(%i1) batch("temp/diffeq.add_full_lin.max") read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.add_full_lin.max (%i2) load("stringproc") (%i3) keepfloat:true (%i4) alias(convfloat,float) (%i5) alias(int_trunc,truncate) (%i6) alias(elapsed_time_seconds,elapsed_real_time) (%i7) alias(ln,log) (%i8) alias(arcsin,asin) (%i9) alias(arccos,acos) (%i10) alias(arctan,atan) (%i11) alias(float_abs,abs) (%i12) mode_declare(display_poles(),fixnum) (%i13) mode_declare(est_size_answer(),convfloat) (%i14) mode_declare(test_suggested_h(),convfloat) (%i15) mode_declare(reached_interval(),boolean) (%i16) mode_declare(display_alot([iter],fixnum),fixnum) (%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum) (%i18) mode_declare(check_for_pole(),fixnum) (%i19) mode_declare(atomall(),fixnum) (%i20) mode_declare(log10([x],convfloat),convfloat) (%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum) (%i22) mode_declare(omniout_timestr(secs_in,number),fixnum) (%i23) mode_declare(zero_ats_ar(ar,array([40],convfloat)),fixnum) (%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a], completearray([40],convfloat),[arr_b], completearray([40],convfloat),[jjj_ats],fixnum), convfloat) (%i25) mode_declare(att([mmm_att],fixnum,[arr_a], completearray([40],convfloat),[arr_b], completearray([40],convfloat),[jjj_att],fixnum), convfloat) (%i26) mode_declare(logitem_ditto([file],fixnum),fixnum) (%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum) (%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum) (%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum) (%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum) (%i31) mode_declare(logstart([file],fixnum),fixnum) (%i32) mode_declare(logend([file],fixnum),fixnum) (%i33) mode_declare(chk_data(),fixnum) (%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat, [t2],convfloat,[clock_sec2],convfloat), convfloat) (%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2], convfloat),convfloat) (%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i42) mode_declare(neg([nnn],convfloat),convfloat) (%i43) mode_declare(factorial_2([nnn],fixnum),convfloat) (%i44) mode_declare(factorial_1([nnn],fixnum),convfloat) (%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat) (%i46) mode_declare(convfloat([mmm],fixnum),convfloat) (%i47) mode_declare(elaped_time_seconds(),convfloat) (%i48) mode_declare(Si([x],convfloat),convfloat) (%i49) mode_declare(Ci([x],convfloat),convfloat) (%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end], convfloat,[estimated_h], convfloat,[estimated_answer], convfloat),convfloat) (%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat) (%i52) mode_declare(main_prog(),fixnum) (%i53) define_variable(always,1,fixnum) (%i54) define_variable(info,2,fixnum) (%i55) define_variable(debugl,3,fixnum) (%i56) define_variable(debugmassive,4,fixnum) (%i57) define_variable(glob_iolevel,5,fixnum) (%i58) define_variable(glob_yes_pole,4,fixnum) (%i59) define_variable(glob_no_pole,3,fixnum) (%i60) define_variable(glob_not_given,0,fixnum) (%i61) define_variable(glob_no_sing_tests,4,fixnum) (%i62) define_variable(glob_ratio_test,1,fixnum) (%i63) define_variable(glob_three_term_test,2,fixnum) (%i64) define_variable(glob_six_term_test,3,fixnum) (%i65) define_variable(ats_max_terms,40,fixnum) (%i66) define_variable(glob_log_10,0.0,convfloat) (%i67) define_variable(max_unchanged,10,fixnum) (%i68) define_variable(glob__small,1.0E-51,convfloat) (%i69) define_variable(glob_small_float,1.0E-51,convfloat) (%i70) define_variable(glob_smallish_float,1.0E-61,convfloat) (%i71) define_variable(glob_large_float,1.0E+100,convfloat) (%i72) define_variable(glob_larger_float,1.1E+100,convfloat) (%i73) define_variable(glob__m2,-2.0,convfloat) (%i74) define_variable(glob__m1,-1.0,convfloat) (%i75) define_variable(glob__0,0.0,convfloat) (%i76) define_variable(glob__1,1.0,convfloat) (%i77) define_variable(glob__2,2.0,convfloat) (%i78) define_variable(glob__3,3.0,convfloat) (%i79) define_variable(glob__4,4.0,convfloat) (%i80) define_variable(glob__5,5.0,convfloat) (%i81) define_variable(glob__8,8.0,convfloat) (%i82) define_variable(glob__10,10.0,convfloat) (%i83) define_variable(glob__100,100.0,convfloat) (%i84) define_variable(glob__pi,0.0,convfloat) (%i85) define_variable(glob__0_5,0.5,convfloat) (%i86) define_variable(glob__0_8,0.8,convfloat) (%i87) define_variable(glob__m0_8,-0.8,convfloat) (%i88) define_variable(glob__0_25,0.25,convfloat) (%i89) define_variable(glob__0_125,0.125,convfloat) (%i90) define_variable(glob_prec,1.0E-16,convfloat) (%i91) define_variable(glob_check_sign,1.0,convfloat) (%i92) define_variable(glob_desired_digits_correct,8.0,convfloat) (%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat) (%i94) define_variable(glob_ratio_of_radius,0.1,convfloat) (%i95) define_variable(glob_percent_done,0.0,convfloat) (%i96) define_variable(glob_total_exp_sec,0.1,convfloat) (%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat) (%i98) define_variable(glob_estimated_size_answer,100.0,convfloat) (%i99) define_variable(glob_almost_1,0.999,convfloat) (%i100) define_variable(glob_clock_sec,0.0,convfloat) (%i101) define_variable(glob_clock_start_sec,0.0,convfloat) (%i102) define_variable(glob_disp_incr,0.1,convfloat) (%i103) define_variable(glob_h,0.1,convfloat) (%i104) define_variable(glob_diff_rc_fm,0.1,convfloat) (%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat) (%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat) (%i107) define_variable(glob_diff_ord_fm,0.1,convfloat) (%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat) (%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat) (%i110) define_variable(glob_six_term_ord_save,0.1,convfloat) (%i111) define_variable(glob_guess_error_rc,0.1,convfloat) (%i112) define_variable(glob_guess_error_ord,0.1,convfloat) (%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat) (%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat) (%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat) (%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat) (%i117) define_variable(glob_last_good_h,0.1,convfloat) (%i118) define_variable(glob_max_h,0.1,convfloat) (%i119) define_variable(glob_min_h,1.0E-6,convfloat) (%i120) define_variable(glob_display_interval,0.1,convfloat) (%i121) define_variable(glob_abserr,1.0E-11,convfloat) (%i122) define_variable(glob_relerr,1.0E-11,convfloat) (%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat) (%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat) (%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat) (%i126) define_variable(glob_max_hours,0.0,convfloat) (%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat) (%i128) define_variable(glob_optimal_start,0.0,convfloat) (%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat) (%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat) (%i131) define_variable(glob_max_sec,10000.0,convfloat) (%i132) define_variable(glob_orig_start_sec,0.0,convfloat) (%i133) define_variable(glob_normmax,0.0,convfloat) (%i134) define_variable(glob_max_minutes,0.0,convfloat) (%i135) define_variable(glob_next_display,0.0,convfloat) (%i136) define_variable(glob_est_digits,1,fixnum) (%i137) define_variable(glob_subiter_method,3,fixnum) (%i138) define_variable(glob_html_log,true,boolean) (%i139) define_variable(glob_min_good_digits,99999,fixnum) (%i140) define_variable(glob_good_digits,0,fixnum) (%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum) (%i142) define_variable(glob_apfp_est_good_digits,0,fixnum) (%i143) define_variable(glob_max_opt_iter,10,fixnum) (%i144) define_variable(glob_dump,false,boolean) (%i145) define_variable(glob_djd_debug,true,boolean) (%i146) define_variable(glob_display_flag,true,boolean) (%i147) define_variable(glob_djd_debug2,true,boolean) (%i148) define_variable(glob_h_reason,0,fixnum) (%i149) define_variable(glob_sec_in_minute,60,fixnum) (%i150) define_variable(glob_min_in_hour,60,fixnum) (%i151) define_variable(glob_hours_in_day,24,fixnum) (%i152) define_variable(glob_days_in_year,365,fixnum) (%i153) define_variable(glob_sec_in_hour,3600,fixnum) (%i154) define_variable(glob_sec_in_day,86400,fixnum) (%i155) define_variable(glob_sec_in_year,31536000,fixnum) (%i156) define_variable(glob_not_yet_finished,true,boolean) (%i157) define_variable(glob_initial_pass,true,boolean) (%i158) define_variable(glob_not_yet_start_msg,true,boolean) (%i159) define_variable(glob_reached_optimal_h,false,boolean) (%i160) define_variable(glob_optimal_done,false,boolean) (%i161) define_variable(glob_type_given_pole,0,fixnum) (%i162) define_variable(glob_optimize,false,boolean) (%i163) define_variable(glob_look_poles,false,boolean) (%i164) define_variable(glob_dump_closed_form,false,boolean) (%i165) define_variable(glob_max_iter,1000,fixnum) (%i166) define_variable(glob_no_eqs,0,fixnum) (%i167) define_variable(glob_unchanged_h_cnt,0,fixnum) (%i168) define_variable(glob_warned,false,boolean) (%i169) define_variable(glob_warned2,false,boolean) (%i170) define_variable(glob_start,0,fixnum) (%i171) define_variable(glob_iter,0,fixnum) (%i172) completearray(array_y_init,[40],convfloat) (%i173) completearray(array_norms,[40],convfloat) (%i174) completearray(array_fact_1,[40],convfloat) (%i175) completearray(array_1st_rel_error,[2],convfloat) (%i176) completearray(array_last_rel_error,[2],convfloat) (%i177) completearray(array_est_rel_error,[2],convfloat) (%i178) completearray(array_max_est_error,[2],convfloat) (%i179) completearray(array_type_pole,[2],convfloat) (%i180) completearray(array_type_real_pole,[2],convfloat) (%i181) completearray(array_type_complex_pole,[2],convfloat) (%i182) completearray(array_est_digits,[2],convfloat) (%i183) completearray(array_y,[40],convfloat) (%i184) completearray(array_x,[40],convfloat) (%i185) completearray(array_tmp0,[40],convfloat) (%i186) completearray(array_tmp1,[40],convfloat) (%i187) completearray(array_tmp2,[40],convfloat) (%i188) completearray(array_tmp3_g,[40],convfloat) (%i189) completearray(array_tmp3,[40],convfloat) (%i190) completearray(array_tmp4,[40],convfloat) (%i191) completearray(array_tmp5,[40],convfloat) (%i192) completearray(array_tmp6,[40],convfloat) (%i193) completearray(array_tmp7,[40],convfloat) (%i194) completearray(array_m1,[40],convfloat) (%i195) completearray(array_y_higher,[2,40],convfloat) (%i196) completearray(array_y_higher_work,[2,40],convfloat) (%i197) completearray(array_y_higher_work2,[2,40],convfloat) (%i198) completearray(array_y_set_initial,[2,40],convfloat) (%i199) completearray(array_given_rad_poles,[2,3],convfloat) (%i200) completearray(array_given_ord_poles,[2,3],convfloat) (%i201) completearray(array_rad_test_poles,[2,4],convfloat) (%i202) completearray(array_ord_test_poles,[2,4],convfloat) (%i203) completearray(array_fact_2,[40,40],convfloat) (%i204) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%i205) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%i206) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%i207) 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)) (%i208) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%i209) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%i210) 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) (%i211) 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) (%i212) 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) (%i213) 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) (%i214) 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) (%i215) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%i216) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%i217) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%i218) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), printf(file,"~d",glob_min_good_digits), printf(file,"")),0) (%i219) log_revs(file,revs):=printf(file,revs) (%i220) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%i221) 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) (%i222) logstart(file):=(printf(file,""),0) (%i223) logend(file):=(printf(file,"~%"),0) (%i224) 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) (%i225) 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) (%i226) 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) (%i227) 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) (%i228) 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) (%i229) c(in_val):=(ret:in_val,ret) (%i230) 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) (%i231) 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) (%i232) 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) (%i233) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%i234) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret) (%i235) 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) (%i236) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret) (%i237) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret) (%i238) 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) (%i239) log10(x):=log(x)/glob_log_10 (%i240) c(x):=x (%i241) 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 (%i242) 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) (%i243) exact_soln_y(x):=block( (-cos(c(0.1)+c(0.3)*c(x)))/c(0.3) +c(0.2)*c(x)+c(0.05)*c(x)*c(x)) - cos(c(0.1) + c(0.3) c(x)) (%o243) exact_soln_y(x) := block(--------------------------- + c(0.2) c(x) c(0.3) + c(0.05) c(x) c(x)) (%i244) 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) (%i245) my_check_sign(x0,xf):=block([ret], if xf > x0 then ret:glob__1 else ret:glob__m1,ret) (%i246) 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) (%i247) 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) (%i248) 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)) (%i249) 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)) (%i250) 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(29) *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) (%i251) 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) (%i252) 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) (%i253) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:array_const_0D3[1]*array_x[1], array_tmp2[1]:array_const_0D1[1]+array_tmp1[1], array_tmp3[1]:sin(array_tmp2[1]), array_tmp3_g[1]:cos(array_tmp2[1]), array_tmp4[1]:array_tmp3[1]+array_const_0D0[1], array_tmp5[1]:array_const_0D1[1]*array_x[1], array_tmp6[1]:array_const_0D2[1]+array_tmp5[1], array_tmp7[1]:array_tmp6[1]+array_tmp4[1], if not array_y_set_initial[1,2] then (if 1 <= ats_max_terms then ( temporary :c(array_tmp7[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_0D3[1]*array_x[2], array_tmp2[2]:array_tmp1[2], array_tmp3[2]:array_tmp3_g[1]*array_tmp2[2]/c(1), array_tmp3_g[2]:neg(array_tmp3[1])*array_tmp2[2]/c(1), array_tmp4[2]:array_tmp3[2], array_tmp5[2]:array_const_0D1[1]*array_x[2], array_tmp6[2]:array_tmp5[2], array_tmp7[2]:array_tmp6[2]+array_tmp4[2], if not array_y_set_initial[1,3] then (if 2 <= ats_max_terms then ( temporary :c(array_tmp7[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_g[2]*array_tmp2[2]/c(2), array_tmp3_g[3]:neg(array_tmp3[2])*array_tmp2[2]/c(2), array_tmp4[3]:array_tmp3[3],array_tmp7[3]:array_tmp4[3], if not array_y_set_initial[1,4] then (if 3 <= ats_max_terms then ( temporary :c(array_tmp7[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_g[3]*array_tmp2[2]/c(3), array_tmp3_g[4]:neg(array_tmp3[3])*array_tmp2[2]/c(3), array_tmp4[4]:array_tmp3[4],array_tmp7[4]:array_tmp4[4], if not array_y_set_initial[1,5] then (if 4 <= ats_max_terms then ( temporary :c(array_tmp7[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_g[4]*array_tmp2[2]/c(4), array_tmp3_g[5]:neg(array_tmp3[4])*array_tmp2[2]/c(4), array_tmp4[5]:array_tmp3[5],array_tmp7[5]:array_tmp4[5], if not array_y_set_initial[1,6] then (if 5 <= ats_max_terms then ( temporary :c(array_tmp7[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_g[kkk-1]*array_tmp2[2]/c(kkk-1), array_tmp3_g[kkk] :neg(array_tmp3[kkk-1])*array_tmp2[2]/c(kkk-1), array_tmp4[kkk]:array_tmp3[kkk], array_tmp7[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_tmp7[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) (%i254) exact_soln_y(x):=block( (-cos(c(0.1)+c(0.3)*c(x)))/c(0.3) +c(0.2)*c(x)+c(0.05)*c(x)*c(x)) - cos(c(0.1) + c(0.3) c(x)) (%o254) exact_soln_y(x) := block(--------------------------- + c(0.2) c(x) c(0.3) + c(0.05) c(x) c(x)) (%i255) 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:40, glob_html_log:true,term:1, while term <= 40 do (array_y_init[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_norms[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_fact_1[term]:c(0.0),term:1+term), term:1, while term <= 2 do (array_1st_rel_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_last_rel_error[term]:c(0.0),term:1+term), term:1, while term <= 2 do (array_est_rel_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_max_est_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_type_pole[term]:0,term:1+term), term:1, while term <= 2 do (array_type_real_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_type_complex_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_est_digits[term]:0,term:1+term), term:1, while term <= 40 do (array_y[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_x[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp0[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp1[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp2[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp3_g[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp3[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp4[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp5[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp6[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_tmp7[term]:c(0.0),term:1+term), term:1, while term <= 40 do (array_m1[term]:c(0.0),term:1+term), ord:1, while ord <= 2 do (term:1, while term <= 40 do (array_y_higher[ord,term]:c(0.0),term:1+term), ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 40 do (array_y_higher_work[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 40 do (array_y_higher_work2[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 40 do (array_y_set_initial[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_rad_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_ord_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 4 do (array_rad_test_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 4 do (array_ord_test_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 40 do (term:1, while term <= 40 do (array_fact_2[ord,term]:c(0.0),term:1+term), ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x), zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2),zero_ats_ar(array_tmp3_g), zero_ats_ar(array_tmp3),zero_ats_ar(array_tmp4), zero_ats_ar(array_tmp5),zero_ats_ar(array_tmp6), zero_ats_ar(array_tmp7),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_0D3),array_const_0D3[1]:c(0.3), zero_ats_ar(array_const_0D1),array_const_0D1[1]:c(0.1), zero_ats_ar(array_const_0D2),array_const_0D2[1]:c(0.2), zero_ats_ar(array_m1),array_m1[1]:glob__m1,iiif:0, while iiif <= ats_max_terms do (jjjf:0, while jjjf <= ats_max_terms do (array_fact_1[iiif]:0, array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf), iiif:1+iiif),array_y_set_initial[1,1]:true, array_y_set_initial[1,2]:false, array_y_set_initial[1,3]:false, array_y_set_initial[1,4]:false, array_y_set_initial[1,5]:false, array_y_set_initial[1,6]:false, array_y_set_initial[1,7]:false, array_y_set_initial[1,8]:false, array_y_set_initial[1,9]:false, array_y_set_initial[1,10]:false, array_y_set_initial[1,11]:false, array_y_set_initial[1,12]:false, array_y_set_initial[1,13]:false, array_y_set_initial[1,14]:false, array_y_set_initial[1,15]:false, array_y_set_initial[1,16]:false, array_y_set_initial[1,17]:false, array_y_set_initial[1,18]:false, array_y_set_initial[1,19]:false, array_y_set_initial[1,20]:false, array_y_set_initial[1,21]:false, array_y_set_initial[1,22]:false, array_y_set_initial[1,23]:false, array_y_set_initial[1,24]:false, array_y_set_initial[1,25]:false, array_y_set_initial[1,26]:false, array_y_set_initial[1,27]:false, array_y_set_initial[1,28]:false, array_y_set_initial[1,29]:false, array_y_set_initial[1,30]:false, array_y_set_initial[1,31]:false, array_y_set_initial[1,32]:false, array_y_set_initial[1,33]:false, array_y_set_initial[1,34]:false, array_y_set_initial[1,35]:false, array_y_set_initial[1,36]:false, array_y_set_initial[1,37]:false, array_y_set_initial[1,38]:false, array_y_set_initial[1,39]:false, array_y_set_initial[1,40]:false,glob_log_10:log(10.0), glob_orig_start_sec:elapsed_time_seconds(), glob_display_flag:true,glob_no_eqs:1,glob_iter:-1, opt_iter:-1,glob_max_iter:50000,glob_max_hours:0.0, glob_max_minutes:15.0, omniout_str(always, "##############ECHO OF PROBLEM#################"), omniout_str(always, "##############temp/add_full_linpostode.ode#################"), omniout_str(always, "diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) + ( 0.1 * x + 0.2 ) ; "), omniout_str(always,"!"), omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(always,"Digits:32,"), omniout_str(always,"max_terms:40,"),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,"x_end:c(5.0),"), omniout_str(always, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(always,"glob_display_interval:c(0.1),"), 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,""), omniout_str(always, " (c(0.05) * c(x) * c(x) + c(0.2) * c(x) - cos(c(0.3) * c(x) + c(0.1)) / c(0.3)) "), omniout_str(always,""),omniout_str(always,"));"), omniout_str(always,"/* END USER DEF BLOCK */"), omniout_str(always, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false, glob_small_float:glob__0,glob_smallish_float:glob__0, glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100), glob_almost_1:c(0.99),x_start:c(1.0),x_end:c(5.0), array_y_init[1+0]:exact_soln_y(x_start), glob_display_interval:c(0.1),glob_look_poles:true, glob_type_given_pole:3,glob_desired_digits_correct:8, glob_max_minutes:3.0,glob_subiter_method:3, glob_max_iter:100000,glob_upper_ratio_limit:c(1.000001), glob_lower_ratio_limit:c(0.999999),glob_look_poles:false, glob_h:c(0.001),glob_display_interval:c(0.01), glob_last_good_h:glob_h, glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes, glob_check_sign:c(my_check_sign(x_start,x_end)), glob__pi:3.141592654,glob_prec:1.0E-16, if glob_optimize then (omniout_str(always,"START of Optimize"), found_h:false,glob_min_pole_est:glob_larger_float, last_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float, glob_min_h:abs(glob_min_h)*glob_check_sign, glob_max_h:abs(glob_max_h)*glob_check_sign, glob_h:abs(glob_min_h)*glob_check_sign, glob_display_interval :c(abs(c(glob_display_interval)) *glob_check_sign), display_max:c(x_end)-c(x_start)/glob__10, if glob_display_interval > display_max then glob_display_interval:c(display_max), chk_data(),min_value:glob_larger_float, est_answer:est_size_answer(),opt_iter:1, est_needed_step_err :estimated_needed_step_error( x_start,x_end,glob_h,est_answer), omniout_float(always,"est_needed_step_err",32, est_needed_step_err,16,""), estimated_step_error:glob_small_float, while opt_iter <= 100 and not found_h do (omniout_int(always,"opt_iter",32,opt_iter, 4,""),array_x[1]:c(x_start), array_x[2]:c(glob_h), glob_next_display:c(x_start),order_diff:1, term_no:1, while term_no <= order_diff do ( array_y[term_no] :array_y_init[term_no] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no),rows:order_diff, r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < ats_max_terms then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h, c(term_no-1)) /c( factorial_1( term_no-1)), term_no:1+term_no), r_order:1+r_order),atomall(), if glob_check_sign*glob_min_h >= glob_check_sign*glob_h then ( omniout_str(always, "SETTING H FOR MIN H"), glob_h:glob_check_sign*abs(glob_min_h), glob_h_reason:1,found_h:true), if glob_check_sign*glob_display_interval <= glob_check_sign*glob_h then ( omniout_str(always, "SETTING H FOR DISPLAY INTERVAL"), glob_h_reason:2, glob_h:glob_display_interval, found_h:true), if glob_look_poles then check_for_pole(), if not found_h then (est_answer:est_size_answer(), est_needed_step_err :estimated_needed_step_error( x_start,x_end,glob_h, est_answer), omniout_float(always, "est_needed_step_err", 32, est_needed_step_err, 16,""), estimated_step_error :test_suggested_h(), omniout_float(always, "estimated_step_error", 32, estimated_step_error, 32,""), if estimated_step_error < est_needed_step_err then ( omniout_str(always, "Double H and LOOP"), glob_h:glob_h*glob__2) else ( omniout_str(always, "Found H for OPTIMAL"), found_h:true,glob_h_reason:3, glob_h:glob_h/glob__2)), opt_iter:1+opt_iter), if not found_h and opt_iter = 1 then (omniout_str(always, "Beginning glob_h too large."), found_h:false), if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then (omniout_str(always, "SETTING H FOR MAX H"), glob_h:glob_check_sign*abs(glob_max_h), glob_h_reason:1,found_h:true)) else (found_h:true,glob_h:glob_h*glob_check_sign), if glob_html_log then html_log_file:openw("entry.html"), if found_h then (omniout_str(always,"START of Soultion"), array_x[1]:c(x_start),array_x[2]:c(glob_h), glob_next_display:c(x_start), glob_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float,order_diff:1, term_no:1, while term_no <= order_diff do (array_y[term_no] :array_y_init[term_no] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no),rows:order_diff, r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < ats_max_terms then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no), r_order:1+r_order),current_iter:1, glob_clock_start_sec:elapsed_time_seconds(), glob_clock_sec:elapsed_time_seconds(),glob_iter:0, omniout_str(debugl," "), glob_reached_optimal_h:true, glob_optimal_clock_start_sec :elapsed_time_seconds(), while glob_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec-glob_orig_start_sec < glob_max_sec do (if reached_interval() then (omniout_str(info," "), omniout_str(info, "TOP MAIN SOLVE Loop")), glob_iter:1+glob_iter, glob_clock_sec:elapsed_time_seconds(), track_estimated_error(),atomall(), track_estimated_error(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display :glob_display_interval +glob_next_display, array_x[1]:glob_h+array_x[1], array_x[2]:glob_h,order_diff:2,ord:2, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[2,iii] :array_y_higher[2,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:2, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:1, calc_term:2,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:1, calc_term:2,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:1, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:1, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)), term_no:ats_max_terms, while term_no >= 1 do ( array_y[term_no] :array_y_higher_work2[1,term_no], ord:1, while ord <= order_diff do ( array_y_higher[ord,term_no] :array_y_higher_work2[ ord,term_no],ord:1+ord), term_no:term_no-1)), omniout_str(always,"Finished!"), if glob_iter >= glob_max_iter then omniout_str(always, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds()-glob_orig_start_sec >= glob_max_sec then omniout_str(always, "Maximum Time Reached before Solution Completed!"), glob_clock_sec:elapsed_time_seconds(), omniout_str(info, "diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) + ( 0.1 * x + 0.2 ) ; "), omniout_int(info, "Iterations ",32, glob_iter,4," "), prog_report(x_start,x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2015-04-24T20:09:47-05:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "add_full_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) + ( 0.1 * x + 0.2 ) ; "), logitem_float(html_log_file,x_start), logitem_float(html_log_file,x_end), logitem_float(html_log_file,array_x[1]), logitem_float(html_log_file,glob_h), logitem_h_reason(html_log_file), logitem_str(html_log_file,"16"), logitem_float(html_log_file, glob_desired_digits_correct), if array_est_digits[1] # -16 then ( logitem_integer(html_log_file, array_est_digits[ 1]),0) else ( logitem_str(html_log_file, "Unknown"),0), if glob_min_good_digits # -16 then ( logitem_integer(html_log_file, glob_min_good_digits), 0) else ( logitem_str(html_log_file, "Unknown"),0), if glob_good_digits # -16 then ( logitem_integer(html_log_file, glob_good_digits),0) else ( logitem_str(html_log_file, "Unknown"),0), logitem_str(html_log_file,"NA"), logitem_str(html_log_file,"NA"), logitem_integer(html_log_file, ats_max_terms), if glob_type_given_pole = 0 then ( logitem_str(html_log_file, "Not Given"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 4 then ( logitem_str(html_log_file, "No Solution"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 5 then ( logitem_str(html_log_file, "Some Pole"), logitem_str(html_log_file,"????"),0) elseif glob_type_given_pole = 3 then ( logitem_str(html_log_file, "No Pole"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 1 then ( logitem_str(html_log_file, "Real Sing"), logitem_float(html_log_file, glob_least_given_sing), 0) elseif glob_type_given_pole = 2 then ( logitem_str(html_log_file, "Complex Sing"), logitem_float(html_log_file, glob_least_given_sing), 0), if glob_least_ratio_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_ratio_sing), 0) else ( logitem_str(html_log_file,"NONE"),0), if glob_least_3_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_3_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), if glob_least_6_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_6_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, glob_clock_sec), if c(glob_percent_done) < glob__100 then ( logitem_time(html_log_file, glob_total_exp_sec),0) else ( logitem_str(html_log_file,"Done"), 0), log_revs(html_log_file, " 308.maple.seems.ok "), logitem_str(html_log_file, "add_full_lin diffeq.max"), logitem_str(html_log_file, "add_full_lin maxima results"), logitem_str(html_log_file,"OK"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i256) main():=(glob_iolevel:2,compile(all),main_prog()) (%i257) 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_0D3 in translation. