(%i1) batch("temp/diffeq.lin_sin_cos.max") read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.lin_sin_cos.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_tmp6,[30],convfloat) (%i193) completearray(array_tmp7_g,[30],convfloat) (%i194) completearray(array_tmp7,[30],convfloat) (%i195) completearray(array_tmp8,[30],convfloat) (%i196) completearray(array_m1,[30],convfloat) (%i197) completearray(array_y_higher,[2,30],convfloat) (%i198) completearray(array_y_higher_work,[2,30],convfloat) (%i199) completearray(array_y_higher_work2,[2,30],convfloat) (%i200) completearray(array_y_set_initial,[2,30],convfloat) (%i201) completearray(array_given_rad_poles,[2,3],convfloat) (%i202) completearray(array_given_ord_poles,[2,3],convfloat) (%i203) completearray(array_rad_test_poles,[2,4],convfloat) (%i204) completearray(array_ord_test_poles,[2,4],convfloat) (%i205) completearray(array_fact_2,[30,30],convfloat) (%i206) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%i207) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%i208) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%i209) 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)) (%i210) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%i211) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%i212) 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) (%i213) 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) (%i214) 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) (%i215) 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) (%i216) 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) (%i217) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%i218) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%i219) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%i220) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), printf(file,"~d",glob_min_good_digits), printf(file,"")),0) (%i221) log_revs(file,revs):=printf(file,revs) (%i222) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%i223) 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) (%i224) logstart(file):=(printf(file,""),0) (%i225) logend(file):=(printf(file,"~%"),0) (%i226) 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) (%i227) 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) (%i228) 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) (%i229) 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) (%i230) 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) (%i231) c(in_val):=(ret:in_val,ret) (%i232) 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) (%i233) 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) (%i234) 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) (%i235) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%i236) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret) (%i237) 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) (%i238) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret) (%i239) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret) (%i240) 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) (%i241) log10(x):=log(x)/glob_log_10 (%i242) c(x):=x (%i243) 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 (%i244) 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) (%i245) exact_soln_y(x):=block( c(2.0)*sin(c(1.5)*c(x)-c(2.0))/c(3.0) +c(-0.5)*cos(c(3.0)+c(2.0)*c(x))) c(2.0) sin(c(1.5) c(x) - c(2.0)) (%o245) exact_soln_y(x) := block(-------------------------------- c(3.0) + c(- 0.5) cos(c(3.0) + c(2.0) c(x))) (%i246) 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) (%i247) my_check_sign(x0,xf):=block([ret], if xf > x0 then ret:glob__1 else ret:glob__m1,ret) (%i248) 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) (%i249) 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) (%i250) 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)) (%i251) 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)) (%i252) 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(30) *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) (%i253) 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) (%i254) 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) (%i255) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:array_const_2D0[1]*array_x[1], array_tmp2[1]:array_const_3D0[1]+array_tmp1[1], array_tmp3[1]:sin(array_tmp2[1]), array_tmp3_g[1]:cos(array_tmp2[1]), array_tmp4[1]:array_tmp3[1]+array_const_0D0[1], array_tmp5[1]:array_const_1D5[1]*array_x[1], array_tmp6[1]:array_tmp5[1]-array_const_2D0[1], array_tmp7[1]:cos(array_tmp6[1]), array_tmp7_g[1]:sin(array_tmp6[1]), array_tmp8[1]:array_tmp7[1]+array_tmp4[1], if not array_y_set_initial[1,2] then (if 1 <= ats_max_terms then ( temporary :c(array_tmp8[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_2D0[1]*array_x[2], array_tmp2[2]:array_tmp1[2], array_tmp3[2]:array_tmp3_g[1]*array_tmp2[2]/c(1), array_tmp3_g[2]:neg(array_tmp3[1])*array_tmp2[2]/c(1), array_tmp4[2]:array_tmp3[2], array_tmp5[2]:array_const_1D5[1]*array_x[2], array_tmp6[2]:array_tmp5[2], array_tmp7[2]:neg(array_tmp7_g[1])*array_tmp6[2]/c(1), array_tmp7_g[2]:array_tmp7[1]*array_tmp6[2]/c(1), array_tmp8[2]:array_tmp7[2]+array_tmp4[2], if not array_y_set_initial[1,3] then (if 2 <= ats_max_terms then ( temporary :c(array_tmp8[2])*expt(glob_h,c(1)) *c(factorial_3(1,2)), if 3 <= ats_max_terms then (array_y[3]:temporary, array_y_higher[1,3]:temporary), temporary:c(temporary)*c(2)/c(glob_h), array_y_higher[2,2]:c(temporary),0)), kkk:3,array_tmp3[3]:array_tmp3_g[2]*array_tmp2[2]/c(2), array_tmp3_g[3]:neg(array_tmp3[2])*array_tmp2[2]/c(2), array_tmp4[3]:array_tmp3[3], array_tmp7[3]:neg(array_tmp7_g[2])*array_tmp6[2]/c(2), array_tmp7_g[3]:array_tmp7[2]*array_tmp6[2]/c(2), array_tmp8[3]:array_tmp7[3]+array_tmp4[3], if not array_y_set_initial[1,4] then (if 3 <= ats_max_terms then ( temporary :c(array_tmp8[3])*expt(glob_h,c(1)) *c(factorial_3(2,3)), if 4 <= ats_max_terms then (array_y[4]:temporary, array_y_higher[1,4]:temporary), temporary:c(temporary)*c(3)/c(glob_h), array_y_higher[2,3]:c(temporary),0)), kkk:4,array_tmp3[4]:array_tmp3_g[3]*array_tmp2[2]/c(3), array_tmp3_g[4]:neg(array_tmp3[3])*array_tmp2[2]/c(3), array_tmp4[4]:array_tmp3[4], array_tmp7[4]:neg(array_tmp7_g[3])*array_tmp6[2]/c(3), array_tmp7_g[4]:array_tmp7[3]*array_tmp6[2]/c(3), array_tmp8[4]:array_tmp7[4]+array_tmp4[4], if not array_y_set_initial[1,5] then (if 4 <= ats_max_terms then ( temporary :c(array_tmp8[4])*expt(glob_h,c(1)) *c(factorial_3(3,4)), if 5 <= ats_max_terms then (array_y[5]:temporary, array_y_higher[1,5]:temporary), temporary:c(temporary)*c(4)/c(glob_h), array_y_higher[2,4]:c(temporary),0)), kkk:5,array_tmp3[5]:array_tmp3_g[4]*array_tmp2[2]/c(4), array_tmp3_g[5]:neg(array_tmp3[4])*array_tmp2[2]/c(4), array_tmp4[5]:array_tmp3[5], array_tmp7[5]:neg(array_tmp7_g[4])*array_tmp6[2]/c(4), array_tmp7_g[5]:array_tmp7[4]*array_tmp6[2]/c(4), array_tmp8[5]:array_tmp7[5]+array_tmp4[5], if not array_y_set_initial[1,6] then (if 5 <= ats_max_terms then ( temporary :c(array_tmp8[5])*expt(glob_h,c(1)) *c(factorial_3(4,5)), if 6 <= ats_max_terms then (array_y[6]:temporary, array_y_higher[1,6]:temporary), temporary:c(temporary)*c(5)/c(glob_h), array_y_higher[2,5]:c(temporary),0)), kkk:6, while kkk <= ats_max_terms do (array_tmp3[kkk] :array_tmp3_g[kkk-1]*array_tmp2[2]/c(kkk-1), array_tmp3_g[kkk] :neg(array_tmp3[kkk-1])*array_tmp2[2]/c(kkk-1), array_tmp4[kkk]:array_tmp3[kkk], array_tmp7[kkk] :neg(array_tmp7_g[kkk-1])*array_tmp6[2] /c(kkk-1), array_tmp7_g[kkk] :array_tmp7[kkk-1]*array_tmp6[2]/c(kkk-1), array_tmp8[kkk]:array_tmp7[kkk]+array_tmp4[kkk], order_d:1, if order_d+kkk <= ats_max_terms then (if not array_y_set_initial[1,order_d+kkk] then ( temporary :c(array_tmp8[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) (%i256) exact_soln_y(x):=block( c(2.0)*sin(c(1.5)*c(x)-c(2.0))/c(3.0) +c(-0.5)*cos(c(3.0)+c(2.0)*c(x))) c(2.0) sin(c(1.5) c(x) - c(2.0)) (%o256) exact_soln_y(x) := block(-------------------------------- c(3.0) + c(- 0.5) cos(c(3.0) + c(2.0) c(x))) (%i257) 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_tmp6[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp7_g[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp7[term]:c(0.0),term:1+term), term:1, while term <= 30 do (array_tmp8[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_tmp6), zero_ats_ar(array_tmp7_g),zero_ats_ar(array_tmp7), zero_ats_ar(array_tmp8),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_2D0),array_const_2D0[1]:c(2.0), zero_ats_ar(array_const_3D0),array_const_3D0[1]:c(3.0), zero_ats_ar(array_const_1D5),array_const_1D5[1]:c(1.5), zero_ats_ar(array_m1),array_m1[1]:glob__m1,iiif:0, while iiif <= ats_max_terms do (jjjf:0, while jjjf <= ats_max_terms do (array_fact_1[iiif]:0, array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf), iiif:1+iiif),array_y_set_initial[1,1]:true, array_y_set_initial[1,2]:false, array_y_set_initial[1,3]:false, array_y_set_initial[1,4]:false, array_y_set_initial[1,5]:false, array_y_set_initial[1,6]:false, array_y_set_initial[1,7]:false, array_y_set_initial[1,8]:false, array_y_set_initial[1,9]:false, array_y_set_initial[1,10]:false, array_y_set_initial[1,11]:false, array_y_set_initial[1,12]:false, array_y_set_initial[1,13]:false, array_y_set_initial[1,14]:false, array_y_set_initial[1,15]:false, array_y_set_initial[1,16]:false, array_y_set_initial[1,17]:false, array_y_set_initial[1,18]:false, array_y_set_initial[1,19]:false, array_y_set_initial[1,20]:false, array_y_set_initial[1,21]:false, array_y_set_initial[1,22]:false, array_y_set_initial[1,23]:false, array_y_set_initial[1,24]:false, array_y_set_initial[1,25]:false, array_y_set_initial[1,26]:false, array_y_set_initial[1,27]:false, array_y_set_initial[1,28]:false, array_y_set_initial[1,29]:false, array_y_set_initial[1,30]:false,glob_log_10:log(10.0), glob_orig_start_sec:elapsed_time_seconds(), glob_display_flag:true,glob_no_eqs:1,glob_iter:-1, opt_iter:-1,glob_max_iter:50000,glob_max_hours:0.0, glob_max_minutes:15.0, omniout_str(always, "##############ECHO OF PROBLEM#################"), omniout_str(always, "##############temp/lin_sin_cospostode.ode#################"), omniout_str(always, "diff ( y , x , 1 ) = sin ( 2.0 * x + 3.0 ) + cos ( 1.5 * x - 2.0 ) ; "), omniout_str(always,"!"), omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(always,"Digits:32,"), omniout_str(always,"max_terms:30,"),omniout_str(always,"!"), omniout_str(always,"/* END FIRST INPUT BLOCK */"), omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(always,"x_start:c(0.1),"), omniout_str(always,"x_end:c(5.0),"), omniout_str(always, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(always,"glob_look_poles:true,"), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""),omniout_str(always,""), omniout_str(always,""), omniout_str(always,"glob_type_given_pole:3,"), omniout_str(always,"/* END SECOND INPUT BLOCK */"), omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"), omniout_str(always,"glob_desired_digits_correct:8,"), omniout_str(always,"glob_max_minutes:(3.0),"), omniout_str(always,"glob_subiter_method:3,"), omniout_str(always,"glob_max_iter:100000,"), omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"), omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"), omniout_str(always,"glob_look_poles:false,"), omniout_str(always,"glob_h:c(0.001),"), omniout_str(always,"glob_display_interval:c(0.01),"), omniout_str(always,"/* END OVERRIDE BLOCK */"), omniout_str(always,"!"), omniout_str(always,"/* BEGIN USER DEF BLOCK */"), omniout_str(always,"exact_soln_y (x) := (block("), omniout_str(always, " (c(-0.5)*cos(c(2.0)*c(x) + c(3.0)) + c(2.0)/c(3.0)*sin(c(1.5)*c(x)-c(2.0))) "), omniout_str(always,"));"), omniout_str(always,"/* END USER DEF BLOCK */"), omniout_str(always, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false, glob_small_float:glob__0,glob_smallish_float:glob__0, glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100), glob_almost_1:c(0.99),x_start:c(0.1),x_end:c(5.0), array_y_init[1+0]:exact_soln_y(x_start), glob_look_poles:true,glob_type_given_pole:3, glob_desired_digits_correct:8,glob_max_minutes:3.0, glob_subiter_method:3,glob_max_iter:100000, glob_upper_ratio_limit:c(1.000001), glob_lower_ratio_limit:c(0.999999),glob_look_poles:false, glob_h:c(0.001),glob_display_interval:c(0.01), glob_last_good_h:glob_h, glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes, glob_check_sign:c(my_check_sign(x_start,x_end)), glob__pi:3.141592654,glob_prec:1.0E-16, if glob_optimize then (omniout_str(always,"START of Optimize"), found_h:false,glob_min_pole_est:glob_larger_float, last_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float, glob_min_h:abs(glob_min_h)*glob_check_sign, glob_max_h:abs(glob_max_h)*glob_check_sign, glob_h:abs(glob_min_h)*glob_check_sign, glob_display_interval :c(abs(c(glob_display_interval)) *glob_check_sign), display_max:c(x_end)-c(x_start)/glob__10, if glob_display_interval > display_max then glob_display_interval:c(display_max), chk_data(),min_value:glob_larger_float, est_answer:est_size_answer(),opt_iter:1, est_needed_step_err :estimated_needed_step_error( x_start,x_end,glob_h,est_answer), omniout_float(always,"est_needed_step_err",32, est_needed_step_err,16,""), estimated_step_error:glob_small_float, while opt_iter <= 100 and not found_h do (omniout_int(always,"opt_iter",32,opt_iter, 4,""),array_x[1]:c(x_start), array_x[2]:c(glob_h), glob_next_display:c(x_start),order_diff:1, term_no:1, while term_no <= order_diff do ( array_y[term_no] :array_y_init[term_no] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no),rows:order_diff, r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < ats_max_terms then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h, c(term_no-1)) /c( factorial_1( term_no-1)), term_no:1+term_no), r_order:1+r_order),atomall(), if glob_check_sign*glob_min_h >= glob_check_sign*glob_h then ( omniout_str(always, "SETTING H FOR MIN H"), glob_h:glob_check_sign*abs(glob_min_h), glob_h_reason:1,found_h:true), if glob_check_sign*glob_display_interval <= glob_check_sign*glob_h then ( omniout_str(always, "SETTING H FOR DISPLAY INTERVAL"), glob_h_reason:2, glob_h:glob_display_interval, found_h:true), if glob_look_poles then check_for_pole(), if not found_h then (est_answer:est_size_answer(), est_needed_step_err :estimated_needed_step_error( x_start,x_end,glob_h, est_answer), omniout_float(always, "est_needed_step_err", 32, est_needed_step_err, 16,""), estimated_step_error :test_suggested_h(), omniout_float(always, "estimated_step_error", 32, estimated_step_error, 32,""), if estimated_step_error < est_needed_step_err then ( omniout_str(always, "Double H and LOOP"), glob_h:glob_h*glob__2) else ( omniout_str(always, "Found H for OPTIMAL"), found_h:true,glob_h_reason:3, glob_h:glob_h/glob__2)), opt_iter:1+opt_iter), if not found_h and opt_iter = 1 then (omniout_str(always, "Beginning glob_h too large."), found_h:false), if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then (omniout_str(always, "SETTING H FOR MAX H"), glob_h:glob_check_sign*abs(glob_max_h), glob_h_reason:1,found_h:true)) else (found_h:true,glob_h:glob_h*glob_check_sign), if glob_html_log then html_log_file:openw("entry.html"), if found_h then (omniout_str(always,"START of Soultion"), array_x[1]:c(x_start),array_x[2]:c(glob_h), glob_next_display:c(x_start), glob_min_pole_est:glob_larger_float, glob_least_given_sing:glob_larger_float, glob_least_ratio_sing:glob_larger_float, glob_least_3_sing:glob_larger_float, glob_least_6_sing:glob_larger_float,order_diff:1, term_no:1, while term_no <= order_diff do (array_y[term_no] :array_y_init[term_no] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no),rows:order_diff, r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < ats_max_terms then array_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h,c(term_no-1)) /c(factorial_1(term_no-1)), term_no:1+term_no), r_order:1+r_order),current_iter:1, glob_clock_start_sec:elapsed_time_seconds(), glob_clock_sec:elapsed_time_seconds(),glob_iter:0, omniout_str(debugl," "), glob_reached_optimal_h:true, glob_optimal_clock_start_sec :elapsed_time_seconds(), while glob_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec-glob_orig_start_sec < glob_max_sec do (if reached_interval() then (omniout_str(info," "), omniout_str(info, "TOP MAIN SOLVE Loop")), glob_iter:1+glob_iter, glob_clock_sec:elapsed_time_seconds(), track_estimated_error(),atomall(), track_estimated_error(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display :glob_display_interval +glob_next_display, array_x[1]:glob_h+array_x[1], array_x[2]:glob_h,order_diff:2,ord:2, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[2,iii] :array_y_higher[2,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:2, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:1, calc_term:2,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:1, calc_term:2,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)),ord:1, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( array_y_higher_work[1,iii] :array_y_higher[1,iii] /expt(glob_h,c(calc_term-1)) /c( factorial_3(iii-calc_term,iii-1)), iii:iii-1),temp_sum:glob__0,ord:1, calc_term:1,iii:ats_max_terms, while