(%i1) batch("temp/diffeq.div_lin_exp.max") read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.div_lin_exp.max (%i2) load("stringproc") (%i3) keepfloat:true (%i4) alias(convfloat,float) (%i5) alias(int_trunc,truncate) (%i6) alias(elapsed_time_seconds,elapsed_real_time) (%i7) alias(ln,log) (%i8) alias(arcsin,asin) (%i9) alias(arccos,acos) (%i10) alias(arctan,atan) (%i11) alias(float_abs,abs) (%i12) mode_declare(display_poles(),fixnum) (%i13) mode_declare(est_size_answer(),convfloat) (%i14) mode_declare(test_suggested_h(),convfloat) (%i15) mode_declare(reached_interval(),boolean) (%i16) mode_declare(display_alot([iter],fixnum),fixnum) (%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum) (%i18) mode_declare(check_for_pole(),fixnum) (%i19) mode_declare(atomall(),fixnum) (%i20) mode_declare(log10([x],convfloat),convfloat) (%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum) (%i22) mode_declare(omniout_timestr(secs_in,number),fixnum) (%i23) mode_declare(zero_ats_ar(ar,array([30],convfloat)),fixnum) (%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a], completearray([30],convfloat),[arr_b], completearray([30],convfloat),[jjj_ats],fixnum), convfloat) (%i25) mode_declare(att([mmm_att],fixnum,[arr_a], completearray([30],convfloat),[arr_b], completearray([30],convfloat),[jjj_att],fixnum), convfloat) (%i26) mode_declare(logitem_ditto([file],fixnum),fixnum) (%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum) (%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum) (%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum) (%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum) (%i31) mode_declare(logstart([file],fixnum),fixnum) (%i32) mode_declare(logend([file],fixnum),fixnum) (%i33) mode_declare(chk_data(),fixnum) (%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat, [t2],convfloat,[clock_sec2],convfloat), convfloat) (%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2], convfloat),convfloat) (%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i42) mode_declare(neg([nnn],convfloat),convfloat) (%i43) mode_declare(factorial_2([nnn],fixnum),convfloat) (%i44) mode_declare(factorial_1([nnn],fixnum),convfloat) (%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat) (%i46) mode_declare(convfloat([mmm],fixnum),convfloat) (%i47) mode_declare(elaped_time_seconds(),convfloat) (%i48) mode_declare(Si([x],convfloat),convfloat) (%i49) mode_declare(Ci([x],convfloat),convfloat) (%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end], convfloat,[estimated_h], convfloat,[estimated_answer], convfloat),convfloat) (%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat) (%i52) mode_declare(main_prog(),fixnum) (%i53) define_variable(always,1,fixnum) (%i54) define_variable(info,2,fixnum) (%i55) define_variable(debugl,3,fixnum) (%i56) define_variable(debugmassive,4,fixnum) (%i57) define_variable(glob_iolevel,5,fixnum) (%i58) define_variable(glob_yes_pole,4,fixnum) (%i59) define_variable(glob_no_pole,3,fixnum) (%i60) define_variable(glob_not_given,0,fixnum) (%i61) define_variable(glob_no_sing_tests,4,fixnum) (%i62) define_variable(glob_ratio_test,1,fixnum) (%i63) define_variable(glob_three_term_test,2,fixnum) (%i64) define_variable(glob_six_term_test,3,fixnum) (%i65) define_variable(ats_max_terms,30,fixnum) (%i66) define_variable(glob_log_10,0.0,convfloat) (%i67) define_variable(max_unchanged,10,fixnum) (%i68) define_variable(glob__small,1.0E-51,convfloat) (%i69) define_variable(glob_small_float,1.0E-51,convfloat) (%i70) define_variable(glob_smallish_float,1.0E-61,convfloat) (%i71) define_variable(glob_large_float,1.0E+100,convfloat) (%i72) define_variable(glob_larger_float,1.1E+100,convfloat) (%i73) define_variable(glob__m2,-2.0,convfloat) (%i74) define_variable(glob__m1,-1.0,convfloat) (%i75) define_variable(glob__0,0.0,convfloat) (%i76) define_variable(glob__1,1.0,convfloat) (%i77) define_variable(glob__2,2.0,convfloat) (%i78) define_variable(glob__3,3.0,convfloat) (%i79) define_variable(glob__4,4.0,convfloat) (%i80) define_variable(glob__5,5.0,convfloat) (%i81) define_variable(glob__8,8.0,convfloat) (%i82) define_variable(glob__10,10.0,convfloat) (%i83) define_variable(glob__100,100.0,convfloat) (%i84) define_variable(glob__pi,0.0,convfloat) (%i85) define_variable(glob__0_5,0.5,convfloat) (%i86) define_variable(glob__0_8,0.8,convfloat) (%i87) define_variable(glob__m0_8,-0.8,convfloat) (%i88) define_variable(glob__0_25,0.25,convfloat) (%i89) define_variable(glob__0_125,0.125,convfloat) (%i90) define_variable(glob_prec,1.0E-16,convfloat) (%i91) define_variable(glob_check_sign,1.0,convfloat) (%i92) define_variable(glob_desired_digits_correct,8.0,convfloat) (%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat) (%i94) define_variable(glob_ratio_of_radius,0.1,convfloat) (%i95) define_variable(glob_percent_done,0.0,convfloat) (%i96) define_variable(glob_total_exp_sec,0.1,convfloat) (%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat) (%i98) define_variable(glob_estimated_size_answer,100.0,convfloat) (%i99) define_variable(glob_almost_1,0.999,convfloat) (%i100) define_variable(glob_clock_sec,0.0,convfloat) (%i101) define_variable(glob_clock_start_sec,0.0,convfloat) (%i102) define_variable(glob_disp_incr,0.1,convfloat) (%i103) define_variable(glob_h,0.1,convfloat) (%i104) define_variable(glob_diff_rc_fm,0.1,convfloat) (%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat) (%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat) (%i107) define_variable(glob_diff_ord_fm,0.1,convfloat) (%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat) (%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat) (%i110) define_variable(glob_six_term_ord_save,0.1,convfloat) (%i111) define_variable(glob_guess_error_rc,0.1,convfloat) (%i112) define_variable(glob_guess_error_ord,0.1,convfloat) (%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat) (%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat) (%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat) (%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat) (%i117) define_variable(glob_last_good_h,0.1,convfloat) (%i118) define_variable(glob_max_h,0.1,convfloat) (%i119) define_variable(glob_min_h,1.0E-6,convfloat) (%i120) define_variable(glob_display_interval,0.1,convfloat) (%i121) define_variable(glob_abserr,1.0E-11,convfloat) (%i122) define_variable(glob_relerr,1.0E-11,convfloat) (%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat) (%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat) (%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat) (%i126) define_variable(glob_max_hours,0.0,convfloat) (%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat) (%i128) define_variable(glob_optimal_start,0.0,convfloat) (%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat) (%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat) (%i131) define_variable(glob_max_sec,10000.0,convfloat) (%i132) define_variable(glob_orig_start_sec,0.0,convfloat) (%i133) define_variable(glob_normmax,0.0,convfloat) (%i134) define_variable(glob_max_minutes,0.0,convfloat) (%i135) define_variable(glob_next_display,0.0,convfloat) (%i136) define_variable(glob_est_digits,1,fixnum) (%i137) define_variable(glob_subiter_method,3,fixnum) (%i138) define_variable(glob_html_log,true,boolean) (%i139) define_variable(glob_min_good_digits,99999,fixnum) (%i140) define_variable(glob_good_digits,0,fixnum) (%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum) (%i142) define_variable(glob_apfp_est_good_digits,0,fixnum) (%i143) define_variable(glob_max_opt_iter,10,fixnum) (%i144) define_variable(glob_dump,false,boolean) (%i145) define_variable(glob_djd_debug,true,boolean) (%i146) define_variable(glob_display_flag,true,boolean) (%i147) define_variable(glob_djd_debug2,true,boolean) (%i148) define_variable(glob_h_reason,0,fixnum) (%i149) define_variable(glob_sec_in_minute,60,fixnum) (%i150) define_variable(glob_min_in_hour,60,fixnum) (%i151) define_variable(glob_hours_in_day,24,fixnum) (%i152) define_variable(glob_days_in_year,365,fixnum) (%i153) define_variable(glob_sec_in_hour,3600,fixnum) (%i154) define_variable(glob_sec_in_day,86400,fixnum) (%i155) define_variable(glob_sec_in_year,31536000,fixnum) (%i156) define_variable(glob_not_yet_finished,true,boolean) (%i157) define_variable(glob_initial_pass,true,boolean) (%i158) define_variable(glob_not_yet_start_msg,true,boolean) (%i159) define_variable(glob_reached_optimal_h,false,boolean) (%i160) define_variable(glob_optimal_done,false,boolean) (%i161) define_variable(glob_type_given_pole,0,fixnum) (%i162) define_variable(glob_optimize,false,boolean) (%i163) define_variable(glob_look_poles,false,boolean) (%i164) define_variable(glob_dump_closed_form,false,boolean) (%i165) define_variable(glob_max_iter,1000,fixnum) (%i166) define_variable(glob_no_eqs,0,fixnum) (%i167) define_variable(glob_unchanged_h_cnt,0,fixnum) (%i168) define_variable(glob_warned,false,boolean) (%i169) define_variable(glob_warned2,false,boolean) (%i170) define_variable(glob_start,0,fixnum) (%i171) define_variable(glob_iter,0,fixnum) (%i172) completearray(array_y_init,[30],convfloat) (%i173) completearray(array_norms,[30],convfloat) (%i174) completearray(array_fact_1,[30],convfloat) (%i175) completearray(array_1st_rel_error,[2],convfloat) (%i176) completearray(array_last_rel_error,[2],convfloat) (%i177) completearray(array_est_rel_error,[2],convfloat) (%i178) completearray(array_max_est_error,[2],convfloat) (%i179) completearray(array_type_pole,[2],convfloat) (%i180) completearray(array_type_real_pole,[2],convfloat) (%i181) completearray(array_type_complex_pole,[2],convfloat) (%i182) completearray(array_est_digits,[2],convfloat) (%i183) completearray(array_y,[30],convfloat) (%i184) completearray(array_x,[30],convfloat) (%i185) completearray(array_tmp0,[30],convfloat) (%i186) completearray(array_tmp1,[30],convfloat) (%i187) completearray(array_tmp2,[30],convfloat) (%i188) completearray(array_tmp3,[30],convfloat) (%i189) completearray(array_tmp4,[30],convfloat) (%i190) completearray(array_tmp5,[30],convfloat) (%i191) completearray(array_m1,[30],convfloat) (%i192) completearray(array_y_higher,[2,30],convfloat) (%i193) completearray(array_y_higher_work,[2,30],convfloat) (%i194) completearray(array_y_higher_work2,[2,30],convfloat) (%i195) completearray(array_y_set_initial,[2,30],convfloat) (%i196) completearray(array_given_rad_poles,[2,3],convfloat) (%i197) completearray(array_given_ord_poles,[2,3],convfloat) (%i198) completearray(array_rad_test_poles,[2,4],convfloat) (%i199) completearray(array_ord_test_poles,[2,4],convfloat) (%i200) completearray(array_fact_2,[30,30],convfloat) (%i201) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%i202) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%i203) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%i204) omniout_float(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (if vallen = 4 then printf(true,"~a = ~g ~s ~%",prelabel, value,postlabel) else printf(true,"~a = ~g ~s ~%",prelabel, value,postlabel)) (%i205) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%i206) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%i207) logitem_time(fd,secs_in):=( block(mode_declare( [[days_int,hours_int,minutes_int,sec_int, years_int],fixnum,[secs,secs_temp],convfloat]), secs:secs_in,printf(fd,"~%"), if secs >= 0 then (years_int :truncate(secs/glob_sec_in_year), sec_temp :mod(truncate(secs), truncate(glob_sec_in_year)), days_int :truncate(sec_temp/glob_sec_in_day), sec_temp :mod(sec_temp, truncate(glob_sec_in_day)), hours_int :truncate(sec_temp/glob_sec_in_hour), sec_temp :mod(sec_temp, truncate(glob_sec_in_hour)), minutes_int :truncate(sec_temp/glob_sec_in_minute), sec_int :mod(sec_temp, truncate(glob_sec_in_minute)), if truncate(years_int) > 0.1 then printf(fd, "~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int,days_int, hours_int,minutes_int, sec_int) elseif days_int > 0.1 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,hours_int, minutes_int,sec_int) elseif hours_int > 0.1 then printf(fd, "~d Hours ~d Minutes ~d Seconds~%", hours_int,minutes_int, sec_int) elseif minutes_int > 0.1 then printf(fd, "~d Minutes ~d Seconds~%", minutes_int,sec_int) else printf(fd,"~d Seconds~%", sec_int)) else printf(fd," 0.0 Seconds~%"), printf(fd,"~%")),0) (%i208) omniout_timestr(secs_in):=( block(mode_declare( [[days_int,hours_int,minutes_int,sec_int, years_int],fixnum,[secs,secs_temp], convfloat]),secs:secs_in, if secs >= 0 then ( years_int:truncate(secs/glob_sec_in_year), sec_temp :mod(truncate(secs), truncate(glob_sec_in_year)), days_int:truncate(sec_temp/glob_sec_in_day), sec_temp :mod(sec_temp,truncate(glob_sec_in_day)), hours_int :truncate(sec_temp/glob_sec_in_hour), sec_temp :mod(sec_temp,truncate(glob_sec_in_hour)), minutes_int :truncate(sec_temp/glob_sec_in_minute), sec_int :mod(sec_temp, truncate(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int,days_int, hours_int,minutes_int, sec_int) elseif days_int > 0.1 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,hours_int, minutes_int,sec_int) elseif hours_int > 0.1 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,minutes_int, sec_int) elseif minutes_int > 0.1 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int,sec_int) else printf(true,"= ~d Seconds~%", sec_int)) else printf(true,"= 0.0 Seconds~%")),0) (%i209) zero_ats_ar(arr_a):=( block(mode_declare([iii],fixnum),iii:1, while iii <= ats_max_terms do (arr_a[iii]:glob__0,iii:1+iii)),0) (%i210) ats(mmm_ats,arr_a,arr_b,jjj_ats):=block( mode_declare([[iii_ats,lll_ats,ma_ats],fixnum,[ret_ats], convfloat]),ret_ats:glob__0, if jjj_ats <= mmm_ats then (ma_ats:1+mmm_ats,iii_ats:jjj_ats, while iii_ats <= mmm_ats do (lll_ats:ma_ats-iii_ats, if lll_ats <= ats_max_terms and iii_ats <= ats_max_terms then ret_ats :c(arr_a[iii_ats])*c(arr_b[lll_ats])+ret_ats, iii_ats:1+iii_ats)),ret_ats) (%i211) att(mmm_att,arr_aa,arr_bb,jjj_att):=block( mode_declare([[al_att,iii_att,lll_att,ma_att],convfloat,[ret_att], fixnum]),ret_att:glob__0, if jjj_att < mmm_att then (ma_att:2+mmm_att,iii_att:jjj_att, while iii_att < mmm_att and iii_att <= ats_max_terms do (lll_att:ma_att-iii_att,al_att:lll_att-1, if lll_att <= ats_max_terms and iii_att <= ats_max_terms then ret_att :c(arr_aa[iii_att])*c(arr_bb[lll_att]) *c(al_att) +ret_att,iii_att:1+iii_att), ret_att:ret_att/c(mmm_att)),ret_att) (%i212) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%i213) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%i214) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%i215) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), printf(file,"~d",glob_min_good_digits), printf(file,"")),0) (%i216) log_revs(file,revs):=printf(file,revs) (%i217) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%i218) logitem_h_reason(file):=(printf(file,""), if glob_h_reason = 1 then printf(file,"Max H") elseif glob_h_reason = 2 then printf(file,"Display_interval") elseif glob_h_reason = 3 then printf(file,"Optimal") elseif glob_h_reason = 4 then printf(file,"Pole Accuracy") elseif glob_h_reason = 5 then printf(file,"Min H (Pole)") elseif glob_h_reason = 6 then printf(file,"Pole") elseif glob_h_reason = 7 then printf(file,"Opt Iter") else printf(file,"Impossible"), printf(file,""),0) (%i219) logstart(file):=(printf(file,""),0) (%i220) logend(file):=(printf(file,"~%"),0) (%i221) chk_data():=( block(mode_declare([[errflag],boolean]),errflag:false, if glob_max_iter < 2 then (omniout_str(always,"Illegal max_iter"), errflag:true),if errflag then quit()),0) (%i222) comp_expect_sec(t_end2,t_start2,t2,clock_sec2):=block( mode_declare([[ms2,rrr,sec_left,sub1,sub2], convfloat]),ms2:c(clock_sec2), sub1:c(t_end2-t_start2),sub2:c(t2-t_start2), if sub1 = glob__0 then sec_left:glob__0 else (if sub2 > glob__0 then (rrr:sub1/sub2, sec_left:rrr*c(ms2)-c(ms2)) else sec_left:glob__0),sec_left) (%i223) comp_percent(t_end2,t_start2,t2):=block( mode_declare([[rrr,sub1,sub2],convfloat]), sub1:t_end2-t_start2,sub2:t2-t_start2, if sub2 > glob_small_float then rrr:glob__100*sub2/sub1 else rrr:0.0,rrr) (%i224) comp_rad_from_ratio(term1,term2,last_no):=( if abs(term2) > glob__0 then ret:abs(term1*glob_h/term2) else ret:glob_larger_float,ret) (%i225) comp_ord_from_ratio(term1,term2,last_no):=( if abs(term2) > glob__0 then ret :abs(term2)*c(last_no) *log(abs(term1*glob_h/term2)) /log(c(last_no)) +glob__1 else ret:glob_larger_float,ret) (%i226) c(in_val):=(ret:in_val,ret) (%i227) comp_rad_from_three_terms(term1,term2,term3,last_no):=( temp:abs( term1*term3-term1*term3*c(last_no) +glob__m2*term2*term2 +term2*term2*c(last_no)), if abs(temp) > glob__0 then ret:abs(term2*glob_h*term1/temp) else ret:glob_larger_float,ret) (%i228) comp_ord_from_three_terms(term1,term2,term3,last_no):=( ret:abs( (-term1*term3*c(last_no*last_no) +term2*term2*c(last_no*last_no) +glob__4*term2*term2 -glob__4*term2*term2*c(last_no) -glob__3*term1*term3 +glob__4*term1*term3*c(last_no)) /(term1*term3-term1*term3*c(last_no) -glob__2*term2*term2 +term2*term2*c(last_no))), ret) (%i229) comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):= ( if term5 # glob__0 and term4 # glob__0 and term3 # glob__0 and term2 # glob__0 and term1 # glob__0 then (rm0:term6/term5,rm1:term5/term4, rm2:term4/term3,rm3:term3/term2, rm4:term2/term1, nr1 :c(last_no-3)*rm2 -glob__2*c(last_no-2)*rm1 +c(last_no-1)*rm0, nr2 :c(last_no-4)*rm3 -glob__2*c(last_no-3)*rm2 +c(last_no-2)*rm1, dr1 :(-glob__1)/rm3+glob__2/rm2 +glob__m1/rm1, dr2 :(-glob__1)/rm4+glob__2/rm3 +glob__m1/rm2, ds1 :glob__5/rm3-glob__8/rm2 +glob__3/rm1, ds2 :glob__5/rm4-glob__8/rm3 +glob__3/rm2, if abs(nr1*dr2-nr2*dr1) = glob__0 or abs(dr1) = glob__0 then (rad_c:glob_larger_float, ord_no:glob_larger_float) else (if abs(nr1*dr2-nr2*dr1) > glob__0 then ( rcs :(dr1*dr2-ds2*dr1+ds1*dr2) /(nr1*dr2-nr2*dr1), ord_no :(rcs*nr1-ds1)/(glob__2*dr1) -c(last_no)/glob__2, if abs(rcs) # glob__0 then (if rcs > glob__0 then rad_c :sqrt(rcs) *abs(glob_h) else ( rad_c :glob_larger_float, ord_no :glob_larger_float)) else ( rad_c:glob_larger_float, ord_no:glob_larger_float)) else (rad_c:glob_larger_float, ord_no:glob_larger_float))) else (rad_c:glob_larger_float, ord_no:glob_larger_float), glob_six_term_ord_save:ord_no,rad_c) (%i230) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%i231) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret) (%i232) factorial_1(nnn):=block(mode_declare([[ret],convfloat]), if nnn <= ats_max_terms then (if array_fact_1[nnn] = 0 then (ret:factorial_2(nnn), array_fact_1[nnn]:ret) else ret:array_fact_1[nnn]) else ret:factorial_2(nnn),ret) (%i233) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret) (%i234) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret) (%i235) factorial_3(mmm,nnn):=block(mode_declare([[ret],convfloat]), if nnn <= ats_max_terms and mmm <= ats_max_terms then (if array_fact_2[mmm,nnn] = 0 then (ret:factorial_1(mmm)/factorial_1(nnn), array_fact_2[mmm,nnn]:ret) else ret:array_fact_2[mmm,nnn]) else ret:factorial_2(mmm)/factorial_2(nnn),ret) (%i236) log10(x):=log(x)/glob_log_10 (%i237) c(x):=x (%i238) expt(x,y):=if y = 0.0 then 1.0 elseif x <= 0.0 and y < 0.0 then print("expt error x = ",x,"y = ",y) else x^y (%i239) estimated_needed_step_error(x_start,x_end,estimated_h, estimated_answer):=block( [desired_abs_gbl_error,range, estimated_steps,step_error], omniout_float(always, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32,""), desired_abs_gbl_error :expt(glob__10, c(-glob_desired_digits_correct)) *c(abs(c(estimated_answer))), omniout_float(always,"estimated_h",32, estimated_h,32,""), omniout_float(always,"estimated_answer", 32,estimated_answer,32,""), omniout_float(always, "desired_abs_gbl_error",32, desired_abs_gbl_error,32, ""),range:x_end-x_start, omniout_float(always,"range",32,range,32, ""), estimated_steps:range/estimated_h, omniout_float(always,"estimated_steps",32, estimated_steps,32,""), step_error :c( abs(desired_abs_gbl_error) /sqrt(c(estimated_steps)) /c(ats_max_terms)), omniout_float(always,"step_error",32, step_error,32,""), step_error) (%i240) exact_soln_y(x):=block(neg(c(0.1)*(c(2.0)*c(x)+c(5.0)))/exp(c(x))) neg(c(0.1) (c(2.0) c(x) + c(5.0))) (%o240) exact_soln_y(x) := block(----------------------------------) exp(c(x)) (%i241) display_poles():=( block(mode_declare([[rad_given],convfloat]), if glob_type_given_pole = 1 or glob_type_given_pole = 2 then (rad_given :sqrt( array_given_rad_poles[1,2] *array_given_rad_poles[1,2] +(array_x[1] -array_given_rad_poles[1,1]) *(array_x[1] -array_given_rad_poles[1,1])), omniout_float(always, "Radius of convergence (given) for eq 1 ", 4,rad_given,4," "), omniout_float(always, "Order of pole (given) ", 4, array_given_ord_poles[ 1,1],4," "), if rad_given < glob_least_given_sing then glob_least_given_sing :rad_given) elseif glob_type_given_pole = 3 then omniout_str(always, "NO POLE (given) for Equation 1") elseif glob_type_given_pole = 5 then omniout_str(always, "SOME