(%i1) batch("temp/diffeq.mult_lin_sin.max") read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.mult_lin_sin.max (%i2) load("stringproc") (%i3) keepfloat:true (%i4) alias(convfloat,float) (%i5) alias(int_trunc,truncate) (%i6) alias(elapsed_time_seconds,elapsed_real_time) (%i7) alias(ln,log) (%i8) alias(arcsin,asin) (%i9) alias(arccos,acos) (%i10) alias(arctan,atan) (%i11) alias(float_abs,abs) (%i12) mode_declare(display_poles(),fixnum) (%i13) mode_declare(est_size_answer(),convfloat) (%i14) mode_declare(test_suggested_h(),convfloat) (%i15) mode_declare(reached_interval(),boolean) (%i16) mode_declare(display_alot([iter],fixnum),fixnum) (%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum) (%i18) mode_declare(check_for_pole(),fixnum) (%i19) mode_declare(atomall(),fixnum) (%i20) mode_declare(log10([x],convfloat),convfloat) (%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum) (%i22) mode_declare(omniout_timestr(secs_in,number),fixnum) (%i23) mode_declare(zero_ats_ar(ar,array([30],convfloat)),fixnum) (%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a], completearray([30],convfloat),[arr_b], completearray([30],convfloat),[jjj_ats],fixnum), convfloat) (%i25) mode_declare(att([mmm_att],fixnum,[arr_a], completearray([30],convfloat),[arr_b], completearray([30],convfloat),[jjj_att],fixnum), convfloat) (%i26) mode_declare(logitem_ditto([file],fixnum),fixnum) (%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum) (%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum) (%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum) (%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum) (%i31) mode_declare(logstart([file],fixnum),fixnum) (%i32) mode_declare(logend([file],fixnum),fixnum) (%i33) mode_declare(chk_data(),fixnum) (%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat, [t2],convfloat,[clock_sec2],convfloat), convfloat) (%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2], convfloat),convfloat) (%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%i42) mode_declare(neg([nnn],convfloat),convfloat) (%i43) mode_declare(factorial_2([nnn],fixnum),convfloat) (%i44) mode_declare(factorial_1([nnn],fixnum),convfloat) (%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat) (%i46) mode_declare(convfloat([mmm],fixnum),convfloat) (%i47) mode_declare(elaped_time_seconds(),convfloat) (%i48) mode_declare(Si([x],convfloat),convfloat) (%i49) mode_declare(Ci([x],convfloat),convfloat) (%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end], convfloat,[estimated_h], convfloat,[estimated_answer], convfloat),convfloat) (%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat) (%i52) mode_declare(main_prog(),fixnum) (%i53) define_variable(always,1,fixnum) (%i54) define_variable(info,2,fixnum) (%i55) define_variable(debugl,3,fixnum) (%i56) define_variable(debugmassive,4,fixnum) (%i57) define_variable(glob_iolevel,5,fixnum) (%i58) define_variable(glob_yes_pole,4,fixnum) (%i59) define_variable(glob_no_pole,3,fixnum) (%i60) define_variable(glob_not_given,0,fixnum) (%i61) define_variable(glob_no_sing_tests,4,fixnum) (%i62) define_variable(glob_ratio_test,1,fixnum) (%i63) define_variable(glob_three_term_test,2,fixnum) (%i64) define_variable(glob_six_term_test,3,fixnum) (%i65) define_variable(ats_max_terms,30,fixnum) (%i66) define_variable(glob_log_10,0.0,convfloat) (%i67) define_variable(max_unchanged,10,fixnum) (%i68) define_variable(glob__small,1.0E-51,convfloat) (%i69) define_variable(glob_small_float,1.0E-51,convfloat) (%i70) define_variable(glob_smallish_float,1.0E-61,convfloat) (%i71) define_variable(glob_large_float,1.0E+100,convfloat) (%i72) define_variable(glob_larger_float,1.1E+100,convfloat) (%i73) define_variable(glob__m2,-2.0,convfloat) (%i74) define_variable(glob__m1,-1.0,convfloat) (%i75) define_variable(glob__0,0.0,convfloat) (%i76) define_variable(glob__1,1.0,convfloat) (%i77) define_variable(glob__2,2.0,convfloat) (%i78) define_variable(glob__3,3.0,convfloat) (%i79) define_variable(glob__4,4.0,convfloat) (%i80) define_variable(glob__5,5.0,convfloat) (%i81) define_variable(glob__8,8.0,convfloat) (%i82) define_variable(glob__10,10.0,convfloat) (%i83) define_variable(glob__100,100.0,convfloat) (%i84) define_variable(glob__pi,0.0,convfloat) (%i85) define_variable(glob__0_5,0.5,convfloat) (%i86) define_variable(glob__0_8,0.8,convfloat) (%i87) define_variable(glob__m0_8,-0.8,convfloat) (%i88) define_variable(glob__0_25,0.25,convfloat) (%i89) define_variable(glob__0_125,0.125,convfloat) (%i90) define_variable(glob_prec,1.0E-16,convfloat) (%i91) define_variable(glob_check_sign,1.0,convfloat) (%i92) define_variable(glob_desired_digits_correct,8.0,convfloat) (%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat) (%i94) define_variable(glob_ratio_of_radius,0.1,convfloat) (%i95) define_variable(glob_percent_done,0.0,convfloat) (%i96) define_variable(glob_total_exp_sec,0.1,convfloat) (%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat) (%i98) define_variable(glob_estimated_size_answer,100.0,convfloat) (%i99) define_variable(glob_almost_1,0.999,convfloat) (%i100) define_variable(glob_clock_sec,0.0,convfloat) (%i101) define_variable(glob_clock_start_sec,0.0,convfloat) (%i102) define_variable(glob_disp_incr,0.1,convfloat) (%i103) define_variable(glob_h,0.1,convfloat) (%i104) define_variable(glob_diff_rc_fm,0.1,convfloat) (%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat) (%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat) (%i107) define_variable(glob_diff_ord_fm,0.1,convfloat) (%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat) (%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat) (%i110) define_variable(glob_six_term_ord_save,0.1,convfloat) (%i111) define_variable(glob_guess_error_rc,0.1,convfloat) (%i112) define_variable(glob_guess_error_ord,0.1,convfloat) (%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat) (%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat) (%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat) (%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat) (%i117) define_variable(glob_last_good_h,0.1,convfloat) (%i118) define_variable(glob_max_h,0.1,convfloat) (%i119) define_variable(glob_min_h,1.0E-6,convfloat) (%i120) define_variable(glob_display_interval,0.1,convfloat) (%i121) define_variable(glob_abserr,1.0E-11,convfloat) (%i122) define_variable(glob_relerr,1.0E-11,convfloat) (%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat) (%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat) (%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat) (%i126) define_variable(glob_max_hours,0.0,convfloat) (%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat) (%i128) define_variable(glob_optimal_start,0.0,convfloat) (%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat) (%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat) (%i131) define_variable(glob_max_sec,10000.0,convfloat) (%i132) define_variable(glob_orig_start_sec,0.0,convfloat) (%i133) define_variable(glob_normmax,0.0,convfloat) (%i134) define_variable(glob_max_minutes,0.0,convfloat) (%i135) define_variable(glob_next_display,0.0,convfloat) (%i136) define_variable(glob_est_digits,1,fixnum) (%i137) define_variable(glob_subiter_method,3,fixnum) (%i138) define_variable(glob_html_log,true,boolean) (%i139) define_variable(glob_min_good_digits,99999,fixnum) (%i140) define_variable(glob_good_digits,0,fixnum) (%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum) (%i142) define_variable(glob_apfp_est_good_digits,0,fixnum) (%i143) define_variable(glob_max_opt_iter,10,fixnum) (%i144) define_variable(glob_dump,false,boolean) (%i145) define_variable(glob_djd_debug,true,boolean) (%i146) define_variable(glob_display_flag,true,boolean) (%i147) define_variable(glob_djd_debug2,true,boolean) (%i148) define_variable(glob_h_reason,0,fixnum) (%i149) define_variable(glob_sec_in_minute,60,fixnum) (%i150) define_variable(glob_min_in_hour,60,fixnum) (%i151) define_variable(glob_hours_in_day,24,fixnum) (%i152) define_variable(glob_days_in_year,365,fixnum) (%i153) define_variable(glob_sec_in_hour,3600,fixnum) (%i154) define_variable(glob_sec_in_day,86400,fixnum) (%i155) define_variable(glob_sec_in_year,31536000,fixnum) (%i156) define_variable(glob_not_yet_finished,true,boolean) (%i157) define_variable(glob_initial_pass,true,boolean) (%i158) define_variable(glob_not_yet_start_msg,true,boolean) (%i159) define_variable(glob_reached_optimal_h,false,boolean) (%i160) define_variable(glob_optimal_done,false,boolean) (%i161) define_variable(glob_type_given_pole,0,fixnum) (%i162) define_variable(glob_optimize,false,boolean) (%i163) define_variable(glob_look_poles,false,boolean) (%i164) define_variable(glob_dump_closed_form,false,boolean) (%i165) define_variable(glob_max_iter,1000,fixnum) (%i166) define_variable(glob_no_eqs,0,fixnum) (%i167) define_variable(glob_unchanged_h_cnt,0,fixnum) (%i168) define_variable(glob_warned,false,boolean) (%i169) define_variable(glob_warned2,false,boolean) (%i170) define_variable(glob_start,0,fixnum) (%i171) define_variable(glob_iter,0,fixnum) (%i172) completearray(array_y_init,[30],convfloat) (%i173) completearray(array_norms,[30],convfloat) (%i174) completearray(array_fact_1,[30],convfloat) (%i175) completearray(array_1st_rel_error,[2],convfloat) (%i176) completearray(array_last_rel_error,[2],convfloat) (%i177) completearray(array_est_rel_error,[2],convfloat) (%i178) completearray(array_max_est_error,[2],convfloat) (%i179) completearray(array_type_pole,[2],convfloat) (%i180) completearray(array_type_real_pole,[2],convfloat) (%i181) completearray(array_type_complex_pole,[2],convfloat) (%i182) completearray(array_est_digits,[2],convfloat) (%i183) completearray(array_y,[30],convfloat) (%i184) completearray(array_x,[30],convfloat) (%i185) completearray(array_tmp0,[30],convfloat) (%i186) completearray(array_tmp1,[30],convfloat) (%i187) completearray(array_tmp2,[30],convfloat) (%i188) completearray(array_tmp3_g,[30],convfloat) (%i189) completearray(array_tmp3,[30],convfloat) (%i190) completearray(array_tmp4,[30],convfloat) (%i191) completearray(array_tmp5,[30],convfloat) (%i192) completearray(array_m1,[30],convfloat) (%i193) completearray(array_y_higher,[2,30],convfloat) (%i194) completearray(array_y_higher_work,[2,30],convfloat) (%i195) completearray(array_y_higher_work2,[2,30],convfloat) (%i196) completearray(array_y_set_initial,[2,30],convfloat) (%i197) completearray(array_given_rad_poles,[2,3],convfloat) (%i198) completearray(array_given_ord_poles,[2,3],convfloat) (%i199) completearray(array_rad_test_poles,[2,4],convfloat) (%i200) completearray(array_ord_test_poles,[2,4],convfloat) (%i201) completearray(array_fact_2,[30,30],convfloat) (%i202) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%i203) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%i204) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%i205) 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)) (%i206) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%i207) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%i208) 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) (%i209) 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) (%i210) 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) (%i211) 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) (%i212) 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) (%i213) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%i214) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%i215) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%i216) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), printf(file,"~d",glob_min_good_digits), printf(file,"")),0) (%i217) log_revs(file,revs):=printf(file,revs) (%i218) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%i219) 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) (%i220) logstart(file):=(printf(file,""),0) (%i221) logend(file):=(printf(file,"~%"),0) (%i222) 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) (%i223) 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) (%i224) 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) (%i225) 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) (%i226) 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) (%i227) c(in_val):=(ret:in_val,ret) (%i228) 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) (%i229) 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) (%i230) 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) (%i231) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%i232) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret) (%i233) 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) (%i234) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret) (%i235) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret) (%i236) 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) (%i237) log10(x):=log(x)/glob_log_10 (%i238) c(x):=x (%i239) 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 (%i240) 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) (%i241) exact_soln_y(x):=block( -c(0.3)*cos(c(x))-c(0.2)*cos(c(x))*c(x)+c(0.2)*sin(c(x))) (%o241) exact_soln_y(x) := block(- c(0.3) cos(c(x)) - c(0.2) cos(c(x)) c(x) + c(0.2) sin(c(x))) (%i242) 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) (%i243) my_check_sign(x0,xf):=block([ret], if xf > x0 then ret:glob__1 else ret:glob__m1,ret) (%i244) 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) (%i245) 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) (%i246) 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)) (%i247) 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)) (%i248) display_alot(iter):=( block(mode_declare( [[abserr,est_rel_err],convfloat, [closed_form_val_y],convfloat,[ind_var], convfloat,[numeric_val],convfloat,[relerr], convfloat,[term_no],fixnum]), if reached_interval() then (if iter >= 0 then (ind_var:array_x[1], omniout_float(always, "x[1] ", 33,ind_var,20, " "), closed_form_val_y :exact_soln_y(ind_var), omniout_float(always, "y[1] (closed_form) ", 33, closed_form_val_y, 20," "), term_no:1, numeric_val:array_y[term_no], abserr :abs( numeric_val -closed_form_val_y), omniout_float(always, "y[1] (numeric) ", 33,numeric_val, 20," "), if c(abs(closed_form_val_y)) > c(glob_prec) then ( relerr :abserr*glob__100 /abs(closed_form_val_y), if c(relerr) > c(glob_prec) then glob_good_digits :3 -floor(log10(c(relerr))) else glob_good_digits:16) else (relerr:glob__m1, glob_good_digits:-16), if glob_good_digits < glob_min_good_digits then glob_min_good_digits :glob_good_digits, if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits then glob_min_apfp_est_good_digits :glob_apfp_est_good_digits, if c(abs(numeric_val)) > c(glob_prec) then ( est_rel_err :c(array_max_est_error[1]) *glob__100 *c(sqrt(glob_iter))*c(25) *c(ats_max_terms) /c(abs(numeric_val)), if est_rel_err > glob_prec then glob_est_digits :3 -floor( log10(est_rel_err)) else glob_est_digits:16) else (relerr:glob__m1, glob_est_digits:-16), array_est_digits[1] :glob_est_digits, if glob_iter = 1 then array_1st_rel_error[1] :relerr else array_last_rel_error[ 1] :relerr, array_est_rel_error[1] :est_rel_err, omniout_float(always, "absolute error ", 4,abserr,20," "), omniout_float(always, "relative error ", 4,relerr,20,"%"), omniout_int(info, "Desired digits ", 32, glob_desired_digits_correct, 4," "), omniout_int(info, "Estimated correct digits ", 32,glob_est_digits, 4," "), omniout_int(info, "Correct digits ", 32, glob_good_digits,4, " "), omniout_float(always, "h ", 4,glob_h,20, " ")))),0) (%i249) 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) (%i250) 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) (%i251) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:array_const_0D2[1]*array_x[1], array_tmp2[1]:array_const_0D3[1]+array_tmp1[1], array_tmp3[1]:sin(array_x[1]), array_tmp3_g[1]:cos(array_x[1]), array_tmp4[1]:array_tmp2[1]*array_tmp3[1], array_tmp5[1]:array_tmp4[1]+array_const_0D0[1], if not array_y_set_initial[1,2] then (if 1 <= ats_max_terms then ( temporary :c(array_tmp5[1])*expt(glob_h,c(1)) *c(factorial_3(0,1)), if 2 <= ats_max_terms then (array_y[2]:temporary, array_y_higher[1,2]:temporary), temporary:c(temporary)*c(1)/c(glob_h), array_y_higher[2,1]:c(temporary),0)), kkk:2,array_tmp1[2]:array_const_0D2[1]*array_x[2], array_tmp2[2]:array_tmp1[2], array_tmp3[2]:array_tmp3_g[1]*array_x[2]/c(1), array_tmp3_g[2]:neg(array_tmp3[1])*array_x[2]/c(1), array_tmp4[2]:array_tmp3[2]*array_tmp2[1] +array_tmp3[1]*array_tmp2[2], array_tmp5[2]:array_tmp4[2], if not array_y_set_initial[1,3] then (if 2 <= ats_max_terms then ( temporary :c(array_tmp5[2])*expt(glob_h,c(1)) *c(factorial_3(1,2)), if 3 <= ats_max_terms then (array_y[3]:temporary, array_y_higher[1,3]:temporary), temporary:c(temporary)*c(2)/c(glob_h), array_y_higher[2,2]:c(temporary),0)), kkk:3,array_tmp3[3]:array_tmp3_g[2]*array_x[2]/c(2), array_tmp3_g[3]:neg(array_tmp3[2])*array_x[2]/c(2), array_tmp4[3]:array_tmp3[3]*array_tmp2[1] +array_tmp3[2]*array_tmp2[2], array_tmp5[3]:array_tmp4[3], if not array_y_set_initial[1,4] then (if 3 <= ats_max_terms then ( temporary :c(array_tmp5[3])*expt(glob_h,c(1)) *c(factorial_3(2,3)), if 4 <= ats_max_terms then (array_y[4]:temporary, array_y_higher[1,4]:temporary), temporary:c(temporary)*c(3)/c(glob_h), array_y_higher[2,3]:c(temporary),0)), kkk:4,array_tmp3[4]:array_tmp3_g[3]*array_x[2]/c(3), array_tmp3_g[4]:neg(array_tmp3[3])*array_x[2]/c(3), array_tmp4[4]:array_tmp3[4]*array_tmp2[1] +array_tmp3[3]*array_tmp2[2], array_tmp5[4]:array_tmp4[4], if not array_y_set_initial[1,5] then (if 4 <= ats_max_terms then ( temporary :c(array_tmp5[4])*expt(glob_h,c(1)) *c(factorial_3(3,4)), if 5 <= ats_max_terms then (array_y[5]:temporary, array_y_higher[1,5]:temporary), temporary:c(temporary)*c(4)/c(glob_h), array_y_higher[2,4]:c(temporary),0)), kkk:5,array_tmp3[5]:array_tmp3_g[4]*array_x[2]/c(4), array_tmp3_g[5]:neg(array_tmp3[4])*array_x[2]/c(4), array_tmp4[5]:array_tmp3[5]*array_tmp2[1] +array_tmp3[4]*array_tmp2[2], array_tmp5[5]:array_tmp4[5], if not array_y_set_initial[1,6] then (if 5 <= ats_max_terms then ( temporary :c(array_tmp5[5])*expt(glob_h,c(1)) *c(factorial_3(4,5)), if 6 <= ats_max_terms then (array_y[6]:temporary, array_y_higher[1,6]:temporary), temporary:c(temporary)*c(5)/c(glob_h), array_y_higher[2,5]:c(temporary),0)), kkk:6, while kkk <= ats_max_terms do (array_tmp3[kkk] :array_tmp3_g[kkk-1]*array_x[2]/c(kkk-1), array_tmp3_g[kkk] :neg(array_tmp3[kkk-1])*array_x[2]/c(kkk-1), array_tmp4[kkk] :array_tmp3[kkk]*array_tmp2[1] +array_tmp3[kkk-1]*array_tmp2[2], array_tmp5[kkk]:array_tmp4[kkk],order_d:1, if order_d+kkk <= ats_max_terms then (if not array_y_set_initial[1,order_d+kkk] then ( temporary :c(array_tmp5[kkk])*expt(glob_h,c(order_d)) *c( factorial_3( kkk-1, -1+order_d+kkk)), array_y[order_d+kkk]:c(temporary), array_y_higher[1,order_d+kkk]:c(temporary), term:-1+order_d+kkk,adj2:-1+order_d+kkk, adj3:2, while term >= 1 and term <= ats_max_terms and adj3 < 1+order_d do ( if adj3 <= 1+order_d then ( if adj2 > 0 then temporary :c(temporary)*c(adj2) /c(glob_h) else temporary:c(temporary), array_y_higher[adj3,term] :c(temporary)),term:term-1, adj2:adj2-1,adj3:1+adj3))), kkk:1+kkk)),0) (%i252) exact_soln_y(x):=block( -c(0.3)*cos(c(x))-c(0.2)*cos(c(x))*c(x)+c(0.2)*sin(c(x))) (%o252) exact_soln_y(x) := block(- c(0.3) cos(c(x)) - c(0.2) cos(c(x)) c(x) + c(0.2) sin(c(x))) (%i253) main_prog():=block( mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat, [niii,done_once,term,ord,order_diff,term_no, html_log_file,iiif,jjjf,rows,r_order, sub_iter,calc_term,iii],fixnum,[temp_sum], convfloat,[current_iter],fixnum, [x_start,x_end],convfloat,[it,opt_iter], fixnum,[tmp],convfloat,[subiter],fixnum, [est_needed_step_err,estimated_step_error, min_value,est_answer,last_min_pole_est], convfloat,[repeat_it],fixnum],[found_h], boolean),Digits:32,max_terms:30, glob_html_log:true,term:1, while term <= 30 do (array_y_init[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_norms[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_fact_1[term]:c(0.0),term:1+term), term:1, while term <= 2 do (array_1st_rel_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_last_rel_error[term]:c(0.0),term:1+term), term:1, while term <= 2 do (array_est_rel_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_max_est_error[term]:c(0.0),term:1+term),term:1, while term <= 2 do (array_type_pole[term]:0,term:1+term), term:1, while term <= 2 do (array_type_real_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_type_complex_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_est_digits[term]:0,term:1+term), term:1, while term <= 30 do (array_y[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_x[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp0[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp1[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp2[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp3_g[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp3[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp4[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp5[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_m1[term]:c(0.0),term:1+term), ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_higher[ord,term]:c(0.0),term:1+term), ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_higher_work[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_higher_work2[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 30 do (array_y_set_initial[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_rad_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 3 do (array_given_ord_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 4 do (array_rad_test_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= 4 do (array_ord_test_poles[ord,term]:c(0.0), term:1+term),ord:1+ord),ord:1, while ord <= 30 do (term:1, while term <= 30 do (array_fact_2[ord,term]:c(0.0),term:1+term), ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x), zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2),zero_ats_ar(array_tmp3_g), zero_ats_ar(array_tmp3),zero_ats_ar(array_tmp4), zero_ats_ar(array_tmp5),zero_ats_ar(array_m1), zero_ats_ar(array_const_1),array_const_1[1]:c(1), zero_ats_ar(array_const_0D0),array_const_0D0[1]:c(0.0), zero_ats_ar(array_const_0D2),array_const_0D2[1]:c(0.2), zero_ats_ar(array_const_0D3),array_const_0D3[1]:c(0.3), zero_ats_ar(array_m1),array_m1[1]:glob__m1,iiif:0, while iiif <= ats_max_terms do (jjjf:0, while jjjf <= ats_max_terms do (array_fact_1[iiif]:0, array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf), iiif:1+iiif),array_y_set_initial[1,1]:true, array_y_set_initial[1,2]:false, array_y_set_initial[1,3]:false, array_y_set_initial[1,4]:false, array_y_set_initial[1,5]:false, array_y_set_initial[1,6]:false, array_y_set_initial[1,7]:false, array_y_set_initial[1,8]:false, array_y_set_initial[1,9]:false, array_y_set_initial[1,10]:false, array_y_set_initial[1,11]:false, array_y_set_initial[1,12]:false, array_y_set_initial[1,13]:false, array_y_set_initial[1,14]:false, array_y_set_initial[1,15]:false, array_y_set_initial[1,16]:false, array_y_set_initial[1,17]:false, array_y_set_initial[1,18]:false, array_y_set_initial[1,19]:false, array_y_set_initial[1,20]:false, array_y_set_initial[1,21]:false, array_y_set_initial[1,22]:false, array_y_set_initial[1,23]:false, array_y_set_initial[1,24]:false, array_y_set_initial[1,25]:false, array_y_set_initial[1,26]:false, array_y_set_initial[1,27]:false, array_y_set_initial[1,28]:false, array_y_set_initial[1,29]:false, array_y_set_initial[1,30]:false,glob_log_10:log(10.0), glob_orig_start_sec:elapsed_time_seconds(), glob_display_flag:true,glob_no_eqs:1,glob_iter:-1, opt_iter:-1,glob_max_iter:50000,glob_max_hours:0.0, glob_max_minutes:15.0, omniout_str(always, "##############ECHO OF PROBLEM#################"), omniout_str(always, "##############temp/mult_lin_sinpostode.ode#################"), omniout_str(always, "diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) * sin ( x ) ; "), omniout_str(always,"!"), omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(always,"Digits:32,"), omniout_str(always,"max_terms:30,"),omniout_str(always,"!"), omniout_str(always,"/* END FIRST INPUT BLOCK */"), omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(always,"x_start:c(0.1),"), omniout_str(always,"x_end:c(5.0),"), omniout_str(always, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(always,"glob_look_poles:true,"), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""), omniout_str(always,"glob_type_given_pole:3,"), omniout_str(always,""), omniout_str(always,"/* END SECOND INPUT BLOCK */"), omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"), omniout_str(always,"glob_desired_digits_correct:8,"), omniout_str(always,"glob_max_minutes:(3.0),"), omniout_str(always,"glob_subiter_method:3,"), omniout_str(always,"glob_max_iter:100000,"), omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"), omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"), omniout_str(always,"glob_look_poles:false,"), omniout_str(always,"glob_h:c(0.001),"), omniout_str(always,"glob_display_interval:c(0.01),"), omniout_str(always,"/* END OVERRIDE BLOCK */"), omniout_str(always,"!"), omniout_str(always,"/* BEGIN USER DEF BLOCK */"), omniout_str(always,"exact_soln_y (x) := (block("), omniout_str(always,""), omniout_str(always, " (c(0.2) * sin(c(x)) - c(0.2) * cos(c(x)) * c(x) - c(0.3) * cos(c(x))) "), omniout_str(always,"));"), omniout_str(always,"/* END USER DEF BLOCK */"), omniout_str(always, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false, glob_small_float:glob__0,glob_smallish_float:glob__0, glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100), glob_almost_1:c(0.99),x_start:c(0.1),x_end:c(5.0), array_y_init[1+0]:exact_soln_y(x_start), glob_look_poles:true,glob_type_given_pole:3, glob_desired_digits_correct:8,glob_max_minutes:3.0, glob_subiter_method:3,glob_max_iter:100000, glob_upper_ratio_limit:c(1.000001), glob_lower_ratio_limit:c(0.999999),glob_look_poles:false, glob_h:c(0.001),glob_display_interval:c(0.01), glob_last_good_h:glob_h, glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes, glob_check_sign:c(my_check_sign(x_start,x_end)), glob__pi:3.141592654,glob_prec:1.0E-16, if glob_optimize then (omniout_str(always,"START of Optimize"), found_h:false,glob_min_pole_est:glob_larger_float, last_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float, glob_min_h:abs(glob_min_h)*glob_check_sign, glob_max_h:abs(glob_max_h)*glob_check_sign, glob_h:abs(glob_min_h)*glob_check_sign, glob_display_interval :c(abs(c(glob_display_interval)) *glob_check_sign), display_max:c(x_end)-c(x_start)/glob__10, if glob_display_interval > display_max then glob_display_interval:c(display_max), chk_data(),min_value:glob_larger_float, est_answer:est_size_answer(),opt_iter:1, est_needed_step_err :estimated_needed_step_error( x_start,x_end,glob_h,est_answer), omniout_float(always,"est_needed_step_err",32, est_needed_step_err,16,""), estimated_step_error:glob_small_float, while opt_iter <= 100 and not found_h do (omniout_int(always,"opt_iter",32,opt_iter, 4,""),array_x[1]:c(x_start), array_x[2]:c(glob_h), glob_next_display:c(x_start),order_diff:1, term_no:1, while term_no <= order_diff do ( array_y[term_no] :array_y_init[term_no] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no),rows:order_diff, r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < ats_max_terms then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h, c(term_no-1)) /c( factorial_1( term_no-1)), term_no:1+term_no), r_order:1+r_order),atomall(), if glob_check_sign*glob_min_h >= glob_check_sign*glob_h then ( omniout_str(always, "SETTING H FOR MIN H"), glob_h:glob_check_sign*abs(glob_min_h), glob_h_reason:1,found_h:true), if glob_check_sign*glob_display_interval <= glob_check_sign*glob_h then ( omniout_str(always, "SETTING H FOR DISPLAY INTERVAL"), glob_h_reason:2, glob_h:glob_display_interval, found_h:true), if glob_look_poles then check_for_pole(), if not found_h then (est_answer:est_size_answer(), est_needed_step_err :estimated_needed_step_error( x_start,x_end,glob_h, est_answer), omniout_float(always, "est_needed_step_err", 32, est_needed_step_err, 16,""), estimated_step_error :test_suggested_h(), omniout_float(always, "estimated_step_error", 32, estimated_step_error, 32,""), if estimated_step_error < est_needed_step_err then ( omniout_str(always, "Double H and LOOP"), glob_h:glob_h*glob__2) else ( omniout_str(always, "Found H for OPTIMAL"), found_h:true,glob_h_reason:3, glob_h:glob_h/glob__2)), opt_iter:1+opt_iter), if not found_h and opt_iter = 1 then (omniout_str(always, "Beginning glob_h too large."), found_h:false), if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then (omniout_str(always, "SETTING H FOR MAX H"), glob_h:glob_check_sign*abs(glob_max_h), glob_h_reason:1,found_h:true)) else (found_h:true,glob_h:glob_h*glob_check_sign), if glob_html_log then html_log_file:openw("entry.html"), if found_h then (omniout_str(always,"START of Soultion"), array_x[1]:c(x_start),array_x[2]:c(glob_h), glob_next_display:c(x_start), glob_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float,order_diff:1, term_no:1, while term_no <= order_diff do (array_y[term_no] :array_y_init[term_no] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no),rows:order_diff, r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < ats_max_terms then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no), r_order:1+r_order),current_iter:1, glob_clock_start_sec:elapsed_time_seconds(), glob_clock_sec:elapsed_time_seconds(),glob_iter:0, omniout_str(debugl," "), glob_reached_optimal_h:true, glob_optimal_clock_start_sec :elapsed_time_seconds(), while glob_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec-glob_orig_start_sec < glob_max_sec do (if reached_interval() then (omniout_str(info," "), omniout_str(info, "TOP MAIN SOLVE Loop")), glob_iter:1+glob_iter, glob_clock_sec:elapsed_time_seconds(), track_estimated_error(),atomall(), track_estimated_error(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display :glob_display_interval +glob_next_display, array_x[1]:glob_h+array_x[1], array_x[2]:glob_h,order_diff:2,ord:2, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[2,iii] :array_y_higher[2,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:2, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:1, calc_term:2,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:1, calc_term:2,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:1, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:1, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)), term_no:ats_max_terms, while term_no >= 1 do ( array_y[term_no] :array_y_higher_work2[1,term_no], ord:1, while ord <= order_diff do ( array_y_higher[ord,term_no] :array_y_higher_work2[ ord,term_no],ord:1+ord), term_no:term_no-1)), omniout_str(always,"Finished!"), if glob_iter >= glob_max_iter then omniout_str(always, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds()-glob_orig_start_sec >= glob_max_sec then omniout_str(always, "Maximum Time Reached before Solution Completed!"), glob_clock_sec:elapsed_time_seconds(), omniout_str(info, "diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) * sin ( x ) ; "), omniout_int(info, "Iterations ",32, glob_iter,4," "), prog_report(x_start,x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2015-04-24T22:08:14-05:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "mult_lin_sin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) * sin ( x ) ; "), logitem_float(html_log_file,x_start), logitem_float(html_log_file,x_end), logitem_float(html_log_file,array_x[1]), logitem_float(html_log_file,glob_h), logitem_h_reason(html_log_file), logitem_str(html_log_file,"16"), logitem_float(html_log_file, glob_desired_digits_correct), if array_est_digits[1] # -16 then ( logitem_integer(html_log_file, array_est_digits[ 1]),0) else ( logitem_str(html_log_file, "Unknown"),0), if glob_min_good_digits # -16 then ( logitem_integer(html_log_file, glob_min_good_digits), 0) else ( logitem_str(html_log_file, "Unknown"),0), if glob_good_digits # -16 then ( logitem_integer(html_log_file, glob_good_digits),0) else ( logitem_str(html_log_file, "Unknown"),0), logitem_str(html_log_file,"NA"), logitem_str(html_log_file,"NA"), logitem_integer(html_log_file, ats_max_terms), if glob_type_given_pole = 0 then ( logitem_str(html_log_file, "Not Given"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 4 then ( logitem_str(html_log_file, "No Solution"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 5 then ( logitem_str(html_log_file, "Some Pole"), logitem_str(html_log_file,"????"),0) elseif glob_type_given_pole = 3 then ( logitem_str(html_log_file, "No Pole"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 1 then ( logitem_str(html_log_file, "Real Sing"), logitem_float(html_log_file, glob_least_given_sing), 0) elseif glob_type_given_pole = 2 then ( logitem_str(html_log_file, "Complex Sing"), logitem_float(html_log_file, glob_least_given_sing), 0), if glob_least_ratio_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_ratio_sing), 0) else ( logitem_str(html_log_file,"NONE"),0), if glob_least_3_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_3_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), if glob_least_6_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_6_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, glob_clock_sec), if c(glob_percent_done) < glob__100 then ( logitem_time(html_log_file, glob_total_exp_sec),0) else ( logitem_str(html_log_file,"Done"), 0), log_revs(html_log_file, " 308.maple.seems.ok "), logitem_str(html_log_file, "mult_lin_sin diffeq.max"), logitem_str(html_log_file, "mult_lin_sin maxima results"), logitem_str(html_log_file,"OK"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i254) main():=(glob_iolevel:2,compile(all),main_prog()) (%i255) main() warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable secs in translation. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable sec_temp in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable years_int in translation. warning: encountered undefined variable days_int in translation. warning: encountered undefined variable hours_int in translation. warning: encountered undefined variable minutes_int in translation. warning: encountered undefined variable sec_int in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable iii in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_ats in translation. warning: encountered undefined variable ma_ats in translation. warning: encountered undefined variable ret_ats in translation. warning: encountered undefined variable lll_ats in translation. warning: encountered undefined variable ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_att in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable ma_att in translation. warning: encountered undefined variable lll_att in translation. warning: encountered undefined variable ret_att in translation. warning: encountered undefined variable al_att in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_h_reason in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable errflag in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable sub1 in translation. warning: encountered undefined variable sub2 in translation. warning: encountered undefined variable rrr in translation. warning: encountered undefined variable ms2 in translation. warning: encountered undefined variable sec_left in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ret in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__m2 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temp in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm0 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm1 in translation. warning: encountered undefined variable rm2 in translation. warning: encountered undefined variable rm3 in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable rm4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__8 in translation. warning: encountered undefined variable glob__5 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable nr1 in translation. warning: encountered undefined variable dr2 in translation. warning: encountered undefined variable nr2 in translation. warning: encountered undefined variable dr1 in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable ds1 in translation. warning: encountered undefined variable ds2 in translation. warning: encountered undefined variable rcs in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable ord_no in translation. warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any. warning: encountered undefined variable rad_c in translation. warning: encountered undefined variable glob_six_term_ord_save in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_2 in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob_log_10 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob__10 in translation. warning: encountered undefined variable ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_x in translation. warning: encountered undefined variable array_given_rad_poles in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable rad_given in translation. warning: encountered undefined variable array_given_ord_poles in translation. warning: variable glob_least_given_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable array_rad_test_poles in translation. warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable array_ord_test_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: variable glob_least_3_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob__small in translation. warning: variable glob_least_6_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_estimated_size_answer in translation. warning: encountered undefined variable array_y in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob__small in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable array_max_est_error in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_next_display in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__10 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable always in translation. warning: encountered undefined variable ind_var in translation. warning: encountered undefined variable closed_form_val_y in translation. warning: encountered undefined variable term_no in translation. warning: encountered undefined variable numeric_val in translation. warning: encountered undefined variable abserr in translation. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable relerr in translation. warning: variable glob_good_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_apfp_est_good_digits in translation. warning: encountered undefined variable glob_min_apfp_est_good_digits in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable est_rel_err in translation. warning: variable glob_est_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_est_digits in translation. warning: encountered undefined variable array_est_digits in translation. warning: encountered undefined variable array_1st_rel_error in translation. warning: encountered undefined variable array_last_rel_error in translation. warning: encountered undefined variable array_est_rel_error in translation. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable clock_sec1 in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_clock_start_sec in translation. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_optimal_clock_start_sec in translation. warning: encountered undefined variable opt_clock_sec in translation. warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_optimal_expect_sec in translation. warning: encountered undefined variable total_clock_sec in translation. warning: variable glob_total_exp_sec (declared type convfloat) assigned type any. warning: encountered undefined variable percent_done in translation. warning: variable glob_percent_done (declared type convfloat) assigned type any. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable expect_sec in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable left_sec in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable last_no in translation. warning: encountered undefined variable found_sing in translation. warning: encountered undefined variable array_y_higher in translation. warning: variable tmp_rad (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_rad in translation. warning: encountered undefined variable prev_tmp_rad in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable cnt in translation. warning: encountered undefined variable tmp_ratio in translation. warning: encountered undefined variable glob_upper_ratio_limit in translation. warning: encountered undefined variable glob_lower_ratio_limit in translation. warning: variable tmp_ord (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_ord in translation. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_ratio_of_radius in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable h_new in translation. warning: variable ratio (declared type convfloat) assigned type any. warning: encountered undefined variable term in translation. warning: encountered undefined variable ratio in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_const_0D2 in translation. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_const_0D3 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable array_tmp3_g in translation. warning: encountered undefined variable array_tmp4 in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp5 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temporary in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable array_y_set_initial in translation. warning: encountered undefined variable kkk in translation. warning: encountered undefined variable order_d in translation. warning: encountered undefined variable adj3 in translation. warning: encountered undefined variable adj2 in translation. modedeclare: [found_h] is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: variable term (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable array_y_init in translation. warning: variable term (declared type [found_h]) assigned type any. warning: encountered undefined variable array_norms in translation. warning: encountered undefined variable array_fact_1 in translation. warning: encountered undefined variable array_type_pole in translation. warning: encountered undefined variable array_type_real_pole in translation. warning: encountered undefined variable array_type_complex_pole in translation. warning: encountered undefined variable array_tmp0 in translation. warning: encountered undefined variable array_m1 in translation. warning: variable ord (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable ord in translation. warning: variable ord (declared type [found_h]) assigned type any. warning: encountered undefined variable array_y_higher_work in translation. warning: encountered undefined variable array_y_higher_work2 in translation. warning: encountered undefined variable array_const_1 in translation. warning: encountered undefined variable glob__m1 in translation. warning: variable iiif (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable iiif in translation. warning: encountered undefined variable ats_max_terms in translation. warning: variable jjjf (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable jjjf in translation. warning: variable jjjf (declared type [found_h]) assigned type any. warning: variable iiif (declared type [found_h]) assigned type any. warning: variable glob_orig_start_sec (declared type convfloat) assigned type any. warning: variable opt_iter (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob__0 in translation. warning: variable glob_large_float (declared type convfloat) assigned type any. warning: variable glob_larger_float (declared type convfloat) assigned type any. warning: variable glob_almost_1 (declared type convfloat) assigned type any. warning: variable x_start (declared type [found_h]) assigned type any. warning: variable x_end (declared type [found_h]) assigned type any. warning: encountered undefined variable x_start in translation. warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any. warning: variable glob_h (declared type convfloat) assigned type any. warning: variable glob_display_interval (declared type convfloat) assigned type any. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_max_minutes in translation. warning: encountered undefined variable glob_max_hours in translation. warning: encountered undefined variable x_end in translation. warning: variable glob_check_sign (declared type convfloat) assigned type any. warning: encountered undefined variable glob_larger_float in translation. warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_max_h in translation. warning: encountered undefined variable glob_display_interval in translation. warning: encountered undefined variable glob__10 in translation. warning: variable display_max (declared type [found_h]) assigned type any. warning: encountered undefined variable display_max in translation. warning: variable min_value (declared type [found_h]) assigned type convfloat. warning: variable est_answer (declared type [found_h]) assigned type any. warning: encountered undefined variable est_answer in translation. warning: variable est_needed_step_err (declared type [found_h]) assigned type any. warning: encountered undefined variable est_needed_step_err in translation. warning: encountered undefined variable glob_small_float in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable opt_iter in translation. warning: encountered undefined variable found_h in translation. warning: variable glob_next_display (declared type convfloat) assigned type any. warning: variable order_diff (declared type [found_h]) assigned type fixnum. warning: variable term_no (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable order_diff in translation. warning: variable term_no (declared type [found_h]) assigned type any. warning: variable r_order (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable r_order in translation. warning: encountered undefined variable rows in translation. warning: variable it (declared type [found_h]) assigned type any. warning: encountered undefined variable it in translation. warning: variable r_order (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_look_poles in translation. warning: variable estimated_step_error (declared type [found_h]) assigned type any. warning: encountered undefined variable estimated_step_error in translation. warning: encountered undefined variable glob__2 in translation. warning: variable opt_iter (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_optimize in translation. warning: variable html_log_file (declared type [found_h]) assigned type any. warning: encountered undefined variable glob_html_log in translation. warning: variable current_iter (declared type [found_h]) assigned type fixnum. warning: variable glob_clock_start_sec (declared type convfloat) assigned type any. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable debugl in translation. warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable info in translation. warning: encountered undefined variable current_iter in translation. warning: encountered undefined variable glob_next_display in translation. warning: variable calc_term (declared type [found_h]) assigned type fixnum. warning: variable iii (declared type [found_h]) assigned type fixnum. warning: encountered undefined variable calc_term in translation. warning: variable iii (declared type [found_h]) assigned type any. warning: variable temp_sum (declared type [found_h]) assigned type convfloat. warning: encountered undefined variable temp_sum in translation. warning: variable temp_sum (declared type [found_h]) assigned type any. warning: encountered undefined variable html_log_file in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob_percent_done in translation. warning: encountered undefined variable glob__100 in translation. WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB__PI is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $LAST_MIN_POLE_EST is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. "##############ECHO OF PROBLEM#################" "##############temp/mult_lin_sinpostode.ode#################" "diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) * sin ( x ) ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:c(0.1)," "x_end:c(5.0)," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "" "" "" "" "" "" "" "glob_type_given_pole:3," "" "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:8," "glob_max_minutes:(3.0)," "glob_subiter_method:3," "glob_max_iter:100000," "glob_upper_ratio_limit:c(1.000001)," "glob_lower_ratio_limit:c(0.999999)," "glob_look_poles:false," "glob_h:c(0.001)," "glob_display_interval:c(0.01)," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" "" " (c(0.2) * sin(c(x)) - c(0.2) * cos(c(x)) * c(x) - c(0.3) * cos(c(x))) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (closed_form) = -0.29843464955960264 " " y[1] (numeric) = -0.29843464955960264 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 15 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000001 " " y[1] (closed_form) = -0.2980982033746214 " " y[1] (numeric) = -0.29809820337462145 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.862176645241189500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12000000000000002 " " y[1] (closed_form) = -0.2977275565588688 " " y[1] (numeric) = -0.2977275565588688 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.13000000000000003 " " y[1] (closed_form) = -0.2973223488270819 " " y[1] (numeric) = -0.2973223488270819 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.14000000000000004 " " y[1] (closed_form) = -0.2968822238288977 " " y[1] (numeric) = -0.29688222382889773 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.869803806887764500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000005 " " y[1] (closed_form) = -0.2964068292241741 " " y[1] (numeric) = -0.29640682922417416 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.872802707567660000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000006 " " y[1] (closed_form) = -0.2958958167578589 " " y[1] (numeric) = -0.29589581675785903 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.75207408063388700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000007 " " y[1] (closed_form) = -0.295348842334394 " " y[1] (numeric) = -0.2953488423343942 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.638534161079402000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000008 " " y[1] (closed_form) = -0.29476556609164395 " " y[1] (numeric) = -0.29476556609164406 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.76646105359532800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000009 " " y[1] (closed_form) = -0.29414565247433727 " " y[1] (numeric) = -0.2941456524743373 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.887199445727007500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2000000000000001 " " y[1] (closed_form) = -0.29348877030700987 " " y[1] (numeric) = -0.29348877030701 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.78284669448778300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2100000000000001 " " y[1] (closed_form) = -0.2927945928664388 " " y[1] (numeric) = -0.2927945928664389 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.791815326082869600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2200000000000001 " " y[1] (closed_form) = -0.29206279795355444 " " y[1] (numeric) = -0.29206279795355455 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.80131612928569800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.23000000000000012 " " y[1] (closed_form) = -0.291293067964822 " " y[1] (numeric) = -0.2912930679648221 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.81136095129882200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.24000000000000013 " " y[1] (closed_form) = -0.29048508996307937 " " y[1] (numeric) = -0.2904850899630795 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.82196216943962900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (closed_form) = -0.28963855574782105 " " y[1] (numeric) = -0.2896385557478212 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.74969907800426900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (closed_form) = -0.2887531619249176 " " y[1] (numeric) = -0.28875316192491773 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.844886120810132600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (closed_form) = -0.287828609975759 " " y[1] (numeric) = -0.28782860997575915 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.78585477335970800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (closed_form) = -0.2868646063258117 " " y[1] (numeric) = -0.28686460632581184 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.805298040310700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (closed_form) = -0.28586086241257846 " " y[1] (numeric) = -0.2858608624125787 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 7.76757626248807300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (closed_form) = -0.28481709475295025 " " y[1] (numeric) = -0.28481709475295036 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.898021028506598600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (closed_form) = -0.2837330250099395 " " y[1] (numeric) = -0.28373302500993963 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.912914348219647700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (closed_form) = -0.2826083800587849 " " y[1] (numeric) = -0.282608380058785 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.9284858587499100000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (closed_form) = -0.28144289205241596 " " y[1] (numeric) = -0.281442892052416 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.972377089591568800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (closed_form) = -0.2802362984862685 " " y[1] (numeric) = -0.2802362984862686 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.980869413816421000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (closed_form) = -0.2789883422624399 " " y[1] (numeric) = -0.27898834226243996 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.989730136431269400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y[1] (closed_form) = -0.2776987717531737 " " y[1] (numeric) = -0.27769877175317376 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.998969994746597800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y[1] (closed_form) = -0.27636734086366443 " " y[1] (numeric) = -0.2763673408636645 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.008600258546547600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y[1] (closed_form) = -0.27499380909417126 " " y[1] (numeric) = -0.27499380909417137 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.03726552347570200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (closed_form) = -0.273577941601432 " " y[1] (numeric) = -0.2735779416014321 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.058159872562420000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y[1] (closed_form) = -0.27211950925936623 " " y[1] (numeric) = -0.27211950925936623 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (closed_form) = -0.2706182887190585 " " y[1] (numeric) = -0.2706182887190586 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.051271238688769600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y[1] (closed_form) = -0.26907406246801224 " " y[1] (numeric) = -0.26907406246801235 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.12608712427323170000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y[1] (closed_form) = -0.26748661888866343 " " y[1] (numeric) = -0.2674866188886635 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.07528703536244400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y[1] (closed_form) = -0.2658557523161458 " " y[1] (numeric) = -0.26585575231614583 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.088017684313485700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y[1] (closed_form) = -0.2641812630952979 " " y[1] (numeric) = -0.2641812630952978 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.10125239696629600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000003 " " y[1] (closed_form) = -0.26246295763690186 " " y[1] (numeric) = -0.2624629576369018 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.11500897997398200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000003 " " y[1] (closed_form) = -0.26070064847314595 " " y[1] (numeric) = -0.26070064847314584 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.25861243969831400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000003 " " y[1] (closed_form) = -0.25889415431229984 " " y[1] (numeric) = -0.25889415431229984 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4900000000000003 " " y[1] (closed_form) = -0.2570433000925967 " " y[1] (numeric) = -0.2570433000925966 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.159603117889500300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000003 " " y[1] (closed_form) = -0.25514791703530837 " " y[1] (numeric) = -0.2551479170353083 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.175645871472114400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000003 " " y[1] (closed_form) = -0.25320784269701047 " " y[1] (numeric) = -0.25320784269701035 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.38463126892026800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000004 " " y[1] (closed_form) = -0.2512229210210231 " " y[1] (numeric) = -0.25122292102102306 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.20963720211709820000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000004 " " y[1] (closed_form) = -0.24919300238802347 " " y[1] (numeric) = -0.24919300238802342 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.22763683969023680000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000004 " " y[1] (closed_form) = -0.24711794366581752 " " y[1] (numeric) = -0.24711794366581746 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.24634239051157900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000004 " " y[1] (closed_form) = -0.24499760825826544 " " y[1] (numeric) = -0.24499760825826536 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 3.39867509070173100000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000004 " " y[1] (closed_form) = -0.24283186615335062 " " y[1] (numeric) = -0.2428318661533506 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.142995606602183200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5700000000000004 " " y[1] (closed_form) = -0.2406205939703853 " " y[1] (numeric) = -0.24062059397038524 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.306999177222957600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5800000000000004 " " y[1] (closed_form) = -0.23836367500634295 " " y[1] (numeric) = -0.23836367500634287 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 3.49326409926642500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5900000000000004 " " y[1] (closed_form) = -0.23606099928131147 " " y[1] (numeric) = -0.23606099928131138 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 3.52733942075957400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6000000000000004 " " y[1] (closed_form) = -0.23371246358305772 " " y[1] (numeric) = -0.23371246358305767 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.3751900253933200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000004 " " y[1] (closed_form) = -0.231317971510696 " " y[1] (numeric) = -0.23131797151069594 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.39977684694036100000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000004 " " y[1] (closed_form) = -0.22887743351745327 " " y[1] (numeric) = -0.22887743351745318 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 3.63804878301980600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6300000000000004 " " y[1] (closed_form) = -0.2263907669525227 " " y[1] (numeric) = -0.22639076695252258 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.90401194169718900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6400000000000005 " " y[1] (closed_form) = -0.2238578961019987 " " y[1] (numeric) = -0.2238578961019986 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 3.719624292767723700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000005 " " y[1] (closed_form) = -0.221278752228886 " " y[1] (numeric) = -0.22127875222888588 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.01730515669559500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000005 " " y[1] (closed_form) = -0.2186532736121748 " " y[1] (numeric) = -0.21865327361217476 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.269387608843166300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000005 " " y[1] (closed_form) = -0.21598140558497653 " " y[1] (numeric) = -0.21598140558497647 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.570181959919568500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6800000000000005 " " y[1] (closed_form) = -0.21326310057171072 " " y[1] (numeric) = -0.2132631005717107 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.301471072174343000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000005 " " y[1] (closed_form) = -0.210498318124339 " " y[1] (numeric) = -0.2104983181243389 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.274260785159148000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000005 " " y[1] (closed_form) = -0.20768702495763652 " " y[1] (numeric) = -0.20768702495763647 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.672827117754749000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000005 " " y[1] (closed_form) = -0.20482919498349714 " " y[1] (numeric) = -0.20482919498349708 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.71011909389822560000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000005 " " y[1] (closed_form) = -0.20192480934426257 " " y[1] (numeric) = -0.20192480934426252 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.749100093818417400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000005 " " y[1] (closed_form) = -0.19897385644507243 " " y[1] (numeric) = -0.1989738564450724 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.394935802698831500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000005 " " y[1] (closed_form) = -0.19597633198522618 " " y[1] (numeric) = -0.19597633198522615 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.416271818870519800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000006 " " y[1] (closed_form) = -0.19293223898855236 " " y[1] (numeric) = -0.19293223898855236 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000006 " " y[1] (closed_form) = -0.18984158783277869 " " y[1] (numeric) = -0.18984158783277869 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000006 " " y[1] (closed_form) = -0.18670439627789676 " " y[1] (numeric) = -0.18670439627789678 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.48660535953939900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000006 " " y[1] (closed_form) = -0.18352068949351624 " " y[1] (numeric) = -0.18352068949351627 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.512394907202520800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000006 " " y[1] (closed_form) = -0.18029050008520234 " " y[1] (numeric) = -0.18029050008520245 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 6.15796741425911800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000006 " " y[1] (closed_form) = -0.1770138681197913 " " y[1] (numeric) = -0.17701386811979145 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 7.83994381639233300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000006 " " y[1] (closed_form) = -0.17369084114967845 " " y[1] (numeric) = -0.17369084114967853 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.793961863258608400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000006 " " y[1] (closed_form) = -0.1703214742360733 " " y[1] (numeric) = -0.17032147423607338 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.88879791701868850000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000006 " " y[1] (closed_form) = -0.16690582997121767 " " y[1] (numeric) = -0.1669058299712178 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 8.31474119879912700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000006 " " y[1] (closed_form) = -0.1634439784995601 " " y[1] (numeric) = -0.16344397849956022 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 6.79268232954904900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000006 " " y[1] (closed_form) = -0.1599359975378828 " " y[1] (numeric) = -0.15993599753788296 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.04125060184983060000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000007 " " y[1] (closed_form) = -0.15638197239437684 " " y[1] (numeric) = -0.15638197239437698 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 8.87428876572570400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8700000000000007 " " y[1] (closed_form) = -0.15278199598665926 " " y[1] (numeric) = -0.15278199598665948 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.4533427416697708000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000007 " " y[1] (closed_form) = -0.14913616885873004 " " y[1] (numeric) = -0.14913616885873027 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.48887159046819930000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000007 " " y[1] (closed_form) = -0.14544459919686206 " " y[1] (numeric) = -0.14544459919686228 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.52666105273864200000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000007 " " y[1] (closed_form) = -0.14170740284442201 " " y[1] (numeric) = -0.14170740284442224 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.56692311388142550000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000007 " " y[1] (closed_form) = -0.13792470331561682 " " y[1] (numeric) = -0.13792470331561701 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.40866012134755550000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000007 " " y[1] (closed_form) = -0.1340966318081625 " " y[1] (numeric) = -0.13409663180816278 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 2.06981899853650340000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000007 " " y[1] (closed_form) = -0.13022332721487123 " " y[1] (numeric) = -0.13022332721487148 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.91824449492435900000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000007 " " y[1] (closed_form) = -0.1263049361341528 " " y[1] (numeric) = -0.12630493613415306 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.97775469578907740000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000007 " " y[1] (closed_form) = -0.12234161287942787 " " y[1] (numeric) = -0.12234161287942813 " " absolute error = 2.6367796834847470000000000000000E-16 " " relative error = 2.15525986737103880000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9600000000000007 " " y[1] (closed_form) = -0.1183335194874487 " " y[1] (numeric) = -0.11833351948744898 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 2.34553791147679550000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000008 " " y[1] (closed_form) = -0.1142808257255247 " " y[1] (numeric) = -0.11428082572552498 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 2.42871675448786050000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000008 " " y[1] (closed_form) = -0.11018370909764934 " " y[1] (numeric) = -0.11018370909764963 " " absolute error = 2.9143354396410360000000000000000E-16 " " relative error = 2.644978521333160000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000008 " " y[1] (closed_form) = -0.10604235484952622 " " y[1] (numeric) = -0.10604235484952644 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.0939237462249110000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0000000000000007 " " y[1] (closed_form) = -0.10185695597249028 " " y[1] (numeric) = -0.1018569559724905 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.17996505790926550000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0099999999999996 " " y[1] (closed_form) = -9.76277132063235600E-2 " " y[1] (numeric) = -9.76277132063233500E-2 " " absolute error = 2.08166817117216850000000000000000E-16 " " relative error = 2.13225128685830380000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0199999999999985 " " y[1] (closed_form) = -9.33548350409594500E-2 " " y[1] (numeric) = -9.33548350409587500E-2 " " absolute error = 7.0776717819853730000000000000000E-16 " " relative error = 7.581473181201640000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0299999999999974 " " y[1] (closed_form) = -8.90385377170778300E-2 " " y[1] (numeric) = -8.9038537717076700E-2 " " absolute error = 1.124100812432971000000000000000E-15 " " relative error = 1.2624879532555100000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0399999999999963 " " y[1] (closed_form) = -8.46790452255853900E-2 " " y[1] (numeric) = -8.46790452255837400E-2 " " absolute error = 1.6514567491299204000000000000000E-15 " " relative error = 1.9502543335608372000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0499999999999952 " " y[1] (closed_form) = -8.0276589305979500E-2 " " y[1] (numeric) = -8.02765893059773900E-2 " " absolute error = 2.1094237467877974000000000000000E-15 " " relative error = 2.6276947800405300000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.059999999999994 " " y[1] (closed_form) = -7.58314094435954800E-2 " " y[1] (numeric) = -7.58314094435928900E-2 " " absolute error = 2.5951463200613034000000000000000E-15 " " relative error = 3.4222577941026020000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.069999999999993 " " y[1] (closed_form) = -7.13437528657333800E-2 " " y[1] (numeric) = -7.13437528657302600E-2 " " absolute error = 3.1225022567582530000000000000000E-15 " " relative error = 4.376700315491814000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0799999999999919 " " y[1] (closed_form) = -6.68138745366640400E-2 " " y[1] (numeric) = -6.68138745366604300E-2 " " absolute error = 3.608224830031759000000000000000E-15 " " relative error = 5.4004124967363620000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0899999999999908 " " y[1] (closed_form) = -6.22420371515126200E-2 " " y[1] (numeric) = -6.224203715150851000E-2 " " absolute error = 4.107825191113079000000000000000E-15 " " relative error = 6.599760192799617000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0999999999999897 " " y[1] (closed_form) = -5.76285111290179500E-2 " " y[1] (numeric) = -5.76285111290133300E-2 " " absolute error = 4.614364446098307000000000000000E-15 " " relative error = 8.007085999094666000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1099999999999886 " " y[1] (closed_form) = -5.29735746031668200E-2 " " y[1] (numeric) = -5.29735746031616400E-2 " " absolute error = 5.176414852314792000000000000000E-15 " " relative error = 9.771692567647382000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1199999999999875 " " y[1] (closed_form) = -4.82775134137020800E-2 " " y[1] (numeric) = -4.82775134136964160E-2 " " absolute error = 5.662137425588298000000000000000E-15 " " relative error = 1.172831205507215600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1299999999999863 " " y[1] (closed_form) = -4.354062109550406000E-2 " " y[1] (numeric) = -4.354062109549785600E-2 " " absolute error = 6.2103100439969690000000000000000E-15 " " relative error = 1.42632555249383800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1399999999999852 " " y[1] (closed_form) = -3.8763198866843496E-2 " " y[1] (numeric) = -3.87631988668367700E-2 " " absolute error = 6.7307270867900120000000000000000E-15 " " relative error = 1.736370393452540000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1499999999999841 " " y[1] (closed_form) = -3.39455556165068200E-2 " " y[1] (numeric) = -3.39455556164995600E-2 " " absolute error = 7.258083023486961000000000000000E-15 " " relative error = 2.138154138787331500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.159999999999983 " " y[1] (closed_form) = -2.908800788979218300E-2 " " y[1] (numeric) = -2.90880078897844200E-2 " " absolute error = 7.764622278472189000000000000000E-15 " " relative error = 2.669355119776703000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.169999999999982 " " y[1] (closed_form) = -2.419087987337667500E-2 " " y[1] (numeric) = -2.41908798733683600E-2 " " absolute error = 8.316264343832813000000000000000E-15 " " relative error = 3.43776844305084400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1799999999999808 " " y[1] (closed_form) = -1.925450337905404400E-2 " " y[1] (numeric) = -1.925450337904518500E-2 " " absolute error = 8.86096751528953100000000000000E-15 " " relative error = 4.60202340244667600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1899999999999797 " " y[1] (closed_form) = -1.42792178263434900E-2 " " y[1] (numeric) = -1.427921782633408000E-2 " " absolute error = 9.409140133698202000000000000000E-15 " " relative error = 6.58939463500545200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1999999999999786 " " y[1] (closed_form) = -9.2653702239691990E-3 " " y[1] (numeric) = -9.265370223959244000E-3 " " absolute error = 9.955578028630896000000000000000E-15 " " relative error = 1.07449327851747920000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2099999999999775 " " y[1] (closed_form) = -4.213315150211255400E-3 " " y[1] (numeric) = -4.213315150200722000E-3 " " absolute error = 1.053324094613117300000000000000E-14 " " relative error = 2.49998886164568950000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2199999999999764 " " y[1] (closed_form) = 8.7658526787191830000E-4 " " y[1] (numeric) = 8.7658526788298570000E-4 " " absolute error = 1.10674273565147810000000000000E-14 " " relative error = 1.262561414405597000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2299999999999753 " " y[1] (closed_form) = 6.003961376348412000E-3 " " y[1] (numeric) = 6.0039613763600430000E-3 " " absolute error = 1.162958618294851500000000000000E-14 " " relative error = 1.93698550906095030000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2399999999999742 " " y[1] (closed_form) = 1.116843601744507700E-2 " " y[1] (numeric) = 1.116843601745728700E-2 " " absolute error = 1.220898382392476800000000000000E-14 " " relative error = 1.0931686231495939000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2499999999999731 " " y[1] (closed_form) = 1.636962455370548400E-2 " " y[1] (numeric) = 1.636962455371824300E-2 " " absolute error = 1.276062588928539300000000000000E-14 " " relative error = 7.79530761223039400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.259999999999972 " " y[1] (closed_form) = 2.160713489327277500E-2 " " y[1] (numeric) = 2.16071348932861100E-2 " " absolute error = 1.33330846363577400000000000000E-14 " " relative error = 6.17068607301049300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.269999999999971 " " y[1] (closed_form) = 2.6880567516296500E-2 " " y[1] (numeric) = 2.68805675163104300E-2 " " absolute error = 1.392982951209376000000000000000E-14 " " relative error = 5.18211883125187700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2799999999999698 " " y[1] (closed_form) = 3.21895155024616600E-2 " " y[1] (numeric) = 3.218951550247619600E-2 " " absolute error = 1.453698272868564300000000000000E-14 " " relative error = 4.5160613640096400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2899999999999687 " " y[1] (closed_form) = 3.75335645596386300E-2 " " y[1] (numeric) = 3.753356455965372600E-2 " " absolute error = 1.509209424099822200000000000000E-14 " " relative error = 4.02095948468144300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2999999999999676 " " y[1] (closed_form) = 4.29122930536521730E-2 " " y[1] (numeric) = 4.29122930536678900E-2 " " absolute error = 1.571659469234987200000000000000E-14 " " relative error = 3.66249239412580600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3099999999999665 " " y[1] (closed_form) = 4.832527203916830000E-2 " " y[1] (numeric) = 4.83252720391845800E-2 " " absolute error = 1.628558399247026500000000000000E-14 " " relative error = 3.36999323651413200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3199999999999654 " " y[1] (closed_form) = 5.37720652916958300E-2 " " y[1] (numeric) = 5.37720652917127200E-2 " " absolute error = 1.688926776211019400000000000000E-14 " " relative error = 3.14089995809003300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3299999999999643 " " y[1] (closed_form) = 5.925222934070198000E-2 " " y[1] (numeric) = 5.92522293407194800E-2 " " absolute error = 1.749295153175012300000000000000E-14 " " relative error = 2.95228580028021600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3399999999999632 " " y[1] (closed_form) = 6.47653135038385600E-2 " " y[1] (numeric) = 6.47653135038566800E-2 " " absolute error = 1.81243908770056800000000000000E-14 " " relative error = 2.798471882010032000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3499999999999621 " " y[1] (closed_form) = 7.03108599222770400E-2 " " y[1] (numeric) = 7.03108599222957900E-2 " " absolute error = 1.87488913283573300000000000000E-14 " " relative error = 2.66657118816107700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.359999999999961 " " y[1] (closed_form) = 7.58884035971495700E-2 " " y[1] (numeric) = 7.5888403597168910E-2 " " absolute error = 1.933175841628553800000000000000E-14 " " relative error = 2.54739294805928100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.36999999999996 " " y[1] (closed_form) = 8.14974724270934300E-2 " " y[1] (numeric) = 8.14974724271133600E-2 " " absolute error = 1.99285032920215600000000000000E-14 " " relative error = 2.445290964066319800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3799999999999588 " " y[1] (closed_form) = 8.71375872468960800E-2 " " y[1] (numeric) = 8.71375872469166300E-2 " " absolute error = 2.05530037433732100000000000000E-14 " " relative error = 2.358684052742730200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3899999999999577 " " y[1] (closed_form) = 9.28082618672375800E-2 " " y[1] (numeric) = 9.28082618672587600E-2 " " absolute error = 2.116362640691704700000000000000E-14 " " relative error = 2.280360172803543900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3999999999999566 " " y[1] (closed_form) = 9.85090031155275200E-2 " " y[1] (numeric) = 9.85090031155493300E-2 " " absolute error = 2.181588243388432600000000000000E-14 " " relative error = 2.214607979364029400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4099999999999555 " " y[1] (closed_form) = 0.10423931087783275 " " y[1] (numeric) = 0.10423931087785523 " " absolute error = 2.24820162486594200000000000000E-14 " " relative error = 2.156769462435153800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4199999999999544 " " y[1] (closed_form) = 0.10999867814189315 " " y[1] (numeric) = 0.10999867814191627 " " absolute error = 2.312039448781888500000000000000E-14 " " relative error = 2.10187930240349400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4299999999999533 " " y[1] (closed_form) = 0.1157865910412208 " " y[1] (numeric) = 0.11578659104124454 " " absolute error = 2.374489493917053600000000000000E-14 " " relative error = 2.050746526488304300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4399999999999522 " " y[1] (closed_form) = 0.1216025289002799 " " y[1] (numeric) = 0.12160252890030429 " " absolute error = 2.439715096613781500000000000000E-14 " " relative error = 2.006302926984741300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.449999999999951 " " y[1] (closed_form) = 0.12744596428074279 " " y[1] (numeric) = 0.12744596428076785 " " absolute error = 2.50632847809129100000000000000E-14 " " relative error = 1.966581281907252800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.45999999999995 " " y[1] (closed_form) = 0.13331636302881839 " " y[1] (numeric) = 0.13331636302884406 " " absolute error = 2.567390744445674500000000000000E-14 " " relative error = 1.925788167421499000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.469999999999949 " " y[1] (closed_form) = 0.13921318432364854 " " y[1] (numeric) = 0.13921318432367488 " " absolute error = 2.63400412592318400000000000000E-14 " " relative error = 1.892065136445369200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4799999999999478 " " y[1] (closed_form) = 0.1451358807267685 " " y[1] (numeric) = 0.14513588072679542 " " absolute error = 2.692290834716004600000000000000E-14 " " relative error = 1.855013950536798500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4899999999999467 " " y[1] (closed_form) = 0.15108389823262616 " " y[1] (numeric) = 0.15108389823265372 " " absolute error = 2.75612865863195100000000000000E-14 " " relative error = 1.824237189318677600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4999999999999456 " " y[1] (closed_form) = 0.15705667632015657 " " y[1] (numeric) = 0.15705667632018477 " " absolute error = 2.819966482547897600000000000000E-14 " " relative error = 1.795508824342785800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5099999999999445 " " y[1] (closed_form) = 0.16305364800540598 " " y[1] (numeric) = 0.16305364800543481 " " absolute error = 2.88380430646384400000000000000E-14 " " relative error = 1.76862299110795300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5199999999999434 " " y[1] (closed_form) = 0.16907423989520062 " " y[1] (numeric) = 0.16907423989523016 " " absolute error = 2.953193245502916400000000000000E-14 " " relative error = 1.746684324787401400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5299999999999423 " " y[1] (closed_form) = 0.17511787224185607 " " y[1] (numeric) = 0.17511787224188624 " " absolute error = 3.01703106941886300000000000000E-14 " " relative error = 1.722857313645307400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5399999999999412 " " y[1] (closed_form) = 0.18118395899892065 " " y[1] (numeric) = 0.18118395899895148 " " absolute error = 3.08364445089637230000000000000E-14 " " relative error = 1.701941202705887800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.54999999999994 " " y[1] (closed_form) = 0.18727190787794848 " " y[1] (numeric) = 0.18727190787797995 " " absolute error = 3.14748227481231900000000000000E-14 " " relative error = 1.680701772346785100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.559999999999939 " " y[1] (closed_form) = 0.19338112040629626 " " y[1] (numeric) = 0.1933811204063284 " " absolute error = 3.21409565628982800000000000000E-14 " " relative error = 1.66205245348510300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.569999999999938 " " y[1] (closed_form) = 0.19951099198593858 " " y[1] (numeric) = 0.19951099198597136 " " absolute error = 3.27793348020577470000000000000E-14 " " relative error = 1.642983901577112800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5799999999999368 " " y[1] (closed_form) = 0.20566091195329497 " " y[1] (numeric) = 0.20566091195332856 " " absolute error = 3.358424649491098500000000000000E-14 " " relative error = 1.632991226963822800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5899999999999357 " " y[1] (closed_form) = 0.21183026364006444 " " y[1] (numeric) = 0.21183026364009871 " " absolute error = 3.42781358853017100000000000000E-14 " " relative error = 1.618188794002828300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5999999999999346 " " y[1] (closed_form) = 0.2180184244350595 " " y[1] (numeric) = 0.21801842443509442 " " absolute error = 3.491651412446117300000000000000E-14 " " relative error = 1.601539604505382300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6099999999999335 " " y[1] (closed_form) = 0.22422476584703507 " " y[1] (numeric) = 0.22422476584707063 " " absolute error = 3.55548923636206400000000000000E-14 " " relative error = 1.585680878261056800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6199999999999324 " " y[1] (closed_form) = 0.23044865356850502 " " y[1] (numeric) = 0.2304486535685413 " " absolute error = 3.62765373296269900000000000000E-14 " " relative error = 1.57417007076776580000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6299999999999313 " " y[1] (closed_form) = 0.2366894475405404 " " y[1] (numeric) = 0.2366894475405773 " " absolute error = 3.691491556878645500000000000000E-14 " " relative error = 