(%i1) batch("temp/diffeq.sing5_back.max") read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.sing5_back.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([20],convfloat)),fixnum) (%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a], completearray([20],convfloat),[arr_b], completearray([20],convfloat),[jjj_ats],fixnum), convfloat) (%i25) mode_declare(att([mmm_att],fixnum,[arr_a], completearray([20],convfloat),[arr_b], completearray([20],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,20,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,[20],convfloat) (%i173) completearray(array_norms,[20],convfloat) (%i174) completearray(array_fact_1,[20],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,[20],convfloat) (%i184) completearray(array_x,[20],convfloat) (%i185) completearray(array_tmp0,[20],convfloat) (%i186) completearray(array_tmp1,[20],convfloat) (%i187) completearray(array_tmp2,[20],convfloat) (%i188) completearray(array_tmp3,[20],convfloat) (%i189) completearray(array_tmp4,[20],convfloat) (%i190) completearray(array_tmp5,[20],convfloat) (%i191) completearray(array_tmp6,[20],convfloat) (%i192) completearray(array_m1,[20],convfloat) (%i193) completearray(array_y_higher,[2,20],convfloat) (%i194) completearray(array_y_higher_work,[2,20],convfloat) (%i195) completearray(array_y_higher_work2,[2,20],convfloat) (%i196) completearray(array_y_set_initial,[2,20],convfloat) (%i197) completearray(array_given_rad_poles,[2,3],convfloat) (%i198) completearray(array_given_ord_poles,[2,3],convfloat) (%i199) completearray(array_rad_test_poles,[2,4],convfloat) (%i200) completearray(array_ord_test_poles,[2,4],convfloat) (%i201) completearray(array_fact_2,[20,20],convfloat) (%i202) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%i203) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%i204) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%i205) omniout_float(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (if vallen = 4 then printf(true,"~a = ~g ~s ~%",prelabel, value,postlabel) else printf(true,"~a = ~g ~s ~%",prelabel, value,postlabel)) (%i206) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%i207) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%i208) logitem_time(fd,secs_in):=( block(mode_declare( [[days_int,hours_int,minutes_int,sec_int, years_int],fixnum,[secs,secs_temp],convfloat]), secs:secs_in,printf(fd,"~%"), if secs >= 0 then (years_int :truncate(secs/glob_sec_in_year), sec_temp :mod(truncate(secs), truncate(glob_sec_in_year)), days_int :truncate(sec_temp/glob_sec_in_day), sec_temp :mod(sec_temp, truncate(glob_sec_in_day)), hours_int :truncate(sec_temp/glob_sec_in_hour), sec_temp :mod(sec_temp, truncate(glob_sec_in_hour)), minutes_int :truncate(sec_temp/glob_sec_in_minute), sec_int :mod(sec_temp, truncate(glob_sec_in_minute)), if truncate(years_int) > 0.1 then printf(fd, "~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int,days_int, hours_int,minutes_int, sec_int) elseif days_int > 0.1 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,hours_int, minutes_int,sec_int) elseif hours_int > 0.1 then printf(fd, "~d Hours ~d Minutes ~d Seconds~%", hours_int,minutes_int, sec_int) elseif minutes_int > 0.1 then printf(fd, "~d Minutes ~d Seconds~%", minutes_int,sec_int) else printf(fd,"~d Seconds~%", sec_int)) else printf(fd," 0.0 Seconds~%"), printf(fd,"~%")),0) (%i209) omniout_timestr(secs_in):=( block(mode_declare( [[days_int,hours_int,minutes_int,sec_int, years_int],fixnum,[secs,secs_temp], convfloat]),secs:secs_in, if secs >= 0 then ( years_int:truncate(secs/glob_sec_in_year), sec_temp :mod(truncate(secs), truncate(glob_sec_in_year)), days_int:truncate(sec_temp/glob_sec_in_day), sec_temp :mod(sec_temp,truncate(glob_sec_in_day)), hours_int :truncate(sec_temp/glob_sec_in_hour), sec_temp :mod(sec_temp,truncate(glob_sec_in_hour)), minutes_int :truncate(sec_temp/glob_sec_in_minute), sec_int :mod(sec_temp, truncate(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int,days_int, hours_int,minutes_int, sec_int) elseif days_int > 0.1 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,hours_int, minutes_int,sec_int) elseif hours_int > 0.1 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,minutes_int, sec_int) elseif minutes_int > 0.1 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int,sec_int) else printf(true,"= ~d Seconds~%", sec_int)) else printf(true,"= 0.0 Seconds~%")),0) (%i210) zero_ats_ar(arr_a):=( block(mode_declare([iii],fixnum),iii:1, while iii <= ats_max_terms do (arr_a[iii]:glob__0,iii:1+iii)),0) (%i211) ats(mmm_ats,arr_a,arr_b,jjj_ats):=block( mode_declare([[iii_ats,lll_ats,ma_ats],fixnum,[ret_ats], convfloat]),ret_ats:glob__0, if jjj_ats <= mmm_ats then (ma_ats:1+mmm_ats,iii_ats:jjj_ats, while iii_ats <= mmm_ats do (lll_ats:ma_ats-iii_ats, if lll_ats <= ats_max_terms and iii_ats <= ats_max_terms then ret_ats :c(arr_a[iii_ats])*c(arr_b[lll_ats])+ret_ats, iii_ats:1+iii_ats)),ret_ats) (%i212) att(mmm_att,arr_aa,arr_bb,jjj_att):=block( mode_declare([[al_att,iii_att,lll_att,ma_att],convfloat,[ret_att], fixnum]),ret_att:glob__0, if jjj_att < mmm_att then (ma_att:2+mmm_att,iii_att:jjj_att, while iii_att < mmm_att and iii_att <= ats_max_terms do (lll_att:ma_att-iii_att,al_att:lll_att-1, if lll_att <= ats_max_terms and iii_att <= ats_max_terms then ret_att :c(arr_aa[iii_att])*c(arr_bb[lll_att]) *c(al_att) +ret_att,iii_att:1+iii_att), ret_att:ret_att/c(mmm_att)),ret_att) (%i213) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%i214) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%i215) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%i216) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), printf(file,"~d",glob_min_good_digits), printf(file,"")),0) (%i217) log_revs(file,revs):=printf(file,revs) (%i218) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%i219) logitem_h_reason(file):=(printf(file,""), if glob_h_reason = 1 then printf(file,"Max H") elseif glob_h_reason = 2 then printf(file,"Display_interval") elseif glob_h_reason = 3 then printf(file,"Optimal") elseif glob_h_reason = 4 then printf(file,"Pole Accuracy") elseif glob_h_reason = 5 then printf(file,"Min H (Pole)") elseif glob_h_reason = 6 then printf(file,"Pole") elseif glob_h_reason = 7 then printf(file,"Opt Iter") else printf(file,"Impossible"), printf(file,""),0) (%i220) logstart(file):=(printf(file,""),0) (%i221) logend(file):=(printf(file,"~%"),0) (%i222) chk_data():=( block(mode_declare([[errflag],boolean]),errflag:false, if glob_max_iter < 2 then (omniout_str(always,"Illegal max_iter"), errflag:true),if errflag then quit()),0) (%i223) comp_expect_sec(t_end2,t_start2,t2,clock_sec2):=block( mode_declare([[ms2,rrr,sec_left,sub1,sub2], convfloat]),ms2:c(clock_sec2), sub1:c(t_end2-t_start2),sub2:c(t2-t_start2), if sub1 = glob__0 then sec_left:glob__0 else (if sub2 > glob__0 then (rrr:sub1/sub2, sec_left:rrr*c(ms2)-c(ms2)) else sec_left:glob__0),sec_left) (%i224) comp_percent(t_end2,t_start2,t2):=block( mode_declare([[rrr,sub1,sub2],convfloat]), sub1:t_end2-t_start2,sub2:t2-t_start2, if sub2 > glob_small_float then rrr:glob__100*sub2/sub1 else rrr:0.0,rrr) (%i225) comp_rad_from_ratio(term1,term2,last_no):=( if abs(term2) > glob__0 then ret:abs(term1*glob_h/term2) else ret:glob_larger_float,ret) (%i226) comp_ord_from_ratio(term1,term2,last_no):=( if abs(term2) > glob__0 then ret :abs(term2)*c(last_no) *log(abs(term1*glob_h/term2)) /log(c(last_no)) +glob__1 else ret:glob_larger_float,ret) (%i227) c(in_val):=(ret:in_val,ret) (%i228) comp_rad_from_three_terms(term1,term2,term3,last_no):=( temp:abs( term1*term3-term1*term3*c(last_no) +glob__m2*term2*term2 +term2*term2*c(last_no)), if abs(temp) > glob__0 then ret:abs(term2*glob_h*term1/temp) else ret:glob_larger_float,ret) (%i229) comp_ord_from_three_terms(term1,term2,term3,last_no):=( ret:abs( (-term1*term3*c(last_no*last_no) +term2*term2*c(last_no*last_no) +glob__4*term2*term2 -glob__4*term2*term2*c(last_no) -glob__3*term1*term3 +glob__4*term1*term3*c(last_no)) /(term1*term3-term1*term3*c(last_no) -glob__2*term2*term2 +term2*term2*c(last_no))), ret) (%i230) comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):= ( if term5 # glob__0 and term4 # glob__0 and term3 # glob__0 and term2 # glob__0 and term1 # glob__0 then (rm0:term6/term5,rm1:term5/term4, rm2:term4/term3,rm3:term3/term2, rm4:term2/term1, nr1 :c(last_no-3)*rm2 -glob__2*c(last_no-2)*rm1 +c(last_no-1)*rm0, nr2 :c(last_no-4)*rm3 -glob__2*c(last_no-3)*rm2 +c(last_no-2)*rm1, dr1 :(-glob__1)/rm3+glob__2/rm2 +glob__m1/rm1, dr2 :(-glob__1)/rm4+glob__2/rm3 +glob__m1/rm2, ds1 :glob__5/rm3-glob__8/rm2 +glob__3/rm1, ds2 :glob__5/rm4-glob__8/rm3 +glob__3/rm2, if abs(nr1*dr2-nr2*dr1) = glob__0 or abs(dr1) = glob__0 then (rad_c:glob_larger_float, ord_no:glob_larger_float) else (if abs(nr1*dr2-nr2*dr1) > glob__0 then ( rcs :(dr1*dr2-ds2*dr1+ds1*dr2) /(nr1*dr2-nr2*dr1), ord_no :(rcs*nr1-ds1)/(glob__2*dr1) -c(last_no)/glob__2, if abs(rcs) # glob__0 then (if rcs > glob__0 then rad_c :sqrt(rcs) *abs(glob_h) else ( rad_c :glob_larger_float, ord_no :glob_larger_float)) else ( rad_c:glob_larger_float, ord_no:glob_larger_float)) else (rad_c:glob_larger_float, ord_no:glob_larger_float))) else (rad_c:glob_larger_float, ord_no:glob_larger_float), glob_six_term_ord_save:ord_no,rad_c) (%i231) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%i232) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret) (%i233) factorial_1(nnn):=block(mode_declare([[ret],convfloat]), if nnn <= ats_max_terms then (if array_fact_1[nnn] = 0 then (ret:factorial_2(nnn), array_fact_1[nnn]:ret) else ret:array_fact_1[nnn]) else ret:factorial_2(nnn),ret) (%i234) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret) (%i235) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret) (%i236) factorial_3(mmm,nnn):=block(mode_declare([[ret],convfloat]), if nnn <= ats_max_terms and mmm <= ats_max_terms then (if array_fact_2[mmm,nnn] = 0 then (ret:factorial_1(mmm)/factorial_1(nnn), array_fact_2[mmm,nnn]:ret) else ret:array_fact_2[mmm,nnn]) else ret:factorial_2(mmm)/factorial_2(nnn),ret) (%i237) log10(x):=log(x)/glob_log_10 (%i238) c(x):=x (%i239) expt(x,y):=if y = 0.0 then 1.0 elseif x <= 0.0 and y < 0.0 then print("expt error x = ",x,"y = ",y) else x^y (%i240) estimated_needed_step_error(x_start,x_end,estimated_h, estimated_answer):=block( [desired_abs_gbl_error,range, estimated_steps,step_error], omniout_float(always, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32,""), desired_abs_gbl_error :expt(glob__10, c(-glob_desired_digits_correct)) *c(abs(c(estimated_answer))), omniout_float(always,"estimated_h",32, estimated_h,32,""), omniout_float(always,"estimated_answer", 32,estimated_answer,32,""), omniout_float(always, "desired_abs_gbl_error",32, desired_abs_gbl_error,32, ""),range:x_end-x_start, omniout_float(always,"range",32,range,32, ""), estimated_steps:range/estimated_h, omniout_float(always,"estimated_steps",32, estimated_steps,32,""), step_error :c( abs(desired_abs_gbl_error) /sqrt(c(estimated_steps)) /c(ats_max_terms)), omniout_float(always,"step_error",32, step_error,32,""), step_error) (%i241) exact_soln_y(x):=block(c(1.0)/c(x)/c(x)/c(x)) c(1.0) ------ c(x) ------ c(x) (%o241) exact_soln_y(x) := block(------) c(x) (%i242) display_poles():=( block(mode_declare([[rad_given],convfloat]), if glob_type_given_pole = 1 or glob_type_given_pole = 2 then (rad_given :sqrt( array_given_rad_poles[1,2] *array_given_rad_poles[1,2] +(array_x[1] -array_given_rad_poles[1,1]) *(array_x[1] -array_given_rad_poles[1,1])), omniout_float(always, "Radius of convergence (given) for eq 1 ", 4,rad_given,4," "), omniout_float(always, "Order of pole (given) ", 4, array_given_ord_poles[ 1,1],4," "), if rad_given < glob_least_given_sing then glob_least_given_sing :rad_given) elseif glob_type_given_pole = 3 then omniout_str(always, "NO POLE (given) for Equation 1") elseif glob_type_given_pole = 5 then omniout_str(always, "SOME POLE (given) for Equation 1") else omniout_str(always, "NO info (given) for Equation 1"), if array_rad_test_poles[1,1] < glob_large_float then (omniout_float(always, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1,1], 4," "), if array_rad_test_poles[1,1] < glob_least_ratio_sing then glob_least_ratio_sing :array_rad_test_poles[1,1], omniout_float(always, "Order of pole (ratio test) ", 4, array_ord_test_poles[1,1], 4," ")) else omniout_str(always, "NO POLE (ratio test) for Equation 1"), if array_rad_test_poles[1,2] > glob__small and array_rad_test_poles[1,2] < glob_large_float then (omniout_float(always, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1,2], 4," "), if array_rad_test_poles[1,2] < glob_least_3_sing then glob_least_3_sing :array_rad_test_poles[1,2], omniout_float(always, "Order of pole (three term test) ", 4, array_ord_test_poles[1,2], 4," ")) else omniout_str(always, "NO REAL POLE (three term test) for Equation 1"), if array_rad_test_poles[1,3] > glob__small and array_rad_test_poles[1,3] < glob_large_float then (omniout_float(always, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1,3], 4," "), if array_rad_test_poles[1,3] < glob_least_6_sing then glob_least_6_sing :array_rad_test_poles[1,3], omniout_float(always, "Order of pole (six term test) ", 4, array_ord_test_poles[1,3], 4," ")) else omniout_str(always, "NO COMPLEX POLE (six term test) for Equation 1")), 0) (%i243) my_check_sign(x0,xf):=block([ret], if xf > x0 then ret:glob__1 else ret:glob__m1,ret) (%i244) est_size_answer():=block([min_size], min_size:glob_estimated_size_answer, if abs(array_y[1]) < min_size then (min_size:abs(array_y[1]), omniout_float(always,"min_size",32,min_size, 32,"")), if min_size < glob__1 then (min_size:glob__1, omniout_float(always,"min_size",32,min_size, 32,"")),min_size) (%i245) test_suggested_h():=block( [max_estimated_step_error,hn_div_ho,hn_div_ho_2, hn_div_ho_3,no_terms,est_tmp], max_estimated_step_error:glob__small, no_terms:ats_max_terms,hn_div_ho:glob__0_5, hn_div_ho_2:glob__0_25,hn_div_ho_3:glob__0_125, omniout_float(always,"hn_div_ho",32,hn_div_ho,32,""), omniout_float(always,"hn_div_ho_2",32,hn_div_ho_2,32, ""), omniout_float(always,"hn_div_ho_3",32,hn_div_ho_3,32, ""), est_tmp:abs(array_y[no_terms]*hn_div_ho_3 +array_y[no_terms-1]*hn_div_ho_2 +array_y[no_terms-2]*hn_div_ho +array_y[no_terms-3]), if est_tmp >= max_estimated_step_error then max_estimated_step_error:est_tmp, omniout_float(always,"max_estimated_step_error",32, max_estimated_step_error,32,""), max_estimated_step_error) (%i246) track_estimated_error():=block( [hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms, est_tmp],no_terms:ats_max_terms, hn_div_ho:glob__0_5,hn_div_ho_2:glob__0_25, hn_div_ho_3:glob__0_125, est_tmp:c(abs(array_y[no_terms]))*c(hn_div_ho_3) +c(abs(array_y[no_terms-1])) *c(hn_div_ho_2) +c(abs(array_y[no_terms-2])) *c(hn_div_ho) +c(abs(array_y[no_terms-3])), if glob_prec*c(abs(array_y[1])) > c(est_tmp) then est_tmp :c(glob_prec)*c(abs(array_y[1])), if c(est_tmp) >= c(array_max_est_error[1]) then array_max_est_error[1]:c(est_tmp)) (%i247) reached_interval():=block(mode_declare([[ret],boolean]), if glob_check_sign*array_x[1] >= glob_check_sign*glob_next_display -glob_h/glob__10 then ret:true else ret:false, return(ret)) (%i248) display_alot(iter):=( block(mode_declare( [[abserr,est_rel_err],convfloat, [closed_form_val_y],convfloat,[ind_var], convfloat,[numeric_val],convfloat,[relerr], convfloat,[term_no],fixnum]), if reached_interval() then (if iter >= 0 then (ind_var:array_x[1], omniout_float(always, "x[1] ", 33,ind_var,20, " "), closed_form_val_y :exact_soln_y(ind_var), omniout_float(always, "y[1] (closed_form) ", 33, closed_form_val_y, 20," "), term_no:1, numeric_val:array_y[term_no], abserr :abs( numeric_val -closed_form_val_y), omniout_float(always, "y[1] (numeric) ", 33,numeric_val, 20," "), if c(abs(closed_form_val_y)) > c(glob_prec) then ( relerr :abserr*glob__100 /abs(closed_form_val_y), if c(relerr) > c(glob_prec) then glob_good_digits :3 -floor(log10(c(relerr))) else glob_good_digits:16) else (relerr:glob__m1, glob_good_digits:-16), if glob_good_digits < glob_min_good_digits then glob_min_good_digits :glob_good_digits, if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits then glob_min_apfp_est_good_digits :glob_apfp_est_good_digits, if c(abs(numeric_val)) > c(glob_prec) then ( est_rel_err :c(array_max_est_error[1]) *glob__100 *c(sqrt(glob_iter))*c(25) *c(ats_max_terms) /c(abs(numeric_val)), if est_rel_err > glob_prec then glob_est_digits :3 -floor( log10(est_rel_err)) else glob_est_digits:16) else (relerr:glob__m1, glob_est_digits:-16), array_est_digits[1] :glob_est_digits, if glob_iter = 1 then array_1st_rel_error[1] :relerr else array_last_rel_error[ 1] :relerr, array_est_rel_error[1] :est_rel_err, omniout_float(always, "absolute error ", 4,abserr,20," "), omniout_float(always, "relative error ", 4,relerr,20,"%"), omniout_int(info, "Desired digits ", 32, glob_desired_digits_correct, 4," "), omniout_int(info, "Estimated correct digits ", 32,glob_est_digits, 4," "), omniout_int(info, "Correct digits ", 32, glob_good_digits,4, " "), omniout_float(always, "h ", 4,glob_h,20, " ")))),0) (%i249) prog_report(x_start,x_end):=( block(mode_declare([[clock_sec],convfloat,[opt_clock_sec], convfloat,[clock_sec1],convfloat, [expect_sec],convfloat,[left_sec], convfloat,[percent_done],convfloat, [total_clock_sec],convfloat]), clock_sec1:elapsed_time_seconds(), total_clock_sec:clock_sec1-glob_orig_start_sec, glob_clock_sec:clock_sec1-glob_clock_start_sec, left_sec:-clock_sec1+glob_orig_start_sec +glob_max_sec, expect_sec:comp_expect_sec(x_end,x_start, glob_h+array_x[1], clock_sec1 -glob_orig_start_sec), opt_clock_sec:clock_sec1 -glob_optimal_clock_start_sec, glob_optimal_expect_sec :comp_expect_sec(x_end,x_start,glob_h+array_x[1], opt_clock_sec), glob_total_exp_sec :c(total_clock_sec)+glob_optimal_expect_sec, percent_done:comp_percent(x_end,x_start, glob_h+array_x[1]), glob_percent_done:percent_done, omniout_str_noeol(info, "Total Elapsed Time "), omniout_timestr(total_clock_sec), omniout_str_noeol(info, "Elapsed Time(since restart) "), omniout_timestr(glob_clock_sec), if c(percent_done) < glob__100 then (omniout_str_noeol(info, "Expected Time Remaining "), omniout_timestr(expect_sec), omniout_str_noeol(info, "Optimized Time Remaining "), omniout_timestr(glob_optimal_expect_sec), omniout_str_noeol(info, "Expected Total Time "), omniout_timestr(glob_total_exp_sec)), omniout_str_noeol(info, "Time to Timeout "), omniout_timestr(left_sec), omniout_float(info, "Percent Done ",33, percent_done,4,"%")),0) (%i250) check_for_pole():=( block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc], convfloat,[m,n],fixnum,[nr1,nr2], convfloat,[ord_no],fixnum, [term1,term2,term3,part1,part2, part3,part4,part5,part6,part7, part8,part9,part10,part11,part12, part13,part14,rad_c,rcs,rm0,rm1, rm2,rm3,rm4],convfloat, [found_sing],fixnum, [h_new,ratio,term,local_test, tmp_rad,tmp_ord,tmp_ratio, prev_tmp_rad],convfloat,[last_no], fixnum),tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,1]:glob_larger_float, array_ord_test_poles[1,1]:glob_larger_float, found_sing:1,last_no:-10-1+ats_max_terms,cnt:0, while last_no < ats_max_terms-3 and found_sing = 1 do (tmp_rad :comp_rad_from_ratio( array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,1] then ( array_rad_test_poles[1,1]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_ratio( array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,1]:rad_c, array_ord_test_poles[1,1] :tmp_ord)), tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,2]:glob_larger_float, array_ord_test_poles[1,2]:glob_larger_float, found_sing:1,last_no:-10-1+ats_max_terms,cnt:0, while last_no < ats_max_terms-4 and found_sing = 1 do (tmp_rad :comp_rad_from_three_terms( array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,2] then ( array_rad_test_poles[1,2]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_three_terms( array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,2]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,2] :tmp_ord)), tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,3]:glob_larger_float, array_ord_test_poles[1,3]:glob_larger_float, found_sing:1,last_no:-10-1+ats_max_terms,cnt:0, while last_no < ats_max_terms-7 and found_sing = 1 do (tmp_rad :comp_rad_from_six_terms( array_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), if abs(prev_tmp_rad) > glob__0 then tmp_ratio:tmp_rad/prev_tmp_rad else tmp_ratio:glob_large_float, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,3] then ( array_rad_test_poles[1,3]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_six_terms( array_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,3]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,3] :tmp_ord)), if abs(glob_min_pole_est)*glob_ratio_of_radius < abs(glob_h) then (h_new :glob_check_sign*glob_min_pole_est *glob_ratio_of_radius, omniout_str(always, "SETTING H FOR POLE"), glob_h_reason:6, if glob_check_sign*glob_min_h > glob_check_sign*h_new then ( omniout_str(always, "SETTING H FOR MIN H"), h_new:glob_min_h,glob_h_reason:5), term:1,ratio:c(1.0), while term <= ats_max_terms do ( array_y[term] :array_y[term]*ratio, array_y_higher[1,term] :array_y_higher[1,term]*ratio, array_x[term] :array_x[term]*ratio, ratio:ratio*h_new/abs(glob_h), term:1+term),glob_h:h_new), if reached_interval() then display_poles()),0) (%i251) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:neg(array_const_3D0[1]), array_tmp2[1]:array_tmp1[1]/array_x[1], array_tmp3[1]:array_tmp2[1]/array_x[1], array_tmp4[1]:array_tmp3[1]/array_x[1], array_tmp5[1]:array_tmp4[1]/array_x[1], array_tmp6[1]:array_tmp5[1]+array_const_0D0[1], if not array_y_set_initial[1,2] then (if 1 <= ats_max_terms then ( temporary :c(array_tmp6[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_tmp2[2]:neg(array_tmp2[1])*array_x[2]/array_x[1], array_tmp3[2]:(array_tmp2[2]-array_tmp3[1]*array_x[2]) /array_x[1], array_tmp4[2]:(array_tmp3[2]-array_tmp4[1]*array_x[2]) /array_x[1], array_tmp5[2]:(array_tmp4[2]-array_tmp5[1]*array_x[2]) /array_x[1],array_tmp6[2]:array_tmp5[2], if not array_y_set_initial[1,3] then (if 2 <= ats_max_terms then ( temporary :c(array_tmp6[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_tmp2[3]:neg(array_tmp2[2])*array_x[2]/array_x[1], array_tmp3[3]:(array_tmp2[3]-array_tmp3[2]*array_x[2]) /array_x[1], array_tmp4[3]:(array_tmp3[3]-array_tmp4[2]*array_x[2]) /array_x[1], array_tmp5[3]:(array_tmp4[3]-array_tmp5[2]*array_x[2]) /array_x[1],array_tmp6[3]:array_tmp5[3], if not array_y_set_initial[1,4] then (if 3 <= ats_max_terms then ( temporary :c(array_tmp6[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_tmp2[4]:neg(array_tmp2[3])*array_x[2]/array_x[1], array_tmp3[4]:(array_tmp2[4]-array_tmp3[3]*array_x[2]) /array_x[1], array_tmp4[4]:(array_tmp3[4]-array_tmp4[3]*array_x[2]) /array_x[1], array_tmp5[4]:(array_tmp4[4]-array_tmp5[3]*array_x[2]) /array_x[1],array_tmp6[4]:array_tmp5[4], if not array_y_set_initial[1,5] then (if 4 <= ats_max_terms then ( temporary :c(array_tmp6[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_tmp2[5]:neg(array_tmp2[4])*array_x[2]/array_x[1], array_tmp3[5]:(array_tmp2[5]-array_tmp3[4]*array_x[2]) /array_x[1], array_tmp4[5]:(array_tmp3[5]-array_tmp4[4]*array_x[2]) /array_x[1], array_tmp5[5]:(array_tmp4[5]-array_tmp5[4]*array_x[2]) /array_x[1],array_tmp6[5]:array_tmp5[5], if not array_y_set_initial[1,6] then (if 5 <= ats_max_terms then ( temporary :c(array_tmp6[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_tmp2[kkk]:array_tmp1[1]*array_x[kkk], array_tmp3[kkk] :neg(ats(kkk,array_x,array_tmp3,2))/array_x[1], array_tmp4[kkk] :neg(ats(kkk,array_x,array_tmp4,2))/array_x[1], array_tmp5[kkk] :neg(ats(kkk,array_x,array_tmp5,2))/array_x[1], array_tmp6[kkk]:array_tmp5[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_tmp6[kkk])*expt(glob_h,c(order_d)) *c( factorial_3( kkk-1, -1+order_d+kkk)), array_y[order_d+kkk]:c(temporary), array_y_higher[1,order_d+kkk]:c(temporary), term:-1+order_d+kkk,adj2:-1+order_d+kkk, adj3:2, while term >= 1 and term <= ats_max_terms and adj3 < 1+order_d do ( if adj3 <= 1+order_d then ( if adj2 > 0 then temporary :c(temporary)*c(adj2) /c(glob_h) else temporary:c(temporary), array_y_higher[adj3,term] :c(temporary)),term:term-1, adj2:adj2-1,adj3:1+adj3))), kkk:1+kkk)),0) (%i252) exact_soln_y(x):=block(c(1.0)/c(x)/c(x)/c(x)) c(1.0) ------ c(x) ------ c(x) (%o252) exact_soln_y(x) := block(------) c(x) (%i253) main_prog():=block( mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat, [niii,done_once,term,ord,order_diff,term_no, html_log_file,iiif,jjjf,rows,r_order, sub_iter,calc_term,iii],fixnum,[temp_sum], convfloat,[current_iter],fixnum, [x_start,x_end],convfloat,[it,opt_iter], fixnum,[tmp],convfloat,[subiter],fixnum, [est_needed_step_err,estimated_step_error, min_value,est_answer,last_min_pole_est], convfloat,[repeat_it],fixnum],[found_h], boolean),Digits:32,max_terms:20, glob_html_log:true,term:1, while term <= 20 do (array_y_init[term]:c(0.0),term:1+term), term:1, while term <= 20 do (array_norms[term]:c(0.0),term:1+term), term:1, while term <= 20 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 <= 20 do (array_y[term]:c(0.0),term:1+term), term:1, while term <= 20 do (array_x[term]:c(0.0),term:1+term), term:1, while term <= 20 do (array_tmp0[term]:c(0.0),term:1+term), term:1, while term <= 20 do (array_tmp1[term]:c(0.0),term:1+term), term:1, while term <= 20 do (array_tmp2[term]:c(0.0),term:1+term), term:1, while term <= 20 do (array_tmp3[term]:c(0.0),term:1+term), term:1, while term <= 20 do (array_tmp4[term]:c(0.0),term:1+term), term:1, while term <= 20 do (array_tmp5[term]:c(0.0),term:1+term), term:1, while term <= 20 do (array_tmp6[term]:c(0.0),term:1+term), term:1, while term <= 20 do (array_m1[term]:c(0.0),term:1+term), ord:1, while ord <= 2 do (term:1, while term <= 20 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 <= 20 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 <= 20 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 <= 20 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 <= 20 do (term:1, while term <= 20 do (array_fact_2[ord,term]:c(0.0),term:1+term), ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x), zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2),zero_ats_ar(array_tmp3), zero_ats_ar(array_tmp4),zero_ats_ar(array_tmp5), zero_ats_ar(array_tmp6),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_3D0),array_const_3D0[1]:c(3.0), zero_ats_ar(array_m1),array_m1[1]:glob__m1,iiif:0, while iiif <= ats_max_terms do (jjjf:0, while jjjf <= ats_max_terms do (array_fact_1[iiif]:0, array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf), iiif:1+iiif),array_y_set_initial[1,1]:true, array_y_set_initial[1,2]:false, array_y_set_initial[1,3]:false, array_y_set_initial[1,4]:false, array_y_set_initial[1,5]:false, array_y_set_initial[1,6]:false, array_y_set_initial[1,7]:false, array_y_set_initial[1,8]:false, array_y_set_initial[1,9]:false, array_y_set_initial[1,10]:false, array_y_set_initial[1,11]:false, array_y_set_initial[1,12]:false, array_y_set_initial[1,13]:false, array_y_set_initial[1,14]:false, array_y_set_initial[1,15]:false, array_y_set_initial[1,16]:false, array_y_set_initial[1,17]:false, array_y_set_initial[1,18]:false, array_y_set_initial[1,19]:false, array_y_set_initial[1,20]:false,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/sing5_backpostode.ode#################"), omniout_str(always, "diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; "), omniout_str(always,"!"), omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(always,"Digits:32,"), omniout_str(always,"max_terms:20,"),omniout_str(always,"!"), omniout_str(always,"/* END FIRST INPUT BLOCK */"), omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(always,"x_start:c(-0.7),"), omniout_str(always,"x_end:c(-1.0),"), 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,""), omniout_str(always,"glob_type_given_pole:1,"), omniout_str(always,""), omniout_str(always,"array_given_rad_poles[1,1]:c(0.0),"), omniout_str(always,""), omniout_str(always,"array_given_rad_poles[1,2]:c(0.0),"), omniout_str(always,""), omniout_str(always,"array_given_ord_poles[1,1]:c(4.0),"), omniout_str(always,""), omniout_str(always,"array_given_ord_poles[1,2]:c(0.0),"), 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(1.0)/c(x)/c(x)/c(x)) "), omniout_str(always,"));"),omniout_str(always,""), omniout_str(always,""), omniout_str(always,"/* END USER DEF BLOCK */"), omniout_str(always, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false, glob_small_float:glob__0,glob_smallish_float:glob__0, glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100), glob_almost_1:c(0.99),x_start:c(-0.7),x_end:c(-1.0), array_y_init[1+0]:exact_soln_y(x_start), glob_look_poles:true,glob_type_given_pole:1, array_given_rad_poles[1,1]:c(0.0), array_given_rad_poles[1,2]:c(0.0), array_given_ord_poles[1,1]:c(4.0), array_given_ord_poles[1,2]:c(0.0), 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 ) = neg ( 3.0 ) / x / x / x / x ; "), omniout_int(info, "Iterations ",32, glob_iter,4," "), prog_report(x_start,x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2015-04-24T23:07:49-05:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "sing5_back"), logitem_str(html_log_file, "diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; "), logitem_float(html_log_file,x_start), logitem_float(html_log_file,x_end), logitem_float(html_log_file,array_x[1]), logitem_float(html_log_file,glob_h), logitem_h_reason(html_log_file), logitem_str(html_log_file,"16"), logitem_float(html_log_file, glob_desired_digits_correct), if array_est_digits[1] # -16 then ( logitem_integer(html_log_file, array_est_digits[ 1]),0) else ( logitem_str(html_log_file, "Unknown"),0), if glob_min_good_digits # -16 then ( logitem_integer(html_log_file, glob_min_good_digits), 0) else ( logitem_str(html_log_file, "Unknown"),0), if glob_good_digits # -16 then ( logitem_integer(html_log_file, glob_good_digits),0) else ( logitem_str(html_log_file, "Unknown"),0), logitem_str(html_log_file,"NA"), logitem_str(html_log_file,"NA"), logitem_integer(html_log_file, ats_max_terms), if glob_type_given_pole = 0 then ( logitem_str(html_log_file, "Not Given"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 4 then ( logitem_str(html_log_file, "No Solution"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 5 then ( logitem_str(html_log_file, "Some Pole"), logitem_str(html_log_file,"????"),0) elseif glob_type_given_pole = 3 then ( logitem_str(html_log_file, "No Pole"), logitem_str(html_log_file,"NA"),0) elseif glob_type_given_pole = 1 then ( logitem_str(html_log_file, "Real Sing"), logitem_float(html_log_file, glob_least_given_sing), 0) elseif glob_type_given_pole = 2 then ( logitem_str(html_log_file, "Complex Sing"), logitem_float(html_log_file, glob_least_given_sing), 0), if glob_least_ratio_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_ratio_sing), 0) else ( logitem_str(html_log_file,"NONE"),0), if glob_least_3_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_3_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), if glob_least_6_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_6_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, glob_clock_sec), if c(glob_percent_done) < glob__100 then ( logitem_time(html_log_file, glob_total_exp_sec),0) else ( logitem_str(html_log_file,"Done"), 0), log_revs(html_log_file, " 308.maple.seems.ok "), logitem_str(html_log_file, "sing5_back diffeq.max"), logitem_str(html_log_file, "sing5_back maxima results"), logitem_str(html_log_file, "Poor Accuracy"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i254) main():=(glob_iolevel:2,compile(all),main_prog()) (%i255) main() warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable secs in translation. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable sec_temp in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable years_int in translation. warning: encountered undefined variable days_int in translation. warning: encountered undefined variable hours_int in translation. warning: encountered undefined variable minutes_int in translation. warning: encountered undefined variable sec_int in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable iii in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_ats in translation. warning: encountered undefined variable ma_ats in translation. warning: encountered undefined variable ret_ats in translation. warning: encountered undefined variable lll_ats in translation. warning: encountered undefined variable ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable iii_att in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable ma_att in translation. warning: encountered undefined variable lll_att in translation. warning: encountered undefined variable ret_att in translation. warning: encountered undefined variable al_att in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_h_reason in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable errflag in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable sub1 in translation. warning: encountered undefined variable sub2 in translation. warning: encountered undefined variable rrr in translation. warning: encountered undefined variable ms2 in translation. warning: encountered undefined variable sec_left in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ret in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__m2 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temp in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob__4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm0 in translation. warning: encountered undefined variable glob__2 in translation. warning: encountered undefined variable rm1 in translation. warning: encountered undefined variable rm2 in translation. warning: encountered undefined variable rm3 in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable rm4 in translation. warning: encountered undefined variable glob__3 in translation. warning: encountered undefined variable glob__8 in translation. warning: encountered undefined variable glob__5 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable nr1 in translation. warning: encountered undefined variable dr2 in translation. warning: encountered undefined variable nr2 in translation. warning: encountered undefined variable dr1 in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable ds1 in translation. warning: encountered undefined variable ds2 in translation. warning: encountered undefined variable rcs in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable ord_no in translation. warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any. warning: encountered undefined variable rad_c in translation. warning: encountered undefined variable glob_six_term_ord_save in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_2 in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob_log_10 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob__10 in translation. warning: encountered undefined variable ats_max_terms in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_x in translation. warning: encountered undefined variable array_given_rad_poles in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable rad_given in translation. warning: encountered undefined variable array_given_ord_poles in translation. warning: variable glob_least_given_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable array_rad_test_poles in translation. warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable array_ord_test_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: variable glob_least_3_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob__small in translation. warning: variable glob_least_6_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_estimated_size_answer in translation. warning: encountered undefined variable array_y in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob__1 in translation. warning: encountered undefined variable glob__small in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable glob__0_5 in translation. warning: encountered undefined variable glob__0_25 in translation. warning: encountered undefined variable glob__0_125 in translation. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable array_max_est_error in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_next_display in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob__10 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable always in translation. warning: encountered undefined variable ind_var in translation. warning: encountered undefined variable closed_form_val_y in translation. warning: encountered undefined variable term_no in translation. warning: encountered undefined variable numeric_val in translation. warning: encountered undefined variable abserr in translation. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable relerr in translation. warning: variable glob_good_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_prec in translation. warning: encountered undefined variable glob__m1 in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_min_good_digits in translation. warning: encountered undefined variable glob_apfp_est_good_digits in translation. warning: encountered undefined variable glob_min_apfp_est_good_digits in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable est_rel_err in translation. warning: variable glob_est_digits (declared type fixnum) assigned type any. warning: encountered undefined variable glob_est_digits in translation. warning: encountered undefined variable array_est_digits in translation. warning: encountered undefined variable array_1st_rel_error in translation. warning: encountered undefined variable array_last_rel_error in translation. warning: encountered undefined variable array_est_rel_error in translation. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable clock_sec1 in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_clock_start_sec in translation. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_optimal_clock_start_sec in translation. warning: encountered undefined variable opt_clock_sec in translation. warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_optimal_expect_sec in translation. warning: encountered undefined variable total_clock_sec in translation. warning: variable glob_total_exp_sec (declared type convfloat) assigned type any. warning: encountered undefined variable percent_done in translation. warning: variable glob_percent_done (declared type convfloat) assigned type any. warning: encountered undefined variable info in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable expect_sec in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob__100 in translation. warning: encountered undefined variable left_sec in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ats_max_terms in translation. warning: encountered undefined variable last_no in translation. warning: encountered undefined variable found_sing in translation. warning: encountered undefined variable array_y_higher in translation. warning: variable tmp_rad (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_rad in translation. warning: encountered undefined variable prev_tmp_rad in translation. warning: encountered undefined variable glob__0 in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable cnt in translation. warning: encountered undefined variable tmp_ratio in translation. warning: encountered undefined variable glob_upper_ratio_limit in translation. warning: encountered undefined variable glob_lower_ratio_limit in translation. warning: variable tmp_ord (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_ord in translation. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_ratio_of_radius in translation. warning: encountered undefined variable always in translation. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable h_new in translation. warning: variable ratio (declared type convfloat) assigned type any. warning: encountered undefined variable term in translation. warning: encountered undefined variable ratio in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_const_3D0 in translation. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable array_tmp4 in translation. warning: encountered undefined variable array_tmp5 in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp6 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/sing5_backpostode.ode#################" "diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:20," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:c(-0.7)," "x_end:c(-1.0)," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "" "" "" "" "" "" "" "" "glob_type_given_pole:1," "" "array_given_rad_poles[1,1]:c(0.0)," "" "array_given_rad_poles[1,2]:c(0.0)," "" "array_given_ord_poles[1,1]:c(4.0)," "" "array_given_ord_poles[1,2]:c(0.0)," "/* 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(1.0)/c(x)/c(x)/c(x)) " "));" "" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = -0.701 " " y[1] (closed_form) = -2.9029927158019686 " " y[1] (numeric) = -2.9029927158019686 " " 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] = -0.702 " " y[1] (closed_form) = -2.8906044279296133 " " y[1] (numeric) = -2.890604427929612 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.608958654728211000000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 15 Correct digits = 17 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.703 " " y[1] (closed_form) = -2.878286527937843 " " y[1] (numeric) = -2.8782865279378416 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.62868313011455100000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.704 " " y[1] (closed_form) = -2.866038516622841 " " y[1] (numeric) = -2.8660385166228393 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 6.19795173406600600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.705 " " y[1] (closed_form) = -2.8538598990233024 " " y[1] (numeric) = -2.853859899023301 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.668300745969133400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.706 " " y[1] (closed_form) = -2.8417501843784363 " " y[1] (numeric) = -2.841750184378434 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 7.81365674384914900000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.707 " " y[1] (closed_form) = -2.829708886086427 " " y[1] (numeric) = -2.8297088860864252 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 6.27752504200884600000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.708 " " y[1] (closed_form) = -2.817735521663382 " " y[1] (numeric) = -2.81773552166338 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 7.88025005249437500000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.709 " " y[1] (closed_form) = -2.8058296127027247 " " y[1] (numeric) = -2.8058296127027225 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 7.91368812702586400000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.71 " " y[1] (closed_form) = -2.7939906848350575 " " y[1] (numeric) = -2.7939906848350544 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.11261089230652000000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.711 " " y[1] (closed_form) = -2.782218267688465 " " y[1] (numeric) = -2.782218267688463 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 7.9808477826404100000000000000E-14 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 17 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.712 " " y[1] (closed_form) = -2.7705118948492777 " " y[1] (numeric) = -2.770511894849274 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.28233114082831860000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.713 " " y[1] (closed_form) = -2.7588711038232527 " " y[1] (numeric) = -2.7588711038232496 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.1267740869236320000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.714 " " y[1] (closed_form) = -2.747295435997215 " " y[1] (numeric) = -2.747295435997211 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 1.45481364555166660000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.715 " " y[1] (closed_form) = -2.7357844366011035 " " y[1] (numeric) = -2.735784436601099 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 1.6232609700850270000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.716 " " y[1] (closed_form) = -2.7243376546704563 " " y[1] (numeric) = -2.7243376546704527 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.30406510834291100000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.717 " " y[1] (closed_form) = -2.712954643009312 " " y[1] (numeric) = -2.712954643009308 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 1.47322879096023480000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.718 " " y[1] (closed_form) = -2.701634958153512 " " y[1] (numeric) = -2.701634958153508 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 1.47940152928072170000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.719 " " y[1] (closed_form) = -2.690378160334427 " " y[1] (numeric) = -2.6903781603344226 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 1.65065720647561360000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.72 " " y[1] (closed_form) = -2.6791838134430725 " " y[1] (numeric) = -2.679183813443069 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.32604327518492940000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.721 " " y[1] (closed_form) = -2.6680514849946344 " " y[1] (numeric) = -2.6680514849946304 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 1.49802314952651730000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.722 " " y[1] (closed_form) = -2.6569807460933728 " " y[1] (numeric) = -2.656980746093368 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 1.8385459945591262000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.723 " " y[1] (closed_form) = -2.6459711713979237 " " y[1] (numeric) = -2.6459711713979193 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 1.67835997100240770000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.724 " " y[1] (closed_form) = -2.6350223390869854 " " y[1] (numeric) = -2.635022339086981 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 1.68533375699553320000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.725 " " y[1] (closed_form) = -2.6241338308253725 " " y[1] (numeric) = -2.624133830825367 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 2.03079220106872040000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.726 " " y[1] (closed_form) = -2.6133052317304517 " " y[1] (numeric) = -2.613305231730446 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 2.20914099813285220000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.727 " " y[1] (closed_form) = -2.602536130338945 " " y[1] (numeric) = -2.602536130338939 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 2.3889193565551628000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.728 " " y[1] (closed_form) = -2.591826118574096 " " y[1] (numeric) = -2.5918261185740903 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 2.22744870370661370000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.729 " " y[1] (closed_form) = -2.5811747917131975 " " y[1] (numeric) = -2.5811747917131913 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 2.4086896237562880000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.73 " " y[1] (closed_form) = -2.57058174835547 " " y[1] (numeric) = -2.5705817483554645 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 2.0730990257789020000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.731 " " y[1] (closed_form) = -2.560046590390301 " " y[1] (numeric) = -2.5600465903902943 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 2.6020378585123180000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.732 " " y[1] (closed_form) = -2.549568922965815 " " y[1] (numeric) = -2.549568922965809 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 2.43854907466811740000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.733 " " y[1] (closed_form) = -2.5391483544578075 " " y[1] (numeric) = -2.5391483544578013 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 2.4485567875487390000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.734 " " y[1] (closed_form) = -2.528784496438997 " " y[1] (numeric) = -2.5287844964389894 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 2.985432953295230000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.735 " " y[1] (closed_form) = -2.518476963648618 " " y[1] (numeric) = -2.5184769636486117 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 2.4686542809959638000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.736 " " y[1] (closed_form) = -2.5082253739623575 " " y[1] (numeric) = -2.5082253739623503 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 2.83285044133663100000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.737 " " y[1] (closed_form) = -2.4980293483625906 " " y[1] (numeric) = -2.4980293483625835 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 2.84441308195937300000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.738 " " y[1] (closed_form) = -2.4878885109089635 " " y[1] (numeric) = -2.4878885109089564 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 2.8560071427818906000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.739 " " y[1] (closed_form) = -2.4778024887092793 " " y[1] (numeric) = -2.4778024887092727 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 2.68840562478445200000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.74 " " y[1] (closed_form) = -2.467770911890707 " " y[1] (numeric) = -2.4677709118907 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 2.87928969555650900000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.741 " " y[1] (closed_form) = -2.4577934135712933 " " y[1] (numeric) = -2.4577934135712853 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 3.2523505568704530000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.742 " " y[1] (closed_form) = -2.4478696298317835 " " y[1] (numeric) = -2.4478696298317764 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 2.9026984407209970000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.743 " " y[1] (closed_form) = -2.4379991996877544 " " y[1] (numeric) = -2.4379991996877473 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 2.91445024203085300000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.744 " " y[1] (closed_form) = -2.4281817650620305 " " y[1] (numeric) = -2.4281817650620234 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 2.92623371933586950000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.745 " " y[1] (closed_form) = -2.4184169707574092 " " y[1] (numeric) = -2.4184169707574013 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 3.3053050296771850000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.746 " " y[1] (closed_form) = -2.4087044644296687 " " y[1] (numeric) = -2.408704464429661 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 3.13426436449049100000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.747 " " y[1] (closed_form) = -2.3990438965608756 " " y[1] (numeric) = -2.3990438965608676 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 3.33199646274096040000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.748 " " y[1] (closed_form) = -2.389434920432964 " " y[1] (numeric) = -2.389434920432956 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 3.3453958963036706000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.749 " " y[1] (closed_form) = -2.3798771921016093 " " y[1] (numeric) = -2.3798771921016013 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 3.35883120516911050000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.75 " " y[1] (closed_form) = -2.3703703703703702 " " y[1] (numeric) = -2.3703703703703622 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 