iii >= calc_term do ( temp_sum :array_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,c(calc_term-1)) /c(factorial_1(calc_term-1)), term_no:ats_max_terms, while term_no >= 1 do ( array_y[term_no] :array_y_higher_work2[1,term_no], ord:1, while ord <= order_diff do ( array_y_higher[ord,term_no] :array_y_higher_work2[ ord,term_no],ord:1+ord), term_no:term_no-1)), omniout_str(always,"Finished!"), if glob_iter >= glob_max_iter then omniout_str(always, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds()-glob_orig_start_sec >= glob_max_sec then omniout_str(always, "Maximum Time Reached before Solution Completed!"), glob_clock_sec:elapsed_time_seconds(), omniout_str(info, "diff ( y , x , 1 ) = sin ( 2.0 * x + 3.0 ) + cos ( 1.5 * x - 2.0 ) ; "), omniout_int(info, "Iterations ",32, glob_iter,4," "), prog_report(x_start,x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2015-04-24T21:30:36-05:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "lin_sin_cos"), logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( 2.0 * x + 3.0 ) + cos ( 1.5 * x - 2.0 ) ; "), logitem_float(html_log_file,x_start), logitem_float(html_log_file,x_end), logitem_float(html_log_file,array_x[1]), logitem_float(html_log_file,glob_h), logitem_h_reason(html_log_file), logitem_str(html_log_file,"16"), logitem_float(html_log_file, glob_desired_digits_correct), if array_est_digits[1] # -16 then ( logitem_integer(html_log_file, array_est_digits[ 1]),0) else ( logitem_str(html_log_file, "Unknown"),0), if glob_min_good_digits # -16 then ( logitem_integer(html_log_file, glob_min_good_digits), 0) else ( logitem_str(html_log_file, "Unknown"),0), if glob_good_digits # -16 then ( logitem_integer(html_log_file, glob_good_digits),0) else ( logitem_str(html_log_file, "Unknown"),0), logitem_str(html_log_file,"NA"), logitem_str(html_log_file,"NA"), logitem_integer(html_log_file, ats_max_terms), if glob_type_given_pole = 0 then ( logitem_str(html_log_file, "Not Given"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 4 then ( logitem_str(html_log_file, "No Solution"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 5 then ( logitem_str(html_log_file, "Some Pole"), logitem_str(html_log_file,"????"),0) elseif glob_type_given_pole = 3 then ( logitem_str(html_log_file, "No Pole"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 1 then ( logitem_str(html_log_file, "Real Sing"), logitem_float(html_log_file, glob_least_given_sing), 0) elseif glob_type_given_pole = 2 then ( logitem_str(html_log_file, "Complex Sing"), logitem_float(html_log_file, glob_least_given_sing), 0), if glob_least_ratio_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_ratio_sing), 0) else ( logitem_str(html_log_file,"NONE"),0), if glob_least_3_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_3_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), if glob_least_6_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_6_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, glob_clock_sec), if c(glob_percent_done) < glob__100 then ( logitem_time(html_log_file, glob_total_exp_sec),0) else ( logitem_str(html_log_file,"Done"), 0), log_revs(html_log_file, " 308.maple.seems.ok "), logitem_str(html_log_file, "lin_sin_cos diffeq.max"), logitem_str(html_log_file, "lin_sin_cos maxima results"), logitem_str(html_log_file,"OK"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i258) main():=(glob_iolevel:2,compile(all),main_prog()) (%i259) 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_2D0 in translation. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_const_3D0 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable array_tmp3_g in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp4 in translation. warning: encountered undefined variable array_const_1D5 in translation. warning: encountered undefined variable array_tmp5 in translation. warning: encountered undefined variable array_tmp6 in translation. warning: encountered undefined variable array_tmp7 in translation. warning: encountered undefined variable array_tmp7_g in translation. warning: encountered undefined variable array_tmp8 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/lin_sin_cospostode.ode#################" "diff ( y , x , 1 ) = sin ( 2.0 * x + 3.0 ) + cos ( 1.5 * x - 2.0 ) ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:c(0.1)," "x_end:c(5.0)," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "" "" "" "" "" "" "" "glob_type_given_pole:3," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:8," "glob_max_minutes:(3.0)," "glob_subiter_method:3," "glob_max_iter:100000," "glob_upper_ratio_limit:c(1.000001)," "glob_lower_ratio_limit:c(0.999999)," "glob_look_poles:false," "glob_h:c(0.001)," "glob_display_interval:c(0.01)," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (c(-0.5)*cos(c(2.0)*c(x) + c(3.0)) + c(2.0)/c(3.0)*sin(c(1.5)*c(x)-c(2.0))) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (closed_form) = -0.14170274741948996 " " y[1] (numeric) = -0.14170274741948996 " " 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) = -0.1450699809230483 " " y[1] (numeric) = -0.14506998092304824 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.826508480807167500000000000000E-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) = -0.14849180092505576 " " y[1] (numeric) = -0.14849180092505565 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 7.47666213022420900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.13000000000000003 " " y[1] (closed_form) = -0.15196728302967055 " " y[1] (numeric) = -0.1519672830296705 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.65283567124245200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.14000000000000004 " " y[1] (closed_form) = -0.15549545593961295 " " y[1] (numeric) = -0.15549545593961278 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.07098598275725280000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000005 " " y[1] (closed_form) = -0.15907530175043105 " " y[1] (numeric) = -0.15907530175043091 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 8.72403676441673200000000000000E-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) = -0.16270575626915507 " " y[1] (numeric) = -0.16270575626915493 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 8.52937727959495400000000000000E-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) = -0.16638570935722935 " " y[1] (numeric) = -0.16638570935722932 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.668146604828772700000000000000E-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) = -0.170114005297606 " " y[1] (numeric) = -0.17011400529760598 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.63158674484631120000000000000E-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) = -0.1738894431858688 " " y[1] (numeric) = -0.17388944318586877 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.59616219979272920000000000000E-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) = -0.17771077734524865 " " y[1] (numeric) = -0.1777107773452485 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 7.80919875267514200000000000000E-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) = -0.18157671776537737 " " y[1] (numeric) = -0.18157671776537726 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 6.11434680772080400000000000000E-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) = -0.18548593056462026 " " y[1] (numeric) = -0.18548593056462018 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.489112818067781400000000000000E-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) = -0.18943703847581145 " " y[1] (numeric) = -0.18943703847581136 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.395482927564810500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.24000000000000013 " " y[1] (closed_form) = -0.19342862135521127 " " y[1] (numeric) = -0.19342862135521113 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 7.1746299542348300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (closed_form) = -0.19745921671448957 " " y[1] (numeric) = -0.19745921671448946 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.6225434451634200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (closed_form) = -0.2015273202755321 " " y[1] (numeric) = -0.20152732027553197 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.88630593055099100000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (closed_form) = -0.20563138654785262 " " y[1] (numeric) = -0.20563138654785254 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.049319913889200000000000000E-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) = -0.20976982942838773 " " y[1] (numeric) = -0.20976982942838757 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 7.93886585823942200000000000000E-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) = -0.21394102282343586 " " y[1] (numeric) = -0.21394102282343574 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.18938822472311200000000000000E-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) = -0.21814330129249787 " " y[1] (numeric) = -0.21814330129249762 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.14511964869237560000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (closed_form) = -0.22237496071375917 " " y[1] (numeric) = -0.222374960713759 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 7.48885815018243800000000000000E-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) = -0.22663425897095174 " " y[1] (numeric) = -0.22663425897095155 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 8.57280051972658300000000000000E-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) = -0.23091941666131555 " " y[1] (numeric) = -0.23091941666131538 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 7.2117562092244690000000000000E-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) = -0.23522861782437826 " " y[1] (numeric) = -0.23522861782437793 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.41592851443022470000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (closed_form) = -0.23956001069125327 " " y[1] (numeric) = -0.23956001069125313 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.79303188698728800000000000000E-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) = -0.2439117084541566 " " y[1] (numeric) = -0.24391170845415647 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.6896767669612700000000000000E-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) = -0.24828179005582168 " " y[1] (numeric) = -0.24828179005582166 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.11790621492573300000000000000E-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) = -0.25266830099849585 " " y[1] (numeric) = -0.2526683009984956 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.09849852577249660000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (closed_form) = -0.2570692541721781 " " y[1] (numeric) = -0.25706925417217796 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.31877016253977600000000000000E-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) = -0.26148263070176525 " " y[1] (numeric) = -0.26148263070176503 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 8.49175351835452900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (closed_form) = -0.26590638081274554 " " y[1] (numeric) = -0.26590638081274554 " " 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] = 0.42000000000000026 " " y[1] (closed_form) = -0.270338424715091 " " y[1] (numeric) = -0.27033842471509084 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.1601843640719100000000000000E-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) = -0.27477665350497055 " " y[1] (numeric) = -0.2747766535049706 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.020228084270400400000000000000E-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) = -0.2792189300839172 " " y[1] (numeric) = -0.27921893008391707 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.97617390873708730000000000000E-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) = -0.2836630900950547 " " y[1] (numeric) = -0.2836630900950548 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.913879046629309400000000000000E-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) = -0.28810694287600114 " " y[1] (numeric) = -0.2881069428760011 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.926755068000890700000000000000E-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) = -0.29254827242803827 " " y[1] (numeric) = -0.2925482724280384 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.79500796709798300000000000000E-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) = -0.29698483840114864 " " y[1] (numeric) = -0.29698483840114864 " " 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) = -0.3014143770944935 " " y[1] (numeric) = -0.30141437709449365 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.52506669718562300000000000000E-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) = -0.30583460247191835 " " y[1] (numeric) = -0.30583460247191835 " " 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] = 0.5100000000000003 " " y[1] (closed_form) = -0.3102432071920454 " " y[1] (numeric) = -0.31024320719204557 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.367835615194846000000000000000E-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) = -0.31463786365252444 " " y[1] (numeric) = -0.31463786365252444 " " 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] = 0.5300000000000004 " " y[1] (closed_form) = -0.3190162250479869 " " y[1] (numeric) = -0.3190162250479871 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.96029190652077500000000000000E-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) = -0.3233759264412623 " " y[1] (numeric) = -0.32337592644126223 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.716613597126897500000000000000E-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) = -0.32771458584738755 " " y[1] (numeric) = -0.3277145858473878 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.77554843495536700000000000000E-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) = -0.3320298053299564 " " y[1] (numeric) = -0.33202980532995635 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.671872534939847500000000000000E-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) = -0.336319172109325 " " y[1] (numeric) = -0.3363191721093251 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.301099421903500000000000000E-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) = -0.34058025968221095 " " y[1] (numeric) = -0.34058025968221084 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.25979851463230660000000000000E-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) = -0.34481062895218856 " " y[1] (numeric) = -0.3448106289521887 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.8297076630101504000000000000E-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) = -0.34900782937060737 " " y[1] (numeric) = -0.3490078293706072 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.771625152194896600000000000000E-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) = -0.35316940008742465 " " y[1] (numeric) = -0.3531694000874246 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.571799573165637600000000000000E-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) = -0.3572928711114689 " " y[1] (numeric) = -0.35729287111146857 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 9.32195781996546300000000000000E-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) = -0.3613757644796157 " " y[1] (numeric) = -0.3613757644796156 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.07221217843395600000000000000E-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) = -0.3654155954343813 " " y[1] (numeric) = -0.36541559543438096 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 9.11474254380466700000000000000E-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) = -0.369409873609408 " " y[1] (numeric) = -0.36940987360940786 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.50809427659900700000000000000E-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) = -0.37335610422233684 " " y[1] (numeric) = -0.3733561042223364 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.1894521204496060000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000005 " " y[1] (closed_form) = -0.37725178927453284 " " y[1] (numeric) = -0.3772517892745327 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.41438472734675740000000000000E-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) = -0.38109442875715216 " " y[1] (numeric) = -0.3810944287571517 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.16529966417602270000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000005 " " y[1] (closed_form) = -0.3848815218630061 " " y[1] (numeric) = -0.38488152186300595 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.32687578472652800000000000000E-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) = -0.3886105682037062 " " y[1] (numeric) = -0.38861056820370576 