1.559635038755313700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6399999999999302 " " y[1] (closed_form) = 0.24294650201854195 " " y[1] (numeric) = 0.2429465020185796 " " absolute error = 3.763656053479280700000000000000E-14 " " relative error = 1.549170711332997200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.649999999999929 " " y[1] (closed_form) = 0.2492191656389816 " " y[1] (numeric) = 0.24921916563901997 " " absolute error = 3.83582055007991600000000000000E-14 " " relative error = 1.53913545944394900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.659999999999928 " " y[1] (closed_form) = 0.25550678148710415 " " y[1] (numeric) = 0.25550678148714323 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 1.529503453464225700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6699999999999269 " " y[1] (closed_form) = 0.26180868716558353 " " y[1] (numeric) = 0.2618086871656233 " " absolute error = 3.974598428158060400000000000000E-14 " " relative error = 1.51813084248204700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6799999999999258 " " y[1] (closed_form) = 0.26812421486412635 " " y[1] (numeric) = 0.2681242148641669 " " absolute error = 4.052314039881821400000000000000E-14 " " relative error = 1.51135698129143510000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6899999999999247 " " y[1] (closed_form) = 0.2744526914300146 " " y[1] (numeric) = 0.27445269143005596 " " absolute error = 4.13558076672870800000000000000E-14 " " relative error = 1.506846496997563700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6999999999999236 " " y[1] (closed_form) = 0.280793438439581 " " y[1] (numeric) = 0.2807934384396231 " " absolute error = 4.21329637845246900000000000000E-14 " " relative error = 1.500496735916090300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7099999999999225 " " y[1] (closed_form) = 0.2871457722706087 " " y[1] (numeric) = 0.28714577227065147 " " absolute error = 4.274358644806852700000000000000E-14 " " relative error = 1.488567500404867000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7199999999999214 " " y[1] (closed_form) = 0.2935090041756484 " " y[1] (numeric) = 0.29350900417569187 " " absolute error = 4.34652314140748800000000000000E-14 " " relative error = 1.480882385061802800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7299999999999203 " " y[1] (closed_form) = 0.29988244035624423 " " y[1] (numeric) = 0.29988244035628836 " " absolute error = 4.41313652288499700000000000000E-14 " " relative error = 1.47162218556125800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7399999999999192 " " y[1] (closed_form) = 0.306265382038061 " " y[1] (numeric) = 0.3062653820381058 " " absolute error = 4.485301019485632400000000000000E-14 " " relative error = 1.46451452973167700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.749999999999918 " " y[1] (closed_form) = 0.31265712554690483 " " y[1] (numeric) = 0.31265712554695035 " " absolute error = 4.55191440096314200000000000000E-14 " " relative error = 1.45588058900012580000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.759999999999917 " " y[1] (closed_form) = 0.31905696238562836 " " y[1] (numeric) = 0.31905696238567455 " " absolute error = 4.61852778244065100000000000000E-14 " " relative error = 1.447555868365118200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7699999999999159 " " y[1] (closed_form) = 0.32546417931191246 " " y[1] (numeric) = 0.3254641793119593 " " absolute error = 4.685141163918160600000000000000E-14 " " relative error = 1.439525902304628300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7799999999999148 " " y[1] (closed_form) = 0.33187805841691637 " " y[1] (numeric) = 0.331878058416964 " " absolute error = 4.762856775641921600000000000000E-14 " " relative error = 1.435122526135385600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7899999999999137 " " y[1] (closed_form) = 0.3382978772047873 " " y[1] (numeric) = 0.33829787720483556 " " absolute error = 4.82391904199630500000000000000E-14 " " relative error = 1.425938312665250300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7999999999999126 " " y[1] (closed_form) = 0.3447229086730203 " " y[1] (numeric) = 0.3447229086730693 " " absolute error = 4.90163465372006600000000000000E-14 " " relative error = 1.42190569016386700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8099999999999115 " " y[1] (closed_form) = 0.3511524213936607 " " y[1] (numeric) = 0.3511524213937105 " " absolute error = 4.97935026544382700000000000000E-14 " " relative error = 1.418002543078496500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8199999999999104 " " y[1] (closed_form) = 0.3575856795953394 " " y[1] (numeric) = 0.3575856795953898 " " absolute error = 5.04041253179821100000000000000E-14 " " relative error = 1.40956778176972200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8299999999999093 " " y[1] (closed_form) = 0.3640219432461312 " " y[1] (numeric) = 0.36402194324618237 " " absolute error = 5.118128143521972000000000000000E-14 " " relative error = 1.405994401843347300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8399999999999082 " " y[1] (closed_form) = 0.37046046813722927 " " y[1] (numeric) = 0.37046046813728123 " " absolute error = 5.195843755245733000000000000000E-14 " " relative error = 1.402536627287595300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.849999999999907 " " y[1] (closed_form) = 0.37690050596742375 " " y[1] (numeric) = 0.37690050596747626 " " absolute error = 5.251354906476990000000000000000E-14 " " relative error = 1.39330004161121400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.859999999999906 " " y[1] (closed_form) = 0.3833413044283762 " " y[1] (numeric) = 0.38334130442842945 " " absolute error = 5.323519403077626000000000000000E-14 " " relative error = 1.388715314937390700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8699999999999048 " " y[1] (closed_form) = 0.3897821072906814 " " y[1] (numeric) = 0.3897821072907353 " " absolute error = 5.39013278455513500000000000000E-14 " " relative error = 1.382857931068504400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8799999999999037 " " y[1] (closed_form) = 0.3962221544907044 " " y[1] (numeric) = 0.3962221544907591 " " absolute error = 5.46784839627889600000000000000E-14 " " relative error = 1.37999562475428800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8899999999999026 " " y[1] (closed_form) = 0.4026606822181857 " " y[1] (numeric) = 0.4026606822182411 " " absolute error = 5.54001289287953100000000000000E-14 " " relative error = 1.375851464404369300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8999999999999015 " " y[1] (closed_form) = 0.4090969230046019 " " y[1] (numeric) = 0.40909692300465805 " " absolute error = 5.61772850460329200000000000000E-14 " " relative error = 1.373202336342212000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9099999999999004 " " y[1] (closed_form) = 0.4155301058122745 " " y[1] (numeric) = 0.41553010581233146 " " absolute error = 5.69544411632705300000000000000E-14 " " relative error = 1.37064536038698100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9199999999998993 " " y[1] (closed_form) = 0.42195945612421465 " " y[1] (numeric) = 0.4219594561242724 " " absolute error = 5.77315972805081400000000000000E-14 " " relative error = 1.36817877743006100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9299999999998982 " " y[1] (closed_form) = 0.42838419603469435 " " y[1] (numeric) = 0.4283841960347528 " " absolute error = 5.84532422465144900000000000000E-14 " " relative error = 1.364505105173871300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9399999999998971 " " y[1] (closed_form) = 0.4348035443405339 " " y[1] (numeric) = 0.4348035443405932 " " absolute error = 5.92859095149833600000000000000E-14 " " relative error = 1.363510263121296400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.949999999999896 " " y[1] (closed_form) = 0.44121671663309525 " " y[1] (numeric) = 0.44121671663315515 " " absolute error = 5.9896532178527200000000000000E-14 " " relative error = 1.35753088948204200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.959999999999895 " " y[1] (closed_form) = 0.4476229253909693 " " y[1] (numeric) = 0.44762292539103 " " absolute error = 6.0673688295764800000000000000E-14 " " relative error = 1.35546427258546510000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9699999999998938 " " y[1] (closed_form) = 0.45402138007334913 " " y[1] (numeric) = 0.4540213800734105 " " absolute error = 6.1339822110539900000000000000E-14 " " relative error = 1.351033779524439500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9799999999998927 " " y[1] (closed_form) = 0.460411287214075 " " y[1] (numeric) = 0.46041128721413715 " " absolute error = 6.21724893790087700000000000000E-14 " " relative error = 1.350368488036236300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9899999999998916 " " y[1] (closed_form) = 0.4667918505163433 " " y[1] (numeric) = 0.4667918505164062 " " absolute error = 6.28941343450151200000000000000E-14 " " relative error = 1.347370016752532700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9999999999998905 " " y[1] (closed_form) = 0.4731622709480664 " " y[1] (numeric) = 0.4731622709481299 " " absolute error = 6.35047570085589500000000000000E-14 " " relative error = 1.342134842689711200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0099999999998897 " " y[1] (closed_form) = 0.479521746837873 " " y[1] (numeric) = 0.47952174683793725 " " absolute error = 6.4226401974565310000000000000E-14 " " relative error = 1.339384551338822500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0199999999998886 " " y[1] (closed_form) = 0.4858694739717383 " " y[1] (numeric) = 0.4858694739718032 " " absolute error = 6.4892535789340400000000000000E-14 " " relative error = 1.335596065726801000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0299999999998875 " " y[1] (closed_form) = 0.4922046456902313 " " y[1] (numeric) = 0.4922046456902969 " " absolute error = 6.56141807553467500000000000000E-14 " " relative error = 1.33306707545058400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0399999999998863 " " y[1] (closed_form) = 0.4985264529863698 " " y[1] (numeric) = 0.498526452986436 " " absolute error = 6.62248034188905900000000000000E-14 " " relative error = 1.328411020562258000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0499999999998852 " " y[1] (closed_form) = 0.504834084604069 " " y[1] (numeric) = 0.5048340846041358 " " absolute error = 6.68354260824344200000000000000E-14 " " relative error = 1.323908747858260600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.059999999999884 " " y[1] (closed_form) = 0.5111267271371748 " " y[1] (numeric) = 0.5111267271372423 " " absolute error = 6.75015598972095200000000000000E-14 " " relative error = 1.320642343930757400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.069999999999883 " " y[1] (closed_form) = 0.5174035651290684 " " y[1] (numeric) = 0.5174035651291368 " " absolute error = 6.83897383169096400000000000000E-14 " " relative error = 1.321787148873811000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.079999999999882 " " y[1] (closed_form) = 0.5236637811728309 " " y[1] (numeric) = 0.5236637811728999 " " absolute error = 6.90558721316847400000000000000E-14 " " relative error = 1.318706288546876400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.089999999999881 " " y[1] (closed_form) = 0.5299065560119556 " " y[1] (numeric) = 0.5299065560120252 " " absolute error = 6.96109836439973200000000000000E-14 " " relative error = 1.31364639395831100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0999999999998797 " " y[1] (closed_form) = 0.5361310686415974 " " y[1] (numeric) = 0.5361310686416678 " " absolute error = 7.03881397612349200000000000000E-14 " " relative error = 1.312890520215109200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1099999999998786 " " y[1] (closed_form) = 0.5423364964103454 " " y[1] (numeric) = 0.5423364964104164 " " absolute error = 7.0943251273547500000000000000E-14 " " relative error = 1.308103949173836400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999998775 " " y[1] (closed_form) = 0.5485220151225078 " " y[1] (numeric) = 0.5485220151225793 " " absolute error = 7.14983627858600800000000000000E-14 " " relative error = 1.303472984031306700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999998764 " " y[1] (closed_form) = 0.5546867991408959 " " y[1] (numeric) = 0.5546867991409681 " " absolute error = 7.21644966006351800000000000000E-14 " " relative error = 1.300995385367097500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999998753 " " y[1] (closed_form) = 0.560830021490097 " " y[1] (numeric) = 0.56083002149017 " " absolute error = 7.3052675020335300000000000000E-14 " " relative error = 1.302581392241414500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1499999999998742 " " y[1] (closed_form) = 0.5669508539602206 " " y[1] (numeric) = 0.5669508539602942 " " absolute error = 7.36077865326478800000000000000E-14 " " relative error = 1.298309827359612500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.159999999999873 " " y[1] (closed_form) = 0.5730484672111078 " " y[1] (numeric) = 0.5730484672111821 " " absolute error = 7.42739203474229700000000000000E-14 " " relative error = 1.296119344126277500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.169999999999872 " " y[1] (closed_form) = 0.5791220308769911 " " y[1] (numeric) = 0.5791220308770659 " " absolute error = 7.48290318597355500000000000000E-14 " " relative error = 1.29211164262596800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.179999999999871 " " y[1] (closed_form) = 0.5851707136715903 " " y[1] (numeric) = 0.5851707136716658 " " absolute error = 7.54951656745106400000000000000E-14 " " relative error = 1.29013916641221500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.18999999999987 " " y[1] (closed_form) = 0.5911936834936348 " " y[1] (numeric) = 0.5911936834937109 " " absolute error = 7.61612994892857400000000000000E-14 " " relative error = 1.288263078847759000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1999999999998687 " " y[1] (closed_form) = 0.5971901075327952 " " y[1] (numeric) = 0.5971901075328724 " " absolute error = 7.71605002114483800000000000000E-14 " " relative error = 1.292059249444466600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2099999999998676 " " y[1] (closed_form) = 0.6031591523760174 " " y[1] (numeric) = 0.6031591523760951 " " absolute error = 7.77156117237609600000000000000E-14 " " relative error = 1.288476041814450000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999998665 " " y[1] (closed_form) = 0.6090999841142378 " " y[1] (numeric) = 0.6090999841143161 " " absolute error = 7.82707232360735400000000000000E-14 " " relative error = 1.285022578844686200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999998654 " " y[1] (closed_form) = 0.6150117684494769 " " y[1] (numeric) = 0.6150117684495559 " " absolute error = 7.89368570508486300000000000000E-14 " " relative error = 1.283501570219680600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2399999999998643 " " y[1] (closed_form) = 0.6208936708022887 " " y[1] (numeric) = 0.6208936708023685 " " absolute error = 7.97140131680862400000000000000E-14 " " relative error = 1.28385932916796600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.249999999999863 " " y[1] (closed_form) = 0.6267448564195588 " " y[1] (numeric) = 0.6267448564196391 " " absolute error = 8.02691246803988200000000000000E-14 " " relative error = 1.280730489580031400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.259999999999862 " " y[1] (closed_form) = 0.6325644904826351 " " y[1] (numeric) = 0.6325644904827159 " " absolute error = 8.0824236192711400000000000000E-14 " " relative error = 1.277723258399218700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.269999999999861 " " y[1] (closed_form) = 0.63835173821578 " " y[1] (numeric) = 0.6383517382158616 " " absolute error = 8.160139230994901000000000000E-14 " " relative error = 1.278313936107205500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.27999999999986 " " y[1] (closed_form) = 0.6441057649949286 " " y[1] (numeric) = 0.6441057649950107 " " absolute error = 8.21565038222615800000000000000E-14 " " relative error = 1.275512629869233500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999859 " " y[1] (closed_form) = 0.6498257364567399 " " y[1] (numeric) = 0.6498257364568227 " " absolute error = 8.28226376370366800000000000000E-14 " " relative error = 1.274536125464004700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2999999999998577 " " y[1] (closed_form) = 0.6555108186079298 " " y[1] (numeric) = 0.6555108186080133 " " absolute error = 8.34887714518117700000000000000E-14 " " relative error = 1.273644447686035400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999998566 " " y[1] (closed_form) = 0.6611601779348688 " " y[1] (numeric) = 0.6611601779349529 " " absolute error = 8.40438829641243500000000000000E-14 " " relative error = 1.271157667520676800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999998555 " " y[1] (closed_form) = 0.666772981513434 " " y[1] (numeric) = 0.6667729815135187 " " absolute error = 8.47100167788994400000000000000E-14 " " relative error = 1.270447650512556400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999998544 " " y[1] (closed_form) = 0.6723483971190996 " " y[1] (numeric) = 0.6723483971191849 " " absolute error = 8.53761505936745400000000000000E-14 " " relative error = 1.269820095645309300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3399999999998533 " " y[1] (closed_form) = 0.6778855933372532 " " y[1] (numeric) = 0.677885593337339 " " absolute error = 8.5820239803524600000000000000E-14 " " relative error = 1.265998874249985600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.349999999999852 " " y[1] (closed_form) = 0.6833837396737245 " " y[1] (numeric) = 0.6833837396738109 " " absolute error = 8.6486373618299700000000000000E-14 " " relative error = 1.265560893497288400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.359999999999851 " " y[1] (closed_form) = 0.6888420066655113 " " y[1] (numeric) = 0.6888420066655982 " " absolute error = 8.69304628281497600000000000000E-14 " " relative error = 1.26197969907432700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.36999999999985 " " y[1] (closed_form) = 0.6942595659916908 " " y[1] (numeric) = 0.6942595659917783 " " absolute error = 8.74855743404623400000000000000E-14 " " relative error = 1.260127747977035400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.379999999999849 " " y[1] (closed_form) = 0.6996355905844996 " " y[1] (numeric) = 0.6996355905845878 " " absolute error = 8.81517081552374300000000000000E-14 " " relative error = 1.259966035770027600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999848 " " y[1] (closed_form) = 0.7049692547405725 " " y[1] (numeric) = 0.7049692547406612 " " absolute error = 8.87068196675500100000000000000E-14 " " relative error = 1.258307636411661300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3999999999998467 " " y[1] (closed_form) = 0.7102597342323209 " " y[1] (numeric) = 0.7102597342324103 " " absolute error = 8.9372953482325100000000000000E-14 " " relative error = 1.258313672799193600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999998456 " " y[1] (closed_form) = 0.7155062064194427 " " y[1] (numeric) = 0.7155062064195329 " " absolute error = 9.01501095995627100000000000000E-14 " " relative error = 1.25994867397020300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999998445 " " y[1] (closed_form) = 0.7207078503605445 " " y[1] (numeric) = 0.720707850360635 " " absolute error = 9.04831765069502600000000000000E-14 " " relative error = 1.255476493862037700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4299999999998434 " " y[1] (closed_form) = 0.7258638469248639 " " y[1] (numeric) = 0.7258638469249549 " " absolute error = 9.09272657168003200000000000000E-14 " " relative error = 1.25267660184503500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4399999999998423 " " y[1] (closed_form) = 0.7309733789040799 " " y[1] (numeric) = 0.7309733789041715 " " absolute error = 9.15933995315754100000000000000E-14 " " relative error = 1.253033313865655000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.449999999999841 " " y[1] (closed_form) = 0.7360356311241936 " " y[1] (numeric) = 0.7360356311242858 " " absolute error = 9.22595333463505100000000000000E-14 " " relative error = 1.253465585700473700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.45999999999984 " " y[1] (closed_form) = 0.7410497905574668 " " y[1] (numeric) = 0.7410497905575595 " " absolute error = 9.27036225562005700000000000000E-14 " " relative error = 1.250976975332018800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.469999999999839 " " y[1] (closed_form) = 0.7460150464344051 " " y[1] (numeric) = 0.7460150464344985 " " absolute error = 9.33697563709756700000000000000E-14 " " relative error = 1.251580069560774000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999838 " " y[1] (closed_form) = 0.7509305903557698 " " y[1] (numeric) = 0.7509305903558635 " " absolute error = 