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_const_0D1 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable array_tmp3_g in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp4 in translation. warning: encountered undefined variable array_tmp5 in translation. warning: encountered undefined variable array_const_0D2 in translation. warning: encountered undefined variable array_tmp6 in translation. warning: encountered undefined variable array_tmp7 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_display_interval (declared type convfloat) assigned type any. warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_h (declared type convfloat) assigned type any. warning: 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/add_full_linpostode.ode#################" "diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) + ( 0.1 * x + 0.2 ) ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:40," "!" "/* 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_display_interval:c(0.1)," "glob_look_poles:true," "" "" "" "" "" "" "" "glob_type_given_pole:3," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:8," "glob_max_minutes:(3.0)," "glob_subiter_method:3," "glob_max_iter:100000," "glob_upper_ratio_limit:c(1.000001)," "glob_lower_ratio_limit:c(0.999999)," "glob_look_poles:false," "glob_h:c(0.001)," "glob_display_interval:c(0.01)," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" "" "" " (c(0.05) * c(x) * c(x) + c(0.2) * c(x) - cos(c(0.3) * c(x) + c(0.1)) / c(0.3)) " "" "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 1. " " y[1] (closed_form) = -2.8202033133429505 " " y[1] (numeric) = -2.8202033133429505 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.009999999999999 " " y[1] (closed_form) = -2.8132903198565886 " " y[1] (numeric) = -2.813290319856588 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.57854028329611100000000000000E-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) = -2.8063397297330464 " " y[1] (numeric) = -2.8063397297330455 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.16489985260841300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0299999999999967 " " y[1] (closed_form) = -2.7993515783926073 " " y[1] (numeric) = -2.799351578392605 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 7.93200134770244500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0399999999999956 " " y[1] (closed_form) = -2.7923259015036064 " " y[1] (numeric) = -2.7923259015036037 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 9.54235054606477600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0499999999999945 " " y[1] (closed_form) = -2.7852627349821097 " " y[1] (numeric) = -2.7852627349821066 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.11609738999017810000000000000E-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) = -2.7781621149915883 " " y[1] (numeric) = -2.7781621149915834 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 1.75834998324620070000000000000E-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) = -2.7710240779425943 " " y[1] (numeric) = -2.771024077942589 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 1.92314118113236800000000000000E-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) = -2.763848660492435 " " y[1] (numeric) = -2.763848660492428 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 2.4101674751482552000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.08999999999999 " " y[1] (closed_form) = -2.756635899544838 " " y[1] (numeric) = -2.7566358995448303 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 2.73867019169909350000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.099999999999989 " " y[1] (closed_form) = -2.7493858322496254 " " y[1] (numeric) = -2.749385832249617 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 3.0689381199899574000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1099999999999879 " " y[1] (closed_form) = -2.7420984960023738 " " y[1] (numeric) = -2.742098496002365 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 3.23904637632446500000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1199999999999868 " " y[1] (closed_form) = -2.734773928444082 " " y[1] (numeric) = -2.734773928444072 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 3.7348797720777620000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1299999999999857 " " y[1] (closed_form) = -2.727412167460829 " " y[1] (numeric) = -2.7274121674608187 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 3.74496086378485860000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1399999999999846 " " y[1] (closed_form) = -2.7200132511834356 " " y[1] (numeric) = -2.7200132511834245 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 4.0816824114445610000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1499999999999835 " " y[1] (closed_form) = -2.71257721798712 " " y[1] (numeric) = -2.7125772179871075 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 4.5840161870226230000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1599999999999824 " " y[1] (closed_form) = -2.7051041064911496 " " y[1] (numeric) = -2.7051041064911363 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 4.9250142586131435000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1699999999999813 " " y[1] (closed_form) = -2.697593955558502 " " y[1] (numeric) = -2.697593955558487 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 5.5972223335502210000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1799999999999802 " " y[1] (closed_form) = -2.690046804295504 " " y[1] (numeric) = -2.690046804295488 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 5.9430979152755450000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.189999999999979 " " y[1] (closed_form) = -2.682462692051488 " " y[1] (numeric) = -2.6824626920514714 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 6.1254536039366210000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.199999999999978 " " y[1] (closed_form) = -2.6748416584184342 " " y[1] (numeric) = -2.6748416584184174 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 6.3089304449820660000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2099999999999769 " " y[1] (closed_form) = -2.6671837432306162 " " y[1] (numeric) = -2.667183743230599 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 6.4935455714701860000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2199999999999758 " " y[1] (closed_form) = -2.6594889865642406 " " y[1] (numeric) = -2.659488986564222 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 7.0132822162195070000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2299999999999747 " " y[1] (closed_form) = -2.6517574287370866 " " y[1] (numeric) = -2.6517574287370675 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 7.2012001613010220000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2399999999999736 " " y[1] (closed_form) = -2.6439891103081443 " " y[1] (numeric) = -2.643989110308125 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 7.390319860706790000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2499999999999725 " " y[1] (closed_form) = -2.6361840720772487 " " y[1] (numeric) = -2.6361840720772283 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 7.7491188378989150000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2599999999999714 " " y[1] (closed_form) = -2.6283423550847145 " " y[1] (numeric) = -2.628342355084693 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 8.1101619169074950000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2699999999999703 " " y[1] (closed_form) = -2.6204640006109616 " " y[1] (numeric) = -2.6204640006109403 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 8.1345449003814240000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2799999999999692 " " y[1] (closed_form) = -2.612549050176151 " " y[1] (numeric) = -2.6125490501761295 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 8.1591892299077630000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.289999999999968 " " y[1] (closed_form) = -2.604597545539804 " " y[1] (numeric) = -2.6045975455397814 " " absolute error = 2.264854970235319300000000000000E-14 " " relative error = 8.6956043328602880000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.299999999999967 " " y[1] (closed_form) = -2.5966095287004314 " " y[1] (numeric) = -2.596609528700408 " " absolute error = 2.35367281220533200000000000000E-14 " " relative error = 9.0644079758242050000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3099999999999659 " " y[1] (closed_form) = -2.5885850418951533 " " y[1] (numeric) = -2.588585041895129 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 9.4356206755608460000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3199999999999648 " " y[1] (closed_form) = -2.5805241275993183 " " y[1] (numeric) = -2.5805241275992934 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 9.637187843207390000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3299999999999637 " " y[1] (closed_form) = -2.5724268285261234 " " y[1] (numeric) = -2.572426828526098 " " absolute error = 2.53130849614535700000000000000E-14 " " relative error = 9.8401574267349510000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3399999999999626 " " y[1] (closed_form) = -2.564293187626229 " " y[1] (numeric) = -2.5642931876262023 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 1.0390915016885964000000000000E-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) = -2.5561232480873692 " " y[1] (numeric) = -2.5561232480873413 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 1.0945333031765321000000000000E-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) = -2.5479170533339683 " " y[1] (numeric) = -2.5479170533339395 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 1.1329175179577748000000000000E-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) = -2.539674647026746 " " y[1] (numeric) = -2.5396746470267164 " " absolute error = 2.975397705995419500000000000000E-14 " " relative error = 1.171566487651788100000000000E-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) = -2.5313960730623264 " " y[1] (numeric) = -2.5313960730622957 " " absolute error = 3.06421554796543200000000000000E-14 " " relative error = 1.2104844360679337000000000000E-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) = -2.5230813755728416 " " y[1] (numeric) = -2.5230813755728096 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 1.2672767283197522000000000000E-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) = -2.5147305989255364 " " y[1] (numeric) = -2.5147305989255035 " " absolute error = 3.286260152890463400000000000000E-14 " " relative error = 1.3068040585717516000000000000E-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) = -2.506343787722367 " " y[1] (numeric) = -2.506343787722333 " " absolute error = 3.41948691584548200000000000000E-14 " " relative error = 1.3643327513951830000000000000E-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) = -2.4979209867996 " " y[1] (numeric) = -2.497920986799565 " " absolute error = 3.508304757815494700000000000000E-14 " " relative error = 1.4044898843299378000000000000E-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) = -2.48946224122741 " " y[1] (numeric) = -2.4894622412273746 " " absolute error = 3.55271367880050100000000000000E-14 " " relative error = 1.4271008493179085000000000000E-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) = -2.4809675963094744 " " y[1] (numeric) = -2.480967596309437 " " absolute error = 3.73034936274052600000000000000E-14 " " relative error = 1.503586491129328000000000000E-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) = -2.4724370975825614 " " y[1] (numeric) = -2.4724370975825236 " " absolute error = 3.77475828372553200000000000000E-14 " " relative error = 1.5267358216782630000000000000E-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) = -2.4638707908161264 " " y[1] (numeric) = -2.463870790816088 " " absolute error = 3.819167204710538500000000000000E-14 " " relative error = 1.5500679739157455000000000000E-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) = -2.455268722011896 " " y[1] (numeric) = -2.455268722011856 " " absolute error = 3.996802888650563500000000000000E-14 " " relative error = 1.6278474338953433000000000000E-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) = -2.4466309374034543 " " y[1] (numeric) = -2.446630937403413 " " absolute error = 4.130029651605582300000000000000E-14 " " relative error = 1.6880476693344992000000000000E-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) = -2.437957483455828 " " y[1] (numeric) = -2.4379574834557856 " " absolute error = 4.26325641456060100000000000000E-14 " " relative error = 1.7487000669582614000000000000E-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) = -2.4292484068650673 " " y[1] (numeric) = -2.4292484068650246 " " absolute error = 4.26325641456060100000000000000E-14 " " relative error = 1.7549693158232063000000000000E-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) = -2.4205037545578265 " " y[1] (numeric) = -2.420503754557783 " " absolute error = 4.352074256530613600000000000000E-14 " " relative error = 1.7980035140766154000000000000E-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) = -2.4117235736909417 " " y[1] (numeric) = -2.411723573690897 " " absolute error = 4.485301019485632400000000000000E-14 " " relative error = 1.8597906776775636000000000000E-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) = -2.4029079116510044 " " y[1] (numeric) = -2.4029079116509586 " " absolute error = 4.57411886145564500000000000000E-14 " " relative error = 1.9035764289081025000000000000E-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) = -2.394056816053937 " " y[1] (numeric) = -2.39405681605389 " " absolute error = 4.662936703425657500000000000000E-14 " " relative error = 1.947713467849713800000000000E-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) = -2.3851703347445645 " " y[1] (numeric) = -2.3851703347445175 " " absolute error = 4.70734562441066400000000000000E-14 " " relative error = 1.973588869456901200000000000E-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) = -2.376248515796183 " " y[1] (numeric) = -2.376248515796135 " " absolute error = 4.79616346638067600000000000000E-14 " " relative error = 2.0183762070751593000000000000E-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) = -2.367291407510126 " " y[1] (numeric) = -2.3672914075100775 " " absolute error = 4.840572387365682500000000000000E-14 " " relative error = 2.0447725075202755000000000000E-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) = -2.3582990584153327 " " y[1] (numeric) = -2.3582990584152825 " " absolute error = 5.018208071305708000000000000000E-14 " " relative error = 2.1278930055112305000000000000E-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) = -2.349271517267907 " " y[1] (numeric) = -2.3492715172678555 " " absolute error = 5.151434834260726000000000000000E-14 " " relative error = 2.1927796750592726000000000000E-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) = -2.340208833050683 " " y[1] (numeric) = -2.3402088330506308 " " absolute error = 5.24025267623073900000000000000E-14 " " relative error = 2.2392243812701002000000000E-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) = -2.3311110549727823 " " y[1] (numeric) = -2.3311110549727294 " " absolute error = 5.28466159721574500000000000000E-14 " " relative error = 2.2670140858121612000000000000E-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) = -2.3219782324691707 " " y[1] (numeric) = -2.3219782324691165 " " absolute error = 5.41788836017076400000000000000E-14 " " relative error = 2.333307127694056700000000000E-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) = -2.312810415200212 " " y[1] (numeric) = -2.3128104152001567 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 2.3809587530174110000000000000E-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) = -2.303607653051226 " " y[1] (numeric) = -2.3036076530511695 " " absolute error = 5.63993296509579500000000000000E-14 " " relative error = 2.4483044921410405000000000000E-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) = -2.2943699961320334 " " y[1] (numeric) = -2.2943699961319757 " " absolute error = 5.77315972805081400000000000000E-14 " " relative error = 2.51622874156457000000000000E-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) = -2.2850974947765086 " " y[1] (numeric) = -2.2850974947764504 " " absolute error = 5.8175686490358200000000000000E-14 " " relative error = 2.5458732777634946000000000000E-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) = -2.2757901995421266 " " y[1] (numeric) = -2.2757901995420675 " " absolute error = 5.90638649100583300000000000000E-14 " " relative error = 2.5953123852076340000000000000E-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) = -2.2664481612095058 " " y[1] (numeric) = -2.2664481612094454 " " absolute error = 6.03961325396085200000000000000E-14 " " relative error = 2.664792143641075000000000000E-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) = -2.257071430781954 " " y[1] (numeric) = -2.257071430781892 " " absolute error = 6.1728400169158700000000000000E-14 " " relative error = 2.734889083584436400000000000E-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) = -2.2476600594850042 " " y[1] (numeric) = -2.2476600594849416 " " absolute error = 6.26165785888588300000000000000E-14 " " relative error = 2.7858562652577396000000000000E-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) = -2.2382140987659627 " " y[1] (numeric) = -2.2382140987658983 " " absolute error = 