(%i1) batch("temp/diffeq.expt_lin_c.max") read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.expt_lin_c.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_c1,[30],convfloat) (%i189) completearray(array_tmp3_a1,[30],convfloat) (%i190) completearray(array_tmp3_a2,[30],convfloat) (%i191) completearray(array_tmp3,[30],convfloat) (%i192) completearray(array_tmp4,[30],convfloat) (%i193) completearray(array_m1,[30],convfloat) (%i194) completearray(array_y_higher,[2,30],convfloat) (%i195) completearray(array_y_higher_work,[2,30],convfloat) (%i196) completearray(array_y_higher_work2,[2,30],convfloat) (%i197) completearray(array_y_set_initial,[2,30],convfloat) (%i198) completearray(array_given_rad_poles,[2,3],convfloat) (%i199) completearray(array_given_ord_poles,[2,3],convfloat) (%i200) completearray(array_rad_test_poles,[2,4],convfloat) (%i201) completearray(array_ord_test_poles,[2,4],convfloat) (%i202) completearray(array_fact_2,[30,30],convfloat) (%i203) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%i204) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%i205) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%i206) 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)) (%i207) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%i208) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%i209) 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) (%i210) 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) (%i211) 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) (%i212) 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) (%i213) 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) (%i214) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%i215) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%i216) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%i217) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), printf(file,"~d",glob_min_good_digits), printf(file,"")),0) (%i218) log_revs(file,revs):=printf(file,revs) (%i219) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%i220) 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) (%i221) logstart(file):=(printf(file,""),0) (%i222) logend(file):=(printf(file,"~%"),0) (%i223) 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) (%i224) 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) (%i225) 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) (%i226) 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) (%i227) 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) (%i228) c(in_val):=(ret:in_val,ret) (%i229) 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) (%i230) 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) (%i231) 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) (%i232) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%i233) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret) (%i234) 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) (%i235) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret) (%i236) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret) (%i237) 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) (%i238) log10(x):=log(x)/glob_log_10 (%i239) c(x):=x (%i240) 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 (%i241) 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) (%i242) exact_soln_y(x):=block(c(5.0)*expt(c(0.3)+c(0.2)*c(x),c(3.0))/c(3.0)) c(5.0) expt(c(0.3) + c(0.2) c(x), c(3.0)) (%o242) exact_soln_y(x) := block(-----------------------------------------) c(3.0) (%i243) 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) (%i244) my_check_sign(x0,xf):=block([ret], if xf > x0 then ret:glob__1 else ret:glob__m1,ret) (%i245) 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) (%i246) 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) (%i247) 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)) (%i248) 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)) (%i249) display_alot(iter):=( block(mode_declare( [[abserr,est_rel_err],convfloat, [closed_form_val_y],convfloat,[ind_var], convfloat,[numeric_val],convfloat,[relerr], convfloat,[term_no],fixnum]), if reached_interval() then (if iter >= 0 then (ind_var:array_x[1], omniout_float(always, "x[1] ", 33,ind_var,20, " "), closed_form_val_y :exact_soln_y(ind_var), omniout_float(always, "y[1] (closed_form) ", 33, closed_form_val_y, 20," "), term_no:1, numeric_val:array_y[term_no], abserr :abs( numeric_val -closed_form_val_y), omniout_float(always, "y[1] (numeric) ", 33,numeric_val, 20," "), if c(abs(closed_form_val_y)) > c(glob_prec) then ( relerr :abserr*glob__100 /abs(closed_form_val_y), if c(relerr) > c(glob_prec) then glob_good_digits :3 -floor(log10(c(relerr))) else glob_good_digits:16) else (relerr:glob__m1, glob_good_digits:-16), if glob_good_digits < glob_min_good_digits then glob_min_good_digits :glob_good_digits, if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits then glob_min_apfp_est_good_digits :glob_apfp_est_good_digits, if c(abs(numeric_val)) > c(glob_prec) then ( est_rel_err :c(array_max_est_error[1]) *glob__100 *c(sqrt(glob_iter))*c(25) *c(ats_max_terms) /c(abs(numeric_val)), if est_rel_err > glob_prec then glob_est_digits :3 -floor( log10(est_rel_err)) else glob_est_digits:16) else (relerr:glob__m1, glob_est_digits:-16), array_est_digits[1] :glob_est_digits, if glob_iter = 1 then array_1st_rel_error[1] :relerr else array_last_rel_error[ 1] :relerr, array_est_rel_error[1] :est_rel_err, omniout_float(always, "absolute error ", 4,abserr,20," "), omniout_float(always, "relative error ", 4,relerr,20,"%"), omniout_int(info, "Desired digits ", 32, glob_desired_digits_correct, 4," "), omniout_int(info, "Estimated correct digits ", 32,glob_est_digits, 4," "), omniout_int(info, "Correct digits ", 32, glob_good_digits,4, " "), omniout_float(always, "h ", 4,glob_h,20, " ")))),0) (%i250) 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) (%i251) 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) (%i252) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:array_const_0D2[1]*array_x[1], array_tmp2[1]:array_const_0D3[1]+array_tmp1[1], array_tmp3[1]:expt(array_tmp2[1],c(array_const_2D0[1])), array_tmp4[1]:array_tmp3[1]+array_const_0D0[1], if not array_y_set_initial[1,2] then (if 1 <= ats_max_terms then ( temporary :c(array_tmp4[1])*expt(glob_h,c(1)) *c(factorial_3(0,1)), if 2 <= ats_max_terms then (array_y[2]:temporary, array_y_higher[1,2]:temporary), temporary:c(temporary)*c(1)/c(glob_h), array_y_higher[2,1]:c(temporary),0)), kkk:2,array_tmp1[2]:array_const_0D2[1]*array_x[2], array_tmp2[2]:array_tmp1[2], array_tmp3[2]:(array_const_2D0[1]-c(0)) *array_tmp2[2]*array_tmp3[1] /array_tmp2[1] /c(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]:(array_const_2D0[1]-c(1)) *array_tmp2[2]*array_tmp3[2] /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]:(array_const_2D0[1]-c(2)) *array_tmp2[2]*array_tmp3[3] /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]:(array_const_2D0[1]-c(3)) *array_tmp2[2]*array_tmp3[4] /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] :(array_const_2D0[1]-c(kkk-2)) *array_tmp2[2]*array_tmp3[kkk-1] /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) (%i253) exact_soln_y(x):=block(c(5.0)*expt(c(0.3)+c(0.2)*c(x),c(3.0))/c(3.0)) c(5.0) expt(c(0.3) + c(0.2) c(x), c(3.0)) (%o253) exact_soln_y(x) := block(-----------------------------------------) c(3.0) (%i254) 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_c1[term]:c(0.0),term:1+term),term:1, while term <= 30 do (array_tmp3_a1[term]:c(0.0),term:1+term),term:1, while term <= 30 do (array_tmp3_a2[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_c1), zero_ats_ar(array_tmp3_a1),zero_ats_ar(array_tmp3_a2), 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_0D2), array_const_0D2[1]:c(0.2),zero_ats_ar(array_const_0D3), array_const_0D3[1]:c(0.3),zero_ats_ar(array_const_2D0), array_const_2D0[1]:c(2.0),zero_ats_ar(array_m1), array_m1[1]:glob__m1,iiif:0, while iiif <= ats_max_terms do (jjjf:0, while jjjf <= ats_max_terms do (array_fact_1[iiif]:0, array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf), iiif:1+iiif),array_y_set_initial[1,1]:true, array_y_set_initial[1,2]:false, array_y_set_initial[1,3]:false, array_y_set_initial[1,4]:false, array_y_set_initial[1,5]:false, array_y_set_initial[1,6]:false, array_y_set_initial[1,7]:false, array_y_set_initial[1,8]:false, array_y_set_initial[1,9]:false, array_y_set_initial[1,10]:false, array_y_set_initial[1,11]:false, array_y_set_initial[1,12]:false, array_y_set_initial[1,13]:false, array_y_set_initial[1,14]:false, array_y_set_initial[1,15]:false, array_y_set_initial[1,16]:false, array_y_set_initial[1,17]:false, array_y_set_initial[1,18]:false, array_y_set_initial[1,19]:false, array_y_set_initial[1,20]:false, array_y_set_initial[1,21]:false, array_y_set_initial[1,22]:false, array_y_set_initial[1,23]:false, array_y_set_initial[1,24]:false, array_y_set_initial[1,25]:false, array_y_set_initial[1,26]:false, array_y_set_initial[1,27]:false, array_y_set_initial[1,28]:false, array_y_set_initial[1,29]:false, array_y_set_initial[1,30]:false,glob_log_10:log(10.0), glob_orig_start_sec:elapsed_time_seconds(), glob_display_flag:true,glob_no_eqs:1,glob_iter:-1, opt_iter:-1,glob_max_iter:50000,glob_max_hours:0.0, glob_max_minutes:15.0, omniout_str(always, "##############ECHO OF PROBLEM#################"), omniout_str(always, "##############temp/expt_lin_cpostode.ode#################"), omniout_str(always, "diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , 2.0 ) ; "), omniout_str(always,"!"), omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(always,"Digits:32,"), omniout_str(always,"max_terms:30,"),omniout_str(always,"!"), omniout_str(always,"/* END FIRST INPUT BLOCK */"), omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(always,"x_start:c(0.1),"), omniout_str(always,"x_end:c(5.0),"), omniout_str(always, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(always,"glob_look_poles:true,"), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""), omniout_str(always,"glob_type_given_pole:3,"), omniout_str(always,"/* END SECOND INPUT BLOCK */"), omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"), omniout_str(always,"glob_desired_digits_correct:8,"), omniout_str(always,"glob_max_minutes:(3.0),"), omniout_str(always,"glob_subiter_method:3,"), omniout_str(always,"glob_max_iter:100000,"), omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"), omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"), omniout_str(always,"glob_look_poles:false,"), omniout_str(always,"glob_h:c(0.001),"), omniout_str(always,"glob_display_interval:c(0.01),"), omniout_str(always,"/* END OVERRIDE BLOCK */"), omniout_str(always,"!"), omniout_str(always,"/* BEGIN USER DEF BLOCK */"), omniout_str(always,"exact_soln_y (x) := (block("), omniout_str(always,""), omniout_str(always, " (c(5.0)/c(3.0) * expt((c(0.2) * c(x) + c(0.3)),c(3.0))) "), omniout_str(always,"));"), omniout_str(always,"/* END USER DEF BLOCK */"), omniout_str(always, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false, glob_small_float:glob__0,glob_smallish_float:glob__0, glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100), glob_almost_1:c(0.99),x_start:c(0.1),x_end:c(5.0), array_y_init[1+0]:exact_soln_y(x_start), glob_look_poles:true,glob_type_given_pole:3, glob_desired_digits_correct:8,glob_max_minutes:3.0, glob_subiter_method:3,glob_max_iter:100000, glob_upper_ratio_limit:c(1.000001), glob_lower_ratio_limit:c(0.999999),glob_look_poles:false, glob_h:c(0.001),glob_display_interval:c(0.01), glob_last_good_h:glob_h, glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes, glob_check_sign:c(my_check_sign(x_start,x_end)), glob__pi:3.141592654,glob_prec:1.0E-16, if glob_optimize then (omniout_str(always,"START of Optimize"), found_h:false,glob_min_pole_est:glob_larger_float, last_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float, glob_min_h:abs(glob_min_h)*glob_check_sign, glob_max_h:abs(glob_max_h)*glob_check_sign, glob_h:abs(glob_min_h)*glob_check_sign, glob_display_interval :c(abs(c(glob_display_interval)) *glob_check_sign), display_max:c(x_end)-c(x_start)/glob__10, if glob_display_interval > display_max then glob_display_interval:c(display_max), chk_data(),min_value:glob_larger_float, est_answer:est_size_answer(),opt_iter:1, est_needed_step_err :estimated_needed_step_error( x_start,x_end,glob_h,est_answer), omniout_float(always,"est_needed_step_err",32, est_needed_step_err,16,""), estimated_step_error:glob_small_float, while opt_iter <= 100 and not found_h do (omniout_int(always,"opt_iter",32,opt_iter, 4,""),array_x[1]:c(x_start), array_x[2]:c(glob_h), glob_next_display:c(x_start),order_diff:1, term_no:1, while term_no <= order_diff do ( array_y[term_no] :array_y_init[term_no] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no),rows:order_diff, r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < ats_max_terms then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h, c(term_no-1)) /c( factorial_1( term_no-1)), term_no:1+term_no), r_order:1+r_order),atomall(), if glob_check_sign*glob_min_h >= glob_check_sign*glob_h then ( omniout_str(always, "SETTING H FOR MIN H"), glob_h:glob_check_sign*abs(glob_min_h), glob_h_reason:1,found_h:true), if glob_check_sign*glob_display_interval <= glob_check_sign*glob_h then ( omniout_str(always, "SETTING H FOR DISPLAY INTERVAL"), glob_h_reason:2, glob_h:glob_display_interval, found_h:true), if glob_look_poles then check_for_pole(), if not found_h then (est_answer:est_size_answer(), est_needed_step_err :estimated_needed_step_error( x_start,x_end,glob_h, est_answer), omniout_float(always, "est_needed_step_err", 32, est_needed_step_err, 16,""), estimated_step_error :test_suggested_h(), omniout_float(always, "estimated_step_error", 32, estimated_step_error, 32,""), if estimated_step_error < est_needed_step_err then ( omniout_str(always, "Double H and LOOP"), glob_h:glob_h*glob__2) else ( omniout_str(always, "Found H for OPTIMAL"), found_h:true,glob_h_reason:3, glob_h:glob_h/glob__2)), opt_iter:1+opt_iter), if not found_h and opt_iter = 1 then (omniout_str(always, "Beginning glob_h too large."), found_h:false), if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then (omniout_str(always, "SETTING H FOR MAX H"), glob_h:glob_check_sign*abs(glob_max_h), glob_h_reason:1,found_h:true)) else (found_h:true,glob_h:glob_h*glob_check_sign), if glob_html_log then html_log_file:openw("entry.html"), if found_h then (omniout_str(always,"START of Soultion"), array_x[1]:c(x_start),array_x[2]:c(glob_h), glob_next_display:c(x_start), glob_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float,order_diff:1, term_no:1, while term_no <= order_diff do (array_y[term_no] :array_y_init[term_no] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no),rows:order_diff, r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < ats_max_terms then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no), r_order:1+r_order),current_iter:1, glob_clock_start_sec:elapsed_time_seconds(), glob_clock_sec:elapsed_time_seconds(),glob_iter:0, omniout_str(debugl," "), glob_reached_optimal_h:true, glob_optimal_clock_start_sec :elapsed_time_seconds(), while glob_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec-glob_orig_start_sec < glob_max_sec do (if reached_interval() then (omniout_str(info," "), omniout_str(info, "TOP MAIN SOLVE Loop")), glob_iter:1+glob_iter, glob_clock_sec:elapsed_time_seconds(), track_estimated_error(),atomall(), track_estimated_error(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display :glob_display_interval +glob_next_display, array_x[1]:glob_h+array_x[1], array_x[2]:glob_h,order_diff:2,ord:2, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[2,iii] :array_y_higher[2,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:2, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:1, calc_term:2,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:1, calc_term:2,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:1, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:1, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)), term_no:ats_max_terms, while term_no >= 1 do ( array_y[term_no] :array_y_higher_work2[1,term_no], ord:1, while ord <= order_diff do ( array_y_higher[ord,term_no] :array_y_higher_work2[ ord,term_no],ord:1+ord), term_no:term_no-1)), omniout_str(always,"Finished!"), if glob_iter >= glob_max_iter then omniout_str(always, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds()-glob_orig_start_sec >= glob_max_sec then omniout_str(always, "Maximum Time Reached before Solution Completed!"), glob_clock_sec:elapsed_time_seconds(), omniout_str(info, "diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , 2.0 ) ; "), 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, "2015-04-24T21:06:43-05:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "expt_lin_c"), logitem_str(html_log_file, "diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , 2.0 ) ; "), 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, "expt_lin_c diffeq.max"), logitem_str(html_log_file, "expt_lin_c maxima results"), logitem_str(html_log_file,"OK"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i255) main():=(glob_iolevel:2,compile(all),main_prog()) (%i256) main() warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable secs in translation. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable sec_temp in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable years_int in translation. warning: encountered undefined variable days_int in translation. warning: encountered undefined variable hours_int in translation. warning: encountered undefined variable minutes_int in translation. warning: encountered undefined variable sec_int in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable iii in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_ats in translation. warning: encountered undefined variable ma_ats in translation. warning: encountered undefined variable ret_ats in translation. warning: encountered undefined variable lll_ats in translation. warning: encountered undefined variable ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_att in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable ma_att in translation. warning: encountered undefined variable lll_att in translation. warning: encountered undefined variable ret_att in translation. warning: encountered undefined variable al_att in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_h_reason in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable errflag in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable sub1 in translation. warning: encountered undefined variable sub2 in translation. warning: encountered undefined variable rrr in translation. warning: encountered undefined variable ms2 in translation. warning: encountered undefined variable sec_left in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ret in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__m2 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temp in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm0 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm1 in translation. warning: encountered undefined variable rm2 in translation. warning: encountered undefined variable rm3 in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable rm4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__8 in translation. warning: encountered undefined variable glob__5 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable nr1 in translation. warning: encountered undefined variable dr2 in translation. warning: encountered undefined variable nr2 in translation. warning: encountered undefined variable dr1 in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable ds1 in translation. warning: encountered undefined variable ds2 in translation. warning: encountered undefined variable rcs in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable ord_no in translation. warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any. warning: encountered undefined variable rad_c in translation. warning: encountered undefined variable glob_six_term_ord_save in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_2 in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob_log_10 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob__10 in translation. warning: encountered undefined variable ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_x in translation. warning: encountered undefined variable array_given_rad_poles in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable rad_given in translation. warning: encountered undefined variable array_given_ord_poles in translation. warning: variable glob_least_given_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable array_rad_test_poles in translation. warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable array_ord_test_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: variable glob_least_3_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob__small in translation. warning: variable glob_least_6_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_estimated_size_answer in translation. warning: encountered undefined variable array_y in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob__small in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable array_max_est_error in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_next_display in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__10 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable always in translation. warning: encountered undefined variable ind_var in translation. warning: encountered undefined variable closed_form_val_y in translation. warning: encountered undefined variable term_no in translation. warning: encountered undefined variable numeric_val in translation. warning: encountered undefined variable abserr in translation. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable relerr in translation. warning: variable glob_good_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_apfp_est_good_digits in translation. warning: encountered undefined variable glob_min_apfp_est_good_digits in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable est_rel_err in translation. warning: variable glob_est_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_est_digits in translation. warning: encountered undefined variable array_est_digits in translation. warning: encountered undefined variable array_1st_rel_error in translation. warning: encountered undefined variable array_last_rel_error in translation. warning: encountered undefined variable array_est_rel_error in translation. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable clock_sec1 in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_clock_start_sec in translation. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_optimal_clock_start_sec in translation. warning: encountered undefined variable opt_clock_sec in translation. warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_optimal_expect_sec in translation. warning: encountered undefined variable total_clock_sec in translation. warning: variable glob_total_exp_sec (declared type convfloat) assigned type any. warning: encountered undefined variable percent_done in translation. warning: variable glob_percent_done (declared type convfloat) assigned type any. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable expect_sec in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable left_sec in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable last_no in translation. warning: encountered undefined variable found_sing in translation. warning: encountered undefined variable array_y_higher in translation. warning: variable tmp_rad (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_rad in translation. warning: encountered undefined variable prev_tmp_rad in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable cnt in translation. warning: encountered undefined variable tmp_ratio in translation. warning: encountered undefined variable glob_upper_ratio_limit in translation. warning: encountered undefined variable glob_lower_ratio_limit in translation. warning: variable tmp_ord (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_ord in translation. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_ratio_of_radius in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable h_new in translation. warning: variable ratio (declared type convfloat) assigned type any. warning: encountered undefined variable term in translation. warning: encountered undefined variable ratio in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_const_0D2 in translation. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_const_0D3 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_const_2D0 in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp4 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temporary in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable array_y_set_initial in translation. warning: encountered undefined variable kkk in translation. warning: encountered undefined variable order_d in translation. warning: encountered undefined variable adj3 in translation. warning: encountered undefined variable adj2 in translation. modedeclare: [found_h] is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: variable term (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable array_y_init in translation. warning: variable term (declared type [found_h]) assigned type any. warning: encountered undefined variable array_norms in translation. warning: encountered undefined variable array_fact_1 in translation. warning: encountered undefined variable array_type_pole in translation. warning: encountered undefined variable array_type_real_pole in translation. warning: encountered undefined variable array_type_complex_pole in translation. warning: encountered undefined variable array_tmp0 in translation. warning: encountered undefined variable array_tmp3_c1 in translation. warning: encountered undefined variable array_tmp3_a1 in translation. warning: encountered undefined variable array_tmp3_a2 in translation. warning: encountered undefined variable array_m1 in translation. warning: variable ord (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable ord in translation. warning: variable ord (declared type [found_h]) assigned type any. warning: encountered undefined variable array_y_higher_work in translation. warning: encountered undefined variable array_y_higher_work2 in translation. warning: encountered undefined variable array_const_1 in translation. warning: encountered undefined variable glob__m1 in translation. warning: variable iiif (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable iiif in translation. warning: encountered undefined variable ats_max_terms in translation. warning: variable jjjf (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable jjjf in translation. warning: variable jjjf (declared type [found_h]) assigned type any. warning: variable iiif (declared type [found_h]) assigned type any. warning: variable glob_orig_start_sec (declared type convfloat) assigned type any. warning: variable opt_iter (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob__0 in translation. warning: variable glob_large_float (declared type convfloat) assigned type any. warning: variable glob_larger_float (declared type convfloat) assigned type any. warning: variable glob_almost_1 (declared type convfloat) assigned type any. warning: variable x_start (declared type [found_h]) assigned type any. warning: variable x_end (declared type [found_h]) assigned type any. warning: encountered undefined variable x_start in translation. warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_h (declared type convfloat) assigned type any. warning: variable glob_display_interval (declared type convfloat) assigned type any. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_max_minutes in translation. warning: encountered undefined variable glob_max_hours in translation. warning: encountered undefined variable x_end in translation. warning: variable glob_check_sign (declared type convfloat) assigned type any. warning: encountered undefined variable glob_larger_float in translation. warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_max_h in translation. warning: encountered undefined variable glob_display_interval in translation. warning: encountered undefined variable glob__10 in translation. warning: variable display_max (declared type [found_h]) assigned type any. warning: encountered undefined variable display_max in translation. warning: variable min_value (declared type [found_h]) assigned type convfloat. warning: variable est_answer (declared type [found_h]) assigned type any. warning: encountered undefined variable est_answer in translation. warning: variable est_needed_step_err (declared type [found_h]) assigned type any. warning: encountered undefined variable est_needed_step_err in translation. warning: encountered undefined variable glob_small_float in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable opt_iter in translation. warning: encountered undefined variable found_h in translation. warning: variable glob_next_display (declared type convfloat) assigned type any. warning: variable order_diff (declared type [found_h]) assigned type fixnum. warning: variable term_no (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable order_diff in translation. warning: variable term_no (declared type [found_h]) assigned type any. warning: variable r_order (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable r_order in translation. warning: encountered undefined variable rows in translation. warning: variable it (declared type [found_h]) assigned type any. warning: encountered undefined variable it in translation. warning: variable r_order (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_look_poles in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type any. warning: encountered undefined variable estimated_step_error in translation. warning: encountered undefined variable glob__2 in translation. warning: variable opt_iter (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_optimize in translation. warning: variable html_log_file (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_html_log in translation. warning: variable current_iter (declared type [found_h]) assigned type fixnum. warning: variable glob_clock_start_sec (declared type convfloat) assigned type any. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable debugl in translation. warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable info in translation. warning: encountered undefined variable current_iter in translation. warning: encountered undefined variable glob_next_display in translation. warning: variable calc_term (declared type [found_h]) assigned type fixnum. warning: variable iii (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable calc_term in translation. warning: variable iii (declared type [found_h]) assigned type any. warning: variable temp_sum (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable temp_sum in translation. warning: variable temp_sum (declared type [found_h]) assigned type any. warning: encountered undefined variable html_log_file in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob_percent_done in translation. warning: encountered undefined variable glob__100 in translation. WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB__PI is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $LAST_MIN_POLE_EST is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. "##############ECHO OF PROBLEM#################" "##############temp/expt_lin_cpostode.ode#################" "diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , 2.0 ) ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:c(0.1)," "x_end:c(5.0)," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "" "" "" "" "" "" "" "glob_type_given_pole:3," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:8," "glob_max_minutes:(3.0)," "glob_subiter_method:3," "glob_max_iter:100000," "glob_upper_ratio_limit:c(1.000001)," "glob_lower_ratio_limit:c(0.999999)," "glob_look_poles:false," "glob_h:c(0.001)," "glob_display_interval:c(0.01)," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" "" " (c(5.0)/c(3.0) * expt((c(0.2) * c(x) + c(0.3)),c(3.0))) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (closed_form) = 5.46133333333333400E-2 " " y[1] (numeric) = 5.46133333333333400E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 15 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000001 " " y[1] (closed_form) = 5.564374666666667000E-2 " " y[1] (numeric) = 5.56437466666666900E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 2.49404266232272400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12000000000000002 " " y[1] (closed_form) = 5.668704000000000000E-2 " " y[1] (numeric) = 5.66870400000000200E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 4.896282398168773000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.13000000000000003 " " y[1] (closed_form) = 5.774329333333333000E-2 " " y[1] (numeric) = 5.774329333333336000E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 3.605038872922214400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.14000000000000004 " " y[1] (closed_form) = 5.88125866666666800E-2 " " y[1] (numeric) = 5.88125866666666900E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 2.359662887549885400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000005 " " y[1] (closed_form) = 5.989500000000001000E-2 " " y[1] (numeric) = 5.989500000000002000E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 3.47552912792748700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000006 " " y[1] (closed_form) = 6.099061333333334000E-2 " " y[1] (numeric) = 6.09906133333333700E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 3.41309597887658800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000007 " " y[1] (closed_form) = 6.20995066666666700E-2 " " y[1] (numeric) = 6.20995066666667000E-2 " " absolute error = 3.46944695195361400000000000000000E-17 " " relative error = 5.58691548159418700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000008 " " y[1] (closed_form) = 6.32217600E-2 " " y[1] (numeric) = 6.32217600000000300E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 4.3901934421991600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000009 " " y[1] (closed_form) = 6.43574533333333300E-2 " " y[1] (numeric) = 6.43574533333333600E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 4.31272124331451400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2000000000000001 " " y[1] (closed_form) = 6.55066666666666900E-2 " " y[1] (numeric) = 6.55066666666666700E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 2.118530603676132800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2100000000000001 " " y[1] (closed_form) = 6.66694800E-2 " " y[1] (numeric) = 6.66694800000000400E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 4.16316065696461300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2200000000000001 " " y[1] (closed_form) = 6.78459733333333500E-2 " " y[1] (numeric) = 6.78459733333333600E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 2.045484370845656600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.23000000000000012 " " y[1] (closed_form) = 6.90362266666666700E-2 " " y[1] (numeric) = 6.90362266666667100E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 6.03065454670128200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.24000000000000013 " " y[1] (closed_form) = 7.02403200000000100E-2 " " y[1] (numeric) = 7.02403200000000700E-2 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 7.9030322229821590000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (closed_form) = 7.14583333333333500E-2 " " y[1] (numeric) = 7.1458333333333400E-2 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 7.7683243705550300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (closed_form) = 7.26903466666666800E-2 " " y[1] (numeric) = 7.26903466666667500E-2 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 9.54582585185161700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (closed_form) = 7.39364400000000400E-2 " " y[1] (numeric) = 7.39364400000000900E-2 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 7.50795564829166900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (closed_form) = 7.51966933333333400E-2 " " y[1] (numeric) = 7.51966933333334100E-2 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 9.22765828697861300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (closed_form) = 7.64711866666666800E-2 " " y[1] (numeric) = 7.64711866666667400E-2 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 7.25909373856425300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (closed_form) = 7.77600000000000100E-2 " " y[1] (numeric) = 7.77600000000000600E-2 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 7.1387797365300700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (closed_form) = 7.90632133333333400E-2 " " y[1] (numeric) = 7.90632133333334200E-2 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 8.77638741376802300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (closed_form) = 8.0380906666666700E-2 " " y[1] (numeric) = 8.03809066666667400E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 5.179509058798460000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (closed_form) = 8.17131600000000400E-2 " " y[1] (numeric) = 8.17131600000000700E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 5.095062218061736000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (closed_form) = 8.30600533333333700E-2 " " y[1] (numeric) = 8.30600533333334200E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 5.01244121001969200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (closed_form) = 8.4421666666666710E-2 " " y[1] (numeric) = 8.44216666666667300E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 3.28773130305753700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y[1] (closed_form) = 8.57980800000000200E-2 " " y[1] (numeric) = 8.57980800000000700E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 4.85248194638427300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y[1] (closed_form) = 8.71893733333333400E-2 " " y[1] (numeric) = 8.71893733333334200E-2 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 7.95841699352416600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y[1] (closed_form) = 8.85956266666666900E-2 " " y[1] (numeric) = 8.85956266666667600E-2 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 7.83209529067863700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (closed_form) = 9.00169200000000300E-2 " " y[1] (numeric) = 9.0016920000000100E-2 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 7.70843293006162200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y[1] (closed_form) = 9.14533333333333800E-2 " " y[1] (numeric) = 9.14533333333334400E-2 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 7.58736029731800400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (closed_form) = 9.29049466666667100E-2 " " y[1] (numeric) = 9.2904946666666800E-2 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 8.9625719441655890000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y[1] (closed_form) = 9.43718400000000500E-2 " " y[1] (numeric) = 9.43718400000001500E-2 " " absolute error = 9.7144514654701200000000000000000E-17 " " relative error = 1.02938031784376720000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y[1] (closed_form) = 9.58540933333333700E-2 " " y[1] (numeric) = 9.58540933333334900E-2 " " absolute error = 1.2490009027033011000000000000000E-16 " " relative error = 1.3030230209991040000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y[1] (closed_form) = 9.73517866666666800E-2 " " y[1] (numeric) = 9.73517866666668200E-2 " " absolute error = 1.2490009027033011000000000000000E-16 " " relative error = 1.28297686716309620000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y[1] (closed_form) = 9.88650000000000400E-2 " " y[1] (numeric) = 9.88650000000001400E-2 " " absolute error = 9.7144514654701200000000000000000E-17 " " relative error = 9.82597629643464900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000003 " " y[1] (closed_form) = 0.10039381333333339 " " y[1] (numeric) = 0.10039381333333348 " " absolute error = 9.7144514654701200000000000000000E-17 " " relative error = 9.67634472974508100000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000003 " " y[1] (closed_form) = 0.10193830666666673 " " y[1] (numeric) = 0.10193830666666683 " " absolute error = 9.7144514654701200000000000000000E-17 " " relative error = 9.5297359580789400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000003 " " y[1] (closed_form) = 0.10349856000000006 " " y[1] (numeric) = 0.10349856000000017 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.0726941752862610000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4900000000000003 " " y[1] (closed_form) = 0.10507465333333339 " " y[1] (numeric) = 0.10507465333333348 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 7.92453024638926900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000003 " " y[1] (closed_form) = 0.1066666666666667 " " y[1] (numeric) = 0.10666666666666681 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.04083408558608380000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000003 " " y[1] (closed_form) = 0.10827468000000005 " " y[1] (numeric) = 0.10827468000000016 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.02537640806249070000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000004 " " y[1] (closed_form) = 0.1098987733333334 " " y[1] (numeric) = 0.1098987733333335 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.01022330909713130000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000004 " " y[1] (closed_form) = 0.11153902666666672 " " y[1] (numeric) = 0.11153902666666685 " " absolute error = 1.2490009027033011000000000000000E-16 " " relative error = 1.11978823917473130000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000004 " " y[1] (closed_form) = 0.11319552000000005 " " y[1] (numeric) = 0.11319552000000019 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.2260015067570210000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000004 " " y[1] (closed_form) = 0.1148683333333334 " " y[1] (numeric) = 0.11486833333333354 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.20814739842554060000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000004 " " y[1] (closed_form) = 0.11655754666666672 " " y[1] (numeric) = 0.11655754666666689 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.42876594829186580000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5700000000000004 " " y[1] (closed_form) = 0.11826324000000007 " " y[1] (numeric) = 0.11826324000000021 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.17346588913126760000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5800000000000004 " " y[1] (closed_form) = 0.11998549333333342 " " y[1] (numeric) = 0.11998549333333354 " " absolute error = 1.2490009027033011000000000000000E-16 " " relative error = 1.04095992607492460000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5900000000000004 " " y[1] (closed_form) = 0.12172438666666673 " " y[1] (numeric) = 0.12172438666666688 " " absolute error = 1.52655665885959020000000000000000E-16 " " relative error = 1.25410914005256280000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6000000000000004 " " y[1] (closed_form) = 0.12348000000000009 " " y[1] (numeric) = 0.12348000000000019 " " absolute error = 9.7144514654701200000000000000000E-17 " " relative error = 7.86722664842088700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000004 " " y[1] (closed_form) = 0.1252524133333334 " " y[1] (numeric) = 0.12525241333333353 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.10798566179172870000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000004 " " y[1] (closed_form) = 0.12704170666666673 " " y[1] (numeric) = 0.12704170666666684 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 8.73904368695369100000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6300000000000004 " " y[1] (closed_form) = 0.12884796000000004 " " y[1] (numeric) = 0.12884796000000018 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.07706694058753060000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6400000000000005 " " y[1] (closed_form) = 0.13067125333333335 " " y[1] (numeric) = 0.1306712533333335 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.06203831782443970000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000005 " " y[1] (closed_form) = 0.1325116666666667 " " y[1] (numeric) = 0.13251166666666683 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.04728799787297630000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000005 " " y[1] (closed_form) = 0.13436928000000004 " " y[1] (numeric) = 0.1343692800000002 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.23937148203647010000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000005 " " y[1] (closed_form) = 0.13624417333333336 " " y[1] (numeric) = 0.13624417333333358 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.62975486945617600000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6800000000000005 " " y[1] (closed_form) = 0.1381364266666667 " " y[1] (numeric) = 0.1381364266666669 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.40650105115456640000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000005 " " y[1] (closed_form) = 0.14004612000000002 " " y[1] (numeric) = 0.14004612000000022 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.38732175735680750000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000005 " " y[1] (closed_form) = 0.1419733333333334 " " y[1] (numeric) = 0.14197333333333353 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 9.77492567229605400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000005 " " y[1] (closed_form) = 0.14391814666666672 " " y[1] (numeric) = 0.14391814666666686 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 9.64283388109300100000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000005 " " y[1] (closed_form) = 0.14588064000000006 " " y[1] (numeric) = 0.1458806400000002 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 9.51311140931000200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000005 " " y[1] (closed_form) = 0.14786089333333338 " " y[1] (numeric) = 0.14786089333333355 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.1262846445702530000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000005 " " y[1] (closed_form) = 0.14985898666666672 " " y[1] (numeric) = 0.14985898666666686 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 9.26056429213884900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000006 " " y[1] (closed_form) = 0.1518750000000001 " " y[1] (numeric) = 0.1518750000000002 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 7.31011045020678700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000006 " " y[1] (closed_form) = 0.15390901333333346 " " y[1] (numeric) = 0.15390901333333354 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.410126739396940000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000006 " " y[1] (closed_form) = 0.15596110666666677 " " y[1] (numeric) = 0.15596110666666688 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 7.11858904026642200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000006 " " y[1] (closed_form) = 0.15803136000000012 " " y[1] (numeric) = 0.15803136000000023 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 7.02533360862777800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000006 " " y[1] (closed_form) = 0.16011985333333345 " " y[1] (numeric) = 0.16011985333333356 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 6.93369998481026900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000006 " " y[1] (closed_form) = 0.1622266666666668 " " y[1] (numeric) = 0.16222666666666688 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.132739799060163000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000006 " " y[1] (closed_form) = 0.16435188000000014 " " y[1] (numeric) = 0.1643518800000002 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.37757932743195700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000006 " " y[1] (closed_form) = 0.16649557333333345 " " y[1] (numeric) = 0.1664955733333335 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.33409171907059600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000006 " " y[1] (closed_form) = 0.1686578266666668 " " y[1] (numeric) = 0.16865782666666687 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.937021215828545400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000006 " " y[1] (closed_form) = 0.17083872000000014 " " y[1] (numeric) = 0.17083872000000017 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.624665392929008600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000006 " " y[1] (closed_form) = 0.1730383333333335 " " y[1] (numeric) = 0.17303833333333352 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.604013115530983600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000007 " " y[1] (closed_form) = 0.1752567466666668 " " y[1] (numeric) = 0.17525674666666682 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.583709394561523300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8700000000000007 " " y[1] (closed_form) = 0.17749404000000013 " " y[1] (numeric) = 0.17749404000000013 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000007 " " y[1] (closed_form) = 0.17975029333333348 " " y[1] (numeric) = 0.1797502933333335 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.544118515798929800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000007 " " y[1] (closed_form) = 0.18202558666666682 " " y[1] (numeric) = 0.18202558666666682 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000007 " " y[1] (closed_form) = 0.18432000000000015 " " y[1] (numeric) = 0.18432000000000015 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000007 " " y[1] (closed_form) = 0.18663361333333348 " " y[1] (numeric) = 0.1866336133333335 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.487169171721311700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000007 " " y[1] (closed_form) = 0.18896650666666684 " " y[1] (numeric) = 0.1889665066666668 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.468809267061765600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000007 " " y[1] (closed_form) = 0.19131876000000017 " " y[1] (numeric) = 0.19131876000000014 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.450750340198153400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000007 " " y[1] (closed_form) = 0.1936904533333335 " " y[1] (numeric) = 0.19369045333333346 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.86597249765972500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000007 " " y[1] (closed_form) = 0.19608166666666685 " " y[1] (numeric) = 0.19608166666666677 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.24653300139669700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9600000000000007 " " y[1] (closed_form) = 0.1984924800000002 " " y[1] (numeric) = 0.1984924800000001 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.19495624453312570000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000008 " " y[1] (closed_form) = 0.20092297333333353 " " y[1] (numeric) = 0.20092297333333342 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.525615145975785000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000008 " " y[1] (closed_form) = 0.20337322666666682 " " y[1] (numeric) = 0.20337322666666674 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.094281642261728400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000008 " " y[1] (closed_form) = 0.2058433200000002 " " y[1] (numeric) = 0.2058433200000001 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.04515078977965700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0000000000000007 " " y[1] (closed_form) = 0.20833333333333345 " " y[1] (numeric) = 0.20833333333333345 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0099999999999996 " " y[1] (closed_form) = 0.21084334666666651 " " y[1] (numeric) = 0.21084334666666682 " " absolute error = 3.05311331771918050000000000000000E-16 " " relative error = 1.44804821493656620000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0199999999999985 " " y[1] (closed_form) = 0.2133734399999996 " " y[1] (numeric) = 0.21337344000000016 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.6015961138958030000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0299999999999974 " " y[1] (closed_form) = 0.2159236933333326 " " y[1] (numeric) = 0.21592369333333347 " " absolute error = 8.6042284408449630000000000000000E-16 " " relative error = 3.9848468262175240000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0399999999999963 " " y[1] (closed_form) = 0.21849418666666567 " " y[1] (numeric) = 0.2184941866666668 " " absolute error = 1.1379786002407855000000000000000E-15 " " relative error = 5.2082786164781750000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0499999999999952 " " y[1] (closed_form) = 0.22108499999999873 " " y[1] (numeric) = 0.22108500000000014 " " absolute error = 1.4155343563970746000000000000000E-15 " " relative error = 6.4026702688879070000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.059999999999994 " " y[1] (closed_form) = 0.22369621333333176 " " y[1] (numeric) = 0.22369621333333345 " " absolute error = 1.6930901125533637000000000000000E-15 " " relative error = 7.5687026048602560000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.069999999999993 " " y[1] (closed_form) = 0.2263279066666648 " " y[1] (numeric) = 0.22632790666666677 " " absolute error = 1.970645868709652900000000000000E-15 " " relative error = 8.7070388169675230000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0799999999999919 " " y[1] (closed_form) = 0.22898015999999774 " " y[1] (numeric) = 0.22898016000000015 " " absolute error = 2.4147350785597155000000000000000E-15 " " relative error = 1.054560831191549000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0899999999999908 " " y[1] (closed_form) = 0.23165305333333078 " " y[1] (numeric) = 0.2316530533333335 " " absolute error = 2.7200464103316335000000000000000E-15 " " relative error = 1.174189751091991000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0999999999999897 " " y[1] (closed_form) = 0.2343466666666638 " " y[1] (numeric) = 0.23434666666666684 " " absolute error = 3.0531133177191805000000000000000E-15 " " relative error = 1.3028191785897890000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1099999999999886 " " y[1] (closed_form) = 0.23706107999999682 " " y[1] (numeric) = 0.23706108000000015 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.4049835063079583000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1199999999999875 " " y[1] (closed_form) = 0.23979637333332982 " " y[1] (numeric) = 0.2397963733333334 " " absolute error = 3.58046925441613000000000000000E-15 " " relative error = 1.4931290263673360000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1299999999999863 " " y[1] (closed_form) = 0.24255262666666286 " " y[1] (numeric) = 0.24255262666666672 " " absolute error = 3.858025010572419000000000000000E-15 " " relative error = 1.5905929626870033000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1399999999999852 " " y[1] (closed_form) = 0.24532991999999584 " " y[1] (numeric) = 0.24532992 " " absolute error = 4.163336342344337000000000000000E-15 " " relative error = 1.6970357069958722000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1499999999999841 " " y[1] (closed_form) = 0.2481283333333288 " " y[1] (numeric) = 0.2481283333333333 " " absolute error = 4.524158825347513000000000000000E-15 " " relative error = 1.8233140748460525000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.159999999999983 " " y[1] (closed_form) = 0.2509479466666618 " " y[1] (numeric) = 0.2509479466666666 " " absolute error = 4.773959005888173000000000000000E-15 " " relative error = 1.9023702203188372000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.169999999999982 " " y[1] (closed_form) = 0.2537888399999948 " " y[1] (numeric) = 0.25378883999999985 " " absolute error = 5.051514762044462000000000000000E-15 " " relative error = 1.990440069013501800000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1799999999999808 " " y[1] (closed_form) = 0.2566510933333278 " " y[1] (numeric) = 0.2566510933333332 " " absolute error = 5.384581669432009000000000000000E-15 " " relative error = 2.098016259934157900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1899999999999797 " " y[1] (closed_form) = 0.25953478666666074 " " y[1] (numeric) = 0.2595347866666665 