9.37028232783632100000000000000E-14 " " relative error = 1.247822694690989100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999837 " " y[1] (closed_form) = 0.7557956164046038 " " y[1] (numeric) = 0.755795616404698 " " absolute error = 9.41469124882132700000000000000E-14 " " relative error = 1.245666294494795600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4999999999998357 " " y[1] (closed_form) = 0.7606093212582596 " " y[1] (numeric) = 0.7606093212583542 " " absolute error = 9.45910016980633400000000000000E-14 " " relative error = 1.243621384255237400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5099999999998346 " " y[1] (closed_form) = 0.7653709043004133 " " y[1] (numeric) = 0.7653709043005084 " " absolute error = 9.5035090907913400000000000000E-14 " " relative error = 1.24168674787526900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999998335 " " y[1] (closed_form) = 0.77007956773305 " " y[1] (numeric) = 0.7700795677331453 " " absolute error = 9.53681578153009500000000000000E-14 " " relative error = 1.238419532361369800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5299999999998324 " " y[1] (closed_form) = 0.7747345166884065 " " y[1] (numeric) = 0.7747345166885025 " " absolute error = 9.59232693276135300000000000000E-14 " " relative error = 1.238143741647608300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5399999999998313 " " y[1] (closed_form) = 0.7793349593408591 " " y[1] (numeric) = 0.7793349593409553 " " absolute error = 9.62563362350010700000000000000E-14 " " relative error = 1.235108666450843400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.54999999999983 " " y[1] (closed_form) = 0.7838801070187367 " " y[1] (numeric) = 0.7838801070188336 " " absolute error = 9.69224700497761700000000000000E-14 " " relative error = 1.236445078551527400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.559999999999829 " " y[1] (closed_form) = 0.7883691743160521 " " y[1] (numeric) = 0.7883691743161495 " " absolute error = 9.73665592596262300000000000000E-14 " " relative error = 1.235037624905823600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999828 " " y[1] (closed_form) = 0.79280137920413 " " y[1] (numeric) = 0.7928013792042279 " " absolute error = 9.79216707719388100000000000000E-14 " " relative error = 1.23513497000017210000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999827 " " y[1] (closed_form) = 0.7971759431431218 " " y[1] (numeric) = 0.7971759431432202 " " absolute error = 9.83657599817888700000000000000E-14 " " relative error = 1.233927852789314200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5899999999998258 " " y[1] (closed_form) = 0.8014920911933912 " " y[1] (numeric) = 0.8014920911934901 " " absolute error = 9.89208714941014500000000000000E-14 " " relative error = 1.234208953288759700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5999999999998247 " " y[1] (closed_form) = 0.8057490521267554 " " y[1] (numeric) = 0.805749052126855 " " absolute error = 9.95870053088765400000000000000E-14 " " relative error = 1.23595559989824410000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6099999999998236 " " y[1] (closed_form) = 0.8099460585375693 " " y[1] (numeric) = 0.8099460585376694 " " absolute error = 1.00142116821189120000000000000E-13 " " relative error = 1.236404767522478700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6199999999998225 " " y[1] (closed_form) = 0.814082346953636 " " y[1] (numeric) = 0.8140823469537366 " " absolute error = 1.00586206031039180000000000000E-13 " " relative error = 1.235577781626651800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6299999999998214 " " y[1] (closed_form) = 0.8181571579469308 " " y[1] (numeric) = 0.8181571579470318 " " absolute error = 1.01030295240889250000000000000E-13 " " relative error = 1.234851938402798800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999998203 " " y[1] (closed_form) = 0.8221697362441232 " " y[1] (numeric) = 0.8221697362442245 " " absolute error = 1.01363362148276790000000000000E-13 " " relative error = 1.232876347545094200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.649999999999819 " " y[1] (closed_form) = 0.826119330836883 " " y[1] (numeric) = 0.8261193308369847 " " absolute error = 1.01696429055664340000000000000E-13 " " relative error = 1.231013792555161300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.659999999999818 " " y[1] (closed_form) = 0.8300051950919558 " " y[1] (numeric) = 0.830005195092058 " " absolute error = 1.0214051826551440000000000000E-13 " " relative error = 1.230600951289206300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.669999999999817 " " y[1] (closed_form) = 0.8338265868609928 " " y[1] (numeric) = 0.8338265868610955 " " absolute error = 1.02695629777826980000000000000E-13 " " relative error = 1.231618557096301500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.679999999999816 " " y[1] (closed_form) = 0.8375827685901212 " " y[1] (numeric) = 0.837582768590224 " " absolute error = 1.0280665208028950000000000000E-13 " " relative error = 1.227420810642283800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6899999999998148 " " y[1] (closed_form) = 0.8412730074292405 " " y[1] (numeric) = 0.8412730074293436 " " absolute error = 1.03139718987677040000000000000E-13 " " relative error = 1.225995819155675500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6999999999998137 " " y[1] (closed_form) = 0.8448965753410305 " " y[1] (numeric) = 0.8448965753411339 " " absolute error = 1.03472785895064590000000000000E-13 " " relative error = 1.224679906570804600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7099999999998126 " " y[1] (closed_form) = 0.8484527492096554 " " y[1] (numeric) = 0.8484527492097594 " " absolute error = 1.04027897407377170000000000000E-13 " " relative error = 1.226089461131223600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7199999999998115 " " y[1] (closed_form) = 0.8519408109491509 " " y[1] (numeric) = 0.8519408109492556 " " absolute error = 1.04694031222152260000000000000E-13 " " relative error = 1.228888555127582300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999998104 " " y[1] (closed_form) = 0.8553600476114787 " " y[1] (numeric) = 0.8553600476115836 " " absolute error = 1.04916075827077300000000000000E-13 " " relative error = 1.22657208645700300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999998093 " " y[1] (closed_form) = 0.8587097514942348 " " y[1] (numeric) = 0.8587097514943401 " " absolute error = 1.05360165036927360000000000000E-13 " " relative error = 1.226958991132811500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.749999999999808 " " y[1] (closed_form) = 0.8619892202479982 " " y[1] (numeric) = 0.8619892202481039 " " absolute error = 1.0569323194431490000000000000E-13 " " relative error = 1.226154915416534800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999807 " " y[1] (closed_form) = 0.8651977569833014 " " y[1] (numeric) = 0.8651977569834075 " " absolute error = 1.06137321154164970000000000000E-13 " " relative error = 1.226740595401398700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.769999999999806 " " y[1] (closed_form) = 0.8683346703772141 " " y[1] (numeric) = 0.8683346703773208 " " absolute error = 1.06692432666477540000000000000E-13 " " relative error = 1.22870174722067900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.779999999999805 " " y[1] (closed_form) = 0.871399274779522 " " y[1] (numeric) = 0.8713992747796289 " " absolute error = 1.06914477271402570000000000000E-13 " " relative error = 1.226928692343170200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7899999999998037 " " y[1] (closed_form) = 0.8743908903184858 " " y[1] (numeric) = 0.8743908903185931 " " absolute error = 1.07247544178790120000000000000E-13 " " relative error = 1.226540044804521800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7999999999998026 " " y[1] (closed_form) = 0.8773088430061702 " " y[1] (numeric) = 0.877308843006278 " " absolute error = 1.0780265569110270000000000000E-13 " " relative error = 1.22878797530078600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8099999999998015 " " y[1] (closed_form) = 0.8801524648433243 " " y[1] (numeric) = 0.8801524648434322 " " absolute error = 1.07913677993565220000000000000E-13 " " relative error = 1.226079370382435900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8199999999998004 " " y[1] (closed_form) = 0.8829210939238008 " " y[1] (numeric) = 0.8829210939239092 " " absolute error = 1.08357767203415280000000000000E-13 " " relative error = 1.227264451479589700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999997993 " " y[1] (closed_form) = 0.8856140745385012 " " y[1] (numeric) = 0.8856140745386101 " " absolute error = 1.08912878715727860000000000000E-13 " " relative error = 1.229800675564952100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8399999999997982 " " y[1] (closed_form) = 0.8882307572788302 " " y[1] (numeric) = 0.8882307572789395 " " absolute error = 1.09356967925577920000000000000E-13 " " relative error = 1.231177450560282700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.849999999999797 " " y[1] (closed_form) = 0.8907704991396468 " " y[1] (numeric) = 0.8907704991397564 " " absolute error = 1.09579012530502950000000000000E-13 " " relative error = 1.230159874359783400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.859999999999796 " " y[1] (closed_form) = 0.8932326636216983 " " y[1] (numeric) = 0.8932326636218082 " " absolute error = 1.0991207943789050000000000000E-13 " " relative error = 1.230497762948360400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.869999999999795 " " y[1] (closed_form) = 0.8956166208335222 " " y[1] (numeric) = 0.8956166208336321 " " absolute error = 1.0991207943789050000000000000E-13 " " relative error = 1.227222417283846100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.879999999999794 " " y[1] (closed_form) = 0.8979217475928014 " " y[1] (numeric) = 0.8979217475929117 " " absolute error = 1.10245146345278040000000000000E-13 " " relative error = 1.227781225266337300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8899999999997927 " " y[1] (closed_form) = 0.9001474275271615 " " y[1] (numeric) = 0.900147427527272 " " absolute error = 1.10467190950203080000000000000E-13 " " relative error = 1.227212205157024600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8999999999997916 " " y[1] (closed_form) = 0.9022930511743923 " " y[1] (numeric) = 0.9022930511745031 " " absolute error = 1.10800257857590620000000000000E-13 " " relative error = 1.227985272782240600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9099999999997905 " " y[1] (closed_form) = 0.904358016082084 " " y[1] (numeric) = 0.904358016082195 " " absolute error = 1.11022302462515650000000000000E-13 " " relative error = 1.227636627178839700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999997894 " " y[1] (closed_form) = 0.9063417269066596 " " y[1] (numeric) = 0.9063417269067707 " " absolute error = 1.11133324764978170000000000000E-13 " " relative error = 1.226174647660499100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9299999999997883 " " y[1] (closed_form) = 0.9082435955117941 " " y[1] (numeric) = 0.9082435955119055 " " absolute error = 1.1135536936990320000000000000E-13 " " relative error = 1.226051798440203500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9399999999997872 " " y[1] (closed_form) = 0.910063041066204 " " y[1] (numeric) = 0.9100630410663153 " " absolute error = 1.1135536936990320000000000000E-13 " " relative error = 1.223600611661390300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.949999999999786 " " y[1] (closed_form) = 0.9117994901407933 " " y[1] (numeric) = 0.9117994901409051 " " absolute error = 1.11799458579753260000000000000E-13 " " relative error = 1.226140832371928800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.959999999999785 " " y[1] (closed_form) = 0.9134523768051457 " " y[1] (numeric) = 0.9134523768052579 " " absolute error = 1.12243547789603330000000000000E-13 " " relative error = 1.228783794752188900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.969999999999784 " " y[1] (closed_form) = 0.9150211427233442 " " y[1] (numeric) = 0.9150211427234567 " " absolute error = 1.12465592394528360000000000000E-13 " " relative error = 1.229103756660759700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.979999999999783 " " y[1] (closed_form) = 0.9165052372491095 " " y[1] (numeric) = 0.9165052372492223 " " absolute error = 1.1279865930191590000000000000E-13 " " relative error = 1.23074756932629300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9899999999997817 " " y[1] (closed_form) = 0.9179041175202408 " " y[1] (numeric) = 0.9179041175203535 " " absolute error = 1.12687636999453390000000000000E-13 " " relative error = 1.227662397940692300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9999999999997806 " " y[1] (closed_form) = 0.9192172485523467 " " y[1] (numeric) = 0.9192172485524593 " " absolute error = 1.12687636999453390000000000000E-13 " " relative error = 1.225908643217068200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0099999999997795 " " y[1] (closed_form) = 0.9204441033318516 " " y[1] (numeric) = 0.9204441033319648 " " absolute error = 1.13242748511765970000000000000E-13 " " relative error = 1.230305546005959800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0199999999997784 " " y[1] (closed_form) = 0.9215841629082688 " " y[1] (numeric) = 0.9215841629083821 " " absolute error = 1.13242748511765970000000000000E-13 " " relative error = 1.228783577990345100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0299999999997773 " " y[1] (closed_form) = 0.9226369164857189 " " y[1] (numeric) = 0.9226369164858323 " " absolute error = 1.134647931166910000000000000E-13 " " relative error = 1.229788133222255200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.039999999999776 " " y[1] (closed_form) = 0.923601861513689 " " y[1] (numeric) = 0.9236018615138025 " " absolute error = 1.13575815419153510000000000000E-13 " " relative error = 1.229705354134024600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.049999999999775 " " y[1] (closed_form) = 0.9244785037770145 " " y[1] (numeric) = 0.9244785037771281 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 1.22974019684764290000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.059999999999774 " " y[1] (closed_form) = 0.9252663574850715 " " y[1] (numeric) = 0.9252663574851854 " " absolute error = 1.13908882326541060000000000000E-13 " " relative error = 1.231092878337780600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.069999999999773 " " y[1] (closed_form) = 0.9259649453601689 " " y[1] (numeric) = 0.9259649453602825 " " absolute error = 1.13575815419153510000000000000E-13 " " relative error = 1.226567117775461500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.079999999999772 " " y[1] (closed_form) = 0.9265737987251232 " " y[1] (numeric) = 0.9265737987252369 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 1.226959340724270600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0899999999997707 " " y[1] (closed_form) = 0.927092457590009 " " y[1] (numeric) = 0.9270924575901226 " " absolute error = 1.13575815419153510000000000000E-13 " " relative error = 1.225075390154673200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0999999999997696 " " y[1] (closed_form) = 0.9275204707380664 " " y[1] (numeric) = 0.9275204707381801 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 1.225707046995423300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1099999999997685 " " y[1] (closed_form) = 0.9278573958107583 " " y[1] (numeric) = 0.9278573958108718 " " absolute error = 1.134647931166910000000000000E-13 " " relative error = 1.222868876499560300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1199999999997674 " " y[1] (closed_form) = 0.9281027993919605 " " y[1] (numeric) = 0.9281027993920737 " " absolute error = 1.13242748511765970000000000000E-13 " " relative error = 1.22015307556400100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1299999999997663 " " y[1] (closed_form) = 0.9282562570912749 " " y[1] (numeric) = 0.9282562570913884 " " absolute error = 1.134647931166910000000000000E-13 " " relative error = 1.222343423487788900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.139999999999765 " " y[1] (closed_form) = 0.9283173536264537 " " y[1] (numeric) = 0.9283173536265672 " " absolute error = 1.134647931166910000000000000E-13 " " relative error = 1.222262975839490400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.149999999999764 " " y[1] (closed_form) = 0.9282856829049202 " " y[1] (numeric) = 0.9282856829050335 " " absolute error = 1.13353770814228480000000000000E-13 " " relative error = 1.221108683476687400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.159999999999763 " " y[1] (closed_form) = 0.928160848104375 " " y[1] (numeric) = 0.9281608481044883 " " absolute error = 1.13242748511765970000000000000E-13 " " relative error = 1.220076765175419200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.169999999999762 " " y[1] (closed_form) = 0.9279424617524779 " " y[1] (numeric) = 0.9279424617525911 " " absolute error = 1.13242748511765970000000000000E-13 " " relative error = 1.220363903790973200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.179999999999761 " " y[1] (closed_form) = 0.9276301458055884 " " y[1] (numeric) = 0.9276301458057015 " " absolute error = 1.13020703906840940000000000000E-13 " " relative error = 1.218381101755695400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1899999999997597 " " y[1] (closed_form) = 0.9272235317265591 " " y[1] (numeric) = 0.9272235317266723 " " absolute error = 1.13131726209303450000000000000E-13 " " relative error = 1.220112759634602700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1999999999997586 " " y[1] (closed_form) = 0.9267222605615653 " " y[1] (numeric) = 0.9267222605616783 " " absolute error = 1.13020703906840940000000000000E-13 " " relative error = 1.21957471743857610000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2099999999997575 " " y[1] (closed_form) = 0.9261259830159598 " " y[1] (numeric) = 0.9261259830160727 " " absolute error = 1.12909681604378420000000000000E-13 " " relative error = 1.21916114734935200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2199999999997564 " " y[1] (closed_form) = 0.9254343595291462 " " y[1] (numeric) = 0.9254343595292592 " " absolute error = 1.13020703906840940000000000000E-13 " " relative error = 1.22127196535413900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2299999999997553 " " y[1] (closed_form) = 0.9246470603484516 " " y[1] (numeric) = 0.9246470603485646 " " absolute error = 1.13020703906840940000000000000E-13 " " relative error = 1.222311828518108100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.239999999999754 " " y[1] (closed_form) = 0.9237637656019924 " " y[1] (numeric) = 0.9237637656021055 " " absolute error = 1.13131726209303450000000000000E-13 " " relative error = 1.224682439623278700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.249999999999753 " " y[1] (closed_form) = 0.9227841653705225 " " y[1] (numeric) = 0.9227841653706356 " " absolute error = 1.13020703906840940000000000000E-13 " " relative error = 1.22477940290035300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.259999999999752 " " y[1] (closed_form) = 0.9217079597582487 " " y[1] (numeric) = 0.9217079597583614 " " absolute error = 1.12687636999453390000000000000E-13 " " relative error = 1.222595897175606500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.269999999999751 " " y[1] (closed_form) = 0.9205348589626041 " " y[1] (numeric) = 0.9205348589627167 " " absolute error = 1.12576614696990870000000000000E-13 " " relative error = 1.222947872108384900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.27999999999975 " " y[1] (closed_form) = 0.9192645833429718 " " y[1] (numeric) = 0.9192645833430845 " " absolute error = 1.12687636999453390000000000000E-13 " " relative error = 1.225845518704274400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2899999999997487 " " y[1] (closed_form) = 0.9178968634883427 " " y[1] (numeric) = 0.9178968634884549 " " absolute error = 1.12243547789603330000000000000E-13 " " relative error = 1.222833983363195600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2999999999997476 " " y[1] (closed_form) = 0.916431440283899 " " y[1] (numeric) = 0.916431440284011 " " absolute error = 1.1202150318467830000000000000E-13 " " relative error = 1.222366434198017500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3099999999997465 " " y[1] (closed_form) = 0.9148680649765146 " " y[1] (numeric) = 0.9148680649766266 " " absolute error = 1.1202150318467830000000000000E-13 " " relative error = 1.224455279106872900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3199999999997454 " " y[1] (closed_form) = 0.9132064992391594 " " y[1] (numeric) = 0.9132064992392714 " " absolute error = 1.1202150318467830000000000000E-13 " " relative error = 1.226683157402069800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3299999999997443 " " y[1] (closed_form) = 0.9114465152341975 " " y[1] (numeric) = 0.9114465152343092 " " absolute error = 1.11688436277290750000000000000E-13 " " relative