.704381188255905 " " absolute error = 3.6133318559450345000000000000E-12 " " relative error = 2.12002566142508370000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.430000000004192 " " y[1] (closed_form) = -1.6950497098273303 " " y[1] (numeric) = -1.695049709830954 " " absolute error = 3.623767952376511000000000000E-12 " " relative error = 2.1378534985535338000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.440000000004204 " " y[1] (closed_form) = -1.6857142990389136 " " y[1] (numeric) = -1.6857142990425515 " " absolute error = 3.637978807091713000000000000E-12 " " relative error = 2.15812300409734650000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.450000000004216 " " y[1] (closed_form) = -1.6763749574327882 " " y[1] (numeric) = -1.676374957436438 " " absolute error = 3.64974717115273960000000000E-12 " " relative error = 2.1771663642255710000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.46000000000423 " " y[1] (closed_form) = -1.6670316865534787 " " y[1] (numeric) = -1.6670316865571382 " " absolute error = 3.659517133769441000000000000E-12 " " relative error = 2.19522949880775600000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.47000000000424 " " y[1] (closed_form) = -1.6576844879442945 " " y[1] (numeric) = -1.657684487947966 " " absolute error = 3.671507542435392700000000000E-12 " " relative error = 2.2148409839971740000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.480000000004253 " " y[1] (closed_form) = -1.6483333631473371 " " y[1] (numeric) = -1.6483333631510206 " " absolute error = 3.683497951101344400000000000E-12 " " relative error = 2.234680213029270000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.490000000004265 " " y[1] (closed_form) = -1.6389783137035003 " " y[1] (numeric) = -1.6389783137071927 " " absolute error = 3.692379735298345600000000000E-12 " " relative error = 2.25285454018906320000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.500000000004277 " " y[1] (closed_form) = -1.6296193411524555 " " y[1] (numeric) = -1.6296193411561635 " " absolute error = 3.707922857643098000000000000E-12 " " relative error = 2.27533066404383780000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.51000000000429 " " y[1] (closed_form) = -1.6202564470326877 " " y[1] (numeric) = -1.6202564470364063 " " absolute error = 3.718580998679499300000000000E-12 " " relative error = 2.29505706055954900000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.520000000004302 " " y[1] (closed_form) = -1.6108896328814595 " " y[1] (numeric) = -1.6108896328851883 " " absolute error = 3.728795050506051000000000000E-12 " " relative error = 2.31474272004359050000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.530000000004314 " " y[1] (closed_form) = -1.6015189002348293 " " y[1] (numeric) = -1.6015189002385721 " " absolute error = 3.742783860616328000000000000E-12 " " relative error = 2.3370213489628670000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.540000000004326 " " y[1] (closed_form) = -1.5921442506276655 " " y[1] (numeric) = -1.592144250631417 " " absolute error = 3.751443600208404000000000000E-12 " " relative error = 2.3562209257920480000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.55000000000434 " " y[1] (closed_form) = -1.5827656855936176 " " y[1] (numeric) = -1.5827656855973804 " " absolute error = 3.7627678750595805000000000000E-12 " " relative error = 2.3773372832810383000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.56000000000435 " " y[1] (closed_form) = -1.5733832066651452 " " y[1] (numeric) = -1.5733832066689193 " " absolute error = 3.774092149910757000000000000E-12 " " relative error = 2.3987113463033020000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.570000000004363 " " y[1] (closed_form) = -1.5639968153735069 " " y[1] (numeric) = -1.563996815377291 " " absolute error = 3.7840841571323836000000000000E-12 " " relative error = 2.4194960756545308000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.580000000004375 " " y[1] (closed_form) = -1.554606513248757 " " y[1] (numeric) = -1.5546065132525553 " " absolute error = 3.7982950118475856000000000000E-12 " " relative error = 2.44325170355169460000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.590000000004387 " " y[1] (closed_form) = -1.5452123018197668 " " y[1] (numeric) = -1.5452123018235764 " " absolute error = 3.809619286698762000000000000E-12 " " relative error = 2.46543422040599040000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.6000000000044 " " y[1] (closed_form) = -1.535814182614203 " " y[1] (numeric) = -1.535814182618023 " " absolute error = 3.8198333385253136000000000000E-12 " " relative error = 2.48717154833362850000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.610000000004412 " " y[1] (closed_form) = -1.5264121571585392 " " y[1] (numeric) = -1.52641215716237 " " absolute error = 3.830935568771565000000000000E-12 " " relative error = 2.50976484352886940000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.620000000004424 " " y[1] (closed_form) = -1.517006226978058 " " y[1] (numeric) = -1.517006226981901 " " absolute error = 3.842925977437517000000000000E-12 " " relative error = 2.5332301931896430000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.630000000004436 " " y[1] (closed_form) = -1.5075963935968524 " " y[1] (numeric) = -1.5075963936007084 " " absolute error = 3.856026609128093700000000000E-12 " " relative error = 2.5577313832174353000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.64000000000445 " " y[1] (closed_form) = -1.4981826585378286 " " y[1] (numeric) = -1.498182658541695 " " absolute error = 3.86646270555957000000000000E-12 " " relative error = 2.580768562181260400000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.65000000000446 " " y[1] (closed_form) = -1.4887650233226992 " " y[1] (numeric) = -1.4887650233265768 " " absolute error = 3.877564935805822000000000000E-12 " " relative error = 2.6045513395738440000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.660000000004473 " " y[1] (closed_form) = -1.4793434894719901 " " y[1] (numeric) = -1.4793434894758821 " " absolute error = 3.891997835125949000000000000E-12 " " relative error = 2.63089530107378070000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.670000000004485 " " y[1] (closed_form) = -1.4699180585050549 " " y[1] (numeric) = -1.4699180585089549 " " absolute error = 3.89999144090325000000000000E-12 " " relative error = 2.65320329819584870000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.680000000004497 " " y[1] (closed_form) = -1.4604887319400426 " " y[1] (numeric) = -1.4604887319439546 " " absolute error = 3.9119818495692016000000000000E-12 " " relative error = 2.678542986341780300000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.69000000000451 " " y[1] (closed_form) = -1.4510555112939336 " " y[1] (numeric) = -1.4510555112978594 " " absolute error = 3.9257486150745535000000000000E-12 " " relative error = 2.7054434406674693000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.700000000004522 " " y[1] (closed_form) = -1.4416183980825288 " " y[1] (numeric) = -1.4416183980864652 " " absolute error = 3.936406756110955000000000000E-12 " " relative error = 2.73054697508487760000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.710000000004534 " " y[1] (closed_form) = -1.4321773938204423 " " y[1] (numeric) = -1.4321773938243891 " " absolute error = 3.9468428525424315000000000000E-12 " " relative error = 2.7558337881691650000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.720000000004546 " " y[1] (closed_form) = -1.4227325000211088 " " y[1] (numeric) = -1.4227325000250701 " " absolute error = 3.9612757518625585000000000000E-12 " " relative error = 2.78427304627102130000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.73000000000456 " " y[1] (closed_form) = -1.4132837181967979 " " y[1] (numeric) = -1.4132837182007696 " " absolute error = 3.971711848294035000000000000E-12 " " relative error = 2.8102721323086660000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.74000000000457 " " y[1] (closed_form) = -1.4038310498585922 " " y[1] (numeric) = -1.403831049862574 " " absolute error = 3.9817038555156614000000000000E-12 " " relative error = 2.83631271435172970000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.750000000004583 " " y[1] (closed_form) = -1.3943744965164022 " " y[1] (numeric) = -1.394374496520396 " " absolute error = 3.993694264181613000000000000E-12 " " relative error = 2.86414752576094200000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.760000000004595 " " y[1] (closed_form) = -1.3849140596789695 " " y[1] (numeric) = -1.3849140596829745 " " absolute error = 4.00501853903278970000000000E-12 " " relative error = 2.8918895804705563000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.770000000004607 " " y[1] (closed_form) = -1.3754497408538597 " " y[1] (numeric) = -1.3754497408578776 " " absolute error = 4.0178971261184415000000000000E-12 " " relative error = 2.92115153813194750000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.78000000000462 " " y[1] (closed_form) = -1.3659815415474768 " " y[1] (numeric) = -1.3659815415515038 " " absolute error = 4.027000954920368000000000000E-12 " " relative error = 2.94806396165376240000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.790000000004632 " " y[1] (closed_form) = -1.3565094632650414 " " y[1] (numeric) = -1.3565094632690826 " " absolute error = 4.04121180963557000000000000E-12 " " relative error = 2.97912540905435450000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.800000000004644 " " y[1] (closed_form) = -1.3470335075106235 " " y[1] (numeric) = -1.347033507514676 " " absolute error = 4.052536084486746400000000000E-12 " " relative error = 3.00848944134731230000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.810000000004656 " " y[1] (closed_form) = -1.3375536757871167 " " y[1] (numeric) = -1.3375536757911797 " " absolute error = 4.062972180918223000000000000E-12 " " relative error = 3.0376143062275730000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.82000000000467 " " y[1] (closed_form) = -1.3280699695962532 " " y[1] (numeric) = -1.328069969600326 " " absolute error = 4.072742143534924000000000000E-12 " " relative error = 3.0666623271160020000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.83000000000468 " " y[1] (closed_form) = -1.3185823904385963 " " y[1] (numeric) = -1.3185823904426826 " " absolute error = 4.086286864435351000000000000E-12 " " relative error = 3.0990000276555650000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.840000000004693 " " y[1] (closed_form) = -1.309090939813558 " " y[1] (numeric) = -1.3090909398176567 " " absolute error = 4.098721362311153000000000000E-12 " " relative error = 3.13096763384131060000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.850000000004705 " " y[1] (closed_form) = -1.2995956192193852 " " y[1] (numeric) = -1.2995956192234939 " " absolute error = 4.108713369532779300000000000E-12 " " relative error = 3.161532178756280000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.860000000004717 " " y[1] (closed_form) = -1.290096430153163 " " y[1] (numeric) = -1.290096430157281 " " absolute error = 4.118039242939630600000000000E-12 " " relative error = 3.1920398713534370000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.87000000000473 " " y[1] (closed_form) = -1.2805933741108149 " " y[1] (numeric) = -1.280593374114947 " " absolute error = 4.132028053049907600000000000E-12 " " relative error = 3.22665112641161270000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.880000000004742 " " y[1] (closed_form) = -1.2710864525871202 " " y[1] (numeric) = -1.2710864525912642 " " absolute error = 4.144018461715859300000000000E-12 " " relative error = 3.2602176297932250000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.890000000004754 " " y[1] (closed_form) = -1.2615756670756966 " " y[1] (numeric) = -1.2615756670798501 " " absolute error = 4.153566379727635600000000000E-12 " " relative error = 3.292364055622210000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.900000000004766 " " y[1] (closed_form) = -1.252061019069 " " y[1] (numeric) = -1.2520610190731685 " " absolute error = 4.168443368257613000000000000E-12 " " relative error = 3.32926535110657700000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.91000000000478 " " y[1] (closed_form) = -1.2425425100583496 " " y[1] (numeric) = -1.2425425100625296 " " absolute error = 4.179989687713714400000000000E-12 " " relative error = 3.3640617152948940000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.92000000000479 " " y[1] (closed_form) = -1.2330201415339026 " " y[1] (numeric) = -1.2330201415380935 " " absolute error = 4.190869873355041000000000000E-12 " " relative error = 3.3988657055849160000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.930000000004803 " " y[1] (closed_form) = -1.2234939149846689 " " y[1] (numeric) = -1.2234939149888706 " " absolute error = 4.2017500589963674000000000000E-12 " " relative error = 3.4342222773122810000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.940000000004815 " " y[1] (closed_form) = -1.213963831898507 " " y[1] (numeric) = -1.213963831902722 " " absolute error = 4.214850690686944300000000000E-12 " " relative error = 3.47197385946447600000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.950000000004827 " " y[1] (closed_form) = -1.2044298937621356 " " y[1] (numeric) = -1.204429893766362 " " absolute error = 4.226397010143046000000000000E-12 " " relative error = 3.5090435998242690000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.96000000000484 " " y[1] (closed_form) = -1.1948921020611216 " " y[1] (numeric) = -1.1948921020653598 " " absolute error = 4.2381653742040726000000000000E-12 " " relative error = 3.54690215701775560000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.970000000004852 " " y[1] (closed_form) = -1.185350458279892 " " y[1] (numeric) = -1.185350458284139 " " absolute error = 4.247047158401074000000000000E-12 " " relative error = 3.58294640098602460000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.980000000004864 " " y[1] (closed_form) = -1.1758049639017187 " " y[1] (numeric) = -1.1758049639059807 " " absolute error = 4.261924146931051000000000000E-12 " " relative error = 3.62468630238517160000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 23.990000000004876 " " y[1] (closed_form) = -1.1662556204087515 " " y[1] (numeric) = -1.1662556204130237 " " absolute error = 4.272138198757602400000000000E-12 " " relative error = 3.66312335306070800000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.00000000000489 " " y[1] (closed_form) = -1.1567024292819816 " " y[1] (numeric) = -1.1567024292862664 " " absolute error = 4.284794741238329000000000000E-12 " " relative error = 3.70431896118528800000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.0100000000049 " " y[1] (closed_form) = -1.1471453920012742 " " y[1] (numeric) = -1.147145392005568 " " absolute error = 4.2938985700402554000000000000E-12 " " relative error = 3.74311626057203970000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.020000000004913 " " y[1] (closed_form) = -1.1375845100453432 " " y[1] (numeric) = -1.1375845100496502 " " absolute error = 4.306999201730832300000000000E-12 " " relative error = 3.7860916386415620000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.030000000004925 " " y[1] (closed_form) = -1.1280197848917766 " " y[1] (numeric) = -1.128019784896097 " " absolute error = 4.320543922631259000000000000E-12 " " relative error = 3.8302022539842040000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.040000000004937 " " y[1] (closed_form) = -1.1184512180170287 " " y[1] (numeric) = -1.1184512180213582 " " absolute error = 4.3294257068282604000000000000E-12 " " relative error = 3.87091152218884100000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.05000000000495 " " y[1] (closed_form) = -1.1088788108964067 " " y[1] (numeric) = -1.1088788109007492 " " absolute error = 4.342526338518837300000000000E-12 " " relative error = 3.9161415078428474000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.060000000004962 " " y[1] (closed_form) = -1.0993025650040984 " " y[1] (numeric) = -1.0993025650084534 " " absolute error = 4.354960836394639000000000000E-12 " " relative error = 3.96156706536785250000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.070000000004974 " " y[1] (closed_form) = -1.0897224818131548 " " y[1] (numeric) = -1.089722481817521 " " absolute error = 4.366285111245815600000000000E-12 " " relative error = 4.00678630028894370000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.080000000004986 " " y[1] (closed_form) = -1.0801385627954971 " " y[1] (numeric) = -1.080138562799874 " " absolute error = 4.376943252282217000000000000E-12 " " relative error = 4.05220534016884740000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.090000000005 " " y[1] (closed_form) = -1.070550809421917 " " y[1] (numeric) = -1.070550809426305 " " absolute error = 4.388045482528468700000000000E-12 " " relative error = 4.0988670915096070000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.10000000000501 " " y[1] (closed_form) = -1.0609592231620795 " " y[1] (numeric) = -1.060959223166479 " " absolute error = 4.39959180198457030000000000E-12 " " relative error = 4.14680574515582300000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.110000000005023 " " y[1] (closed_form) = -1.0513638054845238 " " y[1] (numeric) = -1.0513638054889347 " " absolute error = 4.410916076835747000000000000E-12 " " relative error = 4.1954231768545280000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.120000000005035 " " y[1] (closed_form) = -1.0417645578566628 " " y[1] (numeric) = -1.0417645578610861 " " absolute error = 4.423350574711548700000000000E-12 " " relative error = 4.24601752992268800000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.130000000005047 " " y[1] (closed_form) = -1.0321614817447866 " " y[1] (numeric) = -1.0321614817492235 " " absolute error = 4.436895295611975600000000000E-12 " " relative error = 4.2986445184059363000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.14000000000506 " " y[1] (closed_form) = -1.0225545786140664 " " y[1] (numeric) = -1.0225545786185148 " " absolute error = 4.448441615068077000000000000E-12 " " relative error = 4.3503219369447590000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.150000000005072 " " y[1] (closed_form) = -1.0129438499285506 " " y[1] (numeric) = -1.012943849933008 " " absolute error = 4.4573233992650785000000000000E-12 " " relative error = 4.4003657256811246000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.160000000005084 " " y[1] (closed_form) = -1.0033292971511578 " " y[1] (numeric) = -1.0033292971556294 " " absolute error = 4.4715342539802805000000000000E-12 " " relative error = 4.45669658673050360000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.170000000005096 " " y[1] (closed_form) = -0.9937109217437055 " " y[1] (numeric) = -0.9937109217481883 " " absolute error = 4.482858528831457000000000000E-12 " " relative error = 4.5112300073800143000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.18000000000511 " " y[1] (closed_form) = -0.9840887251668811 " " y[1] (numeric) = -0.9840887251713766 " " absolute error = 4.495515071312184000000000000E-12 " " relative error = 4.5682009724782060000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.19000000000512 " " y[1] (closed_form) = -0.9744627088802638 " " y[1] (numeric) = -0.9744627088847698 " " absolute error = 4.506062190046123000000000000E-12 " " relative error = 4.62415046669559300000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.200000000005133 " " y[1] (closed_form) = -0.96483287434231 " " y[1] (numeric) = -0.9648328743468294 " " absolute error = 4.519384866341625000000000000E-12 " " relative error = 4.6841116078495130000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.210000000005145 " " y[1] (closed_form) = -0.9551992230103714 " " y[1] (numeric) = -0.9551992230149031 " " absolute error = 4.531708341914964000000000000E-12 " " relative error = 4.7442546358371135000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.220000000005157 " " y[1] (closed_form) = -0.9455617563406875 " " y[1] (numeric) = -0.9455617563452268 " " absolute error = 4.539257858482415000000000000E-12 " " relative error = 4.8005937507977140000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.23000000000517 " " y[1] (closed_form) = -0.9359204757883717 " " y[1] (numeric) = -0.9359204757929256 " " absolute error = 4.553912802407467000000000000E-12 " " relative error = 4.8657048544337944000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.240000000005182 " " y[1] (closed_form) = -0.9262753828074501 " " y[1] (numeric) = -0.9262753828120152 " " absolute error = 4.565015032653718700000000000E-12 " " relative error = 4.9283562074354226000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.250000000005194 " " y[1] (closed_form) = -0.9166264788508265 " " y[1] (numeric) = -0.9166264788554025 " " absolute error = 4.576006240597507700000000000E-12 " " relative error = 4.9922256733565457000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.260000000005206 " " y[1] (closed_form) = -0.9069737653702994 " " y[1] (numeric) = -0.9069737653748883 " " absolute error = 4.5888848276831595000000000000E-12 " " relative error = 5.059556299083919000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.27000000000522 " " y[1] (closed_form) = -0.8973172438165662 " " y[1] (numeric) = -0.8973172438211673 " " absolute error = 4.601097280954036000000000000E-12 " " relative error = 5.1276149128530670000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.28000000000523 " " y[1] (closed_form) = -0.8876569156392158 " " y[1] (numeric) = -0.8876569156438293 " " absolute error = 4.613531778829838000000000000E-12 " " relative error = 5.1974267282169050000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.290000000005243 " " y[1] (closed_form) = -0.8779927822867393 " " y[1] (numeric) = -0.8779927822913615 " " absolute error = 4.622191518421914000000000000E-12 " " relative error = 5.2644983098646660000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.300000000005255 " " y[1] (closed_form) = -0.8683248452065122 " " y[1] (numeric) = -0.8683248452111488 " " absolute error = 4.636624417742041000000000000E-12 " " relative error = 5.3397348277410170000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.310000000005267 " " y[1] (closed_form) = -0.8586531058448266 " " y[1] (numeric) = -0.8586531058494757 " " absolute error = 4.6491699379203055000000000000E-12 " " relative error = 5.4144914940312240000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.32000000000528 " " y[1] (closed_form) = -0.8489775656468659 " " y[1] (numeric) = -0.8489775656515269 " " absolute error = 4.661049324283794700000000000E-12 " " relative error = 5.4901913936116520000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.330000000005292 " " y[1] (closed_form) = -0.8392982260567194 " " y[1] (numeric) = -0.8392982260613895 " " absolute error = 4.6700421307832585000000000000E-12 " " relative error = 5.5642225680906640000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.340000000005304 " " y[1] (closed_form) = -0.8296150885173681 " " y[1] (numeric) = -0.8296150885220533 " " absolute error = 4.685252186220623000000000000E-12 " " relative error = 5.6475011738200040000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.350000000005316 " " y[1] (closed_form) = -0.8199281544707162 " " y[1] (numeric) = -0.8199281544754127 " " absolute error = 4.696465438769337000000000000E-12 " " relative error = 5.7278987349824830000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.36000000000533 " " y[1] (closed_form) = -0.8102374253575597 " " y[1] (numeric) = -0.8102374253622671 " " absolute error = 4.707345624410664000000000000E-12 " " relative error = 5.8098348423405650000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.37000000000534 " " y[1] (closed_form) = -0.8005429026176039 " " y[1] (numeric) = -0.8005429026223236 " " absolute error = 4.7197801222864655000000000000E-12 " " relative error = 5.8957241477674650000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.380000000005353 " " y[1] (closed_form) = -0.7908445876894667 " " y[1] (numeric) = -0.7908445876941965 " " absolute error = 4.729772129508092000000000000E-12 " " relative error = 5.9806594154315510000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.390000000005365 " " y[1] (closed_form) = -0.7811424820106687 " " y[1] (numeric) = -0.7811424820154101 " " absolute error = 4.741429471266656000000000000E-12 " " relative error = 6.0698650764226370000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.400000000005377 " " y[1] (closed_form) = -0.771436587017643 " " y[1] (numeric) = -0.7714365870223989 " " absolute error = 4.7559733928892456000000000000E-12 " " relative error = 6.1650866356698690000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.41000000000539 " " y[1] (closed_form) = -0.7617269041457426 " " y[1] (numeric) = -0.761726904150509 " " absolute error = 4.766409489320722000000000000E-12 " " relative error = 6.257373165342149000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.420000000005402 " " y[1] (closed_form) = -0.7520134348292231 " " y[1] (numeric) = -0.7520134348340002 " " absolute error = 4.7770676303571236000000000000E-12 " " relative error = 6.3523700629656470000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.430000000005414 " " y[1] (closed_form) = -0.7422961805012562 " " y[1] (numeric) = -0.7422961805060457 " " absolute error = 4.789502128232925300000000000E-12 " " relative error = 6.4522790956551610000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.440000000005426 " " y[1] (closed_form) = -0.7325751425939337 " " y[1] (numeric) = -0.7325751425987352 " " absolute error = 4.801492536898877000000000000E-12 " " relative error = 6.5542662557420990000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.45000000000544 " " y[1] (closed_form) = -0.7228503225382603 " " y[1] (numeric) = -0.7228503225430742 " " absolute error = 4.813927034774679000000000000E-12 " " relative error = 6.6596456896785550000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.46000000000545 " " y[1] (closed_form) = -0.7131217217641606 " " y[1] (numeric) = -0.7131217217689867 " " absolute error = 4.8261394880455555000000000000E-12 " " relative error = 6.7676237320416780000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.470000000005463 " " y[1] (closed_form) = -0.7033893417004791 " " y[1] (numeric) = -0.7033893417053156 " " absolute error = 4.836575584477032000000000000E-12 " " relative error = 6.8761001876775210000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.480000000005475 " " y[1] (closed_form) = -0.6936531837749733 " " y[1] (numeric) = -0.6936531837798245 " " absolute error = 4.851230528402084000000000000E-12 " " relative error = 6.9937407365463240000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.490000000005487 " " y[1] (closed_form) = -0.6839132494143385 " " y[1] (numeric) = -0.6839132494191983 " " absolute error = 4.859779245691698000000000000E-12 " " relative error = 7.1058416397888410000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.5000000000055 " " y[1] (closed_form) = -0.6741695400441721 " " y[1] (numeric) = -0.674169540049045 " " absolute error = 4.8728798773822746000000000000E-12 " " relative error = 7.2279739560215070000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.510000000005512 " " y[1] (closed_form) = -0.6644220570890091 " " y[1] (numeric) = -0.6644220570938962 " " absolute error = 4.8870907320974766000000000000E-12 " " relative error = 7.3554011037938470000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.520000000005524 " " y[1] (closed_form) = -0.654670801972312 " " y[1] (numeric) = -0.6546708019772095 " " absolute error = 4.897526828528953000000000000E-12 " " relative error = 7.4809000397975360000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.530000000005536 " " y[1] (closed_form) = -0.6449157761164592 " " y[1] (numeric) = -0.6449157761213687 " " absolute error = 4.909517237194905000000000000E-12 " " relative error = 7.6126486884208920000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.54000000000555 " " y[1] (closed_form) = -0.6351569809427637 " " y[1] (numeric) = -0.6351569809476854 " " absolute error = 4.921618668163319000000000000E-12 " " relative error = 7.7486650006714220000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.55000000000556 " " y[1] (closed_form) = -0.6253944178714654 " " y[1] (numeric) = -0.6253944178763995 " " absolute error = 4.934053166039120700000000000E-12 " " relative error = 7.8895062460458280000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.560000000005573 " " y[1] (closed_form) = -0.6156280883217384 " " y[1] (numeric) = -0.6156280883266817 " " absolute error = 4.9432680171435095000000000000E-12 " " relative error = 8.0296336553118220000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.570000000005585 " " y[1] (closed_form) = -0.6058579937116768 " " y[1] (numeric) = -0.6058579937166342 " " absolute error = 4.957367849556249000000000000E-12 " " relative error = 8.1823924104489450000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.580000000005597 " " y[1] (closed_form) = -0.5960841354583231 " " y[1] (numeric) = -0.5960841354632911 " " absolute error = 4.9680259905926505000000000000E-12 " " relative error = 8.3344375316628500000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.59000000000561 " " y[1] (closed_form) = -0.5863065149776396 " " y[1] (numeric) = -0.5863065149826207 " " absolute error = 4.981015599980765000000000000E-12 " " relative error = 8.4955828951870490000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.600000000005622 " " y[1] (closed_form) = -0.5765251336845338 " " y[1] (numeric) = -0.5765251336895262 " " absolute error = 4.9923398748319414000000000000E-12 " " relative error = 8.6593620696572740000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.610000000005634 " " y[1] (closed_form) = -0.5667399929928436 " " y[1] (numeric) = -0.5667399929978469 " " absolute error = 5.0033310827757300000000000000E-12 " " relative error = 8.8282654208927680000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.620000000005646 " " y[1] (closed_form) = -0.5569510943153411 " " y[1] (numeric) = -0.5569510943203596 " " absolute error = 5.018541138213095000000000000E-12 " " relative error = 9.0107393439676750000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.63000000000566 " " y[1] (closed_form) = -0.5471584390637503 " " y[1] (numeric) = -0.5471584390687796 " " absolute error = 5.029310301551959000000000000E-12 " " relative error = 9.1916891753651390000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.64000000000567 " " y[1] (closed_form) = -0.5373620286487188 " " y[1] (numeric) = -0.5373620286537615 " " absolute error = 5.042632977847461000000000000E-12 " " relative error = 9.3840515499912660000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.650000000005683 " " y[1] (closed_form) = -0.5275618644798463 " " y[1] (numeric) = -0.5275618644849015 " " absolute error = 5.055178498025725000000000000E-12 " " relative error = 9.5821529916873680000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.660000000005695 " " y[1] (closed_form) = -0.5177579479656735 " " y[1] (numeric) = -0.5177579479707376 " " absolute error = 5.0640602822227270000000000000E-12 " " relative error = 9.780748517951220000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.670000000005707 " " y[1] (closed_form) = -0.507950280513672 " " y[1] (numeric) = -0.5079502805187514 " " absolute error = 5.079381359962554000000000000E-12 " " relative error = 9.9997609112961940000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.68000000000572 " " y[1] (closed_form) = -0.49813886353027925 " " y[1] (numeric) = -0.49813886353536846 " " absolute error = 5.089206833730486000000000000E-12 " " relative error = 1.021644205325316900000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.690000000005732 " " y[1] (closed_form) = -0.4883236984208601 " " y[1] (numeric) = -0.48832369842596096 " " absolute error = 5.1008641754890500000000000000E-12 " " relative error = 1.0445661744421195000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.700000000005744 " " y[1] (closed_form) = -0.4785047865897347 " " y[1] (numeric) = -0.4785047865948472 " " absolute error = 5.112466006096383000000000000E-12 " " relative error = 1.068425259135341000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.710000000005756 " " y[1] (closed_form) = -0.4686821294401682 " " y[1] (numeric) = -0.4686821294452938 " " absolute error = 5.1256221489381910000000000000E-12 " " relative error = 1.0936244048947734000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.72000000000577 " " y[1] (closed_form) = -0.4588557283743775 " " y[1] (numeric) = -0.45885572837951677 " " absolute error = 5.139277892141081000000000000E-12 " " relative error = 1.1200204278474162000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.73000000000578 " " y[1] (closed_form) = -0.44902558479353516 " " y[1] (numeric) = -0.44902558479868226 " " absolute error = 5.147104964464688000000000000E-12 " " relative error = 1.1462832272311076000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.740000000005793 " " y[1] (closed_form) = -0.4391917000977479 " " y[1] (numeric) = -0.43919170010290826 " " absolute error = 5.160372129608959000000000000E-12 " " relative error = 1.1749703212652814000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.750000000005805 " " y[1] (closed_form) = -0.4293540756860921 " " y[1] (numeric) = -0.4293540756912654 " " absolute error = 5.173306227845842000000000000E-12 " " relative error = 1.20490441824247000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.760000000005817 " " y[1] (closed_form) = -0.41951271295659254 " " y[1] (numeric) = -0.41951271296177844 " " absolute error = 5.1859072591753370000000000000E-12 " " relative error = 1.2361740416939233000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.77000000000583 " " y[1] (closed_form) = -0.4096676133062296 " " y[1] (numeric) = -0.4096676133114272 " " absolute error = 5.197620112085133000000000000E-12 " " relative error = 1.26874078967035000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.780000000005842 " " y[1] (closed_form) = -0.399818778130939 " " y[1] (numeric) = -0.3998187781361479 " " absolute error = 5.208888875785078000000000000E-12 " " relative error = 1.3028124642207745000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.790000000005854 " " y[1] (closed_form) = -0.38996620882561217 " " y[1] (numeric) = -0.38996620883083405 " " absolute error = 5.2218784851731930000000000000E-12 " " relative error = 1.3390592228231620000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.800000000005866 " " y[1] (closed_form) = -0.38010990678410295 " " y[1] (numeric) = -0.38010990678933804 " " absolute error = 5.235090139166232000000000000E-12 " " relative error = 1.3772569579828628000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.81000000000588 " " y[1] (closed_form) = -0.3702498733992279 " " y[1] (numeric) = -0.3702498734044719 " " absolute error = 5.244027434514464000000000000E-12 " " relative error = 1.4163482046245040000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.82000000000589 " " y[1] (closed_form) = -0.3603861100627519 " " y[1] (numeric) = -0.3603861100680085 " " absolute error = 5.25662846584396000000000000E-12 " " relative error = 1.4586101736630900000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.830000000005903 " " y[1] (closed_form) = -0.3505186181654132 " " y[1] (numeric) = -0.3505186181706832 " " absolute error = 5.270006653290693000000000000E-12 " " relative error = 1.5034883684277578000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.840000000005915 " " y[1] (closed_form) = -0.34064739909691255 " " y[1] (numeric) = -0.3406473991021945 " " absolute error = 5.2819415508054130000000000000E-12 " " relative error = 1.5505597767099719000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.850000000005927 " " y[1] (closed_form) = -0.33077245424590984 " " y[1] (numeric) = -0.3307724542512053 " " absolute error = 5.295430760554609000000000000E-12 " " relative error = 1.600928581742713000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.86000000000594 " " y[1] (closed_form) = -0.3208937850000382 " " y[1] (numeric) = -0.32089378500534416 " " absolute error = 5.305977879288548000000000000E-12 " " relative error = 1.6534997333425816000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.870000000005952 " " y[1] (closed_form) = -0.31101139274588974 " " y[1] (numeric) = -0.3110113927512063 " " absolute error = 5.316580509173718000000000000E-12 " " relative error = 1.7094487961467070000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.880000000005964 " " y[1] (closed_form) = -0.3011252788690264 " " y[1] (numeric) = -0.3011252788743551 " " absolute error = 5.3286819401421330000000000000E-12 " " relative error = 1.769589707033473000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.890000000005976 " " y[1] (closed_form) = -0.2912354447539798 " " y[1] (numeric) = -0.2912354447593228 " " absolute error = 5.343003817159797000000000000E-12 " " relative error = 1.8345994326594697000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.90000000000599 " " y[1] (closed_form) = -0.2813418917842583 " " y[1] (numeric) = -0.28134189178961205 " " absolute error = 5.353772980498661000000000000E-12 " " relative error = 1.9029419851218250000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.910000000006 " " y[1] (closed_form) = -0.27144462134233294 " " y[1] (numeric) = -0.27144462134769676 " " absolute error = 5.363820498871519000000000000E-12 " " relative error = 1.9760275493198762000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.920000000006013 " " y[1] (closed_form) = -0.2615436348096445 " " y[1] (numeric) = -0.2615436348150233 " " absolute error = 5.3788085097039580000000000000E-12 " " relative error = 2.0565625745848254000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.930000000006025 " " y[1] (closed_form) = -0.25163893356662115 " " y[1] (numeric) = -0.2516389335720118 " " absolute error = 5.390632384916216000000000000E-12 " " relative error = 2.1422091997099693000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.940000000006037 " " y[1] (closed_form) = -0.24173051899265374 " " y[1] (numeric) = -0.24173051899805714 " " absolute error = 5.403399949699406000000000000E-12 " " relative error = 2.235299031424168900000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.95000000000605 " " y[1] (closed_form) = -0.23181839246611702 " " y[1] (numeric) = -0.23181839247153027 " " absolute error = 5.413253179042954000000000000E-12 " " relative error = 2.3351267004554715000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.960000000006062 " " y[1] (closed_form) = -0.22190255536435188 " " y[1] (numeric) = -0.22190255536977907 " " absolute error = 5.427186478002000000000000E-12 " " relative error = 2.445752131646639000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.970000000006074 " " y[1] (closed_form) = -0.21198300906369028 " " y[1] (numeric) = -0.21198300906912973 " " absolute error = 5.4394544424241080000000000000E-12 " " relative error = 2.565986050697971000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.980000000006086 " " y[1] (closed_form) = -0.2020597549394374 " " y[1] (numeric) = -0.20205975494488787 " " absolute error = 5.450473405943512000000000000E-12 " " relative error = 2.6974562092174975000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 24.9900000000061 " " y[1] (closed_form) = -0.19213279436587882 " " y[1] (numeric) = -0.19213279437133945 " " absolute error = 5.4606319466188320000000000000E-12 " " relative error = 2.8421134271435940000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.00000000000611 " " y[1] (closed_form) = -0.18220212871627695 " " y[1] (numeric) = -0.18220212872175226 " " absolute error = 5.4753146461195000000000000E-12 " " relative error = 3.005077209962567000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.010000000006123 " " y[1] (closed_form) = -0.17226775936288874 " " y[1] (numeric) = -0.17226775936837666 " " absolute error = 5.487915677448996000000000000E-12 " " relative error = 3.185689358093111000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.020000000006135 " " y[1] (closed_form) = -0.162329687676948 " " y[1] (numeric) = -0.16232968768244704 " " absolute error = 5.499045663270863000000000000E-12 " " relative error = 3.3875785396781540000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.030000000006147 " " y[1] (closed_form) = -0.15238791502867244 " " y[1] (numeric) = -0.15238791503418275 " " absolute error = 5.510314426970808000000000000E-12 " " relative error = 3.615978620046097000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.04000000000616 " " y[1] (closed_form) = -0.14244244278726725 " " y[1] (numeric) = -0.14244244279278928 " " absolute error = 5.522027279880604000000000000E-12 " " relative error = 3.876672690967225600000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.05000000000617 " " y[1] (closed_form) = -0.13249327232092512 " " y[1] (numeric) = -0.13249327232645944 " " absolute error = 5.534322999878327000000000000E-12 " " relative error = 4.1770596370154506000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.060000000006184 " " y[1] (closed_form) = -0.12254040499682617 " " y[1] (numeric) = -0.1225404050023744 " " absolute error = 5.548228543261757000000000000E-12 " " relative error = 4.527672765081409000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.070000000006196 " " y[1] (closed_form) = -0.11258384218114514 " " y[1] (numeric) = -0.11258384218670489 " " absolute error = 5.559747107142243000000000000E-12 " " relative error = 4.938317079458632300000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.08000000000621 " " y[1] (closed_form) = -0.1026235852390407 " " y[1] (numeric) = -0.1026235852446122 " " absolute error = 5.571501593415462000000000000E-12 " " relative error = 5.429065434069358000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.09000000000622 " " y[1] (closed_form) = -9.26596355346660500E-2 " " y[1] (numeric) = -9.26596355402494700E-2 " " absolute error = 5.583422613142375000000000000E-12 " " relative error = 6.025733406919662000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.100000000006233 " " y[1] (closed_form) = -8.26919944311654800E-2 " " y[1] (numeric) = -8.26919944367626700E-2 " " absolute error = 5.597189378647727000000000000E-12 " " relative error = 6.768719774085196000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.110000000006245 " " y[1] (closed_form) = -7.27206632906813900E-2 " " y[1] (numeric) = -7.27206632962917900E-2 " " absolute error = 5.610401032640766000000000000E-12 " " relative error = 7.715002557408877000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.120000000006257 " " y[1] (closed_form) = -6.27456434743507400E-2 " " y[1] (numeric) = -6.27456434799718200E-2 " " absolute error = 5.621086929252783000000000000E-12 " " relative error = 8.958529418142918000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.13000000000627 " " y[1] (closed_form) = -5.27669363423015600E-2 " " y[1] (numeric) = -5.27669363479340900E-2 " " absolute error = 5.632529165300326000000000000E-12 " " relative error = 1.067435321384180400000000E-8 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.14000000000628 " " y[1] (closed_form) = -4.27845432536635430E-2 " " y[1] (numeric) = -4.27845432593071840E-2 " " absolute error = 5.643638334440482000000000000E-12 " " relative error = 1.319083459879457600000000E-8 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.150000000006294 " " y[1] (closed_form) = -3.279846556656096400E-2 " " y[1] (numeric) = -3.27984655722181100E-2 " " absolute error = 5.657148360871389000000000000E-12 " " relative error = 1.724821043652427800000000E-8 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.160000000006306 " " y[1] (closed_form) = -2.280870463812334500E-2 " " y[1] (numeric) = -2.28087046437934600E-2 " " absolute error = 5.67011368413084000000000000E-12 " " relative error = 2.48594287755105280000000E-8 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.17000000000632 " " y[1] (closed_form) = -1.281526182447834000E-2 " " y[1] (numeric) = -1.28152618301604300E-2 " " absolute error = 5.682088480285508000000000000E-12 " " relative error = 4.433845018626299500000000E-8 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.18000000000633 " " y[1] (closed_form) = -2.8181384807552945000E-3 " " y[1] (numeric) = -2.81813848644797970E-3 " " absolute error = 5.692685472319381000000000000E-12 " " relative error = 2.02001623099574370000000E-7 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 10 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.190000000006343 " " y[1] (closed_form) = 7.182664038921871000E-3 " " y[1] (numeric) = 7.182664033212084000E-3 " " absolute error = 5.709786810026429000000000000E-12 " " relative error = 7.9493998035908100000000E-8 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.200000000006355 " " y[1] (closed_form) = 1.718714438140622700E-2 " " y[1] (numeric) = 1.71871443756840100E-2 " " absolute error = 5.722217838455279000000000000E-12 " " relative error = 3.32935926496656100000000E-8 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.210000000006367 " " y[1] (closed_form) = 2.719530119455982000E-2 " " y[1] (numeric) = 2.71953011888269900E-2 " " absolute error = 5.732827407234353000000000000E-12 " " relative error = 2.108021296113151700000000E-8 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.22000000000638 " " y[1] (closed_form) = 3.720713312723944500E-2 " " y[1] (numeric) = 3.72071331214940900E-2 " " absolute error = 5.745355580177858000000000000E-12 " " relative error = 1.54415433205512630000000E-8 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.23000000000639 " " y[1] (closed_form) = 4.722263882928956500E-2 " " y[1] (numeric) = 4.72226388235311200E-2 " " absolute error = 5.758442334080627000000000000E-12 " " relative error = 1.219424089131797300000000E-8 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.240000000006404 " " y[1] (closed_form) = 5.72418169515458400E-2 " " y[1] (numeric) = 5.72418169457755700E-2 " " absolute error = 5.770273148186789000000000000E-12 " " relative error = 1.008052059750517600000000E-8 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.250000000006416 " " y[1] (closed_form) = 6.7264666145838700E-2 " " y[1] (numeric) = 6.72646661400554800E-2 " " absolute error = 5.7832211242114800000000000000E-12 " " relative error = 8.597710292165414000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.26000000000643 " " y[1] (closed_form) = 7.72911850649791200E-2 " " y[1] (numeric) = 7.72911850591884200E-2 " " absolute error = 5.7907012518398910000000000000E-12 " " relative error = 7.492059084061937000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.27000000000644 " " y[1] (closed_form) = 8.73213723627870300E-2 " " y[1] (numeric) = 8.73213723569803200E-2 " " absolute error = 5.806716218970109000000000000E-12 " " relative error = 6.649822445352113000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.280000000006453 " " y[1] (closed_form) = 9.73552266940416200E-2 " " y[1] (numeric) = 9.73552266882243700E-2 " " absolute error = 5.8172494599162400000000000000E-12 " " relative error = 5.9752821265550700000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.290000000006465 " " y[1] (closed_form) = 0.10739274671453103 " " y[1] (numeric) = 0.1073927467087001 " " absolute error = 5.8309329586947460000000000000E-12 " " relative error = 5.429540762370480000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.300000000006477 " " y[1] (closed_form) = 0.11743393108101685 " " y[1] (numeric) = 0.11743393107517208 " " absolute error = 5.844769113139137000000000000E-12 " " relative error = 4.977070135808424000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.31000000000649 " " y[1] (closed_form) = 0.12747877845124123 " " y[1] (numeric) = 0.127478778445389 " " absolute error = 5.852235362979741000000000000E-12 " " relative error = 4.5907526210083155000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.3200000000065 " " y[1] (closed_form) = 0.13752728748394816 " " y[1] (numeric) = 0.13752728747808246 " " absolute error = 5.865696817153321000000000000E-12 " " relative error = 4.2651148906270336000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.330000000006514 " " y[1] (closed_form) = 0.14757945683884444 " " y[1] (numeric) = 0.14757945683296603 " " absolute error = 5.878408870785279000000000000E-12 " " relative error = 3.983216225822306000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.340000000006526 " " y[1] (closed_form) = 0.15763528517662806 " " y[1] (numeric) = 0.15763528517073397 " " absolute error = 5.894090771008109000000000000E-12 " " relative error = 3.739068168908925000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.35000000000654 " " y[1] (closed_form) = 0.16769477115896692 " " y[1] (numeric) = 0.16769477115306047 " " absolute error = 5.906442002157064000000000000E-12 " " relative error = 3.5221384431587494000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.36000000000655 " " y[1] (closed_form) = 0.177757913448513 " " y[1] (numeric) = 0.1777579134425982 " " absolute error = 5.914796430417368000000000000E-12 " " relative error = 3.3274447903162246000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.370000000006563 " " y[1] (closed_form) = 0.1878247107089024 " " y[1] (numeric) = 0.1878247107029776 " " absolute error = 5.924788437638995000000000000E-12 " " relative error = 3.154424364758612000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.380000000006575 " " y[1] (closed_form) = 0.19789516160474463 " " y[1] (numeric) = 0.19789516159880546 " " absolute error = 5.9391658258078900000000000000E-12 " " relative error = 3.001167778760639000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.390000000006587 " " y[1] (closed_form) = 0.2079692648016156 " " y[1] (numeric) = 0.20796926479566416 " " absolute error = 5.9514337902299990000000000000E-12 " " relative error = 2.8616891038717396000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.4000000000066 " " y[1] (closed_form) = 0.21804701896607526 " " y[1] (numeric) = 0.2180470189601103 " " absolute error = 5.96495075555481000000000000E-12 " " relative error = 2.7356259140065853000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.41000000000661 " " y[1] (closed_form) = 0.22812842276564993 " " y[1] (numeric) = 0.228128422759674 " " absolute error = 5.975941963498599000000000000E-12 " " relative error = 2.6195516941952995000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.420000000006624 " " y[1] (closed_form) = 0.23821347486885003 " " y[1] (numeric) = 0.23821347486285746 " " absolute error = 5.9925675532923610000000000000E-12 " " relative error = 2.515629124923184000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.430000000006636 " " y[1] (closed_form) = 0.24830217394513454 " " y[1] (numeric) = 0.24830217393913417 " " absolute error = 6.000366870040352000000000000E-12 " " relative error = 2.4165583308047103000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.44000000000665 " " y[1] (closed_form) = 0.25839451866496077 " " y[1] (numeric) = 0.2583945186589477 " " absolute error = 6.01307892367231000000000000E-12 " " relative error = 2.327092290788483000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.45000000000666 " " y[1] (closed_form) = 0.2684905076997346 " " y[1] (numeric) = 0.26849050769371063 " " absolute error = 6.023959109313637000000000000E-12 " " relative error = 2.2436395092412392000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.460000000006673 " " y[1] (closed_form) = 0.278590139721846 " " y[1] (numeric) = 0.27859013971580376 " " absolute error = 6.042222278068721000000000000E-12 " " relative error = 2.1688571907467666000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.470000000006685 " " y[1] (closed_form) = 0.2886934134046264 " " y[1] (numeric) = 0.2886934133985746 " " absolute error = 6.051770196080497000000000000E-12 " " relative error = 2.0962619564854662000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.480000000006697 " " y[1] (closed_form) = 0.2988003274223985 " " y[1] (numeric) = 0.2988003274163367 " " absolute error = 6.0617622033021230000000000000E-12 " " relative error = 2.0286999869089584000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.49000000000671 " " y[1] (closed_form) = 0.3089108804504441 " " y[1] (numeric) = 0.30891088044436843 " " absolute error = 6.075695502261169000000000000E-12 " " relative error = 1.966811752762408800000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.50000000000672 " " y[1] (closed_form) = 0.31902507116499734 " " y[1] (numeric) = 0.31902507115891177 " " absolute error = 6.085576487180333000000000000E-12 " " relative error = 1.907554307552499200000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.510000000006734 " " y[1] (closed_form) = 0.32914289824326914 " " y[1] (numeric) = 0.32914289823717163 " " absolute error = 6.0975113846950530000000000000E-12 " " relative error = 1.8525422900628374000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.520000000006746 " " y[1] (closed_form) = 0.3392643603634262 " " y[1] (numeric) = 0.33926436035731444 " " absolute error = 6.111777750561487000000000000E-12 " " relative error = 1.8014794551406574000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.53000000000676 " " y[1] (closed_form) = 0.34938945620459094 " " y[1] (numeric) = 0.3493894561984675 " " absolute error = 6.123435092320051000000000000E-12 " " relative error = 1.7526101556809343000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.54000000000677 " " y[1] (closed_form) = 0.35951818444685557 " " y[1] (numeric) = 0.3595181844407176 " " absolute error = 6.1379790139426400000000000000E-12 " " relative error = 1.707279152899139000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.550000000006783 " " y[1] (closed_form) = 0.36965054377126094 " " y[1] (numeric) = 0.3696505437651098 " " absolute error = 6.1511351567844490000000000000E-12 " " relative error = 1.664040608199608000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.560000000006795 " " y[1] (closed_form) = 0.3797865328598071 " " y[1] (numeric) = 0.3797865328536471 " " absolute error = 6.16001694098145000000000000E-12 " " relative error = 1.6219682395255794000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.570000000006807 " " y[1] (closed_form) = 0.3899261503954641 " " y[1] (numeric) = 0.3899261503892887 " " absolute error = 6.175393529872508000000000000E-12 " " relative error = 1.5837341310936465000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.58000000000682 " " y[1] (closed_form) = 0.4000693950621361 " " y[1] (numeric) = 0.40006939505594924 " " absolute error = 6.1868843381773790000000000000E-12 " " relative error = 1.5464527940750060000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.59000000000683 " " y[1] (closed_form) = 0.4102162655446975 " " y[1] (numeric) = 0.4102162655384978 " " absolute error = 6.199651902960568000000000000E-12 " " relative error = 1.5113130374604927000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.600000000006844 " " y[1] (closed_form) = 0.4203667605289674 " " y[1] (numeric) = 0.42036676052275673 " " absolute error = 6.210643110904357000000000000E-12 " " relative error = 1.4774343963564604000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.610000000006856 " " y[1] (closed_form) = 0.4305208787017243 " " y[1] (numeric) = 0.4305208786955008 " " absolute error = 6.2234661868387780000000000000E-12 " " relative error = 1.4455666367694447000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.62000000000687 " " y[1] (closed_form) = 0.4406786187506917 " " y[1] (numeric) = 0.44067861874445596 " " absolute error = 6.2357341512608850000000000000E-12 " " relative error = 1.415029884803345200000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.63000000000688 " " y[1] (closed_form) = 0.45083997936454523 " " y[1] (numeric) = 0.4508399793582983 " " absolute error = 6.2469474038096000000000000000E-12 " " relative error = 1.3856240994009925000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.640000000006893 " " y[1] (closed_form) = 0.4610049592329126 " " y[1] (numeric) = 0.46100495922665313 " " absolute error = 6.259492923987864000000000000E-12 " " relative error = 1.3577929691696422000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.650000000006905 " " y[1] (closed_form) = 0.4711735570463702 " " y[1] (numeric) = 0.4711735570400942 " " absolute error = 6.2759797359035470000000000000E-12 " " relative error = 1.3319889543983687000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.660000000006917 " " y[1] (closed_form) = 0.4813457714964251 " " y[1] (numeric) = 0.4813457714901421 " " absolute error = 6.282974140958686000000000000E-12 " " relative error = 1.3052933074338532000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.67000000000693 " " y[1] (closed_form) = 0.49152160127556144 " " y[1] (numeric) = 0.49152160126926375 " " absolute error = 6.297684596034969000000000000E-12 " " relative error = 1.2812630370042072000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.68000000000694 " " y[1] (closed_form) = 0.5017010450771835 " " y[1] (numeric) = 0.501701045070871 " " absolute error = 6.312506073413715000000000000E-12 " " relative error = 1.2582206346495803000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.690000000006954 " " y[1] (closed_form) = 0.5118841015956441 " " y[1] (numeric) = 0.5118841015893197 " " absolute error = 6.324385459777204000000000000E-12 " " relative error = 1.2355112104601106000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.700000000006966 " " y[1] (closed_form) = 0.5220707695262483 " " y[1] (numeric) = 0.5220707695199094 " " absolute error = 6.338929381399794000000000000E-12 " " relative error = 1.214189675310118900000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.71000000000698 " " y[1] (closed_form) = 0.5322610475652283 " " y[1] (numeric) = 0.5322610475588804 " " absolute error = 6.3479221878992580000000000000E-12 " " relative error = 1.1926332420787045000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.72000000000699 " " y[1] (closed_form) = 0.5424549344097755 " " y[1] (numeric) = 0.542454934403415 " " absolute error = 6.360578730379984000000000000E-12 " " relative error = 1.172554313161643000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.730000000007003 " " y[1] (closed_form) = 0.5526524287580088 " " y[1] (numeric) = 0.5526524287516356 " " absolute error = 6.373235272860711000000000000E-12 " " relative error = 1.1532085884763882000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.740000000007015 " " y[1] (closed_form) = 0.5628535293089847 " " y[1] (numeric) = 0.5628535293026028 " " absolute error = 6.381895012452787000000000000E-12 " " relative error = 1.1338464947155684000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.750000000007027 " " y[1] (closed_form) = 0.5730582347627156 " " y[1] (numeric) = 0.5730582347563158 " " absolute error = 6.399769603149252000000000000E-12 " " relative error = 1.1167747385742019000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.76000000000704 " " y[1] (closed_form) = 0.5832665438201232 " " y[1] (numeric) = 0.5832665438137106 " " absolute error = 6.412648190234904000000000000E-12 " " relative error = 1.0994369998037357000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.77000000000705 " " y[1] (closed_form) = 0.5934784551830816 " " y[1] (numeric) = 0.5934784551766588 " " absolute error = 6.422862242061456000000000000E-12 " " relative error = 1.0822401699620372000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.780000000007064 " " y[1] (closed_form) = 0.6036939675544062 " " y[1] (numeric) = 0.6036939675479668 " " absolute error = 6.4394045651283700000000000000E-12 " " relative error = 1.0666670384689636000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.790000000007076 " " y[1] (closed_form) = 0.6139130796378254 " " y[1] (numeric) = 0.6139130796313756 " " absolute error = 6.4497296392573840000000000000E-12 " " relative error = 1.0505932929564502000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.80000000000709 " " y[1] (closed_form) = 0.6241357901380162 " " y[1] (numeric) = 0.6241357901315588 " " absolute error = 6.457390178127298000000000000E-12 " " relative error = 1.034613024947562100000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.8100000000071 " " y[1] (closed_form) = 0.6343620977605937 " " y[1] (numeric) = 0.634362097754122 " " absolute error = 6.4717120551449630000000000000E-12 " " relative error = 1.020192107629256000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.820000000007113 " " y[1] (closed_form) = 0.6445920012120858 " " y[1] (numeric) = 0.644592001205601 " " absolute error = 6.484812686835539000000000000E-12 " " relative error = 1.0060336886963456000000000E-9 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.830000000007125 " " y[1] (closed_form) = 0.6548254991999585 " " y[1] (numeric) = 0.6548254991934624 " " absolute error = 6.4960259393842530000000000000E-12 " " relative error = 9.9202397391684620000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.840000000007137 " " y[1] (closed_form) = 0.665062590432612 " " y[1] (numeric) = 0.6650625904261012 " " absolute error = 6.510791905611768000000000000E-12 " " relative error = 9.7897430997834480000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.85000000000715 " " y[1] (closed_form) = 0.6753032736193632 " " y[1] (numeric) = 0.6753032736128401 " " absolute error = 6.523004358882645000000000000E-12 " " relative error = 9.6593702617816080000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.86000000000716 " " y[1] (closed_form) = 0.6855475474704633 " " y[1] (numeric) = 0.685547547463929 " " absolute error = 6.534328633733821000000000000E-12 " " relative error = 9.5315469479020380000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.870000000007174 " " y[1] (closed_form) = 0.6957954106970945 " " y[1] (numeric) = 0.6957954106905436 " " absolute error = 6.550870956800736000000000000E-12 " " relative error = 9.4149384374893120000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.880000000007186 " " y[1] (closed_form) = 0.7060468620113447 " " y[1] (numeric) = 0.7060468620047847 " " absolute error = 6.5599747856026620000000000000E-12 " " relative error = 9.2911322726015570000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.8900000000072 " " y[1] (closed_form) = 0.716301900126247 " " y[1] (numeric) = 0.7163019001196764 " " absolute error = 6.5705219043366010000000000000E-12 " " relative error = 9.172838859115909000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.90000000000721 " " y[1] (closed_form) = 0.7265605237557509 " " y[1] (numeric) = 0.7265605237491664 " " absolute error = 6.5845107144468780000000000000E-12 " " relative error = 9.0625770313119900000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.910000000007223 " " y[1] (closed_form) = 0.7368227316147227 " " y[1] (numeric) = 0.7368227316081237 " " absolute error = 6.5989436137670050000000000000E-12 " " relative error = 8.9559446670512430000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.920000000007235 " " y[1] (closed_form) = 0.7470885224189523 " " y[1] (numeric) = 0.7470885224123388 " " absolute error = 6.613487535389595000000000000E-12 " " relative error = 8.8523479305721190000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.930000000007247 " " y[1] (closed_form) = 0.7573578948851463 " " y[1] (numeric) = 0.7573578948785216 " " absolute error = 6.624700787938309000000000000E-12 " " relative error = 8.7471205260796140000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.94000000000726 " " y[1] (closed_form) = 0.7676308477309384 " " y[1] (numeric) = 0.7676308477243009 " " absolute error = 6.637468352721498000000000000E-12 " " relative error = 8.6466930977844080000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.95000000000727 " " y[1] (closed_form) = 0.7779073796748683 " " y[1] (numeric) = 0.7779073796682241 " " absolute error = 6.644240713171712000000000000E-12 " " relative error = 8.5411719785313220000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.960000000007284 " " y[1] (closed_form) = 0.7881874894364138 " " y[1] (numeric) = 0.7881874894297548 " " absolute error = 6.6590066793992260000000000000E-12 " " relative error = 8.4485059311975230000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.970000000007296 " " y[1] (closed_form) = 0.7984711757359477 " " y[1] (numeric) = 0.798471175729273 " " absolute error = 6.674771846348904000000000000E-12 " " relative error = 8.3594399512252810000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.98000000000731 " " y[1] (closed_form) = 0.8087584372947596 " " y[1] (numeric) = 0.8087584372880736 " " absolute error = 6.685985098897618000000000000E-12 " " relative error = 8.266974155177620000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 25.99000000000732 " " y[1] (closed_form) = 0.8190492728350627 " " y[1] (numeric) = 0.8190492728283657 " " absolute error = 6.696976306841407000000000000E-12 " " relative error = 8.1765243300448190000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.000000000007333 " " y[1] (closed_form) = 0.8293436810799797 " " y[1] (numeric) = 0.8293436810732713 " " absolute error = 6.708411603995046000000000000E-12 " " relative error = 8.0888198186538120000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.010000000007345 " " y[1] (closed_form) = 0.83964166075355 " " y[1] (numeric) = 0.8396416607468241 " " absolute error = 6.725842105481661000000000000E-12 " " relative error = 8.0103720668712960000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.020000000007357 " " y[1] (closed_form) = 0.8499432105807045 " " y[1] (numeric) = 0.8499432105739693 " " absolute error = 6.735279001190975000000000000E-12 " " relative error = 7.9243870853315560000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.03000000000737 " " y[1] (closed_form) = 0.860248329287316 " " y[1] (numeric) = 0.8602483292805622 " " absolute error = 6.753819725702215000000000000E-12 " " relative error = 7.8510117320396370000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.04000000000738 " " y[1] (closed_form) = 0.8705570156001272 " " y[1] (numeric) = 0.870557015593367 " " absolute error = 6.760259019245041000000000000E-12 " " relative error = 7.7654408592466370000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.050000000007394 " " y[1] (closed_form) = 0.8808692682468298 " " y[1] (numeric) = 0.8808692682400563 " " absolute error = 6.77347067323808000000000000E-12 " " relative error = 7.6895300101899740000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.060000000007406 " " y[1] (closed_form) = 0.8911850859559962 " " y[1] (numeric) = 0.8911850859492098 " " absolute error = 6.786460282626194000000000000E-12 " " relative error = 7.615096335848340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.07000000000742 " " y[1] (closed_form) = 0.9015044674571122 " " y[1] (numeric) = 0.9015044674503131 " " absolute error = 6.799116825106921000000000000E-12 " " relative error = 7.5419668682123080000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.08000000000743 " " y[1] (closed_form) = 0.9118274114805729 " " y[1] (numeric) = 0.9118274114737576 " " absolute error = 6.8153260812664480000000000000E-12 " " relative error = 7.4743597258170980000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.090000000007443 " " y[1] (closed_form) = 0.9221539167576616 " " y[1] (numeric) = 0.9221539167508386 " " absolute error = 6.822986620136362000000000000E-12 " " relative error = 7.3989672397925910000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.100000000007455 " " y[1] (closed_form) = 0.9324839820205959 " " y[1] (numeric) = 0.932483982013755 " " absolute error = 6.840861210832827000000000000E-12 " " relative error = 7.3361702106768540000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.110000000007467 " " y[1] (closed_form) = 0.9428176060024605 " " y[1] (numeric) = 0.9428176059956078 " " absolute error = 6.852629574893854000000000000E-12 " " relative error = 7.2682452377495910000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.12000000000748 " " y[1] (closed_form) = 0.9531547874372635 " " y[1] (numeric) = 0.9531547874303993 " " absolute error = 6.864175894349955000000000000E-12 " " relative error = 7.201533250234820000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.13000000000749 " " y[1] (closed_form) = 0.9634955250599084 " " y[1] (numeric) = 0.9634955250530324 " " absolute error = 6.8760552807134450000000000000E-12 " " relative error = 7.1365720980239140000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.140000000007504 " " y[1] (closed_form) = 0.9738398176061978 " " y[1] (numeric) = 0.9738398175993097 " " absolute error = 6.888045689379396000000000000E-12 " " relative error = 7.0730787187475540000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.150000000007516 " " y[1] (closed_form) = 0.9841876638128326 " " y[1] (numeric) = 0.9841876638059318 " " absolute error = 6.9008132541625860000000000000E-12 " " relative error = 7.0116843645735280000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.16000000000753 " " y[1] (closed_form) = 0.994539062417406 " " y[1] (numeric) = 0.994539062410497 " " absolute error = 6.908917882242349000000000000E-12 " " relative error = 6.9468542195305860000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.17000000000754 " " y[1] (closed_form) = 1.0048940121584273 " " y[1] (numeric) = 1.0048940121515006 " " absolute error = 6.926681450636352000000000000E-12 " " relative error = 6.8929472828267990000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.180000000007553 " " y[1] (closed_form) = 1.015252511775273 " " y[1] (numeric) = 1.015252511768333 " " absolute error = 6.9400041269318540000000000000E-12 " " relative error = 6.8357418932128970000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.190000000007565 " " y[1] (closed_form) = 1.0256145600082327 " " y[1] (numeric) = 1.0256145600012796 " " absolute error = 6.95310475862243000000000000E-12 " " relative error = 6.7794520765838360000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.200000000007577 " " y[1] (closed_form) = 1.0359801555984838 " " y[1] (numeric) = 1.0359801555915193 " " absolute error = 6.964429033473607000000000000E-12 " " relative error = 6.722550616281130000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.21000000000759 " " y[1] (closed_form) = 1.0463492972881028 " " y[1] (numeric) = 1.0463492972811246 " " absolute error = 6.978195798978959000000000000E-12 " " relative error = 6.6690882452588640000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.2200000000076 " " y[1] (closed_form) = 1.0567219838200472 " " y[1] (numeric) = 1.0567219838130584 " " absolute error = 6.9888539400153600000000000000E-12 " " relative error = 6.613711124614510000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.230000000007614 " " y[1] (closed_form) = 1.067098213938177 " " y[1] (numeric) = 1.0670982139311753 " " absolute error = 7.001732527101012000000000000E-12 " " relative error = 6.5614696338594580000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.240000000007626 " " y[1] (closed_form) = 1.0774779863872332 " " y[1] (numeric) = 1.0774779863802202 " " absolute error = 7.013056801952189000000000000E-12 " " relative error = 6.5087703791210230000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.25000000000764 " " y[1] (closed_form) = 1.0878612999128556 " " y[1] (numeric) = 1.0878612999058264 " " absolute error = 7.029266058111716000000000000E-12 " " relative error = 6.461546208762830000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.26000000000765 " " y[1] (closed_form) = 1.098248153261558 " " y[1] (numeric) = 1.0982481532545154 " " absolute error = 7.042588734407218000000000000E-12 " " relative error = 6.4125659701700950000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.270000000007663 " " y[1] (closed_form) = 1.1086385451807494 " " y[1] (numeric) = 1.108638545173696 " " absolute error = 7.0534689200485450000000000000E-12 " " relative error = 6.3622800692885580000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.280000000007675 " " y[1] (closed_form) = 1.1190324744187308 " " y[1] (numeric) = 1.1190324744116626 " " absolute error = 7.068123863973597000000000000E-12 " " relative error = 6.3162812747190890000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.290000000007687 " " y[1] (closed_form) = 1.1294299397246732 " " y[1] (numeric) = 1.1294299397175953 " " absolute error = 7.077893826590298000000000000E-12 " " relative error = 6.2667843109557650000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.3000000000077 " " y[1] (closed_form) = 1.1398309398486504 " " y[1] (numeric) = 1.1398309398415585 " " absolute error = 7.091882636700575000000000000E-12 " " relative error = 6.2218723748999590000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.31000000000771 " " y[1] (closed_form) = 1.1502354735416063 " " y[1] (numeric) = 1.1502354735345 " " absolute error = 7.106315536020702000000000000E-12 " " relative error = 6.1781397804922180000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.320000000007724 " " y[1] (closed_form) = 1.160643539555366 " " y[1] (numeric) = 1.1606435395482497 " " absolute error = 7.116307543242328000000000000E-12 " " relative error = 6.1313463614922930000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.330000000007736 " " y[1] (closed_form) = 1.1710551366426536 " " y[1] (numeric) = 1.1710551366355195 " " absolute error = 7.134071111636331000000000000E-12 " " relative error = 6.0920027489818240000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.34000000000775 " " y[1] (closed_form) = 1.181470263557042 " " y[1] (numeric) = 1.1814702635499008 " " absolute error = 7.141176538993932000000000000E-12 " " relative error = 6.0443133943075770000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.35000000000776 " " y[1] (closed_form) = 1.1918889190530173 " " y[1] (numeric) = 1.1918889190458652 " " absolute error = 7.1520567246352580000000000000E-12 " " relative error = 6.0006067766094580000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.360000000007773 " " y[1] (closed_form) = 1.2023111018859325 " " y[1] (numeric) = 1.2023111018787636 " " absolute error = 7.168932114609561000000000000E-12 " " relative error = 5.9626265642598240000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.370000000007785 " " y[1] (closed_form) = 1.2127368108120038 " " y[1] (numeric) = 1.2127368108048233 " " absolute error = 7.1804784340656620000000000000E-12 " " relative error = 5.9208876732766770000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.380000000007797 " " y[1] (closed_form) = 1.2231660445883428 " " y[1] (numeric) = 1.2231660445811505 " " absolute error = 7.192246798126689000000000000E-12 " " relative error = 5.8800248992746060000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.39000000000781 " " y[1] (closed_form) = 1.2335988019729314 " " y[1] (numeric) = 1.2335988019657251 " " absolute error = 7.206235608236966000000000000E-12 " " relative error = 5.8416363543088880000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.40000000000782 " " y[1] (closed_form) = 1.2440350817246255 " " y[1] (numeric) = 1.2440350817174033 " " absolute error = 7.222222819791568000000000000E-12 " " relative error = 5.8054816346330730000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.410000000007834 " " y[1] (closed_form) = 1.254474882603148 " " y[1] (numeric) = 1.2544748825959149 " " absolute error = 7.233103005432895000000000000E-12 " " relative error = 5.7658412342410200000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.420000000007846 " " y[1] (closed_form) = 1.2649182033691062 " " y[1] (numeric) = 1.264918203361863 " " absolute error = 7.243317057259446000000000000E-12 " " relative error = 5.7263126089630870000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.43000000000786 " " y[1] (closed_form) = 1.275365042783978 " " y[1] (numeric) = 1.2753650427767222 " " absolute error = 7.255751555135248000000000000E-12 " " relative error = 5.6891566819933850000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.44000000000787 " " y[1] (closed_form) = 1.2858153996101116 " " y[1] (numeric) = 1.2858153996028394 " " absolute error = 7.2721828558997000000000000E-12 " " relative error = 5.6556974337877670000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.450000000007883 " " y[1] (closed_form) = 1.296269272610715 " " y[1] (numeric) = 1.2962692726034315 " " absolute error = 7.283507130750877000000000000E-12 " " relative error = 5.6188226355792050000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.460000000007895 " " y[1] (closed_form) = 1.3067266605498808 " " y[1] (numeric) = 1.3067266605425845 " " absolute error = 7.296385717836529000000000000E-12 " " relative error = 5.5837122927959170000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.470000000007907 " " y[1] (closed_form) = 1.317187562192558 " " y[1] (numeric) = 1.3171875621852533 " " absolute error = 7.304601368218755000000000000E-12 " " relative error = 5.5456045728671290000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.48000000000792 " " y[1] (closed_form) = 1.3276519763045798 " " y[1] (numeric) = 1.32765197629726 " " absolute error = 7.319700401353657000000000000E-12 " " relative error = 5.5132674315203420000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.49000000000793 " " y[1] (closed_form) = 1.3381199016526288 " " y[1] (numeric) = 1.338119901645294 " " absolute error = 7.33479943448855900000000000E-12 " " relative error = 5.4814216763608430000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.500000000007944 " " y[1] (closed_form) = 1.3485913370042546 " " y[1] (numeric) = 1.34859133699691 " " absolute error = 7.34456939710526100000000000E-12 " " relative error = 5.4461045355818490000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.510000000007956 " " y[1] (closed_form) = 1.359066281127891 " " y[1] (numeric) = 1.3590662811205283 " " absolute error = 7.362777054709113000000000000E-12 " " relative error = 5.4175261037296380000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.52000000000797 " " y[1] (closed_form) = 1.3695447327928072 " " y[1] (numeric) = 1.3695447327854318 " " absolute error = 7.37543359718984000000000000E-12 " " relative error = 5.3853177779375520000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.53000000000798 " " y[1] (closed_form) = 1.3800266907691565 " " y[1] (numeric) = 1.380026690761767 " " absolute error = 7.389422407300117000000000000E-12 " " relative error = 5.3545503552410490000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.540000000007993 " " y[1] (closed_form) = 1.3905121538279452 " " y[1] (numeric) = 1.390512153820544 " " absolute error = 7.401190771361144000000000000E-12 " " relative error = 5.3226365199228090000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.550000000008005 " " y[1] (closed_form) = 1.4010011207410429 " " y[1] (numeric) = 1.4010011207336326 " " absolute error = 7.41029460016307000000000000E-12 " " relative error = 5.2892852764054050000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.560000000008017 " " y[1] (closed_form) = 1.4114935902811894 " " y[1] (numeric) = 1.4114935902737629 " " absolute error = 7.426503856322597000000000000E-12 " " relative error = 5.2614506416873870000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.57000000000803 " " y[1] (closed_form) = 1.421989561221963 " " y[1] (numeric) = 1.4219895612145248 " " absolute error = 7.438272220383624000000000000E-12 " " relative error = 5.2308908751704670000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.58000000000804 " " y[1] (closed_form) = 1.4324890323378163 " " y[1] (numeric) = 1.4324890323303672 " " absolute error = 7.44915240602495000000000000E-12 " " relative error = 5.2001462055649830000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.590000000008054 " " y[1] (closed_form) = 1.4429920024040577 " " y[1] (numeric) = 1.4429920023965959 " " absolute error = 7.461808948505677000000000000E-12 " " relative error = 5.1710674321646510000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.600000000008066 " " y[1] (closed_form) = 1.4534984701968447 " " y[1] (numeric) = 1.4534984701893732 " " absolute error = 7.471578911122378000000000000E-12 " " relative error = 5.1404105778732010000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.61000000000808 " " y[1] (closed_form) = 1.4640084344932056 " " y[1] (numeric) = 1.4640084344857187 " " absolute error = 7.486899988862206000000000000E-12 " " relative error = 5.113973261673139000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.62000000000809 " " y[1] (closed_form) = 1.4745218940710068 " " y[1] (numeric) = 1.4745218940635056 " " absolute error = 7.501110843577408000000000000E-12 " " relative error = 5.0871478231276680000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.630000000008103 " " y[1] (closed_form) = 1.4850388477089744 " " y[1] (numeric) = 1.4850388477014613 " " absolute error = 7.51310125224335900000000000E-12 " " relative error = 5.0591950936732090000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.640000000008115 " " y[1] (closed_form) = 1.4955592941866946 " " y[1] (numeric) = 1.4955592941791669 " " absolute error = 7.527756196168411000000000000E-12 " " relative error = 5.0334053791308280000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.650000000008127 " " y[1] (closed_form) = 1.5060832322845954 " " y[1] (numeric) = 1.506083232277055 " " absolute error = 7.540412738649138000000000000E-12 " " relative error = 5.0066374666498330000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.66000000000814 " " y[1] (closed_form) = 1.516610660783961 " " y[1] (numeric) = 1.5166106607764098 " " absolute error = 7.55107087968554000000000000E-12 " " relative error = 4.9789119085990520000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.67000000000815 " " y[1] (closed_form) = 1.5271415784669315 " " y[1] (numeric) = 1.527141578459367 " " absolute error = 7.564615600585967000000000000E-12 " " relative error = 4.9534474781178710000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.680000000008164 " " y[1] (closed_form) = 1.5376759841164862 " " y[1] (numeric) = 1.53767598410891 " " absolute error = 7.576161920042068000000000000E-12 " " relative error = 4.9270210358362065000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.690000000008176 " " y[1] (closed_form) = 1.5482138765164635 " " y[1] (numeric) = 1.5482138765088724 " " absolute error = 7.591038908572045000000000000E-12 " " relative error = 