POLE (given) for Equation 1") else omniout_str(always, "NO info (given) for Equation 1"), if array_rad_test_poles[1,1] < glob_large_float then (omniout_float(always, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1,1], 4," "), if array_rad_test_poles[1,1] < glob_least_ratio_sing then glob_least_ratio_sing :array_rad_test_poles[1,1], omniout_float(always, "Order of pole (ratio test) ", 4, array_ord_test_poles[1,1], 4," ")) else omniout_str(always, "NO POLE (ratio test) for Equation 1"), if array_rad_test_poles[1,2] > glob__small and array_rad_test_poles[1,2] < glob_large_float then (omniout_float(always, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1,2], 4," "), if array_rad_test_poles[1,2] < glob_least_3_sing then glob_least_3_sing :array_rad_test_poles[1,2], omniout_float(always, "Order of pole (three term test) ", 4, array_ord_test_poles[1,2], 4," ")) else omniout_str(always, "NO REAL POLE (three term test) for Equation 1"), if array_rad_test_poles[1,3] > glob__small and array_rad_test_poles[1,3] < glob_large_float then (omniout_float(always, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1,3], 4," "), if array_rad_test_poles[1,3] < glob_least_6_sing then glob_least_6_sing :array_rad_test_poles[1,3], omniout_float(always, "Order of pole (six term test) ", 4, array_ord_test_poles[1,3], 4," ")) else omniout_str(always, "NO COMPLEX POLE (six term test) for Equation 1")), 0) (%i242) my_check_sign(x0,xf):=block([ret], if xf > x0 then ret:glob__1 else ret:glob__m1,ret) (%i243) est_size_answer():=block([min_size], min_size:glob_estimated_size_answer, if abs(array_y[1]) < min_size then (min_size:abs(array_y[1]), omniout_float(always,"min_size",32,min_size, 32,"")), if min_size < glob__1 then (min_size:glob__1, omniout_float(always,"min_size",32,min_size, 32,"")),min_size) (%i244) test_suggested_h():=block( [max_estimated_step_error,hn_div_ho,hn_div_ho_2, hn_div_ho_3,no_terms,est_tmp], max_estimated_step_error:glob__small, no_terms:ats_max_terms,hn_div_ho:glob__0_5, hn_div_ho_2:glob__0_25,hn_div_ho_3:glob__0_125, omniout_float(always,"hn_div_ho",32,hn_div_ho,32,""), omniout_float(always,"hn_div_ho_2",32,hn_div_ho_2,32, ""), omniout_float(always,"hn_div_ho_3",32,hn_div_ho_3,32, ""), est_tmp:abs(array_y[no_terms]*hn_div_ho_3 +array_y[no_terms-1]*hn_div_ho_2 +array_y[no_terms-2]*hn_div_ho +array_y[no_terms-3]), if est_tmp >= max_estimated_step_error then max_estimated_step_error:est_tmp, omniout_float(always,"max_estimated_step_error",32, max_estimated_step_error,32,""), max_estimated_step_error) (%i245) track_estimated_error():=block( [hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms, est_tmp],no_terms:ats_max_terms, hn_div_ho:glob__0_5,hn_div_ho_2:glob__0_25, hn_div_ho_3:glob__0_125, est_tmp:c(abs(array_y[no_terms]))*c(hn_div_ho_3) +c(abs(array_y[no_terms-1])) *c(hn_div_ho_2) +c(abs(array_y[no_terms-2])) *c(hn_div_ho) +c(abs(array_y[no_terms-3])), if glob_prec*c(abs(array_y[1])) > c(est_tmp) then est_tmp :c(glob_prec)*c(abs(array_y[1])), if c(est_tmp) >= c(array_max_est_error[1]) then array_max_est_error[1]:c(est_tmp)) (%i246) reached_interval():=block(mode_declare([[ret],boolean]), if glob_check_sign*array_x[1] >= glob_check_sign*glob_next_display -glob_h/glob__10 then ret:true else ret:false, return(ret)) (%i247) display_alot(iter):=( block(mode_declare( [[abserr,est_rel_err],convfloat, [closed_form_val_y],convfloat,[ind_var], convfloat,[numeric_val],convfloat,[relerr], convfloat,[term_no],fixnum]), if reached_interval() then (if iter >= 0 then (ind_var:array_x[1], omniout_float(always, "x[1] ", 33,ind_var,20, " "), closed_form_val_y :exact_soln_y(ind_var), omniout_float(always, "y[1] (closed_form) ", 33, closed_form_val_y, 20," "), term_no:1, numeric_val:array_y[term_no], abserr :abs( numeric_val -closed_form_val_y), omniout_float(always, "y[1] (numeric) ", 33,numeric_val, 20," "), if c(abs(closed_form_val_y)) > c(glob_prec) then ( relerr :abserr*glob__100 /abs(closed_form_val_y), if c(relerr) > c(glob_prec) then glob_good_digits :3 -floor(log10(c(relerr))) else glob_good_digits:16) else (relerr:glob__m1, glob_good_digits:-16), if glob_good_digits < glob_min_good_digits then glob_min_good_digits :glob_good_digits, if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits then glob_min_apfp_est_good_digits :glob_apfp_est_good_digits, if c(abs(numeric_val)) > c(glob_prec) then ( est_rel_err :c(array_max_est_error[1]) *glob__100 *c(sqrt(glob_iter))*c(25) *c(ats_max_terms) /c(abs(numeric_val)), if est_rel_err > glob_prec then glob_est_digits :3 -floor( log10(est_rel_err)) else glob_est_digits:16) else (relerr:glob__m1, glob_est_digits:-16), array_est_digits[1] :glob_est_digits, if glob_iter = 1 then array_1st_rel_error[1] :relerr else array_last_rel_error[ 1] :relerr, array_est_rel_error[1] :est_rel_err, omniout_float(always, "absolute error ", 4,abserr,20," "), omniout_float(always, "relative error ", 4,relerr,20,"%"), omniout_int(info, "Desired digits ", 32, glob_desired_digits_correct, 4," "), omniout_int(info, "Estimated correct digits ", 32,glob_est_digits, 4," "), omniout_int(info, "Correct digits ", 32, glob_good_digits,4, " "), omniout_float(always, "h ", 4,glob_h,20, " ")))),0) (%i248) prog_report(x_start,x_end):=( block(mode_declare([[clock_sec],convfloat,[opt_clock_sec], convfloat,[clock_sec1],convfloat, [expect_sec],convfloat,[left_sec], convfloat,[percent_done],convfloat, [total_clock_sec],convfloat]), clock_sec1:elapsed_time_seconds(), total_clock_sec:clock_sec1-glob_orig_start_sec, glob_clock_sec:clock_sec1-glob_clock_start_sec, left_sec:-clock_sec1+glob_orig_start_sec +glob_max_sec, expect_sec:comp_expect_sec(x_end,x_start, glob_h+array_x[1], clock_sec1 -glob_orig_start_sec), opt_clock_sec:clock_sec1 -glob_optimal_clock_start_sec, glob_optimal_expect_sec :comp_expect_sec(x_end,x_start,glob_h+array_x[1], opt_clock_sec), glob_total_exp_sec :c(total_clock_sec)+glob_optimal_expect_sec, percent_done:comp_percent(x_end,x_start, glob_h+array_x[1]), glob_percent_done:percent_done, omniout_str_noeol(info, "Total Elapsed Time "), omniout_timestr(total_clock_sec), omniout_str_noeol(info, "Elapsed Time(since restart) "), omniout_timestr(glob_clock_sec), if c(percent_done) < glob__100 then (omniout_str_noeol(info, "Expected Time Remaining "), omniout_timestr(expect_sec), omniout_str_noeol(info, "Optimized Time Remaining "), omniout_timestr(glob_optimal_expect_sec), omniout_str_noeol(info, "Expected Total Time "), omniout_timestr(glob_total_exp_sec)), omniout_str_noeol(info, "Time to Timeout "), omniout_timestr(left_sec), omniout_float(info, "Percent Done ",33, percent_done,4,"%")),0) (%i249) check_for_pole():=( block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc], convfloat,[m,n],fixnum,[nr1,nr2], convfloat,[ord_no],fixnum, [term1,term2,term3,part1,part2, part3,part4,part5,part6,part7, part8,part9,part10,part11,part12, part13,part14,rad_c,rcs,rm0,rm1, rm2,rm3,rm4],convfloat, [found_sing],fixnum, [h_new,ratio,term,local_test, tmp_rad,tmp_ord,tmp_ratio, prev_tmp_rad],convfloat,[last_no], fixnum),tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,1]:glob_larger_float, array_ord_test_poles[1,1]:glob_larger_float, found_sing:1,last_no:-10-1+ats_max_terms,cnt:0, while last_no < ats_max_terms-3 and found_sing = 1 do (tmp_rad :comp_rad_from_ratio( array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,1] then ( array_rad_test_poles[1,1]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_ratio( array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,1]:rad_c, array_ord_test_poles[1,1] :tmp_ord)), tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,2]:glob_larger_float, array_ord_test_poles[1,2]:glob_larger_float, found_sing:1,last_no:-10-1+ats_max_terms,cnt:0, while last_no < ats_max_terms-4 and found_sing = 1 do (tmp_rad :comp_rad_from_three_terms( array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,2] then ( array_rad_test_poles[1,2]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_three_terms( array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,2]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,2] :tmp_ord)), tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,3]:glob_larger_float, array_ord_test_poles[1,3]:glob_larger_float, found_sing:1,last_no:-10-1+ats_max_terms,cnt:0, while last_no < ats_max_terms-7 and found_sing = 1 do (tmp_rad :comp_rad_from_six_terms( array_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,3] then ( array_rad_test_poles[1,3]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_six_terms( array_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,3]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,3] :tmp_ord)), if abs(glob_min_pole_est)*glob_ratio_of_radius < abs(glob_h) then (h_new :glob_check_sign*glob_min_pole_est *glob_ratio_of_radius, omniout_str(always, "SETTING H FOR POLE"), glob_h_reason:6, if glob_check_sign*glob_min_h > glob_check_sign*h_new then ( omniout_str(always, "SETTING H FOR MIN H"), h_new:glob_min_h,glob_h_reason:5), term:1,ratio:c(1.0), while term <= ats_max_terms do ( array_y[term] :array_y[term]*ratio, array_y_higher[1,term] :array_y_higher[1,term]*ratio, array_x[term] :array_x[term]*ratio, ratio:ratio*h_new/abs(glob_h), term:1+term),glob_h:h_new), if reached_interval() then display_poles()),0) (%i250) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:array_const_0D2[1]*array_x[1], array_tmp2[1]:array_const_0D3[1]+array_tmp1[1], array_tmp3[1]:exp(array_x[1]), array_tmp4[1]:array_tmp2[1]/array_tmp3[1], array_tmp5[1]:array_tmp4[1]+array_const_0D0[1], if not array_y_set_initial[1,2] then (if 1 <= ats_max_terms then ( temporary :c(array_tmp5[1])*expt(glob_h,c(1)) *c(factorial_3(0,1)), if 2 <= ats_max_terms then (array_y[2]:temporary, array_y_higher[1,2]:temporary), temporary:c(temporary)*c(1)/c(glob_h), array_y_higher[2,1]:c(temporary),0)), kkk:2,array_tmp1[2]:array_const_0D2[1]*array_x[2], array_tmp2[2]:array_tmp1[2], array_tmp3[2]:array_tmp3[1]*array_x[2]/c(1), array_tmp4[2]:(array_tmp2[2] -array_tmp4[1]*array_tmp3[2]) /array_tmp3[1], array_tmp5[2]:array_tmp4[2], if not array_y_set_initial[1,3] then (if 2 <= ats_max_terms then ( temporary :c(array_tmp5[2])*expt(glob_h,c(1)) *c(factorial_3(1,2)), if 3 <= ats_max_terms then (array_y[3]:temporary, array_y_higher[1,3]:temporary), temporary:c(temporary)*c(2)/c(glob_h), array_y_higher[2,2]:c(temporary),0)), kkk:3,array_tmp3[3]:array_tmp3[2]*array_x[2]/c(2), array_tmp4[3]:neg(ats(3,array_tmp3,array_tmp4,2)) /array_tmp3[1], array_tmp5[3]:array_tmp4[3], if not array_y_set_initial[1,4] then (if 3 <= ats_max_terms then ( temporary :c(array_tmp5[3])*expt(glob_h,c(1)) *c(factorial_3(2,3)), if 4 <= ats_max_terms then (array_y[4]:temporary, array_y_higher[1,4]:temporary), temporary:c(temporary)*c(3)/c(glob_h), array_y_higher[2,3]:c(temporary),0)), kkk:4,array_tmp3[4]:array_tmp3[3]*array_x[2]/c(3), array_tmp4[4]:neg(ats(4,array_tmp3,array_tmp4,2)) /array_tmp3[1], array_tmp5[4]:array_tmp4[4], if not array_y_set_initial[1,5] then (if 4 <= ats_max_terms then ( temporary :c(array_tmp5[4])*expt(glob_h,c(1)) *c(factorial_3(3,4)), if 5 <= ats_max_terms then (array_y[5]:temporary, array_y_higher[1,5]:temporary), temporary:c(temporary)*c(4)/c(glob_h), array_y_higher[2,4]:c(temporary),0)), kkk:5,array_tmp3[5]:array_tmp3[4]*array_x[2]/c(4), array_tmp4[5]:neg(ats(5,array_tmp3,array_tmp4,2)) /array_tmp3[1], array_tmp5[5]:array_tmp4[5], if not array_y_set_initial[1,6] then (if 5 <= ats_max_terms then ( temporary :c(array_tmp5[5])*expt(glob_h,c(1)) *c(factorial_3(4,5)), if 6 <= ats_max_terms then (array_y[6]:temporary, array_y_higher[1,6]:temporary), temporary:c(temporary)*c(5)/c(glob_h), array_y_higher[2,5]:c(temporary),0)), kkk:6, while kkk <= ats_max_terms do (array_tmp3[kkk] :array_tmp3[kkk-1]*array_x[2]/c(kkk-1), array_tmp4[kkk] :neg(ats(kkk,array_tmp3,array_tmp4,2)) /array_tmp3[1],array_tmp5[kkk]:array_tmp4[kkk], order_d:1, if order_d+kkk <= ats_max_terms then (if not array_y_set_initial[1,order_d+kkk] then ( temporary :c(array_tmp5[kkk])*expt(glob_h,c(order_d)) *c( factorial_3( kkk-1, -1+order_d+kkk)), array_y[order_d+kkk]:c(temporary), array_y_higher[1,order_d+kkk]:c(temporary), term:-1+order_d+kkk,adj2:-1+order_d+kkk, adj3:2, while term >= 1 and term <= ats_max_terms and adj3 < 1+order_d do ( if adj3 <= 1+order_d then ( if adj2 > 0 then temporary :c(temporary)*c(adj2) /c(glob_h) else temporary:c(temporary), array_y_higher[adj3,term] :c(temporary)),term:term-1, adj2:adj2-1,adj3:1+adj3))), kkk:1+kkk)),0) (%i251) exact_soln_y(x):=block(neg(c(0.1)*(c(2.0)*c(x)+c(5.0)))/exp(c(x))) neg(c(0.1) (c(2.0) c(x) + c(5.0))) (%o251) exact_soln_y(x) := block(----------------------------------) exp(c(x)) (%i252) main_prog():=block( mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat, [niii,done_once,term,ord,order_diff,term_no, html_log_file,iiif,jjjf,rows,r_order, sub_iter,calc_term,iii],fixnum,[temp_sum], convfloat,[current_iter],fixnum, [x_start,x_end],convfloat,[it,opt_iter], fixnum,[tmp],convfloat,[subiter],fixnum, [est_needed_step_err,estimated_step_error, min_value,est_answer,last_min_pole_est], convfloat,[repeat_it],fixnum],[found_h], boolean),Digits:32,max_terms:30, glob_html_log:true,term:1, while term <= 30 do (array_y_init[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_norms[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_fact_1[term]:c(0.0),term:1+term), term:1, while term <= 2 do (array_1st_rel_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_last_rel_error[term]:c(0.0),term:1+term), term:1, while term <= 2 do (array_est_rel_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_max_est_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_type_pole[term]:0,term:1+term), term:1, while term <= 2 do (array_type_real_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_type_complex_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_est_digits[term]:0,term:1+term), term:1, while term <= 30 do (array_y[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_x[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp0[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp1[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp2[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp3[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp4[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp5[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_m1[term]:c(0.0),term:1+term), ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_higher[ord,term]:c(0.0),term:1+term), ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_higher_work[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_higher_work2[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_set_initial[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_rad_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_ord_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 4 do (array_rad_test_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 4 do (array_ord_test_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 30 do (term:1, while term <= 30 do (array_fact_2[ord,term]:c(0.0),term:1+term), ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x), zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2),zero_ats_ar(array_tmp3), zero_ats_ar(array_tmp4),zero_ats_ar(array_tmp5), zero_ats_ar(array_m1),zero_ats_ar(array_const_1), array_const_1[1]:c(1),zero_ats_ar(array_const_0D0), array_const_0D0[1]:c(0.0),zero_ats_ar(array_const_0D2), array_const_0D2[1]:c(0.2),zero_ats_ar(array_const_0D3), array_const_0D3[1]:c(0.3),zero_ats_ar(array_m1), array_m1[1]:glob__m1,iiif:0, while iiif <= ats_max_terms do (jjjf:0, while jjjf <= ats_max_terms do (array_fact_1[iiif]:0, array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf), iiif:1+iiif),array_y_set_initial[1,1]:true, array_y_set_initial[1,2]:false, array_y_set_initial[1,3]:false, array_y_set_initial[1,4]:false, array_y_set_initial[1,5]:false, array_y_set_initial[1,6]:false, array_y_set_initial[1,7]:false, array_y_set_initial[1,8]:false, array_y_set_initial[1,9]:false, array_y_set_initial[1,10]:false, array_y_set_initial[1,11]:false, array_y_set_initial[1,12]:false, array_y_set_initial[1,13]:false, array_y_set_initial[1,14]:false, array_y_set_initial[1,15]:false, array_y_set_initial[1,16]:false, array_y_set_initial[1,17]:false, array_y_set_initial[1,18]:false, array_y_set_initial[1,19]:false, array_y_set_initial[1,20]:false, array_y_set_initial[1,21]:false, array_y_set_initial[1,22]:false, array_y_set_initial[1,23]:false, array_y_set_initial[1,24]:false, array_y_set_initial[1,25]:false, array_y_set_initial[1,26]:false, array_y_set_initial[1,27]:false, array_y_set_initial[1,28]:false, array_y_set_initial[1,29]:false, array_y_set_initial[1,30]:false,glob_log_10:log(10.0), glob_orig_start_sec:elapsed_time_seconds(), glob_display_flag:true,glob_no_eqs:1,glob_iter:-1, opt_iter:-1,glob_max_iter:50000,glob_max_hours:0.0, glob_max_minutes:15.0, omniout_str(always, "##############ECHO OF PROBLEM#################"), omniout_str(always, "##############temp/div_lin_exppostode.ode#################"), omniout_str(always, "diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / exp ( x ) ; "), omniout_str(always,"!"), omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(always,"Digits:32,"), omniout_str(always,"max_terms:30,"),omniout_str(always,"!"), omniout_str(always,"/* END FIRST INPUT BLOCK */"), omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(always,"x_start:c(1.0),"), omniout_str(always,""),omniout_str(always,"x_end:c(5.0),"), omniout_str(always, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(always,"glob_look_poles:true,"), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""), omniout_str(always,"glob_type_given_pole:3,"), omniout_str(always,"/* END SECOND INPUT BLOCK */"), omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"), omniout_str(always,"glob_desired_digits_correct:8,"), omniout_str(always,"glob_max_minutes:(3.0),"), omniout_str(always,"glob_subiter_method:3,"), omniout_str(always,"glob_max_iter:100000,"), omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"), omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"), omniout_str(always,"glob_look_poles:false,"), omniout_str(always,"glob_h:c(0.001),"), omniout_str(always,"glob_display_interval:c(0.01),"), omniout_str(always,"/* END OVERRIDE BLOCK */"), omniout_str(always,"!"), omniout_str(always,"/* BEGIN USER DEF BLOCK */"), omniout_str(always,"exact_soln_y (x) := (block("), omniout_str(always,""), omniout_str(always, " (neg (c(0.1) * (c(5.0) + c(2.0)*c(x)))/exp(c(x))) "), omniout_str(always,"));"), omniout_str(always,"/* END USER DEF BLOCK */"), omniout_str(always, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false, glob_small_float:glob__0,glob_smallish_float:glob__0, glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100), glob_almost_1:c(0.99),x_start:c(1.0),x_end:c(5.0), array_y_init[1+0]:exact_soln_y(x_start), glob_look_poles:true,glob_type_given_pole:3, glob_desired_digits_correct:8,glob_max_minutes:3.0, glob_subiter_method:3,glob_max_iter:100000, glob_upper_ratio_limit:c(1.000001), glob_lower_ratio_limit:c(0.999999),glob_look_poles:false, glob_h:c(0.001),glob_display_interval:c(0.01), glob_last_good_h:glob_h, glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes, glob_check_sign:c(my_check_sign(x_start,x_end)), glob__pi:3.141592654,glob_prec:1.0E-16, if glob_optimize then (omniout_str(always,"START of Optimize"), found_h:false,glob_min_pole_est:glob_larger_float, last_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float, glob_min_h:abs(glob_min_h)*glob_check_sign, glob_max_h:abs(glob_max_h)*glob_check_sign, glob_h:abs(glob_min_h)*glob_check_sign, glob_display_interval :c(abs(c(glob_display_interval)) *glob_check_sign), display_max:c(x_end)-c(x_start)/glob__10, if glob_display_interval > display_max then glob_display_interval:c(display_max), chk_data(),min_value:glob_larger_float, est_answer:est_size_answer(),opt_iter:1, est_needed_step_err :estimated_needed_step_error( x_start,x_end,glob_h,est_answer), omniout_float(always,"est_needed_step_err",32, est_needed_step_err,16,""), estimated_step_error:glob_small_float, while opt_iter <= 100 and not found_h do (omniout_int(always,"opt_iter",32,opt_iter, 4,""),array_x[1]:c(x_start), array_x[2]:c(glob_h), glob_next_display:c(x_start),order_diff:1, term_no:1, while term_no <= order_diff do ( array_y[term_no] :array_y_init[term_no] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no),rows:order_diff, r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < ats_max_terms then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h, c(term_no-1)) /c( factorial_1( term_no-1)), term_no:1+term_no), r_order:1+r_order),atomall(), if glob_check_sign*glob_min_h >= glob_check_sign*glob_h then ( omniout_str(always, "SETTING H FOR MIN H"), glob_h:glob_check_sign*abs(glob_min_h), glob_h_reason:1,found_h:true), if