error = 1.225397589551288600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.339999999999743 " " y[1] (closed_form) = 0.9095878956755692 " " y[1] (numeric) = 0.9095878956756807 " " absolute error = 1.11466391672365720000000000000E-13 " " relative error = 1.225460367297185700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.349999999999742 " " y[1] (closed_form) = 0.9076304338898479 " " y[1] (numeric) = 0.9076304338899595 " " absolute error = 1.11577413974828230000000000000E-13 " " relative error = 1.229326494668528500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.359999999999741 " " y[1] (closed_form) = 0.905573933876161 " " y[1] (numeric) = 0.9055739338762722 " " absolute error = 1.11133324764978170000000000000E-13 " " relative error = 1.227214262774660200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.36999999999974 " " y[1] (closed_form) = 0.9034182103649628 " " y[1] (numeric) = 0.9034182103650736 " " absolute error = 1.10800257857590620000000000000E-13 " " relative error = 1.226455882628595100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3799999999997388 " " y[1] (closed_form) = 0.9011630888756534 " " y[1] (numeric) = 0.9011630888757639 " " absolute error = 1.10467190950203080000000000000E-13 " " relative error = 1.225829068165993800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3899999999997377 " " y[1] (closed_form) = 0.8988084057730314 " " y[1] (numeric) = 0.8988084057731418 " " absolute error = 1.10356168647740560000000000000E-13 " " relative error = 1.22780525792732600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3999999999997366 " " y[1] (closed_form) = 0.8963540083225714 " " y[1] (numeric) = 0.8963540083226816 " " absolute error = 1.10245146345278040000000000000E-13 " " relative error = 1.229928636695559500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4099999999997355 " " y[1] (closed_form) = 0.8937997547445174 " " y[1] (numeric) = 0.8937997547446271 " " absolute error = 1.09690034832965470000000000000E-13 " " relative error = 1.227232769428529400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4199999999997344 " " y[1] (closed_form) = 0.8911455142667811 " " y[1] (numeric) = 0.8911455142668906 " " absolute error = 1.09467990228040430000000000000E-13 " " relative error = 1.228396355875827800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4299999999997333 " " y[1] (closed_form) = 0.8883911671766397 " " y[1] (numeric) = 0.8883911671767488 " " absolute error = 1.09134923320652890000000000000E-13 " " relative error = 1.228455745091322800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.439999999999732 " " y[1] (closed_form) = 0.8855366048712188 " " y[1] (numeric) = 0.8855366048713276 " " absolute error = 1.08801856413265340000000000000E-13 " " relative error = 1.228654533474515100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.449999999999731 " " y[1] (closed_form) = 0.8825817299067567 " " y[1] (numeric) = 0.8825817299068655 " " absolute error = 1.08801856413265340000000000000E-13 " " relative error = 1.232768056786764500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.45999999999973 " " y[1] (closed_form) = 0.879526456046638 " " y[1] (numeric) = 0.8795264560467465 " " absolute error = 1.0846878950587780000000000000E-13 " " relative error = 1.233263522207523900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.469999999999729 " " y[1] (closed_form) = 0.8763707083081886 " " y[1] (numeric) = 0.876370708308297 " " absolute error = 1.08357767203415280000000000000E-13 " " relative error = 1.236437573462458400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4799999999997278 " " y[1] (closed_form) = 0.8731144230082252 " " y[1] (numeric) = 0.873114423008333 " " absolute error = 1.0780265569110270000000000000E-13 " " relative error = 1.234691042208188900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4899999999997267 " " y[1] (closed_form) = 0.869757547807347 " " y[1] (numeric) = 0.8697575478074545 " " absolute error = 1.07469588783715150000000000000E-13 " " relative error = 1.235626975065008300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4999999999997256 " " y[1] (closed_form) = 0.8663000417529685 " " y[1] (numeric) = 0.8663000417530757 " " absolute error = 1.07247544178790120000000000000E-13 " " relative error = 1.23799537123158210000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5099999999997245 " " y[1] (closed_form) = 0.862741875321076 " " y[1] (numeric) = 0.8627418753211825 " " absolute error = 1.06470388061552510000000000000E-13 " " relative error = 1.234093198755754800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5199999999997234 " " y[1] (closed_form) = 0.859083030456707 " " y[1] (numeric) = 0.8590830304568131 " " absolute error = 1.06137321154164970000000000000E-13 " " relative error = 1.235472211547934800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5299999999997222 " " y[1] (closed_form) = 0.8553235006131434 " " y[1] (numeric) = 0.8553235006132491 " " absolute error = 1.0569323194431490000000000000E-13 " " relative error = 1.235710603865649800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.539999999999721 " " y[1] (closed_form) = 0.8514632907898081 " " y[1] (numeric) = 0.8514632907899132 " " absolute error = 1.05138120432002320000000000000E-13 " " relative error = 1.234793344226001200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.54999999999972 " " y[1] (closed_form) = 0.847502417568859 " " y[1] (numeric) = 0.8475024175689638 " " absolute error = 1.04805053524614780000000000000E-13 " " relative error = 1.236634272091612500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.559999999999719 " " y[1] (closed_form) = 0.8434409091504755 " " y[1] (numeric) = 0.8434409091505797 " " absolute error = 1.04138919709839680000000000000E-13 " " relative error = 1.234691352767436100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.569999999999718 " " y[1] (closed_form) = 0.8392788053868254 " " y[1] (numeric) = 0.8392788053869289 " " absolute error = 1.03472785895064590000000000000E-13 " " relative error = 1.232877385094620200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5799999999997167 " " y[1] (closed_form) = 0.8350161578147094 " " y[1] (numeric) = 0.8350161578148125 " " absolute error = 1.03139718987677040000000000000E-13 " " relative error = 1.235182313808157500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5899999999997156 " " y[1] (closed_form) = 0.8306530296868746 " " y[1] (numeric) = 0.8306530296869771 " " absolute error = 1.02473585172901950000000000000E-13 " " relative error = 1.233650892858726800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5999999999997145 " " y[1] (closed_form) = 0.8261894960019884 " " y[1] (numeric) = 0.8261894960020906 " " absolute error = 1.0214051826551440000000000000E-13 " " relative error = 1.236284396736854500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6099999999997134 " " y[1] (closed_form) = 0.8216256435332714 " " y[1] (numeric) = 0.8216256435333732 " " absolute error = 1.01807451358126850000000000000E-13 " " relative error = 1.239097783271709600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6199999999997123 " " y[1] (closed_form) = 0.8169615708557761 " " y[1] (numeric) = 0.8169615708558774 " " absolute error = 1.01252339845814280000000000000E-13 " " relative error = 1.239377021611326700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6299999999997112 " " y[1] (closed_form) = 0.8121973883723104 " " y[1] (numeric) = 0.8121973883724111 " " absolute error = 1.0069722833350170000000000000E-13 " " relative error = 1.239812264544517300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.63999999999971 " " y[1] (closed_form) = 0.8073332183379964 " " y[1] (numeric) = 0.8073332183380967 " " absolute error = 1.00253139123651640000000000000E-13 " " relative error = 1.241781421183636600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.649999999999709 " " y[1] (closed_form) = 0.802369194883462 " " y[1] (numeric) = 0.8023691948835618 " " absolute error = 9.98090499138015700000000000000E-14 " " relative error = 1.24392923544750600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.659999999999708 " " y[1] (closed_form) = 0.7973054640366545 " " y[1] (numeric) = 0.797305464036754 " " absolute error = 9.94759830064140300000000000000E-14 " " relative error = 1.247652091869281700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.669999999999707 " " y[1] (closed_form) = 0.7921421837432758 " " y[1] (numeric) = 0.7921421837433746 " " absolute error = 9.88098491916389300000000000000E-14 " " relative error = 1.247375171016799000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6799999999997057 " " y[1] (closed_form) = 0.786879523885829 " " y[1] (numeric) = 0.7868795238859272 " " absolute error = 9.81437153768638400000000000000E-14 " " relative error = 1.247252119259667500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6899999999997046 " " y[1] (closed_form) = 0.7815176663012745 " " y[1] (numeric) = 0.7815176663013723 " " absolute error = 9.78106484694762900000000000000E-14 " " relative error = 1.251547504132432000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6999999999997035 " " y[1] (closed_form) = 0.7760568047972891 " " y[1] (numeric) = 0.7760568047973864 " " absolute error = 9.72555369571637100000000000000E-14 " " relative error = 1.253201265113157200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7099999999997024 " " y[1] (closed_form) = 0.770497145167122 " " y[1] (numeric) = 0.7704971451672185 " " absolute error = 9.6478380839926100000000000000E-14 " " relative error = 1.252157538091848400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7199999999997013 " " y[1] (closed_form) = 0.764838905203044 " " y[1] (numeric) = 0.7648389052031397 " " absolute error = 9.5701224722688490000000000000E-14 " " relative error = 1.251259893706406200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7299999999997 " " y[1] (closed_form) = 0.7590823147083854 " " y[1] (numeric) = 0.7590823147084804 " " absolute error = 9.5035090907913400000000000000E-14 " " relative error = 1.251973456191280000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.739999999999699 " " y[1] (closed_form) = 0.7532276155081571 " " y[1] (numeric) = 0.7532276155082516 " " absolute error = 9.44799793956008200000000000000E-14 " " relative error = 1.254335043622383500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.749999999999698 " " y[1] (closed_form) = 0.7472750614582513 " " y[1] (numeric) = 0.7472750614583452 " " absolute error = 9.39248678832882400000000000000E-14 " " relative error = 1.256898198904174700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.759999999999697 " " y[1] (closed_form) = 0.741224918453216 " " y[1] (numeric) = 0.7412249184533094 " " absolute error = 9.33697563709756700000000000000E-14 " " relative error = 1.259668341504480700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.769999999999696 " " y[1] (closed_form) = 0.7350774644326021 " " y[1] (numeric) = 0.7350774644326946 " " absolute error = 9.24815779512755400000000000000E-14 " " relative error = 1.258120163194786600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7799999999996947 " " y[1] (closed_form) = 0.7288329893858749 " " y[1] (numeric) = 0.7288329893859669 " " absolute error = 9.19264664389629600000000000000E-14 " " relative error = 1.261283006912482200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7899999999996936 " " y[1] (closed_form) = 0.722491795355892 " " y[1] (numeric) = 0.7224917953559834 " " absolute error = 9.13713549266503800000000000000E-14 " " relative error = 1.264669792985563300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7999999999996925 " " y[1] (closed_form) = 0.7160541964409373 " " y[1] (numeric) = 0.7160541964410279 " " absolute error = 9.05941988094127700000000000000E-14 " " relative error = 1.265186340080129700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8099999999996914 " " y[1] (closed_form) = 0.7095205187953141 " " y[1] (numeric) = 0.7095205187954038 " " absolute error = 8.97060203897126500000000000000E-14 " " relative error = 1.264318902884209500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8199999999996903 " " y[1] (closed_form) = 0.7028911006284881 " " y[1] (numeric) = 0.7028911006285772 " " absolute error = 8.90398865749375500000000000000E-14 " " relative error = 1.266766452090840000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.829999999999689 " " y[1] (closed_form) = 0.6961662922027843 " " y[1] (numeric) = 0.6961662922028723 " " absolute error = 8.80406858527749100000000000000E-14 " " relative error = 1.264650225655134200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.839999999999688 " " y[1] (closed_form) = 0.689346455829625 " " y[1] (numeric) = 0.6893464558297123 " " absolute error = 8.73745520379998200000000000000E-14 " " relative error = 1.267498386320779500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.849999999999687 " " y[1] (closed_form) = 0.682431965864318 " " y[1] (numeric) = 0.6824319658644046 " " absolute error = 8.65973959207622100000000000000E-14 " " relative error = 1.268952807787723500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.859999999999686 " " y[1] (closed_form) = 0.6754232086993812 " " y[1] (numeric) = 0.6754232086994671 " " absolute error = 8.59312621059871200000000000000E-14 " " relative error = 1.272258059823845600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.869999999999685 " " y[1] (closed_form) = 0.6683205827564098 " " y[1] (numeric) = 0.668320582756495 " " absolute error = 8.51541059887495100000000000000E-14 " " relative error = 1.274150582607248000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8799999999996837 " " y[1] (closed_form) = 0.6611244984764788 " " y[1] (numeric) = 0.6611244984765632 " " absolute error = 8.4376949871511900000000000000E-14 " " relative error = 1.276264153967270000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8899999999996826 " " y[1] (closed_form) = 0.6538353783090801 " " y[1] (numeric) = 0.6538353783091635 " " absolute error = 8.33777491493492600000000000000E-14 " " relative error = 1.275210120397233200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8999999999996815 " " y[1] (closed_form) = 0.6464536566995932 " " y[1] (numeric) = 0.6464536566996759 " " absolute error = 8.27116153345741600000000000000E-14 " " relative error = 1.279467050381466500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9099999999996804 " " y[1] (closed_form) = 0.638979780075287 " " y[1] (numeric) = 0.6389797800753692 " " absolute error = 8.21565038222615800000000000000E-14 " " relative error = 1.285744970092505800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9199999999996793 " " y[1] (closed_form) = 0.631414206829851 " " y[1] (numeric) = 0.6314142068299323 " " absolute error = 8.12683254025614600000000000000E-14 " " relative error = 1.28708420753765300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.929999999999678 " " y[1] (closed_form) = 0.6237574073064549 " " y[1] (numeric) = 0.6237574073065354 " " absolute error = 8.04911692853238500000000000000E-14 " " relative error = 1.290424263383187000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.939999999999677 " " y[1] (closed_form) = 0.616009863779335 " " y[1] (numeric) = 0.6160098637794145 " " absolute error = 7.94919685631612100000000000000E-14 " " relative error = 1.290433371885690600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.949999999999676 " " y[1] (closed_form) = 0.6081720704339063 " " y[1] (numeric) = 0.608172070433985 " " absolute error = 7.8714812445923600000000000000E-14 " " relative error = 1.294285224077517000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.959999999999675 " " y[1] (closed_form) = 0.6002445333454024 " " y[1] (numeric) = 0.6002445333454803 " " absolute error = 7.79376563286859900000000000000E-14 " " relative error = 1.298431755709765800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.969999999999674 " " y[1] (closed_form) = 0.5922277704560356 " " y[1] (numeric) = 0.5922277704561124 " " absolute error = 7.68274333040608300000000000000E-14 " " relative error = 1.297261579694263300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9799999999996727 " " y[1] (closed_form) = 0.5841223115506847 " " y[1] (numeric) = 0.5841223115507607 " " absolute error = 7.59392548843607100000000000000E-14 " " relative error = 1.300057426033989200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9899999999996716 " " y[1] (closed_form) = 0.575928698231105 " " y[1] (numeric) = 0.5759286982311799 " " absolute error = 7.48290318597355500000000000000E-14 " " relative error = 1.299275970958971600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9999999999996705 " " y[1] (closed_form) = 0.5676474838886618 " " y[1] (numeric) = 0.5676474838887358 " " absolute error = 7.39408534400354300000000000000E-14 " " relative error = 1.302584007481272800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.009999999999674 " " y[1] (closed_form) = 0.559279233675584 " " y[1] (numeric) = 0.5592792336756609 " " absolute error = 7.69384556065233500000000000000E-14 " " relative error = 1.375671596116374900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.019999999999677 " " y[1] (closed_form) = 0.5508245244747572 " " y[1] (numeric) = 0.5508245244748369 " " absolute error = 7.97140131680862400000000000000E-14 " " relative error = 1.447176180909848500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0299999999996805 " " y[1] (closed_form) = 0.5422839448680176 " " y[1] (numeric) = 0.5422839448680998 " " absolute error = 8.2267526124724100000000000000E-14 " " relative error = 1.51705627472977420000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.039999999999684 " " y[1] (closed_form) = 0.5336580951029856 " " y[1] (numeric) = 0.5336580951030708 " " absolute error = 8.52651282912120200000000000000E-14 " " relative error = 1.597748241310900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.049999999999687 " " y[1] (closed_form) = 0.5249475870584223 " " y[1] (numeric) = 0.5249475870585106 " " absolute error = 8.83737527601624600000000000000E-14 " " relative error = 1.683477644984911800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0599999999996905 " " y[1] (closed_form) = 0.5161530442081118 " " y[1] (numeric) = 0.5161530442082033 " " absolute error = 9.1482377229112900000000000000E-14 " " relative error = 1.772388601707585700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.069999999999694 " " y[1] (closed_form) = 0.5072751015832709 " " y[1] (numeric) = 0.5072751015833652 " " absolute error = 9.42579347906757900000000000000E-14 " " relative error = 1.85812263398074580000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.079999999999697 " " y[1] (closed_form) = 0.4983144057334876 " " y[1] (numeric) = 0.4983144057335848 " " absolute error = 9.72000258059324600000000000000E-14 " " relative error = 1.950576276494758500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0899999999997005 " " y[1] (closed_form) = 0.4892716146861906 " " y[1] (numeric) = 0.48927161468629093 " " absolute error = 1.00308650274882900000000000000E-13 " " relative error = 2.050162880166651600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.099999999999704 " " y[1] (closed_form) = 0.48014739790465044 " " y[1] (numeric) = 0.48014739790475386 " " absolute error = 1.03417274743833330000000000000E-13 " " relative error = 2.153865150475528500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.109999999999707 " " y[1] (closed_form) = 0.47094243624451404 " " y[1] (numeric) = 0.47094243624462057 " " absolute error = 1.06525899212783770000000000000E-13 " " relative error = 2.261972823308608400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.119999999999710 " " y[1] (closed_form) = 0.4616574219088755 " " y[1] (numeric) = 0.4616574219089852 " " absolute error = 1.09690034832965470000000000000E-13 " " relative error = 2.376005012102170600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.129999999999714 " " y[1] (closed_form) = 0.45229305840188494 " " y[1] (numeric) = 0.45229305840199774 " " absolute error = 1.1279865930191590000000000000E-13 " " relative error = 2.493928597986323200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.139999999999717 " " y[1] (closed_form) = 0.4428500604808968 " " y[1] (numeric) = 0.4428500604810129 " " absolute error = 1.16073817224560120000000000000E-13 " " relative error = 2.62106359652551470000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.149999999999720 " " y[1] (closed_form) = 0.4333291541071626 " " y[1] (numeric) = 0.4333291541072819 " " absolute error = 1.19293463995973070000000000000E-13 " " relative error = 2.75295264270337300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.159999999999724 " " y[1] (closed_form) = 0.42373107639506735 " " y[1] (numeric) = 0.4237310763951898 " " absolute error = 1.22457599616154770000000000000E-13 " " relative error = 2.889983917582220000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.169999999999727 " " y[1] (closed_form) = 0.4140565755599158 " " y[1] (numeric) = 0.4140565755600416 " " absolute error = 1.25788268690030240000000000000E-13 " " relative error = 3.03794882426225600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.179999999999730 " " y[1] (closed_form) = 