3.3723024372989130000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.751 " " y[1] (closed_form) = -2.3609141167651133 " " y[1] (numeric) = -2.360914116765105 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 3.57391017624664130000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.752 " " y[1] (closed_form) = -2.351508095508702 " " y[1] (numeric) = -2.351508095508694 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 3.39935286319814600000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.753 " " y[1] (closed_form) = -2.342151973495964 " " y[1] (numeric) = -2.3421519734959566 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 3.22332481106357760000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.754 " " y[1] (closed_form) = -2.3328454202689146 " " y[1] (numeric) = -2.332845420268906 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 3.6169113108996953000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.755 " " y[1] (closed_form) = -2.323588107992243 " " y[1] (numeric) = -2.3235881079922343 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 3.8224434728562070000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.756 " " y[1] (closed_form) = -2.3143797114290665 " " y[1] (numeric) = -2.3143797114290576 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 3.8376521160898840000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.757 " " y[1] (closed_form) = -2.3052199079169307 " " y[1] (numeric) = -2.3052199079169218 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 3.8529010470966790000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.758 " " y[1] (closed_form) = -2.296108377344067 " " y[1] (numeric) = -2.2961083773440585 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 3.6747808032089330000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.759 " " y[1] (closed_form) = -2.2870448021259016 " " y[1] (numeric) = -2.2870448021258927 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 3.8835199855924430000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.76 " " y[1] (closed_form) = -2.2780288671818054 " " y[1] (numeric) = -2.278028867181796 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 4.0938346046459617000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.761 " " y[1] (closed_form) = -2.269060259912094 " " y[1] (numeric) = -2.2690602599120853 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 3.91430071466913900000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.762 " " y[1] (closed_form) = -2.26013867017527 " " y[1] (numeric) = -2.2601386701752606 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 4.1262394780972045000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.763 " " y[1] (closed_form) = -2.251263790265493 " " y[1] (numeric) = -2.2512637902654844 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 3.7479814776197890000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.764 " " y[1] (closed_form) = -2.2424353148903013 " " y[1] (numeric) = -2.2424353148902925 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 3.96077609821077260000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.765 " " y[1] (closed_form) = -2.23365294114855 " " y[1] (numeric) = -2.2336529411485406 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 4.17516671236128840000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.766 " " y[1] (closed_form) = -2.224916368508591 " " y[1] (numeric) = -2.2249163685085813 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 4.39115948580592830000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.767 " " y[1] (closed_form) = -2.216225298786674 " " y[1] (numeric) = -2.216225298786665 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 4.2079988040732990000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.768 " " y[1] (closed_form) = -2.2075794361255783 " " y[1] (numeric) = -2.207579436125569 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 4.2244791984558117000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.769 " " y[1] (closed_form) = -2.1989784869734565 " " y[1] (numeric) = -2.198978486973447 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 4.2410025664629820000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.77 " " y[1] (closed_form) = -2.190422160062909 " " y[1] (numeric) = -2.190422160062899 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 4.6630517225310080000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.771 " " y[1] (closed_form) = -2.181910166390266 " " y[1] (numeric) = -2.181910166390255 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 4.8847753681968690000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.772 " " y[1] (closed_form) = -2.17344221919509 " " y[1] (numeric) = -2.17344221919508 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 4.6994816500500750000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.773 " " y[1] (closed_form) = -2.1650180339398917 " " y[1] (numeric) = -2.1650180339398815 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 4.7177675503995440000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.774 " " y[1] (closed_form) = -2.1566373282900457 " " y[1] (numeric) = -2.1566373282900346 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.1479356777406330000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.775 " " y[1] (closed_form) = -2.1482998220939207 " " y[1] (numeric) = -2.14829982209391 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 4.9611981189912063000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.776 " " y[1] (closed_form) = -2.140005237363217 " " y[1] (numeric) = -2.140005237363207 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 4.7729097332194230000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.777 " " y[1] (closed_form) = -2.1317532982535 " " y[1] (numeric) = -2.1317532982534884 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.4163488174552290000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.778 " " y[1] (closed_form) = -2.1235437310449305 " " y[1] (numeric) = -2.123543731044919 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.4372882871689390000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.779 " " y[1] (closed_form) = -2.115376264123207 " " y[1] (numeric) = -2.1153762641231952 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.4582816551018700000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.78 " " y[1] (closed_form) = -2.1072506279606866 " " y[1] (numeric) = -2.107250627960676 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.0578421451064070000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.781 " " y[1] (closed_form) = -2.0991665550977134 " " y[1] (numeric) = -2.0991665550977023 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.2888753487856390000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.782 " " y[1] (closed_form) = -2.091123780124123 " " y[1] (numeric) = -2.0911237801241116 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.5215858409951570000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.783 " " y[1] (closed_form) = -2.083122039660948 " " y[1] (numeric) = -2.0831220396609367 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.542795494584140000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.784 " " y[1] (closed_form) = -2.075161072342306 " " y[1] (numeric) = -2.075161072342295 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.3500571084441630000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.785 " " y[1] (closed_form) = -2.06724061879747 " " y[1] (numeric) = -2.067240618797459 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.3705553892946530000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.786 " " y[1] (closed_form) = -2.0593604216331234 " " y[1] (numeric) = -2.0593604216331114 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 5.8223944385815680000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.787 " " y[1] (closed_form) = -2.0515202254157905 " " y[1] (numeric) = -2.0515202254157785 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 5.8446456034921820000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.788 " " y[1] (closed_form) = -2.0437197766544553 " " y[1] (numeric) = -2.043719776654443 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.0842479570055720000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.789 " " y[1] (closed_form) = -2.0359588237833433 " " y[1] (numeric) = -2.0359588237833317 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.6711949776300240000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.79 " " y[1] (closed_form) = -2.0282371171448905 " " y[1] (numeric) = -2.028237117144879 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.6927857983168930000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.791 " " y[1] (closed_form) = -2.020554408972873 " " y[1] (numeric) = -2.020554408972861 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 5.9342171696563640000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.792 " " y[1] (closed_form) = -2.0129104533757114 " " y[1] (numeric) = -2.0129104533757 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.736131697631209000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.793 " " y[1] (closed_form) = -2.00530500631995 " " y[1] (numeric) = -2.005305006319937 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.422258481908469000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.794 " " y[1] (closed_form) = -1.997737825613885 " " y[1] (numeric) = -1.9977378256138727 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.113141131081080000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.795 " " y[1] (closed_form) = -1.9902086708913818 " " y[1] (numeric) = -1.9902086708913695 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.136267743928060000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.796 " " y[1] (closed_form) = -1.98271730359583 " " y[1] (numeric) = -1.982717303595818 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.0474625627193770000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.797 " " y[1] (closed_form) = -1.975263486964277 " " y[1] (numeric) = -1.9752634869642645 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.2951084540685550000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.798 " " y[1] (closed_form) = -1.967846986011709 " " y[1] (numeric) = -1.9678469860116963 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 