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.14276153606114750000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000005 " " y[1] (closed_form) = -0.39227906903153853 " " y[1] (numeric) = -0.39227906903153836 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.24528012939646500000000000000E-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) = -0.39588452846554456 " " y[1] (numeric) = -0.39588452846554406 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.2619850616991280000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000005 " " y[1] (closed_form) = -0.39942445472125077 " " y[1] (numeric) = -0.3994244547212505 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.94889240945422400000000000000E-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) = -0.40289636134352 " " y[1] (numeric) = -0.4028963613435195 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.2400220230714570000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000006 " " y[1] (closed_form) = -0.4062977684419616 " " y[1] (numeric) = -0.40629776844196147 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.73253537395135470000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000006 " " y[1] (closed_form) = -0.4096262039283677 " " y[1] (numeric) = -0.4096262039283674 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.77583009813566500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000006 " " y[1] (closed_form) = -0.4128792047556107 " " y[1] (numeric) = -0.4128792047556106 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.68897782169076300000000000000E-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) = -0.4160543181574645 " " y[1] (numeric) = -0.4160543181574642 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 8.00537076174488300000000000000E-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) = -0.4191491028887819 " " y[1] (numeric) = -0.4191491028887818 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.324377192952916600000000000000E-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) = -0.4221611304654882 " " y[1] (numeric) = -0.4221611304654878 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 9.20449635404250300000000000000E-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) = -0.4250879864038214 " " y[1] (numeric) = -0.42508798640382134 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.305874383815773500000000000000E-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) = -0.42792727145827775 " " y[1] (numeric) = -0.4279272714582773 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.03776795607512610000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000006 " " y[1] (closed_form) = -0.43067660285769027 " " y[1] (numeric) = -0.4306766028576902 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.288928882203534400000000000000E-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) = -0.43333361553890143 " " y[1] (numeric) = -0.43333361553890115 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.40512866307673500000000000000E-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) = -0.4358959633774544 " " y[1] (numeric) = -0.43589596337745434 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.27349541852006500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000007 " " y[1] (closed_form) = -0.43836132041476544 " " y[1] (numeric) = -0.4383613204147651 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.59799945561821500000000000000E-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) = -0.4407273820812036 " " y[1] (numeric) = -0.4407273820812036 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000007 " " y[1] (closed_form) = -0.44299186641453997 " " y[1] (numeric) = -0.44299186641453964 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.51857839023779800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000007 " " y[1] (closed_form) = -0.4451525152731952 " " y[1] (numeric) = -0.44515251527319516 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.247014210336203200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000007 " " y[1] (closed_form) = -0.44720709554374993 " " y[1] (numeric) = -0.4472070955437496 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.44771070733074500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000007 " " y[1] (closed_form) = -0.44915340034214857 " " y[1] (numeric) = -0.4491534003421485 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.235906289231506900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000007 " " y[1] (closed_form) = -0.45098925020806513 " " y[1] (numeric) = -0.4509892502080648 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.385251582690400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000007 " " y[1] (closed_form) = -0.45271249429186466 " " y[1] (numeric) = -0.4527124942918648 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.452379906946843500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000007 " " y[1] (closed_form) = -0.45432101153363363 " " y[1] (numeric) = -0.45432101153363336 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.1092432247268300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000007 " " y[1] (closed_form) = -0.455812711833716 " " y[1] (numeric) = -0.4558127118337161 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.217850002645576200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9600000000000007 " " y[1] (closed_form) = -0.45718553721423505 " " y[1] (numeric) = -0.45718553721423477 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.0709653644670690000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000008 " " y[1] (closed_form) = -0.45843746297104226 " " y[1] (numeric) = -0.4584374629710422 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.21087728894364500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000008 " " y[1] (closed_form) = -0.4595664988155791 " " y[1] (numeric) = -0.45956649881557876 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.24741486261391800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000008 " " y[1] (closed_form) = -0.4605706900061 " " y[1] (numeric) = -0.4605706900060999 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.410537727901122300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0000000000000007 " " y[1] (closed_form) = -0.4614481184677488 " " y[1] (numeric) = -0.46144811846774836 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 9.62381667791111700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0099999999999996 " " y[1] (closed_form) = -0.46219690390094403 " " y[1] (numeric) = -0.4621969039009437 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.20616915813283800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0199999999999985 " " y[1] (closed_form) = -0.46281520487757327 " " y[1] (numeric) = -0.46281520487757305 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.7976946864519700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0299999999999974 " " y[1] (closed_form) = -0.4633012199244638 " " y[1] (numeric) = -0.4633012199244637 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.396330889882323500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0399999999999963 " " y[1] (closed_form) = -0.46365318859362803 " " y[1] (numeric) = -0.4636531885936279 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.394511785830117600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0499999999999952 " " y[1] (closed_form) = -0.4638693925187736 " " y[1] (numeric) = -0.4638693925187736 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.059999999999994 " " y[1] (closed_form) = -0.4639481564575767 " " y[1] (numeric) = -0.46394815645757675 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.196494704389104400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.069999999999993 " " y[1] (closed_form) = -0.46388784931922145 " " y[1] (numeric) = -0.46388784931922145 " " absolute error = 0.0 " " relative error = 0.0 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0799999999999919 " " y[1] (closed_form) = -0.4636868851767149 " " y[1] (numeric) = -0.46368688517671497 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.197168887148966200000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0899999999999908 " " y[1] (closed_form) = -0.46334372426349113 " " y[1] (numeric) = -0.4633437242634911 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.198055532520607300000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0999999999999897 " " y[1] (closed_form) = -0.4628568739538236 " " y[1] (numeric) = -0.46285687395382347 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.39863138499249500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1099999999999886 " " y[1] (closed_form) = -0.4622248897265733 " " y[1] (numeric) = -0.4622248897265732 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.2009554756797100000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1199999999999875 " " y[1] (closed_form) = -0.46144637611180356 " " y[1] (numeric) = -0.46144637611180334 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.811926508037680500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1299999999999863 " " y[1] (closed_form) = -0.4605199876197991 " " y[1] (numeric) = -0.4605199876197989 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.82160624716139800000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1399999999999852 " " y[1] (closed_form) = -0.459444429652037 " " y[1] (numeric) = -0.4594444296520366 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 9.66578722450495700000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 17 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1499999999999841 " " y[1] (closed_form) = -0.458218459393658 " " y[1] (numeric) = -0.4582184593936575 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.09031042036678630000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.159999999999983 " " y[1] (closed_form) = -0.45684088668699946 " " y[1] (numeric) = -0.4568408866869988 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 1.45813090331271020000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.169999999999982 " " y[1] (closed_form) = -0.45531057488575444 " " y[1] (numeric) = -0.45531057488575355 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.95070896370677320000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1799999999999808 " " y[1] (closed_form) = -0.45362644168933103 " " y[1] (numeric) = -0.45362644168933 " " absolute error = 1.0547118733938987000000000000000E-15 " " relative error = 2.32506700770371970000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1899999999999797 " " y[1] (closed_form) = -0.45178745995699165 " " y[1] (numeric) = -0.4517874599569905 " " absolute error = 1.1657341758564144000000000000000E-15 " " relative error = 2.58027120975732160000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1999999999999786 " " y[1] (closed_form) = -0.44979265850136263 " " y[1] (numeric) = -0.4497926585013612 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 3.20878943827477100000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2099999999999775 " " y[1] (closed_form) = -0.4476411228609086 " " y[1] (numeric) = -0.4476411228609069 " " absolute error = 1.7208456881689926000000000000000E-15 " " relative error = 3.8442529077108390000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2199999999999764 " " y[1] (closed_form) = -0.44533199605097784 " " y[1] (numeric) = -0.44533199605097595 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 4.23813954218262570000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2299999999999753 " " y[1] (closed_form) = -0.44286447929303063 " " y[1] (numeric) = -0.4428644792930285 " " absolute error = 2.1094237467877974000000000000000E-15 " " relative error = 4.7631360052971250000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2399999999999742 " " y[1] (closed_form) = -0.44023783272167283 " " y[1] (numeric) = -0.4402378327216704 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 5.5481162059044020000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2499999999999731 " " y[1] (closed_form) = -0.43745137606912304 " " y[1] (numeric) = -0.43745137606912027 " " absolute error = 2.7755575615628914000000000000000E-15 " " relative error = 6.3448367370647320000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.259999999999972 " " y[1] (closed_form) = -0.4345044893267545 " " y[1] (numeric) = -0.4345044893267515 " " absolute error = 2.9976021664879227000000000000000E-15 " " relative error = 6.8988980324060050000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.269999999999971 " " y[1] (closed_form) = -0.4313966133833573 " " y[1] (numeric) = -0.43139661338335394 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 7.7206657876929050000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2799999999999698 " " y[1] (closed_form) = -0.4281272506397792 " " y[1] (numeric) = -0.42812725063977547 " " absolute error = 3.7192471324942744000000000000000E-15 " " relative error = 8.6872469036632320000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2899999999999687 " " y[1] (closed_form) = -0.42469596559961054 " " y[1] (numeric) = -0.4246959655996063 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 9.9338063822178770000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2999999999999676 " " y[1] (closed_form) = -0.4211023854355892 " " y[1] (numeric) = -0.4211023854355846 " " absolute error = 4.6074255521943996000000000000E-15 " " relative error = 1.0941342798209203000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3099999999999665 " " y[1] (closed_form) = -0.4173462005314109 " " y[1] (numeric) = -0.417346200531406 " " absolute error = 4.9404924595819466000000000000000E-15 " " relative error = 1.1837875733123172000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3199999999999654 " " y[1] (closed_form) = -0.413427164998639 " " y[1] (numeric) = -0.41342716499863363 " " absolute error = 5.384581669432009000000000000000E-15 " " relative error = 1.3024257052508230000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3299999999999643 " " y[1] (closed_form) = -0.40934509716841955 " " y[1] (numeric) = -0.40934509716841366 " " absolute error = 5.88418203051333000000000000000E-15 " " relative error = 1.4374624421340906000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3399999999999632 " " y[1] (closed_form) = -0.4050998800577161 " " y[1] (numeric) = -0.4050998800577097 " " absolute error = 6.38378239159465000000000000000E-15 " " relative error = 1.5758539327844603000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3499999999999621 " " y[1] (closed_form) = -0.4006914618097889 " " y[1] (numeric) = -0.40069146180978205 " " absolute error = 6.827871601444713000000000000000E-15 " " relative error = 1.7040222346155087000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.359999999999961 " " y[1] (closed_form) = -0.396119856108654 " " y[1] (numeric) = -0.3961198561086468 " " absolute error = 7.216449660063518000000000000000E-15 " " relative error = 1.8217843788381252000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.36999999999996 " " y[1] (closed_form) = -0.3913851425672686 " " y[1] (numeric) = -0.39138514256726076 " " absolute error = 7.827072323607354000000000000000E-15 " " relative error = 1.9998388983971435000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3799999999999588 " " y[1] (closed_form) = -0.38648746708919635 " " y[1] (numeric) = -0.3864874670891879 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 2.18317428264856980000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3899999999999577 " " y[1] (closed_form) = -0.381427042203523 " " y[1] (numeric) = -0.381427042203514 " " absolute error = 9.048317650695026000000000000000E-15 " " relative error = 2.372227621414162200000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3999999999999566 " " y[1] (closed_form) = -0.3762041473727972 " " y[1] (numeric) = -0.3762041473727876 " " absolute error = 9.603429163007604000000000000000E-15 " " relative error = 2.55271751523014000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4099999999999555 " " y[1] (closed_form) = -0.37081912927378563 " " y[1] (numeric) = -0.37081912927377536 " " absolute error = 1.026956297778269800000000000000E-14 " " relative error = 2.76942643112686000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4199999999999544 " " y[1] (closed_form) = -0.36527240205084205 " " y[1] (numeric) = -0.3652724020508312 " " absolute error = 1.082467449009527600000000000000E-14 " " relative error = 2.9634525984770665000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4299999999999533 " " y[1] (closed_form) = -0.35956444754170114 " " y[1] (numeric) = -0.35956444754168965 " " absolute error = 1.14908083048703700000000000000E-14 " " relative error = 3.1957576405096900000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4399999999999522 " " y[1] (closed_form) = -0.35369581547551754 " " y[1] (numeric) = -0.3536958154755054 " " absolute error = 1.215694211964546400000000000000E-14 " " relative error = 3.4371178814488845000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.449999999999951 " " y[1] (closed_form) = -0.34766712364298397 " " y[1] (numeric) = -0.3476671236429712 " " absolute error = 1.2767564783189300000000000000E-14 " " relative error = 3.672353212292857000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.45999999999995 " " y[1] (closed_form) = -0.3414790580383722 " " y[1] (numeric) = -0.3414790580383588 " " absolute error = 1.337818744673313600000000000000E-14 " " relative error = 3.917718270509526500000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.469999999999949 " " y[1] (closed_form) = -0.3351323729733531 " " y[1] (numeric) = -0.3351323729733389 " " absolute error = 1.415534356397074600000000000000E-14 " " relative error = 4.223806682231877600000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4799999999999478 " " y[1] (closed_form) = -0.32862789116246116 " " y[1] (numeric) = -0.3286278911624463 " " absolute error = 1.487698852997709800000000000000E-14 " " relative error = 4.527001185855671000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4899999999999467 " " y[1] (closed_form) = -0.3219665037800852 " " y[1] (numeric) = -0.3219665037800695 " " absolute error = 1.565414464721470700000000000000E-14 " " relative error = 4.8620413811453683000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4999999999999456 " " y[1] (closed_form) = -0.31514917048887203 " " y[1] (numeric) = -0.3151491704888556 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 5.213816916910625000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5099999999999445 " " y[1] (closed_form) = -0.3081769194394485 " " y[1] (numeric) = -0.3081769194394314 " " absolute error = 1.71529457304586690000000000000E-14 " " relative error = 5.565941071011624000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5199999999999434 " " y[1] (closed_form) = -0.301050847241373 " " y[1] (numeric) = -0.30105084724135506 " " absolute error = 1.793010184769627800000000000000E-14 " " relative error = 5.955838361524520000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5299999999999423 " " y[1] (closed_form) = -0.2937721189052438 " " y[1] (numeric) = -0.29377211890522503 " " absolute error = 1.876276911616514600000000000000E-14 " " relative error = 6.386844737371784000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5399999999999412 " " y[1] (closed_form) = -0.2863419677559008 " " y[1] (numeric) = -0.2863419677558813 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 6.823982312666106000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.54999999999994 " " y[1] (closed_form) = -0.27876169531667094 " " y[1] (numeric) = -0.27876169531665074 " " absolute error = 2.02060590481778500000000000000E-14 " " relative error = 7.248506300416897000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.559999999999939 " " y[1] (closed_form) = -0.2710326711646175 " " y[1] (numeric) = -0.27103267116459645 " " absolute error = 2.103872631664671600000000000000E-14 " " relative error = 7.762431822792462000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.569999999999938 " " y[1] (closed_form) = -0.26315633275676736 " " y[1] (numeric) = -0.2631563327567453 " " absolute error = 2.203792703880935700000000000000E-14 " " relative error = 8.374461981570014000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5799999999999368 " " y[1] (closed_form) = -0.2551341852273017 " " y[1] (numeric) = -0.2551341852272788 " " absolute error = 2.287059430727822500000000000000E-14 " " relative error = 8.964143431779859000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5899999999999357 " " y[1] (closed_form) = -0.2469678011557071 " " y[1] (numeric) = -0.24696780115568345 " " absolute error = 2.364775042451583400000000000000E-14 " " relative error = 9.575236250982578000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5999999999999346 " " y[1] (closed_form) = -0.23865882030589664 " " y[1] (numeric) = -0.2386588203058721 " " absolute error = 2.45359288442159600000000000000E-14 " " relative error = 1.02807551016834310000000000E-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) = -0.2302089493363224 " " y[1] (numeric) = -0.2302089493362969 " " absolute error = 2.55073739907629700000000000000E-14 " " relative error = 1.108009660975348100000000000E-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) = -0.2216199614811133 " " y[1] (numeric) = -0.22161996148108684 " " absolute error = 2.645106356169435500000000000000E-14 " " relative error = 1.193532540341522600000000000E-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) = -0.21289369620228354 " " y[1] (numeric) = -0.21289369620225618 " " absolute error = 2.73669975570101100000000000000E-14 " " relative error = 1.285477120515913500000000000E-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) = -0.20403205881307018 " " y[1] (numeric) = -0.20403205881304184 " " absolute error = 2.83384427035571200000000000000E-14 " " relative error = 1.388921077815530600000000000E-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) = -0.19503702007246826 " " y[1] (numeric) = -0.19503702007243895 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 1.502785873123661500000000000E-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) = -0.18591061575104717 " " y[1] (numeric) = -0.18591061575101683 " " absolute error = 3.0336844147882400000000000000E-14 " " relative error = 1.6317973035228100000000000E-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) = -0.17665494616814092 " " y[1] (numeric) = -0.17665494616810956 " " absolute error = 3.13638004456606700000000000000E-14 " " relative error = 1.775427245371803700000000000E-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) = -0.16727217570051922 " " y[1] (numeric) = -0.16727217570048683 " " absolute error = 3.23907567434389400000000000000E-14 " " relative error = 1.9364103209508501000000000E-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) = -0.15776453226265674 " " y[1] (numeric) = -0.15776453226262327 " " absolute error = 3.34732241924484700000000000000E-14 " " relative error = 2.121720497780835400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6999999999999236 " " y[1] (closed_form) = -0.14813430675873107 " " y[1] (numeric) = -0.14813430675869652 " " absolute error = 3.455569164145800000000000000E-14 " " relative error = 2.33272713104463100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7099999999999225 " " y[1] (closed_form) = -0.138383852506491 " " y[1] (numeric) = -0.13838385250645538 " " absolute error = 3.561040351485189600000000000000E-14 " " relative error = 2.573306268748485000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7199999999999214 " " y[1] (closed_form) = -0.12851558463314972 " " y[1] (numeric) = -0.12851558463311302 " " absolute error = 3.669287096386142400000000000000E-14 " " relative error = 2.855130066022883400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7299999999999203 " " y[1] (closed_form) = -0.1185319794434676 " " y[1] (numeric) = -0.11853197944342986 " " absolute error = 3.77475828372553200000000000000E-14 " " relative error = 3.184590607065545500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7399999999999192 " " y[1] (closed_form) = -0.10843557376020319 " " y[1] (numeric) = -0.10843557376016436 " " absolute error = 3.88300502862648500000000000000E-14 " " relative error = 3.58093280090300170000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.749999999999918 " " y[1] (closed_form) = -9.82289642371210700E-2 " " y[1] (numeric) = -9.82289642370810700E-2 " " absolute error = 3.999578446212126400000000000000E-14 " " relative error = 4.071689523832597000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.759999999999917 " " y[1] (closed_form) = -8.79148066447580400E-2 " " y[1] (numeric) = -8.7914806644716900E-2 " " absolute error = 4.11337630623620500000000000000E-14 " " relative error = 4.678820853075796300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7699999999999159 " " y[1] (closed_form) = -7.7495815129160210E-2 " " y[1] (numeric) = -7.74958151291179200E-2 " " absolute error = 4.22856194504106500000000000000E-14 " " relative error = 5.45650360344417800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7799999999999148 " " y[1] (closed_form) = -6.69747614438151500E-2 " " y[1] (numeric) = -6.69747614437717500E-2 " " absolute error = 4.339584247503580600000000000000E-14 " " relative error = 6.47943218303814400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7899999999999137 " " y[1] (closed_form) = -5.635447415501516000E-2 " " y[1] (numeric) = -5.63544741549705500E-2 " " absolute error = 4.460321001431566400000000000000E-14 " " relative error = 7.91475933066554800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7999999999999126 " " y[1] (closed_form) = -4.56378378208981400E-2 " " y[1] (numeric) = -4.56378378208523800E-2 " " absolute error = 4.57620052962681700000000000000E-14 " " relative error = 1.00272071336633680000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8099999999999115 " " y[1] (closed_form) = -3.482779214442599500E-2 " " y[1] (numeric) = -3.48277921443789800E-2 " " absolute error = 4.70179450928753800000000000000E-14 " " relative error = 1.35001222293674300000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8199999999999104 " " y[1] (closed_form) = -2.39273311005681600E-2 " " y[1] (numeric) = -2.39273311005200380E-2 " " absolute error = 4.81212292235966300000000000000E-14 " " relative error = 2.01114069184481580000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8299999999999093 " " y[1] (closed_form) = -1.293950203797422600E-2 " " y[1] (numeric) = -1.293950203792490000E-2 " " absolute error = 4.932859676287648700000000000000E-14 " " relative error = 3.8122484635119110000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8399999999999082 " " y[1] (closed_form) = -1.8674047554240736000E-3 " " y[1] (numeric) = -1.867404755373474000E-3 " " absolute error = 5.059949854946400000000000000000E-14 " " relative error = 2.709616027403402000000000E-9 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.849999999999907 " " y[1] (closed_form) = 9.285809446638593000E-3 " " y[1] (numeric) = 9.285809446690435000E-3 " " absolute error = 5.18422110795668800000000000000E-14 " " relative error = 5.5829501324015920000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.859999999999906 " " y[1] (closed_form) = 2.051693873917670400E-2 " " y[1] (numeric) = 2.051693873922976800E-2 " " absolute error = 5.306172168317858000000000000000E-14 " " relative error = 2.58623970942888400000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8699999999999048 " " y[1] (closed_form) = 3.18227317619098600E-2 " " y[1] (numeric) = 3.18227317619641400E-2 " " absolute error = 5.42760281163623400000000000000E-14 " " relative error = 1.7055741324296960000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8799999999999037 " " y[1] (closed_form) = 4.31998886446084400E-2 " " y[1] (numeric) = 4.31998886446639640E-2 " " absolute error = 5.55250290190656400000000000000E-14 " " relative error = 1.28530491075688100000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8899999999999026 " " y[1] (closed_form) = 5.46450620519862700E-2 " " y[1] (numeric) = 5.464506205204307000E-2 " " absolute error = 5.679484660348066000000000000000E-14 " " relative error = 1.03934087492570160000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8999999999999015 " " y[1] (closed_form) = 6.61548582518356500E-2 " " y[1] (numeric) = 6.6154858251893700E-2 " " absolute error = 5.80507864000878700000000000000E-14 " " relative error = 8.77498462457624500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9099999999999004 " " y[1] (closed_form) = 7.77258382060381800E-2 " " y[1] (numeric) = 7.77258382060975700E-2 " " absolute error = 5.93969318174458700000000000000E-14 " " relative error = 7.64185156292487500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9199999999998993 " " y[1] (closed_form) = 8.93545186840761200E-2 " " y[1] (numeric) = 8.9354518684136700E-2 " " absolute error = 6.0576543781110100000000000000E-14 " " relative error = 6.77934867460770700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9299999999998982 " " y[1] (closed_form) = 0.10103737339865548 " " y[1] (numeric) = 0.10103737339871735 " " absolute error = 6.18671780472368500000000000000E-14 " " relative error = 6.12319738391577400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9399999999998971 " " y[1] (closed_form) = 0.11277083416304778 " " y[1] (numeric) = 0.112770834163111 " " absolute error = 6.32133234645948500000000000000E-14 " " relative error = 5.60546740065777500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.949999999999896 " " y[1] (closed_form) = 0.12455129206974158 " " y[1] (numeric) = 0.12455129206980611 " " absolute error = 6.45317133063372200000000000000E-14 " " relative error = 5.18113559754989600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.959999999999895 " " y[1] (closed_form) = 0.13637509868998993 " " y[1] (numeric) = 0.13637509869005576 " " absolute error = 6.58362253602717800000000000000E-14 " " relative error = 4.82758406723002700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9699999999998938 " " y[1] (closed_form) = 0.14823856729382817 " " y[1] (numeric) = 0.14823856729389528 " " absolute error = 6.71129818385907100000000000000E-14 " " relative error = 4.52736309205984400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9799999999998927 " " y[1] (closed_form) = 0.1601379740901286 " " y[1] (numeric) = 0.16013797409019698 " " absolute error = 6.83897383169096400000000000000E-14 " " relative error = 4.270675878440840500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9899999999998916 " " y[1] (closed_form) = 0.17206955948624753 " " y[1] (numeric) = 0.17206955948631725 " " absolute error = 6.97220059464598300000000000000E-14 " " relative error = 4.0519663184255600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9999999999998905 " " y[1] (closed_form) = 0.18402952936681438 " " y[1] (numeric) = 0.18402952936688546 " " absolute error = 7.10820291516256500000000000000E-14 " " relative error = 3.8625338768292106000000000E-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) = 0.1960140563912003 " " y[1] (numeric) = 0.1960140563912725 " " absolute error = 7.22200077518664300000000000000E-14 " " relative error = 3.68443003943204100000000000E-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) = 0.20801928130919706 " " y[1] (numeric) = 0.20801928130927053 " " absolute error = 7.34690086545697300000000000000E-14 " " relative error = 3.531836481319555000000000000E-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) = 0.22004131429443025 " " y[1] (numeric) = 0.22004131429450513 " " absolute error = 7.48845430109668100000000000000E-14 " " relative error = 3.403203768850708000000000000E-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) = 0.23207623629501845 " " y[1] (numeric) = 0.2320762362950946 " " absolute error = 7.61612994892857400000000000000E-14 " " relative error = 3.28173623914119600000000000E-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) = 0.24412010040098459 " " y[1] (numeric) = 0.24412010040106202 " " absolute error = 7.74380559676046700000000000000E-14 " " relative error = 3.172129449414742000000000000E-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) = 0.25616893322791934 " " y[1] (numeric) = 0.25616893322799816 " " absolute error = 7.88258347483861100000000000000E-14 " " relative error = 3.07710360327936300000000000E-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) = 0.26821873631638543 " " y[1] (numeric) = 0.2682187363164656 " " absolute error = 8.0158102377936300000000000000E-14 " " relative error = 2.98853478615242700000000000E-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) = 0.2802654875465457 " " y[1] (numeric) = 0.2802654875466272 " " absolute error = 8.15458811587177500000000000000E-14 " " relative error = 2.909594109234547000000000000E-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) = 0.29230514256749196 " " y[1] (numeric) = 0.29230514256757484 " " absolute error = 8.28781487882679400000000000000E-14 " " relative error = 2.835329822126948500000000000E-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) = 0.30433363624074217 " " y[1] (numeric) = 0.30433363624082627 " " absolute error = 8.40993941153556100000000000000E-14 " " relative error = 2.76339464655260900000000000E-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) = 0.31634688409736766 " " y[1] (numeric) = 0.3163468840974531 " " absolute error = 8.5431661744905800000000000000E-14 " " relative error = 2.700569091700330500000000000E-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) = 0.32834078380820714 " " y[1] (numeric) = 0.3283407838082939 " " absolute error = 8.67639293744559800000000000000E-14 " " relative error = 2.642496261601701700000000000E-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) = 0.3403112166666142 " " y[1] (numeric) = 0.34031121666670217 " " absolute error = 8.79851747015436600000000000000E-14 " " relative error = 2.585432697851341400000000000E-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) = 0.3522540490831815 " " y[1] (numeric) = 0.3522540490832708 " " absolute error = 8.93174423310938400000000000000E-14 " " relative error = 2.535597321409423500000000000E-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) = 0.3641651340918792 " " y[1] (numeric) = 0.3641651340919699 " " absolute error = 9.07052211118752900000000000000E-14 " " relative error = 2.490771702735009300000000000E-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) = 0.37604031286703704 " " y[1] (numeric) = 0.37604031286712897 " " absolute error = 9.19264664389629600000000000000E-14 " " relative error = 2.4445907338521700000000000E-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) = 0.3878754162505952 " " y[1] (numeric) = 0.3878754162506885 " " absolute error = 9.33142452197444100000000000000E-14 " " relative error = 2.405778796753046700000000000E-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) = 0.3996662662890449 " " y[1] (numeric) = 0.3996662662891395 " " absolute error = 9.45910016980633400000000000000E-14 " " relative error = 2.366749702854672700000000000E-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) = 0.4114086777794719 " " y[1] (numeric) = 0.41140867777956774 " " absolute error = 9.58677581763822700000000000000E-14 " " relative error = 2.330231795153587500000000000E-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) = 0.42309845982411354 " " y[1] (numeric) = 0.42309845982421074 " " absolute error = 9.72000258059324600000000000000E-14 " " relative error = 2.29733820932223500000000000E-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) = 0.43473141739283483 " " y[1] (numeric) = 0.43473141739293325 " " absolute error = 9.84212711330201300000000000000E-14 " " relative error = 2.26395579420670320000000000E-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) = 0.44630335289292244 " " y[1] (numeric) = 0.4463033528930221 " " absolute error = 9.9642516460107800000000000000E-14 " " relative error = 2.232618594824093400000000000E-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) = 0.457810067745595 " " y[1] (numeric) = 0.45781006774569605 " " absolute error = 1.01030295240889250000000000000E-13 " " relative error = 2.206816808079279000000000000E-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) = 0.46924736396862154 " " y[1] (numeric) = 0.46924736396872374 " " absolute error = 1.02196029416745660000000000000E-13 " " relative error = 2.177871145666776300000000000E-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) = 0.48061104576443603 " " y[1] (numeric) = 0.48061104576453934 " " absolute error = 1.03306252441370820000000000000E-13 " " relative error = 2.149477282134808800000000000E-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) = 0.49189692111313366 " " y[1] (numeric) = 0.4918969211132383 " " absolute error = 1.046385200709210000000000000E-13 " " relative error = 2.127244867362255700000000000E-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) = 0.5031008033697326 " " y[1] (numeric) = 0.5031008033698386 " " absolute error = 1.06026298851702450000000000000E-13 " " relative error = 2.107456361459691700000000000E-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) = 0.5142185128650774 " " y[1] (numeric) = 0.5142185128651847 " " absolute error = 1.07358566481252640000000000000E-13 " " relative error = 2.08780049327826900000000000E-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) = 0.5252458785097613 " " y[1] (numeric) = 0.5252458785098698 " " absolute error = 1.0846878950587780000000000000E-13 " " relative error = 2.06510500974567800000000000E-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) = 0.5361787394004431 " " y[1] (numeric) = 0.5361787394005526 " " absolute error = 1.09467990228040430000000000000E-13 " " relative error = 2.04163242933593200000000000E-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) = 0.5470129464279267 " " y[1] (numeric) = 0.5470129464280374 " " absolute error = 1.10689235555128110000000000000E-13 " " relative error = 2.02352131294048420000000000E-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) = 0.5577443638863762 " " y[1] (numeric) = 0.5577443638864881 " " absolute error = 1.11910480882215780000000000000E-13 " " relative error = 2.00648340222428900000000000E-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) = 0.5683688710830306 " " y[1] (numeric) = 0.5683688710831438 " " absolute error = 1.13242748511765970000000000000E-13 " " relative error = 1.992416444200773600000000000E-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) = 0.5788823639477879 " " y[1] (numeric) = 0.5788823639479022 " " absolute error = 1.1424194923392861000000000000E-13 " " relative error = 1.973491616756744300000000000E-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) = 0.5892807566420207 " " y[1] (numeric) = 0.5892807566421362 " " absolute error = 1.15463194561016280000000000000E-13 " " relative error = 1.9593919071611302000000000E-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) = 0.5995599831659888 " " y[1] (numeric) = 0.5995599831661055 " " absolute error = 1.16684439888103950000000000000E-13 " " relative error = 1.946167909204836700000000000E-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) = 0.6097159989642108 " " y[1] (numeric) = 0.6097159989643285 " " absolute error = 1.1768364061026660000000000000E-13 " " relative error = 1.930138635203738600000000000E-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) = 0.6197447825281581 " " y[1] (numeric) = 0.6197447825282769 " " absolute error = 1.18793863634891750000000000000E-13 " " relative error = 1.91681910011875480000000000E-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) = 0.6296423369956335 " " y[1] (numeric) = 0.6296423369957537 " " absolute error = 1.20126131264441940000000000000E-13 " " relative error = 1.907847109481695700000000000E-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) = 0.6394046917461966 " " y[1] (numeric) = 0.639404691746318 " " absolute error = 1.2134737659152961000000000000E-13 " " relative error = 1.897818051039526500000000000E-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) = 0.6490279039919977 " " y[1] (numeric) = 0.6490279039921203 " " absolute error = 1.22568621918617280000000000000E-13 " " relative error = 1.888495412365636700000000000E-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) = 0.6585080603633856 " " y[1] (numeric) = 0.6585080603635094 " " absolute error = 1.23789867245704950000000000000E-13 " " relative error = 1.879853485428770200000000000E-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) = 0.6678412784886503 " " y[1] (numeric) = 0.6678412784887752 " " absolute error = 1.2490009027033011000000000000E-13 " " relative error = 1.870206204578783700000000000E-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) = 0.677023708567268 " " y[1] (numeric) = 0.6770237085673937 " " absolute error = 1.25677246387567720000000000000E-13 " " relative error = 1.856319724068874500000000000E-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) = 0.6860515349360127 " " y[1] (numeric) = 0.6860515349361395 " " absolute error = 1.26787469412192880000000000000E-13 " " relative error = 1.848075005385976200000000000E-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) = 0.6949209776273033 " " y[1] (numeric) = 0.694920977627431 " " absolute error = 1.276756478318930000000000000E-13 " " relative error = 1.837268580779085300000000000E-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) = 0.703628293919155 " " y[1] (numeric) = 0.7036282939192838 " " absolute error = 1.28785870856518160000000000000E-13 " " relative error = 1.830311145380337500000000000E-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) = 0.7121697798761061 " " y[1] (numeric) = 0.7121697798762359 " " absolute error = 1.2978507157868080000000000000E-13 " " relative error = 1.82238948135736800000000000E-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) = 0.7205417718804952 " " y[1] (numeric) = 0.720541771880626 " " absolute error = 1.30784272300843440000000000000E-13 " " relative error = 1.815082447746479400000000000E-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) = 0.7287406481534646 " " y[1] (numeric) = 0.7287406481535964 " " absolute error = 1.31783473023006080000000000000E-13 " " relative error = 1.80837275040068800000000000E-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) = 0.7367628302650686 " " y[1] (numeric) = 0.7367628302652012 " " absolute error = 1.3256062914024370000000000000E-13 " " relative error = 1.799230684487051800000000000E-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) = 0.7446047846328676 " " y[1] (numeric) = 0.7446047846330014 " " absolute error = 1.33781874467331360000000000000E-13 " " relative error = 1.796682981741695700000000000E-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) = 0.7522630240083984 " " y[1] (numeric) = 0.7522630240085328 " " absolute error = 1.34448008282106460000000000000E-13 " " relative error = 1.787247332265602400000000000E-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) = 0.7597341089509022 " " y[1] (numeric) = 0.7597341089510377 " " absolute error = 1.3544720900426910000000000000E-13 " " relative error = 1.782823851245862200000000000E-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) = 0.7670146492877105 " " y[1] (numeric) = 0.7670146492878467 " " absolute error = 1.3622436512150670000000000000E-13 " " relative error = 1.776033420587360700000000000E-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) = 0.7741013055606799 " " y[1] (numeric) = 0.7741013055608168 " " absolute error = 1.3689049893628180000000000000E-13 " " relative error = 1.768379641694730300000000000E-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) = 0.780990790458081 " " y[1] (numeric) = 0.7809907904582186 " " absolute error = 1.3766765505351940000000000000E-13 " " relative error = 1.762730838000945700000000000E-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) = 0.7876798702313442 " " y[1] (numeric) = 0.7876798702314826 " " absolute error = 1.3833378886829450000000000000E-13 " " relative error = 1.75621840923350500000000000E-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) = 0.7941653660960752 " " y[1] (numeric) = 0.7941653660962141 " " absolute error = 1.38888900380607080000000000000E-13 " " relative error = 1.748866247634939300000000000E-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) = 0.8004441556167523 " " y[1] (numeric) = 0.8004441556168919 " " absolute error = 1.39555034195382180000000000000E-13 " " relative error = 1.74346996247168900000000000E-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) = 0.8065131740745309 " " y[1] (numeric) = 0.8065131740746712 " " absolute error = 1.40221168010157270000000000000E-13 " " relative error = 1.738609765067510900000000000E-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) = 0.8123694158175768 " " y[1] (numeric) = 0.8123694158177176 " " absolute error = 1.40776279522469850000000000000E-13 " " relative error = 1.73290964407850300000000000E-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) = 0.8180099355933625 " " y[1] (numeric) = 0.8180099355935038 " " absolute error = 1.4122036873231990000000000000E-13 " " relative error = 1.726389406626001600000000000E-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) = 0.8234318498623641 " " y[1] (numeric) = 0.823431849862506 " " absolute error = 1.418865025470950000000000000E-13 " " relative error = 1.723111664563511700000000000E-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) = 0.8286323380926028 " " y[1] (numeric) = 0.8286323380927452 " " absolute error = 1.42330591756945070000000000000E-13 " " relative error = 1.717656736455282800000000000E-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) = 0.833608644034481 " " y[1] (numeric) = 0.8336086440346238 " " absolute error = 1.42774680966795130000000000000E-13 " " relative error = 1.712730332015240700000000000E-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) = 0.8383580769753696 " " y[1] (numeric) = 0.838358076975513 " " absolute error = 1.43440814781570230000000000000E-13 " " relative error = 1.7109731357163800000000000E-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) = 0.8428780129734134 " " y[1] (numeric) = 0.8428780129735572 " " absolute error = 1.4388490399142030000000000000E-13 " " relative error = 1.707066761462180700000000000E-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) = 0.8471658960700206 " " y[1] (numeric) = 0.8471658960701648 " " absolute error = 1.44217970898807830000000000000E-13 " " relative error = 1.702358080841439300000000000E-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) = 0.8512192394805197 " " y[1] (numeric) = 0.8512192394806642 " " absolute error = 1.44551037806195380000000000000E-13 " " relative error = 1.698164598516496000000000000E-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) = 0.8550356267624664 " " y[1] (numeric) = 0.8550356267626117 " " absolute error = 1.453281939234330000000000000E-13 " " relative error = 1.69967413490953820000000000E-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) = 0.8586127129610969 " " y[1] (numeric) = 0.8586127129612428 " " absolute error = 1.45883305435745570000000000000E-13 " " relative error = 1.699058297572114000000000000E-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) = 0.8619482257314255 " " y[1] (numeric) = 0.8619482257315717 " " absolute error = 1.46216372343133120000000000000E-13 " " relative error = 1.69634750647648190000000000E-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) = 0.8650399664364994 " " y[1] (numeric) = 0.8650399664366456 " " absolute error = 1.46216372343133120000000000000E-13 " " relative error = 1.690284588184591500000000000E-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) = 0.8678858112213276 " " y[1] (numeric) = 0.8678858112214741 " " absolute error = 1.46549439250520660000000000000E-13 " " relative error = 1.688579734288889500000000000E-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) = 0.8704837120620117 " " y[1] (numeric) = 0.8704837120621588 " " absolute error = 1.47104550762833240000000000000E-13 " " relative error = 1.6899173267052900000000000E-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) = 0.8728316977896118 " " y[1] (numeric) = 0.8728316977897591 " " absolute error = 1.47326595367758270000000000000E-13 " " relative error = 1.687915273252026400000000000E-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) = 0.874927875088293 " " y[1] (numeric) = 0.8749278750884402 " " absolute error = 1.47215573065295760000000000000E-13 " " relative error = 1.682602386516026400000000000E-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) = 0.8767704294673067 " " y[1] (numeric) = 0.8767704294674542 " " absolute error = 1.4754863997268330000000000000E-13 " " relative error = 1.68286514934506200000000000E-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) = 0.8783576262063708 " " y[1] (numeric) = 0.8783576262065187 " " absolute error = 1.47881706880070850000000000000E-13 " " relative error = 1.683616131606580400000000000E-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) = 0.8796878112740176 " " y[1] (numeric) = 0.8796878112741652 " " absolute error = 1.4754863997268330000000000000E-13 " " relative error = 1.67728412377334570000000000E-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) = 0.8807594122184927 " " y[1] (numeric) = 0.8807594122186403 " " absolute error = 1.4754863997268330000000000000E-13 " " relative error = 1.675243408424461300000000000E-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) = 0.8815709390308006 " " y[1] (numeric) = 0.8815709390309485 " " absolute error = 1.47881706880070850000000000000E-13 " " relative error = 1.677479376108428000000000000E-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) = 0.882120984979496 " " y[1] (numeric) = 0.8821209849796442 " " absolute error = 1.4821477378745840000000000000E-13 " " relative error = 1.680209135835301600000000000E-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) = 0.8824082274168312 " " y[1] (numeric) = 0.8824082274169794 " " absolute error = 1.4821477378745840000000000000E-13 " " relative error = 1.67966219242247420000000000E-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) = 0.8824314285558862 " " y[1] (numeric) = 0.8824314285560343 " " absolute error = 1.48103751484995880000000000000E-13 " " relative error = 1.678359889417925200000000000E-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) = 0.8821894362183135 " " y[1] (numeric) = 0.8821894362184618 " " absolute error = 1.48325796089920900000000000000E-13 " " relative error = 1.681337250259422300000000000E-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) = 0.8816811845523423 " " y[1] (numeric) = 0.8816811845524908 " " absolute error = 1.48436818392383430000000000000E-13 " " relative error = 1.68356568103185200000000000E-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) = 0.8809056947206951 " " y[1] (numeric) = 0.8809056947208432 " " absolute error = 1.48103751484995880000000000000E-13 " " relative error = 1.681266818600309600000000000E-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) = 0.8798620755580822 " " y[1] (numeric) = 0.8798620755582298 " " absolute error = 1.47659662275145820000000000000E-13 " " relative error = 1.67821373800533100000000000E-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) = 