0.4043064108642702 " " y[1] (numeric) = 0.40430641086439917 " " absolute error = 1.28952404310211930000000000000E-13 " " relative error = 3.18947216381148540000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.189999999999734 " " y[1] (closed_form) = 0.39448135256284167 " " y[1] (numeric) = 0.39448135256297384 " " absolute error = 1.32172051081624900000000000000E-13 " " relative error = 3.35052722322456600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.199999999999737 " " y[1] (closed_form) = 0.38458218184594095 " " y[1] (numeric) = 0.38458218184607657 " " absolute error = 1.35613742457962870000000000000E-13 " " relative error = 3.52626171620941400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.209999999999740 " " y[1] (closed_form) = 0.37460969078149076 " " y[1] (numeric) = 0.37460969078162965 " " absolute error = 1.38888900380607080000000000000E-13 " " relative error = 3.70756293279184700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.219999999999744 " " y[1] (closed_form) = 0.36456468225560323 " " y[1] (numeric) = 0.3645646822557455 " " absolute error = 1.4227508060571380000000000000E-13 " " relative error = 3.90260185724633700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.229999999999747 " " y[1] (closed_form) = 0.3544479699117277 " " y[1] (numeric) = 0.3544479699118733 " " absolute error = 1.45550238528358020000000000000E-13 " " relative error = 4.10639221786503900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.239999999999750 " " y[1] (closed_form) = 0.34426037808837123 " " y[1] (numeric) = 0.34426037808852017 " " absolute error = 1.48936418753464750000000000000E-13 " " relative error = 4.326272444725920400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.249999999999754 " " y[1] (closed_form) = 0.3340027417553982 " " y[1] (numeric) = 0.33400274175555056 " " absolute error = 1.52378110129802740000000000000E-13 " " relative error = 4.56218141590569700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.259999999999757 " " y[1] (closed_form) = 0.32367590644891175 " " y[1] (numeric) = 0.3236759064490676 " " absolute error = 1.55819801506140720000000000000E-13 " " relative error = 4.814068591501264000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.269999999999760 " " y[1] (closed_form) = 0.3132807282047225 " " y[1] (numeric) = 0.3132807282048818 " " absolute error = 1.5926149288247870000000000000E-13 " " relative error = 5.08366709293412300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.279999999999764 " " y[1] (closed_form) = 0.30281807349041 " " y[1] (numeric) = 0.3028180734905727 " " absolute error = 1.6270318425881670000000000000E-13 " " relative error = 5.37296807893368200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.289999999999767 " " y[1] (closed_form) = 0.29228881913597965 " " y[1] (numeric) = 0.29228881913614585 " " absolute error = 1.66200386786385930000000000000E-13 " " relative error = 5.68616983973874100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.299999999999770 " " y[1] (closed_form) = 0.28169385226312404 " " y[1] (numeric) = 0.28169385226329385 " " absolute error = 1.6980861161641770000000000000E-13 " " relative error = 6.02812628859941100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.309999999999774 " " y[1] (closed_form) = 0.2710340702130905 " " y[1] (numeric) = 0.2710340702132639 " " absolute error = 1.73416836446449450000000000000E-13 " " relative error = 6.39834085471641600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.319999999999777 " " y[1] (closed_form) = 0.2603103804731621 " " y[1] (numeric) = 0.260310380473339 " " absolute error = 1.7691403897401870000000000000E-13 " " relative error = 6.79627292052068200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.329999999999780 " " y[1] (closed_form) = 0.2495237006017575 " " y[1] (numeric) = 0.24952370060193801 " " absolute error = 1.80522263804050450000000000000E-13 " " relative error = 7.23467403572079600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.339999999999784 " " y[1] (closed_form) = 0.2386749581521569 " " y[1] (numeric) = 0.238674958152341 " " absolute error = 1.84102733058466580000000000000E-13 " " relative error = 7.71353368965921700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.349999999999787 " " y[1] (closed_form) = 0.22776509059485678 " " y[1] (numeric) = 0.2277650905950445 " " absolute error = 1.87710957888498340000000000000E-13 " " relative error = 8.24142792902333700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.359999999999790 " " y[1] (closed_form) = 0.2167950452385637 " " y[1] (numeric) = 0.2167950452387551 " " absolute error = 1.914024494453770000000000000E-13 " " relative error = 8.82872803826100300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.369999999999794 " " y[1] (closed_form) = 0.20576577914983063 " " y[1] (numeric) = 0.20576577915002578 " " absolute error = 1.9514945215348690000000000000E-13 " " relative error = 9.48405769704721700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.379999999999797 " " y[1] (closed_form) = 0.19467825907134426 " " y[1] (numeric) = 0.19467825907154307 " " absolute error = 1.9881318813474990000000000000E-13 " " relative error = 1.02123980912470730000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.389999999999800 " " y[1] (closed_form) = 0.18353346133886833 " " y[1] (numeric) = 0.18353346133907086 " " absolute error = 2.02532435267244180000000000000E-13 " " relative error = 1.1035177661325579000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.399999999999804 " " y[1] (closed_form) = 0.172332371796852 " " y[1] (numeric) = 0.17233237179705832 " " absolute error = 2.06307193550969710000000000000E-13 " " relative error = 1.19714706761053420000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.409999999999807 " " y[1] (closed_form) = 0.16107598571270848 " " y[1] (numeric) = 0.16107598571291848 " " absolute error = 2.09998685107848360000000000000E-13 " " relative error = 1.3037243520731720000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.419999999999810 " " y[1] (closed_form) = 0.1497653076897721 " " y[1] (numeric) = 0.14976530768998586 " " absolute error = 2.1377344339157390000000000000E-13 " " relative error = 1.42738960503716930000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.429999999999814 " " y[1] (closed_form) = 0.13840135157894154 " " y[1] (numeric) = 0.13840135157915912 " " absolute error = 2.17575957250915050000000000000E-13 " " relative error = 1.5720652635882232000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.439999999999817 " " y[1] (closed_form) = 0.1269851403890161 " " y[1] (numeric) = 0.12698514038923753 " " absolute error = 2.21433982261487470000000000000E-13 " " relative error = 1.74377869397261380000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.449999999999820 " " y[1] (closed_form) = 0.11551770619573355 " " y[1] (numeric) = 0.11551770619595876 " " absolute error = 2.252087405452130000000000000E-13 " " relative error = 1.94956035712498170000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.459999999999824 " " y[1] (closed_form) = 0.10400009004951645 " " y[1] (numeric) = 0.10400009004974552 " " absolute error = 2.2906676555578542000000000000E-13 " " relative error = 2.20256314630806860000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4699999999998274 " " y[1] (closed_form) = 9.24333418819366500E-2 " " y[1] (numeric) = 9.24333418821696200E-2 " " absolute error = 2.3296642392978129000000000000E-13 " " relative error = 2.520372185908250000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.479999999999830 " " y[1] (closed_form) = 8.08185204109048800E-2 " " y[1] (numeric) = 8.08185204111416700E-2 " " absolute error = 2.36782815576930260000000000000E-13 " " relative error = 2.9298088405115250000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.489999999999834 " " y[1] (closed_form) = 6.91566930445942200E-2 " " y[1] (numeric) = 6.91566930448349200E-2 " " absolute error = 2.40696351738733940000000000000E-13 " " relative error = 3.48044912418709830000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4999999999998375 " " y[1] (closed_form) = 5.7448935784106900E-2 " " y[1] (numeric) = 5.74489357843515100E-2 " " absolute error = 2.4460988790053761000000000000E-13 " " relative error = 4.25786630443045270000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.509999999999840 " " y[1] (closed_form) = 4.56963331248919700E-2 " " y[1] (numeric) = 4.56963331251405200E-2 " " absolute error = 2.4855117963795692000000000000E-13 " " relative error = 5.4391930958364950000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.519999999999844 " " y[1] (closed_form) = 3.389997795692374400E-2 " " y[1] (numeric) = 3.38999779571762200E-2 " " absolute error = 2.5247165469366450000000000000E-13 " " relative error = 7.447546279070650000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5299999999998475 " " y[1] (closed_form) = 2.20609714636495700E-2 " " y[1] (numeric) = 2.20609714639060100E-2 " " absolute error = 2.56440702006699440000000000000E-13 " " relative error = 1.162417994281183000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.539999999999850 " " y[1] (closed_form) = 1.01804230197167290E-2 " " y[1] (numeric) = 1.018042301997712200E-2 " " absolute error = 2.6039240208497460000000000000E-13 " " relative error = 2.557775856471434000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.549999999999854 " " y[1] (closed_form) = -1.740549912512726000E-3 " " y[1] (numeric) = -1.7405499122483434000E-3 " " absolute error = 2.64382699760590260000000000000E-13 " " relative error = 1.518960748324172400000000E-8 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5599999999998575 " " y[1] (closed_form) = -1.370082188764890600E-2 " " y[1] (numeric) = -1.370082188738053800E-2 " " absolute error = 2.68368660627515960000000000000E-13 " " relative error = 1.9587778224417796000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.569999999999860 " " y[1] (closed_form) = -2.569925958315369000E-2 " " y[1] (numeric) = -2.569925958288132000E-2 " " absolute error = 2.7236893296311850000000000000E-13 " " relative error = 1.0598318293250016000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.579999999999864 " " y[1] (closed_form) = -3.77347219064025630E-2 " " y[1] (numeric) = -3.77347219061261400E-2 " " absolute error = 2.76424716449952260000000000000E-13 " " relative error = 7.3254737940191480000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5899999999998675 " " y[1] (closed_form) = -4.980606010291873700E-2 " " y[1] (numeric) = -4.980606010263831700E-2 " " absolute error = 2.8042151933860280000000000000E-13 " " relative error = 5.6302690628237330000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.599999999999870 " " y[1] (closed_form) = -6.19121178657698300E-2 " " y[1] (numeric) = -6.19121178654853400E-2 " " absolute error = 2.84494650060196360000000000000E-13 " " relative error = 4.59513678205940750000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.609999999999874 " " y[1] (closed_form) = -7.40517314461155900E-2 " " y[1] (numeric) = -7.40517314458270500E-2 " " absolute error = 2.88533086312270370000000000000E-13 " " relative error = 3.8963719102533630000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.6199999999998775 " " y[1] (closed_form) = -8.62237297648974300E-2 " " y[1] (numeric) = -8.62237297646048200E-2 " " absolute error = 2.92599278139960000000000000E-13 " " relative error = 3.39348899586897960000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.629999999999880 " " y[1] (closed_form) = -9.84269345256580000E-2 " " y[1] (numeric) = -9.84269345253613400E-2 " " absolute error = 2.96665469967649640000000000000E-13 " " relative error = 3.0140679621624780000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.639999999999884 " " y[1] (closed_form) = -0.11066016032848074 " " y[1] (numeric) = -0.11066016032817998 " " absolute error = 3.0075941737095490000000000000E-13 " " relative error = 2.7178653679715310000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.649999999999888 " " y[1] (closed_form) = -0.12292221478503766 " " y[1] (numeric) = -0.12292221478473281 " " absolute error = 3.04853364774260170000000000000E-13 " " relative error = 2.48005102501104250000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.659999999999891 " " y[1] (closed_form) = -0.13521189863473498 " " y[1] (numeric) = -0.1352118986344261 " " absolute error = 3.0889180102633420000000000000E-13 " " relative error = 2.28450161668672880000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.669999999999894 " " y[1] (closed_form) = -0.1475280058619447 " " y[1] (numeric) = -0.1475280058616317 " " absolute error = 3.12999626217447260000000000000E-13 " " relative error = 2.12162853004567360000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.679999999999898 " " y[1] (closed_form) = -0.15986932381431088 " " y[1] (numeric) = -0.1598693238139937 " " absolute error = 3.1716296255979160000000000000E-13 " " relative error = 1.98388880988937060000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.689999999999901 " " y[1] (closed_form) = -0.17223463332211897 " " y[1] (numeric) = -0.17223463332179767 " " absolute error = 3.2129854332652030000000000000E-13 " " relative error = 1.86547001104950260000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.699999999999904 " " y[1] (closed_form) = -0.18462270881871698 " " y[1] (numeric) = -0.18462270881839152 " " absolute error = 3.25461879668864640000000000000E-13 " " relative error = 1.76284857779028220000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.709999999999908 " " y[1] (closed_form) = -0.1970323184619752 " " y[1] (numeric) = -0.19703231846164562 " " absolute error = 3.2956970485997770000000000000E-13 " " relative error = 1.67266825784004870000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.719999999999911 " " y[1] (closed_form) = -0.2094622242567744 " " y[1] (numeric) = -0.20946222425644062 " " absolute error = 3.3378855235355330000000000000E-13 " " relative error = 1.59355011882414880000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.729999999999914 " " y[1] (closed_form) = -0.22191118217850841 " " y[1] (numeric) = -0.22191118217817046 " " absolute error = 3.37951888695897650000000000000E-13 " " relative error = 1.52291509322880570000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.739999999999918 " " y[1] (closed_form) = -0.23437794229759001 " " y[1] (numeric) = -0.23437794229724795 " " absolute error = 3.42059713887010730000000000000E-13 " " relative error = 1.459436457773389800000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.749999999999921 " " y[1] (closed_form) = -0.24686124890494754 " " y[1] (numeric) = -0.2468612489046013 " " absolute error = 3.4625080580497070000000000000E-13 " " relative error = 1.40261303603099100000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.759999999999924 " " y[1] (closed_form) = -0.25935984063849876 " " y[1] (numeric) = -0.2593598406381483 " " absolute error = 3.50441897722930660000000000000E-13 " " relative error = 1.35118026314406950000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.769999999999928 " " y[1] (closed_form) = -0.2718724506105904 " " y[1] (numeric) = -0.2718724506102356 " " absolute error = 3.54771767518968800000000000000E-13 " " relative error = 1.30491988696242370000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.779999999999931 " " y[1] (closed_form) = -0.2843978065363895 " " y[1] (numeric) = -0.2843978065360305 " " absolute error = 3.5904612616377560000000000000E-13 " " relative error = 1.26247853503692410000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.789999999999934 " " y[1] (closed_form) = -0.2969346308632147 " " y[1] (numeric) = -0.2969346308628515 " " absolute error = 3.63209462506119960000000000000E-13 " " relative error = 1.22319670646107730000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.799999999999938 " " y[1] (closed_form) = -0.30948164090079255 " " y[1] (numeric) = -0.3094816409004251 " " absolute error = 3.67428309999695560000000000000E-13 " " relative error = 1.18723782428657330000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.809999999999941 " " y[1] (closed_form) = -0.3220375489524279 " " y[1] (numeric) = -0.32203754895205633 " " absolute error = 3.7159164634203990000000000000E-13 " " relative error = 1.15387676856568120000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.819999999999944 " " y[1] (closed_form) = -0.3346010624470726 " " y[1] (numeric) = -0.33460106244669685 " " absolute error = 3.75754982684384230000000000000E-13 " " relative error = 1.12299399152033880000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.829999999999948 " " y[1] (closed_form) = -0.3471708840722808 " " y[1] (numeric) = -0.34717088407190083 " " absolute error = 3.79973830177959800000000000000E-13 " " relative error = 1.09448645497255890000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.839999999999951 " " y[1] (closed_form) = -0.3597457119080363 " " y[1] (numeric) = -0.3597457119076521 " " absolute error = 3.8419267767153540000000000000E-13 " " relative error = 1.06795623951661910000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.849999999999954 " " y[1] (closed_form) = -0.37232423956143795 " " y[1] (numeric) = -0.37232423956104954 " " absolute error = 3.884115251651110000000000000E-13 " " relative error = 1.04320773104276620000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.859999999999958 " " y[1] (closed_form) = -0.38490515630223027 " " y[1] (numeric) = -0.38490515630183775 " " absolute error = 3.9251935035622410000000000000E-13 " " relative error = 1.01978200065476670000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.869999999999961 " " y[1] (closed_form) = -0.3974871471991637 " " y[1] (numeric) = -0.3974871471987671 " " absolute error = 3.96627175547337200000000000000E-13 " " relative error = 9.97836479348109400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.879999999999964 " " y[1] (closed_form) = -0.4100688932571722 " " y[1] (numeric) = -0.41006889325677137 " " absolute error = 4.00846023040912770000000000000E-13 " " relative error = 9.7750897381412590000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.889999999999968 " " y[1] (closed_form) = -0.42264907155535164 " " y[1] (numeric) = -0.4226490715549465 " " absolute error = 4.0512038168571960000000000000E-13 " " relative error = 9.58526609782611600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.899999999999971 " " y[1] (closed_form) = -0.4352263553857266 " " y[1] (numeric) = -0.4352263553853173 " " absolute error = 4.0933922917929520000000000000E-13 " " relative error = 9.40520315725162100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.909999999999974 " " y[1] (closed_form) = -0.4477994143927903 " " y[1] (numeric) = -0.44779941439237675 " " absolute error = 4.1355807667287080000000000000E-13 " " relative error = 9.23534206121394100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.919999999999978 " " y[1] (closed_form) = -0.4603669147138023 " " y[1] (numeric) = -0.46036691471338465 " " absolute error = 4.1766590186398390000000000000E-13 " " relative error = 9.0724569580252200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.929999999999981 " " y[1] (closed_form) = -0.472927519119831 " " y[1] (numeric) = -0.47292751911940906 " " absolute error = 4.21940260508790740000000000000E-13 " " relative error = 8.92188006513274900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.939999999999984 " " y[1] (closed_form) = -0.48547988715752344 " " y[1] (numeric) = -0.48547988715709733 " " absolute error = 4.2610359685113510000000000000E-13 " " relative error = 8.77695674162660800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.949999999999988 " " y[1] (closed_form) = -0.4980226752915906 " " y[1] (numeric) = -0.49802267529116034 " " absolute error = 4.3026693319347940000000000000E-13 " " relative error = 8.63950487679219800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.959999999999991 " " y[1] (closed_form) = -0.51055453704799 " " y[1] (numeric) = -0.5105545370475557 " " absolute error = 4.34319247233361240000000000000E-13 " " relative error = 8.50681397808314900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.969999999999994 " " y[1] (closed_form) = -0.5230741231577929 " " y[1] (numeric) = -0.5230741231573546 " " absolute error = 4.3831605012201180000000000000E-13 " " relative error = 8.37961640074837600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.979999999999998 " " y[1] (closed_form) = -0.5355800817017191 " " y[1] (numeric) = -0.5355800817012765 " " absolute error = 4.4264591991804990000000000000E-13 " " relative error = 8.26479428644198400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.990000000000001 " " y[1] (closed_form) = -0.5480710582553248 " " y[1] (numeric) = -0.5480710582548778 " " absolute error = 4.469757897140880000000000000E-13 " " relative error = 8.15543501123643700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " "Finished!" "diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) * sin ( x ) ; " Iterations = 4900 "Total Elapsed Time "= 1 Minutes 14 Seconds "Elapsed Time(since restart) "= 1 Minutes 14 Seconds "Time to Timeout "= 1 Minutes 45 Seconds Percent Done = 100.0204081632654 "%" (%o255) temp/diffeq.mult_lin_sin.max