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 2.224426175079836000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1999999999999786 " " y[1] (closed_form) = 0.26243999999999373 " " y[1] (numeric) = 0.2624399999999998 " " absolute error = 6.050715484207103000000000000000E-15 " " relative error = 2.305561455649767000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2099999999999775 " " y[1] (closed_form) = 0.2653668133333267 " " y[1] (numeric) = 0.2653668133333331 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 2.4265632397437448000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2199999999999764 " " y[1] (closed_form) = 0.26831530666665965 " " y[1] (numeric) = 0.26831530666666636 " " absolute error = 6.716849298982197000000000000000E-15 " " relative error = 2.503341826609559000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2299999999999753 " " y[1] (closed_form) = 0.2712855599999926 " " y[1] (numeric) = 0.2712855599999996 " " absolute error = 6.994405055138486000000000000000E-15 " " relative error = 2.5782445092686385000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2399999999999742 " " y[1] (closed_form) = 0.27427765333332554 " " y[1] (numeric) = 0.27427765333333287 " " absolute error = 7.327471962526033000000000000000E-15 " " relative error = 2.671552666968849000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2499999999999731 " " y[1] (closed_form) = 0.27729166666665844 " " y[1] (numeric) = 0.27729166666666616 " " absolute error = 7.716050021144838000000000000000E-15 " " relative error = 2.7826476409839457000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.259999999999972 " " y[1] (closed_form) = 0.2803276799999914 " " y[1] (numeric) = 0.2803276799999994 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 2.851522110589068700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.269999999999971 " " y[1] (closed_form) = 0.2833857733333244 " " y[1] (numeric) = 0.2833857733333326 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 2.899104738247652000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2799999999999698 " " y[1] (closed_form) = 0.28646602666665727 " " y[1] (numeric) = 0.2864660266666658 " " absolute error = 8.548717289613705000000000000000E-15 " " relative error = 2.9841993443646000000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2899999999999687 " " y[1] (closed_form) = 0.28956851999999017 " " y[1] (numeric) = 0.2895685199999991 " " absolute error = 8.93729534823251000000000000000E-15 " " relative error = 3.0864181466385965000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2999999999999676 " " y[1] (closed_form) = 0.29269333333332315 " " y[1] (numeric) = 0.29269333333333236 " " absolute error = 9.2148511043887990000000000000E-15 " " relative error = 3.148295521269971000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3099999999999665 " " y[1] (closed_form) = 0.29584054666665605 " " y[1] (numeric) = 0.29584054666666554 " " absolute error = 9.492406860545088000000000000000E-15 " " relative error = 3.2086226744438917000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3199999999999654 " " y[1] (closed_form) = 0.29901023999998894 " " y[1] (numeric) = 0.29901023999999876 " " absolute error = 9.825473767932635000000000000000E-15 " " relative error = 3.285999090844848000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3299999999999643 " " y[1] (closed_form) = 0.3022024933333219 " " y[1] (numeric) = 0.3022024933333321 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 3.3798701373669980000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3399999999999632 " " y[1] (closed_form) = 0.30541738666665474 " " y[1] (numeric) = 0.30541738666666535 " " absolute error = 1.060262988517024500000000000000E-14 " " relative error = 3.4715213828813213000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3499999999999621 " " y[1] (closed_form) = 0.3086549999999877 " " y[1] (numeric) = 0.3086549999999986 " " absolute error = 1.093569679255779200000000000000E-14 " " relative error = 3.5430162455033054000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.359999999999961 " " y[1] (closed_form) = 0.31191541333332046 " " y[1] (numeric) = 0.31191541333333195 " " absolute error = 1.14908083048703700000000000000E-14 " " relative error = 3.683950139581917000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.36999999999996 " " y[1] (closed_form) = 0.3151987066666534 " " y[1] (numeric) = 0.3151987066666652 " " absolute error = 1.182387521225791700000000000000E-14 " " relative error = 3.7512448376771307000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3799999999999588 " " y[1] (closed_form) = 0.31850495999998624 " " y[1] (numeric) = 0.31850495999999845 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 3.834305522550496300000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3899999999999577 " " y[1] (closed_form) = 0.32183425333331916 " " y[1] (numeric) = 0.32183425333333165 " " absolute error = 1.249000902703301100000000000000E-14 " " relative error = 3.880882441092211600000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3999999999999566 " " y[1] (closed_form) = 0.325186666666652 " " y[1] (numeric) = 0.3251866666666649 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 3.960367507580998500000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4099999999999555 " " y[1] (closed_form) = 0.3285622799999849 " " y[1] (numeric) = 0.3285622799999982 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 4.054840469058862000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4199999999999544 " " y[1] (closed_form) = 0.3319611733333177 " " y[1] (numeric) = 0.33196117333333147 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 4.147101110384653000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4299999999999533 " " y[1] (closed_form) = 0.33538342666665055 " " y[1] (numeric) = 0.33538342666666476 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 4.237196469856179000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4399999999999522 " " y[1] (closed_form) = 0.33882911999998344 " " y[1] (numeric) = 0.3388291199999979 " " absolute error = 1.443289932012703500000000000000E-14 " " relative error = 4.2596395847345536000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.449999999999951 " " y[1] (closed_form) = 0.3422983333333162 " " y[1] (numeric) = 0.342298333333331 " " absolute error = 1.476596622751458200000000000000E-14 " " relative error = 4.3137709972826780000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.45999999999995 " " y[1] (closed_form) = 0.34579114666664906 " " y[1] (numeric) = 0.3457911466666642 " " absolute error = 1.515454428613338700000000000000E-14 " " relative error = 4.382571512376727000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.469999999999949 " " y[1] (closed_form) = 0.34930763999998193 " " y[1] (numeric) = 0.3493076399999973 " " absolute error = 1.537658889105841800000000000000E-14 " " relative error = 4.402019060063849000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4799999999999478 " " y[1] (closed_form) = 0.35284789333331473 " " y[1] (numeric) = 0.35284789333333055 " " absolute error = 1.58206781009084800000000000000E-14 " " relative error = 4.483710516577638000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4899999999999467 " " y[1] (closed_form) = 0.35641198666664753 " " y[1] (numeric) = 0.35641198666666385 " " absolute error = 1.6320278461989800000000000000E-14 " " relative error = 4.57904870557963970000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4999999999999456 " " y[1] (closed_form) = 0.35999999999998034 " " y[1] (numeric) = 0.3599999999999971 " " absolute error = 1.676436767183986400000000000000E-14 " " relative error = 4.65676879773355000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5099999999999445 " " y[1] (closed_form) = 0.3636120133333134 " " y[1] (numeric) = 0.3636120133333304 " " absolute error = 1.698641227676489500000000000000E-14 " " relative error = 4.671576200424904000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5199999999999434 " " y[1] (closed_form) = 0.36724810666664615 " " y[1] (numeric) = 0.36724810666666363 " " absolute error = 1.748601263784621600000000000000E-14 " " relative error = 4.761362229082477000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5299999999999423 " " y[1] (closed_form) = 0.37090835999997895 " " y[1] (numeric) = 0.37090835999999694 " " absolute error = 1.798561299892753600000000000000E-14 " " relative error = 4.849071883666509000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5399999999999412 " " y[1] (closed_form) = 0.3745928533333117 " " y[1] (numeric) = 0.37459285333333014 " " absolute error = 1.8429702208777599000000000000E-14 " " relative error = 4.91992894279243000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.54999999999994 " " y[1] (closed_form) = 0.3783016666666445 " " y[1] (numeric) = 0.37830166666666326 " " absolute error = 1.876276911616514600000000000000E-14 " " relative error = 4.959737365550309000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.559999999999939 " " y[1] (closed_form) = 0.38203487999997726 " " y[1] (numeric) = 0.38203487999999636 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 4.998453550511887700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.569999999999938 " " y[1] (closed_form) = 0.38579257333331 " " y[1] (numeric) = 0.38579257333332956 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 5.0648785342275130000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5799999999999368 " " y[1] (closed_form) = 0.38957482666664284 " " y[1] (numeric) = 0.3895748266666626 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 5.072701952387185000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5899999999999357 " " y[1] (closed_form) = 0.39338171999997557 " " y[1] (numeric) = 0.3933817199999958 " " absolute error = 2.026157019940910700000000000000E-14 " " relative error = 5.150613048163591000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5999999999999346 " " y[1] (closed_form) = 0.39721333333330827 " " y[1] (numeric) = 0.39721333333332903 " " absolute error = 2.076117056049042700000000000000E-14 " " relative error = 5.22670535408976000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6099999999999335 " " y[1] (closed_form) = 0.4010697466666411 " " y[1] (numeric) = 0.40106974666666223 " " absolute error = 2.114974861910923200000000000000E-14 " " relative error = 5.273334325236045000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6199999999999324 " " y[1] (closed_form) = 0.40495103999997384 " " y[1] (numeric) = 0.40495103999999543 " " absolute error = 2.159383782895929500000000000000E-14 " " relative error = 5.33245644435453000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6299999999999313 " " y[1] (closed_form) = 0.40885729333330656 " " y[1] (numeric) = 0.4088572933333286 " " absolute error = 2.203792703880935700000000000000E-14 " " relative error = 5.390126921581831000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6399999999999302 " " y[1] (closed_form) = 0.41278858666663926 " " y[1] (numeric) = 0.41278858666666174 " " absolute error = 2.24820162486594200000000000000E-14 " " relative error = 5.446375450980067000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.649999999999929 " " y[1] (closed_form) = 0.41674499999997205 " " y[1] (numeric) = 0.41674499999999487 " " absolute error = 2.281508315604696700000000000000E-14 " " relative error = 5.474590734393573000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.659999999999928 " " y[1] (closed_form) = 0.42072661333330474 " " y[1] (numeric) = 0.42072661333332806 " " absolute error = 2.331468351712828700000000000000E-14 " " relative error = 5.54152810358543000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6699999999999269 " " y[1] (closed_form) = 0.4247335066666374 " " y[1] (numeric) = 0.42473350666666126 " " absolute error = 2.386979502944086600000000000000E-14 " " relative error = 5.619946308633396000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6799999999999258 " " y[1] (closed_form) = 0.4287657599999701 " " y[1] (numeric) = 0.4287657599999945 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 5.696561810755400000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6899999999999247 " " y[1] (closed_form) = 0.43282345333330274 " " y[1] (numeric) = 0.43282345333332767 " " absolute error = 2.492450690283476400000000000000E-14 " " relative error = 5.758585102282164000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6999999999999236 " " y[1] (closed_form) = 0.4369066666666355 " " y[1] (numeric) = 0.4369066666666608 " " absolute error = 2.52575738102223100000000000000E-14 " " relative error = 5.780999865011012000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7099999999999225 " " y[1] (closed_form) = 0.4410154799999682 " " y[1] (numeric) = 0.4410154799999939 " " absolute error = 2.570166302007237400000000000000E-14 " " relative error = 5.827836932180754000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7199999999999214 " " y[1] (closed_form) = 0.4451499733333008 " " y[1] (numeric) = 0.44514997333332695 " " absolute error = 2.614575222992243700000000000000E-14 " " relative error = 5.873470469770447000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7299999999999203 " " y[1] (closed_form) = 0.44931022666663356 " " y[1] (numeric) = 0.4493102266666601 " " absolute error = 2.65343302885412400000000000000E-14 " " relative error = 5.905570074688826000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7399999999999192 " " y[1] (closed_form) = 0.4534963199999662 " " y[1] (numeric) = 0.45349631999999324 " " absolute error = 2.703393064962256000000000000000E-14 " " relative error = 5.9612238197709240000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.749999999999918 " " y[1] (closed_form) = 0.4577083333332989 " " y[1] (numeric) = 0.4577083333333263 " " absolute error = 2.73669975570101100000000000000E-14 " " relative error = 5.979134650598926000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.759999999999917 " " y[1] (closed_form) = 0.4619463466666315 " " y[1] (numeric) = 0.46194634666665946 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 6.056465306509783000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7699999999999159 " " y[1] (closed_form) = 0.46621043999996414 " " y[1] (numeric) = 0.46621043999999257 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 6.096326249237617000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7799999999999148 " " y[1] (closed_form) = 0.47050069333329675 " " y[1] (numeric) = 0.47050069333332567 " " absolute error = 2.89213097914853300000000000000E-14 " " relative error = 6.1469218220679300000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7899999999999137 " " y[1] (closed_form) = 0.4748171866666294 " " y[1] (numeric) = 0.4748171866666587 " " absolute error = 2.925437669887287500000000000000E-14 " " relative error = 6.161187404408859000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7999999999999126 " " y[1] (closed_form) = 0.47915999999996206 " " y[1] (numeric) = 0.4791599999999917 " " absolute error = 2.96429547574916800000000000000E-14 " " relative error = 6.186441847711417000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8099999999999115 " " y[1] (closed_form) = 0.4835292133332946 " " y[1] (numeric) = 0.4835292133333248 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 6.245344735559722000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8199999999999104 " " y[1] (closed_form) = 0.48792490666662736 " " y[1] (numeric) = 0.48792490666665794 " " absolute error = 3.05866443284230600000000000000E-14 " " relative error = 6.268719614537173000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8299999999999093 " " y[1] (closed_form) = 0.4923471599999599 " " y[1] (numeric) = 0.492347159999991 " " absolute error = 3.10862446895043830000000000000E-14 " " relative error = 6.3138872761055250000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8399999999999082 " " y[1] (closed_form) = 0.4967960533332926 " " y[1] (numeric) = 0.49679605333332416 " " absolute error = 3.158584505058570400000000000000E-14 " " relative error = 6.357909818054707000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.849999999999907 " " y[1] (closed_form) = 0.501271666666625 " " y[1] (numeric) = 0.5012716666666572 " " absolute error = 3.21964677141295400000000000000E-14 " " relative error = 6.422957820103978000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.859999999999906 " " y[1] (closed_form) = 0.5057740799999577 " " y[1] (numeric) = 0.5057740799999904 " " absolute error = 3.2640556923979600000000000000E-14 " " relative error = 6.453584360033304000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8699999999999048 " " y[1] (closed_form) = 0.5103033733332902 " " y[1] (numeric) = 0.5103033733333235 " " absolute error = 3.330669073875469600000000000000E-14 " " relative error = 6.526841184920283000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8799999999999037 " " y[1] (closed_form) = 0.5148596266666228 " " y[1] (numeric) = 0.5148596266666566 " " absolute error = 3.386180225106727400000000000000E-14 " " relative error = 6.5768998960551950000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8899999999999026 " " y[1] (closed_form) = 0.5194429199999554 " " y[1] (numeric) = 0.5194429199999897 " " absolute error = 3.43058914609173370000000000000E-14 " " relative error = 6.604362123353281000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8999999999999015 " " y[1] (closed_form) = 0.524053333333288 " " y[1] (numeric) = 0.5240533333333228 " " absolute error = 3.486100297322991500000000000000E-14 " " relative error = 6.652186095543634000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9099999999999004 " " y[1] (closed_form) = 0.5286909466666205 " " y[1] (numeric) = 0.528690946666656 " " absolute error = 3.541611448554249400000000000000E-14 " " relative error = 6.6988312754057840000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9199999999998993 " " y[1] (closed_form) = 0.5333558399999531 " " y[1] (numeric) = 0.5333558399999889 " " absolute error = 3.586020369539255600000000000000E-14 " " relative error = 6.723504460998442000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9299999999998982 " " y[1] (closed_form) = 0.5380480933332856 " " y[1] (numeric) = 0.538048093333322 " " absolute error = 3.641531520770513500000000000000E-14 " " relative error = 6.768040935171241000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9399999999998971 " " y[1] (closed_form) = 0.5427677866666182 " " y[1] (numeric) = 0.5427677866666549 " " absolute error = 3.67483821150926800000000000000E-14 " " relative error = 6.77055326749973000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.949999999999896 " " y[1] (closed_form) = 0.5475149999999507 " " y[1] (numeric) = 0.5475149999999879 " " absolute error = 3.719247132494274400000000000000E-14 " " relative error = 6.7929593390036970000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.959999999999895 " " y[1] (closed_form) = 0.5522898133332832 " " y[1] (numeric) = 0.5522898133333211 " " absolute error = 3.78586051397178400000000000000E-14 " " relative error = 6.854844001417748000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9699999999998938 " " y[1] (closed_form) = 0.5570923066666157 " " y[1] (numeric) = 0.5570923066666542 " " absolute error = 3.85247389544929300000000000000E-14 " " relative error = 6.9153241740147620000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9799999999998927 " " y[1] (closed_form) = 0.5619225599999482 " " y[1] (numeric) = 0.5619225599999873 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 6.954668356224941000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9899999999998916 " " y[1] (closed_form) = 0.5667806533332808 " " y[1] (numeric) = 0.5667806533333204 " " absolute error = 3.96349619791180900000000000000E-14 " " relative error = 6.992998392944751000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9999999999998905 " " y[1] (closed_form) = 0.5716666666666131 " " y[1] (numeric) = 0.5716666666666534 " " absolute error = 4.03010957938931800000000000000E-14 " " relative error = 7.049754366279352000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0099999999998897 " " y[1] (closed_form) = 0.5765806799999457 " " y[1] (numeric) = 0.5765806799999864 " " absolute error = 4.074518500374324500000000000000E-14 " " relative error = 7.066692731318553000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0199999999998886 " " y[1] (closed_form) = 0.5815227733332782 " " y[1] (numeric) = 0.5815227733333194 " " absolute error = 4.11892742135933100000000000000E-14 " " relative error = 7.083002782074573000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0299999999998875 " " y[1] (closed_form) = 0.5864930266666107 " " y[1] (numeric) = 0.5864930266666524 " " absolute error = 4.16333634234433700000000000000E-14 " " relative error = 7.098697091092553000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0399999999998863 " " y[1] (closed_form) = 0.5914915199999431 " " y[1] (numeric) = 0.5914915199999855 " " absolute error = 4.24105195406809800000000000000E-14 " " relative error = 7.170097644119237000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0499999999998852 " " y[1] (closed_form) = 0.5965183333332755 " " y[1] (numeric) = 0.5965183333333185 " " absolute error = 4.29656310529935600000000000000E-14 " " relative error = 7.20273437580813000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.059999999999884 " " y[1] (closed_form) = 0.601573546666608 " " y[1] (numeric) = 0.6015735466666515 " " absolute error = 4.352074256530613600000000000000E-14 " " relative error = 7.234484096991939000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.069999999999883 " " y[1] (closed_form) = 0.6066572399999404 " " y[1] (numeric) = 0.6066572399999846 " " absolute error = 4.41868763800812300000000000000E-14 " " relative error = 7.283664228598933000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.079999999999882 " " y[1] (closed_form) = 0.6117694933332729 " " y[1] (numeric) = 0.6117694933333174 " " absolute error = 4.45199432874687800000000000000E-14 " " relative error = 7.277241472911383000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.089999999999881 " " y[1] (closed_form) = 0.6169103866666052 " " y[1] (numeric) = 0.6169103866666504 " " absolute error = 4.51860771022438700000000000000E-14 " " relative error = 7.324577131275247000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0999999999998797 " " y[1] (closed_form) = 0.6220799999999377 " " y[1] (numeric) = 0.6220799999999835 " " absolute error = 4.585221091701896500000000000000E-14 " " relative error = 7.370790077968036000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1099999999998786 " " y[1] (closed_form) = 0.6272784133332702 " " y[1] (numeric) = 0.6272784133333166 " " absolute error = 4.640732242933154300000000000000E-14 " " relative error = 7.398201730349606000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999998775 " " y[1] (closed_form) = 0.6325057066666024 " " y[1] (numeric) = 0.6325057066666494 " " absolute error = 4.69624339416441200000000000000E-14 " " relative error = 7.424823752048500000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999998764 " " y[1] (closed_form) = 0.6377619599999349 " " y[1] (numeric) = 0.6377619599999824 " " absolute error = 4.7517545453956700000000000000E-14 " " relative error = 7.450671008029633000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999998753 " " y[1] (closed_form) = 0.6430472533332674 " " y[1] (numeric) = 0.6430472533333155 " " absolute error = 4.80726569662692800000000000000E-14 " " relative error = 7.475758074866548000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1499999999998742 " " y[1] (closed_form) = 0.6483616666665997 " " y[1] (numeric) = 0.6483616666666484 " " absolute error = 4.87387907810443700000000000000E-14 " " relative error = 7.517222761120887000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.159999999999873 " " y[1] (closed_form) = 0.653705279999932 " " y[1] (numeric) = 0.6537052799999812 " " absolute error = 4.918287999089443500000000000000E-14 " " relative error = 7.523708542005282000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.169999999999872 " " y[1] (closed_form) = 0.6590781733332645 " " y[1] (numeric) = 0.6590781733333141 " " absolute error = 4.9626969200744500000000000000E-14 " " relative error = 7.52975461920668100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.179999999999871 " " y[1] (closed_form) = 0.6644804266665969 " " y[1] (numeric) = 0.6644804266666472 " " absolute error = 5.02931030155195900000000000000E-14 " " relative error = 7.568786227130534000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.18999999999987 " " y[1] (closed_form) = 0.6699121199999291 " " y[1] (numeric) = 0.6699121199999802 " " absolute error = 5.118128143521972000000000000000E-14 " " relative error = 7.63999932337769000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1999999999998687 " " y[1] (closed_form) = 0.6753733333332615 " " y[1] (numeric) = 0.6753733333333133 " " absolute error = 5.173639294753230000000000000000E-14 " " relative error = 7.660413936124878000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2099999999998676 " " y[1] (closed_form) = 0.6808641466665938 " " y[1] (numeric) = 0.6808641466666464 " " absolute error = 5.26245713672324200000000000000E-14 " " relative error = 7.729085401966637000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999998665 " " y[1] (closed_form) = 0.6863846399999262 " " y[1] (numeric) = 0.6863846399999793 " " absolute error = 5.317968287954500000000000000E-14 " " relative error = 7.747796174394391000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999998654 " " y[1] (closed_form) = 0.6919348933332585 " " y[1] (numeric) = 0.6919348933333122 " " absolute error = 5.36237720893950600000000000000E-14 " " relative error = 7.749829153877935000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2399999999998643 " " y[1] (closed_form) = 0.6975149866665907 " " y[1] (numeric) = 0.6975149866666451 " " absolute error = 5.44009282066326700000000000000E-14 " " relative error = 7.799248653654534000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.249999999999863 " " y[1] (closed_form) = 0.7031249999999232 " " y[1] (numeric) = 0.7031249999999781 " " absolute error = 5.49560397189452500000000000000E-14 " " relative error = 7.815970093361957000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.259999999999862 " " y[1] (closed_form) = 0.7087650133332555 " " y[1] (numeric) = 0.7087650133333112 " " absolute error = 5.57331958361828600000000000000E-14 " " relative error = 7.863423671842218000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.269999999999861 " " y[1] (closed_form) = 0.7144351066665877 " " y[1] (numeric) = 0.7144351066666441 " " absolute error = 5.63993296509579500000000000000E-14 " " relative error = 7.894255072949315000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.27999999999986 " " y[1] (closed_form) = 0.7201353599999201 " " y[1] (numeric) = 0.7201353599999771 " " absolute error = 5.70654634657330500000000000000E-14 " " relative error = 7.924269052104229000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999859 " " y[1] (closed_form) = 0.7258658533332523 " " y[1] (numeric) = 0.7258658533333101 " " absolute error = 5.78426195829706600000000000000E-14 " " relative error = 7.968775403519984000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2999999999998577 " " y[1] (closed_form) = 0.7316266666665846 " " y[1] (numeric) = 0.7316266666666431 " " absolute error = 5.85087533977457500000000000000E-14 " " relative error = 7.997077753374076000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999998566 " " y[1] (closed_form) = 0.7374178799999169 " " y[1] (numeric) = 0.737417879999976 " " absolute error = 5.90638649100583300000000000000E-14 " " relative error = 8.009551505594763000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999998555 " " y[1] (closed_form) = 0.7432395733332491 " " y[1] (numeric) = 0.7432395733333089 " " absolute error = 5.98410210272959400000000000000E-14 " " relative error = 8.051377129843004000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999998544 " " y[1] (closed_form) = 0.7490918266665813 " " y[1] (numeric) = 0.7490918266666416 " " absolute error = 6.03961325396085200000000000000E-14 " " relative error = 8.062580632920278000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3399999999998533 " " y[1] (closed_form) = 0.7549747199999136 " " y[1] (numeric) = 0.7549747199999745 " " absolute error = 6.08402217494585800000000000000E-14 " " relative error = 8.058577345406418000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.349999999999852 " " y[1] (closed_form) = 0.7608883333332458 " " y[1] (numeric) = 0.7608883333333072 " " absolute error = 6.13953332617711600000000000000E-14 " " relative error = 8.068901910062785000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.359999999999851 " " y[1] (closed_form) = 0.766832746666578 " " y[1] (numeric) = 0.7668327466666399 " " absolute error = 6.19504447740837300000000000000E-14 " " relative error = 8.07874273019538100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.36999999999985 " " y[1] (closed_form) = 0.7728080399999102 " " y[1] (numeric) = 0.7728080399999727 " " absolute error = 6.25055562863963100000000000000E-14 " " relative error = 8.088108954767548000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.379999999999849 " " y[1] (closed_form) = 0.7788142933332425 " " y[1] (numeric) = 0.7788142933333057 " " absolute error = 6.31716901011714100000000000000E-14 " " relative error = 8.111264860176524000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999848 " " y[1] (closed_form) = 0.7848515866665746 " " y[1] (numeric) = 0.7848515866666385 " " absolute error = 6.3837823915946500000000000000E-14 " " relative error = 8.133744646816452000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3999999999998467 " " y[1] (closed_form) = 0.7909199999999067 " " y[1] (numeric) = 0.7909199999999712 " " absolute error = 6.4503957730721600000000000000E-14 " " relative error = 8.155560326041723000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999998456 " " y[1] (closed_form) = 0.797019613333239 " " y[1] (numeric) = 0.7970196133333038 " " absolute error = 6.48370246381091400000000000000E-14 " " relative error = 8.134934643195583000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999998445 " " y[1] (closed_form) = 0.8031505066665712 " " y[1] (numeric) = 0.8031505066666367 " " absolute error = 6.55031584528842400000000000000E-14 " " relative error = 8.155776272214685000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4299999999998434 " " y[1] (closed_form) = 0.8093127599999033 " " y[1] (numeric) = 0.8093127599999694 " " absolute error = 6.61692922676593300000000000000E-14 " " relative error = 8.175985297410515000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4399999999998423 " " y[1] (closed_form) = 0.8155064533332355 " " y[1] (numeric) = 0.8155064533333024 " " absolute error = 6.69464483848969400000000000000E-14 " " relative error = 8.20918683246041900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.449999999999841 " " y[1] (closed_form) = 0.8217316666665677 " " y[1] (numeric) = 0.8217316666666353 " " absolute error = 6.76125821996720300000000000000E-14 " " relative error = 8.228060928204078000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.45999999999984 " " y[1] (closed_form) = 0.8279884799998998 " " y[1] (numeric) = 0.8279884799999679 " " absolute error = 6.81676937119846100000000000000E-14 " " relative error = 8.232927795323054000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.469999999999839 " " y[1] (closed_form) = 0.8342769733332318 " " y[1] (numeric) = 0.8342769733333006 " " absolute error = 6.8833827526759700000000000000E-14 " " relative error = 8.250716455920412000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999838 " " y[1] (closed_form) = 0.8405972266665639 " " y[1] (numeric) = 0.8405972266666336 " " absolute error = 6.97220059464598300000000000000E-14 " " relative error = 8.294341657888453000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999837 " " y[1] (closed_form) = 0.8469493199998961 " " y[1] (numeric) = 0.8469493199999664 " " absolute error = 7.02771174587724100000000000000E-14 " " relative error = 8.297676826611188000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4999999999998357 " " y[1] (closed_form) = 0.8533333333332281 " " y[1] (numeric) = 0.8533333333332993 " " absolute error = 7.11652958784725300000000000000E-14 " " relative error = 8.33968311075952900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5099999999998346 " " y[1] (closed_form) = 0.8597493466665604 " " y[1] (numeric) = 0.8597493466666319 " " absolute error = 7.14983627858600800000000000000E-14 " " relative error = 8.316186928559486000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999998335 " " y[1] (closed_form) = 0.8661974399998924 " " y[1] (numeric) = 0.8661974399999647 " " absolute error = 7.22755189030976900000000000000E-14 " " relative error = 8.344000520609558000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5299999999998324 " " y[1] (closed_form) = 0.8726776933332245 " " y[1] (numeric) = 0.8726776933332976 " " absolute error = 7.3052675020335300000000000000E-14 " " relative error = 8.371094572305146000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5399999999998313 " " y[1] (closed_form) = 0.8791901866665565 " " y[1] (numeric) = 0.8791901866666304 " " absolute error = 7.39408534400354300000000000000E-14 " " relative error = 8.410109048234679000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.54999999999983 " " y[1] (closed_form) = 0.8857349999998886 " " y[1] (numeric) = 0.8857349999999631 " " absolute error = 7.449596495234800000000000000E-14 " " relative error = 8.41063805227945000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.559999999999829 " " y[1] (closed_form) = 0.8923122133332207 " " y[1] (numeric) = 0.8923122133332957 " " absolute error = 7.49400541621980700000000000000E-14 " " relative error = 8.398411793811548000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999828 " " y[1] (closed_form) = 0.8989219066665526 " " y[1] (numeric) = 0.8989219066666284 " " absolute error = 7.58282325818981900000000000000E-14 " " relative error = 8.43546386171519000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999827 " " y[1] (closed_form) = 0.9055641599998849 " " y[1] (numeric) = 0.9055641599999611 " " absolute error = 7.61612994892857400000000000000E-14 " " relative error = 8.410370336354236000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5899999999998258 " " y[1] (closed_form) = 0.9122390533332169 " " y[1] (numeric) = 0.912239053333294 " " absolute error = 7.71605002114483800000000000000E-14 " " relative error = 8.458364058139449000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5999999999998247 " " y[1] (closed_form) = 0.9189466666665489 " " y[1] (numeric) = 0.9189466666666269 " " absolute error = 7.8048678631148500000000000000E-14 " " relative error = 8.493276210932644000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6099999999998236 " " y[1] (closed_form) = 0.925687079999881 " " y[1] (numeric) = 0.9256870799999596 " " absolute error = 7.86037901434610800000000000000E-14 " " relative error = 8.491399722622378000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6199999999998225 " " y[1] (closed_form) = 0.9324603733332127 " " y[1] (numeric) = 0.9324603733332922 " " absolute error = 7.94919685631612100000000000000E-14 " " relative error = 8.524970158142572000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6299999999998214 " " y[1] (closed_form) = 0.9392666266665448 " " y[1] (numeric) = 0.9392666266666251 " " absolute error = 8.02691246803988200000000000000E-14 " " relative error = 8.545935988939984000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999998203 " " y[1] (closed_form) = 0.9461059199998768 " " y[1] (numeric) = 0.9461059199999577 " " absolute error = 8.09352584951739100000000000000E-14 " " relative error = 8.554566331768059000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.649999999999819 " " y[1] (closed_form) = 0.9529783333332088 " " y[1] (numeric) = 0.9529783333332904 " " absolute error = 8.160139230994901000000000000E-14 " " relative error = 8.562775191806703000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.659999999999818 " " y[1] (closed_form) = 0.9598839466665409 " " y[1] (numeric) = 0.9598839466666231 " " absolute error = 8.2267526124724100000000000000E-14 " " relative error = 8.570570058018009000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.669999999999817 " " y[1] (closed_form) = 0.9668228399998727 " " y[1] (numeric) = 0.9668228399999558 " " absolute error = 8.30446822419617100000000000000E-14 " " relative error = 8.589441499124352000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.679999999999816 " " y[1] (closed_form) = 0.9737950933332047 " " y[1] (numeric) = 0.9737950933332887 " " absolute error = 8.40438829641243500000000000000E-14 " " relative error = 8.630551081999235000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6899999999998148 " " y[1] (closed_form) = 0.9808007866665367 " " y[1] (numeric) = 0.9808007866666214 " " absolute error = 8.47100167788994400000000000000E-14 " " relative error = 8.636821863367865000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6999999999998137 " " y[1] (closed_form) = 0.9878399999998686 " " y[1] (numeric) = 0.9878399999999542 " " absolute error = 8.55981951985995700000000000000E-14 " " relative error = 8.665188208476166000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7099999999998126 " " y[1] (closed_form) = 0.9949128133332006 " " y[1] (numeric) = 0.9949128133332868 " " absolute error = 8.62643290133746600000000000000E-14 " " relative error = 8.670541564779743000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7199999999998115 " " y[1] (closed_form) = 1.0020193066665326 " " y[1] (numeric) = 1.0020193066666196 " " absolute