4.9030944779103480000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.70000000000819 " " y[1] (closed_form) = 1.5587552544515404 " " y[1] (numeric) = 1.5587552544439351 " " absolute error = 7.605249763287247000000000000E-12 " " relative error = 4.8790531685894540000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.7100000000082 " " y[1] (closed_form) = 1.5693001167072431 " " y[1] (numeric) = 1.5693001166996257 " " absolute error = 7.617462216558124000000000000E-12 " " relative error = 4.8540506277035990000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.720000000008213 " " y[1] (closed_form) = 1.579848462069947 " " y[1] (numeric) = 1.5798484620623183 " " absolute error = 7.628564446804376000000000000E-12 " " relative error = 4.8286684640685650000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.730000000008225 " " y[1] (closed_form) = 1.5904002893268725 " " y[1] (numeric) = 1.5904002893192313 " " absolute error = 7.641220989285102000000000000E-12 " " relative error = 4.8045897882219346000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.740000000008237 " " y[1] (closed_form) = 1.6009555972660863 " " y[1] (numeric) = 1.600955597258429 " " absolute error = 7.657208200839705000000000000E-12 " " relative error = 4.7828985475398167000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.75000000000825 " " y[1] (closed_form) = 1.611514384676486 " " y[1] (numeric) = 1.6115143846688167 " " absolute error = 7.669198609505656000000000000E-12 " " relative error = 4.7590010256379195000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.76000000000826 " " y[1] (closed_form) = 1.6220766503478252 " " y[1] (numeric) = 1.6220766503401443 " " absolute error = 7.680966973566683000000000000E-12 " " relative error = 4.7352675793216287000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.770000000008274 " " y[1] (closed_form) = 1.6326423930706966 " " y[1] (numeric) = 1.6326423930630023 " " absolute error = 7.694289649862185000000000000E-12 " " relative error = 4.7127832050169044000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.780000000008286 " " y[1] (closed_form) = 1.6432116116365307 " " y[1] (numeric) = 1.6432116116288222 " " absolute error = 7.708500504577387000000000000E-12 " " relative error = 4.6911185692634116000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.7900000000083 " " y[1] (closed_form) = 1.6537843048375933 " " y[1] (numeric) = 1.653784304829875 " " absolute error = 7.718270467194088000000000000E-12 " " relative error = 4.6670357462075730000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.80000000000831 " " y[1] (closed_form) = 1.6643604714670026 " " y[1] (numeric) = 1.6643604714592715 " " absolute error = 7.73114905427974000000000000E-12 " " relative error = 4.64511696042945600000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.810000000008323 " " y[1] (closed_form) = 1.6749401103187047 " " y[1] (numeric) = 1.67494011031096 " " absolute error = 7.744693775180167000000000000E-12 " " relative error = 4.62386310260760400000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.820000000008335 " " y[1] (closed_form) = 1.6855232201874841 " " y[1] (numeric) = 1.6855232201797261 " " absolute error = 7.758016451475669000000000000E-12 " " relative error = 4.60273484135847600000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.830000000008347 " " y[1] (closed_form) = 1.6961097998689603 " " y[1] (numeric) = 1.6961097998611925 " " absolute error = 7.76778641409237000000000000E-12 " " relative error = 4.57976624785288170000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.84000000000836 " " y[1] (closed_form) = 1.7066998481596016 " " y[1] (numeric) = 1.7066998481518159 " " absolute error = 7.785772027091298000000000000E-12 " " relative error = 4.5618871036327730000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.85000000000837 " " y[1] (closed_form) = 1.7172933638566832 " " y[1] (numeric) = 1.7172933638488888 " " absolute error = 7.794431766683374000000000000E-12 " " relative error = 4.53878873041162000000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.860000000008384 " " y[1] (closed_form) = 1.7278903457583468 " " y[1] (numeric) = 1.727890345750537 " " absolute error = 7.809752844423201000000000000E-12 " " relative error = 4.5198197117049170000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.870000000008396 " " y[1] (closed_form) = 1.7384907926635442 " " y[1] (numeric) = 1.7384907926557194 " " absolute error = 7.824851877558103000000000000E-12 " " relative error = 4.50094525123692860000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.88000000000841 " " y[1] (closed_form) = 1.7490947033720623 " " y[1] (numeric) = 1.7490947033642275 " " absolute error = 7.83484388477973000000000000E-12 " " relative error = 4.4793708823627520000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.89000000000842 " " y[1] (closed_form) = 1.7597020766845297 " " y[1] (numeric) = 1.759702076676683 " " absolute error = 7.846612248840756000000000000E-12 " " relative error = 4.4590572192905680000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.900000000008433 " " y[1] (closed_form) = 1.770312911402403 " " y[1] (numeric) = 1.7703129113945382 " " absolute error = 7.864819906444609000000000000E-12 " " relative error = 4.44261568437314960000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.910000000008445 " " y[1] (closed_form) = 1.7809272063279487 " " y[1] (numeric) = 1.7809272063200745 " " absolute error = 7.87414577985146000000000000E-12 " " relative error = 4.4213742997879030000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.920000000008457 " " y[1] (closed_form) = 1.7915449602642894 " " y[1] (numeric) = 1.791544960256403 " " absolute error = 7.886358233122337000000000000E-12 " " relative error = 4.401987339440780000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.93000000000847 " " y[1] (closed_form) = 1.8021661720153617 " " y[1] (numeric) = 1.8021661720074615 " " absolute error = 7.900124998627689000000000000E-12 " " relative error = 4.3836828819137040000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.94000000000848 " " y[1] (closed_form) = 1.812790840385933 " " y[1] (numeric) = 1.8127908403780149 " " absolute error = 7.918110611626616000000000000E-12 " " relative error = 4.36791186011337930000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.950000000008494 " " y[1] (closed_form) = 1.8234189641815775 " " y[1] (numeric) = 1.823418964173654 " " absolute error = 7.923439682144817000000000000E-12 " " relative error = 4.34537527457446950000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.960000000008506 " " y[1] (closed_form) = 1.834050542208736 " " y[1] (numeric) = 1.8340505422007956 " " absolute error = 7.940537116724045000000000000E-12 " " relative error = 4.3295083390457190000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.97000000000852 " " y[1] (closed_form) = 1.8446855732746315 " " y[1] (numeric) = 1.8446855732666803 " " absolute error = 7.951195257760446000000000000E-12 " " relative error = 4.3103254955508324000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.98000000000853 " " y[1] (closed_form) = 1.8553240561873352 " " y[1] (numeric) = 1.8553240561793711 " " absolute error = 7.964073844846098000000000000E-12 " " relative error = 4.29255138383326850000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 26.990000000008543 " " y[1] (closed_form) = 1.8659659897557361 " " y[1] (numeric) = 1.8659659897477554 " " absolute error = 7.980727190215475000000000000E-12 " " relative error = 4.27699499027856900000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.000000000008555 " " y[1] (closed_form) = 1.8766113727895295 " " y[1] (numeric) = 1.8766113727815406 " " absolute error = 7.988942840597701000000000000E-12 " " relative error = 4.2571109588461910000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.010000000008567 " " y[1] (closed_form) = 1.8872602040992597 " " y[1] (numeric) = 1.8872602040912563 " " absolute error = 8.003375739917828000000000000E-12 " " relative error = 4.24073782859085500000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.02000000000858 " " y[1] (closed_form) = 1.8979124824962668 " " y[1] (numeric) = 1.8979124824882514 " " absolute error = 8.01536614858378000000000000E-12 " " relative error = 4.2232538236122520000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.03000000000859 " " y[1] (closed_form) = 1.9085682067927294 " " y[1] (numeric) = 1.9085682067846947 " " absolute error = 8.034684029212258000000000000E-12 " " relative error = 4.2097966426435530000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.040000000008604 " " y[1] (closed_form) = 1.9192273758016185 " " y[1] (numeric) = 1.9192273757935725 " " absolute error = 8.046008304063434000000000000E-12 " " relative error = 4.1923163485008114000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.050000000008616 " " y[1] (closed_form) = 1.9298899883367433 " " y[1] (numeric) = 1.9298899883286889 " " absolute error = 8.054445999050586000000000000E-12 " " relative error = 4.17352597698702530000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.06000000000863 " " y[1] (closed_form) = 1.9405560432127373 " " y[1] (numeric) = 1.9405560432046651 " " absolute error = 8.072209567444588000000000000E-12 " " relative error = 4.1597405010166233000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.07000000000864 " " y[1] (closed_form) = 1.9512255392450228 " " y[1] (numeric) = 1.9512255392369378 " " absolute error = 8.08508815453024000000000000E-12 " " relative error = 4.1435948801995280000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.080000000008653 " " y[1] (closed_form) = 1.9618984752498534 " " y[1] (numeric) = 1.9618984752417588 " " absolute error = 8.094636072542016000000000000E-12 " " relative error = 4.1259199569494240000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.090000000008665 " " y[1] (closed_form) = 1.9725748500443032 " " y[1] (numeric) = 1.972574850036193 " " absolute error = 8.110179194886769000000000000E-12 " " relative error = 4.111468416371940000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.100000000008677 " " y[1] (closed_form) = 1.983254662446246 " " y[1] (numeric) = 1.9832546624381204 " " absolute error = 8.125500272626596000000000000E-12 " " relative error = 4.0970534074550950000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.11000000000869 " " y[1] (closed_form) = 1.9939379112743723 " " y[1] (numeric) = 1.993937911266233 " " absolute error = 8.139267038131948000000000000E-12 " " relative error = 4.0820062611327507000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.1200000000087 " " y[1] (closed_form) = 2.0046245953481794 " " y[1] (numeric) = 2.0046245953400326 " " absolute error = 8.146816554699399000000000000E-12 " " relative error = 4.0640110739958235000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.130000000008714 " " y[1] (closed_form) = 2.0153147134879994 " " y[1] (numeric) = 2.015314713479835 " " absolute error = 8.164580123093401000000000000E-12 " " relative error = 4.05126805677043960000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.140000000008726 " " y[1] (closed_form) = 2.0260082645149353 " " y[1] (numeric) = 2.026008264506762 " " absolute error = 8.173461907290402000000000000E-12 " " relative error = 4.03426878875406960000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.15000000000874 " " y[1] (closed_form) = 2.0367052472509357 " " y[1] (numeric) = 2.0367052472427476 " " absolute error = 8.188116851215455000000000000E-12 " " relative error = 4.02027581667374350000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.16000000000875 " " y[1] (closed_form) = 2.0474056605187307 " " y[1] (numeric) = 2.0474056605105324 " " absolute error = 8.198330903042006000000000000E-12 " " relative error = 4.0042533148828335000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.170000000008763 " " y[1] (closed_form) = 2.0581095031418783 " " y[1] (numeric) = 2.058109503133666 " " absolute error = 8.212541757757208000000000000E-12 " " relative error = 3.99033275208149400000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.180000000008775 " " y[1] (closed_form) = 2.0688167739447287 " " y[1] (numeric) = 2.068816773936503 " " absolute error = 8.22586443405271000000000000E-12 " " relative error = 3.97612033006093300000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.190000000008787 " " y[1] (closed_form) = 2.079527471752442 " " y[1] (numeric) = 2.0795274717442047 " " absolute error = 8.237410753508811000000000000E-12 " " relative error = 3.9611935237225060000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.2000000000088 " " y[1] (closed_form) = 2.0902415953909887 " " y[1] (numeric) = 2.0902415953827376 " " absolute error = 8.251177519014163000000000000E-12 " " relative error = 3.9474755153701480000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.21000000000881 " " y[1] (closed_form) = 2.1009591436871347 " " y[1] (numeric) = 2.100959143678872 " " absolute error = 8.262723838470265000000000000E-12 " " relative error = 3.93283413592202260000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.220000000008824 " " y[1] (closed_form) = 2.1116801154684595 " " y[1] (numeric) = 2.1116801154601816 " " absolute error = 8.277822871605167000000000000E-12 " " relative error = 3.9200174358647105000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.230000000008836 " " y[1] (closed_form) = 2.1224045095633315 " " y[1] (numeric) = 2.1224045095550412 " " absolute error = 8.290257369480969000000000000E-12 " " relative error = 3.9060684860618894000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.24000000000885 " " y[1] (closed_form) = 2.1331323248009326 " " y[1] (numeric) = 2.133132324792629 " " absolute error = 8.30358004577647100000000000E-12 " " relative error = 3.89266992452115000000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.25000000000886 " " y[1] (closed_form) = 2.143863560011237 " " y[1] (numeric) = 2.1438635600029237 " " absolute error = 8.313350008393172000000000000E-12 " " relative error = 3.8777421116993090000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.260000000008873 " " y[1] (closed_form) = 2.1545982140250324 " " y[1] (numeric) = 2.154598214016704 " " absolute error = 8.328449041528074000000000000E-12 " " relative error = 3.86543021678719070000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.270000000008885 " " y[1] (closed_form) = 2.1653362856738916 " " y[1] (numeric) = 2.1653362856655467 " " absolute error = 8.344880342292527000000000000E-12 " " relative error = 3.85384958332024130000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.280000000008897 " " y[1] (closed_form) = 2.176077773790187 " " y[1] (numeric) = 2.1760777737818295 " " absolute error = 8.357314840168328000000000000E-12 " " relative error = 3.8405405086289550000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.29000000000891 " " y[1] (closed_form) = 2.186822677207097 " " y[1] (numeric) = 2.1868226771987245 " " absolute error = 8.37241387330323000000000000E-12 " " relative error = 3.82857465333955150000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.30000000000892 " " y[1] (closed_form) = 2.197570994758589 " " y[1] (numeric) = 2.197570994750203 " " absolute error = 8.386180638808582000000000000E-12 " " relative error = 3.81611363583265500000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.310000000008934 " " y[1] (closed_form) = 2.2083227252794266 " " y[1] (numeric) = 2.2083227252710307 " " absolute error = 8.395950601425284000000000000E-12 " " relative error = 3.8019581582501333000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.320000000008946 " " y[1] (closed_form) = 2.219077867605179 " " y[1] (numeric) = 2.21907786759677 " " absolute error = 8.409273277720786000000000000E-12 " " relative error = 3.7895350138370960000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.33000000000896 " " y[1] (closed_form) = 2.229836420572198 " " y[1] (numeric) = 2.229836420563775 " " absolute error = 8.423040043226138000000000000E-12 " " relative error = 3.77742509070001800000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.34000000000897 " " y[1] (closed_form) = 2.240598383017634 " " y[1] (numeric) = 2.2405983830091967 " " absolute error = 8.43725089794134000000000000E-12 " " relative error = 3.76562393416443760000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.350000000008983 " " y[1] (closed_form) = 2.2513637537794295 " " y[1] (numeric) = 2.2513637537709763 " " absolute error = 8.453238109495942000000000000E-12 " " relative error = 3.7547189321606720000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.360000000008995 " " y[1] (closed_form) = 2.262132531696313 " " y[1] (numeric) = 2.2621325316878473 " " absolute error = 8.465672607371744000000000000E-12 " " relative error = 3.7423415687424655000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.370000000009007 " " y[1] (closed_form) = 2.2729047156078117 " " y[1] (numeric) = 2.2729047155993345 " " absolute error = 8.477218926827845000000000000E-12 " " relative error = 3.72968513313190030000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.38000000000902 " " y[1] (closed_form) = 2.2836803043542417 " " y[1] (numeric) = 2.2836803043457534 " " absolute error = 8.488321157074097000000000000E-12 " " relative error = 3.71694809509439950000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.39000000000903 " " y[1] (closed_form) = 2.2944592967767115 " " y[1] (numeric) = 2.294459296768208 " " absolute error = 8.503420190208999000000000000E-12 " " relative error = 3.70606713405407700000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.400000000009044 " " y[1] (closed_form) = 2.3052416917171037 " " y[1] (numeric) = 2.3052416917085914 " " absolute error = 8.512301974406000000000000E-12 " " relative error = 3.69258546945047100000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.410000000009056 " " y[1] (closed_form) = 2.316027488018115 " " y[1] (numeric) = 2.3160274880095844 " " absolute error = 8.530509632009853000000000000E-12 " " relative error = 3.683250598769720000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.42000000000907 " " y[1] (closed_form) = 2.326816684523198 " " y[1] (numeric) = 2.326816684514655 " " absolute error = 8.542944129885655000000000000E-12 " " relative error = 3.67151576087148430000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.43000000000908 " " y[1] (closed_form) = 2.3376092800766166 " " y[1] (numeric) = 2.3376092800680577 " " absolute error = 8.558931341440257000000000000E-12 " " relative error = 3.66140373174756230000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.440000000009093 " " y[1] (closed_form) = 2.3484052735233973 " " y[1] (numeric) = 2.3484052735148317 " " absolute error = 8.565592679588008000000000000E-12 " " relative error = 3.6474082119295960000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.450000000009105 " " y[1] (closed_form) = 2.3592046637093844 " " y[1] (numeric) = 2.359204663700802 " " absolute error = 8.58246806956231000000000000E-12 " " relative error = 3.6378649981422430000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.460000000009117 " " y[1] (closed_form) = 2.3700074494811716 " " y[1] (numeric) = 2.3700074494725754 " " absolute error = 8.596234835067662000000000000E-12 " " relative error = 3.6270919051117330000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.47000000000913 " " y[1] (closed_form) = 2.380813629686152 " " y[1] (numeric) = 2.380813629677544 " " absolute error = 8.607781154523764000000000000E-12 " " relative error = 3.6154787788485880000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.48000000000914 " " y[1] (closed_form) = 2.3916232031725038 " " y[1] (numeric) = 2.391623203163881 " " absolute error = 8.622880187658666000000000000E-12 " " relative error = 3.60545096577937500000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.490000000009154 " " y[1] (closed_form) = 2.4024361687891727 " " y[1] (numeric) = 2.4024361687805404 " " absolute error = 8.632206061065517000000000000E-12 " " relative error = 3.5931052708951460000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.500000000009166 " " y[1] (closed_form) = 2.413252525385907 " " y[1] (numeric) = 2.413252525377258 " " absolute error = 8.64908145103982000000000000E-12 " " relative error = 3.58399353571865860000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.510000000009178 " " y[1] (closed_form) = 2.4240722718132126 " " y[1] (numeric) = 2.4240722718045493 " " absolute error = 8.663292305755022000000000000E-12 " " relative error = 3.5738589176942550000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.52000000000919 " " y[1] (closed_form) = 2.4348954069223865 " " y[1] (numeric) = 2.4348954069137076 " " absolute error = 8.678835428099774000000000000E-12 " " relative error = 3.564356564732070000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.530000000009203 " " y[1] (closed_form) = 2.4457219295654973 " " y[1] (numeric) = 2.4457219295568065 " " absolute error = 8.690825836765725000000000000E-12 " " relative error = 3.5534807664376310000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.540000000009215 " " y[1] (closed_form) = 2.456551838595395 " " y[1] (numeric) = 2.456551838586695 " " absolute error = 8.700151710172577000000000000E-12 " " relative error = 3.54161128354089250000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.550000000009227 " " y[1] (closed_form) = 2.467385132865722 " " y[1] (numeric) = 2.467385132857001 " " absolute error = 8.72102390303553000000000000E-12 " " relative error = 3.5345207308218540000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.56000000000924 " " y[1] (closed_form) = 2.47822181123086 " " y[1] (numeric) = 2.4782218112221264 " " absolute error = 8.733458400911331000000000000E-12 " " relative error = 3.5240826149349724000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.57000000000925 " " y[1] (closed_form) = 2.4890618725459888 " " y[1] (numeric) = 2.4890618725372478 " " absolute error = 8.741007917478782000000000000E-12 " " relative error = 3.51176803352737150000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.580000000009264 " " y[1] (closed_form) = 2.4999053156670783 " " y[1] (numeric) = 2.4999053156583186 " " absolute error = 8.759659664292485000000000000E-12 " " relative error = 3.5039965751483050000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.590000000009276 " " y[1] (closed_form) = 2.5107521394508368 " " y[1] (numeric) = 2.5107521394420633 " " absolute error = 8.773426429797837000000000000E-12 " " relative error = 3.49434191131140550000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.600000000009288 " " y[1] (closed_form) = 2.5216023427547682 " " y[1] (numeric) = 2.5216023427459815 " " absolute error = 8.786749106093339000000000000E-12 " " relative error = 3.48458952353847440000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.6100000000093 " " y[1] (closed_form) = 2.532455924437137 " " y[1] (numeric) = 2.532455924428342 " " absolute error = 8.79518680108049000000000000E-12 " " relative error = 3.47298711745015100000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.620000000009313 " " y[1] (closed_form) = 2.5433128833569967 " " y[1] (numeric) = 2.5433128833481855 " " absolute error = 8.811174012635092000000000000E-12 " " relative error = 3.4644475205130690000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.630000000009325 " " y[1] (closed_form) = 2.554173218374146 " " y[1] (numeric) = 2.554173218365325 " " absolute error = 8.820943975251794000000000000E-12 " " relative error = 3.45354180045265250000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.640000000009337 " " y[1] (closed_form) = 2.56503692834918 " " y[1] (numeric) = 2.5650369283403425 " " absolute error = 8.837375276016246000000000000E-12 " " relative error = 3.44532087563505450000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.65000000000935 " " y[1] (closed_form) = 2.5759040121434325 " " y[1] (numeric) = 2.575904012134586 " " absolute error = 8.846257060213247000000000000E-12 " " relative error = 3.43423396932100700000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.66000000000936 " " y[1] (closed_form) = 2.5867744686190406 " " y[1] (numeric) = 2.5867744686101757 " " absolute error = 8.86490880702695000000000000E-12 " " relative error = 3.42701264241235370000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.670000000009374 " " y[1] (closed_form) = 2.597648296638873 " " y[1] (numeric) = 2.5976482966299974 " " absolute error = 8.875566948063351000000000000E-12 " " relative error = 3.41677006835280600000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.680000000009386 " " y[1] (closed_form) = 2.608525495066587 " " y[1] (numeric) = 2.6085254950577013 " " absolute error = 8.885780999889903000000000000E-12 " " relative error = 3.4064382413341443000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.690000000009398 " " y[1] (closed_form) = 2.6194060627666076 " " y[1] (numeric) = 2.6194060627577067 " " absolute error = 8.900880033024805000000000000E-12 " " relative error = 3.39805277217069800000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.70000000000941 " " y[1] (closed_form) = 2.6302899986041055 " " y[1] (numeric) = 2.6302899985951953 " " absolute error = 8.910205906431656000000000000E-12 " " relative error = 3.3875374620898463000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.710000000009423 " " y[1] (closed_form) = 2.6411773014450404 " " y[1] (numeric) = 2.6411773014361146 " " absolute error = 8.925749028776409000000000000E-12 " " relative error = 3.37945848008498140000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.720000000009435 " " y[1] (closed_form) = 2.652067970156118 " " y[1] (numeric) = 2.652067970147175 " " absolute error = 8.942624418750711000000000000E-12 " " relative error = 3.3719439016581050000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.730000000009447 " " y[1] (closed_form) = 2.662962003604804 " " y[1] (numeric) = 2.6629620035958497 " " absolute error = 8.954170738206813000000000000E-12 " " relative error = 3.36248535506166100000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.74000000000946 " " y[1] (closed_form) = 2.673859400659346 " " y[1] (numeric) = 2.6738594006503726 " " absolute error = 8.973266574230365000000000000E-12 " " relative error = 3.35592311698126370000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.75000000000947 " " y[1] (closed_form) = 2.6847601601887234 " " y[1] (numeric) = 2.6847601601797413 " " absolute error = 8.982148358427366000000000000E-12 " " relative error = 3.34560550011885340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.760000000009484 " " y[1] (closed_form) = 2.6956642810627045 " " y[1] (numeric) = 2.695664281053711 " " absolute error = 8.993694677883468000000000000E-12 " " relative error = 3.3363556215308490000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.770000000009496 " " y[1] (closed_form) = 2.7065717621518033 " " y[1] (numeric) = 2.706571762142797 " " absolute error = 9.00612917575927000000000000E-12 " " relative error = 3.327504299608570000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.780000000009508 " " y[1] (closed_form) = 2.717482602327294 " " y[1] (numeric) = 2.7174826023182757 " " absolute error = 9.018563673635072000000000000E-12 " " relative error = 3.3187199306856410000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.79000000000952 " " y[1] (closed_form) = 2.728396800461212 " " y[1] (numeric) = 2.7283968004521775 " " absolute error = 9.034550885189674000000000000E-12 " " relative error = 3.3113038703397030000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.800000000009533 " " y[1] (closed_form) = 2.7393143554263375 " " y[1] (numeric) = 2.7393143554172945 " " absolute error = 9.042988580176825000000000000E-12 " " relative error = 3.30118686899277260000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.810000000009545 " " y[1] (closed_form) = 2.750235266096233 " " y[1] (numeric) = 2.7502352660871723 " " absolute error = 9.060752148570828000000000000E-12 " " relative error = 3.2945371111584690000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.820000000009557 " " y[1] (closed_form) = 2.7611595313451858 " " y[1] (numeric) = 2.761159531336113 " " absolute error = 9.07274255723677900000000000E-12 " " relative error = 3.28584511479375060000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.83000000000957 " " y[1] (closed_form) = 2.7720871500482573 " " y[1] (numeric) = 2.7720871500391753 " " absolute error = 9.08206843064363100000000000E-12 " " relative error = 3.2762564591396510000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.84000000000958 " " y[1] (closed_form) = 2.7830181210812626 " " y[1] (numeric) = 2.7830181210721685 " " absolute error = 9.094058839309582000000000000E-12 " " relative error = 3.26769659544162260000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.850000000009594 " " y[1] (closed_form) = 2.7939524433207694 " " y[1] (numeric) = 2.793952443311659 " " absolute error = 9.110490140074035000000000000E-12 " " relative error = 3.26078926713788460000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.860000000009606 " " y[1] (closed_form) = 2.804890115644092 " " y[1] (numeric) = 2.8048901156349637 " " absolute error = 9.128253708468037000000000000E-12 " " relative error = 3.25440688658560850000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.870000000009618 " " y[1] (closed_form) = 2.8158311369292903 " " y[1] (numeric) = 2.8158311369201536 " " absolute error = 9.136691403455188000000000000E-12 " " relative error = 3.24475828242275170000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.88000000000963 " " y[1] (closed_form) = 2.826775506055206 " " y[1] (numeric) = 2.826775506046049 " " absolute error = 9.157119507108291000000000000E-12 " " relative error = 3.2394222631025780000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.890000000009643 " " y[1] (closed_form) = 2.837723221901385 " " y[1] (numeric) = 2.837723221892221 " " absolute error = 9.163780845256042000000000000E-12 " " relative error = 3.22927224703611240000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.900000000009655 " " y[1] (closed_form) = 2.848674283348174 " " y[1] (numeric) = 2.8486742833389904 " " absolute error = 9.183764859699295000000000000E-12 " " relative error = 3.2238732639188240000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.910000000009667 " " y[1] (closed_form) = 2.8596286892766187 " " y[1] (numeric) = 2.859628689267428 " " absolute error = 9.190870287056896000000000000E-12 " " relative error = 3.21400828069809630000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.92000000000968 " " y[1] (closed_form) = 2.8705864385685587 " " y[1] (numeric) = 2.870586438559351 " " absolute error = 9.207745677031198000000000000E-12 " " relative error = 3.20761832959216340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.93000000000969 " " y[1] (closed_form) = 2.8815475301065447 " " y[1] (numeric) = 2.8815475300973254 " " absolute error = 9.2192919964873000000000000E-12 " " relative error = 3.19942388600698100000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.940000000009704 " " y[1] (closed_form) = 2.892511962773895 " " y[1] (numeric) = 2.8925119627646643 " " absolute error = 9.230838315943402000000000000E-12 " " relative error = 3.19128786146526570000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.950000000009716 " " y[1] (closed_form) = 2.903479735454667 " " y[1] (numeric) = 2.903479735445425 " " absolute error = 9.241940546189653000000000000E-12 " " relative error = 3.183056672769380400000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.960000000009728 " " y[1] (closed_form) = 2.9144508470336703 " " y[1] (numeric) = 2.9144508470244115 " " absolute error = 9.258815936163955000000000000E-12 " " relative error = 3.17686467266640800000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.97000000000974 " " y[1] (closed_form) = 2.9254252963964404 " " y[1] (numeric) = 2.925425296387171 " " absolute error = 9.269474077200357000000000000E-12 " " relative error = 3.16859025202884560000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.980000000009753 " " y[1] (closed_form) = 2.9364030824292797 " " y[1] (numeric) = 2.9364030824199965 " " absolute error = 9.283240842705709000000000000E-12 " " relative error = 3.16143274002617660000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 27.990000000009765 " " y[1] (closed_form) = 2.9473842040192224 " " y[1] (numeric) = 2.9473842040099214 " " absolute error = 9.301004411099711000000000000E-12 " " relative error = 3.15568102672747150000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.000000000009777 " " y[1] (closed_form) = 2.9583686600540346 " " y[1] (numeric) = 2.958368660044723 " " absolute error = 9.311662552136113000000000000E-12 " " relative error = 3.1475666565390250000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.01000000000979 " " y[1] (closed_form) = 2.969356449422243 " " y[1] (numeric) = 2.9693564494129197 " " absolute error = 9.323208871592215000000000000E-12 " " relative error = 3.13980791137630550000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.0200000000098 " " y[1] (closed_form) = 2.9803475710131053 " " y[1] (numeric) = 2.9803475710037706 " " absolute error = 9.334755191048316000000000000E-12 " " relative error = 3.1321028734494770000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.030000000009814 " " y[1] (closed_form) = 2.9913420237166264 " " y[1] (numeric) = 2.9913420237072748 " " absolute error = 9.351630581022619000000000000E-12 " " relative error = 3.12623247588504740000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.040000000009826 " " y[1] (closed_form) = 3.002339806423535 " " y[1] (numeric) = 3.00233980641417 " " absolute error = 9.36495325731812000000000000E-12 " " relative error = 3.119218296770309700000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.050000000009838 " " y[1] (closed_form) = 3.013340918025314 " " y[1] (numeric) = 3.0133409180159347 " " absolute error = 9.379164112033322000000000000E-12 " " relative error = 3.1125466275417735000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.06000000000985 " " y[1] (closed_form) = 3.0243453574141697 " " y[1] (numeric) = 3.024345357404782 " " absolute error = 9.387601807020474000000000000E-12 " " relative error = 3.10401118179403970000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.070000000009863 " " y[1] (closed_form) = 3.0353531234830697 " " y[1] (numeric) = 3.035353123473664 " " absolute error = 9.405809464624326000000000000E-12 " " relative error = 3.098752956239620000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.080000000009875 " " y[1] (closed_form) = 3.046364215125685 " " y[1] (numeric) = 3.0463642151162684 " " absolute error = 9.416467605660728000000000000E-12 " " relative error = 3.0910511484170090000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.090000000009887 " " y[1] (closed_form) = 3.0573786312364533 " " y[1] (numeric) = 3.0573786312270195 " " absolute error = 9.43378708484488000000000000E-12 " " relative error = 3.0855802380713650000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.1000000000099 " " y[1] (closed_form) = 3.0683963707105235 " " y[1] (numeric) = 3.0683963707010755 " " absolute error = 9.447997939560082000000000000E-12 " " relative error = 3.0791321583307330000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.11000000000991 " " y[1] (closed_form) = 3.0794174324437833 " " y[1] (numeric) = 3.0794174324343295 " " absolute error = 9.453771099288133000000000000E-12 " " relative error = 3.0699868746880965000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.120000000009924 " " y[1] (closed_form) = 3.0904418153328805 " " y[1] (numeric) = 3.090441815323406 " " absolute error = 9.474643292151086000000000000E-12 " " relative error = 3.0657892490140753000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.130000000009936 " " y[1] (closed_form) = 3.1014695182751453 " " y[1] (numeric) = 3.101469518265664 " " absolute error = 9.481304630298837000000000000E-12 " " relative error = 3.0570362128117190000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.140000000009948 " " y[1] (closed_form) = 3.112500540168689 " " y[1] (numeric) = 3.1125005401591936 " " absolute error = 9.495515485014039000000000000E-12 " " relative error = 3.05076749785862200000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.15000000000996 " " y[1] (closed_form) = 3.1235348799123273 " " y[1] (numeric) = 3.123534879902819 " " absolute error = 9.50839407209969100000000000E-12 " " relative error = 3.0441133003664670000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.160000000009973 " " y[1] (closed_form) = 3.1345725364056136 " " y[1] (numeric) = 3.1345725363960906 " " absolute error = 9.523049016024743000000000000E-12 " " relative error = 3.03806943544038640000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.170000000009985 " " y[1] (closed_form) = 3.145613508548827 " " y[1] (numeric) = 3.1456135085392893 " " absolute error = 9.537703959949795000000000000E-12 " " relative error = 3.03206478927852960000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.180000000009997 " " y[1] (closed_form) = 3.156657795242978 " " y[1] (numeric) = 3.156657795233427 " " absolute error = 9.551026636245297000000000000E-12 " " relative error = 3.02567692026627260000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.19000000001001 " " y[1] (closed_form) = 3.1677053953898096 " " y[1] (numeric) = 3.167705395380243 " " absolute error = 9.566569758590049000000000000E-12 " " relative error = 3.0200313995464884000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.20000000001002 " " y[1] (closed_form) = 3.1787563078917813 " " y[1] (numeric) = 3.1787563078822045 " " absolute error = 9.5767838104166000000000000E-12 " " relative error = 3.0127455151691473000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.210000000010034 " " y[1] (closed_form) = 3.1898105316520926 " " y[1] (numeric) = 3.1898105316425047 " " absolute error = 9.587886040662852000000000000E-12 " " relative error = 3.0057854363208886000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.220000000010046 " " y[1] (closed_form) = 3.2008680655746673 " " y[1] (numeric) = 3.2008680655650634 " " absolute error = 9.603873252217454000000000000E-12 " " relative error = 3.000396472290470000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.230000000010058 " " y[1] (closed_form) = 3.211928908564147 " " y[1] (numeric) = 3.211928908554525 " " absolute error = 9.622080909821307000000000000E-12 " " relative error = 2.99573283959224950000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.24000000001007 " " y[1] (closed_form) = 3.2229930595258907 " " y[1] (numeric) = 3.2229930595162597 " " absolute error = 9.630962694018308000000000000E-12 " " relative error = 2.9882046024123440000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.250000000010083 " " y[1] (closed_form) = 3.2340605173660038 " " y[1] (numeric) = 3.234060517356362 " " absolute error = 9.64162083505471000000000000E-12 " " relative error = 2.9812740928259973000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.260000000010095 " " y[1] (closed_form) = 3.245131280991309 " " y[1] (numeric) = 3.2451312809816484 " " absolute error = 9.660716671078262000000000000E-12 " " relative error = 2.9769879350234320000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.270000000010107 " " y[1] (closed_form) = 3.256205349309326 " " y[1] (numeric) = 3.256205349299659 " " absolute error = 9.666933920016163000000000000E-12 " " relative error = 2.9687728146711070000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.28000000001012 " " y[1] (closed_form) = 3.267282721228341 " " y[1] (numeric) = 3.267282721218654 " " absolute error = 9.686917934459416000000000000E-12 " " relative error = 2.9648239105606390000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.29000000001013 " " y[1] (closed_form) = 3.2783633956573155 " " y[1] (numeric) = 3.278363395647616 " " absolute error = 9.699352432335218000000000000E-12 " " relative error = 2.9585958790241090000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.300000000010144 " " y[1] (closed_form) = 3.2894473715059576 " " y[1] (numeric) = 3.2894473714962498 " " absolute error = 9.707790127322369000000000000E-12 " " relative error = 2.9511918054727837000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.310000000010156 " " y[1] (closed_form) = 3.3005346476846995 " " y[1] (numeric) = 3.3005346476749766 " " absolute error = 9.722889160457271000000000000E-12 " " relative error = 2.945852777906090000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.320000000010168 " " y[1] (closed_form) = 3.311625223104677 " " y[1] (numeric) = 3.3116252230949375 " " absolute error = 9.739764550431573000000000000E-12 " " relative error = 2.9410829711281340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.33000000001018 " " y[1] (closed_form) = 3.3227190966777442 " " y[1] (numeric) = 3.322719096667992 " " absolute error = 9.752199048307375000000000000E-12 " " relative error = 2.9350055675961940000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.340000000010193 " " y[1] (closed_form) = 3.333816267316486 " " y[1] (numeric) = 3.333816267306718 " " absolute error = 9.767742170652127000000000000E-12 " " relative error = 2.92989816697803550000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.350000000010205 " " y[1] (closed_form) = 3.344916733934184 " " y[1] (numeric) = 3.3449167339244097 " " absolute error = 9.774403508799878000000000000E-12 " " relative error = 2.9221664652033170000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.360000000010217 " " y[1] (closed_form) = 3.3560204954448736 " " y[1] (numeric) = 3.356020495435077 " " absolute error = 9.796607969292381000000000000E-12 " " relative error = 2.9191144638685360000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.37000000001023 " " y[1] (closed_form) = 3.36712755076325 " " y[1] (numeric) = 3.3671275507534455 " " absolute error = 9.804601575069682000000000000E-12 " " relative error = 2.9118592709228386000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.38000000001024 " " y[1] (closed_form) = 3.3782378988047768 " " y[1] (numeric) = 3.3782378987949553 " " absolute error = 9.821476965043985000000000000E-12 " " relative error = 2.9072780719554510000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.390000000010254 " " y[1] (closed_form) = 3.389351538485599 " " y[1] (numeric) = 3.389351538475761 " " absolute error = 9.837908265808437000000000000E-12 " " relative error = 2.9025930636289580000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.400000000010266 " " y[1] (closed_form) = 3.400468468722579 " " y[1] (numeric) = 3.4004684687127305 " " absolute error = 9.848566406844839000000000000E-12 " " relative error = 2.8962381205506527000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.410000000010278 " " y[1] (closed_form) = 3.411588688433305 " " y[1] (numeric) = 3.411588688423443 " " absolute error = 9.86188908314034000000000000E-12 " " relative error = 2.8907028319610210000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.42000000001029 " " y[1] (closed_form) = 3.422712196536061 " " y[1] (numeric) = 3.422712196526191 " " absolute error = 9.869882688917642000000000000E-12 " " relative error = 2.88364376616485840000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.430000000010303 " " y[1] (closed_form) = 3.4338389919498695 " " y[1] (numeric) = 3.4338389919399774 " " absolute error = 9.892087149410145000000000000E-12 " " relative error = 2.88076615490728800000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.440000000010315 " " y[1] (closed_form) = 3.4449690735944145 " " y[1] (numeric) = 3.4449690735845175 " " absolute error = 9.896972130718495000000000000E-12 " " relative error = 2.8728769168288020000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.450000000010327 " " y[1] (closed_form) = 3.456102440390147 " " y[1] (numeric) = 3.456102440380233 " " absolute error = 9.913847520692798000000000000E-12 " " relative error = 2.8685051128211520000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.46000000001034 " " y[1] (closed_form) = 3.467239091258186 " " y[1] (numeric) = 3.467239091248257 " " absolute error = 9.9289465538277000000000000E-12 " " relative error = 2.8636463458378640000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.47000000001035 " " y[1] (closed_form) = 3.4783790251203683 " " y[1] (numeric) = 3.478379025110431 " " absolute error = 9.937384248814851000000000000E-12 " " relative error = 2.8569009234038173000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.480000000010364 " " y[1] (closed_form) = 3.4895222408992552 " " y[1] (numeric) = 3.4895222408893023 " " absolute error = 9.952927371159603000000000000E-12 " " relative error = 2.85223210630539460000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.490000000010376 " " y[1] (closed_form) = 3.5006687375181045 " " y[1] (numeric) = 3.500668737508128 " " absolute error = 9.976464099281657000000000000E-12 " " relative error = 2.84987379478663400000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.500000000010388 " " y[1] (closed_form) = 3.511818513900856 " " y[1] (numeric) = 3.5118185138908697 " " absolute error = 9.986234061898358000000000000E-12 " " relative error = 2.84360767003470700000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.5100000000104 " " y[1] (closed_form) = 3.5229715689721885 " " y[1] (numeric) = 3.5229715689621948 " " absolute error = 9.993783578465809000000000000E-12 " " relative error = 2.8367482912674913000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.520000000010413 " " y[1] (closed_form) = 3.5341279016574845 " " y[1] (numeric) = 3.5341279016474756 " " absolute error = 1.000888261160071100000000000E-11 " " relative error = 2.8320657571296750000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.530000000010425 " " y[1] (closed_form) = 3.5452875108828152 " " y[1] (numeric) = 3.545287510872789 " " absolute error = 1.002620209078486400000000000E-11 " " relative error = 2.8280363891526050000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.540000000010437 " " y[1] (closed_form) = 3.556450395574956 " " y[1] (numeric) = 3.5564503955649145 " " absolute error = 1.004130112391976600000000000E-11 " " relative error = 2.82340536407128250000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.55000000001045 " " y[1] (closed_form) = 3.5676165546613916 " " y[1] (numeric) = 3.567616554651336 " " absolute error = 1.005551197863496800000000000E-11 " " relative error = 2.8185517766747090000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.56000000001046 " " y[1] (closed_form) = 3.5787859870703045 " " y[1] (numeric) = 3.5787859870602383 " " absolute error = 1.00661701196713700000000000E-11 " " relative error = 2.8127331883044010000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.570000000010474 " " y[1] (closed_form) = 3.589958691730587 " " y[1] (numeric) = 3.5899586917205077 " " absolute error = 1.007904870675702100000000000E-11 " " relative error = 2.8075667639223680000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.580000000010486 " " y[1] (closed_form) = 3.601134667571827 " " y[1] (numeric) = 3.601134667561732 " " absolute error = 1.009503591831162300000000000E-11 " " relative error = 2.8032930868199113000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.590000000010498 " " y[1] (closed_form) = 3.6123139135243036 " " y[1] (numeric) = 3.6123139135141984 " " absolute error = 1.010524997013817500000000000E-11 " " relative error = 2.7974451313061910000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.60000000001051 " " y[1] (closed_form) = 3.6234964285190117 " " y[1] (numeric) = 3.6234964285088926 " " absolute error = 1.011901673564352700000000000E-11 " " relative error = 2.7926112072309540000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.610000000010523 " " y[1] (closed_form) = 3.634682211487636 " " y[1] (numeric) = 3.6346822114775024 " " absolute error = 1.013367167956857900000000000E-11 " " relative error = 2.78804888293686000000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.620000000010535 " " y[1] (closed_form) = 3.645871261362558 " " y[1] (numeric) = 3.64587126135241 " " absolute error = 1.014788253428378100000000000E-11 " " relative error = 2.78339025347023650000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.630000000010547 " " y[1] (closed_form) = 3.6570635770768547 " " y[1] (numeric) = 3.6570635770666957 " " absolute error = 1.015898476453003200000000000E-11 " " relative error = 2.77790761642986300000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.64000000001056 " " y[1] (closed_form) = 3.6682591575643144 " " y[1] (numeric) = 3.6682591575541377 " " absolute error = 1.017674833292403500000000000E-11 " " relative error = 2.77427190822615970000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.65000000001057 " " y[1] (closed_form) = 3.6794580017594 " " y[1] (numeric) = 3.6794580017492096 " " absolute error = 1.019051509842938700000000000E-11 " " relative error = 2.76956961964414500000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.660000000010584 " " y[1] (closed_form) = 3.690660108597278 " " y[1] (numeric) = 3.69066010858708 " " absolute error = 1.019806461499683800000000000E-11 " " relative error = 2.76320883389959470000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.670000000010596 " " y[1] (closed_form) = 3.7018654770138326 " " y[1] (numeric) = 3.7018654770036123 " " absolute error = 1.022026907548934100000000000E-11 " " relative error = 2.76084291526813700000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.680000000010608 " " y[1] (closed_form) = 3.713074105945587 " " y[1] (numeric) = 3.7130741059353634 " " absolute error = 1.022382178916814200000000000E-11 " " relative error = 2.7534655914346480000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.69000000001062 " " y[1] (closed_form) = 3.7242859943298257 " " y[1] (numeric) = 3.724285994319585 " " absolute error = 1.024069717914244400000000000E-11 " " relative error = 2.74970751299276340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.700000000010633 " " y[1] (closed_form) = 3.7355011411044714 " " y[1] (numeric) = 3.735501141094219 " " absolute error = 1.025224349859854600000000000E-11 " " relative error = 2.74454299740014950000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.710000000010645 " " y[1] (closed_form) = 3.7467195452081725 " " y[1] (numeric) = 3.7467195451979007 " " absolute error = 1.027178342383194800000000000E-11 " " relative error = 2.7415405129452340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.720000000010657 " " y[1] (closed_form) = 3.757941205580238 " " y[1] (numeric) = 3.7579412055699573 " " absolute error = 1.02806652080289500000000000E-11 " " relative error = 2.73571741696304270000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.73000000001067 " " y[1] (closed_form) = 3.7691661211607013 " " y[1] (numeric) = 3.769166121150404 " " absolute error = 1.029709650879340200000000000E-11 " " relative error = 2.73192960400016800000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.74000000001068 " " y[1] (closed_form) = 3.780394290890264 " " y[1] (numeric) = 3.780394290879949 " " absolute error = 1.031530416639725400000000000E-11 " " relative error = 2.7286318232080630000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.750000000010694 " " y[1] (closed_form) = 3.79162571371031 " " y[1] (numeric) = 3.7916257136999865 " " absolute error = 1.032374186138440600000000000E-11 " " relative error = 2.72277451438688260000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.760000000010706 " " y[1] (closed_form) = 3.802860388562941 " " y[1] (numeric) = 3.8028603885526016 " " absolute error = 1.033928498372915800000000000E-11 " " relative error = 2.71881792316763460000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.770000000010718 " " y[1] (closed_form) = 3.814098314390918 " " y[1] (numeric) = 3.814098314380567 " " absolute error = 1.03512753923951100000000000E-11 " " relative error = 2.7139508578839890000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.78000000001073 " " y[1] (closed_form) = 3.825339490137708 " " y[1] (numeric) = 3.825339490127342 " " absolute error = 1.036593033632016200000000000E-11 " " relative error = 2.70980663625936150000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.790000000010743 " " y[1] (closed_form) = 3.836583914747443 " " y[1] (numeric) = 3.8365839147370715 " " absolute error = 1.037170349604821200000000000E-11 " " relative error = 2.7033693844621580000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.800000000010755 " " y[1] (closed_form) = 3.8478315871649826 " " y[1] (numeric) = 3.847831587154588 " " absolute error = 1.039479613496041600000000000E-11 " " relative error = 2.7014685802865730000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.810000000010767 " " y[1] (closed_form) = 3.8590825063358167 " " y[1] (numeric) = 3.8590825063254077 " " absolute error = 1.040900698967561800000000000E-11 " " relative error = 2.6972750576299360000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.82000000001078 " " y[1] (closed_form) = 3.8703366712061538 " " y[1] (numeric) = 3.8703366711957323 " " absolute error = 1.04214414875514200000000000E-11 " " relative error = 2.69264469033999500000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.83000000001079 " " y[1] (closed_form) = 3.881594080722884 " " y[1] (numeric) = 3.881594080712448 " " absolute error = 1.043609643147647100000000000E-11 " " relative error = 2.6886109712772740000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.840000000010804 " " y[1] (closed_form) = 3.892854733833566 " " y[1] (numeric) = 3.8928547338231225 " " absolute error = 1.044364594804392300000000000E-11 " " relative error = 2.6827730963799240000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.850000000010816 " " y[1] (closed_form) = 3.9041186294864687 " " y[1] (numeric) = 3.9041186294760064 " " absolute error = 1.046229769485762500000000000E-11 " " relative error = 2.67981039711229050000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.860000000010828 " " y[1] (closed_form) = 3.9153857666305143 " " y[1] (numeric) = 3.915385766620034 " " absolute error = 1.048050535246147800000000000E-11 " " relative error = 2.6767491065077720000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.87000000001084 " " y[1] (closed_form) = 3.9266561442153076 " " y[1] (numeric) = 3.926656144204817 " " absolute error = 1.049071940428802900000000000E-11 " " relative error = 2.67166744909477340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.880000000010853 " " y[1] (closed_form) = 3.937929761191157 " " y[1] (numeric) = 3.9379297611806514 " " absolute error = 1.050537434821308100000000000E-11 " " relative error = 2.6677404081060563000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.890000000010865 " " y[1] (closed_form) = 3.9492066165090307 " " y[1] (numeric) = 3.949206616498512 " " absolute error = 1.051869702450858300000000000E-11 " " relative error = 2.66349625277564450000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.900000000010877 " " y[1] (closed_form) = 3.9604867091205875 " " y[1] (numeric) = 3.9604867091100515 " " absolute error = 1.053601650369273600000000000E-11 " " relative error = 2.6602832625165457000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.91000000001089 " " y[1] (closed_form) = 3.9717700379781533 " " y[1] (numeric) = 3.9717700379676018 " " absolute error = 1.055155962603748800000000000E-11 " " relative error = 2.6566391118174620000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.9200000000109 " " y[1] (closed_form) = 3.983056602034729 " " y[1] (numeric) = 3.983056602024174 " " absolute error = 1.055511233971628800000000000E-11 " " relative error = 2.6500030992088464000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.930000000010914 " " y[1] (closed_form) = 3.9943464002440336 " " y[1] (numeric) = 3.994346400233455 " " absolute error = 1.057864906783834200000000000E-11 " " relative error = 2.64840552316445100000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.940000000010926 " " y[1] (closed_form) = 4.005639431560397 " " y[1] (numeric) = 4.005639431549806 " " absolute error = 1.059063947650429300000000000E-11 " " relative error = 2.6439323003115910000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.950000000010938 " " y[1] (closed_form) = 4.016935694938873 " " y[1] (numeric) = 4.01693569492827 " " absolute error = 1.060307397438009500000000000E-11 " " relative error = 2.63959265958362440000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.96000000001095 " " y[1] (closed_form) = 4.028235189335177 " " y[1] (numeric) = 4.028235189324561 " " absolute error = 1.061639665067559700000000000E-11 " " relative error = 2.6354957324196690000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.970000000010963 " " y[1] (closed_form) = 4.039537913705700 " " y[1] (numeric) = 4.039537913695069 " " absolute error = 1.063149568381049900000000000E-11 " " relative error = 2.63185936384927150000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.980000000010975 " " y[1] (closed_form) = 4.050843867007500 " " y[1] (numeric) = 4.050843866996856 " " absolute error = 1.064481836010600100000000000E-11 " " relative error = 2.6278026775615270000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 28.990000000010987 " " y[1] (closed_form) = 4.062153048198319 " " y[1] (numeric) = 4.06215304818766 " " absolute error = 1.065814103640150300000000000E-11 " " relative error = 2.62376648785517640000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.000000000011 " " y[1] (closed_form) = 4.073465456236562 " " y[1] (numeric) = 4.073465456225891 " " absolute error = 1.067057553427730500000000000E-11 " " relative error = 2.6195325942780306000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.01000000001101 " " y[1] (closed_form) = 4.0847810900813215 " " y[1] (numeric) = 4.08478109007063 " " absolute error = 1.069189181635010800000000000E-11 " " relative error = 2.61749444598443500000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.020000000011024 " " y[1] (closed_form) = 4.096099948692327 " " y[1] (numeric) = 4.096099948681628 " " absolute error = 1.069899724370770900000000000E-11 " " relative error = 2.6119961372337470000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.030000000011036 " " y[1] (closed_form) = 4.107422031030020 " " y[1] (numeric) = 4.1074220310193095 " " absolute error = 1.07096553847441100000000000E-11 " " relative error = 2.60739103599209400000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.040000000011048 " " y[1] (closed_form) = 4.118747336055492 " " y[1] (numeric) = 4.118747336044769 " " absolute error = 1.072297806103961200000000000E-11 " " relative error = 2.6034561448260540000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.05000000001106 " " y[1] (closed_form) = 4.130075862730514 " " y[1] (numeric) = 4.130075862719770 " " absolute error = 1.074518252153211500000000000E-11 " " relative error = 2.60169131964277270000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.060000000011073 " " y[1] (closed_form) = 4.141407610017495 " " y[1] (numeric) = 4.141407610006742 " " absolute error = 1.075317612730941600000000000E-11 " " relative error = 2.5965027207896570000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.070000000011085 " " y[1] (closed_form) = 4.152742576879554 " " y[1] (numeric) = 4.1527425768687865 " " absolute error = 1.076738698202461800000000000E-11 " " relative error = 2.59283757244481700000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.080000000011097 " " y[1] (closed_form) = 4.164080762280449 " " y[1] (numeric) = 4.164080762269669 " " absolute error = 1.07798214799004200000000000E-11 " " relative error = 2.58876378612716340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.09000000001111 " " y[1] (closed_form) = 4.175422165184620 " " y[1] (numeric) = 4.175422165173824 " " absolute error = 1.079669686987472200000000000E-11 " " relative error = 2.58577371167385550000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.10000000001112 " " y[1] (closed_form) = 4.1867667845571646 " " y[1] (numeric) = 4.186766784546354 " " absolute error = 1.081090772458992400000000000E-11 " " relative error = 2.58216143408460660000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.110000000011134 " " y[1] (closed_form) = 4.198114619363842 " " y[1] (numeric) = 4.198114619353020 " " absolute error = 1.082156586562632600000000000E-11 " " relative error = 2.577720440435750000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.120000000011146 " " y[1] (closed_form) = 4.209465668571092 " " y[1] (numeric) = 4.209465668560257 " " absolute error = 1.083488854192182800000000000E-11 " " relative error = 2.57393441234543700000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.130000000011158 " " y[1] (closed_form) = 4.220819931146010 " " y[1] (numeric) = 4.220819931135157 " " absolute error = 1.08535402887355300000000000E-11 " " relative error = 2.5714293587001340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.14000000001117 " " y[1] (closed_form) = 4.232177406056351 " " y[1] (numeric) = 4.232177406045482 " " absolute error = 1.086952750029013300000000000E-11 " " relative error = 2.5683062068087150000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.150000000011183 " " y[1] (closed_form) = 4.2435380922705335 " " y[1] (numeric) = 4.2435380922596515 " " absolute error = 1.088196199816593400000000000E-11 " " relative error = 2.5643606258624320000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.160000000011195 " " y[1] (closed_form) = 4.254901988757645 " " y[1] (numeric) = 4.25490198874675 " " absolute error = 1.089528467446143600000000000E-11 " " relative error = 2.5606429250894830000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.170000000011207 " " y[1] (closed_form) = 4.266269094487427 " " y[1] (numeric) = 4.266269094476522 " " absolute error = 1.090505463707813800000000000E-11 " " relative error = 2.5561103614324010000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.18000000001122 " " y[1] (closed_form) = 4.277639408430296 " " y[1] (numeric) = 4.277639408419375 " " absolute error = 1.09210418486327400000000000E-11 " " relative error = 2.55305340303106100000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.19000000001123 " " y[1] (closed_form) = 4.289012929557309 " " y[1] (numeric) = 4.2890129295463755 " " absolute error = 1.093347634650854200000000000E-11 " " relative error = 2.5491824170455557000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.200000000011244 " " y[1] (closed_form) = 4.300389656840196 " " y[1] (numeric) = 4.300389656829248 " " absolute error = 1.094768720122374400000000000E-11 " " relative error = 2.54574307791164000000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.210000000011256 " " y[1] (closed_form) = 4.311769589251341 " " y[1] (numeric) = 4.311769589240383 " " absolute error = 1.095834534226014500000000000E-11 " " relative error = 2.54149604134177750000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.220000000011268 " " y[1] (closed_form) = 4.323152725763790 " " y[1] (numeric) = 4.32315272575282 " " absolute error = 1.097077984013594700000000000E-11 " " relative error = 2.53768037727551960000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.23000000001128 " " y[1] (closed_form) = 4.334539065351251 " " y[1] (numeric) = 4.334539065340264 " " absolute error = 1.098676705169054900000000000E-11 " " relative error = 2.5347025107040380000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.240000000011293 " " y[1] (closed_form) = 4.345928606988082 " " y[1] (numeric) = 4.3459286069770755 " " absolute error = 1.100630697692395200000000000E-11 " " relative error = 2.53255586371719130000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.250000000011305 " " y[1] (closed_form) = 4.357321349649283 " " y[1] (numeric) = 4.35732134963827 " " absolute error = 1.101252422586185300000000000E-11 " " relative error = 2.527361041835539700000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.260000000011317 " " y[1] (closed_form) = 4.368717292310550 " " y[1] (numeric) = 4.368717292299517 " " absolute error = 1.103206415109525600000000000E-11 " " relative error = 2.52524102910320460000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.27000000001133 " " y[1] (closed_form) = 4.380116433948189 " " y[1] (numeric) = 4.380116433937147 " " absolute error = 1.104183411371195700000000000E-11 " " relative error = 2.52089967931719340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.28000000001134 " " y[1] (closed_form) = 4.391518773539204 " " y[1] (numeric) = 4.391518773528143 " " absolute error = 1.10604858605256600000000000E-11 " " relative error = 2.51860152054224700000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.290000000011354 " " y[1] (closed_form) = 4.402924310061210 " " y[1] (numeric) = 4.40292431005014 " " absolute error = 1.10693676447226610000000000E-11 " " relative error = 2.514094466586180300000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.300000000011366 " " y[1] (closed_form) = 4.414333042492508 " " y[1] (numeric) = 4.4143330424814256 " " absolute error = 1.108269032101816300000000000E-11 " " relative error = 2.5106149024860240000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.310000000011378 " " y[1] (closed_form) = 4.425744969812044 " " y[1] (numeric) = 4.425744969800944 " " absolute error = 1.109956571099246500000000000E-11 " " relative error = 2.50795420583483140000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.32000000001139 " " y[1] (closed_form) = 4.437160090999399 " " y[1] (numeric) = 4.437160090988291 " " absolute error = 1.110755931676976600000000000E-11 " " relative error = 2.50330370979875260000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.330000000011403 " " y[1] (closed_form) = 4.448578405034837 " " y[1] (numeric) = 4.448578405023713 " " absolute error = 1.112443470674406900000000000E-11 " " relative error = 2.50067183128740430000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.340000000011415 " " y[1] (closed_form) = 4.459999910899242 " " y[1] (numeric) = 4.459999910888108 " " absolute error = 1.11342046693607700000000000E-11 " " relative error = 2.49645849591863530000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.350000000011427 " " y[1] (closed_form) = 4.471424607574171 " " y[1] (numeric) = 4.471424607563023 " " absolute error = 1.114841552407597200000000000E-11 " " relative error = 2.4932580782401229000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.36000000001144 " " y[1] (closed_form) = 4.482852494041815 " " y[1] (numeric) = 4.482852494030655 " " absolute error = 1.115996184353207400000000000E-11 " " relative error = 2.48947781760940000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.37000000001145 " " y[1] (closed_form) = 4.494283569285024 " " y[1] (numeric) = 4.4942835692738505 " " absolute error = 1.117328451982757500000000000E-11 " " relative error = 2.4861102659806320000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.380000000011464 " " y[1] (closed_form) = 4.505717832287296 " " y[1] (numeric) = 4.505717832276106 " " absolute error = 1.119015990980187800000000000E-11 " " relative error = 2.48354653494164160000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.390000000011476 " " y[1] (closed_form) = 4.517155282032775 " " y[1] (numeric) = 4.517155282021563 " " absolute error = 1.121147619187468100000000000E-11 " " relative error = 2.48197714974929540000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.400000000011488 " " y[1] (closed_form) = 4.52859591750623 " " y[1] (numeric) = 4.528595917495013 " " absolute error = 1.121769344081258200000000000E-11 " " relative error = 2.4770797936394040000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.4100000000115 " " y[1] (closed_form) = 4.540039737693128 " " y[1] (numeric) = 4.540039737681893 " " absolute error = 1.123545700920658400000000000E-11 " " relative error = 2.47474860537575640000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.420000000011512 " " y[1] (closed_form) = 4.551486741579538 " " y[1] (numeric) = 4.551486741568285 " " absolute error = 1.125322057760058700000000000E-11 " " relative error = 2.4724274103224770000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.430000000011525 " " y[1] (closed_form) = 4.562936928152183 " " y[1] (numeric) = 4.562936928140918 " " absolute error = 1.126565507547638800000000000E-11 " " relative error = 2.46894823506546960000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.440000000011537 " " y[1] (closed_form) = 4.574390296398441 " " y[1] (numeric) = 4.574390296387164 " " absolute error = 1.12772013949324900000000000E-11 " " relative error = 2.4652905992327281000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.45000000001155 " " y[1] (closed_form) = 4.585846845306335 " " y[1] (numeric) = 4.585846845295043 " " absolute error = 1.129230042806739200000000000E-11 " " relative error = 2.4624242389658493000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.46000000001156 " " y[1] (closed_form) = 4.597306573864522 " " y[1] (numeric) = 4.597306573853214 " " absolute error = 1.130739946120229400000000000E-11 " " relative error = 2.4595704636023938000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.470000000011574 " " y[1] (closed_form) = 4.608769481062296 " " y[1] (numeric) = 4.608769481050982 " " absolute error = 1.131450488855989500000000000E-11 " " relative error = 2.4549947518642140000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.480000000011586 " " y[1] (closed_form) = 4.620235565889622 " " y[1] (numeric) = 4.62023556587829 " " absolute error = 1.133226845695389800000000000E-11 " " relative error = 2.45274689901485150000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.490000000011598 " " y[1] (closed_form) = 4.6317048273370744 " " y[1] (numeric) = 4.631704827325729 " " absolute error = 1.1345591133249400000000000E-11 " " relative error = 2.4495496920023652000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.50000000001161 " " y[1] (closed_form) = 4.643177264395888 " " y[1] (numeric) = 4.6431772643845255 " " absolute error = 1.136246652322370200000000000E-11 " " relative error = 2.4471317540150050000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.510000000011622 " " y[1] (closed_form) = 4.654652876057930 " " y[1] (numeric) = 4.65465287604655 " " absolute error = 1.138023009161770500000000000E-11 " " relative error = 2.4449148829451980000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.520000000011635 " " y[1] (closed_form) = 4.666131661315703 " " y[1] (numeric) = 4.666131661304314 " " absolute error = 1.138911187581470600000000000E-11 " " relative error = 2.440803796908579700000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.530000000011647 " " y[1] (closed_form) = 4.677613619162365 " " y[1] (numeric) = 4.677613619150962 " " absolute error = 1.140332273052990800000000000E-11 " " relative error = 2.43785050646657260000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.54000000001166 " " y[1] (closed_form) = 4.689098748591697 " " y[1] (numeric) = 4.689098748580282 " " absolute error = 1.14148690499860100000000000E-11 " " relative error = 2.4343417918878980000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.55000000001167 " " y[1] (closed_form) = 4.7005870485981305 " " y[1] (numeric) = 4.7005870485867005 " " absolute error = 1.142996808312091200000000000E-11 " " relative error = 2.43160438578192140000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.560000000011684 " " y[1] (closed_form) = 4.7120785181767175 " " y[1] (numeric) = 4.7120785181652804 " " absolute error = 1.143707351047851300000000000E-11 " " relative error = 2.42718228619499960000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.570000000011696 " " y[1] (closed_form) = 4.723573156323177 " " y[1] (numeric) = 4.723573156311720 " " absolute error = 1.145750161413161500000000000E-11 " " relative error = 2.42560054326545450000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.580000000011708 " " y[1] (closed_form) = 4.735070962033824 " " y[1] (numeric) = 4.735070962022355 " " absolute error = 1.146904793358771700000000000E-11 " " relative error = 2.4221491136135990000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.59000000001172 " " y[1] (closed_form) = 4.746571934305642 " " y[1] (numeric) = 4.746571934294157 " " absolute error = 1.14850351451423200000000000E-11 " " relative error = 2.4196483913231628000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.600000000011732 " " y[1] (closed_form) = 4.758076072136241 " " y[1] (numeric) = 4.758076072124735 " " absolute error = 1.150635142721512200000000000E-11 " " relative error = 2.4182781554497293000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.610000000011745 " " y[1] (closed_form) = 4.76958337452384 " " y[1] (numeric) = 4.769583374512326 " " absolute error = 1.151434503299242400000000000E-11 " " relative error = 2.41411966808147670000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.620000000011757 " " y[1] (closed_form) = 4.781093840467335 " " y[1] (numeric) = 4.7810938404558065 " " absolute error = 1.152855588770762600000000000E-11 " " relative error = 2.41127998579102330000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.63000000001177 " " y[1] (closed_form) = 4.7926074689662315 " " y[1] (numeric) = 4.792607468954686 " " absolute error = 1.154543127768192800000000000E-11 " " relative error = 2.40900832218005230000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.64000000001178 " " y[1] (closed_form) = 4.804124259020668 " " y[1] (numeric) = 4.804124259009103 " " absolute error = 1.15649712029153300000000000E-11 " " relative error = 2.4073005982723850000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.650000000011794 " " y[1] (closed_form) = 4.815644209631408 " " y[1] (numeric) = 4.815644209619830 " " absolute error = 1.157740570079113200000000000E-11 " " relative error = 2.4041239752795760000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.660000000011806 " " y[1] (closed_form) = 4.827167319799862 " " y[1] (numeric) = 4.827167319788272 " " absolute error = 1.159072837708663400000000000E-11 " " relative error = 2.40114493847028960000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.670000000011818 " " y[1] (closed_form) = 4.838693588528066 " " y[1] (numeric) = 4.838693588516464 " " absolute error = 1.160227469654273600000000000E-11 " " relative error = 2.39781141009843430000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.68000000001183 " " y[1] (closed_form) = 4.850223014818688 " " y[1] (numeric) = 4.850223014807070 " " absolute error = 1.161737372967763800000000000E-11 " " relative error = 2.39522465135799940000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.690000000011842 " " y[1] (closed_form) = 4.861755597675014 " " y[1] (numeric) = 4.861755597663386 " " absolute error = 1.16280318707140400000000000E-11 " " relative error = 2.39173517407472950000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.700000000011855 " " y[1] (closed_form) = 4.873291336100976 " " y[1] (numeric) = 4.873291336089334 " " absolute error = 1.164224272542924200000000000E-11 " " relative error = 2.38898968325254450000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.710000000011867 " " y[1] (closed_form) = 4.8848302291011265 " " y[1] (numeric) = 4.8848302290894665 " " absolute error = 1.166000629382324400000000000E-11 " " relative error = 2.3869829138297072000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.72000000001188 " " y[1] (closed_form) = 4.8963722756806405 " " y[1] (numeric) = 4.896372275668965 " " absolute error = 1.167510532695814600000000000E-11 " " relative error = 2.38443988112305020000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.73000000001189 " " y[1] (closed_form) = 4.90791747484532 " " y[1] (numeric) = 4.907917474833636 " " absolute error = 1.168398711115514700000000000E-11 " " relative error = 2.3806404999756820000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.740000000011904 " " y[1] (closed_form) = 4.919465825601613 " " y[1] (numeric) = 4.919465825589910 " " absolute error = 1.17017506795491500000000000E-11 " " relative error = 2.3786628659257159000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.750000000011916 " " y[1] (closed_form) = 4.931017326956564 " " y[1] (numeric) = 4.931017326944851 " " absolute error = 1.171240882058555100000000000E-11 " " relative error = 2.3752520106869060000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.760000000011928 " " y[1] (closed_form) = 4.942571977917872 " " y[1] (numeric) = 4.942571977906144 " " absolute error = 1.172839603214015400000000000E-11 " " relative error = 2.37293378519110730000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.77000000001194 " " y[1] (closed_form) = 4.95412977749384 " " y[1] (numeric) = 4.9541297774820965 " " absolute error = 1.174349506527505600000000000E-11 " " relative error = 2.3704455863519530000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.780000000011952 " " y[1] (closed_form) = 4.965690724693403 " " y[1] (numeric) = 4.9656907246816475 " " absolute error = 1.175504138473115700000000000E-11 " " relative error = 2.3672520171817488000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.790000000011965 " " y[1] (closed_form) = 4.97725481852612 " " y[1] (numeric) = 4.977254818514352 " " absolute error = 1.17683640610266600000000000E-11 " " relative error = 2.3644286841057383000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.800000000011977 " " y[1] (closed_form) = 4.988822058002178 " " y[1] (numeric) = 4.988822057990391 " " absolute error = 1.178701580784036200000000000E-11 " " relative error = 2.36268515308813930000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.81000000001199 " " y[1] (closed_form) = 5.000392442132366 " " y[1] (numeric) = 5.000392442120572 " " absolute error = 1.179412123519796300000000000E-11 " " relative error = 2.3586391211663540000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.820000000012 " " y[1] (closed_form) = 5.011965969928127 " " y[1] (numeric) = 5.011965969916319 " " absolute error = 1.180833208991316500000000000E-11 " " relative error = 2.35602798597662840000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.830000000012014 " " y[1] (closed_form) = 5.023542640401509 " " y[1] (numeric) = 5.023542640389677 " " absolute error = 1.183142472882536800000000000E-11 " " relative error = 2.3551954418923250000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.840000000012026 " " y[1] (closed_form) = 5.035122452565155 " " y[1] (numeric) = 5.035122452553317 " " absolute error = 1.183764197776326900000000000E-11 " " relative error = 2.35101372196669350000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.850000000012038 " " y[1] (closed_form) = 5.046705405432377 " " y[1] (numeric) = 5.046705405420527 " " absolute error = 1.185007647563907100000000000E-11 " " relative error = 2.34808167381504150000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.86000000001205 " " y[1] (closed_form) = 5.058291498017084 " " y[1] (numeric) = 5.0582914980052145 " " absolute error = 1.186961640087247400000000000E-11 " " relative error = 2.3465663071267280000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.870000000012062 " " y[1] (closed_form) = 5.069880729333790 " " y[1] (numeric) = 5.069880729321905 " " absolute error = 1.188471543400737600000000000E-11 " " relative error = 2.3441804784960090000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.880000000012075 " " y[1] (closed_form) = 5.0814730983976375 " " y[1] (numeric) = 5.081473098385744 " " absolute error = 1.189359721820437700000000000E-11 " " relative error = 2.34058057336854450000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.890000000012087 " " y[1] (closed_form) = 5.093068604224399 " " y[1] (numeric) = 5.093068604212497 " " absolute error = 1.190247900240137800000000000E-11 " " relative error = 2.33699561645978550000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.9000000000121 " " y[1] (closed_form) = 5.104667245830463 " " y[1] (numeric) = 5.104667245818542 " " absolute error = 1.192113074921508100000000000E-11 " " relative error = 2.3353394403822042000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.91000000001211 " " y[1] (closed_form) = 5.116269022232807 " " y[1] (numeric) = 5.1162690222208775 " " absolute error = 1.192912435499238200000000000E-11 " " relative error = 2.3316061573686278000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.920000000012124 " " y[1] (closed_form) = 5.127873932449063 " " y[1] (numeric) = 5.127873932437114 " " absolute error = 1.194866428022578500000000000E-11 " " relative error = 2.3301400224788920000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.930000000012136 " " y[1] (closed_form) = 5.139481975497440 " " y[1] (numeric) = 5.139481975485483 " " absolute error = 1.195665788600308600000000000E-11 " " relative error = 2.326432497089519800000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.940000000012148 " " y[1] (closed_form) = 5.151093150396797 " " y[1] (numeric) = 5.151093150384826 " " absolute error = 1.197086874071828800000000000E-11 " " relative error = 2.32394724599304800000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.95000000001216 " " y[1] (closed_form) = 5.1627074561665935 " " y[1] (numeric) = 5.162707456154601 " " absolute error = 1.199218502279109100000000000E-11 " " relative error = 2.3228480646268330000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.960000000012172 " " y[1] (closed_form) = 5.174324891826885 " " y[1] (numeric) = 5.174324891814883 " " absolute error = 1.200195498540779200000000000E-11 " " relative error = 2.31952094936394570000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.970000000012185 " " y[1] (closed_form) = 5.185945456398372 " " y[1] (numeric) = 5.185945456386353 " " absolute error = 1.201883037538209500000000000E-11 " " relative error = 2.31757747481770640000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.980000000012197 " " y[1] (closed_form) = 5.197569148902346 " " y[1] (numeric) = 5.197569148890311 " " absolute error = 1.203481758693669700000000000E-11 " " relative error = 2.3154704136025360000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 29.99000000001221 " " y[1] (closed_form) = 5.209195968360717 " " y[1] (numeric) = 5.209195968348667 " " absolute error = 1.204991662007159900000000000E-11 " " relative error = 2.31320086502017130000000000E-10 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 13 h = 1.000E-3 " " "Finished!" "diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; " Iterations = 10000 "Total Elapsed Time "= 2 Minutes 21 Seconds "Elapsed Time(since restart) "= 2 Minutes 21 Seconds "Time to Timeout "= 38 Seconds Percent Done = 100.01000000012223 "%" (%o253) temp/diffeq.lin_ln.max