6.43929354282590800000000000000E-14 " " relative error = 2.876978366982947000000000000E-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) = -2.2287336002934346 " " y[1] (numeric) = -2.22873360029337 " " absolute error = 6.43929354282590800000000000000E-14 " " relative error = 2.8892163432983253000000000000E-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) = -2.219218615956869 " " y[1] (numeric) = -2.219218615956803 " " absolute error = 6.61692922676593300000000000000E-14 " " relative error = 2.9816482158126120000000000000E-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) = -2.209669197866085 " " y[1] (numeric) = -2.2096691978660177 " " absolute error = 6.75015598972095200000000000000E-14 " " relative error = 3.0548264854484514000000000000E-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) = -2.2000853983508057 " " y[1] (numeric) = -2.200085398350738 " " absolute error = 6.79456491070595800000000000000E-14 " " relative error = 3.0883187151731456000000000000E-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) = -2.1904672699601884 " " y[1] (numeric) = -2.190467269960119 " " absolute error = 6.92779167366097700000000000000E-14 " " relative error = 3.1627003830040745000000000000E-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) = -2.1808148654623487 " " y[1] (numeric) = -2.180814865462278 " " absolute error = 7.06101843661599600000000000000E-14 " " relative error = 3.2377890248464575000000000000E-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) = -2.171128237843887 " " y[1] (numeric) = -2.171128237843815 " " absolute error = 7.23865412055602100000000000000E-14 " " relative error = 3.334051851190795000000000000E-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) = -2.161407440309412 " " y[1] (numeric) = -2.161407440309339 " " absolute error = 7.32747196252603300000000000000E-14 " " relative error = 3.390139140761486000000000000E-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) = -2.1516525262810617 " " y[1] (numeric) = -2.151652526280987 " " absolute error = 7.46069872548105200000000000000E-14 " " relative error = 3.4674273073153683000000000000E-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) = -2.141863549398022 " " y[1] (numeric) = -2.1418635493979465 " " absolute error = 7.54951656745106400000000000000E-14 " " relative error = 3.5247420731226700000000000000E-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) = -2.1320405635160444 " " y[1] (numeric) = -2.1320405635159676 " " absolute error = 7.68274333040608300000000000000E-14 " " relative error = 3.6034695877155937000000000000E-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) = -2.1221836227069617 " " y[1] (numeric) = -2.122183622706883 " " absolute error = 7.86037901434610800000000000000E-14 " " relative error = 3.703910882282544000000000000E-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) = -2.1122927812582 " " y[1] (numeric) = -2.1122927812581196 " " absolute error = 8.03801469828613300000000000000E-14 " " relative error = 3.805350645329688700000000000E-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) = -2.102368093672291 " " y[1] (numeric) = -2.1023680936722102 " " absolute error = 8.0824236192711400000000000000E-14 " " relative error = 3.84443791912445000000000000E-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) = -2.092409614666384 " " y[1] (numeric) = -2.092409614666302 " " absolute error = 8.21565038222615800000000000000E-14 " " relative error = 3.92640634254401000000000000E-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) = -2.082417399171746 " " y[1] (numeric) = -2.082417399171663 " " absolute error = 8.30446822419617100000000000000E-14 " " relative error = 3.987898020588554000000000000E-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) = -2.072391502333277 " " y[1] (numeric) = -2.0723915023331925 " " absolute error = 8.4376949871511900000000000000E-14 " " relative error = 4.071477313843116500000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.889999999999902 " " y[1] (closed_form) = -2.0623319795090067 " " y[1] (numeric) = -2.0623319795089214 " " absolute error = 8.52651282912120200000000000000E-14 " " relative error = 4.13440363328466950000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8999999999999009 " " y[1] (closed_form) = -2.052238886269598 " " y[1] (numeric) = -2.052238886269512 " " absolute error = 8.61533067109121500000000000000E-14 " " relative error = 4.198015508200168600000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9099999999998998 " " y[1] (closed_form) = -2.0421122783978496 " " y[1] (numeric) = -2.0421122783977617 " " absolute error = 8.7929663550312400000000000000E-14 " " relative error = 4.305819248062996000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9199999999998987 " " y[1] (closed_form) = -2.0319522118881888 " " y[1] (numeric) = -2.0319522118881004 " " absolute error = 8.83737527601624600000000000000E-14 " " relative error = 4.349204289506458000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9299999999998976 " " y[1] (closed_form) = -2.0217587429461736 " " y[1] (numeric) = -2.0217587429460826 " " absolute error = 9.10382880192628400000000000000E-14 " " relative error = 4.5029254027905846000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9399999999998965 " " y[1] (closed_form) = -2.0115319279879813 " " y[1] (numeric) = -2.011531927987889 " " absolute error = 9.23705556488130200000000000000E-14 " " relative error = 4.592050186407229000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9499999999998954 " " y[1] (closed_form) = -2.001271823639904 " " y[1] (numeric) = -2.001271823639811 " " absolute error = 9.28146448586630900000000000000E-14 " " relative error = 4.6377830218911614000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9599999999998943 " " y[1] (closed_form) = -1.990978486737838 " " y[1] (numeric) = -1.990978486737744 " " absolute error = 9.39248678832882400000000000000E-14 " " relative error = 4.717522992284135000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9699999999998932 " " y[1] (closed_form) = -1.9806519743267739 " " y[1] (numeric) = -1.980651974326678 " " absolute error = 9.59232693276135300000000000000E-14 " " relative error = 4.843014854248585000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.979999999999892 " " y[1] (closed_form) = -1.9702923436602782 " " y[1] (numeric) = -1.970292343660182 " " absolute error = 9.61453139325385600000000000000E-14 " " relative error = 4.879748644504509000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.989999999999891 " " y[1] (closed_form) = -1.9598996521999865 " " y[1] (numeric) = -1.9598996521998888 " " absolute error = 9.76996261670137800000000000000E-14 " " relative error = 4.984930022174655000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9999999999998899 " " y[1] (closed_form) = -1.949473957615077 " " y[1] (numeric) = -1.9494739576149775 " " absolute error = 9.94759830064140300000000000000E-14 " " relative error = 5.102708995821094000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0099999999998888 " " y[1] (closed_form) = -1.9390153177817573 " " y[1] (numeric) = -1.9390153177816574 " " absolute error = 9.99200722162640900000000000000E-14 " " relative error = 5.153134753498138000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0199999999998877 " " y[1] (closed_form) = -1.9285237907827435 " " y[1] (numeric) = -1.9285237907826422 " " absolute error = 1.01252339845814280000000000000E-13 " " relative error = 5.2502510121857660000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0299999999998866 " " y[1] (closed_form) = -1.9179994349067342 " " y[1] (numeric) = -1.9179994349066318 " " absolute error = 1.02362562870439430000000000000E-13 " " relative error = 5.336944370654467000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0399999999998855 " " y[1] (closed_form) = -1.9074423086478889 " " y[1] (numeric) = -1.907442308647785 " " absolute error = 1.03916875104914650000000000000E-13 " " relative error = 5.447969494740696000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0499999999998844 " " y[1] (closed_form) = -1.8968524707052992 " " y[1] (numeric) = -1.896852470705194 " " absolute error = 1.05249142734464840000000000000E-13 " " relative error = 5.548620378227437000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0599999999998833 " " y[1] (closed_form) = -1.8862299799824627 " " y[1] (numeric) = -1.8862299799823565 " " absolute error = 1.06137321154164970000000000000E-13 " " relative error = 5.626955476296256000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.069999999999882 " " y[1] (closed_form) = -1.8755748955867517 " " y[1] (numeric) = -1.8755748955866445 " " absolute error = 1.07247544178790120000000000000E-13 " " relative error = 5.718115785786255000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.079999999999881 " " y[1] (closed_form) = -1.8648872768288811 " " y[1] (numeric) = -1.8648872768287728 " " absolute error = 1.08357767203415280000000000000E-13 " " relative error = 5.810419136306757000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.08999999999988 " " y[1] (closed_form) = -1.8541671832223754 " " y[1] (numeric) = -1.8541671832222657 " " absolute error = 1.09690034832965470000000000000E-13 " " relative error = 5.915865399059327000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.099999999999879 " " y[1] (closed_form) = -1.8434146744830324 " " y[1] (numeric) = -1.8434146744829212 " " absolute error = 1.11244347067440690000000000000E-13 " " relative error = 6.034689243137228000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1099999999998778 " " y[1] (closed_form) = -1.8326298105283847 " " y[1] (numeric) = -1.8326298105282728 " " absolute error = 1.11910480882215780000000000000E-13 " " relative error = 6.1065513743853000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999998766 " " y[1] (closed_form) = -1.8218126514771638 " " y[1] (numeric) = -1.821812651477051 " " absolute error = 1.1279865930191590000000000000E-13 " " relative error = 6.1915619704614730000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999998755 " " y[1] (closed_form) = -1.8109632576487562 " " y[1] (numeric) = -1.8109632576486416 " " absolute error = 1.14575016141316150000000000000E-13 " " relative error = 6.326744380781825000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999998744 " " y[1] (closed_form) = -1.80008168956266 " " y[1] (numeric) = -1.8000816895625444 " " absolute error = 1.15463194561016280000000000000E-13 " " relative error = 6.41433081790131000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1499999999998733 " " y[1] (closed_form) = -1.7891680079379433 " " y[1] (numeric) = -1.7891680079378263 " " absolute error = 1.1701750679549150000000000000E-13 " " relative error = 6.540330828425489000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1599999999998722 " " y[1] (closed_form) = -1.7782222736926943 " " y[1] (numeric) = -1.7782222736925761 " " absolute error = 1.18127729820116660000000000000E-13 " " relative error = 6.64302385408828000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.169999999999871 " " y[1] (closed_form) = -1.7672445479434757 " " y[1] (numeric) = -1.7672445479433565 " " absolute error = 1.1923795284474181000000000000E-13 " " relative error = 6.747111087907884000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.17999999999987 " " y[1] (closed_form) = -1.756234892004773 " " y[1] (numeric) = -1.7562348920046529 " " absolute error = 1.20126131264441940000000000000E-13 " " relative error = 6.839980905248719000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.189999999999869 " " y[1] (closed_form) = -1.745193367388444 " " y[1] (numeric) = -1.7451933673883229 " " absolute error = 1.2123635428906710000000000000E-13 " " relative error = 6.946872281006232000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.199999999999868 " " y[1] (closed_form) = -1.7341200358031639 " " y[1] (numeric) = -1.7341200358030415 " " absolute error = 1.22346577313692250000000000000E-13 " " relative error = 7.055254237751022000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2099999999998667 " " y[1] (closed_form) = -1.7230149591538706 " " y[1] (numeric) = -1.7230149591537467 " " absolute error = 1.23900889548167470000000000000E-13 " " relative error = 7.190935220261354000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999998656 " " y[1] (closed_form) = -1.7118781995412071 " " y[1] (numeric) = -1.7118781995410817 " " absolute error = 1.2545520178264270000000000000E-13 " " relative error = 7.32851214626515900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999998645 " " y[1] (closed_form) = -1.7007098192609629 " " y[1] (numeric) = -1.700709819260836 " " absolute error = 1.26787469412192880000000000000E-13 " " relative error = 7.454973680771002000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2399999999998634 " " y[1] (closed_form) = -1.6895098808035138 " " y[1] (numeric) = -1.6895098808033862 " " absolute error = 1.276756478318930000000000000E-13 " " relative error = 7.556963666360551000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2499999999998623 " " y[1] (closed_form) = -1.6782784468532599 " " y[1] (numeric) = -1.6782784468531304 " " absolute error = 1.29452004671293250000000000000E-13 " " relative error = 7.713380632040725000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2599999999998612 " " y[1] (closed_form) = -1.6670155802880584 " " y[1] (numeric) = -1.6670155802879276 " " absolute error = 1.30784272300843440000000000000E-13 " " relative error = 7.84541391498237000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.26999999999986 " " y[1] (closed_form) = -1.655721344178661 " " y[1] (numeric) = -1.6557213441785295 " " absolute error = 1.31450406115618530000000000000E-13 " " relative error = 7.939162382473602000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.279999999999859 " " y[1] (closed_form) = -1.6443958017881464 " " y[1] (numeric) = -1.6443958017880134 " " absolute error = 1.33004718350093750000000000000E-13 " " relative error = 8.08836401828939000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999858 " " y[1] (closed_form) = -1.6330390165713475 " " y[1] (numeric) = -1.6330390165712134 " " absolute error = 1.3411494137471890000000000000E-13 " " relative error = 8.2125987201641000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.299999999999857 " " y[1] (closed_form) = -1.6216510521742842 " " y[1] (numeric) = -1.6216510521741487 " " absolute error = 1.3544720900426910000000000000E-13 " " relative error = 8.352426301741279000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999998557 " " y[1] (closed_form) = -1.6102319724335876 " " y[1] (numeric) = -1.6102319724334506 " " absolute error = 1.37001521238744320000000000000E-13 " " relative error = 8.508185378513518000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999998546 " " y[1] (closed_form) = -1.5987818413759276 " " y[1] (numeric) = -1.5987818413757895 " " absolute error = 1.38111744263369470000000000000E-13 " " relative error = 8.63856097743198900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999998535 " " y[1] (closed_form) = -1.5873007232174352 " " y[1] (numeric) = -1.5873007232172962 " " absolute error = 1.3899992268306960000000000000E-13 " " relative error = 8.756999896107829000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3399999999998524 " " y[1] (closed_form) = -1.5757886823631262 " " y[1] (numeric) = -1.5757886823629859 " " absolute error = 1.40332190312619800000000000000E-13 " " relative error = 8.905520891428862000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3499999999998513 " " y[1] (closed_form) = -1.5642457834063195 " " y[1] (numeric) = -1.5642457834061776 " " absolute error = 1.418865025470950000000000000E-13 " " relative error = 9.070601567365029000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.35999999999985 " " y[1] (closed_form) = -1.5526720911280574 " " y[1] (numeric) = -1.5526720911279142 " " absolute error = 1.4321877017664520000000000000E-13 " " relative error = 9.224019095531818000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.369999999999849 " " y[1] (closed_form) = -1.5410676704965212 " " y[1] (numeric) = -1.5410676704963768 " " absolute error = 1.44328993201270350000000000000E-13 " " relative error = 9.365519500825592000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.379999999999848 " " y[1] (closed_form) = -1.5294325866664482 " " y[1] (numeric) = -1.5294325866663023 " " absolute error = 1.45883305435745570000000000000E-13 " " relative error = 9.538393957834577000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999847 " " y[1] (closed_form) = -1.517766904978543 " " y[1] (numeric) = -1.5177669049783962 " " absolute error = 1.4677148385544570000000000000E-13 " " relative error = 9.670225604077238000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.399999999999846 " " y[1] (closed_form) = -1.5060706909588926 " " y[1] (numeric) = -1.5060706909587445 " " absolute error = 1.48103751484995880000000000000E-13 " " relative error = 9.833784853133318000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999998447 " " y[1] (closed_form) = -1.4943440103183736 " " y[1] (numeric) = -1.4943440103182242 " " absolute error = 1.49436019114546070000000000000E-13 " " relative error = 1.000010828046939300000000000E-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) = -1.4825869289520623 " " y[1] (numeric) = -1.4825869289519116 " " absolute error = 1.50768286744096260000000000000E-13 " " relative error = 1.016927127845811100000000000E-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) = -1.4707995129386415 " " y[1] (numeric) = -1.4707995129384897 " " absolute error = 1.51878509768721410000000000000E-13 " " relative error = 1.032625510361162700000000000E-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) = -1.4589818285398057 " " y[1] (numeric) = -1.458981828539652 " " absolute error = 1.53654866608121670000000000000E-13 " " relative error = 1.053165047037660500000000000E-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) = -1.4471339421996643 " " y[1] (numeric) = -1.4471339421995089 " " absolute error = 1.55431223447521920000000000000E-13 " " relative error = 1.074062454863468000000000000E-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) = -1.4352559205441442 " " y[1] (numeric) = -1.435255920543988 " " absolute error = 1.560973572622970000000000000E-13 " " relative error = 1.087592498507975500000000000E-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) = -1.4233478303803913 " " y[1] (numeric) = -1.4233478303802336 " " absolute error = 1.57651669496772230000000000000E-13 " " relative error = 1.107611689369278500000000000E-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) = -1.4114097386961655 " " y[1] (numeric) = -1.411409738696007 " " absolute error = 1.58539847916472350000000000000E-13 " " relative error = 1.123273019661381700000000000E-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) = -1.3994417126592427 " " y[1] (numeric) = -1.3994417126590826 " " absolute error = 1.60094160150947570000000000000E-13 " " relative error = 1.14398591025798400000000000E-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) = -1.387443819616806 " " y[1] (numeric) = -1.3874438196166445 " " absolute error = 1.61426427780497760000000000000E-13 " " relative error = 1.163480823498004200000000000E-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) = -1.3754161270948424 " " y[1] (numeric) = -1.3754161270946796 " " absolute error = 1.62758695410047950000000000000E-13 " " relative error = 1.183341479017170600000000000E-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) = -1.3633587027975338 " " y[1] (numeric) = -1.36335870279737 " " absolute error = 1.6386891843467310000000000000E-13 " " relative error = 1.201950140476042700000000000E-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) = -1.351271614606648 " " y[1] (numeric) = -1.351271614606483 " " absolute error = 1.64979141459298260000000000000E-13 " " relative error = 1.220917687280238800000000000E-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) = -1.3391549305809276 " " y[1] (numeric) = -1.3391549305807608 " " absolute error = 1.6675549829869850000000000000E-13 " " relative error = 1.245229319555726800000000000E-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) = -1.3270087189554776 " " y[1] (numeric) = -1.3270087189553097 " " absolute error = 1.67865721323323670000000000000E-13 " " relative error = 1.264993356301796200000000000E-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) = -1.3148330481411512 " " y[1] (numeric) = -1.3148330481409825 " " absolute error = 1.6875389974302380000000000000E-13 " " relative error = 1.283462565696839600000000000E-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) = -1.302627986723935 " " y[1] (numeric) = -1.3026279867237645 " " absolute error = 1.70530256582424040000000000000E-13 " " relative error = 1.309124771772344800000000000E-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) = -1.2903936034643295 " " y[1] (numeric) = -1.2903936034641577 " " absolute error = 1.71862524211974230000000000000E-13 " " relative error = 1.33186125342355720000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.589999999999825 " " y[1] (closed_form) = -1.2781299672967326 " " y[1] (numeric) = -1.2781299672965594 " " absolute error = 1.73194791841524420000000000000E-13 " " relative error = 1.355064009709704700000000000E-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) = -1.2658371473288181 " " y[1] (numeric) = -1.265837147328643 " " absolute error = 1.7519319328584970000000000000E-13 " " relative error = 1.384010523435373000000000000E-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) = -1.2535152128409128 " " y[1] (numeric) = -1.2535152128407365 " " absolute error = 1.76303416310474860000000000000E-13 " " relative error = 1.406472091478717700000000000E-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) = -1.241164233285376 " " y[1] (numeric) = -1.2411642332851989 " " absolute error = 1.77191594730174980000000000000E-13 " " relative error = 1.427624080506628700000000000E-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) = -1.2287842782859717 " " y[1] (numeric) = -1.228784278285793 " " absolute error = 1.7874590696465020000000000000E-13 " " relative error = 1.454656526155937200000000000E-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) = -1.2163754176372414 " " y[1] (numeric) = -1.2163754176370618 " " absolute error = 1.79634085384350330000000000000E-13 " " relative error = 1.476798057406340000000000000E-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) = -1.20393772130388 " " y[1] (numeric) = -1.2039377213036986 " " absolute error = 1.81410442223750580000000000000E-13 " " relative error = 1.506809189658753800000000000E-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) = -1.1914712594201007 " " y[1] (numeric) = -1.1914712594199173 " " absolute error = 1.83408843668075860000000000000E-13 " " relative error = 1.53934761093056100000000000E-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) = -1.1789761022890077 " " y[1] (numeric) = -1.1789761022888232 " " absolute error = 1.84519066692701020000000000000E-13 " " relative error = 1.565078938703280000000000000E-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) = -1.166452320381963 " " y[1] (numeric) = -1.1664523203817774 " " absolute error = 1.85629289717326170000000000000E-13 " " relative error = 1.591400578264018000000000000E-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) = -1.1538999843379503 " " y[1] (numeric) = -1.1538999843377633 " " absolute error = 1.86961557346876360000000000000E-13 " " relative error = 1.62025790696362220000000000E-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) = -1.1413191649629413 " " y[1] (numeric) = -1.1413191649627532 " " absolute error = 1.88071780371501520000000000000E-13 " " relative error = 1.647845634639879500000000000E-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) = -1.1287099332292565 " " y[1] (numeric) = -1.1287099332290675 " " absolute error = 1.88959958791201640000000000000E-13 " " relative error = 1.674123290920141700000000000E-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) = -1.116072360274929 " " y[1] (numeric) = -1.1160723602747384 " " absolute error = 1.90514271025676860000000000000E-13 " " relative error = 1.707006443370269500000000000E-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) = -1.1034065174030614 " " y[1] (numeric) = -1.1034065174028693 " " absolute error = 1.92068583260152080000000000000E-13 " " relative error = 1.74068740967923520000000000E-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) = -1.090712476081186 " " y[1] (numeric) = -1.0907124760809928 " " absolute error = 1.93178806284777240000000000000E-13 " " relative error = 1.771124934582651300000000000E-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) = -1.0779903079406208 " " y[1] (numeric) = -1.0779903079404263 " " absolute error = 1.94511073914327430000000000000E-13 " " relative error = 1.80438611072412100000000000E-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) = -1.0652400847758257 " " y[1] (numeric) = -1.0652400847756296 " " absolute error = 1.96065386148802650000000000000E-13 " " relative error = 1.840574617411844800000000000E-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) = -1.0524618785437547 " " y[1] (numeric) = -1.0524618785435569 " " absolute error = 1.9784174298820290000000000000E-13 " " relative error = 1.879799611002992700000000000E-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) = -1.0396557613632103 " " y[1] (numeric) = -1.039655761363011 " " absolute error = 1.99174010617753080000000000000E-13 " " relative error = 1.915768834451448700000000000E-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) = -1.0268218055141922 " " y[1] (numeric) = -1.0268218055139917 " " absolute error = 2.00506278247303270000000000000E-13 " " relative error = 1.952688160404789700000000000E-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) = -1.0139600834372497 " " y[1] (numeric) = -1.0139600834370477 " " absolute error = 2.0206059048177850000000000000E-13 " " relative error = 1.9927864398449300000000000E-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) = -1.001070667732826 " " y[1] (numeric) = -1.001070667732623 " " absolute error = 2.02948768901478620000000000000E-13 " " relative error = 2.0273171060051800000000000E-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) = -0.9881536311606087 " " y[1] (numeric) = -0.9881536311604044 " " absolute error = 2.0428103653102880000000000000E-13 " " relative error = 2.067300367971082700000000000E-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) = -0.9752090466388716 " " y[1] (numeric) = -0.9752090466386659 " " absolute error = 2.0572432646304150000000000000E-13 " " relative error = 2.109540792018749200000000000E-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) = -0.9622369872438215 " " y[1] (numeric) = -0.962236987243614 " " absolute error = 2.07500683302441760000000000000E-13 " " relative error = 2.156440524041746700000000000E-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) = -0.9492375262089368 " " y[1] (numeric) = -0.9492375262087281 " " absolute error = 2.08610906327066910000000000000E-13 " " relative error = 2.197668134341641500000000000E-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) = -0.9362107369243129 " " y[1] (numeric) = -0.9362107369241025 " " absolute error = 2.10387263166467160000000000000E-13 " " relative error = 2.247221217069589300000000000E-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) = -0.9231566929359977 " " y[1] (numeric) = -0.9231566929357858 " " absolute error = 2.11830553098479870000000000000E-13 " " relative error = 2.294632695829526600000000000E-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) = -0.9100754679453313 " " y[1] (numeric) = -0.9100754679451185 " " absolute error = 2.1282975382064250000000000000E-13 " " relative error = 2.338594559648401500000000000E-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) = -0.8969671358082842 " " y[1] (numeric) = -0.8969671358080701 " " absolute error = 2.1416202145019270000000000000E-13 " " relative error = 2.387623948531902300000000000E-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) = -0.8838317705347898 " " y[1] (numeric) = -0.8838317705345741 " " absolute error = 2.15716333684667920000000000000E-13 " " relative error = 2.4406944949958300000000000E-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) = -0.8706694462880795 " " y[1] (numeric) = -0.8706694462878624 " " absolute error = 2.17159623616680620000000000000E-13 " " relative error = 2.494168418824114200000000000E-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) = -0.8574802373840162 " " y[1] (numeric) = -0.8574802373837977 " " absolute error = 2.1849189124623080000000000000E-13 " " relative error = 2.54806911833678600000000000E-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) = -0.8442642182904241 " " y[1] (numeric) = -0.8442642182902041 " " absolute error = 2.1993518117824350000000000000E-13 " " relative error = 2.605051551558076000000000000E-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) = -0.8310214636264193 " " y[1] (numeric) = -0.8310214636261977 " " absolute error = 2.21600515715181250000000000000E-13 " " relative error = 2.666603997785555000000000000E-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) = -0.8177520481617373 " " y[1] (numeric) = -0.8177520481615141 " " absolute error = 2.23154827949656460000000000000E-13 " " relative error = 2.72888130884290100000000000E-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) = -0.8044560468160613 " " y[1] (numeric) = -0.8044560468158366 " " absolute error = 2.24709140184131680000000000000E-13 " " relative error = 2.793305377882396300000000000E-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) = -0.791133534658347 " " y[1] (numeric) = -0.7911335346581209 " " absolute error = 2.26152430116144400000000000000E-13 " " relative error = 2.858587333348331400000000000E-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) = -0.7777845869061477 " " y[1] (numeric) = -0.77778458690592 " " absolute error = 2.2770674235061960000000000000E-13 " " relative error = 2.927632485703861600000000000E-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) = -0.7644092789249362 " " y[1] (numeric) = -0.764409278924707 " " absolute error = 2.2915003228263230000000000000E-13 " " relative error = 2.997740066746815700000000000E-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) = -0.7510076862274282 " " y[1] (numeric) = -0.7510076862271975 " " absolute error = 2.30704344517107530000000000000E-13 " " relative error = 3.071930537435846300000000000E-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) = -0.7375798844729007 " " y[1] (numeric) = -0.7375798844726684 " " absolute error = 2.32258656751582750000000000000E-13 " " relative error = 3.148928836604086300000000000E-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) = -0.7241259494665129 " " y[1] (numeric) = -0.7241259494662792 " " absolute error = 2.33701946683595450000000000000E-13 " " relative error = 3.22736599697568200000000000E-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) = -0.7106459571586228 " " y[1] (numeric) = -0.7106459571583877 " " absolute error = 2.35034214313145640000000000000E-13 " " relative error = 3.30733203989344300000000000E-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) = -0.6971399836441046 " " y[1] (numeric) = -0.6971399836438679 " " absolute error = 2.36699548850083370000000000000E-13 " " relative error = 3.39529440863228900000000000E-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) = -0.683608105161662 " " y[1] (numeric) = -0.6836081051614241 " " absolute error = 2.37920794177171050000000000000E-13 " " relative error = 3.48036824579349700000000000E-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) = -0.6700503980931445 " " y[1] (numeric) = -0.670050398092905 " " absolute error = 2.39475106411646270000000000000E-13 " " relative error = 3.57398648061629130000000000E-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) = -0.6564669389628581 " " y[1] (numeric) = -0.6564669389626173 " " absolute error = 2.40807374041196450000000000000E-13 " " relative error = 3.668233078449377000000000000E-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) = -0.6428578044368778 " " y[1] (numeric) = -0.6428578044366354 " " absolute error = 2.42361686275671670000000000000E-13 " " relative error = 3.770066795532995300000000000E-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) = -0.6292230713223563 " " y[1] (numeric) = -0.6292230713221124 " " absolute error = 2.4391599851014690000000000000E-13 " " relative error = 3.876463048272218400000000000E-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) = -0.6155628165668345 " " y[1] (numeric) = -0.6155628165665888 " " absolute error = 2.45692355349547140000000000000E-13 " " relative error = 3.99134497304177500000000000E-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) = -0.6018771172575468 " " y[1] (numeric) = -0.6018771172572995 " " absolute error = 2.47246667584022360000000000000E-13 " " relative error = 4.107926028332857000000000000E-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) = -0.5881660506207287 " " y[1] (numeric) = -0.5881660506204802 " " absolute error = 2.48467912911110030000000000000E-13 " " relative error = 4.22445179637427500000000000E-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) = -0.5744296940209235 " " y[1] (numeric) = -0.5744296940206732 " " absolute error = 2.5024426975051030000000000000E-13 " " relative error = 4.35639508812361630000000000E-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) = -0.5606681249602807 " " y[1] (numeric) = -0.5606681249600292 " " absolute error = 2.51576537380060470000000000000E-13 " " relative error = 4.487084715184813700000000000E-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) = -0.5468814210778647 " " y[1] (numeric) = -0.5468814210776117 " " absolute error = 2.5301982731207320000000000000E-13 " " relative error = 4.62659394816135700000000000E-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) = -0.533069660148952 " " y[1] (numeric) = -0.5330696601486975 " " absolute error = 2.5446311724408590000000000000E-13 " " relative error = 4.77354342719454370000000000E-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) = -0.519232920084332 " " y[1] (numeric) = -0.5192329200840761 " " absolute error = 2.5590640717609860000000000000E-13 " " relative error = 4.92854742597089500000000000E-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) = -0.5053712789296074 " " y[1] (numeric) = -0.5053712789293499 " " absolute error = 2.5757174171303630000000000000E-13 " " relative error = 5.09668341775538800000000000E-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) = -0.49148481486448947 " " y[1] (numeric) = -0.4914848148642304 " " absolute error = 2.5907054279628030000000000000E-13 " " relative error = 5.271181020469785000000000000E-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) = -0.4775736062020963 " " y[1] (numeric) = -0.4775736062018355 " " absolute error = 2.60846899635680530000000000000E-13 " " relative error = 5.46192034585129800000000000E-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) = -0.4636377313882467 " " y[1] (numeric) = -0.4636377313879845 " " absolute error = 2.622346784164620000000000000E-13 " " relative error = 5.656025397917165000000000000E-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) = -0.44967726900075533 " " y[1] (numeric) = -0.4496772690004917 " " absolute error = 2.6362245719724340000000000000E-13 " " relative error = 5.8624812809206200000000000E-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) = -0.43569229774872476 " " y[1] (numeric) = -0.4356922977484595 " " absolute error = 2.6523228058294990000000000000E-13 " " relative error = 6.08760544892433100000000000E-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) = -0.4216828964718369 " " y[1] (numeric) = -0.4216828964715701 " " absolute error = 2.6678659281742510000000000000E-13 " " relative error = 6.32671125743045500000000000E-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) = -0.40764914413964415 " " y[1] (numeric) = -0.4076491441393758 " " absolute error = 2.68340905051900340000000000000E-13 " " relative error = 6.58264365103088700000000000E-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) = -0.39359111985085815 " " y[1] (numeric) = -0.3935911198505882 " " absolute error = 2.6995072843760680000000000000E-13 " " relative error = 6.85865902004847300000000000E-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) = -0.37950890283263794 " " y[1] (numeric) = -0.37950890283236643 " " absolute error = 2.71505040672082030000000000000E-13 " " relative error = 7.15411519059448200000000000E-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) = -0.3654025724398773 " " y[1] (numeric) = -0.3654025724396043 " " absolute error = 2.730038417553260000000000000E-13 " " relative error = 7.4713169076073100000000000E-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) = -0.3512722081544901 " " y[1] (numeric) = -0.35127220815421556 " " absolute error = 2.7455815398980120000000000000E-13 " " relative error = 7.81610806708198500000000000E-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) = -0.33711788958469535 " " y[1] (numeric) = -0.3371178895844192 " " absolute error = 2.7616797737550770000000000000E-13 " " relative error = 8.19202972929518800000000000E-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) = -0.3229396964643003 " " y[1] (numeric) = -0.3229396964640224 " " absolute error = 2.77944334214907940000000000000E-13 " " relative error = 8.60669460143725600000000000E-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) = -0.3087377086519827 " " y[1] (numeric) = -0.3087377086517035 " " absolute error = 2.7916557954199560000000000000E-13 " " relative error = 9.04216011581139400000000000E-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) = -0.2945120061305737 " " y[1] (numeric) = -0.2945120061302928 " " absolute error = 2.8088642523016460000000000000E-13 " " relative error = 9.53735057937270900000000000E-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) = -0.28026266900633456 " " y[1] (numeric) = -0.280262669006053 " " absolute error = 2.8155255904493970000000000000E-13 " " relative error = 1.00460243257933140000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.349999999999741 " " y[1] (closed_form) = -0.26598977750824115 " " y[1] (numeric) = -0.2659897775079579 " " absolute error = 2.8327340473310870000000000000E-13 " " relative error = 1.06497853935131780000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.35999999999974 " " y[1] (closed_form) = -0.2516934119872556 " " y[1] (numeric) = -0.2516934119869707 " " absolute error = 2.84883228118815170000000000000E-13 " " relative error = 1.13186605032490920000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.369999999999739 " " y[1] (closed_form) = -0.23737365291560697 " " y[1] (numeric) = -0.2373736529153208 " " absolute error = 2.8615998459713410000000000000E-13 " " relative error = 1.20552547042308890000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.379999999999738 " " y[1] (closed_form) = -0.2230305808860673 " " y[1] (numeric) = -0.22303058088577937 " " absolute error = 2.87936341436534350000000000000E-13 " " relative error = 1.29101731382578160000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.389999999999737 " " y[1] (closed_form) = -0.20866427661122366 " " y[1] (numeric) = -0.2086642766109341 " " absolute error = 2.89573920397856450000000000000E-13 " " relative error = 1.38775033801008970000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3999999999997357 " " y[1] (closed_form) = -0.19427482092275405 " " y[1] (numeric) = -0.1942748209224629 " " absolute error = 2.9115598820794730000000000000E-13 " " relative error = 1.49868102734586670000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4099999999997346 " " y[1] (closed_form) = -0.17986229477069893 " " y[1] (numeric) = -0.17986229477040627 " " absolute error = 2.92654789291191260000000000000E-13 " " relative error = 1.62710472288974260000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4199999999997335 " " y[1] (closed_form) = -0.1654267792227333 " " y[1] (numeric) = -0.16542677922243879 " " absolute error = 2.9451441285743840000000000000E-13 " " relative error = 1.78033093699357740000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4299999999997324 " " y[1] (closed_form) = -0.15096835546343534 " " y[1] (numeric) = -0.1509683554631395 " " absolute error = 2.9584668048698860000000000000E-13 " " relative error = 1.95966021871810670000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4399999999997313 " " y[1] (closed_form) = -0.13648710479355897 " " y[1] (numeric) = -0.13648710479326115 " " absolute error = 2.97817326355698240000000000000E-13 " " relative error = 2.18201805076132520000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.44999999999973 " " y[1] (closed_form) = -0.12198310862929795 " " y[1] (numeric) = -0.12198310862899878 " " absolute error = 2.99177349560864060000000000000E-13 " " relative error = 2.45261293077923330000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.459999999999729 " " y[1] (closed_form) = -0.10745644850155767 " " y[1] (numeric) = -0.10745644850125675 " " absolute error = 3.00912073036840870000000000000E-13 " " relative error = 2.80031656762301130000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.469999999999728 " " y[1] (closed_form) = -9.2907206055217410E-2 " " y[1] (numeric) = -9.290720605491499E-2 " " absolute error = 3.02410874120084800000000000000E-13 " " relative error = 3.25497759496021670000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.479999999999727 " " y[1] (closed_form) = -7.83354630483983300E-2 " " y[1] (numeric) = -7.83354630480941800E-2 " " absolute error = 3.04159475383869450000000000000E-13 " " relative error = 3.88278135530965460000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4899999999997258 " " y[1] (closed_form) = -6.3741301351725400E-2 " " y[1] (numeric) = -6.37413013514199300E-2 " " absolute error = 3.054639874378040000000000000E-13 " " relative error = 4.7922458588074540000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4999999999997247 " " y[1] (closed_form) = -4.91248029475932500E-2 " " y[1] (numeric) = -4.91248029472860560E-2 " " absolute error = 3.0719177201987690000000000000E-13 " " relative error = 6.2532927073029010000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5099999999997236 " " y[1] (closed_form) = -3.4486049929425500E-2 " " y[1] (numeric) = -3.44860499291166240E-2 " " absolute error = 3.08877923238526360000000000000E-13 " " relative error = 8.9566048843121870000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5199999999997225 " " y[1] (closed_form) = -1.98251245009373200E-2 " " y[1] (numeric) = -1.98251245006271400E-2 " " absolute error = 3.10178965845508970000000000000E-13 " " relative error = 1.5645751219915108000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5299999999997214 " " y[1] (closed_form) = -5.142108975396686000E-3 " " y[1] (numeric) = -5.142108975084732000E-3 " " absolute error = 3.1195532268490920000000000000E-13 " " relative error = 6.066680503612694000000000E-9 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5399999999997203 " " y[1] (closed_form) = 9.562914225119012000E-3 " " y[1] (numeric) = 9.562914225432697000E-3 " " absolute error = 3.1368484199045810000000000000E-13 " " relative error = 3.280222269133175000000000E-9 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.549999999999719 " " y[1] (closed_form) = 2.42898625704628400E-2 " " y[1] (numeric) = 2.428986257077823000E-2 " " absolute error = 3.15393544614295250000000000000E-13 " " relative error = 1.2984575095860063000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.559999999999718 " " y[1] (closed_form) = 3.90386534231619300E-2 " " y[1] (numeric) = 3.903865342347874000E-2 " " absolute error = 3.16816017864596230000000000000E-13 " " relative error = 8.1154443118324080000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.569999999999717 " " y[1] (closed_form) = 5.38092040391600100E-2 " " y[1] (numeric) = 5.38092040394786200E-2 " " absolute error = 3.1861319138570820000000000000E-13 " " relative error = 5.9211652927226980000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.579999999999716 " " y[1] (closed_form) = 6.86014315685643500E-2 " " y[1] (numeric) = 6.86014315688844400E-2 " " absolute error = 3.20091175787240450000000000000E-13 " " relative error = 4.6659547544182406000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5899999999997148 " " y[1] (closed_form) = 8.34152530563889700E-2 " " y[1] (numeric) = 8.34152530567106600E-2 " " absolute error = 3.2168712138513910000000000000E-13 " " relative error = 3.8564544204844364000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5999999999997137 " " y[1] (closed_form) = 9.8250585443302900E-2 " " y[1] (numeric) = 9.82505854436262100E-2 " " absolute error = 3.2332470034646120000000000000E-13 " " relative error = 3.2908170357217975000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6099999999997125 " " y[1] (closed_form) = 0.1131073455663767 " " y[1] (numeric) = 0.11310734556670193 " " absolute error = 3.2523983506393960000000000000E-13 " " relative error = 2.8754970195377240000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6199999999997114 " " y[1] (closed_form) = 0.12798545015983254 " " y[1] (numeric) = 0.12798545016015922 " " absolute error = 3.2668312499595230000000000000E-13 " " relative error = 2.5525020585385250000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6299999999997103 " " y[1] (closed_form) = 0.14288481585579071 " " y[1] (numeric) = 0.14288481585611926 " " absolute error = 3.28542748562199450000000000000E-13 " " relative error = 2.29935382982743000000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6399999999997092 " " y[1] (closed_form) = 0.15780535918502347 " " y[1] (numeric) = 0.15780535918535335 " " absolute error = 3.29875016191749640000000000000E-13 " " relative error = 2.09039171987168120000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.649999999999708 " " y[1] (closed_form) = 0.17274699657770265 " " y[1] (numeric) = 0.17274699657803422 " " absolute error = 3.315681063043030000000000000E-13 " " relative error = 1.91938564995636080000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.659999999999707 " " y[1] (closed_form) = 0.18770964436415483 " " y[1] (numeric) = 0.18770964436448806 " " absolute error = 3.33233440841240740000000000000E-13 " " relative error = 1.77526009369433970000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.669999999999706 " " y[1] (closed_form) = 0.20269321877561297 " " y[1] (numeric) = 0.20269321877594773 " " absolute error = 3.34759997500100300000000000000E-13 " " relative error = 1.65155992648520180000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.679999999999705 " " y[1] (closed_form) = 0.2176976359449696 " " y[1] (numeric) = 0.21769763594530628 " " absolute error = 3.3667513221757870000000000000E-13 " " relative error = 1.54652635870921760000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6899999999997037 " " y[1] (closed_form) = 0.23272281190753397 " " y[1] (numeric) = 0.2327228119078722 " " absolute error = 3.38229444452053940000000000000E-13 " " relative error = 1.45335750148309540000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6999999999997026 " " y[1] (closed_form) = 0.24776866260178498 " " y[1] (numeric) = 0.2477686626021249 " " absolute error = 3.3992253456460730000000000000E-13 " " relative error = 1.3719351389926680000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7099999999997015 " " y[1] (closed_form) = 0.26283510387012976 " " y[1] (numeric) = 0.2628351038704713 " " absolute error = 3.4156011352592940000000000000E-13 " " relative error = 1.2995224324932590000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7199999999997004 " " y[1] (closed_form) = 0.27792205145965987 " " y[1] (numeric) = 0.2779220514600031 " " absolute error = 3.43225448062867140000000000000E-13 " " relative error = 1.2349701877207321000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7299999999996993 " " y[1] (closed_form) = 0.2930294210229103 " " y[1] (numeric) = 0.29302942102325524 " " absolute error = 3.44946293751036140000000000000E-13 " " relative error = 1.17717290143390340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7399999999996982 " " y[1] (closed_form) = 0.3081571281186184 " " y[1] (numeric) = 0.30815712811896506 " " absolute error = 3.46667139439205130000000000000E-13 " " relative error = 1.12496875070098370000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.749999999999697 " " y[1] (closed_form) = 0.3233050882124837 " " y[1] (numeric) = 0.32330508821283205 " " absolute error = 3.48332473976142860000000000000E-13 " " relative error = 1.07741104818990840000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.759999999999696 " " y[1] (closed_form) = 0.33847321667792896 " " y[1] (numeric) = 0.33847321667827884 " " absolute error = 3.4988678621061810000000000000E-13 " " relative error = 1.03372074648833910000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.769999999999695 " " y[1] (closed_form) = 0.35366142879686113 " " y[1] (numeric) = 0.35366142879721285 " " absolute error = 3.5171865420124960000000000000E-13 " " relative error = 9.94506682274567500000000000E-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) = 0.36886963976043496 " " y[1] (numeric) = 0.3688696397607885 " " absolute error = 3.5355052219188110000000000000E-13 " " relative error = 9.58470104564574600000000000E-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) = 0.3840977646698156 " " y[1] (numeric) = 0.38409776467017076 " " absolute error = 3.5516034557758760000000000000E-13 " " relative error = 9.24661318669470300000000000E-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) = 0.39934571853694245 " " y[1] (numeric) = 0.3993457185372993 " " absolute error = 3.5682568011452530000000000000E-13 " " relative error = 8.93525743613340600000000000E-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) = 0.4146134162852948 " " y[1] (numeric) = 0.414613416285653 " " absolute error = 3.58213458895306760000000000000E-13 " " relative error = 8.63969772383874500000000000E-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) = 0.4299007727506561 " " y[1] (numeric) = 0.42990077275101624 " " absolute error = 3.6015634918840080000000000000E-13 " " relative error = 8.37766228899739000000000000E-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) = 0.4452077026818828 " " y[1] (numeric) = 0.4452077026822446 " " absolute error = 3.61766172574107260000000000000E-13 " " relative error = 8.1257842214963290000000000E-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) = 0.4605341207416691 " " y[1] (numeric) = 0.4605341207420327 " " absolute error = 3.63598040564738770000000000000E-13 " " relative error = 7.89513793199906200000000000E-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) = 0.4758799415073167 " " y[1] (numeric) = 0.47587994150768215 " " absolute error = 3.6542990855537030000000000000E-13 " " relative error = 7.67903575422608500000000000E-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) = 0.49124507947150287 " " y[1] (numeric) = 0.49124507947187007 " " absolute error = 3.67206265394770500000000000000E-13 " " relative error = 7.47501157242781500000000000E-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) = 0.5066294490430503 " " y[1] (numeric) = 0.506629449043419 " " absolute error = 3.6870506647801450000000000000E-13 " " relative error = 7.27760826328680600000000000E-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) = 0.5220329645476969 " " y[1] (numeric) = 0.5220329645480671 " " absolute error = 3.7025937871248970000000000000E-13 " " relative error = 7.09264364240469300000000000E-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) = 0.537455540228867 " " y[1] (numeric) = 0.5374555402292394 " " absolute error = 3.7236880245927750000000000000E-13 " " relative error = 6.9283647592638100000000000E-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) = 0.5528970902484446 " " y[1] (numeric) = 0.5528970902488186 " " absolute error = 3.74034136996215240000000000000E-13 " " relative error = 6.76498653353633700000000000E-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) = 0.5683575286875436 " " y[1] (numeric) = 0.5683575286879192 " " absolute error = 3.75588449230690460000000000000E-13 " " relative error = 6.60831308240084000000000000E-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) = 0.5838367695472826 " " y[1] (numeric) = 0.5838367695476598 " " absolute error = 3.7725378376762820000000000000E-13 " " relative error = 6.46163111754947300000000000E-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) = 0.5993347267495585 " " y[1] (numeric) = 0.5993347267499373 " " absolute error = 3.7880809600210340000000000000E-13 " " relative error = 6.32047633976654900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.939999999999676 " " y[1] (closed_form) = 0.6148513141378206 " " y[1] (numeric) = 0.6148513141382015 " " absolute error = 3.8091751974889120000000000000E-13 " " relative error = 6.1952786143595610000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.949999999999675 " " y[1] (closed_form) = 0.6303864454778477 " " y[1] (numeric) = 0.6303864454782303 " " absolute error = 3.82582854285828940000000000000E-13 " " relative error = 6.06902094786987600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.959999999999674 " " y[1] (closed_form) = 0.6459400344585224 " " y[1] (numeric) = 0.6459400344589066 " " absolute error = 3.84137166520304160000000000000E-13 " " relative error = 5.94694779744249800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.969999999999673 " " y[1] (closed_form) = 0.6615119946926086 " " y[1] (numeric) = 0.6615119946929943 " " absolute error = 3.8569147875477940000000000000E-13 " " relative error = 5.83045329259679700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.979999999999672 " " y[1] (closed_form) = 0.6771022397175286 " " y[1] (numeric) = 0.6771022397179163 " " absolute error = 3.87689880199104660000000000000E-13 " " relative error = 5.72572142666135500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9899999999996707 " " y[1] (closed_form) = 0.6927106829961427 " " y[1] (numeric) = 0.692710682996532 " " absolute error = 3.8935521473604240000000000000E-13 " " relative error = 5.62074794417759100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9999999999996696 " " y[1] (closed_form) = 0.7083372379175261 " " y[1] (numeric) = 0.708337237917917 " " absolute error = 3.9090952697051760000000000000E-13 " " relative error = 5.51869231271492800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.009999999999673 " " y[1] (closed_form) = 0.7239818177977563 " " y[1] (numeric) = 0.723981817798142 " " absolute error = 3.8569147875477940000000000000E-13 " " relative error = 5.3273641585087700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.019999999999676 " " y[1] (closed_form) = 0.7396443358806727 " " y[1] (numeric) = 0.739644335881053 " " absolute error = 3.80362408236578630000000000000E-13 " " relative error = 5.14250417105800400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.02999999999968 " " y[1] (closed_form) = 0.7553247053386776 " " y[1] (numeric) = 0.7553247053390529 " " absolute error = 3.75366404625765400000000000000E-13 " " relative error = 4.969603165005123700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.039999999999683 " " y[1] (closed_form) = 0.7710228392735115 " " y[1] (numeric) = 0.7710228392738812 " " absolute error = 3.69704267200177130000000000000E-13 " " relative error = 4.794984640773123000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.049999999999686 " " y[1] (closed_form) = 0.7867386507170334 " " y[1] (numeric) = 0.786738650717398 " " absolute error = 3.6459724128690140000000000000E-13 " " relative error = 4.63428663323719460000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.05999999999969 " " y[1] (closed_form) = 0.8024720526320062 " " y[1] (numeric) = 0.8024720526323654 " " absolute error = 3.59268170768700660000000000000E-13 " " relative error = 4.47701785489409640000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.069999999999693 " " y[1] (closed_form) = 0.8182229579128777 " " y[1] (numeric) = 0.8182229579132315 " " absolute error = 3.5382807794803740000000000000E-13 " " relative error = 4.32434796073898600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.079999999999696 " " y[1] (closed_form) = 0.8339912793865658 " " y[1] (numeric) = 0.8339912793869144 " " absolute error = 3.48610029732299150000000000000E-13 " " relative error = 4.18002008352792200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0899999999997 " " y[1] (closed_form) = 0.8497769298132427 " " y[1] (numeric) = 0.8497769298135861 " " absolute error = 3.4339198151656090000000000000E-13 " " relative error = 4.04096615793075200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.099999999999703 " " y[1] (closed_form) = 0.8655798218871203 " " y[1] (numeric) = 0.8655798218874583 " " absolute error = 3.37951888695897650000000000000E-13 " " relative error = 3.904341115058591600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.109999999999706 " " y[1] (closed_form) = 0.881399868237235 " " y[1] (numeric) = 0.8813998682375678 " " absolute error = 3.3273384048015940000000000000E-13 " " relative error = 3.7750611552236100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.11999999999971 " " y[1] (closed_form) = 0.8972369814282354 " " y[1] (numeric) = 0.8972369814285629 " " absolute error = 3.2751579226442120000000000000E-13 " " relative error = 3.650270765066734000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.129999999999713 " " y[1] (closed_form) = 0.9130910739611685 " " y[1] (numeric) = 0.9130910739614908 " " absolute error = 3.22297744048682940000000000000E-13 " " relative error = 3.529743672232956700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.139999999999716 " " y[1] (closed_form) = 0.9289620582742673 " " y[1] (numeric) = 0.9289620582745842 " " absolute error = 3.1696867353048220000000000000E-13 " " relative error = 3.41207340716707900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.14999999999972 " " y[1] (closed_form) = 0.9448498467437383 " " y[1] (numeric) = 0.9448498467440501 " " absolute error = 3.11861647617206470000000000000E-13 " " relative error = 3.30064770282795460000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.159999999999723 " " y[1] (closed_form) = 0.9607543516845515 " " y[1] (numeric) = 0.960754351684858 " " absolute error = 3.0653257709900570000000000000E-13 " " relative error = 3.190540605530880500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.169999999999726 " " y[1] (closed_form) = 0.9766754853512278 " " y[1] (numeric) = 0.976675485351529 " " absolute error = 3.01203506580804970000000000000E-13 " " relative error = 3.083967101646740700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.17999999999973 " " y[1] (closed_form) = 0.9926131599386304 " " y[1] (numeric) = 0.9926131599389263 " " absolute error = 2.9587443606260420000000000000E-13 " " relative error = 2.98076277853194100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.189999999999733 " " y[1] (closed_form) = 1.0085672875827534 " " y[1] (numeric) = 1.0085672875830445 " " absolute error = 2.91100477056716040000000000000E-13 " " relative error = 2.886277203719352000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.199999999999736 " " y[1] (closed_form) = 1.0245377803615145 " " y[1] (numeric) = 1.0245377803618 " " absolute error = 2.85549361933590260000000000000E-13 " " relative error = 2.78710426698791300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.20999999999974 " " y[1] (closed_form) = 1.0405245502955447 " " y[1] (numeric) = 1.040524550295825 " " absolute error = 2.8022029141538950000000000000E-13 " " relative error = 2.69306756227709700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.219999999999743 " " y[1] (closed_form) = 1.0565275093489803 " " y[1] (numeric) = 1.0565275093492548 " " absolute error = 2.7444713168733870000000000000E-13 " " relative error = 2.59763356144365600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.229999999999746 " " y[1] (closed_form) = 1.0725465694302563 " " y[1] (numeric) = 1.0725465694305252 " " absolute error = 2.6889601656421290000000000000E-13 " " relative error = 2.507080104755285400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.23999999999975 " " y[1] (closed_form) = 1.0885816423928976 " " y[1] (numeric) = 1.088581642393161 " " absolute error = 2.63344901441087130000000000000E-13 " " relative error = 2.419156186229705600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.249999999999753 " " y[1] (closed_form) = 1.1046326400363133 " " y[1] (numeric) = 1.1046326400365716 " " absolute error = 2.5823787552781140000000000000E-13 " " relative error = 2.337771546559788000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.259999999999756 " " y[1] (closed_form) = 1.1206994741065919 " " y[1] (numeric) = 1.1206994741068448 " " absolute error = 2.52908805009610660000000000000E-13 " " relative error = 2.25670494948011400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.26999999999976 " " y[1] (closed_form) = 1.1367820562972923 " " y[1] (numeric) = 1.1367820562975397 " " absolute error = 2.4735768988648488000000000000E-13 " " relative error = 2.17594646674996120000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.279999999999763 " " y[1] (closed_form) = 1.1528802982502413 " " y[1] (numeric) = 1.1528802982504829 " " absolute error = 2.41584530158434060000000000000E-13 " " relative error = 2.095486673899221400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.2899999999997664 " " y[1] (closed_form) = 1.1689941115563274 " " y[1] (numeric) = 1.1689941115565636 " " absolute error = 2.3625545964023330000000000000E-13 " " relative error = 2.021014967523636400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.29999999999977 " " y[1] (closed_form) = 1.1851234077562975 " " y[1] (numeric) = 1.1851234077565285 " " absolute error = 2.30926389122032560000000000000E-13 " " relative error = 1.948542975446140600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.309999999999773 " " y[1] (closed_form) = 1.201268098341552 " " y[1] (numeric) = 1.2012680983417774 " " absolute error = 2.25375273998906780000000000000E-13 " " relative error = 1.876144670037068500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.3199999999997765 " " y[1] (closed_form) = 1.2174280947549418 " " y[1] (numeric) = 1.2174280947551621 " " absolute error = 2.20268248085631060000000000000E-13 " " relative error = 1.809291645515781000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.32999999999978 " " y[1] (closed_form) = 1.233603308391566 " " y[1] (numeric) = 1.2336033083917812 " " absolute error = 2.15161222172355340000000000000E-13 " " relative error = 1.744168653802439500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.339999999999783 " " y[1] (closed_form) = 1.2497936505995684 " " y[1] (numeric) = 1.2497936505997782 " " absolute error = 2.09832151654154600000000000000E-13 " " relative error = 1.678934370913878500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.3499999999997865 " " y[1] (closed_form) = 1.2659990326809356 " " y[1] (numeric) = 1.26599903268114 " " absolute error = 2.0428103653102880000000000000E-13 " " relative error = 1.613595518303313500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.35999999999979 " " y[1] (closed_form) = 1.2822193658922951 " " y[1] (numeric) = 1.2822193658924939 " " absolute error = 1.98729921407903020000000000000E-13 " " relative error = 