error = 8.70414851306122700000000000000E-14 " " relative error = 8.68660758844832100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999998104 " " y[1] (closed_form) = 1.0091595599998642 " " y[1] (numeric) = 1.0091595599999525 " " absolute error = 8.83737527601624600000000000000E-14 " " relative error = 8.757163511404911000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999998093 " " y[1] (closed_form) = 1.0163336533331961 " " y[1] (numeric) = 1.0163336533332854 " " absolute error = 8.92619311798625900000000000000E-14 " " relative error = 8.782738905389649000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.749999999999808 " " y[1] (closed_form) = 1.0235416666665282 " " y[1] (numeric) = 1.0235416666666182 " " absolute error = 8.99280649946376800000000000000E-14 " " relative error = 8.785970119566848000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999807 " " y[1] (closed_form) = 1.03078367999986 " " y[1] (numeric) = 1.030783679999951 " " absolute error = 9.10382880192628400000000000000E-14 " " relative error = 8.831948912818954000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.769999999999806 " " y[1] (closed_form) = 1.038059773333192 " " y[1] (numeric) = 1.038059773333284 " " absolute error = 9.19264664389629600000000000000E-14 " " relative error = 8.85560434962128000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.779999999999805 " " y[1] (closed_form) = 1.0453700266665236 " " y[1] (numeric) = 1.0453700266666164 " " absolute error = 9.28146448586630900000000000000E-14 " " relative error = 8.878640337013533000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7899999999998037 " " y[1] (closed_form) = 1.0527145199998555 " " y[1] (numeric) = 1.052714519999949 " " absolute error = 9.34807786734381800000000000000E-14 " " relative error = 8.879974285284011000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7999999999998026 " " y[1] (closed_form) = 1.0600933333331874 " " y[1] (numeric) = 1.060093333333281 " " absolute error = 9.34807786734381800000000000000E-14 " " relative error = 8.818164942091675000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8099999999998015 " " y[1] (closed_form) = 1.0675065466665192 " " y[1] (numeric) = 1.0675065466666136 " " absolute error = 9.4368957093138310000000000000E-14 " " relative error = 8.840129120315215000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8199999999998004 " " y[1] (closed_form) = 1.074954239999851 " " y[1] (numeric) = 1.074954239999946 " " absolute error = 9.5035090907913400000000000000E-14 " " relative error = 8.840849905194715000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999997993 " " y[1] (closed_form) = 1.082436493333183 " " y[1] (numeric) = 1.0824364933332788 " " absolute error = 9.59232693276135300000000000000E-14 " " relative error = 8.861791885104852000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8399999999997982 " " y[1] (closed_form) = 1.0899533866665148 " " y[1] (numeric) = 1.0899533866666113 " " absolute error = 9.65894031423886200000000000000E-14 " " relative error = 8.861792102669194000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.849999999999797 " " y[1] (closed_form) = 1.0975049999998465 " " y[1] (numeric) = 1.0975049999999442 " " absolute error = 9.76996261670137800000000000000E-14 " " relative error = 8.90197549596835100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.859999999999796 " " y[1] (closed_form) = 1.1050914133331782 " " y[1] (numeric) = 1.105091413333277 " " absolute error = 9.88098491916389300000000000000E-14 " " relative error = 8.94132811091243000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.869999999999795 " " y[1] (closed_form) = 1.1127127066665101 " " y[1] (numeric) = 1.1127127066666096 " " absolute error = 9.94759830064140300000000000000E-14 " " relative error = 8.939952101780739000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.879999999999794 " " y[1] (closed_form) = 1.1203689599998419 " " y[1] (numeric) = 1.1203689599999425 " " absolute error = 1.00586206031039180000000000000E-13 " " relative error = 8.977953658324609000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8899999999997927 " " y[1] (closed_form) = 1.1280602533331736 " " y[1] (numeric) = 1.128060253333275 " " absolute error = 1.01474384450739310000000000000E-13 " " relative error = 8.99547556532592000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8999999999997916 " " y[1] (closed_form) = 1.1357866666665053 " " y[1] (numeric) = 1.1357866666666072 " " absolute error = 1.01918473660589370000000000000E-13 " " relative error = 8.973381767169056000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9099999999997905 " " y[1] (closed_form) = 1.1435482799998373 " " y[1] (numeric) = 1.14354827999994 " " absolute error = 1.02584607475364460000000000000E-13 " " relative error = 8.97072815109993000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999997894 " " y[1] (closed_form) = 1.151345173333169 " " y[1] (numeric) = 1.1513451733332722 " " absolute error = 1.03250741290139560000000000000E-13 " " relative error = 8.967835509417774000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9299999999997883 " " y[1] (closed_form) = 1.1591774266665007 " " y[1] (numeric) = 1.1591774266666048 " " absolute error = 1.04138919709839680000000000000E-13 " " relative error = 8.983863670406066000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9399999999997872 " " y[1] (closed_form) = 1.1670451199998322 " " y[1] (numeric) = 1.1670451199999374 " " absolute error = 1.05249142734464840000000000000E-13 " " relative error = 9.018429616027183000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.949999999999786 " " y[1] (closed_form) = 1.174948333333164 " " y[1] (numeric) = 1.1749483333332698 " " absolute error = 1.0569323194431490000000000000E-13 " " relative error = 8.995564225745825000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.959999999999785 " " y[1] (closed_form) = 1.1828871466664956 " " y[1] (numeric) = 1.1828871466666022 " " absolute error = 1.06581410364015030000000000000E-13 " " relative error = 9.01027715656333100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.969999999999784 " " y[1] (closed_form) = 1.1908616399998273 " " y[1] (numeric) = 1.1908616399999346 " " absolute error = 1.07247544178790120000000000000E-13 " " relative error = 9.005877809516618000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.979999999999783 " " y[1] (closed_form) = 1.198871893333159 " " y[1] (numeric) = 1.1988718933332672 " " absolute error = 1.08135722598490250000000000000E-13 " " relative error = 9.019789620544554000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9899999999997817 " " y[1] (closed_form) = 1.2069179866664905 " " y[1] (numeric) = 1.2069179866665996 " " absolute error = 1.09023901018190370000000000000E-13 " " relative error = 9.033248507573788000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9999999999997806 " " y[1] (closed_form) = 1.2149999999998224 " " y[1] (numeric) = 1.2149999999999321 " " absolute error = 1.09690034832965470000000000000E-13 " " relative error = 9.027986406006707000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0099999999997795 " " y[1] (closed_form) = 1.223118013333154 " " y[1] (numeric) = 1.2231180133332644 " " absolute error = 1.10356168647740560000000000000E-13 " " relative error = 9.0225282797532990000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0199999999997784 " " y[1] (closed_form) = 1.2312721066664856 " " y[1] (numeric) = 1.231272106666597 " " absolute error = 1.11466391672365720000000000000E-13 " " relative error = 9.052945410592217000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0299999999997773 " " y[1] (closed_form) = 1.2394623599998174 " " y[1] (numeric) = 1.239462359999929 " " absolute error = 1.11688436277290750000000000000E-13 " " relative error = 9.011038969937514000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.039999999999776 " " y[1] (closed_form) = 1.247688853333149 " " y[1] (numeric) = 1.2476888533332615 " " absolute error = 1.12576614696990870000000000000E-13 " " relative error = 9.02281160853903000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.049999999999775 " " y[1] (closed_form) = 1.2559516666664805 " " y[1] (numeric) = 1.2559516666665942 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 9.051848151399102000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.059999999999774 " " y[1] (closed_form) = 1.264250879999812 " " y[1] (numeric) = 1.2642508799999266 " " absolute error = 1.14575016141316150000000000000E-13 " " relative error = 9.06268035513119100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.069999999999773 " " y[1] (closed_form) = 1.2725865733331438 " " y[1] (numeric) = 1.2725865733332589 " " absolute error = 1.15019105351166220000000000000E-13 " " relative error = 9.038214590769219000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.079999999999772 " " y[1] (closed_form) = 1.280958826666475 " " y[1] (numeric) = 1.2809588266665912 " " absolute error = 1.16129328375791370000000000000E-13 " " relative error = 9.065812730140789000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0899999999997707 " " y[1] (closed_form) = 1.2893677199998068 " " y[1] (numeric) = 1.2893677199999238 " " absolute error = 1.1701750679549150000000000000E-13 " " relative error = 9.075572854849276000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0999999999997696 " " y[1] (closed_form) = 1.2978133333331385 " " y[1] (numeric) = 1.2978133333332569 " " absolute error = 1.18349774425041690000000000000E-13 " " relative error = 9.119167709664933000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1099999999997685 " " y[1] (closed_form) = 1.30629574666647 " " y[1] (numeric) = 1.3062957466665892 " " absolute error = 1.1923795284474181000000000000E-13 " " relative error = 9.127944659471225000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1199999999997674 " " y[1] (closed_form) = 1.3148150399998015 " " y[1] (numeric) = 1.3148150399999219 " " absolute error = 1.20348175869366970000000000000E-13 " " relative error = 9.153239977341995000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1299999999997663 " " y[1] (closed_form) = 1.323371293333133 " " y[1] (numeric) = 1.3233712933332547 " " absolute error = 1.21680443498917160000000000000E-13 " " relative error = 9.19473197823753000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.139999999999765 " " y[1] (closed_form) = 1.3319645866664644 " " y[1] (numeric) = 1.331964586666587 " " absolute error = 1.22568621918617280000000000000E-13 " " relative error = 9.20209314463625000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.149999999999764 " " y[1] (closed_form) = 1.340594999999796 " " y[1] (numeric) = 1.3405949999999196 " " absolute error = 1.23678844943242440000000000000E-13 " " relative error = 9.225668075985757000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.159999999999763 " " y[1] (closed_form) = 1.3492626133331274 " " y[1] (numeric) = 1.349262613333252 " " absolute error = 1.24567023362942560000000000000E-13 " " relative error = 9.232229673600797000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.169999999999762 " " y[1] (closed_form) = 1.357967506666459 " " y[1] (numeric) = 1.3579675066665842 " " absolute error = 1.25233157177717660000000000000E-13 " " relative error = 9.222102632274334000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.179999999999761 " " y[1] (closed_form) = 1.3667097599997904 " " y[1] (numeric) = 1.3667097599999165 " " absolute error = 1.26121335597417780000000000000E-13 " " relative error = 9.228099431838193000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1899999999997597 " " y[1] (closed_form) = 1.375489453333122 " " y[1] (numeric) = 1.3754894533332491 " " absolute error = 1.27231558622042940000000000000E-13 " " relative error = 9.249911608826379000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1999999999997586 " " y[1] (closed_form) = 1.3843066666664536 " " y[1] (numeric) = 1.384306666666581 " " absolute error = 1.27453603226967970000000000000E-13 " " relative error = 9.207035283149272000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2099999999997575 " " y[1] (closed_form) = 1.3931614799997847 " " y[1] (numeric) = 1.3931614799999137 " " absolute error = 1.2900791546144320000000000000E-13 " " relative error = 9.26008343709468000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2199999999997564 " " y[1] (closed_form) = 1.4020539733331163 " " y[1] (numeric) = 1.4020539733332458 " " absolute error = 1.29452004671293250000000000000E-13 " " relative error = 9.233025770295117000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2299999999997553 " " y[1] (closed_form) = 1.4109842266664476 " " y[1] (numeric) = 1.4109842266665784 " " absolute error = 1.30784272300843440000000000000E-13 " " relative error = 9.269010229110127000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.239999999999754 " " y[1] (closed_form) = 1.4199523199997792 " " y[1] (numeric) = 1.4199523199999111 " " absolute error = 1.3189449532546860000000000000E-13 " " relative error = 9.288656630772582000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.249999999999753 " " y[1] (closed_form) = 1.4289583333331106 " " y[1] (numeric) = 1.4289583333332434 " " absolute error = 1.32782673745168720000000000000E-13 " " relative error = 9.292270505568001000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.259999999999752 " " y[1] (closed_form) = 1.438002346666442 " " y[1] (numeric) = 1.438002346666576 " " absolute error = 1.33892896769793880000000000000E-13 " " relative error = 9.311034650269009000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.269999999999751 " " y[1] (closed_form) = 1.4470844399997733 " " y[1] (numeric) = 1.4470844399999083 " " absolute error = 1.35003119794419040000000000000E-13 " " relative error = 9.3293187365376000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.27999999999975 " " y[1] (closed_form) = 1.4562046933331048 " " y[1] (numeric) = 1.4562046933332407 " " absolute error = 1.35891298214119160000000000000E-13 " " relative error = 9.331881626001202000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2899999999997487 " " y[1] (closed_form) = 1.465363186666436 " " y[1] (numeric) = 1.4653631866665733 " " absolute error = 1.37223565843669350000000000000E-13 " " relative error = 9.364474765866071000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2999999999997476 " " y[1] (closed_form) = 1.4745599999997674 " " y[1] (numeric) = 1.474559999999906 " " absolute error = 1.38555833473219540000000000000E-13 " " relative error = 9.396418828209188000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3099999999997465 " " y[1] (closed_form) = 1.4837952133330987 " " y[1] (numeric) = 1.4837952133332384 " " absolute error = 1.3966605649784470000000000000E-13 " " relative error = 9.412758259551744000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3199999999997454 " " y[1] (closed_form) = 1.4930689066664302 " " y[1] (numeric) = 1.4930689066665708 " " absolute error = 1.40554234917544820000000000000E-13 " " relative error = 9.413780856997401000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3299999999997443 " " y[1] (closed_form) = 1.5023811599997614 " " y[1] (numeric) = 1.5023811599999033 " " absolute error = 1.418865025470950000000000000E-13 " " relative error = 9.44410821466355000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.339999999999743 " " y[1] (closed_form) = 1.5117320533330927 " " y[1] (numeric) = 1.5117320533332357 " " absolute error = 1.42996725571720160000000000000E-13 " " relative error = 9.459131679879282000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.349999999999742 " " y[1] (closed_form) = 1.521121666666424 " " y[1] (numeric) = 1.5211216666665681 " " absolute error = 1.44106948596345320000000000000E-13 " " relative error = 9.4737292719102000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.359999999999741 " " y[1] (closed_form) = 1.5305500799997553 " " y[1] (numeric) = 1.5305500799999006 " " absolute error = 1.45217171620970480000000000000E-13 " " relative error = 9.487907224897448000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.36999999999974 " " y[1] (closed_form) = 1.5400173733330866 " " y[1] (numeric) = 1.5400173733332332 " " absolute error = 1.46549439250520660000000000000E-13 " " relative error = 9.516089999253783000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3799999999997388 " " y[1] (closed_form) = 1.5495236266664179 " " y[1] (numeric) = 1.5495236266665655 " " absolute error = 1.47659662275145820000000000000E-13 " " relative error = 9.529358554720125000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3899999999997377 " " y[1] (closed_form) = 1.5590689199997492 " " y[1] (numeric) = 1.5590689199998977 " " absolute error = 1.48547840694845950000000000000E-13 " " relative error = 9.52798422117669100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3999999999997366 " " y[1] (closed_form) = 1.5686533333330803 " " y[1] (numeric) = 1.5686533333332298 " " absolute error = 1.49436019114546070000000000000E-13 " " relative error = 9.526389033134801000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4099999999997355 " " y[1] (closed_form) = 1.5782769466664115 " " y[1] (numeric) = 1.578276946666562 " " absolute error = 1.50546242139171230000000000000E-13 " " relative error = 9.538645448579252000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4199999999997344 " " y[1] (closed_form) = 1.5879398399997429 " " y[1] (numeric) = 1.587939839999894 " " absolute error = 1.51212375953946320000000000000E-13 " " relative error = 9.522550675091748000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4299999999997333 " " y[1] (closed_form) = 1.5976420933330742 " " y[1] (numeric) = 1.5976420933332263 " " absolute error = 1.52100554373646450000000000000E-13 " " relative error = 9.52031465672810900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.439999999999732 " " y[1] (closed_form) = 1.6073837866664051 " " y[1] (numeric) = 1.6073837866665586 " " absolute error = 1.53432822003196630000000000000E-13 " " relative error = 9.545500164674733000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.449999999999731 " " y[1] (closed_form) = 1.6171649999997366 " " y[1] (numeric) = 1.617164999999891 " " absolute error = 1.54321000422896760000000000000E-13 " " relative error = 9.542687383348136000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.45999999999973 " " y[1] (closed_form) = 1.6269858133330677 " " y[1] (numeric) = 1.6269858133332233 " " absolute error = 1.55653268052446950000000000000E-13 " " relative error = 9.566971437419808000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.469999999999729 " " y[1] (closed_form) = 1.636846306666399 " " y[1] (numeric) = 1.6368463066665555 " " absolute error = 1.56541446472147070000000000000E-13 " " relative error = 9.563600799574113000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4799999999997278 " " y[1] (closed_form) = 1.64674655999973 " " y[1] (numeric) = 1.6467465599998876 " " absolute error = 