0.8785495241979563 " " y[1] (numeric) = 0.878549524198104 " " absolute error = 1.47659662275145820000000000000E-13 " " relative error = 1.680720986218130200000000000E-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) = 0.8769673266682121 " " y[1] (numeric) = 0.8769673266683596 " " absolute error = 1.4754863997268330000000000000E-13 " " relative error = 1.682487311508541500000000000E-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) = 0.8751148584555275 " " y[1] (numeric) = 0.8751148584556747 " " absolute error = 1.47215573065295760000000000000E-13 " " relative error = 1.682242869525876200000000000E-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) = 0.8729915850380651 " " y[1] (numeric) = 0.8729915850382116 " " absolute error = 1.46549439250520660000000000000E-13 " " relative error = 1.678703916076472700000000000E-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) = 0.870597062386251 " " y[1] (numeric) = 0.8705970623863973 " " absolute error = 1.46327394645595630000000000000E-13 " " relative error = 1.68077059948400910000000000E-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) = 0.8679309374313727 " " y[1] (numeric) = 0.8679309374315191 " " absolute error = 1.46327394645595630000000000000E-13 " " relative error = 1.685933619080904300000000000E-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) = 0.8649929485017351 " " y[1] (numeric) = 0.8649929485018809 " " absolute error = 1.45772283133283050000000000000E-13 " " relative error = 1.68524244487515200000000000E-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) = 0.8617829257261387 " " y[1] (numeric) = 0.8617829257262837 " " absolute error = 1.44995127016045440000000000000E-13 " " relative error = 1.682501737823042500000000000E-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) = 0.858300791404452 " " y[1] (numeric) = 0.8583007914045969 " " absolute error = 1.44884104713582930000000000000E-13 " " relative error = 1.68803415031817280000000000E-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) = 0.8545465603450613 " " y[1] (numeric) = 0.8545465603452059 " " absolute error = 1.4466206010865790000000000000E-13 " " relative error = 1.692851704303205400000000000E-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) = 0.8505203401689895 " " y[1] (numeric) = 0.8505203401691335 " " absolute error = 1.4399592629388280000000000000E-13 " " relative error = 1.693033305532379600000000000E-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) = 0.8462223315804982 " " y[1] (numeric) = 0.8462223315806414 " " absolute error = 1.4321877017664520000000000000E-13 " " relative error = 1.692448483475424400000000000E-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) = 0.8416528286039923 " " y[1] (numeric) = 0.8416528286041354 " " absolute error = 1.43107747874182680000000000000E-13 " " relative error = 1.700318029127857700000000000E-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) = 0.8368122187870618 " " y[1] (numeric) = 0.8368122187872047 " " absolute error = 1.42885703269257650000000000000E-13 " " relative error = 1.70750020209273320000000000E-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) = 0.8317009833695039 " " y[1] (numeric) = 0.8317009833696458 " " absolute error = 1.418865025470950000000000000E-13 " " relative error = 1.70597973772093510000000000E-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) = 0.8263196974181882 " " y[1] (numeric) = 0.8263196974183292 " " absolute error = 1.40998324127394880000000000000E-13 " " relative error = 1.70634107559023500000000000E-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) = 0.8206690299276379 " " y[1] (numeric) = 0.8206690299277786 " " absolute error = 1.40665257220007330000000000000E-13 " " relative error = 1.714031504666508600000000000E-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) = 0.8147497438862117 " " y[1] (numeric) = 0.8147497438863519 " " absolute error = 1.40221168010157270000000000000E-13 " " relative error = 1.721033594209274400000000000E-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) = 0.8085626963077817 " " y[1] (numeric) = 0.8085626963079208 " " absolute error = 1.39110944985532110000000000000E-13 " " relative error = 1.720471963655606800000000000E-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) = 0.8021088382288222 " " y[1] (numeric) = 0.8021088382289604 " " absolute error = 1.382227665658320000000000000E-13 " " relative error = 1.72324203372510900000000000E-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) = 0.7953892146708348 " " y[1] (numeric) = 0.7953892146709726 " " absolute error = 1.37778677355981930000000000000E-13 " " relative error = 1.732217068256331500000000000E-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) = 0.7884049645680458 " " y[1] (numeric) = 0.7884049645681829 " " absolute error = 1.37112543541206830000000000000E-13 " " relative error = 1.73911314239793700000000000E-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) = 0.7811573206603266 " " y[1] (numeric) = 0.7811573206604628 " " absolute error = 1.3622436512150670000000000000E-13 " " relative error = 1.74387874911488720000000000E-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) = 0.7736476093513014 " " y[1] (numeric) = 0.7736476093514366 " " absolute error = 1.35225164399344070000000000000E-13 " " relative error = 1.74789093593567120000000000E-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) = 0.7658772505316229 " " y[1] (numeric) = 0.7658772505317575 " " absolute error = 1.34559030584568970000000000000E-13 " " relative error = 1.756926850760571800000000000E-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) = 0.7578477573674057 " " y[1] (numeric) = 0.75784775736754 " " absolute error = 1.34225963677181430000000000000E-13 " " relative error = 1.771146808475788400000000000E-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) = 0.7495607360538195 " " y[1] (numeric) = 0.7495607360539525 " " absolute error = 1.33004718350093750000000000000E-13 " " relative error = 1.77443550539103800000000000E-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) = 0.7410178855338593 " " y[1] (numeric) = 0.7410178855339911 " " absolute error = 1.31783473023006080000000000000E-13 " " relative error = 1.778411501202348500000000000E-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) = 0.7322209971823318 " " y[1] (numeric) = 0.7322209971824629 " " absolute error = 1.311173392082310000000000000E-13 " " relative error = 1.790679859124296400000000000E-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) = 0.7231719544550943 " " y[1] (numeric) = 0.7231719544552249 " " absolute error = 1.3056222769591840000000000000E-13 " " relative error = 1.805410551274713700000000000E-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) = 0.7138727325036056 " " y[1] (numeric) = 0.7138727325037348 " " absolute error = 1.29229960066368220000000000000E-13 " " relative error = 1.810266090611823700000000000E-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) = 0.7043253977548609 " " y[1] (numeric) = 0.704325397754989 " " absolute error = 1.28119737041743060000000000000E-13 " " relative error = 1.81904184415531880000000000E-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) = 0.6945321074567998 " " y[1] (numeric) = 0.6945321074569271 " " absolute error = 1.27231558622042940000000000000E-13 " " relative error = 1.831903194338021200000000000E-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) = 0.6844951091892795 " " y[1] (numeric) = 0.6844951091894058 " " absolute error = 1.26343380202342810000000000000E-13 " " relative error = 1.845789378275978500000000000E-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) = 0.6742167403407265 " " y[1] (numeric) = 0.6742167403408517 " " absolute error = 1.25122134875255140000000000000E-13 " " relative error = 1.855814716377742200000000000E-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) = 0.6636994275505919 " " y[1] (numeric) = 0.6636994275507156 " " absolute error = 1.23789867245704950000000000000E-13 " " relative error = 1.865149525630242200000000000E-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) = 0.6529456861177495 " " y[1] (numeric) = 0.6529456861178724 " " absolute error = 1.22901688826004830000000000000E-13 " " relative error = 1.882265116976992400000000000E-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) = 0.6419581193749891 " " y[1] (numeric) = 0.6419581193751112 " " absolute error = 1.2201351040630470000000000000E-13 " " relative error = 1.900645956859259300000000000E-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) = 0.6307394180297637 " " y[1] (numeric) = 0.6307394180298844 " " absolute error = 1.20681242776754520000000000000E-13 " " relative error = 1.913329646555556300000000000E-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) = 0.6192923594713737 " " y[1] (numeric) = 0.6192923594714927 " " absolute error = 1.19015908239816780000000000000E-13 " " relative error = 1.921804886167309500000000000E-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) = 0.6076198070447779 " " y[1] (numeric) = 0.607619807044896 " " absolute error = 1.18127729820116660000000000000E-13 " " relative error = 1.944105976311785200000000000E-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) = 0.5957247092912368 " " y[1] (numeric) = 0.5957247092913539 " " absolute error = 1.17128529097954020000000000000E-13 " " relative error = 1.9661519368116800000000000E-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) = 0.583610099156 " " y[1] (numeric) = 0.5836100991561155 " " absolute error = 1.15463194561016280000000000000E-13 " " relative error = 1.97843037205825900000000000E-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) = 0.5712790931632697 " " y[1] (numeric) = 0.5712790931633835 " " absolute error = 1.13797860024078550000000000000E-13 " " relative error = 1.9919836273713498000000000E-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) = 0.558734890558688 " " y[1] (numeric) = 0.5587348905588007 " " absolute error = 1.12687636999453390000000000000E-13 " " relative error = 2.016835513650762400000000000E-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) = 0.5459807724195975 " " y[1] (numeric) = 0.545980772419709 " " absolute error = 1.11466391672365720000000000000E-13 " " relative error = 2.041580899971720800000000000E-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) = 0.5330201007333448 " " y[1] (numeric) = 0.5330201007334546 " " absolute error = 1.09801057135427980000000000000E-13 " " relative error = 2.059979670266851900000000000E-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) = 0.5198563174439064 " " y[1] (numeric) = 0.5198563174440145 " " absolute error = 1.08135722598490250000000000000E-13 " " relative error = 2.080107886928936300000000000E-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) = 0.5064929434671352 " " y[1] (numeric) = 0.5064929434672422 " " absolute error = 1.06914477271402570000000000000E-13 " " relative error = 2.11087792338295300000000000E-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) = 0.4929335776749299 " " y[1] (numeric) = 0.4929335776750356 " " absolute error = 1.0569323194431490000000000000E-13 " " relative error = 2.144167829727667600000000000E-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) = 0.47918189584864307 " " y[1] (numeric) = 0.4791818958487469 " " absolute error = 1.03805852802452140000000000000E-13 " " relative error = 2.166314163823100700000000000E-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) = 0.46524164960206044 " " y[1] (numeric) = 0.4652416496021623 " " absolute error = 1.01862962509358110000000000000E-13 " " relative error = 2.18946353140320800000000000E-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) = 0.45111666527429617 " " y[1] (numeric) = 0.45111666527439676 " " absolute error = 1.00586206031039180000000000000E-13 " " relative error = 2.2297160307717500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.439999999999732 " " y[1] (closed_form) = 0.43681084279295623 " " y[1] (numeric) = 0.4368108427930556 " " absolute error = 9.93649607039515100000000000000E-14 " " relative error = 2.274782376477075300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.449999999999731 " " y[1] (closed_form) = 0.4223281545079333 " " y[1] (numeric) = 0.42232815450803074 " " absolute error = 9.74220704108574900000000000000E-14 " " relative error = 2.306786070759756800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.45999999999973 " " y[1] (closed_form) = 0.4076726439962134 " " y[1] (numeric) = 0.407672643996309 " " absolute error = 9.55902024202259800000000000000E-14 " " relative error = 2.344778435050301200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.469999999999729 " " y[1] (closed_form) = 0.3928484248380866 " " y[1] (numeric) = 0.39284842483818083 " " absolute error = 9.42579347906757900000000000000E-14 " " relative error = 2.399346130241566400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4799999999997278 " " y[1] (closed_form) = 0.3778596793651599 " " y[1] (numeric) = 0.3778596793652527 " " absolute error = 9.28146448586630900000000000000E-14 " " relative error = 2.45632571897061090000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4899999999997267 " " y[1] (closed_form) = 0.3627106573805827 " " y[1] (numeric) = 0.3627106573806736 " " absolute error = 9.08717545655690600000000000000E-14 " " relative error = 2.505351103323653600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4999999999997256 " " y[1] (closed_form) = 0.34740567485190976 " " y[1] (numeric) = 0.3474056748519986 " " absolute error = 8.88178419700125200000000000000E-14 " " relative error = 2.55660308392697700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5099999999997245 " " y[1] (closed_form) = 0.3319491125770394 " " y[1] (numeric) = 0.33194911257712684 " " absolute error = 8.74300631892310800000000000000E-14 " " relative error = 2.6338393409303100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5199999999997234 " " y[1] (closed_form) = 0.3163454148236698 " " y[1] (numeric) = 0.31634541482375583 " " absolute error = 8.60422844084496300000000000000E-14 " " relative error = 2.71988403740289400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5299999999997222 " " y[1] (closed_form) = 0.30059908794272655 " " y[1] (numeric) = 0.30059908794281054 " " absolute error = 8.39883718128930900000000000000E-14 " " relative error = 2.79403282251127370000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.539999999999721 " " y[1] (closed_form) = 0.2847146989562308 " " y[1] (numeric) = 0.2847146989563127 " " absolute error = 8.1878948066105300000000000000E-14 " " relative error = 2.875824408303294000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.54999999999972 " " y[1] (closed_form) = 0.2686968741200877 " " y[1] (numeric) = 0.26869687412016807 " " absolute error = 8.03801469828613300000000000000E-14 " " relative error = 2.9914805390306600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.559999999999719 " " y[1] (closed_form) = 0.25255029746227897 " " y[1] (numeric) = 0.25255029746235785 " " absolute error = 7.88813458996173700000000000000E-14 " " relative error = 3.12339152605429500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.569999999999718 " " y[1] (closed_form) = 0.23627970929695608 " " y[1] (numeric) = 0.2362797092970329 " " absolute error = 7.68274333040608300000000000000E-14 " " relative error = 3.25154595511645050000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5799999999997167 " " y[1] (closed_form) = 0.21988990471494183 " " y[1] (numeric) = 0.21988990471501654 " " absolute error = 7.47180095572730400000000000000E-14 " " relative error = 3.397973620213945400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5899999999997156 " " y[1] (closed_form) = 0.20338573205116064 " " y[1] (numeric) = 0.2033857320512338 " " absolute error = 7.31636973227978200000000000000E-14 " " relative error = 3.59728760640858800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5999999999997145 " " y[1] (closed_form) = 0.18677209132952113 " " y[1] (numeric) = 0.1867720913295928 " " absolute error = 7.16648962395538500000000000000E-14 " " relative error = 3.83702381492938450000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6099999999997134 " " y[1] (closed_form) = 0.17005393268578425 " " y[1] (numeric) = 0.17005393268585373 " " absolute error = 6.94722057659191700000000000000E-14 " " relative error = 4.08530427192682840000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6199999999997123 " " y[1] (closed_form) = 0.15323625476896385 " " y[1] (numeric) = 0.15323625476903116 " " absolute error = 6.73072708679001200000000000000E-14 " " relative error = 4.392385533657169000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6299999999997112 " " y[1] (closed_form) = 0.13632410312181575 " " y[1] (numeric) = 0.13632410312188148 " " absolute error = 6.57252030578092700000000000000E-14 " " relative error = 4.82124595377523900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.63999999999971 " " y[1] (closed_form) = 0.11932256854097562 " " y[1] (numeric) = 0.11932256854103983 " " absolute error = 6.42125241867574900000000000000E-14 " " relative error = 5.38142322713299400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.649999999999709 " " y[1] (closed_form) = 0.10223678541731368 " " y[1] (numeric) = 0.1022367854173757 " " absolute error = 6.20198337131228100000000000000E-14 " " relative error = 6.06629340505651500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.659999999999708 " " y[1] (closed_form) = 8.50719300570875200E-2 " " y[1] (numeric) = 8.50719300571473700E-2 " " absolute error = 5.98548988151037500000000000000E-14 " " relative error = 7.03579885573750600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.669999999999707 " " y[1] (closed_form) = 6.7833218984483300E-2 " " y[1] (numeric) = 6.78332189845415800E-2 " " absolute error = 5.8272831005012900000000000000E-14 " " relative error = 8.59060381880781500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6799999999997057 " " y[1] (closed_form) = 5.05259072261374200E-2 " " y[1] (numeric) = 5.052590722619407000E-2 " " absolute error = 5.664219093759470000000000000000E-14 " " relative error = 1.12105242730393340000000000E-10 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6899999999997046 " " y[1] (closed_form) = 3.31552865782389600E-2 " " y[1] (numeric) = 3.31552865782933600E-2 " " absolute error = 5.439398931272876000000000000000E-14 " " relative error = 1.64058269212577200000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6999999999997035 " " y[1] (closed_form) = 1.57266838568257400E-2 " " y[1] (numeric) = 1.572668385687792400E-2 " " absolute error = 5.21839516043343100000000000000E-14 " " relative error = 3.31817896763310860000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7099999999997024 " " y[1] (closed_form) = -1.7545408681064467000E-3 " " y[1] (numeric) = -1.754540868055868800E-3 " " absolute error = 5.057781450601428000000000000000E-14 " " relative error = 2.882680901049594000000000E-9 "%" Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7199999999997013 " " y[1] (closed_form) = -1.92829960540598100E-2 " " y[1] (numeric) = -1.928299605401091700E-2 " " absolute error = 4.88914464469303300000000000000E-14 " " relative error = 2.53546940059850350000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7299999999997 " " y[1] (closed_form) = -3.68532604824272100E-2 " " y[1] (numeric) = -3.685326048238049500E-2 " " absolute error = 4.67126337611034600000000000000E-14 " " relative error = 1.2675305563093260000000000E-10 "%" Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.739999999999699 " " y[1] (closed_form) = -5.44598850691804800E-2 " " y[1] (numeric) = -5.44598850691359600E-2 " " absolute error = 4.45199432874687800000000000000E-14 " " relative error = 8.17481403622409700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.749999999999698 " " y[1] (closed_form) = -7.20973946892099700E-2 " " y[1] (numeric) = -7.20973946891671800E-2 " " absolute error = 4.279909759929978500000000000000E-14 " " relative error = 5.93628906894538000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.759999999999697 " " y[1] (closed_form) = -8.97602900136670300E-2 " " y[1] (numeric) = -8.9760290013625900E-2 " " absolute error = 4.11337630623620500000000000000E-14 " " relative error = 4.58262368092827670000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.769999999999696 " " y[1] (closed_form) = -0.10744304935965543 " " y[1] (numeric) = -0.10744304935961659 " " absolute error = 3.884392807407266400000000000000E-14 " " relative error = 3.615303949913623600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7799999999996947 " " y[1] (closed_form) = -0.12514013055161022 " " y[1] (numeric) = -0.12514013055157355 " " absolute error = 3.666511538824579500000000000000E-14 " " relative error = 2.92992465539456900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7899999999996936 " " y[1] (closed_form) = -0.14284597279369296 " " y[1] (numeric) = -0.14284597279365796 " " absolute error = 3.49997808513080600000000000000E-14 " " relative error = 2.450176239960010500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7999999999996925 " " y[1] (closed_form) = -0.1605549985525365 " " y[1] (numeric) = -0.16055499855250324 " " absolute error = 3.32511795875234400000000000000E-14 " " relative error = 2.071014909986938500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8099999999996914 " " y[1] (closed_form) = -0.17826161544966385 " " y[1] (numeric) = -0.17826161544963268 " " absolute error = 3.11695114163512700000000000000E-14 " " relative error = 1.748526251023046500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8199999999996903 " " y[1] (closed_form) = -0.19596021816289766 " " y[1] (numeric) = -0.1959602181628687 " " absolute error = 2.894906536710095700000000000000E-14 " " relative error = 1.47729297499741500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.829999999999689 " " y[1] (closed_form) = -0.21364519033607543 " " y[1] (numeric) = -0.21364519033604812 " " absolute error = 2.73114864057788500000000000000E-14 " " relative error = 1.278357184770525800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.839999999999688 " " y[1] (closed_form) = -0.23131090649638059 " " y[1] (numeric) = -0.23131090649635494 " " absolute error = 2.564615186884111600000000000000E-14 " " relative error = 1.108730766624807200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.849999999999687 " " y[1] (closed_form) = -0.24895173397860104 " " y[1] (numeric) = -0.24895173397857762 " " absolute error = 2.342570581959080300000000000000E-14 " " relative error = 9.40973796214023900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.859999999999686 " " y[1] (closed_form) = -0.26656203485561525 " " y[1] (numeric) = -0.2665620348555941 " " absolute error = 2.114974861910923200000000000000E-14 " " relative error = 7.934268895630657000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.869999999999685 " " y[1] (closed_form) = -0.2841361678744052 " " y[1] (numeric) = -0.28413616787438567 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 6.876958107649237000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8799999999996837 " " y[1] (closed_form) = -0.3016684903968945 " " y[1] (numeric) = -0.30166849039687677 " " absolute error = 1.770805724277124700000000000000E-14 " " relative error = 5.8700387367183730000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8899999999996826 " " y[1] (closed_form) = -0.31915336034491004 " " y[1] (numeric) = -0.31915336034489455 " " absolute error = 1.548761119352093400000000000000E-14 " " relative error = 4.852717570256326000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8999999999996815 " " y[1] (closed_form) = -0.3365851381485559 " " y[1] (numeric) = -0.3365851381485424 " " absolute error = 1.348920974919565200000000000000E-14 " " relative error = 4.0076664773125026000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9099999999996804 " " y[1] (closed_form) = -0.3539581886972877 " " y[1] (numeric) = -0.35395818869727586 " " absolute error = 1.182387521225791700000000000000E-14 " " relative error = 3.3404722901805606000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9199999999996793 " " y[1] (closed_form) = -0.37126688329297913 " " y[1] (numeric) = -0.37126688329296903 " " absolute error = 1.010302952408892500000000000000E-14 " " relative error = 2.7212310008582924000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.929999999999678 " " y[1] (closed_form) = -0.3885056016042673 " " y[1] (numeric) = -0.3885056016042593 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 2.0575265180972688000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.939999999999677 " " y[1] (closed_form) = -0.4056687336214601 " " y[1] (numeric) = -0.4056687336214543 " " absolute error = 5.828670879282072000000000000000E-15 " " relative error = 1.4368055499985743000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.949999999999676 " " y[1] (closed_form) = -0.4227506816112901 " " y[1] (numeric) = -0.4227506816112859 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 9.9795167153739360000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.959999999999675 " " y[1] (closed_form) = -0.43974586207079613 " " y[1] (numeric) = -0.43974586207079347 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 6.0592616984566480000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.969999999999674 " " y[1] (closed_form) = -0.45664870767962096 " " y[1] (numeric) = -0.4566487076796204 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.21562046049200160000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9799999999996727 " " y[1] (closed_form) = -0.473453669250003 " " y[1] (numeric) = -0.4734536692500046 " " absolute error = 1.609823385706477000000000000000E-15 " " relative error = 3.4001708937151020000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9899999999996716 " " y[1] (closed_form) = -0.4901552176737433 " " y[1] (numeric) = -0.49015521767374665 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 6.7951313253028080000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9999999999996705 " " y[1] (closed_form) = -0.5067478458654329 " " y[1] (numeric) = -0.506747845865438 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 1.0078041682750229000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.009999999999674 " " y[1] (closed_form) = -0.5232260707012307 " " y[1] (numeric) = -0.5232260707012307 " " 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] = 4.019999999999677 " " y[1] (closed_form) = -0.5395844349524423 " " y[1] (numeric) = -0.5395844349524364 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 1.111078071313204000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0299999999996805 " " y[1] (closed_form) = -0.5558175092132447 " " y[1] (numeric) = -0.5558175092132337 " " absolute error = 1.09912079437890500000000000000E-14 " " relative error = 1.9774850129041485000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.039999999999684 " " y[1] (closed_form) = -0.5719198938217938 " " y[1] (numeric) = -0.5719198938217768 " " absolute error = 1.698641227676489500000000000000E-14 " " relative error = 2.9700684414481554000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.049999999999687 " " y[1] (closed_form) = -0.58788622077401 " " y[1] (numeric) = -0.5878862207739882 " " absolute error = 2.176037128265306800000000000000E-14 " " relative error = 3.701459655578149000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0599999999996905 " " y[1] (closed_form) = -0.6037111556293546 " " y[1] (numeric) = -0.6037111556293275 " " absolute error = 2.70894418008538200000000000000E-14 " " relative error = 4.487152763081496700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.069999999999694 " " y[1] (closed_form) = -0.619389399407861 " " y[1] (numeric) = -0.619389399407829 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 5.162249005193211000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.079999999999697 " " y[1] (closed_form) = -0.6349156904777388 " " y[1] (numeric) = -0.6349156904777012 " " absolute error = 3.75255382323302900000000000000E-14 " " relative error = 5.9103182981813550000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.0899999999997005 " " y[1] (closed_form) = -0.6502848064328286 " " y[1] (numeric) = -0.6502848064327863 " " absolute error = 4.229949723821846400000000000000E-14 " " relative error = 6.504764807631686000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.099999999999704 " " y[1] (closed_form) = -0.6654915659592253 " " y[1] (numeric) = -0.6654915659591777 " " absolute error = 4.762856775641921600000000000000E-14 " " relative error = 7.156900281338414000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.109999999999707 " " y[1] (closed_form) = -0.6805308306903556 " " y[1] (numeric) = -0.6805308306903031 " " absolute error = 5.251354906476990000000000000000E-14 " " relative error = 7.716556942982028000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.119999999999710 " " y[1] (closed_form) = -0.6953975070498336 " " y[1] (numeric) = -0.6953975070497759 " " absolute error = 5.77315972805081400000000000000E-14 " " relative error = 8.301956319261148000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.129999999999714 " " y[1] (closed_form) = -0.7100865480813898 " " y[1] (numeric) = -0.7100865480813273 " " absolute error = 6.25055562863963100000000000000E-14 " " relative error = 8.802526460370568000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.139999999999717 " " y[1] (closed_form) = -0.724592955265203 " " y[1] (numeric) = -0.7245929552651353 " " absolute error = 6.76125821996720300000000000000E-14 " " relative error = 9.331112275984749000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.149999999999720 " " y[1] (closed_form) = -0.7389117803199379 " " y[1] (numeric) = -0.7389117803198657 " " absolute error = 7.21644966006351800000000000000E-14 " " relative error = 9.766321030825768000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.159999999999724 " " y[1] (closed_form) = -0.7530381269898301 " " y[1] (numeric) = -0.7530381269897529 " " absolute error = 7.71605002114483800000000000000E-14 " " relative error = 1.024655956264621500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.169999999999727 " " y[1] (closed_form) = -0.7669671528161288 " " y[1] (numeric) = -0.7669671528160474 " " absolute error = 8.13793477050239700000000000000E-14 " " relative error = 1.061053884853054300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.179999999999730 " " y[1] (closed_form) = -0.780694070892248 " " y[1] (numeric) = -0.7806940708921616 " " absolute error = 8.63753513158371800000000000000E-14 " " relative error = 1.10639179335792300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.189999999999734 " " y[1] (closed_form) = -0.7942141516019462 " " y[1] (numeric) = -0.7942141516018556 " " absolute error = 9.05941988094127700000000000000E-14 " " relative error = 1.140677216927983900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.199999999999737 " " y[1] (closed_form) = -0.8075227243399019 " " y[1] (numeric) = -0.8075227243398064 " " absolute error = 9.54791801177634600000000000000E-14 " " relative error = 1.182371433519862600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.209999999999740 " " y[1] (closed_form) = -0.8206151792140098 " " y[1] (numeric) = -0.8206151792139101 " " absolute error = 9.96980276113390600000000000000E-14 " " relative error = 1.214918150878349900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.219999999999744 " " y[1] (closed_form) = -0.8334869687287787 " " y[1] (numeric) = -0.8334869687286746 " " absolute error = 1.04138919709839680000000000000E-13 " " relative error = 1.249436687278635300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.229999999999747 " " y[1] (closed_form) = -0.8461336094491722 " " y[1] (numeric) = -0.8461336094490639 " " absolute error = 1.08246744900952760000000000000E-13 " " relative error = 1.279310308586143200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.239999999999750 " " y[1] (closed_form) = -0.8585506836442801 " " y[1] (numeric) = -0.8585506836441674 " " absolute error = 1.12687636999453390000000000000E-13 " " relative error = 1.312533309287338400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.249999999999754 " " y[1] (closed_form) = -0.8707338409101809 " " y[1] (numeric) = -0.8707338409100644 " " absolute error = 1.16462395283178920000000000000E-13 " " relative error = 1.337520029788212000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.259999999999757 " " y[1] (closed_form) = -0.8826787997713927 " " y[1] (numeric) = -0.882678799771272 " " absolute error = 1.20792265079217030000000000000E-13 " " relative error = 1.368473618155339500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.269999999999760 " " y[1] (closed_form) = -0.8943813492602894 " " y[1] (numeric) = -0.894381349260165 " " absolute error = 1.24456001060480050000000000000E-13 " " relative error = 1.391531712545360200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.279999999999764 " " y[1] (closed_form) = -0.9058373504738958 " " y[1] (numeric) = -0.9058373504737673 " " absolute error = 1.2845280394913060000000000000E-13 " " relative error = 1.418055944391446400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.289999999999767 " " y[1] (closed_form) = -0.9170427381074497 " " y[1] (numeric) = -0.9170427381073178 " " absolute error = 1.3189449532546860000000000000E-13 " " relative error = 1.438258980139424700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.299999999999770 " " y[1] (closed_form) = -0.9279935219641647 " " y[1] (numeric) = -0.9279935219640287 " " absolute error = 1.36002320516581680000000000000E-13 " " relative error = 1.46555247744319400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.309999999999774 " " y[1] (closed_form) = -0.9386857884405957 " " y[1] (numeric) = -0.9386857884404564 " " absolute error = 1.39332989590457150000000000000E-13 " " relative error = 1.484341100145192500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.319999999999777 " " y[1] (closed_form) = -0.9491157019870581 " " y[1] (numeric) = -0.949115701986915 " " absolute error = 1.43107747874182680000000000000E-13 " " relative error = 1.507800867424001800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.329999999999780 " " y[1] (closed_form) = -0.9592795065425206 " " y[1] (numeric) = -0.9592795065423744 " " absolute error = 1.46216372343133120000000000000E-13 " " relative error = 1.524231168766785600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.339999999999784 " " y[1] (closed_form) = -0.9691735269434383 " " y[1] (numeric) = -0.9691735269432885 " " absolute error = 1.49769086021933620000000000000E-13 " " relative error = 1.545327868109157300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.349999999999787 " " y[1] (closed_form) = -0.978794170305967 " " y[1] (numeric) = -0.9787941703058142 " " absolute error = 1.52877710490884060000000000000E-13 " " relative error = 1.561898457600080800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.359999999999790 " " y[1] (closed_form) = -0.9881379273810396 " " y[1] (numeric) = -0.9881379273808836 " " absolute error = 1.5598633495983450000000000000E-13 " " relative error = 1.578588683193859500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.369999999999794 " " y[1] (closed_form) = -0.9972013738817709 " " y[1] (numeric) = -0.9972013738816118 " " absolute error = 1.59094959428784930000000000000E-13 " " relative error = 1.595414563153694200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.379999999999797 " " y[1] (closed_form) = -1.0059811717826836 " " y[1] (numeric) = -1.0059811717825216 " " absolute error = 1.62092561595272850000000000000E-13 " " relative error = 1.61128822429182400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.389999999999800 " " y[1] (closed_form) = -1.0144740705902469 " " y[1] (numeric) = -1.014474070590082 " " absolute error = 1.64757096854373230000000000000E-13 " " relative error = 1.624064149402196000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.399999999999804 " " y[1] (closed_form) = -1.0226769085842375 " " y[1] (numeric) = -1.0226769085840703 " " absolute error = 1.67199587508548570000000000000E-13 " " relative error = 1.634920922777209600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.409999999999807 " " y[1] (closed_form) = -1.030586614029439 " " y[1] (numeric) = -1.0305866140292697 " " absolute error = 1.6942003355779890000000000000E-13 " " relative error = 1.643918436854055200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.419999999999810 " " y[1] (closed_form) = -1.0382002063572047 " " y[1] (numeric) = -1.0382002063570326 " " absolute error = 1.72084568816899260000000000000E-13 " " relative error = 1.657527784748788500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.429999999999814 " " y[1] (closed_form) = -1.0455147973164236 " " y[1] (numeric) = -1.0455147973162495 " " absolute error = 1.74082970261224550000000000000E-13 " " relative error = 1.665045494411482300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.439999999999817 " " y[1] (closed_form) = -1.0525275920934416 " " y[1] (numeric) = -1.0525275920932649 " " absolute error = 1.76747505520324920000000000000E-13 " " relative error = 1.679267193069781000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.449999999999820 " " y[1] (closed_form) = -1.0592358904004884 " " y[1] (numeric) = -1.0592358904003096 " " absolute error = 1.7874590696465020000000000000E-13 " " relative error = 1.68749858822351500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.459999999999824 " " y[1] (closed_form) = -1.0656370875321948 " " y[1] (numeric) = -1.0656370875320138 " " absolute error = 1.80966353013900520000000000000E-13 " " relative error = 1.698198712593448600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4699999999998274 " " y[1] (closed_form) = -1.0717286753897701 " " y[1] (numeric) = -1.0717286753895874 " " absolute error = 1.82742709853300770000000000000E-13 " " relative error = 1.705121025961540400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.479999999999830 " " y[1] (closed_form) = -1.0775082434724434 " " y[1] (numeric) = -1.0775082434722585 " " absolute error = 1.84963155902551080000000000000E-13 " " relative error = 1.716582281602575800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.489999999999834 " " y[1] (closed_form) = -1.0829734798357686 " " y[1] (numeric) = -1.0829734798355821 " " absolute error = 1.8651746813702630000000000000E-13 " " relative error = 1.72227179713866500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4999999999998375 " " y[1] (closed_form) = -1.088122172016417 " " y[1] (numeric) = -1.0881221720162289 " " absolute error = 1.88071780371501520000000000000E-13 " " relative error = 1.72840683893962600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.509999999999840 " " y[1] (closed_form) = -1.09295220792308 " " y[1] (numeric) = -1.0929522079228904 " " absolute error = 1.89626092605976740000000000000E-13 " " relative error = 1.734989793984864400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.519999999999844 " " y[1] (closed_form) = -1.0974615766931335 " " y[1] (numeric) = -1.0974615766929425 " " absolute error = 1.90958360235526920000000000000E-13 " " relative error = 1.74000041815515600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5299999999998475 " " y[1] (closed_form) = -1.1016483695147088 " " y[1] (numeric) = -1.1016483695145165 " " absolute error = 1.92290627865077100000000000000E-13 " " relative error = 1.745480982736658200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.539999999999850 " " y[1] (closed_form) = -1.105510780413846 " " y[1] (numeric) = -1.1055107804136528 " " absolute error = 1.93178806284777240000000000000E-13 " " relative error = 1.74741675709811800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.549999999999854 " " y[1] (closed_form) = -1.1090471070064039 " " y[1] (numeric) = -1.1090471070062096 " " absolute error = 1.9428902930940240000000000000E-13 " " relative error = 1.7518555170648900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5599999999998575 " " y[1] (closed_form) = -1.1122557512144209 " " y[1] (numeric) = -1.1122557512142255 " " absolute error = 1.95399252334027550000000000000E-13 " " relative error = 1.756783474670102500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.569999999999860 " " y[1] (closed_form) = -1.1151352199466338 " " y[1] (numeric) = -1.115135219946437 " " absolute error = 1.96731519963577740000000000000E-13 " " relative error = 1.764194300786165000000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.579999999999864 " " y[1] (closed_form) = -1.1176841257428687 " " y[1] (numeric) = -1.1176841257426715 " " absolute error = 1.9717560917342780000000000000E-13 " " relative error = 1.764144310829994500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5899999999998675 " " y[1] (closed_form) = -1.1199011873820441 " " y[1] (numeric) = -1.1199011873818463 " " absolute error = 1.9784174298820290000000000000E-13 " " relative error = 1.766599993082344800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.599999999999870 " " y[1] (closed_form) = -1.1217852304535183 " " y[1] (numeric) = -1.1217852304533198 " " absolute error = 1.985078768029780000000000000E-13 " " relative error = 1.769571139055955700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.609999999999874 " " y[1] (closed_form) = -1.123335187891552 " " y[1] (numeric) = -1.1233351878913533 " " absolute error = 1.98729921407903020000000000000E-13 " " relative error = 1.769106171960212700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.6199999999998775 " " y[1] (closed_form) = -1.1245501004726512 " " y[1] (numeric) = -1.1245501004724523 " " absolute error = 1.98951966012828050000000000000E-13 " " relative error = 1.769169429883186400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.629999999999880 " " y[1] (closed_form) = -1.125429117275575 " " y[1] (numeric) = -1.1254291172753754 " " absolute error = 1.99618099827603150000000000000E-13 " " relative error = 1.773706551247191700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.639999999999884 " " y[1] (closed_form) = -1.1259714961038099 " " y[1] (numeric) = -1.1259714961036107 " " absolute error = 1.99174010617753080000000000000E-13 " " relative error = 1.768908105639914700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.649999999999888 " " y[1] (closed_form) = -1.126176603870324 " " y[1] (numeric) = -1.1261766038701244 " " absolute error = 1.99618099827603150000000000000E-13 " " relative error = 1.7725292741971100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.659999999999891 " " y[1] (closed_form) = -1.126043916944421 " " y[1] (numeric) = -1.1260439169442218 " " absolute error = 1.99174010617753080000000000000E-13 " " relative error = 1.768794339373744600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.669999999999894 " " y[1] (closed_form) = -1.1255730214605442 " " y[1] (numeric) = -1.125573021460345 " " absolute error = 1.99174010617753080000000000000E-13 " " relative error = 1.76953433335941900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.679999999999898 " " y[1] (closed_form) = -1.1247636135888741 " " y[1] (numeric) = -1.1247636135886754 " " absolute error = 1.98729921407903020000000000000E-13 " " relative error = 1.7668594450152900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.689999999999901 " " y[1] (closed_form) = -1.123615499767597 " " y[1] (numeric) = -1.1236154997673984 " " absolute error = 1.985078768029780000000000000E-13 " " relative error = 1.76668866568711780000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.699999999999904 " " y[1] (closed_form) = -1.1221285968967187 " " y[1] (numeric) = -1.122128596896521 " " absolute error = 1.9784174298820290000000000000E-13 " " relative error = 1.76309331689202400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.709999999999908 " " y[1] (closed_form) = -1.1203029324933276 " " y[1] (numeric) = -1.1203029324931306 " " absolute error = 1.96953564568502770000000000000E-13 " " relative error = 1.758038463133950700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.719999999999911 " " y[1] (closed_form) = -1.1181386448082093 " " y[1] (numeric) = -1.118138644808013 " " absolute error = 1.96287430753727680000000000000E-13 " " relative error = 1.75548382720817400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.729999999999914 " " y[1] (closed_form) = -1.1156359829037452 " " y[1] (numeric) = -1.1156359829035494 " " absolute error = 1.95843341543877600000000000000E-13 " " relative error = 1.755441241991336500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.739999999999918 " " y[1] (closed_form) = -1.1127953066930265 " " y[1] (numeric) = -1.1127953066928322 " " absolute error = 1.9428902930940240000000000000E-13 " " relative error = 1.74595478737940600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.749999999999921 " " y[1] (closed_form) = -1.1096170869401458 " " y[1] (numeric) = -1.1096170869399522 " " absolute error = 1.9362289549462730000000000000E-13 " " relative error = 1.744952360354843600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.759999999999924 " " y[1] (closed_form) = -1.1061019052216219 " " y[1] (numeric) = -1.1061019052214291 " " absolute error = 1.92734717074927180000000000000E-13 " " relative error = 1.742467996529761800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.769999999999928 " " y[1] (closed_form) = -1.1022504538489521 " " y[1] (numeric) = -1.1022504538487607 " " absolute error = 1.914024494453770000000000000E-13 " " relative error = 1.736469681432365200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.779999999999931 " " y[1] (closed_form) = -1.098063535752278 " " y[1] (numeric) = -1.0980635357520883 " " absolute error = 1.89848137210901770000000000000E-13 " " relative error = 1.728935813179860400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.789999999999934 " " y[1] (closed_form) = -1.0935420643251827 " " y[1] (numeric) = -1.093542064324994 " " absolute error = 1.8873791418627660000000000000E-13 " " relative error = 1.725931908277762200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.799999999999938 " " y[1] (closed_form) = -1.0886870632306356 " " y[1] (numeric) = -1.0886870632304488 " " absolute error = 1.86739512741951330000000000000E-13 " " relative error = 1.7152726347992900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.809999999999941 " " y[1] (closed_form) = -1.0834996661681366 " " y[1] (numeric) = -1.0834996661679515 " " absolute error = 1.8518520050747610000000000000E-13 " " relative error = 1.7091394329856600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.819999999999944 " " y[1] (closed_form) = -1.0779811166020965 " " y[1] (numeric) = -1.0779811166019138 " " absolute error = 1.82742709853300770000000000000E-13 " " relative error = 1.695231085580830300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.829999999999948 " " y[1] (closed_form) = -1.0721327674515395 " " y[1] (numeric) = -1.0721327674513585 " " absolute error = 1.80966353013900520000000000000E-13 " " relative error = 1.687909916642671700000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.839999999999951 " " y[1] (closed_form) = -1.0659560807411919 " " y[1] (numeric) = -1.0659560807410136 " " absolute error = 1.78301817754800140000000000000E-13 " " relative error = 1.67269384711255100000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.849999999999954 " " y[1] (closed_form) = -1.0594526272140703 " " y[1] (numeric) = -1.0594526272138938 " " absolute error = 1.7652546091539990000000000000E-13 " " relative error = 1.666194942378783600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.859999999999958 " " y[1] (closed_form) = -1.0526240859056637 " " y[1] (numeric) = -1.0526240859054894 " " absolute error = 1.74305014866149580000000000000E-13 " " relative error = 1.655909428636908600000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.869999999999961 " " y[1] (closed_form) = -1.0454722436798503 " " y[1] (numeric) = -1.045472243679678 " " absolute error = 1.7230661342182430000000000000E-13 " " relative error = 1.648122314709570500000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.879999999999964 " " y[1] (closed_form) = -1.037998994726671 " " y[1] (numeric) = -1.0379989947265014 " " absolute error = 1.69642078162723920000000000000E-13 " " relative error = 1.634318328096209200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.889999999999968 " " y[1] (closed_form) = -1.0302063400221313 " " y[1] (numeric) = -1.0302063400219643 " " absolute error = 1.66977542903623540000000000000E-13 " " relative error = 1.620816494878457900000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.899999999999971 " " y[1] (closed_form) = -1.0220963867501784 " " y[1] (numeric) = -1.0220963867500146 " " absolute error = 1.6386891843467310000000000000E-13 " " relative error = 1.603262867954214400000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.909999999999974 " " y[1] (closed_form) = -1.0136713476870565 " " y[1] (numeric) = -1.0136713476868948 " " absolute error = 1.6164847238542280000000000000E-13 " " relative error = 1.594683254629461800000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.919999999999978 " " y[1] (closed_form) = -1.004933540548211 " " y[1] (numeric) = -1.0049335405480526 " " absolute error = 1.58317803311547320000000000000E-13 " " relative error = 1.575405705189040200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.929999999999981 " " y[1] (closed_form) = -0.9958853872979797 " " y[1] (numeric) = -0.9958853872978237 " " absolute error = 1.5598633495983450000000000000E-13 " " relative error = 1.566308100805195200000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.939999999999984 " " y[1] (closed_form) = -0.9865294134222606 " " y[1] (numeric) = -0.9865294134221081 " " absolute error = 1.5254464358349650000000000000E-13 " " relative error = 1.546275676204328000000000000E-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) = -0.9768682471644263 " " y[1] (numeric) = -0.9768682471642767 " " absolute error = 1.4965806371947110000000000000E-13 " " relative error = 1.532018920196109900000000000E-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) = -0.9669046187247059 " " y[1] (numeric) = -0.9669046187245599 " " absolute error = 1.45994327738208090000000000000E-13 " " relative error = 1.509914472544009500000000000E-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) = -0.956641359423323 " " y[1] (numeric) = -0.95664135942318 " " absolute error = 1.42996725571720160000000000000E-13 " " relative error = 1.494778833918707400000000000E-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) = -0.9460814008276436 " " y[1] (numeric) = -0.9460814008275046 " " absolute error = 1.3899992268306960000000000000E-13 " " relative error = 1.469217369260940300000000000E-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) = -0.9352277738436507 " " y[1] (numeric) = -0.9352277738435151 " " absolute error = 1.35669253609194130000000000000E-13 " " relative error = 1.4506546683447300000000000E-11 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 1.000E-3 " " "Finished!" "diff ( y , x , 1 ) = sin ( 2.0 * x + 3.0 ) + cos ( 1.5 * x - 2.0 ) ; " Iterations = 4900 "Total Elapsed Time "= 1 Minutes 24 Seconds "Elapsed Time(since restart) "= 1 Minutes 24 Seconds "Time to Timeout "= 1 Minutes 35 Seconds Percent Done = 100.0204081632654 "%" (%o259) temp/diffeq.lin_sin_cos.max