6.4316700285615990000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.799 " " y[1] (closed_form) = -1.9604675675154986 " " y[1] (numeric) = -1.9604675675154855 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 6.6824016411448630000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8 " " y[1] (closed_form) = -1.953125 " " y[1] (numeric) = -1.9531249999999867 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.8212102632969620000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.801 " " y[1] (closed_form) = -1.9458190537213027 " " y[1] (numeric) = -1.9458190537212896 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 6.7327080930379430000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.802 " " y[1] (closed_form) = -1.938549500652135 " " y[1] (numeric) = -1.9385495006521223 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 6.5288724773182630000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.803 " " y[1] (closed_form) = -1.9313161144669193 " " y[1] (numeric) = -1.9313161144669062 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 6.7832663914746430000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.804 " " y[1] (closed_form) = -1.9241186705269717 " " y[1] (numeric) = -1.9241186705269584 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.9240408606674480000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.805 " " y[1] (closed_form) = -1.9169569458658544 " " y[1] (numeric) = -1.9169569458658409 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 7.0657407980068140000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.806 " " y[1] (closed_form) = -1.9098307191748698 " " y[1] (numeric) = -1.909830719174856 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 7.208369499522860000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.807 " " y[1] (closed_form) = -1.9027397707886982 " " y[1] (numeric) = -1.9027397707886846 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 7.1185356549374770000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.808 " " y[1] (closed_form) = -1.8956838826711804 " " y[1] (numeric) = -1.8956838826711664 " " absolute error = 1.398881011027697200000000000000E-14 " " relative error = 7.379294743259380000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.809 " " y[1] (closed_form) = -1.8886628384012343 " " y[1] (numeric) = -1.8886628384012207 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 7.1715928460225360000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.81 " " y[1] (closed_form) = -1.8816764231589203 " " y[1] (numeric) = -1.8816764231589065 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 7.3162236269297430000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.811 " " y[1] (closed_form) = -1.874724423711633 " " y[1] (numeric) = -1.8747244237116194 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 7.2249130214086010000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.812 " " y[1] (closed_form) = -1.8678066284004382 " " y[1] (numeric) = -1.8678066284004247 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 7.251671931385320000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8130000000000001 " " y[1] (closed_form) = -1.8609228271265388 " " y[1] (numeric) = -1.8609228271265243 " " absolute error = 1.443289932012703500000000000000E-14 " " relative error = 7.7557753119794630000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8140000000000001 " " y[1] (closed_form) = -1.8540728113378715 " " y[1] (numeric) = -1.8540728113378573 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 7.6646691695714260000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8150000000000001 " " y[1] (closed_form) = -1.8472563740158454 " " y[1] (numeric) = -1.8472563740158308 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 7.9333568048234330000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8160000000000001 " " y[1] (closed_form) = -1.8404733096621957 " " y[1] (numeric) = -1.8404733096621817 " " absolute error = 1.398881011027697200000000000000E-14 " " relative error = 7.6006590461474880000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8170000000000001 " " y[1] (closed_form) = -1.833723414285981 " " y[1] (numeric) = -1.8337234142859666 " " absolute error = 1.443289932012703500000000000000E-14 " " relative error = 7.8708158535167890000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8180000000000001 " " y[1] (closed_form) = -1.8270064853906929 " " y[1] (numeric) = -1.8270064853906787 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 7.7782179914720500000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8190000000000001 " " y[1] (closed_form) = -1.8203223219615043 " " y[1] (numeric) = -1.8203223219614901 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 7.8067793509717410000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8200000000000001 " " y[1] (closed_form) = -1.8136707244526342 " " y[1] (numeric) = -1.8136707244526193 " " absolute error = 1.487698852997709800000000000000E-14 " " relative error = 8.2026954117964120000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8210000000000001 " " y[1] (closed_form) = -1.807051494774835 " " y[1] (numeric) = -1.8070514947748206 " " absolute error = 1.443289932012703500000000000000E-14 " " relative error = 7.9869883962135920000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8220000000000001 " " y[1] (closed_form) = -1.8004644362830107 " " y[1] (numeric) = -1.8004644362829962 " " absolute error = 1.443289932012703500000000000000E-14 " " relative error = 8.016209056549430000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8230000000000001 " " y[1] (closed_form) = -1.7939093537639414 " " y[1] (numeric) = -1.7939093537639272 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 7.921723963022490000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8240000000000001 " " y[1] (closed_form) = -1.7873860534241393 " " y[1] (numeric) = -1.7873860534241248 " " absolute error = 1.443289932012703500000000000000E-14 " " relative error = 8.0748640129968440000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8250000000000001 " " y[1] (closed_form) = -1.780894342877813 " " y[1] (numeric) = -1.780894342877799 " " absolute error = 1.398881011027697200000000000000E-14 " " relative error = 7.8549354520784980000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8260000000000001 " " y[1] (closed_form) = -1.7744340311349576 " " y[1] (numeric) = -1.7744340311349427 " " absolute error = 1.487698852997709800000000000000E-14 " " relative error = 8.384075298906170000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8270000000000001 " " y[1] (closed_form) = -1.7680049285895465 " " y[1] (numeric) = -1.768004928589532 " " absolute error = 1.443289932012703500000000000000E-14 " " relative error = 8.1633818360682430000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8280000000000001 " " y[1] (closed_form) = -1.761606847007855 " " y[1] (numeric) = -1.7616068470078405 " " absolute error = 1.443289932012703500000000000000E-14 " " relative error = 8.1930308937217010000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8290000000000001 " " y[1] (closed_form) = -1.7552395995168795 " " y[1] (numeric) = -1.7552395995168648 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 8.3492555256192740000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8300000000000001 " " y[1] (closed_form) = -1.7489030005928776 " " y[1] (numeric) = -1.7489030005928627 " " absolute error = 1.487698852997709800000000000000E-14 " " relative error = 8.5064686405900170000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8310000000000001 " " y[1] (closed_form) = -1.7425968660500166 " " y[1] (numeric) = -1.7425968660500015 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 8.6646736425777280000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8320000000000001 " " y[1] (closed_form) = -1.7363210130291304 " " y[1] (numeric) = -1.7363210130291151 " " absolute error = 1.53210777398271600000000000000E-14 " " relative error = 8.8238739408552660000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8330000000000001 " " y[1] (closed_form) = -1.7300752599865836 " " y[1] (numeric) = -1.7300752599865683 " " absolute error = 1.53210777398271600000000000000E-14 " " relative error = 8.8557290507385060000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8340000000000001 " " y[1] (closed_form) = -1.7238594266832443 " " y[1] (numeric) = -1.7238594266832292 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 8.7588540580441120000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8350000000000001 " " y[1] (closed_form) = -1.7176733341735615 " " y[1] (numeric) = -1.7176733341735462 " " absolute error = 1.53210777398271600000000000000E-14 " " relative error = 8.919669086671080000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8360000000000001 " " y[1] (closed_form) = -1.7115168047947438 " " y[1] (numeric) = -1.7115168047947287 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 8.822018628507070000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8370000000000001 " " y[1] (closed_form) = -1.7053896621560487 " " y[1] (numeric) = -1.7053896621560334 " " absolute error = 1.53210777398271600000000000000E-14 " " relative error = 8.9839161570015620000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8380000000000001 " " y[1] (closed_form) = -1.6992917311281652 " " y[1] (numeric) = -1.69929173112815 " " absolute error = 1.53210777398271600000000000000E-14 " " relative error = 9.0161550598821830000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8390000000000001 " " y[1] (closed_form) = -1.6932228378327052 " " y[1] (numeric) = -1.6932228378326895 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 9.3107455187979580000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8400000000000001 " " y[1] (closed_form) = -1.6871828096317891 " " y[1] (numeric) = -1.6871828096317734 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 9.344077511741489000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8410000000000001 " " y[1] (closed_form) = -1.681171475117734 " " y[1] (numeric) = -1.6811714751177191 " " absolute error = 1.487698852997709800000000000000E-14 " " relative error = 8.8491797238798910000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8420000000000001 " " y[1] (closed_form) = -1.6751886641028417 " " y[1] (numeric) = -1.675188664102826 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 