glob_check_sign*glob_display_interval <= glob_check_sign*glob_h then ( omniout_str(always, "SETTING H FOR DISPLAY INTERVAL"), glob_h_reason:2, glob_h:glob_display_interval, found_h:true), if glob_look_poles then check_for_pole(), if not found_h then (est_answer:est_size_answer(), est_needed_step_err :estimated_needed_step_error( x_start,x_end,glob_h, est_answer), omniout_float(always, "est_needed_step_err", 32, est_needed_step_err, 16,""), estimated_step_error :test_suggested_h(), omniout_float(always, "estimated_step_error", 32, estimated_step_error, 32,""), if estimated_step_error < est_needed_step_err then ( omniout_str(always, "Double H and LOOP"), glob_h:glob_h*glob__2) else ( omniout_str(always, "Found H for OPTIMAL"), found_h:true,glob_h_reason:3, glob_h:glob_h/glob__2)), opt_iter:1+opt_iter), if not found_h and opt_iter = 1 then (omniout_str(always, "Beginning glob_h too large."), found_h:false), if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then (omniout_str(always, "SETTING H FOR MAX H"), glob_h:glob_check_sign*abs(glob_max_h), glob_h_reason:1,found_h:true)) else (found_h:true,glob_h:glob_h*glob_check_sign), if glob_html_log then html_log_file:openw("entry.html"), if found_h then (omniout_str(always,"START of Soultion"), array_x[1]:c(x_start),array_x[2]:c(glob_h), glob_next_display:c(x_start), glob_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float,order_diff:1, term_no:1, while term_no <= order_diff do (array_y[term_no] :array_y_init[term_no] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no),rows:order_diff, r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < ats_max_terms then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no), r_order:1+r_order),current_iter:1, glob_clock_start_sec:elapsed_time_seconds(), glob_clock_sec:elapsed_time_seconds(),glob_iter:0, omniout_str(debugl," "), glob_reached_optimal_h:true, glob_optimal_clock_start_sec :elapsed_time_seconds(), while glob_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec-glob_orig_start_sec < glob_max_sec do (if reached_interval() then (omniout_str(info," "), omniout_str(info, "TOP MAIN SOLVE Loop")), glob_iter:1+glob_iter, glob_clock_sec:elapsed_time_seconds(), track_estimated_error(),atomall(), track_estimated_error(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display :glob_display_interval +glob_next_display, array_x[1]:glob_h+array_x[1], array_x[2]:glob_h,order_diff:2,ord:2, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[2,iii] :array_y_higher[2,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:2, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:1, calc_term:2,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:1, calc_term:2,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:1, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:1, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)), term_no:ats_max_terms, while term_no >= 1 do ( array_y[term_no] :array_y_higher_work2[1,term_no], ord:1, while ord <= order_diff do ( array_y_higher[ord,term_no] :array_y_higher_work2[ ord,term_no],ord:1+ord), term_no:term_no-1)), omniout_str(always,"Finished!"), if glob_iter >= glob_max_iter then omniout_str(always, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds()-glob_orig_start_sec >= glob_max_sec then omniout_str(always, "Maximum Time Reached before Solution Completed!"), glob_clock_sec:elapsed_time_seconds(), omniout_str(info, "diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / exp ( x ) ; "), omniout_int(info, "Iterations ",32, glob_iter,4," "), prog_report(x_start,x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2015-04-24T20:50:41-05:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "div_lin_exp"), logitem_str(html_log_file, "diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / exp ( x ) ; "), logitem_float(html_log_file,x_start), logitem_float(html_log_file,x_end), logitem_float(html_log_file,array_x[1]), logitem_float(html_log_file,glob_h), logitem_h_reason(html_log_file), logitem_str(html_log_file,"16"), logitem_float(html_log_file, glob_desired_digits_correct), if array_est_digits[1] # -16 then ( logitem_integer(html_log_file, array_est_digits[ 1]),0) else ( logitem_str(html_log_file, "Unknown"),0), if glob_min_good_digits # -16 then ( logitem_integer(html_log_file, glob_min_good_digits), 0) else ( logitem_str(html_log_file, "Unknown"),0), if glob_good_digits # -16 then ( logitem_integer(html_log_file, glob_good_digits),0) else ( logitem_str(html_log_file, "Unknown"),0), logitem_str(html_log_file,"NA"), logitem_str(html_log_file,"NA"), logitem_integer(html_log_file, ats_max_terms), if glob_type_given_pole = 0 then ( logitem_str(html_log_file, "Not Given"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 4 then ( logitem_str(html_log_file, "No Solution"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 5 then ( logitem_str(html_log_file, "Some Pole"), logitem_str(html_log_file,"????"),0) elseif glob_type_given_pole = 3 then ( logitem_str(html_log_file, "No Pole"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 1 then ( logitem_str(html_log_file, "Real Sing"), logitem_float(html_log_file, glob_least_given_sing), 0) elseif glob_type_given_pole = 2 then ( logitem_str(html_log_file, "Complex Sing"), logitem_float(html_log_file, glob_least_given_sing), 0), if glob_least_ratio_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_ratio_sing), 0) else ( logitem_str(html_log_file,"NONE"),0), if glob_least_3_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_3_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), if glob_least_6_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_6_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, glob_clock_sec), if c(glob_percent_done) < glob__100 then ( logitem_time(html_log_file, glob_total_exp_sec),0) else ( logitem_str(html_log_file,"Done"), 0), log_revs(html_log_file, " 308.maple.seems.ok "), logitem_str(html_log_file, "div_lin_exp diffeq.max"), logitem_str(html_log_file, "div_lin_exp maxima results"), logitem_str(html_log_file,"OK"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i253) main():=(glob_iolevel:2,compile(all),main_prog()) (%i254) main() warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable secs in translation. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable sec_temp in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable years_int in translation. warning: encountered undefined variable days_int in translation. warning: encountered undefined variable hours_int in translation. warning: encountered undefined variable minutes_int in translation. warning: encountered undefined variable sec_int in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable iii in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_ats in translation. warning: encountered undefined variable ma_ats in translation. warning: encountered undefined variable ret_ats in translation. warning: encountered undefined variable lll_ats in translation. warning: encountered undefined variable ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_att in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable ma_att in translation. warning: encountered undefined variable lll_att in translation. warning: encountered undefined variable ret_att in translation. warning: encountered undefined variable al_att in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_h_reason in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable errflag in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable sub1 in translation. warning: encountered undefined variable sub2 in translation. warning: encountered undefined variable rrr in translation. warning: encountered undefined variable ms2 in translation. warning: encountered undefined variable sec_left in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ret in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__m2 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temp in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm0 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm1 in translation. warning: encountered undefined variable rm2 in translation. warning: encountered undefined variable rm3 in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable rm4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__8 in translation. warning: encountered undefined variable glob__5 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable nr1 in translation. warning: encountered undefined variable dr2 in translation. warning: encountered undefined variable nr2 in translation. warning: encountered undefined variable dr1 in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable ds1 in translation. warning: encountered undefined variable ds2 in translation. warning: encountered undefined variable rcs in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable ord_no in translation. warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any. warning: encountered undefined variable rad_c in translation. warning: encountered undefined variable glob_six_term_ord_save in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_2 in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob_log_10 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob__10 in translation. warning: encountered undefined variable ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_x in translation. warning: encountered undefined variable array_given_rad_poles in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable rad_given in translation. warning: encountered undefined variable array_given_ord_poles in translation. warning: variable glob_least_given_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable array_rad_test_poles in translation. warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable array_ord_test_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: variable glob_least_3_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob__small in translation. warning: variable glob_least_6_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_estimated_size_answer in translation. warning: encountered undefined variable array_y in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob__small in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable array_max_est_error in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_next_display in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__10 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable always in translation. warning: encountered undefined variable ind_var in translation. warning: encountered undefined variable closed_form_val_y in translation. warning: encountered undefined variable term_no in translation. warning: encountered undefined variable numeric_val in translation. warning: encountered undefined variable abserr in translation. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable relerr in translation. warning: variable glob_good_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_apfp_est_good_digits in translation. warning: encountered undefined variable glob_min_apfp_est_good_digits in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable est_rel_err in translation. warning: variable glob_est_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_est_digits in translation. warning: encountered undefined variable array_est_digits in translation. warning: encountered undefined variable array_1st_rel_error in translation. warning: encountered undefined variable array_last_rel_error in translation. warning: encountered undefined variable array_est_rel_error in translation. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable clock_sec1 in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_clock_start_sec in translation. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_optimal_clock_start_sec in translation. warning: encountered undefined variable opt_clock_sec in translation. warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_optimal_expect_sec in translation. warning: encountered undefined variable total_clock_sec in translation. warning: variable glob_total_exp_sec (declared type convfloat) assigned type any. warning: encountered undefined variable percent_done in translation. warning: variable glob_percent_done (declared type convfloat) assigned type any. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable expect_sec in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable left_sec in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable last_no in translation. warning: encountered undefined variable found_sing in translation. warning: encountered undefined variable array_y_higher in translation. warning: variable tmp_rad (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_rad in translation. warning: encountered undefined variable prev_tmp_rad in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable cnt in translation. warning: encountered undefined variable tmp_ratio in translation. warning: encountered undefined variable glob_upper_ratio_limit in translation. warning: encountered undefined variable glob_lower_ratio_limit in translation. warning: variable tmp_ord (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_ord in translation. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_ratio_of_radius in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable h_new in translation. warning: variable ratio (declared type convfloat) assigned type any. warning: encountered undefined variable term in translation. warning: encountered undefined variable ratio in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_const_0D2 in translation. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_const_0D3 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable array_tmp4 in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp5 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temporary in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable array_y_set_initial in translation. warning: encountered undefined variable kkk in translation. warning: encountered undefined variable order_d in translation. warning: encountered undefined variable adj3 in translation. warning: encountered undefined variable adj2 in translation. modedeclare: [found_h] is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: variable term (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable array_y_init in translation. warning: variable term (declared type [found_h]) assigned type any. warning: encountered undefined variable array_norms in translation. warning: encountered undefined variable array_fact_1 in translation. warning: encountered undefined variable array_type_pole in translation. warning: encountered undefined variable array_type_real_pole in translation. warning: encountered undefined variable array_type_complex_pole in translation. warning: encountered undefined variable array_tmp0 in translation. warning: encountered undefined variable array_m1 in translation. warning: variable ord (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable ord in translation. warning: variable ord (declared type [found_h]) assigned type any. warning: encountered undefined variable array_y_higher_work in translation. warning: encountered undefined variable array_y_higher_work2 in translation. warning: encountered undefined variable array_const_1 in translation. warning: encountered undefined variable glob__m1 in translation. warning: variable iiif (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable iiif in translation. warning: encountered undefined variable ats_max_terms in translation. warning: variable jjjf (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable jjjf in translation. warning: variable jjjf (declared type [found_h]) assigned type any. warning: variable iiif (declared type [found_h]) assigned type any. warning: variable glob_orig_start_sec (declared type convfloat) assigned type any. warning: variable opt_iter (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob__0 in translation. warning: variable glob_large_float (declared type convfloat) assigned type any. warning: variable glob_larger_float (declared type convfloat) assigned type any. warning: variable glob_almost_1 (declared type convfloat) assigned type any. warning: variable x_start (declared type [found_h]) assigned type any. warning: variable x_end (declared type [found_h]) assigned type any. warning: encountered undefined variable x_start in translation. warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_h (declared type convfloat) assigned type any. warning: variable glob_display_interval (declared type convfloat) assigned type any. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_max_minutes in translation. warning: encountered undefined variable glob_max_hours in translation. warning: encountered undefined variable x_end in translation. warning: variable glob_check_sign (declared type convfloat) assigned type any. warning: encountered undefined variable glob_larger_float in translation. warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_max_h in translation. warning: encountered undefined variable glob_display_interval in translation. warning: encountered undefined variable glob__10 in translation. warning: variable display_max (declared type [found_h]) assigned type any. warning: encountered undefined variable display_max in translation. warning: variable min_value (declared type [found_h]) assigned type convfloat. warning: variable est_answer (declared type [found_h]) assigned type any. warning: encountered undefined variable est_answer in translation. warning: variable est_needed_step_err (declared type [found_h]) assigned type any. warning: encountered undefined variable est_needed_step_err in translation. warning: encountered undefined variable glob_small_float in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable opt_iter in translation. warning: encountered undefined variable found_h in translation. warning: variable glob_next_display (declared type convfloat) assigned type any. warning: variable order_diff (declared type [found_h]) assigned type fixnum. warning: variable term_no (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable order_diff in translation. warning: variable term_no (declared type [found_h]) assigned type any. warning: variable r_order (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable r_order in translation. warning: encountered undefined variable rows in translation. warning: variable it (declared type [found_h]) assigned type any. warning: encountered undefined variable it in translation. warning: variable r_order (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_look_poles in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type any. warning: encountered undefined variable estimated_step_error in translation. warning: encountered undefined variable glob__2 in translation. warning: variable opt_iter (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_optimize in translation. warning: variable html_log_file (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_html_log in translation. warning: variable current_iter (declared type [found_h]) assigned type fixnum. warning: variable glob_clock_start_sec (declared type convfloat) assigned type any. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable debugl in translation. warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable info in translation. warning: encountered undefined variable current_iter in translation. warning: encountered undefined variable glob_next_display in translation. warning: variable calc_term (declared type [found_h]) assigned type fixnum. warning: variable iii (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable calc_term in translation. warning: variable iii (declared type [found_h]) assigned type any. warning: variable temp_sum (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable temp_sum in translation. warning: variable temp_sum (declared type [found_h]) assigned type any. warning: encountered undefined variable html_log_file in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob_percent_done in translation. warning: encountered undefined variable glob__100 in translation. WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB__PI is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $LAST_MIN_POLE_EST is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. "##############ECHO OF PROBLEM#################" "##############temp/div_lin_exppostode.ode#################" "diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / exp ( x ) ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:c(1.0)," "" "x_end:c(5.0)," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "" "" "" "" "" "" "" "glob_type_given_pole:3," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:8," "glob_max_minutes:(3.0)," "glob_subiter_method:3," "glob_max_iter:100000," "glob_upper_ratio_limit:c(1.000001)," "glob_lower_ratio_limit:c(0.999999)," "glob_look_poles:false," "glob_h:c(0.001)," "glob_display_interval:c(0.01)," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" "" " (neg (c(0.1) * (c(5.0) + c(2.0)*c(x)))/exp(c(x))) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 1. " " y[1] (closed_form) = -0.2575156088200097 " " y[1] (numeric) = -0.2575156088200097 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 15 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.009999999999999 " " y[1] (closed_form) = -0.2556817236592096 " " y[1] (numeric) = -0.25568172365920944 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.51331081902986700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0199999999999978 " " y[1] (closed_form) = -0.25385883788184754 " " y[1] (numeric) = -0.2538588378818472 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.31201619831949640000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0299999999999967 " " y[1] (closed_form) = -0.2520469141618187 " " y[1] (numeric) = -0.2520469141618181 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.2024134441740740000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0399999999999956 " " y[1] (closed_form) = -0.2502459148268172 " " y[1] (numeric) = -0.2502459148268164 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 3.10556964646332370000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0499999999999945 " " y[1] (closed_form) = -0.24845580186892133 " " y[1] (numeric) = -0.24845580186892038 " " absolute error = 9.436895709313831000000000000000E-16 " " relative error = 3.7982190950374690000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0599999999999934 " " y[1] (closed_form) = -0.2466765369550021 " " y[1] (numeric) = -0.24667653695500094 " " absolute error = 1.1657341758564144000000000000000E-15 " " relative error = 4.7257602617838906000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0699999999999923 " " y[1] (closed_form) = -0.24490808143695794 " " y[1] (numeric) = -0.24490808143695658 " " absolute error = 1.3600232051658168000000000000000E-15 " " relative error = 5.5531985599907690000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0799999999999912 " " y[1] (closed_form) = -0.243150396361778 " " y[1] (numeric) = -0.24315039636177643 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 6.3923902972487580000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.08999999999999 " " y[1] (closed_form) = -0.24140344248143628 " " y[1] (numeric) = -0.24140344248143455 " " absolute error = 1.7208456881689926000000000000000E-15 " " relative error = 7.1285051715918430000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.099999999999989 " " y[1] (closed_form) = -0.2396671802626192 " " y[1] (numeric) = -0.2396671802626173 " " absolute error = 1.915134717478395000000000000000E-15 " " relative error = 7.9908092354566660000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1099999999999879 " " y[1] (closed_form) = -0.23794156989628862 " " y[1] (numeric) = -0.2379415698962865 " " absolute error = 2.1094237467877974000000000000000E-15 " " relative error = 8.8653014591238940000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1199999999999868 " " y[1] (closed_form) = -0.23622657130708286 " " y[1] (numeric) = -0.23622657130708058 " " absolute error = 2.275957200481571000000000000000E-15 " " relative error = 9.634636729849240000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1299999999999857 " " y[1] (closed_form) = -0.2345221441625581 " " y[1] (numeric) = -0.23452214416255562 " " absolute error = 2.4702462297909733000000000000000E-15 " " relative error = 1.0533104405180312000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1399999999999846 " " y[1] (closed_form) = -0.23282824788227185 " " y[1] (numeric) = -0.2328282478822692 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.1444209555052277000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1499999999999835 " " y[1] (closed_form) = -0.23114484164671165 " " y[1] (numeric) = -0.23114484164670882 " " absolute error = 2.831068712794149000000000000000E-15 " " relative error = 1.224802895286426100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1599999999999824 " " y[1] (closed_form) = -0.22947188440607003 " " y[1] (numeric) = -0.22947188440606706 " " absolute error = 2.9698465908722940000000000000000E-15 " " relative error = 1.2942093531671606000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1699999999999813 " " y[1] (closed_form) = -0.22780933488886912 " " y[1] (numeric) = -0.22780933488886593 " " absolute error = 3.191891195797325000000000000000E-15 " " relative error = 1.401123969460868200000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1799999999999802 " " y[1] (closed_form) = -0.22615715161043587 " " y[1] (numeric) = -0.22615715161043254 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.4727233033128537000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.189999999999979 " " y[1] (closed_form) = -0.22451529288123104 " " y[1] (numeric) = -0.2245152928812275 " " absolute error = 3.524958103184872000000000000000E-15 " " relative error = 1.5700302896736665000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.199999999999978 " " y[1] (closed_form) = -0.22288371681503316 " " y[1] (numeric) = -0.22288371681502947 " " absolute error = 3.6914915568786455000000000000000E-15 " " relative error = 1.6562410254231996000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2099999999999769 " " y[1] (closed_form) = -0.22126238133698017 " " y[1] (numeric) = -0.22126238133697634 " " absolute error = 3.83026943495679000000000000000E-15 " " relative error = 1.7310983511125336000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2199999999999758 " " y[1] (closed_form) = -0.2196512441914705 " " y[1] (numeric) = -0.21965124419146648 " " absolute error = 4.0245584642661925000000000000000E-15 " " relative error = 1.8322493364790482000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2299999999999747 " " y[1] (closed_form) = -0.2180502629499252 " " y[1] (numeric) = -0.218050262949921 " " absolute error = 4.191091917959966000000000000000E-15 " " relative error = 1.922076066894008700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2399999999999736 " " y[1] (closed_form) = -0.21645939501841407 " " y[1] (numeric) = -0.21645939501840972 " " absolute error = 4.3576253716537394000000000000000E-15 " " relative error = 2.0131375546360733000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2499999999999725 " " y[1] (closed_form) = -0.21487859764514697 " " y[1] (numeric) = -0.21487859764514242 " " absolute error = 4.551914400963142000000000000000E-15 " " relative error = 2.1183656496494016000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2599999999999714 " " y[1] (closed_form) = -0.21330782792783182 " " y[1] (numeric) = -0.21330782792782713 " " absolute error = 4.690692279041286400000000000000E-15 " " relative error = 2.199024913716848300000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2699999999999703 " " y[1] (closed_form) = -0.21174704282090298 " " y[1] (numeric) = -0.21174704282089812 " " absolute error = 4.85722573273506000000000000000E-15 " " relative error = 2.2938812594626565000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2799999999999692 " " y[1] (closed_form) = -0.21019619914261953 " " y[1] (numeric) = -0.21019619914261453 " " absolute error = 4.9960036108132044000000000000000E-15 " " relative error = 2.3768287110764466000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.289999999999968 " " y[1] (closed_form) = -0.20865525358203718 " " y[1] (numeric) = -0.208655253582032 " " absolute error = 5.190292640122607000000000000000E-15 " " relative error = 2.4874967445197513000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.299999999999967 " " y[1] (closed_form) = -0.20712416270585465 " " y[1] (numeric) = -0.20712416270584927 " " absolute error = 5.384581669432009000000000000000E-15 " " relative error = 2.5996878389697440000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3099999999999659 " " y[1] (closed_form) = -0.2056028829651366 " " y[1] (numeric) = -0.20560288296513107 " " absolute error = 5.523359547510154000000000000000E-15 " " relative error = 2.6864212543394794000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3199999999999648 " " y[1] (closed_form) = -0.204091370701915 " " y[1] (numeric) = -0.20409137070190936 " " absolute error = 5.6343818499726690000000000000000E-15 " " relative error = 2.760715374978763000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3299999999999637 " " y[1] (closed_form) = -0.2025895821556706 " " y[1] (numeric) = -0.20258958215566478 " " absolute error = 5.828670879282072000000000000000E-15 " " relative error = 2.8770832227707044000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3399999999999626 " " y[1] (closed_form) = -0.20109747346969595 " " y[1] (numeric) = -0.20109747346968992 " " absolute error = 6.022959908591474000000000000000E-15 " " relative error = 2.9950450419254493000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3499999999999615 " " y[1] (closed_form) = -0.19961500069734217 " " y[1] (numeric) = -0.19961500069733595 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 3.114620101786597700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3599999999999604 " " y[1] (closed_form) = -0.19814211980815097 " " y[1] (numeric) = -0.19814211980814458 " " absolute error = 6.38378239159465000000000000000E-15 " " relative error = 3.2218199733482616000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3699999999999593 " " y[1] (closed_form) = -0.1966787866938734 " " y[1] (numeric) = -0.19667878669386685 " " absolute error = 6.5503158452884240000000000000000E-15 " " relative error = 3.3304638265253590000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3799999999999581 " " y[1] (closed_form) = -0.19522495717437716 " " y[1] (numeric) = -0.1952249571743704 " " absolute error = 6.744604874597826000000000000000E-15 " " relative error = 3.454786197531839000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.389999999999957 " " y[1] (closed_form) = -0.19378058700344403 " " y[1] (numeric) = -0.19378058700343714 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 3.5521529060873540000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.399999999999956 " " y[1] (closed_form) = -0.19234563187445938 " " y[1] (numeric) = -0.1923456318744523 " " absolute error = 7.077671781985373000000000000000E-15 " " relative error = 3.679663381492773000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4099999999999548 " " y[1] (closed_form) = -0.1909200474259942 " " y[1] (numeric) = -0.190920047425987 " " absolute error = 7.188694084447889000000000000000E-15 " " relative error = 3.765290330359059000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4199999999999537 " " y[1] (closed_form) = -0.18950378924728312 " " y[1] (numeric) = -0.18950378924727573 " " absolute error = 7.382983113757291000000000000000E-15 " " relative error = 3.895955401779988000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4299999999999526 " " y[1] (closed_form) = -0.18809681288359772 " " y[1] (numeric) = -0.18809681288359018 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 4.013633432546795000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4399999999999515 " " y[1] (closed_form) = -0.18669907384151874 " " y[1] (numeric) = -0.18669907384151102 " " absolute error = 7.716050021144838000000000000000E-15 " " relative error = 4.132880716748857400000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4499999999999504 " " y[1] (closed_form) = -0.18531052759410702 " " y[1] (numeric) = -0.1853105275940992 " " absolute error = 7.827072323607354000000000000000E-15 " " relative error = 4.2237602068411895000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4599999999999493 " " y[1] (closed_form) = -0.183931129585976 " " y[1] (numeric) = -0.183931129585968 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 4.345977646793404700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4699999999999482 " " y[1] (closed_form) = -0.18256083523826583 " " y[1] (numeric) = -0.18256083523825772 " " absolute error = 8.104628079763643000000000000000E-15 " " relative error = 4.439412248079408500000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4799999999999471 " " y[1] (closed_form) = -0.18119959995352214 " " y[1] (numeric) = -0.18119959995351387 " " absolute error = 8.271161533457416000000000000000E-15 " " relative error = 4.564668760625838000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.489999999999946 " " y[1] (closed_form) = -0.17984737912047938 " " y[1] (numeric) = -0.179847379120471 " " absolute error = 8.382183835919932000000000000000E-15 " " relative error = 4.660720593712252000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.499999999999945 " " y[1] (closed_form) = -0.17850412811875127 " " y[1] (numeric) = -0.17850412811874275 " " absolute error = 8.520961713998076000000000000000E-15 " " relative error = 4.773537622799087000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5099999999999438 " " y[1] (closed_form) = -0.17716980232342877 " " y[1] (numeric) = -0.17716980232342014 " " absolute error = 8.631984016460592000000000000000E-15 " " relative error = 4.8721531001669505000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5199999999999427 " " y[1] (closed_form) = -0.17584435710958823 " " y[1] (numeric) = -0.1758443571095794 " " absolute error = 8.826273045769994000000000000000E-15 " " relative error = 5.019366666551238000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5299999999999416 " " y[1] (closed_form) = -0.17452774785670935 " " y[1] (numeric) = -0.1745277478567004 " " absolute error = 8.965050923848139000000000000000E-15 " " relative error = 5.136748187003833000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5399999999999405 " " y[1] (closed_form) = -0.17321992995300595 " " y[1] (numeric) = -0.1732199299529968 " " absolute error = 9.159339953157541000000000000000E-15 " " relative error = 5.2876940636348500000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5499999999999394 " " y[1] (closed_form) = -0.17192085879966973 " " y[1] (numeric) = -0.1719208587996604 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 5.4245153682708510000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5599999999999383 " " y[1] (closed_form) = -0.17063048981502893 " " y[1] (numeric) = -0.17063048981501944 " " absolute error = 9.492406860545088000000000000000E-15 " " relative error = 5.563136383676377000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5699999999999372 " " y[1] (closed_form) = -0.1693487784386227 " " y[1] (numeric) = -0.16934877843861312 " " absolute error = 9.575673587391975000000000000000E-15 " " relative error = 5.654409601107633000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5799999999999361 " " y[1] (closed_form) = -0.16807568013519303 " " y[1] (numeric) = -0.16807568013518334 " " absolute error = 9.686695889854491000000000000000E-15 " " relative error = 5.763294179183401000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.589999999999935 " " y[1] (closed_form) = -0.16681115039859482 " " y[1] (numeric) = -0.1668111503985849 " " absolute error = 9.908740494779522000000000000000E-15 " " relative error = 5.9400948144669060000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.599999999999934 " " y[1] (closed_form) = -0.16555514475562572 " " y[1] (numeric) = -0.1655551447556157 " " absolute error = 1.001976279724203800000000000000E-14 " " relative error = 6.052220734083564000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6099999999999328 " " y[1] (closed_form) = -0.16430761876977718 " " y[1] (numeric) = -0.16430761876976702 " " absolute error = 1.015854067532018200000000000000E-14 " " relative error = 6.182635200595306000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6199999999999317 " " y[1] (closed_form) = -0.16306852804490696 " " y[1] (numeric) = -0.16306852804489663 " " absolute error = 1.032507412901395600000000000000E-14 " " relative error = 6.331739332417696000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6299999999999306 " " y[1] (closed_form) = -0.16183782822883563 " " y[1] (numeric) = -0.16183782822882517 " " absolute error = 1.0463852007092100000000000000E-14 " " relative error = 6.465640401634908000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6399999999999295 " " y[1] (closed_form) = -0.1606154750168671 " " y[1] (numeric) = -0.1606154750168565 " " absolute error = 1.060262988517024500000000000000E-14 " " relative error = 6.6012505233737940000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6499999999999284 " " y[1] (closed_form) = -0.1594014241552346 " " y[1] (numeric) = -0.1594014241552239 " " absolute error = 1.068589661201713200000000000000E-14 " " relative error = 6.703764830614418000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6599999999999273 " " y[1] (closed_form) = -0.15819563144447382 " " y[1] (numeric) = -0.158195631444463 " " absolute error = 1.082467449009527600000000000000E-14 " " relative error = 6.8425874919907030000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6699999999999262 " " y[1] (closed_form) = -0.1569980527427236 " " y[1] (numeric) = -0.1569980527427127 " " absolute error = 1.090794121694216300000000000000E-14 " " relative error = 6.94781943239593000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.679999999999925 " " y[1] (closed_form) = -0.15580864396895563 " " y[1] (numeric) = -0.1558086439689446 " " absolute error = 1.104671909502030800000000000000E-14 " " relative error = 7.08992698583612000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.689999999999924 " " y[1] (closed_form) = -0.15462736110613395 " " y[1] (numeric) = -0.1546273611061228 " " absolute error = 1.115774139748282300000000000000E-14 " " relative error = 7.2158907179592310000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.699999999999923 " " y[1] (closed_form) = -0.15345416020430613 " " y[1] (numeric) = -0.15345416020429484 " " absolute error = 1.129651927556096800000000000000E-14 " " relative error = 7.361494312386828000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7099999999999218 " " y[1] (closed_form) = -0.1522889973836259 " " y[1] (numeric) = -0.15228899738361443 " " absolute error = 1.146305272925474100000000000000E-14 " " relative error = 7.527170659859665000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7199999999999207 " " y[1] (closed_form) = -0.1511318288373094 " " y[1] (numeric) = -0.15113182883729787 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 7.639899248841239000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7299999999999196 " " y[1] (closed_form) = -0.14998261083452585 " " y[1] (numeric) = -0.14998261083451414 " " absolute error = 1.171285290979540200000000000000E-14 " " relative error = 7.809473941427824000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7399999999999185 " " y[1] (closed_form) = -0.14884129972322263 " " y[1] (numeric) = -0.14884129972321078 " " absolute error = 1.185163078787354600000000000000E-14 " " relative error = 7.962595603446226000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7499999999999174 " " y[1] (closed_form) = -0.14770785193288768 " " y[1] (numeric) = -0.14770785193287572 " " absolute error = 1.196265309033606200000000000000E-14 " " relative error = 8.098860645384915000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7599999999999163 " " y[1] (closed_form) = -0.14658222397724846 " " y[1] (numeric) = -0.14658222397723636 " " absolute error = 1.210143096841420600000000000000E-14 " " relative error = 8.255728859928139000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7699999999999152 " " y[1] (closed_form) = -0.14546437245690913 " " y[1] (numeric) = -0.1454643724568969 " " absolute error = 1.224020884649235100000000000000E-14 " " relative error = 8.414575087874706000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.779999999999914 " " y[1] (closed_form) = -0.14435425406192726 " " y[1] (numeric) = -0.144354254061915 " " absolute error = 1.22679644221079800000000000000E-14 " " relative error = 8.498512566761687000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.789999999999913 " " y[1] (closed_form) = -0.1432518255743305 " " y[1] (numeric) = -0.14325182557431812 " " absolute error = 1.237898672457049500000000000000E-14 " " relative error = 8.641416383309745000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.799999999999912 " " y[1] (closed_form) = -0.14215704387057404 " " y[1] (numeric) = -0.1421570438705616 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.747014947161297000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8099999999999108 " " y[1] (closed_form) = -0.14106986592394058 " " y[1] (numeric) = -0.141069865923928 " " absolute error = 1.257327575387989800000000000000E-14 " " relative error = 8.912800527264216000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8199999999999097 " " y[1] (closed_form) = -0.1399902488068827 " " y[1] (numeric) = -0.13999024880686997 " " absolute error = 1.273980920757367000000000000000E-14 " " relative error = 9.10049758190537000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8299999999999086 " " y[1] (closed_form) = -0.13891814969330937 " " y[1] (numeric) = -0.13891814969329655 " " absolute error = 1.282307593442055800000000000000E-14 " " relative error = 9.230669975615251000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8399999999999075 " " y[1] (closed_form) = -0.13785352586081698 " " y[1] (numeric) = -0.13785352586080402 " " absolute error = 1.296185381249870300000000000000E-14 " " relative error = 9.402627703251903000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8499999999999064 " " y[1] (closed_form) = -0.1367963346928659 " " y[1] (numeric) = -0.1367963346928528 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 9.576741745303546000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8599999999999053 " " y[1] (closed_form) = -0.13574653368090359 " " y[1] (numeric) = -0.13574653368089035 " " absolute error = 1.323940956865499200000000000000E-14 " " relative error = 9.753036935570365000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8699999999999042 " " y[1] (closed_form) = -0.13470408042643484 " " y[1] (numeric) = -0.1347040804264215 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 9.89032867699781000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.879999999999903 " " y[1] (closed_form) = -0.13366893264304028 " " y[1] (numeric) = -0.13366893264302684 " " absolute error = 1.343369859796439400000000000000E-14 " " relative error = 1.004997820536112800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.889999999999902 " " y[1] (closed_form) = -0.13264104815834366 " " y[1] (numeric) = -0.13264104815833008 " " absolute error = 1.357247647604254000000000000000E-14 " " relative error = 1.023248584392973700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8999999999999009 " " y[1] (closed_form) = -0.13162038491592895 " " y[1] (numeric) = -0.13162038491591527 " " absolute error = 1.368349877850505400000000000000E-14 " " relative error = 1.039618504933353300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9099999999998998 " " y[1] (closed_form) = -0.13060690097720803 " " y[1] (numeric) = -0.13060690097719424 " " absolute error = 1.37945210809675700000000000000E-14 " " relative error = 1.056186233480482400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9199999999998987 " " y[1] (closed_form) = -0.1296005545232397 " " y[1] (numeric) = -0.12960055452322583 " " absolute error = 1.387778780781445700000000000000E-14 " " relative error = 1.070812378763851700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9299999999998976 " " y[1] (closed_form) = -0.12860130385650084 " " y[1] (numeric) = -0.12860130385648683 " " absolute error = 1.401656568589260000000000000000E-14 " " relative error = 1.089924072739800500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9399999999998965 " " y[1] (closed_form) = -0.12760910740261044 " " y[1] (numeric) = -0.1276091074025963 " " absolute error = 1.415534356397074600000000000000E-14 " " relative error = 1.109273769881504200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9499999999998954 " " y[1] (closed_form) = -0.12662392371200734 " " y[1] (numeric) = -0.1266239237119931 " " absolute error = 1.423861029081763300000000000000E-14 " " relative error = 1.124480261976547000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9599999999998943 " " y[1] (closed_form) = -0.12564571146158243 " " y[1] (numeric) = -0.1256457114615681 " " absolute error = 1.43218770176645200000000000000E-14 " " relative error = 1.139861985822221400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9699999999998932 " " y[1] (closed_form) = -0.12467442945626588 " " y[1] (numeric) = -0.12467442945625141 " " absolute error = 1.446065489574266400000000000000E-14 " " relative error = 1.159873356454000800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.979999999999892 " " y[1] (closed_form) = -0.12371003663057033 " " y[1] (numeric) = -0.12371003663055578 " " absolute error = 1.45439216225895500000000000000E-14 " " relative error = 1.17564605255282590000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.989999999999891 " " y[1] (closed_form) = -0.12275249205009083 " " y[1] (numeric) = -0.12275249205007618 " " absolute error = 1.464106613724425200000000000000E-14 " " relative error = 1.192730664178269100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9999999999998899 " " y[1] (closed_form) = -0.12180175491296184 " " y[1] (numeric) = -0.12180175491294712 " " absolute error = 1.47243328640911400000000000000E-14 " " relative error = 1.208876906134314600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0099999999998888 " " y[1] (closed_form) = -0.12085778455127254 " " y[1] (numeric) = -0.12085778455125772 " " absolute error = 1.48214773787458400000000000000E-14 " " relative error = 1.226356865118439800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0199999999998877 " " y[1] (closed_form) = -0.11992054043244053 " " y[1] (numeric) = -0.11992054043242562 " " absolute error = 1.49186218934005400000000000000E-14 " " relative error = 1.244042249943430200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0299999999998866 " " y[1] (closed_form) = -0.11898998216054525 " " y[1] (numeric) = -0.11898998216053024 " " absolute error = 1.501576640805524200000000000000E-14 " " relative error = 1.261935344085981200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0399999999998855 " " y[1] (closed_form) = -0.11806606947762129 " " y[1] (numeric) = -0.11806606947760616 " " absolute error = 1.512678871051775800000000000000E-14 " " relative error = 1.281213881129916700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0499999999998844 " " y[1] (closed_form) = -0.11714876226491241 " " y[1] (numeric) = -0.11714876226489719 " " absolute error = 1.52239332251724600000000000000E-14 " " relative error = 1.299538546616998700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0599999999998833 " " y[1] (closed_form) = -0.11623802054408712 " " y[1] (numeric) = -0.11623802054407181 " " absolute error = 1.530719995201934600000000000000E-14 " " relative error = 1.316884086667114400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.069999999999882 " " y[1] (closed_form) = -0.11533380447841604 " " y[1] (numeric) = -0.11533380447840065 " " absolute error = 1.539046667886623300000000000000E-14 " " relative error = 1.334428075833261600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.079999999999881 " " y[1] (closed_form) = -0.11443607437391214 " " y[1] (numeric) = -0.11443607437389666 " " absolute error = 1.54737334057131200000000000000E-14 " " relative error = 1.35217268596209800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.08999999999988 " " y[1] (closed_form) = -0.1135447906804342 " " y[1] (numeric) = -0.11354479068041859 " " absolute error = 1.561251128379126400000000000000E-14 " " relative error = 1.375009033019564000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.099999999999879 " " y[1] (closed_form) = -0.11265991399275406 " " y[1] (numeric) = -0.11265991399273836 " " absolute error = 1.56957780106381500000000000000E-14 " " relative error = 1.393199892878282700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1099999999998778 " " y[1] (closed_form) = -0.11178140505158861 " " y[1] (numeric) = -0.11178140505157283 " " absolute error = 1.577904473748503700000000000000E-14 " " relative error = 1.411598353966189400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999998766 " " y[1] (closed_form) = -0.11090922474459675 " " y[1] (numeric) = -0.11090922474458088 " " absolute error = 1.586231146433192400000000000000E-14 " " relative error = 1.430206684868627600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999998755 " " y[1] (closed_form) = -0.11004333410734209 " " y[1] (numeric) = -0.11004333410732611 " " absolute error = 1.59733337667944400000000000000E-14 " " relative error = 1.451549418814701300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999998744 " " y[1] (closed_form) = -0.10918369432422186 " " y[1] (numeric) = -0.10918369432420577 " " absolute error = 1.608435606925695500000000000000E-14 " " relative error = 1.473146349261120500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1499999999998733 " " y[1] (closed_form) = -0.10833026672936295 " " y[1] (numeric) = -0.10833026672934679 " " absolute error = 1.616762279610384200000000000000E-14 " " relative error = 1.49243819702712900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1599999999998722 " " y[1] (closed_form) = -0.10748301280748505 " " y[1] (numeric) = -0.10748301280746882 " " absolute error = 1.623701173514291400000000000000E-14 " " relative error = 1.51065841113193820000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.169999999999871 " " y[1] (closed_form) = -0.10664189419473208 " " y[1] (numeric) = -0.10664189419471574 " " absolute error = 1.633415624979761600000000000000E-14 " " relative error = 1.53168286939566500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.17999999999987 " " y[1] (closed_form) = -0.10580687267947189 " " y[1] (numeric) = -0.10580687267945549 " " absolute error = 1.640354518883668800000000000000E-14 " " relative error = 1.550328893901730400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.189999999999869 " " y[1] (closed_form) = -0.10497791020306531 " " y[1] (numeric) = -0.10497791020304884 " " absolute error = 1.64729341278757600000000000000E-14 " " relative error = 1.569180992078346700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.199999999999868 " " y[1] (closed_form) = -0.10415496886060469 " " y[1] (numeric) = -0.10415496886058814 " " absolute error = 1.654232306691483200000000000000E-14 " " relative error = 1.588241372243524300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2099999999998667 " " y[1] (closed_form) = -0.10333801090162259 " " y[1] (numeric) = -0.10333801090160595 " " absolute error = 1.663946758156953400000000000000E-14 " " relative error = 1.61019816777877100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999998656 " " y[1] (closed_form) = -0.1025269987307712 " " y[1] (numeric) = -0.10252699873075444 " " absolute error = 1.676436767183986400000000000000E-14 " " relative error = 1.635117371948235000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999998645 " " y[1] (closed_form) = -0.10172189490847289 " " y[1] (numeric) = -0.10172189490845605 " " absolute error = 1.683375661087893600000000000000E-14 " " relative error = 1.654880360420495400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2399999999998634 " " y[1] (closed_form) = -0.10092266215154255 " " y[1] (numeric) = -0.10092266215152564 " " absolute error = 1.691702333772582300000000000000E-14 " " relative error = 1.676236335534204400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2499999999998623 " " y[1] (closed_form) = -0.10012926333378201 " " y[1] (numeric) = -0.10012926333376498 " " absolute error = 1.70280456401883380000000000000E-14 " " relative error = 1.700606303616272500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2599999999998612 " " y[1] (closed_form) = -9.93416614865471700E-2 " " y[1] (numeric) = -9.93416614865301000E-2 " " absolute error = 1.708355679141959600000000000000E-14 " " relative error = 1.719676974975201700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.26999999999986 " " y[1] (closed_form) = -9.85598197992885000E-2 " " y[1] (numeric) = -9.85598197992713100E-2 " " absolute error = 1.718070130607429700000000000000E-14 " " relative error = 1.743174991701671700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.279999999999859 " " y[1] (closed_form) = -9.77837016200647200E-2 " " y[1] (numeric) = -9.77837016200474600E-2 " " absolute error = 1.726396803292118400000000000000E-14 " " relative error = 1.76552613031563800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999858 " " y[1] (closed_form) = -9.70132704560312300E-2 " " y[1] (numeric) = -9.70132704560138800E-2 " " absolute error = 1.73472347597680700000000000000E-14 " " relative error = 1.788130085525800300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.299999999999857 " " y[1] (closed_form) = -9.62484899739025000E-2 " " y[1] (numeric) = -9.62484899738850900E-2 " " absolute error = 1.74027459109993300000000000000E-14 " " relative error = 1.808105863865296600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999998557 " " y[1] (closed_form) = -9.54893240003900500E-2 " " y[1] (numeric) = -9.54893240003725600E-2 " " absolute error = 1.74998904256540300000000000000E-14 " " relative error = 1.832654132684251600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999998546 " " y[1] (closed_form) = -9.47357365226154400E-2 " " y[1] (numeric) = -9.47357365225978600E-2 " " absolute error = 1.758315715250091700000000000000E-14 " " relative error = 1.856021581497225600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999998535 " " y[1] (closed_form) = -9.39876916884995800E-2 " " y[1] (numeric) = -9.39876916884819200E-2 " " absolute error = 1.76525460915399900000000000000E-14 " " relative error = 1.878176362714094600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3399999999998524 " " y[1] (closed_form) = -9.32451538071281700E-2 " " y[1] (numeric) = -9.32451538071104500E-2 " " absolute error = 1.77219350305790600000000000000E-14 " " relative error = 1.90057437915066190000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3499999999998513 " " y[1] (closed_form) = -9.25080873490940500E-2 " " y[1] (numeric) = -9.25080873490762500E-2 " " absolute error = 1.779132396961813400000000000000E-14 " " relative error = 1.923218226583772200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.35999999999985 " " y[1] (closed_form) = -9.1776456946816800E-2 " " y[1] (numeric) = -9.17764569467989100E-2 " " absolute error = 1.788846848427283500000000000000E-14 " " relative error = 1.9491347867829500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.369999999999849 " " y[1] (closed_form) = -9.10502273948398800E-2 " " y[1] (numeric) = -9.1050227394821890E-2 " " absolute error = 1.798561299892753600000000000000E-14 " " relative error = 1.975350695274248600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.379999999999848 " " y[1] (closed_form) = -9.03293636501059600E-2 " " y[1] (numeric) = -9.0329363650087900E-2 " " absolute error = 1.806887972577442300000000000000E-14 " " relative error = 2.000332892387560500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999847 " " y[1] (closed_form) = -8.96138308322106600E-2 " " y[1] (numeric) = -8.96138308321925400E-2 " " absolute error = 1.81243908770056800000000000000E-14 " " relative error = 2.0224992848415402000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.399999999999846 " " y[1] (closed_form) = -8.89035942236351900E-2 " " y[1] (numeric) = -8.89035942236169800E-2 " " absolute error = 1.820765760385256700000000000000E-14 " " relative error = 2.048022665771147300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999998447 " " y[1] (closed_form) = -8.8198619269958100E-2 " " y[1] (numeric) = -8.81986192699398400E-2 " " absolute error = 1.826316875508382500000000000000E-14 " " relative error = 2.070686469499478700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999998436 " " y[1] (closed_form) = -8.74988715800470600E-2 " " y[1] (numeric) = -8.74988715800287400E-2 " " absolute error = 1.831867990631508300000000000000E-14 " " relative error = 2.093590417284011400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4299999999998425 " " y[1] (closed_form) = -8.68043169262302500E-2 " " y[1] (numeric) = -8.68043169262118400E-2 " " absolute error = 1.84019466331619700000000000000E-14 " " relative error = 2.119934501506494400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4399999999998414 " " y[1] (closed_form) = -8.61149212444484200E-2 " " y[1] (numeric) = -8.61149212444299600E-2 " " absolute error = 1.845745778439322700000000000000E-14 " " relative error = 2.143351874177452700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4499999999998403 " " y[1] (closed_form) = -8.54306506343877000E-2 " " y[1] (numeric) = -8.54306506343691500E-2 " " absolute error = 1.854072451124011400000000000000E-14 " " relative error = 2.17026610163461300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.459999999999839 " " y[1] (closed_form) = -8.47514713595935300E-2 " " y[1] (numeric) = -8.47514713595749400E-2 " " absolute error = 1.859623566247137200000000000000E-14 " " relative error = 2.194208001837404400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.469999999999838 " " y[1] (closed_form) = -8.4077349847566200E-2 " " y[1] (numeric) = -8.40773498475475100E-2 " " absolute error = 1.86795023893182600000000000000E-14 " " relative error = 2.221704468942532800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999837 " " y[1] (closed_form) = -8.34082526898380500E-2 " " y[1] (numeric) = -8.34082526898192800E-2 " " absolute error = 1.876276911616514600000000000000E-14 " " relative error = 2.24950991191919390000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999836 " " y[1] (closed_form) = -8.2744146642033200E-2 " " y[1] (numeric) = -8.27441466420143700E-2 " " absolute error = 1.881828026739640300000000000000E-14 " " relative error = 2.27427329075104680000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.499999999999835 " " y[1] (closed_form) = -8.20849986239096600E-2 " " y[1] (numeric) = -8.20849986238907500E-2 " " absolute error = 1.89015469942432900000000000000E-14 " " relative error = 2.30267982105291300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5099999999998337 " " y[1] (closed_form) = -8.14307757193843100E-2 " " y[1] (numeric) = -8.14307757193653600E-2 " " absolute error = 1.895705814547454800000000000000E-14 " " relative error = 2.327996752824974500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999998326 " " y[1] (closed_form) = -8.07814451765413900E-2 " " y[1] (numeric) = -8.07814451765223600E-2 " " absolute error = 1.90264470845136200000000000000E-14 " " relative error = 2.35529917085945200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5299999999998315 " " y[1] (closed_form) = -8.01369744076242400E-2 " " y[1] (numeric) = -8.01369744076051300E-2 " " absolute error = 1.910971381136050700000000000000E-14 " " relative error = 2.384631308159596300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5399999999998304 " " y[1] (closed_form) = -7.94973309890111500E-2 " " y[1] (numeric) = -7.94973309889919900E-2 " " absolute error = 1.916522496259176500000000000000E-14 " " relative error = 2.410801057615501200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5499999999998293 " " y[1] (closed_form) = -7.88624826611754700E-2 " " y[1] (numeric) = -7.88624826611562400E-2 " " absolute error = 1.923461390163083700000000000000E-14 " " relative error = 2.439006895619856800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.559999999999828 " " y[1] (closed_form) = -7.82323973286301200E-2 " " y[1] (numeric) = -7.82323973286108300E-2 " " absolute error = 1.929012505286209500000000000000E-14 " " relative error = 2.465746380215122800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999827 " " y[1] (closed_form) = -7.76070430598570400E-2 " " y[1] (numeric) = -7.76070430598376800E-2 " " absolute error = 1.935951399190116700000000000000E-14 " " relative error = 2.49455632228759080000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999826 " " y[1] (closed_form) = -7.69863880872217600E-2 " " y[1] (numeric) = -7.69863880872023300E-2 " " absolute error = 1.94289029309402400000000000000E-14 " " relative error = 2.523680278249741400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.589999999999825 " " y[1] (closed_form) = -7.6370400806873610E-2 " " y[1] (numeric) = -7.63704008068540900E-2 " " absolute error = 1.951216965778712600000000000000E-14 " " relative error = 2.554938752662793700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.599999999999824 " " y[1] (closed_form) = -7.57590497786312800E-2 " " y[1] (numeric) = -7.57590497786117100E-2 " " absolute error = 1.956768080901838400000000000000E-14 " " relative error = 2.582883611422708000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6099999999998227 " " y[1] (closed_form) = -7.51523037258550600E-2 " " y[1] (numeric) = -7.51523037258354100E-2 " " absolute error = 1.96509475358652700000000000000E-14 " " relative error = 2.614816387738310700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6199999999998216 " " y[1] (closed_form) = -7.45501315353047400E-2 " " y[1] (numeric) = -7.45501315352850500E-2 " " absolute error = 1.969258089928871400000000000000E-14 " " relative error = 2.641521952240002400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6299999999998205 " " y[1] (closed_form) = -7.3952502256984700E-2 " " y[1] (numeric) = -7.39525022569649500E-2 " " absolute error = 1.974809205051997200000000000000E-14 " " relative error = 2.670375098586308400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999998194 " " y[1] (closed_form) = -7.33593851039755400E-2 " " y[1] (numeric) = -7.33593851039557300E-2 " " absolute error = 1.98036032017512300000000000000E-14 " " relative error = 2.699532333004523000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6499999999998183 " " y[1] (closed_form) = -7.27707494522531400E-2 " " y[1] (numeric) = -7.27707494522332500E-2 " " absolute error = 1.988686992859811700000000000000E-14 " " relative error = 2.732810927232023300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.659999999999817 " " y[1] (closed_form) = -7.21865648404949700E-2 " " y[1] (numeric) = -7.21865648404750300E-2 " " absolute error = 1.994238107982937400000000000000E-14 " " relative error = 2.76261671737594100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.669999999999816 " " y[1] (closed_form) = -7.16068009698743600E-2 " " y[1] (numeric) = -7.16068009698543700E-2 " " absolute error = 1.999789223106063200000000000000E-14 " " relative error = 2.79273643846677800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.679999999999815 " " y[1] (closed_form) = -7.10314277038425300E-2 " " y[1] (numeric) = -7.10314277038224700E-2 " " absolute error = 2.006728117009970400000000000000E-14 " " relative error = 2.825127104831392500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.689999999999814 " " y[1] (closed_form) = -7.04604150678989600E-2 " " y[1] (numeric) = -7.04604150678788200E-2 " " absolute error = 2.013667010913877700000000000000E-14 " " relative error = 2.8578699245149400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6999999999998128 " " y[1] (closed_form) = -6.98937332493503200E-2 " " y[1] (numeric) = -6.98937332493301400E-2 " " absolute error = 2.01783034725622200000000000000E-14 " " relative error = 2.88699752244952300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7099999999998117 " " y[1] (closed_form) = -6.93313525970581200E-2 " " y[1] (numeric) = -6.93313525970378300E-2 " " absolute error = 2.02754479872169200000000000000E-14 " " relative error = 2.92442700563687800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7199999999998106 " " y[1] (closed_form) = -6.87732436211752200E-2 " " y[1] (numeric) = -6.87732436211548800E-2 " " absolute error = 2.034483692625599400000000000000E-14 " " relative error = 2.958248855953601300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999998095 " " y[1] (closed_form) = -6.8219376992871890E-2 " " y[1] (numeric) = -6.82193769928514800E-2 " " absolute error = 2.041422586529506600000000000000E-14 " " relative error = 2.992438038158587400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999998084 " " y[1] (closed_form) = -6.76697235440510700E-2 " " y[1] (numeric) = -6.76697235440305700E-2 " " absolute error = 2.049749259214195300000000000000E-14 " " relative error = 3.029049258461750000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7499999999998073 " " y[1] (closed_form) = -6.71242542670534200E-2 " " y[1] (numeric) = -6.71242542670328600E-2 " " absolute error = 2.05530037433732100000000000000E-14 " " relative error = 3.06193401592265200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999806 " " y[1] (closed_form) = -6.6582940314352500E-2 " " y[1] (numeric) = -6.65829403143318800E-2 " " absolute error = 2.060851489460446800000000000000E-14 " " relative error = 3.095164436612021000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.769999999999805 " " y[1] (closed_form) = -6.60457529982398500E-2 " " y[1] (numeric) = -6.60457529982191900E-2 " " absolute error = 2.066402604583572600000000000000E-14 " " relative error = 3.12874410658720600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.779999999999804 " " y[1] (closed_form) = -6.55126637905007900E-2 " " y[1] (numeric) = -6.55126637904800300E-2 " " absolute error = 2.076117056049042700000000000000E-14 " " relative error = 3.169031658807431300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.789999999999803 " " y[1] (closed_form) = -6.49836443220805200E-2 " " y[1] (numeric) = -6.49836443220597200E-2 " " absolute error = 2.08028039239138700000000000000E-14 " " relative error = 3.201236886747727600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7999999999998018 " " y[1] (closed_form) = -6.4458666382741400E-2 " " y[1] (numeric) = -6.44586663827205600E-2 " " absolute error = 2.084443728733731400000000000000E-14 " " relative error = 3.233768003136711600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8099999999998007 " " y[1] (closed_form) = -6.39377019207110400E-2 " " y[1] (numeric) = -6.39377019206901500E-2 " " absolute error = 2.089994843856857200000000000000E-14 " " relative error = 3.26879881677426200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8199999999997996 " " y[1] (closed_form) = -6.3420723042321800E-2 " " y[1] (numeric) = -6.34207230423008300E-2 " " absolute error = 2.096933737760764400000000000000E-14 " " relative error = 3.30638573193409100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999997985 " " y[1] (closed_form) = -6.2907702011641700E-2 " " y[1] (numeric) = -6.29077020116206700E-2 " " absolute error = 2.102484852883890200000000000000E-14 " " relative error = 3.34217398768564900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8399999999997974 " " y[1] (closed_form) = -6.23986112500971600E-2 " " y[1] (numeric) = -6.23986112500760300E-2 " " absolute error = 2.11289319373975100000000000000E-14 " " relative error = 3.38612214504447200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8499999999997963 " " y[1] (closed_form) = -6.189342333608740000E-2 " " y[1] (numeric) = -6.189342333606622000E-2 " " absolute error = 2.11775041947248600000000000000E-14 " " relative error = 3.42160815370139100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.859999999999795 " " y[1] (closed_form) = -6.13921110045912300E-2 " " y[1] (numeric) = -6.13921110045699900E-2 " " absolute error = 2.123995423986002600000000000000E-14 " " relative error = 3.4597204579382500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.869999999999794 " " y[1] (closed_form) = -6.08946471467657900E-2 " " y[1] (numeric) = -6.08946471467444800E-2 " " absolute error = 2.13024042849951900000000000000E-14 " " relative error = 3.4982392185725303000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.879999999999793 " " y[1] (closed_form) = -6.04010048095380700E-2 " " y[1] (numeric) = -6.04010048095167100E-2 " " absolute error = 2.13579154362264500000000000000E-14 " " relative error = 3.53601988966477700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.889999999999792 " " y[1] (closed_form) = -5.9911157195188900E-2 " " y[1] (numeric) = -5.99111571951675000E-2 " " absolute error = 2.1406487693553800000000000000E-14 " " relative error = 3.57303859510041730000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8999999999997907 " " y[1] (closed_form) = -5.942507766092994000E-2 " " y[1] (numeric) = -5.94250776609084500E-2 " " absolute error = 2.147587663259287200000000000000E-14 " " relative error = 3.61394170237871900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9099999999997896 " " y[1] (closed_form) = -5.894273971847355000E-2 " " y[1] (numeric) = -5.89427397184520100E-2 " " absolute error = 2.153832667772803700000000000000E-14 " " relative error = 3.654110206040795400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999997885 " " y[1] (closed_form) = -5.846411703359600E-2 " " y[1] (numeric) = -5.84641170335744100E-2 " " absolute error = 2.158689893505538700000000000000E-14 " " relative error = 3.692333012170632700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9299999999997874 " " y[1] (closed_form) = -5.79891834256940900E-2 " " y[1] (numeric) = -5.79891834256724500E-2 " " absolute error = 2.164241008628664500000000000000E-14 " " relative error = 3.732146032719825000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9399999999997863 " " y[1] (closed_form) = -5.75179128673352200E-2 " " y[1] (numeric) = -5.75179128673135400E-2 " " absolute error = 2.169098234361399600000000000000E-14 " " relative error = 3.771169929904121000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9499999999997852 " " y[1] (closed_form) = -5.705027948380131000E-2 " " y[1] (numeric) = -5.70502794837795600E-2 " " absolute error = 2.174649349484525400000000000000E-14 " " relative error = 3.81181191251129400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.959999999999784 " " y[1] (closed_form) = -5.658625755262658000E-2 " " y[1] (numeric) = -5.658625755260480000E-2 " " absolute error = 2.178812685826869700000000000000E-14 " " relative error = 3.85042725930500300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.969999999999783 " " y[1] (closed_form) = -5.61258215031294700E-2 " " y[1] (numeric) = -5.612582150310762000E-2 " " absolute error = 2.184363800949995500000000000000E-14 " " relative error = 3.891905262942475500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.979999999999782 " " y[1] (closed_form) = -5.56689459159386700E-2 " " y[1] (numeric) = -5.56689459159167800E-2 " " absolute error = 2.189221026682730600000000000000E-14 " " relative error = 3.93257136570989200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.989999999999781 " " y[1] (closed_form) = -5.52156055225137700E-2 " " y[1] (numeric) = -5.521560552249182000E-2 " " absolute error = 2.19546603119624700000000000000E-14 " " relative error = 3.976169436919534400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9999999999997797 " " y[1] (closed_form) = -5.4765775204660200E-2 " " y[1] (numeric) = -5.4765775204638200E-2 " " absolute error = 2.20032325692898200000000000000E-14 " " relative error = 4.01769763818069600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0099999999997786 " " y[1] (closed_form) = -5.43194299940391400E-2 " " y[1] (numeric) = -5.43194299940170800E-2 " " absolute error = 2.206568261442498600000000000000E-14 " " relative error = 4.062208056462745500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0199999999997775 " " y[1] (closed_form) = -5.38765450716721200E-2 " " y[1] (numeric) = -5.38765450716500E-2 " " absolute error = 2.211425487175233700000000000000E-14 " " relative error = 4.104616367351262600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0299999999997764 " " y[1] (closed_form) = -5.34370957674407500E-2 " " y[1] (numeric) = -5.343709576741859000E-2 " " absolute error = 2.216282712907968700000000000000E-14 " " relative error = 4.147461012015461000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0399999999997753 " " y[1] (closed_form) = -5.30010575595815500E-2 " " y[1] (numeric) = -5.30010575595593500E-2 " " absolute error = 2.22044604925031300000000000000E-14 " " relative error = 4.18943725180234600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0499999999997742 " " y[1] (closed_form) = -5.25684060741761400E-2 " " y[1] (numeric) = -5.256840607415390000E-2 " " absolute error = 2.22530327498304810000000000000E-14 " " relative error = 4.233157215843781000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.059999999999773 " " y[1] (closed_form) = -5.21391170846369000E-2 " " y[1] (numeric) = -5.21391170846146200E-2 " " absolute error = 2.22807883254461100000000000000E-14 " " relative error = 4.273334412103283500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.069999999999772 " " y[1] (closed_form) = -5.1713166511188090E-2 " " y[1] (numeric) = -5.17131665111657600E-2 " " absolute error = 2.23293605827734600000000000000E-14 " " relative error = 4.31792560564677900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.079999999999771 " " y[1] (closed_form) = -5.12905304203429700E-2 " " y[1] (numeric) = -5.1290530420320600E-2 " " absolute error = 2.23779328401008120000000000000E-14 " " relative error = 4.36297551550085370000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.08999999999977 " " y[1] (closed_form) = -5.08711850243765200E-2 " " y[1] (numeric) = -5.087118502435409000E-2 " " absolute error = 2.242650509742816200000000000000E-14 " " relative error = 4.40848883050037100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0999999999997687 " " y[1] (closed_form) = -5.04551066807943300E-2 " " y[1] (numeric) = -5.04551066807718400E-2 " " absolute error = 2.247507735475551300000000000000E-14 " " relative error = 4.45447028720893100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1099999999997676 " " y[1] (closed_form) = -5.00422718917975700E-2 " " y[1] (numeric) = -5.004227189177506000E-2 " " absolute error = 2.252364961208286300000000000000E-14 " " relative error = 4.500924670403445600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1199999999997665 " " y[1] (closed_form) = -4.96326573037443100E-2 " " y[1] (numeric) = -4.96326573037217500E-2 " " absolute error = 2.2558344081602400000000000000E-14 " " relative error = 4.54506071346306600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1299999999997654 " " y[1] (closed_form) = -4.92262397066070500E-2 " " y[1] (numeric) = -4.92262397065844500E-2 " " absolute error = 2.259997744502584300000000000000E-14 " " relative error = 4.59104282182100530000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1399999999997643 " " y[1] (closed_form) = -4.882299603342700000E-2 " " y[1] (numeric) = -4.882299603340435300E-2 " " absolute error = 2.264854970235319300000000000000E-14 " " relative error = 4.63891025590619340000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.149999999999763 " " y[1] (closed_form) = -4.842290335976484600E-2 " " y[1] (numeric) = -4.842290335974215300E-2 " " absolute error = 2.269018306577663700000000000000E-14 " " relative error = 4.685836967931621000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.159999999999762 " " y[1] (closed_form) = -4.802593890314829600E-2 " " y[1] (numeric) = -4.802593890312556500E-2 " " absolute error = 2.27318164292000800000000000000E-14 " " relative error = 4.733237277264331600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.169999999999761 " " y[1] (closed_form) = -4.763208002251663000E-2 " " y[1] (numeric) = -4.763208002249385600E-2 " " absolute error = 2.27803886865274300000000000000E-14 " " relative error = 4.782572727405288700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.17999999999976 " " y[1] (closed_form) = -4.72413042176620600E-2 " " y[1] (numeric) = -4.72413042176392350E-2 " " absolute error = 2.282202204995087400000000000000E-14 " " relative error = 4.83094665312360840000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.189999999999759 " " y[1] (closed_form) = -4.685358912866839400E-2 " " y[1] (numeric) = -4.685358912864552300E-2 " " absolute error = 2.287059430727822500000000000000E-14 " " relative error = 4.881289722431178500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1999999999997577 " " y[1] (closed_form) = -4.64689125353467700E-2 " " y[1] (numeric) = -4.646891253532386000E-2 " " absolute error = 2.291222767070166800000000000000E-14 " " relative error = 4.93065716854755100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2099999999997566 " " y[1] (closed_form) = -4.60872523566688230E-2 " " y[1] (numeric) = -4.60872523566458700E-2 " " absolute error = 2.29538610341251110000000000000E-14 " " relative error = 4.98052278241397200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2199999999997555 " " y[1] (closed_form) = -4.57085866501972860E-2 " " y[1] (numeric) = -4.570858665017430400E-2 " " absolute error = 2.29816166097407400000000000000E-14 " " relative error = 5.02785544117049200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2299999999997544 " " y[1] (closed_form) = -4.53328936115141250E-2 " " y[1] (numeric) = -4.5332893611491100E-2 " " absolute error = 2.302324997316418400000000000000E-14 " " relative error = 5.0787073444869400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2399999999997533 " " y[1] (closed_form) = -4.496015157364631000E-2 " " y[1] (numeric) = -4.49601515736232500E-2 " " absolute error = 2.306488333658762700000000000000E-14 " " relative error = 5.13007241508217200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.249999999999752 " " y[1] (closed_form) = -4.45903390064894430E-2 " " y[1] (numeric) = -4.45903390064663300E-2 " " absolute error = 2.311345559391497800000000000000E-14 " " relative error = 5.183511968938198000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.259999999999751 " " y[1] (closed_form) = -4.42234345162290700E-2 " " y[1] (numeric) = -4.42234345162059200E-2 " " absolute error = 2.31550889573384200000000000000E-14 " " relative error = 5.235931856183850000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.26999999999975 " " y[1] (closed_form) = -4.385941684476022400E-2 " " y[1] (numeric) = -4.38594168447370300E-2 " " absolute error = 2.319672232076186400000000000000E-14 " " relative error = 5.28888069872573300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.279999999999749 " " y[1] (closed_form) = -4.34982648691047300E-2 " " y[1] (numeric) = -4.3498264869081504E-2 " " absolute error = 2.322447789637749300000000000000E-14 " " relative error = 5.33917340525300300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.289999999999748 " " y[1] (closed_form) = -4.31399576008269060E-2 " " y[1] (numeric) = -4.313995760080363600E-2 " " absolute error = 2.327305015370484400000000000000E-14 " " relative error = 5.39477817040291700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2999999999997467 " " y[1] (closed_form) = -4.278447418544737400E-2 " " y[1] (numeric) = -4.27844741854240700E-2 " " absolute error = 2.33077446232243800000000000000E-14 " " relative error = 5.44771089676082200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3099999999997456 " " y[1] (closed_form) = -4.24317939018552860E-2 " " y[1] (numeric) = -4.24317939018319400E-2 " " absolute error = 2.334937798664782300000000000000E-14 " " relative error = 5.502802460026771000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3199999999997445 " " y[1] (closed_form) = -4.20818961617189300E-2 " " y[1] (numeric) = -4.208189616169555000E-2 " " absolute error = 2.33840724561673600000000000000E-14 " " relative error = 5.55680104487292300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3299999999997434 " " y[1] (closed_form) = -4.17347605088949500E-2 " " y[1] (numeric) = -4.17347605088715300E-2 " " absolute error = 2.341876692568689600000000000000E-14 " " relative error = 5.61133372759995600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3399999999997423 " " y[1] (closed_form) = -4.13903666188360440E-2 " " y[1] (numeric) = -4.139036661881257400E-2 " " absolute error = 2.346733918301424600000000000000E-14 " " relative error = 5.66975871441898900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.349999999999741 " " y[1] (closed_form) = -4.10486942979974900E-2 " " y[1] (numeric) = -4.104869429797397600E-2 " " absolute error = 2.351591144034159700000000000000E-14 " " relative error = 5.72878427499429400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.35999999999974 " " y[1] (closed_form) = -4.07097234832423600E-2 " " y[1] (numeric) = -4.070972348321882000E-2 " " absolute error = 2.354366701595722600000000000000E-14 " " relative error = 5.783303103409355000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.369999999999739 " " y[1] (closed_form) = -4.037343424124570400E-2 " " y[1] (numeric) = -4.03734342412221100E-2 " " absolute error = 2.359223927328457600000000000000E-14 " " relative error = 5.84350569047768200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.379999999999738 " " y[1] (closed_form) = -4.003980676789753400E-2 " " y[1] (numeric) = -4.003980676787389000E-2 " " absolute error = 2.364081153061192700000000000000E-14 " " relative error = 5.90432707821314200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.389999999999737 " " y[1] (closed_form) = -3.97088213877049730E-2 " " y[1] (numeric) = -3.97088213876812870E-2 " " absolute error = 2.36824448940353700000000000000E-14 " " relative error = 5.96402614492309200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3999999999997357 " " y[1] (closed_form) = -3.938045855319341500E-2 " " y[1] (numeric) = -3.93804585531696900E-2 " " absolute error = 2.372407825745881400000000000000E-14 " " relative error = 6.02432757998827200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4099999999997346 " " y[1] (closed_form) = -3.90546988443069800E-2 " " y[1] (numeric) = -3.90546988442832200E-2 " " absolute error = 2.37587727269783500000000000000E-14 " " relative error = 6.08346074353142300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4199999999997335 " " y[1] (closed_form) = -3.87315229678080400E-2 " " y[1] (numeric) = -3.87315229677842540E-2 " " absolute error = 2.37865283025939800000000000000E-14 " " relative error = 6.14138729384958800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4299999999997324 " " y[1] (closed_form) = -3.84109117566762900E-2 " " y[1] (numeric) = -3.841091175665247700E-2 " " absolute error = 2.381428387820960800000000000000E-14 " " relative error = 6.19987466818472200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4399999999997313 " " y[1] (closed_form) = -3.80928461695071100E-2 " " y[1] (numeric) = -3.80928461694832470E-2 " " absolute error = 2.386285613553695800000000000000E-14 " " relative error = 6.26439306460615900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.44999999999973 " " y[1] (closed_form) = -3.77773072899093300E-2 " " y[1] (numeric) = -3.77773072898854370E-2 " " absolute error = 2.389061171115258700000000000000E-14 " " relative error = 6.32406421342105300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.459999999999729 " " y[1] (closed_form) = -3.746427632590275700E-2 " " y[1] (numeric) = -3.74642763258788300E-2 " " absolute error = 2.392530618067212300000000000000E-14 " " relative error = 6.38616530919888600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.469999999999728 " " y[1] (closed_form) = -3.715373460931508700E-2 " " y[1] (numeric) = -3.71537346092911170E-2 " " absolute error = 2.396693954409556700000000000000E-14 " " relative error = 6.45074843649409000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.479999999999727 " " y[1] (closed_form) = -3.684566359517866000E-2 " " y[1] (numeric) = -3.68456635951546650E-2 " " absolute error = 2.400163401361510300000000000000E-14 " " relative error = 6.51410007899973600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4899999999997258 " " y[1] (closed_form) = -3.65400448611268900E-2 " " y[1] (numeric) = -3.65400448611028500E-2 " " absolute error = 2.404326737703854600000000000000E-14 " " relative error = 6.5799775201198400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4999999999997247 " " y[1] (closed_form) = -3.62368601067905140E-2 " " y[1] (numeric) = -3.62368601067664330E-2 " " absolute error = 2.40849007404619900000000000000E-14 " " relative error = 6.64651977833715800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5099999999997236 " " y[1] (closed_form) = -3.59360911531937170E-2 " " y[1] (numeric) = -3.593609115316958600E-2 " " absolute error = 2.41334729977893400000000000000E-14 " " relative error = 6.71566445413041100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5199999999997225 " " y[1] (closed_form) = -3.563771994215022600E-2 " " y[1] (numeric) = -3.56377199421260600E-2 " " absolute error = 2.41612285734049700000000000000E-14 " " relative error = 6.77967855761402800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5299999999997214 " " y[1] (closed_form) = -3.53417285356593670E-2 " " y[1] (numeric) = -3.53417285356351700E-2 " " absolute error = 2.419592304292450500000000000000E-14 " " relative error = 6.84627607235201200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5399999999997203 " " y[1] (closed_form) = -3.504809911530222000E-2 " " y[1] (numeric) = -3.504809911527800000E-2 " " absolute error = 2.42306175124440410000000000000E-14 " " relative error = 6.91353258067704900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.549999999999719 " " y[1] (closed_form) = -3.47568139816378600E-2 " " y[1] (numeric) = -3.4756813981613600E-2 " " absolute error = 2.42583730880596700000000000000E-14 " " relative error = 6.97945821526548700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.559999999999718 " " y[1] (closed_form) = -3.44678555535997400E-2 " " y[1] (numeric) = -3.44678555535754500E-2 " " absolute error = 2.429306755757920700000000000000E-14 " " relative error = 7.04803567480486800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.569999999999717 " " y[1] (closed_form) = -3.41812063678924100E-2 " " y[1] (numeric) = -3.41812063678680830E-2 " " absolute error = 2.432776202709874300000000000000E-14 " " relative error = 7.11729181388713300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.579999999999716 " " y[1] (closed_form) = -3.38968490783884250E-2 " " y[1] (numeric) = -3.38968490783640700E-2 " " absolute error = 2.435551760271437200000000000000E-14 " " relative error = 7.18518631227074500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5899999999997148 " " y[1] (closed_form) = -3.36147664555256460E-2 " " y[1] (numeric) = -3.36147664555012600E-2 " " absolute error = 2.439021207223390800000000000000E-14 " " relative error = 7.25580292354659700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5999999999997137 " " y[1] (closed_form) = -3.33349413857049140E-2 " " y[1] (numeric) = -3.333494138568049400E-2 " " absolute error = 2.441796764784953700000000000000E-14 " " relative error = 7.32503692306498000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6099999999997125 " " y[1] (closed_form) = -3.30573568706881600E-2 " " y[1] (numeric) = -3.30573568706637200E-2 " " absolute error = 2.443878432956125800000000000000E-14 " " relative error = 7.39284281715548800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6199999999997114 " " y[1] (closed_form) = -3.278199602699704600E-2 " " y[1] (numeric) = -3.27819960269725930E-2 " " absolute error = 2.445266211736907300000000000000E-14 " " relative error = 7.459174266640600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6299999999997103 " " y[1] (closed_form) = -3.25088420853121500E-2 " " y[1] (numeric) = -3.25088420852876500E-2 " " absolute error = 2.450123437469642300000000000000E-14 " " relative error = 7.5367908553612710000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6399999999997092 " " y[1] (closed_form) = -3.223787838987266500E-2 " " y[1] (numeric) = -3.22378783898481400E-2 " " absolute error = 2.452898995031205200000000000000E-14 " " relative error = 7.60874821030954800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.649999999999708 " " y[1] (closed_form) = -3.19690883978768900E-2 " " y[1] (numeric) = -3.196908839785233500E-2 " " absolute error = 2.45567455259276800000000000000E-14 " " relative error = 7.68140311675528700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.659999999999707 " " y[1] (closed_form) = -3.17024556788832400E-2 " " y[1] (numeric) = -3.17024556788586430E-2 " " absolute error = 2.459837888935112500000000000000E-14 " " relative error = 7.75913990339111600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.669999999999706 " " y[1] (closed_form) = -3.14379639142121200E-2 " " y[1] (numeric) = -3.1437963914187506E-2 " " absolute error = 2.461919557106284600000000000000E-14 " " relative error = 7.83104008842419800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.679999999999705 " " y[1] (closed_form) = -3.117559689634855600E-2 " " y[1] (numeric) = -3.117559689632390000E-2 " " absolute error = 2.465735948753433600000000000000E-14 " " relative error = 7.90918601158277600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6899999999997037 " " y[1] (closed_form) = -3.091533852834556000E-2 " " y[1] (numeric) = -3.091533852832088000E-2 " " absolute error = 2.468511506314996500000000000000E-14 " " relative error = 7.98474680796936800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6999999999997026 " " y[1] (closed_form) = -3.065717282322849600E-2 " " y[1] (numeric) = -3.06571728232037800E-2 " " absolute error = 2.471634008571754700000000000000E-14 " " relative error = 8.06217201704598700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7099999999997015 " " y[1] (closed_form) = -3.04010839034002300E-2 " " y[1] (numeric) = -3.040108390337549000E-2 " " absolute error = 2.473368732047731600000000000000E-14 " " relative error = 8.13579127608373100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7199999999997004 " " y[1] (closed_form) = -3.014705600004733400E-2 " " y[1] (numeric) = -3.014705600002257600E-2 " " absolute error = 2.476144289609294400000000000000E-14 " " relative error = 8.21355255917993100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7299999999996993 " " y[1] (closed_form) = -2.989507345254718300E-2 " " y[1] (numeric) = -2.989507345252239700E-2 " " absolute error = 2.478919847170857300000000000000E-14 " " relative error = 8.2920680931113200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7399999999996982 " " y[1] (closed_form) = -2.964512070787616000E-2 " " y[1] (numeric) = -2.964512070785133600E-2 " " absolute error = 2.482042349427615600000000000000E-14 " " relative error = 8.37251557814768200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.749999999999697 " " y[1] (closed_form) = -2.93971823200188700E-2 " " y[1] (numeric) = -2.93971823199940200E-2 " " absolute error = 2.484817906989178500000000000000E-14 " " relative error = 8.45257167826274600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.759999999999696 " " y[1] (closed_form) = -2.915124294937850300E-2 " " y[1] (numeric) = -2.91512429493536230E-2 " " absolute error = 2.48828735394113200000000000000E-14 " " relative error = 8.53578476314740300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.769999999999695 " " y[1] (closed_form) = -2.890728736218828300E-2 " " y[1] (numeric) = -2.89072873621633800E-2 " " absolute error = 2.490369022112304300000000000000E-14 " " relative error = 8.61502150274325600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.779999999999694 " " y[1] (closed_form) = -2.866530042992416000E-2 " " y[1] (numeric) = -2.866530042989924000E-2 " " absolute error = 2.492797634978671800000000000000E-14 " " relative error = 8.6962201602338710000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7899999999996927 " " y[1] (closed_form) = -2.842526712871865600E-2 " " y[1] (numeric) = -2.842526712869370400E-2 " " absolute error = 2.495573192540234700000000000000E-14 " " relative error = 8.77941861105292300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7999999999996916 " " y[1] (closed_form) = -2.818717253877597000E-2 " " y[1] (numeric) = -2.818717253875098000E-2 " " absolute error = 2.498348750101797600000000000000E-14 " " relative error = 8.86342447673642700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8099999999996905 " " y[1] (closed_form) = -2.795100184378837600E-2 " " y[1] (numeric) = -2.79510018437633730E-2 " " absolute error = 2.500430418272970000000000000000E-14 " " relative error = 8.9457631330973100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8199999999996894 " " y[1] (closed_form) = -2.771674033035393400E-2 " " y[1] (numeric) = -2.771674033032890400E-2 " " absolute error = 2.503205975834532600000000000000E-14 " " relative error = 9.03138661328493700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8299999999996883 " " y[1] (closed_form) = -2.74843733873955100E-2 " " y[1] (numeric) = -2.74843733873704530E-2 " " absolute error = 2.505981533396095500000000000000E-14 " " relative error = 9.11784124773007500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.839999999999687 " " y[1] (closed_form) = -2.725388650558120400E-2 " " y[1] (numeric) = -2.72538865055561200E-2 " " absolute error = 2.50841014626246300000000000000E-14 " " relative error = 9.20386215649932000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.849999999999686 " " y[1] (closed_form) = -2.702526527674615000E-2 " " y[1] (numeric) = -2.702526527672105000E-2 " " absolute error = 2.5101448697384400000000000000E-14 " " relative error = 9.28814146330800300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.859999999999685 " " y[1] (closed_form) = -2.67984953933158200E-2 " " y[1] (numeric) = -2.679849539329068300E-2 " " absolute error = 2.513614316690393500000000000000E-14 " " relative error = 9.37968449272472500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.869999999999684 " " y[1] (closed_form) = -2.657356264773063600E-2 " " y[1] (numeric) = -2.657356264770548000E-2 " " absolute error = 2.515695984861565600000000000000E-14 " " relative error = 9.46691272905556200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.879999999999683 " " y[1] (closed_form) = -2.63504529318722800E-2 " " y[1] (numeric) = -2.6350452931847100E-2 " " absolute error = 2.518124597727933000000000000000E-14 " " relative error = 9.55628582263239500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8899999999996817 " " y[1] (closed_form) = -2.612915223649134300E-2 " " y[1] (numeric) = -2.61291522364661300E-2 " " absolute error = 2.521247099984691400000000000000E-14 " " relative error = 9.64917298948405400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8999999999996806 " " y[1] (closed_form) = -2.590964665063660300E-2 " " y[1] (numeric) = -2.590964665061136000E-2 " " absolute error = 2.524022657546254300000000000000E-14 " " relative error = 9.74163288129689200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9099999999996795 " " y[1] (closed_form) = -2.56919223610858600E-2 " " y[1] (numeric) = -2.5691922361060600E-2 " " absolute error = 2.526104325717426500000000000000E-14 " " relative error = 9.83229004904505600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9199999999996784 " " y[1] (closed_form) = -2.54759656517783700E-2 " " y[1] (numeric) = -2.54759656517530900E-2 " " absolute error = 2.528185993888598700000000000000E-14 " " relative error = 9.92380830012665900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9299999999996773 " " y[1] (closed_form) = -2.526176290324886000E-2 " " y[1] (numeric) = -2.52617629032235500E-2 " " absolute error = 2.530614606754966000000000000000E-14 " " relative error = 1.00175693060182650000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.939999999999676 " " y[1] (closed_form) = -2.50493005920632400E-2 " " y[1] (numeric) = -2.504930059203791000E-2 " " absolute error = 2.532696274926138400000000000000E-14 " " relative error = 1.01108462714069240000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.949999999999675 " " y[1] (closed_form) = -2.483856529025595400E-2 " " y[1] (numeric) = -2.483856529023060200E-2 " " absolute error = 2.53512488779250600000000000000E-14 " " relative error = 1.02064062805874820000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.959999999999674 " " y[1] (closed_form) = -2.462954366476902400E-2 " " y[1] (numeric) = -2.46295436647436500E-2 " " absolute error = 2.537553500658873400000000000000E-14 " " relative error = 1.03028847598531840000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.969999999999673 " " y[1] (closed_form) = -2.442222247689278300E-2 " " y[1] (numeric) = -2.44222224768673900E-2 " " absolute error = 2.539288224134850000000000000000E-14 " " relative error = 1.03974493989538080000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.979999999999672 " " y[1] (closed_form) = -2.421658858170839300E-2 " " y[1] (numeric) = -2.42165885816829800E-2 " " absolute error = 2.541369892306022400000000000000E-14 " " relative error = 1.04943348388286410000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9899999999996707 " " y[1] (closed_form) = -2.401262892753207300E-2 " " y[1] (numeric) = -2.40126289275066320E-2 " " absolute error = 2.544145449867585300000000000000E-14 " " relative error = 1.05950308795658500000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9999999999996696 " " y[1] (closed_form) = -2.38103305553610920E-2 " " y[1] (numeric) = -2.381033055533563200E-2 " " absolute error = 2.54588017334356200000000000000E-14 " " relative error = 1.06923344361984770000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.009999999999673 " " y[1] (closed_form) = -2.360968059832153000E-2 " " y[1] (numeric) = -2.360968059829614300E-2 " " absolute error = 2.53894127943965500000000000000E-14 " " relative error = 1.07538146010334180000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.019999999999676 " " y[1] (closed_form) = -2.341066628111814200E-2 " " y[1] (numeric) = -2.341066628109282300E-2 " " absolute error = 2.532002385535747600000000000000E-14 " " relative error = 1.08155930084652590000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.02999999999968 " " y[1] (closed_form) = -2.32132749194855380E-2 " " y[1] (numeric) = -2.321327491946028600E-2 " " absolute error = 2.525410436327036000000000000000E-14 " " relative error = 1.08791648101628770000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.039999999999683 " " y[1] (closed_form) = -2.30174939196415820E-2 " " y[1] (numeric) = -2.301749391961639700E-2 " " absolute error = 2.518471542423128500000000000000E-14 " " relative error = 1.09415540684645720000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.049999999999686 " " y[1] (closed_form) = -2.28233107777425730E-2 " " y[1] (numeric) = -2.28233107777174480E-2 " " absolute error = 2.51222653790961200000000000000E-14 " " relative error = 1.10072835723708860000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.05999999999969 " " y[1] (closed_form) = -2.263071307934026400E-2 " " y[1] (numeric) = -2.263071307931520700E-2 " " absolute error = 2.505634588700900000000000000000E-14 " " relative error = 1.10718322481332320000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.069999999999693 " " y[1] (closed_form) = -2.24396884988408700E-2 " " y[1] (numeric) = -2.243968849881587700E-2 " " absolute error = 2.499389584187383700000000000000E-14 " " relative error = 1.11382543671071480000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.079999999999696 " " y[1] (closed_form) = -2.22502247989658790E-2 " " y[1] (numeric) = -2.225022479894094900E-2 " " absolute error = 2.49314457967386720000000000000E-14 " " relative error = 1.1205030970247730000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0899999999997 " " y[1] (closed_form) = -2.206230983021489600E-2 " " y[1] (numeric) = -2.206230983019002400E-2 " " absolute error = 2.48724651985554600000000000000E-14 " " relative error = 1.12737357919305380000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.099999999999703 " " y[1] (closed_form) = -2.18759315303303610E-2 " " y[1] (numeric) = -2.18759315303055500E-2 " " absolute error = 2.481001515342029500000000000000E-14 " " relative error = 1.13412382549387280000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.109999999999706 " " y[1] (closed_form) = -2.169107792376429600E-2 " " y[1] (numeric) = -2.169107792373954300E-2 " " absolute error = 2.475450400218903700000000000000E-14 " " relative error = 1.14122977609464550000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.11999999999971 " " y[1] (closed_form) = -2.150773712114693600E-2 " " y[1] (numeric) = -2.150773712112224700E-2 " " absolute error = 2.46885845101019190000000000000E-14 " " relative error = 1.14789316844622850000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.129999999999713 " " y[1] (closed_form) = -2.13258973187574600E-2 " " y[1] (numeric) = -2.13258973187328300E-2 " " absolute error = 2.462960391191870700000000000000E-14 " " relative error = 1.15491524430512120000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.139999999999716 " " y[1] (closed_form) = -2.114554679799662600E-2 " " y[1] (numeric) = -2.114554679797205300E-2 " " absolute error = 2.457062331373549600000000000000E-14 " " relative error = 1.16197625667752280000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.14999999999972 " " y[1] (closed_form) = -2.09666739248614700E-2 " " y[1] (numeric) = -2.096667392483696500E-2 " " absolute error = 2.450470382164837700000000000000E-14 " " relative error = 1.16874540565977150000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.159999999999723 " " y[1] (closed_form) = -2.07892671494220300E-2 " " y[1] (numeric) = -2.078926714939758300E-2 " " absolute error = 2.444572322346516600000000000000E-14 " " relative error = 1.1758819129006569000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.169999999999726 " " y[1] (closed_form) = -2.06133150053000900E-2 " " y[1] (numeric) = -2.061331500527570400E-2 " " absolute error = 2.438674262528195400000000000000E-14 " " relative error = 1.18305777692775950000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.17999999999973 " " y[1] (closed_form) = -2.043880610914998700E-2 " " y[1] (numeric) = -2.04388061091256600E-2 " " absolute error = 2.432776202709874300000000000000E-14 " " relative error = 1.19027314497629850000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.189999999999733 " " y[1] (closed_form) = -2.02657291601414690E-2 " " y[1] (numeric) = -2.0265729160117202E-2 " " absolute error = 2.42687814289155300000000000000E-14 " " relative error = 1.19752816378535450000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.199999999999736 " " y[1] (closed_form) = -2.009407293944463800E-2 " " y[1] (numeric) = -2.009407293942042400E-2 " " absolute error = 2.421327027768427300000000000000E-14 " " relative error = 1.20499563979155540000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.20999999999974 " " y[1] (closed_form) = -1.99238263097169400E-2 " " y[1] (numeric) = -1.992382630969278800E-2 " " absolute error = 2.415428967950106200000000000000E-14 " " relative error = 1.21233187360807820000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.219999999999743 " " y[1] (closed_form) = -1.975497821459231100E-2 " " y[1] (numeric) = -1.975497821456821400E-2 " " absolute error = 2.409877852826980400000000000000E-14 " " relative error = 1.21988383214054270000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.229999999999746 " " y[1] (closed_form) = -1.958751767817234500E-2 " " y[1] (numeric) = -1.9587517678148300E-2 " " absolute error = 2.404326737703854600000000000000E-14 " " relative error = 1.22747903905309740000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.23999999999975 " " y[1] (closed_form) = -1.942143380451959400E-2 " " y[1] (numeric) = -1.942143380449560800E-2 " " absolute error = 2.39877562258072890000000000000E-14 " " relative error = 1.23511767808950620000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.249999999999753 " " y[1] (closed_form) = -1.925671577715304700E-2 " " y[1] (numeric) = -1.925671577712911600E-2 " " absolute error = 2.39322450745760300000000000000E-14 " " relative error = 1.24279993284058450000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.259999999999756 " " y[1] (closed_form) = -1.90933528585456370E-2 " " y[1] (numeric) = -1.909335285852176400E-2 " " absolute error = 2.38732644763928200000000000000E-14 " " relative error = 1.25034427705073450000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.26999999999976 " " y[1] (closed_form) = -1.89313343896239380E-2 " " y[1] (numeric) = -1.893133438960012400E-2 " " absolute error = 2.381428387820960800000000000000E-14 " " relative error = 1.25792949340443550000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.279999999999763 " " y[1] (closed_form) = -1.87706497892700E-2 " " y[1] (numeric) = -1.877064978924623800E-2 " " absolute error = 2.376224217393030400000000000000E-14 " " relative error = 1.26592539100663840000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.2899999999997664 " " y[1] (closed_form) = -1.861128855382530600E-2 " " y[1] (numeric) = -1.8611288553801597E-2 " " absolute error = 2.370673102269904600000000000000E-14 " " relative error = 1.27378235817134980000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.29999999999977 " " y[1] (closed_form) = -1.845324025659689200E-2 " " y[1] (numeric) = -1.84532402565732420E-2 " " absolute error = 2.365121987146778800000000000000E-14 " " relative error = 1.28168384211074570000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.309999999999773 " " y[1] (closed_form) = -1.829649454736565500E-2 " " y[1] (numeric) = -1.82964945473420510E-2 " " absolute error = 2.36061170610923900000000000000E-14 " " relative error = 1.29019889574919780000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.3199999999997765 " " y[1] (closed_form) = -1.814104115189676700E-2 " " y[1] (numeric) = -1.81410411518732080E-2 " " absolute error = 2.35575448037650400000000000000E-14 " " relative error = 1.298577331174950000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.32999999999978 " " y[1] (closed_form) = -1.798686987145232700E-2 " " y[1] (numeric) = -1.798686987142881800E-2 " " absolute error = 2.35089725464376900000000000000E-14 " " relative error = 1.30700742899962340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.339999999999783 " " y[1] (closed_form) = -1.783397058230612500E-2 " " y[1] (numeric) = -1.783397058228266800E-2 " " absolute error = 2.345693084215838600000000000000E-14 " " relative error = 1.31529491617705440000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.3499999999997865 " " y[1] (closed_form) = -1.76823332352606500E-2 " " y[1] (numeric) = -1.768233323523724400E-2 " " absolute error = 2.34048891378790800000000000000E-14 " " relative error = 1.3236312666705650000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.35999999999979 " " y[1] (closed_form) = -1.753194785516622000E-2 " " y[1] (numeric) = -1.75319478551428680E-2 " " absolute error = 2.334937798664782300000000000000E-14 " " relative error = 1.33181881326251800000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.369999999999793 " " y[1] (closed_form) = -1.738280454044236500E-2 " " y[1] (numeric) = -1.738280454041907200E-2 " " absolute error = 2.329386683541656600000000000000E-14 " " relative error = 1.34005227874602640000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.3799999999997965 " " y[1] (closed_form) = -1.72348934626013500E-2 " " y[1] (numeric) = -1.723489346257810500E-2 " " absolute error = 2.324529457808921500000000000000E-14 " " relative error = 1.34873445133444320000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.3899999999998 " " y[1] (closed_form) = -1.708820486577393400E-2 " " y[1] (numeric) = -1.70882048657507420E-2 " " absolute error = 2.31932528738099100000000000000E-14 " " relative error = 1.35726678466172950000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.399999999999803 " " y[1] (closed_form) = -1.694272906623730500E-2 " " y[1] (numeric) = -1.694272906621416300E-2 " " absolute error = 2.314121116953060700000000000000E-14 " " relative error = 1.3658490954474010000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4099999999998065 " " y[1] (closed_form) = -1.679845645194522600E-2 " " y[1] (numeric) = -1.679845645192213400E-2 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 1.37468814341743740000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.41999999999981 " " y[1] (closed_form) = -1.66553774820604130E-2 " " y[1] (numeric) = -1.665537748203737600E-2 " " absolute error = 2.303712776097199800000000000000E-14 " " relative error = 1.3831645536575440000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.429999999999813 " " y[1] (closed_form) = -1.651348268648908700E-2 " " y[1] (numeric) = -1.651348268646609700E-2 " " absolute error = 2.2992024950596600000000000000E-14 " " relative error = 1.3923183490184110000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4399999999998165 " " y[1] (closed_form) = -1.637276266541774800E-2 " " y[1] (numeric) = -1.6372762665394802E-2 " " absolute error = 2.294692214022120400000000000000E-14 " " relative error = 1.40153024930174290000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.44999999999982 " " y[1] (closed_form) = -1.623320808885217500E-2 " " y[1] (numeric) = -1.623320808882927300E-2 " " absolute error = 2.290181932984580700000000000000E-14 " " relative error = 1.41080057647835880000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.459999999999823 " " y[1] (closed_form) = -1.60948096961586400E-2 " " y[1] (numeric) = -1.609480969613578000E-2 " " absolute error = 2.28567165194704100000000000000E-14 " " relative error = 1.42012965365633630000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.469999999999827 " " y[1] (closed_form) = -1.59575582956073300E-2 " " y[1] (numeric) = -1.595755829558451500E-2 " " absolute error = 2.281508315604696700000000000000E-14 " " relative error = 1.42973522223179500000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.47999999999983 " " y[1] (closed_form) = -1.582144476391798600E-2 " " y[1] (numeric) = -1.58214447638952180E-2 " " absolute error = 2.276651089871961600000000000000E-14 " " relative error = 1.43896535609948750000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.489999999999833 " " y[1] (closed_form) = -1.568646004580778700E-2 " " y[1] (numeric) = -1.568646004578506000E-2 " " absolute error = 2.272487753529617300000000000000E-14 " " relative error = 1.44869380784031030000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.499999999999837 " " y[1] (closed_form) = -1.55525951535414100E-2 " " y[1] (numeric) = -1.555259515351873000E-2 " " absolute error = 2.2678040001444800000000000000E-14 " " relative error = 1.45815150317732600000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.50999999999984 " " y[1] (closed_form) = -1.541984116648336400E-2 " " y[1] (numeric) = -1.541984116646072700E-2 " " absolute error = 2.263640663802135600000000000000E-14 " " relative error = 1.46800517551529300000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.519999999999843 " " y[1] (closed_form) = -1.5288189230652500E-2 " " y[1] (numeric) = -1.52881892306299100E-2 " " absolute error = 2.258956910416998200000000000000E-14 " " relative error = 1.4775830389957740000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.529999999999847 " " y[1] (closed_form) = -1.515763055827877300E-2 " " y[1] (numeric) = -1.51576305582562300E-2 " " absolute error = 2.254446629379458500000000000000E-14 " " relative error = 1.48733446214529080000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.53999999999985 " " y[1] (closed_form) = -1.502815642736222000E-2 " " y[1] (numeric) = -1.502815642733971700E-2 " " absolute error = 2.250109820689516500000000000000E-14 " " relative error = 1.49726270921207200000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.549999999999853 " " y[1] (closed_form) = -1.489975818123411800E-2 " " y[1] (numeric) = -1.489975818121166400E-2 " " absolute error = 2.245599539651976800000000000000E-14 " " relative error = 1.50713824502216040000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.559999999999857 " " y[1] (closed_form) = -1.477242722812046300E-2 " " y[1] (numeric) = -1.477242722809804800E-2 " " absolute error = 2.2416096756572300000000000000E-14 " " relative error = 1.51742813895210940000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.56999999999986 " " y[1] (closed_form) = -1.464615504070753400E-2 " " y[1] (numeric) = -1.464615504068516000E-2 " " absolute error = 2.23727286696728800000000000000E-14 " " relative error = 1.52754962701747350000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.579999999999863 " " y[1] (closed_form) = -1.452093315570980300E-2 " " y[1] (numeric) = -1.452093315568747000E-2 " " absolute error = 2.233283002972541500000000000000E-14 " " relative error = 1.53797485259711990000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.589999999999867 " " y[1] (closed_form) = -1.439675317343997500E-2 " " y[1] (numeric) = -1.439675317341768400E-2 " " absolute error = 2.228946194282599400000000000000E-14 " " relative error = 1.54822838693567250000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.59999999999987 " " y[1] (closed_form) = -1.427360675738128200E-2 " " y[1] (numeric) = -1.427360675735903400E-2 " " absolute error = 2.22478285794025500000000000000E-14 " " relative error = 1.5586690146061072000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.609999999999873 " " y[1] (closed_form) = -1.415148563376199800E-2 " " y[1] (numeric) = -1.415148563373979400E-2 " " absolute error = 2.22044604925031300000000000000E-14 " " relative error = 1.5690550848971432000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.619999999999877 " " y[1] (closed_form) = -1.403038159113214600E-2 " " y[1] (numeric) = -1.403038159110997800E-2 " " absolute error = 2.21662965760316400000000000000E-14 " " relative error = 1.57987838264083830000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.62999999999988 " " y[1] (closed_form) = -1.391028647994241600E-2 " " y[1] (numeric) = -1.391028647992029000E-2 " " absolute error = 2.212639793608417400000000000000E-14 " " relative error = 1.5906500536842840000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.639999999999883 " " y[1] (closed_form) = -1.379119221212532800E-2 " " y[1] (numeric) = -1.379119221210323700E-2 " " absolute error = 2.208823401961268500000000000000E-14 " " relative error = 1.6016188941368340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.649999999999887 " " y[1] (closed_form) = -1.367309076067855000E-2 " " y[1] (numeric) = -1.367309076065650300E-2 " " absolute error = 2.204486593271326500000000000000E-14 " " relative error = 1.61228110882657930000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.65999999999989 " " y[1] (closed_form) = -1.355597415925047000E-2 " " y[1] (numeric) = -1.35559741592284600E-2 " " absolute error = 2.200843673971775200000000000000E-14 " " relative error = 1.62352306674318940000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.669999999999893 " " y[1] (closed_form) = -1.343983450172791800E-2 " " y[1] (numeric) = -1.343983450170595000E-2 " " absolute error = 2.197027282324626200000000000000E-14 " " relative error = 1.6347130480231442000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.679999999999897 " " y[1] (closed_form) = -1.332466394182615400E-2 " " y[1] (numeric) = -1.332466394180422000E-2 " " absolute error = 2.193210890677477200000000000000E-14 " " relative error = 1.64597839033897330000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.6899999999999 " " y[1] (closed_form) = -1.32104546926809700E-2 " " y[1] (numeric) = -1.321045469265907700E-2 " " absolute error = 2.189221026682730600000000000000E-14 " " relative error = 1.65718824795306360000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.699999999999903 " " y[1] (closed_form) = -1.309719902644306800E-2 " " y[1] (numeric) = -1.30971990264212080E-2 " " absolute error = 2.18575157973077700000000000000E-14 " " relative error = 1.6688694852370908000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.709999999999907 " " y[1] (closed_form) = -1.298488927387456400E-2 " " y[1] (numeric) = -1.298488927385274300E-2 " " absolute error = 2.182108660431225600000000000000E-14 " " relative error = 1.68049847357697620000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.71999999999991 " " y[1] (closed_form) = -1.287351782394771000E-2 " " y[1] (numeric) = -1.287351782392592600E-2 " " absolute error = 2.178465741131674300000000000000E-14 " " relative error = 1.69220703379089300000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.729999999999913 " " y[1] (closed_form) = -1.276307712344580000E-2 " " y[1] (numeric) = -1.276307712342405500E-2 " " absolute error = 2.17482282183212300000000000000E-14 " " relative error = 1.7039956750217930000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.739999999999917 " " y[1] (closed_form) = -1.265355967656624000E-2 " " y[1] (numeric) = -1.265355967654452600E-2 " " absolute error = 2.171353374880169400000000000000E-14 " " relative error = 1.71600200289994900000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.74999999999992 " " y[1] (closed_form) = -1.254495804452578400E-2 " " y[1] (numeric) = -1.25449580445041120E-2 " " absolute error = 2.167363510885422800000000000000E-14 " " relative error = 1.72767697045522640000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.759999999999923 " " y[1] (closed_form) = -1.243726484516800300E-2 " " y[1] (numeric) = -1.243726484514636500E-2 " " absolute error = 2.163894063933469200000000000000E-14 " " relative error = 1.73984721791476730000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.769999999999927 " " y[1] (closed_form) = -1.233047275257282600E-2 " " y[1] (numeric) = -1.23304727525512190E-2 " " absolute error = 2.160598089329113200000000000000E-14 " " relative error = 1.75224270203126780000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.77999999999993 " " y[1] (closed_form) = -1.222457449666832500E-2 " " y[1] (numeric) = -1.22245744966467500E-2 " " absolute error = 2.15747558707235500000000000000E-14 " " relative error = 1.76486763417438500000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.789999999999933 " " y[1] (closed_form) = -1.211956286284460400E-2 " " y[1] (numeric) = -1.211956286282306900E-2 " " absolute error = 2.15365919542520600000000000000E-14 " " relative error = 1.77701062307103450000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.799999999999937 " " y[1] (closed_form) = -1.201543069156989900E-2 " " y[1] (numeric) = -1.201543069154839500E-2 " " absolute error = 2.1503632208208500000000000000E-14 " " relative error = 1.78966803273190870000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.80999999999994 " " y[1] (closed_form) = -1.191217087800875700E-2 " " y[1] (numeric) = -1.191217087798728800E-2 " " absolute error = 2.146893773868896500000000000000E-14 " " relative error = 1.80226912109891780000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.819999999999943 " " y[1] (closed_form) = -1.180977637164241600E-2 " " y[1] (numeric) = -1.180977637162098400E-2 " " absolute error = 2.143250854569345200000000000000E-14 " " relative error = 1.81481070184843630000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.829999999999947 " " y[1] (closed_form) = -1.170824017589130700E-2 " " y[1] (numeric) = -1.170824017586990500E-2 " " absolute error = 2.14012835231258700000000000000E-14 " " relative error = 1.8278821754266470000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.83999999999995 " " y[1] (closed_form) = -1.160755534773967300E-2 " " y[1] (numeric) = -1.160755534771830400E-2 " " absolute error = 2.13683237770823100000000000000E-14 " " relative error = 1.84089785806994620000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.8499999999999535 " " y[1] (closed_form) = -1.150771499736234800E-2 " " y[1] (numeric) = -1.150771499734101500E-2 " " absolute error = 2.133362930756277400000000000000E-14 " " relative error = 1.85385450651607160000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.859999999999957 " " y[1] (closed_form) = -1.140871228775364200E-2 " " y[1] (numeric) = -1.14087122877323400E-2 " " absolute error = 2.13024042849951900000000000000E-14 " " relative error = 1.8672049700001330000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.86999999999996 " " y[1] (closed_form) = -1.131054043435834200E-2 " " y[1] (numeric) = -1.131054043433707300E-2 " " absolute error = 2.126944453895163200000000000000E-14 " " relative error = 1.88049763513871120000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.8799999999999635 " " y[1] (closed_form) = -1.121319270470484500E-2 " " y[1] (numeric) = -1.121319270468360600E-2 " " absolute error = 2.123995423986002600000000000000E-14 " " relative error = 1.89419327743722280000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.889999999999967 " " y[1] (closed_form) = -1.11166624180403710E-2 " " y[1] (numeric) = -1.111666241801916300E-2 " " absolute error = 2.120699449381646700000000000000E-14 " " relative error = 1.90767639569600270000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.89999999999997 " " y[1] (closed_form) = -1.102094294496831000E-2 " " y[1] (numeric) = -1.102094294494713700E-2 " " absolute error = 2.11723000242969300000000000000E-14 " " relative error = 1.92109696330142940000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.9099999999999735 " " y[1] (closed_form) = -1.092602770708764500E-2 " " y[1] (numeric) = -1.092602770706650600E-2 " " absolute error = 2.11393402782533700000000000000E-14 " " relative error = 1.93476905284986760000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.919999999999977 " " y[1] (closed_form) = -1.083191017663447400E-2 " " y[1] (numeric) = -1.083191017661336600E-2 " " absolute error = 2.11081152556857900000000000000E-14 " " relative error = 1.94869740530327930000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.92999999999998 " " y[1] (closed_form) = -1.073858387612560600E-2 " " y[1] (numeric) = -1.07385838761045310E-2 " " absolute error = 2.10751555096422300000000000000E-14 " " relative error = 1.96256375633450640000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.9399999999999835 " " y[1] (closed_form) = -1.06460423780042500E-2 " " y[1] (numeric) = -1.064604237798320900E-2 " " absolute error = 2.10421957635986700000000000000E-14 " " relative error = 1.97652752229071280000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.949999999999987 " " y[1] (closed_form) = -1.05542793042877810E-2 " " y[1] (numeric) = -1.055427930426676700E-2 " " absolute error = 2.101270546450706400000000000000E-14 " " relative error = 1.99091807774789940000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.95999999999999 " " y[1] (closed_form) = -1.046328832621754200E-2 " " y[1] (numeric) = -1.04632883261965600E-2 " " absolute error = 2.098148044193948200000000000000E-14 " " relative error = 2.00524727865587230000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.9699999999999935 " " y[1] (closed_form) = -1.037306316391075000E-2 " " y[1] (numeric) = -1.037306316388979800E-2 " " absolute error = 2.095372486632385300000000000000E-14 " " relative error = 2.0200132338174331000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.979999999999997 " " y[1] (closed_form) = -1.028359758601442200E-2 " " y[1] (numeric) = -1.028359758599349500E-2 " " absolute error = 2.092596929070822400000000000000E-14 " " relative error = 2.03488799670334340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.99 " " y[1] (closed_form) = -1.019488540936135700E-2 " " y[1] (numeric) = -1.019488540934046200E-2 " " absolute error = 2.08947442681406410000000000000E-14 " " relative error = 2.04953203779556400000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " "Finished!" "diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) / exp ( x ) ; " Iterations = 4000 "Total Elapsed Time "= 1 Minutes 22 Seconds "Elapsed Time(since restart) "= 1 Minutes 22 Seconds "Time to Timeout "= 1 Minutes 37 Seconds Percent Done = 100.02500000000009 "%" (%o254) temp/diffeq.div_lin_exp.max