1.549890188014802500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.369999999999793 " " y[1] (closed_form) = 1.2984545614457148 " " y[1] (numeric) = 1.2984545614459082 " " absolute error = 1.93400850889702270000000000000E-13 " " relative error = 1.489469532721787700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.3799999999997965 " " y[1] (closed_form) = 1.3147045305095015 " " y[1] (numeric) = 1.3147045305096896 " " absolute error = 1.88071780371501520000000000000E-13 " " relative error = 1.430525080023996300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.3899999999998 " " y[1] (closed_form) = 1.3309691842090001 " " y[1] (numeric) = 1.3309691842091826 " " absolute error = 1.82520665248375740000000000000E-13 " " relative error = 1.37133652239175200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.399999999999803 " " y[1] (closed_form) = 1.347248433627394 " " y[1] (numeric) = 1.3472484336275712 " " absolute error = 1.77191594730174980000000000000E-13 " " relative error = 1.315210990842246900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4099999999998065 " " y[1] (closed_form) = 1.3635421898065052 " " y[1] (numeric) = 1.363542189806677 " " absolute error = 1.71862524211974230000000000000E-13 " " relative error = 1.26041222264169600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.41999999999981 " " y[1] (closed_form) = 1.379850363747595 " " y[1] (numeric) = 1.3798503637477613 " " absolute error = 1.66311409088848450000000000000E-13 " " relative error = 1.20528582995880900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.429999999999813 " " y[1] (closed_form) = 1.3961728664121644 " " y[1] (numeric) = 1.396172866412325 " " absolute error = 1.60538249360797640000000000000E-13 " " relative error = 1.149845074509599600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4399999999998165 " " y[1] (closed_form) = 1.4125096087227564 " " y[1] (numeric) = 1.4125096087229114 " " absolute error = 1.54987134237671850000000000000E-13 " " relative error = 1.097246583531682900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.44999999999982 " " y[1] (closed_form) = 1.428860501563757 " " y[1] (numeric) = 1.4288605015639064 " " absolute error = 1.49436019114546070000000000000E-13 " " relative error = 1.04584050683045700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.459999999999823 " " y[1] (closed_form) = 1.445225455782197 " " y[1] (numeric) = 1.4452254557823414 " " absolute error = 1.44328993201270350000000000000E-13 " " relative error = 9.986607461405071000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.469999999999827 " " y[1] (closed_form) = 1.4616043821885567 " " y[1] (numeric) = 1.461604382188695 " " absolute error = 1.3833378886829450000000000000E-13 " " relative error = 9.46451656508844000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.47999999999983 " " y[1] (closed_form) = 1.4779971915575638 " " y[1] (numeric) = 1.477997191557697 " " absolute error = 1.33226762955018780000000000000E-13 " " relative error = 9.014006502584752000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.489999999999833 " " y[1] (closed_form) = 1.4944037946290023 " " y[1] (numeric) = 1.4944037946291295 " " absolute error = 1.27231558622042940000000000000E-13 " " relative error = 8.513867475398721000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.499999999999837 " " y[1] (closed_form) = 1.5108241021085103 " " y[1] (numeric) = 1.5108241021086322 " " absolute error = 1.2190248810384219000000000000E-13 " " relative error = 8.068608909118854000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.50999999999984 " " y[1] (closed_form) = 1.527258024668388 " " y[1] (numeric) = 1.5272580246685046 " " absolute error = 1.16573417585641440000000000000E-13 " " relative error = 7.632856773560112000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.519999999999843 " " y[1] (closed_form) = 1.5437054729483997 " " y[1] (numeric) = 1.5437054729485105 " " absolute error = 1.10800257857590620000000000000E-13 " " relative error = 7.177551663787763000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.529999999999847 " " y[1] (closed_form) = 1.5601663575565774 " " y[1] (numeric) = 1.5601663575566826 " " absolute error = 1.05249142734464840000000000000E-13 " " relative error = 6.746020526894235000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.53999999999985 " " y[1] (closed_form) = 1.5766405890700268 " " y[1] (numeric) = 1.576640589070127 " " absolute error = 1.00142116821189120000000000000E-13 " " relative error = 6.351613520254318000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.549999999999853 " " y[1] (closed_form) = 1.5931280780357318 " " y[1] (numeric) = 1.5931280780358263 " " absolute error = 9.45910016980633400000000000000E-14 " " relative error = 5.937438615399370000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.559999999999857 " " y[1] (closed_form) = 1.6096287349713583 " " y[1] (numeric) = 1.6096287349714475 " " absolute error = 8.92619311798625900000000000000E-14 " " relative error = 5.545498116461677000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.56999999999986 " " y[1] (closed_form) = 1.6261424703660616 " " y[1] (numeric) = 1.6261424703661451 " " absolute error = 8.34887714518117700000000000000E-14 " " relative error = 5.134160934436304000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.579999999999863 " " y[1] (closed_form) = 1.6426691946812895 " " y[1] (numeric) = 1.6426691946813674 " " absolute error = 7.79376563286859900000000000000E-14 " " relative error = 4.74457404942128000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.589999999999867 " " y[1] (closed_form) = 1.659208818351591 " " y[1] (numeric) = 1.659208818351663 " " absolute error = 7.19424519957101400000000000000E-14 " " relative error = 4.3359492307414527000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.59999999999987 " " y[1] (closed_form) = 1.67576125178542 " " y[1] (numeric) = 1.6757612517854865 " " absolute error = 6.66133814775093900000000000000E-14 " " relative error = 3.97511169365784960000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.609999999999873 " " y[1] (closed_form) = 1.6923264053659424 " " y[1] (numeric) = 1.6923264053660036 " " absolute error = 6.12843109593086400000000000000E-14 " " relative error = 3.621305604225725000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.619999999999877 " " y[1] (closed_form) = 1.708904189451844 " " y[1] (numeric) = 1.7089041894518995 " " absolute error = 5.55111512312578300000000000000E-14 " " relative error = 3.248347775954826000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.62999999999988 " " y[1] (closed_form) = 1.7254945143781346 " " y[1] (numeric) = 1.7254945143781848 " " absolute error = 5.018208071305708000000000000000E-14 " " relative error = 2.9082723992978105000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.639999999999883 " " y[1] (closed_form) = 1.742097290456958 " " y[1] (numeric) = 1.7420972904570025 " " absolute error = 4.44089209850062600000000000000E-14 " " relative error = 2.5491642302800230000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.649999999999887 " " y[1] (closed_form) = 1.7587124279783959 " " y[1] (numeric) = 1.7587124279784347 " " absolute error = 3.88578058618804800000000000000E-14 " " relative error = 2.209446254186464000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.65999999999989 " " y[1] (closed_form) = 1.7753398372112783 " " y[1] (numeric) = 1.7753398372113118 " " absolute error = 3.35287353436797300000000000000E-14 " " relative error = 1.8885812530600904000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.669999999999893 " " y[1] (closed_form) = 1.7919794284039894 " " y[1] (numeric) = 1.7919794284040171 " " absolute error = 2.775557561562891400000000000000E-14 " " relative error = 1.5488780270401412000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.679999999999897 " " y[1] (closed_form) = 1.8086311117852756 " " y[1] (numeric) = 1.8086311117852976 " " absolute error = 2.1982415887578100000000000000E-14 " " relative error = 1.215417325530774000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.6899999999999 " " y[1] (closed_form) = 1.825294797565054 " " y[1] (numeric) = 1.8252947975650702 " " absolute error = 1.620925615952728500000000000000E-14 " " relative error = 8.8803497282468890000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.699999999999903 " " y[1] (closed_form) = 1.8419703959352196 " " y[1] (numeric) = 1.8419703959352307 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 6.027366276217839000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.709999999999907 " " y[1] (closed_form) = 1.8586578170704549 " " y[1] (numeric) = 1.8586578170704606 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 3.1060906827649680000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.71999999999991 " " y[1] (closed_form) = 1.8753569711290372 " " y[1] (numeric) = 1.8753569711290372 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.729999999999913 " " y[1] (closed_form) = 1.8920677682536466 " " y[1] (numeric) = 1.892067768253641 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 2.93388810711013140000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.739999999999917 " " y[1] (closed_form) = 1.9087901185721772 " " y[1] (numeric) = 1.9087901185721656 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 6.0490251619379520000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.74999999999992 " " y[1] (closed_form) = 1.925523932198543 " " y[1] (numeric) = 1.9255239321985258 " " absolute error = 1.70974345792274100000000000000E-14 " " relative error = 8.8793674767291730000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.759999999999923 " " y[1] (closed_form) = 1.9422691192334889 " " y[1] (numeric) = 1.9422691192334662 " " absolute error = 2.264854970235319300000000000000E-14 " " relative error = 1.1660871028671548000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.769999999999927 " " y[1] (closed_form) = 1.959025589765399 " " y[1] (numeric) = 1.959025589765371 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 1.4281395999479707000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.77999999999993 " " y[1] (closed_form) = 1.9757932538711063 " " y[1] (numeric) = 1.9757932538710723 " " absolute error = 3.39728245535297900000000000000E-14 " " relative error = 1.7194524015591190000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.789999999999933 " " y[1] (closed_form) = 1.9925720216167007 " " y[1] (numeric) = 1.9925720216166614 " " absolute error = 3.93018950717305400000000000000E-14 " " relative error = 1.9724203012668223000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.799999999999937 " " y[1] (closed_form) = 2.0093618030583404 " " y[1] (numeric) = 2.009361803058296 " " absolute error = 4.44089209850062600000000000000E-14 " " relative error = 2.2101007851056914000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.80999999999994 " " y[1] (closed_form) = 2.02616250824306 " " y[1] (numeric) = 2.02616250824301 " " absolute error = 4.97379915032070130000000000000E-14 " " relative error = 2.4547878712026985000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.819999999999943 " " y[1] (closed_form) = 2.04297404720958 " " y[1] (numeric) = 2.042974047209525 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 2.695436199819658000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.829999999999947 " " y[1] (closed_form) = 2.059796329989117 " " y[1] (numeric) = 2.0597963299890565 " " absolute error = 6.03961325396085200000000000000E-14 " " relative error = 2.9321409918196920000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.83999999999995 " " y[1] (closed_form) = 2.076629266606194 " " y[1] (numeric) = 2.0766292666061275 " " absolute error = 6.66133814775093900000000000000E-14 " " relative error = 3.2077647439870044000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.8499999999999535 " " y[1] (closed_form) = 2.0934727670794486 " " y[1] (numeric) = 2.0934727670793762 " " absolute error = 7.23865412055602100000000000000E-14 " " relative error = 3.4577254762451415000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.859999999999957 " " y[1] (closed_form) = 2.110326741422444 " " y[1] (numeric) = 2.110326741422366 " " absolute error = 7.81597009336110200000000000000E-14 " " relative error = 3.703677700682894000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.86999999999996 " " y[1] (closed_form) = 2.1271910996444787 " " y[1] (numeric) = 2.127191099644395 " " absolute error = 8.39328606616618300000000000000E-14 " " relative error = 3.945713230733698400000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.8799999999999635 " " y[1] (closed_form) = 2.144065751751396 " " y[1] (numeric) = 2.144065751751306 " " absolute error = 9.01501095995627100000000000000E-14 " " relative error = 4.204633627766449000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.889999999999967 " " y[1] (closed_form) = 2.160950607746395 " " y[1] (numeric) = 2.1609506077462997 " " absolute error = 9.54791801177634600000000000000E-14 " " relative error = 4.4183878972290100000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.89999999999997 " " y[1] (closed_form) = 2.177845577630839 " " y[1] (numeric) = 2.177845577630737 " " absolute error = 1.0214051826551440000000000000E-13 " " relative error = 4.689979827524207000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.9099999999999735 " " y[1] (closed_form) = 2.1947505714050664 " " y[1] (numeric) = 2.194750571404959 " " absolute error = 1.07469588783715150000000000000E-13 " " relative error = 4.896665260458903000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.919999999999977 " " y[1] (closed_form) = 2.2116654990692006 " " y[1] (numeric) = 2.211665499069088 " " absolute error = 1.1279865930191590000000000000E-13 " " relative error = 5.100168147009041000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.92999999999998 " " y[1] (closed_form) = 2.2285902706239598 " " y[1] (numeric) = 2.228590270623842 " " absolute error = 1.1768364061026660000000000000E-13 " " relative error = 5.280631534719820000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.9399999999999835 " " y[1] (closed_form) = 2.245524796071469 " " y[1] (numeric) = 2.2455247960713445 " " absolute error = 1.24344978758017530000000000000E-13 " " relative error = 5.537457389718353000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.949999999999987 " " y[1] (closed_form) = 2.2624689854160644 " " y[1] (numeric) = 2.2624689854159343 " " absolute error = 1.30118138486068350000000000000E-13 " " relative error = 5.751156781587431000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.95999999999999 " " y[1] (closed_form) = 2.2794227486651115 " " y[1] (numeric) = 2.279422748664975 " " absolute error = 1.36335387423969220000000000000E-13 " " relative error = 5.981136562044523000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.9699999999999935 " " y[1] (closed_form) = 2.2963859958298074 " " y[1] (numeric) = 2.2963859958296657 " " absolute error = 1.41664457942169970000000000000E-13 " " relative error = 6.16901767383314000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.979999999999997 " " y[1] (closed_form) = 2.3133586369259955 " " y[1] (numeric) = 2.313358636925848 " " absolute error = 1.4743761767022080000000000000E-13 " " relative error = 6.373314336861177000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.99 " " y[1] (closed_form) = 2.3303405819749727 " " y[1] (numeric) = 2.33034058197482 " " absolute error = 1.52766688188421540000000000000E-13 " " relative error = 6.555551981116476000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " "Finished!" "diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) + ( 0.1 * x + 0.2 ) ; " Iterations = 4000 "Total Elapsed Time "= 1 Minutes 19 Seconds "Elapsed Time(since restart) "= 1 Minutes 19 Seconds "Time to Timeout "= 1 Minutes 40 Seconds Percent Done = 100.02500000000009 "%" (%o257) temp/diffeq.add_full_lin.max