1.57651669496772230000000000000E-13 " " relative error = 9.573523535813433000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4899999999997267 " " y[1] (closed_form) = 1.6566866533330613 " " y[1] (numeric) = 1.6566866533332196 " " absolute error = 1.58317803311547320000000000000E-13 " " relative error = 9.556291347734966000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4999999999997256 " " y[1] (closed_form) = 1.6666666666663923 " " y[1] (numeric) = 1.666666666666552 " " absolute error = 1.5965007094109750000000000000E-13 " " relative error = 9.579004256467427000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5099999999997245 " " y[1] (closed_form) = 1.6766866799997233 " " y[1] (numeric) = 1.676686679999884 " " absolute error = 1.60760293965722670000000000000E-13 " " relative error = 9.587974657599665000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5199999999997234 " " y[1] (closed_form) = 1.6867467733330546 " " y[1] (numeric) = 1.6867467733332164 " " absolute error = 1.61870516990347820000000000000E-13 " " relative error = 9.59661044262664100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5299999999997222 " " y[1] (closed_form) = 1.6968470266663855 " " y[1] (numeric) = 1.6968470266665485 " " absolute error = 1.62980740014972980000000000000E-13 " " relative error = 9.604916498287055000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.539999999999721 " " y[1] (closed_form) = 1.706987519999717 " " y[1] (numeric) = 1.7069875199998807 " " absolute error = 1.63646873829748070000000000000E-13 " " relative error = 9.586881679707606000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.54999999999972 " " y[1] (closed_form) = 1.7171683333330476 " " y[1] (numeric) = 1.7171683333332128 " " absolute error = 1.6520118606422330000000000000E-13 " " relative error = 9.620558617195408000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.559999999999719 " " y[1] (closed_form) = 1.727389546666379 " " y[1] (numeric) = 1.727389546666545 " " absolute error = 1.66089364483923420000000000000E-13 " " relative error = 9.615049761326433000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.569999999999718 " " y[1] (closed_form) = 1.73765123999971 " " y[1] (numeric) = 1.7376512399998771 " " absolute error = 1.67199587508548570000000000000E-13 " " relative error = 9.622160285085543000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5799999999997167 " " y[1] (closed_form) = 1.7479534933330412 " " y[1] (numeric) = 1.7479534933332095 " " absolute error = 1.68309810533173730000000000000E-13 " " relative error = 9.628963881197802000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5899999999997156 " " y[1] (closed_form) = 1.7582963866663721 " " y[1] (numeric) = 1.7582963866665415 " " absolute error = 1.6942003355779890000000000000E-13 " " relative error = 9.635465035505727000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5999999999997145 " " y[1] (closed_form) = 1.7686799999997034 " " y[1] (numeric) = 1.768679999999874 " " absolute error = 1.70530256582424040000000000000E-13 " " relative error = 9.641668169620997000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6099999999997134 " " y[1] (closed_form) = 1.7791044133330343 " " y[1] (numeric) = 1.7791044133332061 " " absolute error = 1.71862524211974230000000000000E-13 " " relative error = 9.660058337441881000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6199999999997123 " " y[1] (closed_form) = 1.789569706666365 " " y[1] (numeric) = 1.7895697066665384 " " absolute error = 1.73416836446449450000000000000E-13 " " relative error = 9.690420876060354000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6299999999997112 " " y[1] (closed_form) = 1.800075959999696 " " y[1] (numeric) = 1.8000759599998706 " " absolute error = 1.7452705947107460000000000000E-13 " " relative error = 9.695538596665891000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.63999999999971 " " y[1] (closed_form) = 1.810623253333027 " " y[1] (numeric) = 1.810623253333203 " " absolute error = 1.7585932710062480000000000000E-13 " " relative error = 9.712640483154067000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.649999999999709 " " y[1] (closed_form) = 1.8212116666663583 " " y[1] (numeric) = 1.8212116666665352 " " absolute error = 1.76969550125249950000000000000E-13 " " relative error = 9.71713246539785000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.659999999999708 " " y[1] (closed_form) = 1.8318412799996893 " " y[1] (numeric) = 1.8318412799998673 " " absolute error = 1.7807977314987510000000000000E-13 " " relative error = 9.721353869146640000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.669999999999707 " " y[1] (closed_form) = 1.8425121733330199 " " y[1] (numeric) = 1.8425121733331997 " " absolute error = 1.79856129989275360000000000000E-13 " " relative error = 9.761462235764982000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6799999999997057 " " y[1] (closed_form) = 1.853224426666351 " " y[1] (numeric) = 1.8532244266665319 " " absolute error = 1.80966353013900520000000000000E-13 " " relative error = 9.764945378980868000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6899999999997046 " " y[1] (closed_form) = 1.863978119999682 " " y[1] (numeric) = 1.863978119999864 " " absolute error = 1.81854531433600640000000000000E-13 " " relative error = 9.756258911109518000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6999999999997035 " " y[1] (closed_form) = 1.8747733333330125 " " y[1] (numeric) = 1.8747733333331962 " " absolute error = 1.8363088827300090000000000000E-13 " " relative error = 9.79483146085387900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7099999999997024 " " y[1] (closed_form) = 1.8856101466663435 " " y[1] (numeric) = 1.8856101466665285 " " absolute error = 1.84963155902551080000000000000E-13 " " relative error = 9.809193922166569000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7199999999997013 " " y[1] (closed_form) = 1.8964886399996748 " " y[1] (numeric) = 1.8964886399998608 " " absolute error = 1.86073378927176240000000000000E-13 " " relative error = 9.81146815238546000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7299999999997 " " y[1] (closed_form) = 1.9074088933330053 " " y[1] (numeric) = 1.9074088933331927 " " absolute error = 1.87405646556726420000000000000E-13 " " relative error = 9.825142747932453000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.739999999999699 " " y[1] (closed_form) = 1.9183709866663365 " " y[1] (numeric) = 1.918370986666525 " " absolute error = 1.88515869581351580000000000000E-13 " " relative error = 9.826872429349364000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.749999999999698 " " y[1] (closed_form) = 1.929374999999667 " " y[1] (numeric) = 1.9293749999998573 " " absolute error = 1.90292226420751830000000000000E-13 " " relative error = 9.862894793432313000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.759999999999697 " " y[1] (closed_form) = 1.9404210133329978 " " y[1] (numeric) = 1.9404210133331892 " " absolute error = 1.914024494453770000000000000E-13 " " relative error = 9.863964991628866000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.769999999999696 " " y[1] (closed_form) = 1.9515091066663288 " " y[1] (numeric) = 1.9515091066665213 " " absolute error = 1.92512672470002140000000000000E-13 " " relative error = 9.864810356886445000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7799999999996947 " " y[1] (closed_form) = 1.9626393599996597 " " y[1] (numeric) = 1.9626393599998535 " " absolute error = 1.93844940099552330000000000000E-13 " " relative error = 9.876747814717521000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7899999999996936 " " y[1] (closed_form) = 1.9738118533329903 " " y[1] (numeric) = 1.9738118533331857 " " absolute error = 1.95399252334027550000000000000E-13 " " relative error = 9.899588555214887000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7999999999996925 " " y[1] (closed_form) = 1.9850266666663214 " " y[1] (numeric) = 1.985026666666518 " " absolute error = 1.9650947535865270000000000000E-13 " " relative error = 9.899588688582868000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8099999999996914 " " y[1] (closed_form) = 1.996283879999652 " " y[1] (numeric) = 1.9962838799998501 " " absolute error = 1.98063787593127930000000000000E-13 " " relative error = 9.921624353003464000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8199999999996903 " " y[1] (closed_form) = 2.0075835733329828 " " y[1] (numeric) = 2.0075835733331817 " " absolute error = 1.98951966012828050000000000000E-13 " " relative error = 9.91002161282525000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.829999999999689 " " y[1] (closed_form) = 2.0189258266663135 " " y[1] (numeric) = 2.018925826666514 " " absolute error = 2.0072832285222830000000000000E-13 " " relative error = 9.942332709848707000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.839999999999688 " " y[1] (closed_form) = 2.030310719999644 " " y[1] (numeric) = 2.0303107199998465 " " absolute error = 2.02504679691628550000000000000E-13 " " relative error = 9.974073312860411000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.849999999999687 " " y[1] (closed_form) = 2.041738333332975 " " y[1] (numeric) = 2.041738333333179 " " absolute error = 2.03836947321178740000000000000E-13 " " relative error = 9.983500039813191000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.859999999999686 " " y[1] (closed_form) = 2.053208746666306 " " y[1] (numeric) = 2.053208746666511 " " absolute error = 2.05169214950728930000000000000E-13 " " relative error = 9.992613526698252000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.869999999999685 " " y[1] (closed_form) = 2.0647220399996367 " " y[1] (numeric) = 2.0647220399998427 " " absolute error = 2.06057393370429050000000000000E-13 " " relative error = 9.979909613909353000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8799999999996837 " " y[1] (closed_form) = 2.076278293332967 " " y[1] (numeric) = 2.076278293333175 " " absolute error = 2.0783375020982930000000000000E-13 " " relative error = 1.0009917787860800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8899999999996826 " " y[1] (closed_form) = 2.087877586666298 " " y[1] (numeric) = 2.0878775866665067 " " absolute error = 2.08721928629529430000000000000E-13 " " relative error = 9.996847035596302000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8999999999996815 " " y[1] (closed_form) = 2.0995199999996284 " " y[1] (numeric) = 2.0995199999998384 " " absolute error = 2.10054196259079620000000000000E-13 " " relative error = 1.000486760112391500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9099999999996804 " " y[1] (closed_form) = 2.111205613332959 " " y[1] (numeric) = 2.11120561333317 " " absolute error = 2.10942374678779740000000000000E-13 " " relative error = 9.991559957334764000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9199999999996793 " " y[1] (closed_form) = 2.1229345066662897 " " y[1] (numeric) = 2.1229345066665024 " " absolute error = 2.12718731518180000000000000E-13 " " relative error = 1.002003268825371600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.929999999999678 " " y[1] (closed_form) = 2.1347067599996206 " " y[1] (numeric) = 2.134706759999834 " " absolute error = 2.13606909937880120000000000000E-13 " " relative error = 1.000638185724010700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.939999999999677 " " y[1] (closed_form) = 2.146522453332951 " " y[1] (numeric) = 2.1465224533331644 " " absolute error = 2.13162820728030060000000000000E-13 " " relative error = 9.930612204733642000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.949999999999676 " " y[1] (closed_form) = 2.158381666666282 " " y[1] (numeric) = 2.1583816666664966 " " absolute error = 2.14495088357580240000000000000E-13 " " relative error = 9.937773827039479000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.959999999999675 " " y[1] (closed_form) = 2.1702844799996126 " " y[1] (numeric) = 2.1702844799998284 " " absolute error = 2.15827355987130430000000000000E-13 " " relative error = 9.944657392894822000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.969999999999674 " " y[1] (closed_form) = 2.1822309733329432 " " y[1] (numeric) = 2.1822309733331604 " " absolute error = 2.17159623616680620000000000000E-13 " " relative error = 9.951266674810804000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9799999999996727 " " y[1] (closed_form) = 2.1942212266662735 " " y[1] (numeric) = 2.1942212266664924 " " absolute error = 2.18935980456080870000000000000E-13 " " relative error = 9.97784443042304000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9899999999996716 " " y[1] (closed_form) = 2.206255319999604 " " y[1] (numeric) = 2.2062553199998245 " " absolute error = 2.20712337295481120000000000000E-13 " " relative error = 1.000393450815659600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9999999999996705 " " y[1] (closed_form) = 2.218333333332935 " " y[1] (numeric) = 2.2183333333331565 " " absolute error = 2.21600515715181250000000000000E-13 " " relative error = 9.989504840656095000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.009999999999674 " " y[1] (closed_form) = 2.230455346666271 " " y[1] (numeric) = 2.230455346666489 " " absolute error = 2.18047802036380740000000000000E-13 " " relative error = 9.775932181842771000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.019999999999677 " " y[1] (closed_form) = 2.2426214399996067 " " y[1] (numeric) = 2.2426214399998208 " " absolute error = 2.14050999147730180000000000000E-13 " " relative error = 9.544678175723127000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0299999999996805 " " y[1] (closed_form) = 2.2548316933329424 " " y[1] (numeric) = 2.254831693333153 " " absolute error = 2.10498285468929680000000000000E-13 " " relative error = 9.335432267132324000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.039999999999684 " " y[1] (closed_form) = 2.2670861866662784 " " y[1] (numeric) = 2.2670861866664853 " " absolute error = 2.06945571790129180000000000000E-13 " " relative error = 9.128262216375638000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.049999999999687 " " y[1] (closed_form) = 2.2793849999996145 " " y[1] (numeric) = 2.279384999999817 " " absolute error = 2.02504679691628550000000000000E-13 " " relative error = 8.884180587819206000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0599999999996905 " " y[1] (closed_form) = 2.291728213332951 " " y[1] (numeric) = 2.291728213333149 " " absolute error = 1.98063787593127930000000000000E-13 " " relative error = 8.642551347966168000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.069999999999694 " " y[1] (closed_form) = 2.304115906666287 " " y[1] (numeric) = 2.30411590666648 " " absolute error = 1.93178806284777240000000000000E-13 " " relative error = 8.384075025300193000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.079999999999697 " " y[1] (closed_form) = 2.316548159999623 " " y[1] (numeric) = 2.3165481599998117 " " absolute error = 1.8873791418627660000000000000E-13 " " relative error = 8.147377095165046000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0899999999997005 " " y[1] (closed_form) = 2.329025053332959 " " y[1] (numeric) = 2.3290250533331434 " " absolute error = 1.84297022087775990000000000000E-13 " " relative error = 7.913054512833048000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.099999999999704 " " y[1] (closed_form) = 2.341546666666295 " " y[1] (numeric) = 2.3415466666664755 " " absolute error = 1.80300219199125420000000000000E-13 " " relative error = 7.700048082143170000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.109999999999707 " " y[1] (closed_form) = 2.3541130799996313 " " y[1] (numeric) = 2.3541130799998076 " " absolute error = 1.76303416310474860000000000000E-13 " " relative error = 7.48916514709235900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.119999999999710 " " y[1] (closed_form) = 2.3667243733329677 " " y[1] (numeric) = 2.3667243733331396 " " absolute error = 1.71862524211974230000000000000E-13 " " relative error = 7.261619736900194000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.129999999999714 " " y[1] (closed_form) = 2.379380626666304 " " y[1] (numeric) = 2.3793806266664714 " " absolute error = 1.6742163211347360000000000000E-13 " " relative error = 7.036353504653194000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.139999999999717 " " y[1] (closed_form) = 2.39208191999964 " " y[1] (numeric) = 2.392081919999804 " " absolute error = 1.6386891843467310000000000000E-13 " " relative error = 6.850472680914613000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.149999999999720 " " y[1] (closed_form) = 2.4048283333329765 " " y[1] (numeric) = 2.4048283333331364 " " absolute error = 1.59872115546022540000000000000E-13 " " relative error = 6.647963737371950000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.159999999999724 " " y[1] (closed_form) = 2.417619946666313 " " y[1] (numeric) = 2.4176199466664685 " " absolute error = 1.55431223447521920000000000000E-13 " " relative error = 6.4291008047748790000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.169999999999727 " " y[1] (closed_form) = 2.4304568399996493 " " y[1] (numeric) = 2.4304568399998003 " " absolute error = 1.5099033134902130000000000000E-13 " " relative error = 6.212425946598710000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.179999999999730 " " y[1] (closed_form) = 2.4433390933329857 " " y[1] (numeric) = 2.4433390933331327 " " absolute error = 1.46993528460370730000000000000E-13 " " relative error = 6.016092030020084000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.189999999999734 " " y[1] (closed_form) = 2.456266786666322 " " y[1] (numeric) = 2.4562667866664647 " " absolute error = 1.4255263636187010000000000000E-13 " " relative error = 5.8036300102133630000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.199999999999737 " " y[1] (closed_form) = 2.469239999999659 " " y[1] (numeric) = 2.4692399999997967 " " absolute error = 1.3766765505351940000000000000E-13 " " relative error = 5.57530475180777900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.209999999999740 " " y[1] (closed_form) = 2.482258813332995 " " y[1] (numeric) = 2.4822588133331296 " " absolute error = 1.34559030584568970000000000000E-13 " " relative error = 5.4208300061947600000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.219999999999744 " " y[1] (closed_form) = 2.4953233066663314 " " y[1] (numeric) = 2.495323306666462 " " absolute error = 1.3056222769591840000000000000E-13 " " relative error = 5.23227700984147000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.229999999999747 " " y[1] (closed_form) = 2.508433559999668 " " y[1] (numeric) = 2.508433559999794 " " absolute error = 1.25677246387567720000000000000E-13 " " relative error = 5.010188365825577000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.239999999999750 " " y[1] (closed_form) = 2.5215896533330047 " " y[1] (numeric) = 2.5215896533331263 " " absolute error = 1.21680443498917160000000000000E-13 " " relative error = 4.825545002458331300000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.249999999999754 " " y[1] (closed_form) = 2.5347916666663415 " " y[1] (numeric) = 2.5347916666664583 " " absolute error = 1.16795462190566470000000000000E-13 " " relative error = 4.60769473588223000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.259999999999757 " " y[1] (closed_form) = 2.548039679999678 " " y[1] (numeric) = 2.5480396799997904 " " absolute error = 1.12354570092065840000000000000E-13 " " relative error = 4.409451350933437700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.269999999999760 " " y[1] (closed_form) = 2.5613337733330144 " " y[1] (numeric) = 2.561333773333122 " " absolute error = 1.07469588783715150000000000000E-13 " " relative error = 4.195844754893738300000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.279999999999764 " " y[1] (closed_form) = 2.5746740266663513 " " y[1] (numeric) = 2.5746740266664534 " " absolute error = 1.0214051826551440000000000000E-13 " " relative error = 3.967124273116795000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.289999999999767 " " y[1] (closed_form) = 2.5880605199996882 " " y[1] (numeric) = 2.588060519999786 " " absolute error = 9.76996261670137800000000000000E-14 " " relative error = 3.7750131966398354000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.299999999999770 " " y[1] (closed_form) = 2.601493333333025 " " y[1] (numeric) = 2.6014933333331185 " " absolute error = 9.37028232783632100000000000000E-14 " " relative error = 3.601885965946776000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.309999999999774 " " y[1] (closed_form) = 2.6149725466663614 " " y[1] (numeric) = 2.61497254666645 " " absolute error = 8.88178419700125200000000000000E-14 " " relative error = 3.396511450311015000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.319999999999777 " " y[1] (closed_form) = 2.6284982399996983 " " y[1] (numeric) = 2.6284982399997823 " " absolute error = 8.39328606616618300000000000000E-14 " " relative error = 3.1931868693840737000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.329999999999780 " " y[1] (closed_form) = 2.6420704933330352 " " y[1] (numeric) = 2.6420704933331147 " " absolute error = 7.94919685631612100000000000000E-14 " " relative error = 3.0086997589106784000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.339999999999784 " " y[1] (closed_form) = 2.6556893866663724 " " y[1] (numeric) = 2.655689386666446 " " absolute error = 7.3718808835110390000000000000E-14 " " relative error = 2.7758821948544204000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.349999999999787 " " y[1] (closed_form) = 2.6693549999997086 " " y[1] (numeric) = 2.6693549999997783 " " absolute error = 6.97220059464598300000000000000E-14 " " relative error = 2.611942058904396000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.359999999999790 " " y[1] (closed_form) = 2.683067413333046 " " y[1] (numeric) = 2.6830674133331103 " " absolute error = 6.43929354282590800000000000000E-14 " " relative error = 2.3999745630046182000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.369999999999794 " " y[1] (closed_form) = 2.696826706666383 " " y[1] (numeric) = 2.6968267066664424 " " absolute error = 5.95079541199083900000000000000E-14 " " relative error = 2.2065916943349953000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.379999999999797 " " y[1] (closed_form) = 2.7106329599997196 " " y[1] (numeric) = 2.7106329599997747 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 2.0315204173350518000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.389999999999800 " " y[1] (closed_form) = 2.724486253333057 " " y[1] (numeric) = 2.7244862533331067 " " absolute error = 4.97379915032070130000000000000E-14 " " relative error = 1.82559157501195000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.399999999999804 " " y[1] (closed_form) = 2.7383866666663943 " " y[1] (numeric) = 2.738386666666439 " " absolute error = 4.485301019485632400000000000000E-14 " " relative error = 1.637935604231474000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.409999999999807 " " y[1] (closed_form) = 2.752334279999731 " " y[1] (numeric) = 2.7523342799997708 " " absolute error = 3.996802888650563500000000000000E-14 " " relative error = 1.4521502412312196000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.419999999999810 " " y[1] (closed_form) = 2.766329173333068 " " y[1] (numeric) = 2.7663291733331032 " " absolute error = 3.508304757815494700000000000000E-14 " " relative error = 1.2682166647537618000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.429999999999814 " " y[1] (closed_form) = 2.780371426666405 " " y[1] (numeric) = 2.780371426666435 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 1.086116264186004000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.439999999999817 " " y[1] (closed_form) = 2.7944611199997422 " " y[1] (numeric) = 2.7944611199997675 " " absolute error = 2.53130849614535700000000000000E-14 " " relative error = 9.0583063690848210000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.449999999999820 " " y[1] (closed_form) = 2.8085983333330797 " " y[1] (numeric) = 2.8085983333330997 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 7.1152981208021160000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.459999999999824 " " y[1] (closed_form) = 2.8227831466664166 " " y[1] (numeric) = 2.8227831466664317 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 5.3489879846893040000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4699999999998274 " " y[1] (closed_form) = 2.837015639999754 " " y[1] (numeric) = 2.837015639999764 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 3.44374647744353830000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.479999999999830 " " y[1] (closed_form) = 2.8512958933330914 " " y[1] (numeric) = 2.851295893333096 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 1.55749955972101420000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.489999999999834 " " y[1] (closed_form) = 2.865623986666429 " " y[1] (numeric) = 2.8656239866664284 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.54971207637981200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4999999999998375 " " y[1] (closed_form) = 2.879999999999766 " " y[1] (numeric) = 2.879999999999761 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 1.69617406539968260000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.509999999999840 " " y[1] (closed_form) = 2.8944240133331034 " " y[1] (numeric) = 2.8944240133330927 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 3.68230120649393400000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.519999999999844 " " y[1] (closed_form) = 2.9088961066664405 " " y[1] (numeric) = 2.908896106666426 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 5.0379743337916780000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5299999999998475 " " y[1] (closed_form) = 2.9234163599997784 " " y[1] (numeric) = 2.9234163599997585 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 6.8358427204171270000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.539999999999850 " " y[1] (closed_form) = 2.9379848533331154 " " y[1] (numeric) = 2.9379848533330897 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 8.766952675771069000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.549999999999854 " " y[1] (closed_form) = 2.952601666666453 " " y[1] (numeric) = 2.9526016666664217 " " absolute error = 3.153033389935444600000000000000E-14 " " relative error = 1.0678830895246641000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5599999999998575 " " y[1] (closed_form) = 2.9672668799997908 " " y[1] (numeric) = 2.967266879999754 " " absolute error = 3.6859404417555197000000000000E-14 " " relative error = 1.242200513408413000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.569999999999860 " " y[1] (closed_form) = 2.9819805733331286 " " y[1] (numeric) = 2.9819805733330864 " " absolute error = 4.21884749357559500000000000000E-14 " " relative error = 1.4147803413957022000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.579999999999864 " " y[1] (closed_form) = 2.9967428266664657 " " y[1] (numeric) = 2.9967428266664196 " " absolute error = 4.61852778244065100000000000000E-14 " " relative error = 1.5411825603928236000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5899999999998675 " " y[1] (closed_form) = 3.011553719999804 " " y[1] (numeric) = 3.011553719999752 " " absolute error = 5.195843755245733000000000000000E-14 " " relative error = 1.7253033610989582000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.599999999999870 " " y[1] (closed_form) = 3.0264133333331413 " " y[1] (numeric) = 3.026413333333084 " " absolute error = 5.72875080706580800000000000000E-14 " " relative error = 1.892917515254417000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.609999999999874 " " y[1] (closed_form) = 3.041321746666479 " " y[1] (numeric) = 3.0413217466664184 " " absolute error = 6.03961325396085200000000000000E-14 " " relative error = 1.985851467566932000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.6199999999998775 " " y[1] (closed_form) = 3.0562790399998168 " " y[1] (numeric) = 3.0562790399997506 " " absolute error = 6.61692922676593300000000000000E-14 " " relative error = 2.165027846006603000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.629999999999880 " " y[1] (closed_form) = 3.0712852933331543 " " y[1] (numeric) = 3.071285293333083 " " absolute error = 7.10542735760100200000000000000E-14 " " relative error = 2.31350287549800970000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.639999999999884 " " y[1] (closed_form) = 3.0863405866664917 " " y[1] (numeric) = 3.0863405866664158 " " absolute error = 7.59392548843607100000000000000E-14 " " relative error = 2.4604949697525608000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.649999999999888 " " y[1] (closed_form) = 3.10144499999983 " " y[1] (numeric) = 3.101444999999748 " " absolute error = 8.17124146124115200000000000000E-14 " " relative error = 2.634656252566659000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.659999999999891 " " y[1] (closed_form) = 3.1165986133331676 " " y[1] (numeric) = 3.116598613333081 " " absolute error = 8.65973959207622100000000000000E-14 " " relative error = 2.7785867435828465000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.669999999999894 " " y[1] (closed_form) = 3.1318015066665055 " " y[1] (numeric) = 3.131801506666414 " " absolute error = 9.1482377229112900000000000000E-14 " " relative error = 2.9210783963919507000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.679999999999898 " " y[1] (closed_form) = 3.1470537599998436 " " y[1] (numeric) = 3.1470537599997472 " " absolute error = 9.63673585374635900000000000000E-14 " " relative error = 3.062145291647905000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.689999999999901 " " y[1] (closed_form) = 3.1623554533331815 " " y[1] (numeric) = 3.16235545333308 " " absolute error = 1.01252339845814280000000000000E-13 " " relative error = 3.2018013578800075000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.699999999999904 " " y[1] (closed_form) = 3.1777066666665195 " " y[1] (numeric) = 3.1777066666664133 " " absolute error = 1.06137321154164970000000000000E-13 " " relative error = 3.3400603733353784000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.709999999999908 " " y[1] (closed_form) = 3.1931074799998576 " " y[1] (numeric) = 3.193107479999746 " " absolute error = 1.11466391672365720000000000000E-13 " " relative error = 3.4908437116676916000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.719999999999911 " " y[1] (closed_form) = 3.2085579733331957 " " y[1] (numeric) = 3.208557973333079 " " absolute error = 1.16795462190566470000000000000E-13 " " relative error = 3.640123169388584400000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.729999999999914 " " y[1] (closed_form) = 3.224058226666534 " " y[1] (numeric) = 3.224058226666412 " " absolute error = 1.21680443498917160000000000000E-13 " " relative error = 3.774139142168248000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.739999999999918 " " y[1] (closed_form) = 3.2396083199998715 " " y[1] (numeric) = 3.239608319999744 " " absolute error = 1.27453603226967970000000000000E-13 " " relative error = 3.934228790564811600000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.749999999999921 " " y[1] (closed_form) = 3.25520833333321 " " y[1] (numeric) = 3.2552083333330764 " " absolute error = 1.33670852164868850000000000000E-13 " " relative error = 4.106368578504926400000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.759999999999924 " " y[1] (closed_form) = 3.2708583466665484 " " y[1] (numeric) = 3.2708583466664094 " " absolute error = 1.3899992268306960000000000000E-13 " " relative error = 4.249646666133662400000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.769999999999928 " " y[1] (closed_form) = 3.2865584399998866 " " y[1] (numeric) = 3.2865584399997423 " " absolute error = 1.44328993201270350000000000000E-13 " " relative error = 4.3914932850326965000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.779999999999931 " " y[1] (closed_form) = 3.302308693333224 " " y[1] (numeric) = 3.302308693333075 " " absolute error = 1.49213974509621040000000000000E-13 " " relative error = 4.518474448220349000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.789999999999934 " " y[1] (closed_form) = 3.3181091866665624 " " y[1] (numeric) = 3.3181091866664083 " " absolute error = 1.54098955817971730000000000000E-13 " " relative error = 4.6441797767596240000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.799999999999938 " " y[1] (closed_form) = 3.333959999999901 " " y[1] (numeric) = 3.333959999999741 " " absolute error = 1.59872115546022540000000000000E-13 " " relative error = 4.795261957132877500000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.809999999999941 " " y[1] (closed_form) = 3.3498612133332397 " " y[1] (numeric) = 3.3498612133330745 " " absolute error = 1.6520118606422330000000000000E-13 " " relative error = 4.9315829983249304000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.819999999999944 " " y[1] (closed_form) = 3.365812906666578 " " y[1] (numeric) = 3.3658129066664078 " " absolute error = 1.70086167372573980000000000000E-13 " " relative error = 5.053345865888408000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.829999999999948 " " y[1] (closed_form) = 3.3818151599999164 " " y[1] (numeric) = 3.3818151599997406 " " absolute error = 1.7585932710062480000000000000E-13 " " relative error = 5.200146039342646000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.839999999999951 " " y[1] (closed_form) = 3.3978680533332546 " " y[1] (numeric) = 3.397868053333074 " " absolute error = 1.80744308408975480000000000000E-13 " " relative error = 5.319344529334156000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.849999999999954 " " y[1] (closed_form) = 3.4139716666665927 " " y[1] (numeric) = 3.4139716666664066 " " absolute error = 1.86073378927176240000000000000E-13 " " relative error = 5.450349244077312000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.859999999999958 " " y[1] (closed_form) = 3.4301260799999316 " " y[1] (numeric) = 3.43012607999974 " " absolute error = 1.914024494453770000000000000E-13 " " relative error = 5.580041228262397000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.869999999999961 " " y[1] (closed_form) = 3.4463313733332703 " " y[1] (numeric) = 3.4463313733330727 " " absolute error = 1.97619698383277860000000000000E-13 " " relative error = 5.734204781130531000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.879999999999964 " " y[1] (closed_form) = 3.4625876266666085 " " y[1] (numeric) = 3.462587626666406 " " absolute error = 2.02504679691628550000000000000E-13 " " relative error = 5.8483625983085190000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.889999999999968 " " y[1] (closed_form) = 3.478894919999947 " " y[1] (numeric) = 3.4788949199997394 " " absolute error = 2.07389660999979240000000000000E-13 " " relative error = 5.9613660593112250000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.899999999999971 " " y[1] (closed_form) = 3.4952533333332854 " " y[1] (numeric) = 3.4952533333330726 " " absolute error = 2.12718731518180000000000000E-13 " " relative error = 6.085931726022232000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.909999999999974 " " y[1] (closed_form) = 3.5116629466666245 " " y[1] (numeric) = 3.5116629466664055 " " absolute error = 2.18935980456080870000000000000E-13 " " relative error = 6.23453855854535900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.919999999999978 " " y[1] (closed_form) = 3.5281238399999633 " " y[1] (numeric) = 3.5281238399997386 " " absolute error = 2.24709140184131680000000000000E-13 " " relative error = 6.369083126745744000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.929999999999981 " " y[1] (closed_form) = 3.5446360933333017 " " y[1] (numeric) = 3.5446360933330716 " " absolute error = 2.30038210702332440000000000000E-13 " " relative error = 6.489755355563435000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.939999999999984 " " y[1] (closed_form) = 3.5611997866666405 " " y[1] (numeric) = 3.5611997866664047 " " absolute error = 2.35811370430383250000000000000E-13 " " relative error = 6.621683268466882000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.949999999999988 " " y[1] (closed_form) = 3.5778149999999793 " " y[1] (numeric) = 3.5778149999997377 " " absolute error = 2.41584530158434060000000000000E-13 " " relative error = 6.7522923951751400000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.959999999999991 " " y[1] (closed_form) = 3.5944818133333185 " " y[1] (numeric) = 3.594481813333071 " " absolute error = 2.4735768988648488000000000000E-13 " " relative error = 6.881595254396332000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.969999999999994 " " y[1] (closed_form) = 3.611200306666657 " " y[1] (numeric) = 3.6112003066664045 " " absolute error = 2.52686760404685630000000000000E-13 " " relative error = 6.997306683270912000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.979999999999998 " " y[1] (closed_form) = 3.627970559999996 " " y[1] (numeric) = 3.627970559999738 " " absolute error = 2.5801583092288640000000000000E-13 " " relative error = 7.111850183340150000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.990000000000001 " " y[1] (closed_form) = 3.644792653333335 " " y[1] (numeric) = 3.6447926533330715 " " absolute error = 2.63344901441087130000000000000E-13 " " relative error = 7.225236837553594000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " "Finished!" "diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , 2.0 ) ; " Iterations = 4900 "Total Elapsed Time "= 1 Minutes 7 Seconds "Elapsed Time(since restart) "= 1 Minutes 7 Seconds "Time to Timeout "= 1 Minutes 52 Seconds Percent Done = 100.0204081632654 "%" (%o256) temp/diffeq.expt_lin_c.max