9.410979961543829000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8430000000000001 " " y[1] (closed_form) = -1.6692342076092717 " " y[1] (numeric) = -1.6692342076092561 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 9.31152876804120100000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8440000000000001 " " y[1] (closed_form) = -1.6633079378590274 " " y[1] (numeric) = -1.6633079378590125 " " absolute error = 1.487698852997709800000000000000E-14 " " relative error = 8.9442178392573670000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8450000000000001 " " y[1] (closed_form) = -1.6574096882640261 " " y[1] (numeric) = -1.6574096882640112 " " absolute error = 1.487698852997709800000000000000E-14 " " relative error = 8.9760477661737830000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8460000000000001 " " y[1] (closed_form) = -1.6515392934162625 " " y[1] (numeric) = -1.651539293416247 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 9.4112943038737760000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8470000000000001 " " y[1] (closed_form) = -1.6456965890780682 " " y[1] (numeric) = -1.6456965890780524 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 9.5796315398022360000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8480000000000001 " " y[1] (closed_form) = -1.6398814121724639 " " y[1] (numeric) = -1.6398814121724485 " " absolute error = 1.53210777398271600000000000000E-14 " " relative error = 9.3427961473935320000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8490000000000001 " " y[1] (closed_form) = -1.6340936007736018 " " y[1] (numeric) = -1.634093600773586 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 9.6476523390176560000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8500000000000001 " " y[1] (closed_form) = -1.6283329940972922 " " y[1] (numeric) = -1.6283329940972768 " " absolute error = 1.53210777398271600000000000000E-14 " " relative error = 9.4090568669713580000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8510000000000001 " " y[1] (closed_form) = -1.6225994324916295 " " y[1] (numeric) = -1.6225994324916135 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 9.8528393603913860000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8520000000000001 " " y[1] (closed_form) = -1.6168927574276943 " " y[1] (numeric) = -1.6168927574276786 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 9.7502860825216010000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8530000000000001 " " y[1] (closed_form) = -1.6112128114903546 " " y[1] (numeric) = -1.6112128114903388 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 9.7846583873018080000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8540000000000001 " " y[1] (closed_form) = -1.605559438369143 " " y[1] (numeric) = -1.6055594383691267 " " absolute error = 1.620925615952728500000000000000E-14 " " relative error = 1.0095706064916499000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8550000000000001 " " y[1] (closed_form) = -1.5999324828492234 " " y[1] (numeric) = -1.5999324828492074 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 9.9924288843311640000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8560000000000001 " " y[1] (closed_form) = -1.5943317908024446 " " y[1] (numeric) = -1.5943317908024288 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 9.8882597967531230000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8570000000000001 " " y[1] (closed_form) = -1.5887572091784725 " " y[1] (numeric) = -1.588757209178457 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 9.783195478174639000000000000E-13 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8580000000000001 " " y[1] (closed_form) = -1.5832085859960079 " " y[1] (numeric) = -1.583208585995992 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.0097981842704942000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8590000000000001 " " y[1] (closed_form) = -1.5776857703340827 " " y[1] (numeric) = -1.5776857703340665 " " absolute error = 1.620925615952728500000000000000E-14 " " relative error = 1.0274071341909166000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8600000000000001 " " y[1] (closed_form) = -1.5721886123234425 " " y[1] (numeric) = -1.5721886123234265 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.0168761832574097000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8610000000000001 " " y[1] (closed_form) = -1.5667169631380051 " " y[1] (numeric) = -1.5667169631379894 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 1.0062549471667742000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8620000000000001 " " y[1] (closed_form) = -1.5612706749863983 " " y[1] (numeric) = -1.5612706749863825 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 1.0097651356844045000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8630000000000001 " " y[1] (closed_form) = -1.555849601103577 " " y[1] (numeric) = -1.5558496011035612 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 1.0132834779463813000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8640000000000001 " " y[1] (closed_form) = -1.550453595742518 " " y[1] (numeric) = -1.5504535957425023 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 1.0168099834118044000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8650000000000001 " " y[1] (closed_form) = -1.5450825141659918 " " y[1] (numeric) = -1.5450825141659759 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.034715713110756900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8660000000000001 " " y[1] (closed_form) = -1.5397362126384084 " " y[1] (numeric) = -1.539736212638392 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 1.0671503748227452000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8670000000000001 " " y[1] (closed_form) = -1.5344145484177392 " " y[1] (numeric) = -1.5344145484177232 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.0419095394453853000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8680000000000001 " " y[1] (closed_form) = -1.5291173797475177 " " y[1] (numeric) = -1.5291173797475013 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 1.0745611149332038000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8690000000000001 " " y[1] (closed_form) = -1.523844565848903 " " y[1] (numeric) = -1.5238445658488873 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 1.0345652898591245000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8700000000000001 " " y[1] (closed_form) = -1.5185959669128308 " " y[1] (numeric) = -1.5185959669128144 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 1.0820060847294145000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8710000000000001 " " y[1] (closed_form) = -1.51337144409222 " " y[1] (numeric) = -1.5133714440922035 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 1.0857414304066283000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8720000000000001 " " y[1] (closed_form) = -1.5081708594942653 " " y[1] (numeric) = -1.5081708594942493 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.0600398127280647000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8730000000000001 " " y[1] (closed_form) = -1.5029940761727947 " " y[1] (numeric) = -1.502994076172778 " " absolute error = 1.665334536937734800000000000000E-14 " " relative error = 1.108011377648487900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8740000000000001 " " y[1] (closed_form) = -1.49784095812069 " " y[1] (numeric) = -1.4978409581206735 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 1.0969990288600687000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8750000000000001 " " y[1] (closed_form) = -1.4927113702623904 " " y[1] (numeric) = -1.4927113702623738 " " absolute error = 1.665334536937734800000000000000E-14 " " relative error = 1.1156440354875842000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8760000000000001 " " y[1] (closed_form) = -1.4876051784464521 " " y[1] (numeric) = -1.4876051784464357 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 1.1045471609349992000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8770000000000001 " " y[1] (closed_form) = -1.4825222494381838 " " y[1] (numeric) = -1.4825222494381673 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 1.108334176480596900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8780000000000001 " " y[1] (closed_form) = -1.4774624509123433 " " y[1] (numeric) = -1.477462450912327 " " absolute error = 1.620925615952728500000000000000E-14 " " relative error = 1.0971010565796753000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8790000000000001 " " y[1] (closed_form) = -1.4724256514459058 " " y[1] (numeric) = -1.4724256514458895 " " absolute error = 1.620925615952728500000000000000E-14 " " relative error = 1.1008539645862578000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8800000000000001 " " y[1] (closed_form) = -1.4674117205108934 " " y[1] (numeric) = -1.4674117205108768 " " absolute error = 1.665334536937734800000000000000E-14 " " relative error = 1.1348788575560326000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8810000000000001 " " y[1] (closed_form) = -1.4624205284672716 " " y[1] (numeric) = -1.4624205284672551 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 1.123568798755415100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8820000000000001 " " y[1] (closed_form) = -1.4574519465559126 " " y[1] (numeric) = -1.457451946555896 " " absolute error = 1.665334536937734800000000000000E-14 " " relative error = 1.1426342672038463000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8830000000000001 " " y[1] (closed_form) = -1.4525058468916163 " " y[1] (numeric) = -1.4525058468915997 " " absolute error = 1.665334536937734800000000000000E-14 " " relative error = 1.146525186457304000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8840000000000001 " " y[1] (closed_form) = -1.4475821024562008 " " y[1] (numeric) = -1.4475821024561841 " " absolute error = 1.665334536937734800000000000000E-14 " " relative error = 1.1504249286531384000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8850000000000001 " " y[1] (closed_form) = -1.4426805870916508 " " y[1] (numeric) = -1.442680587091634 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 1.1697246171671344000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8860000000000001 " " y[1] (closed_form) = -1.4378011754933295 " " y[1] (numeric) = -1.4378011754933124 " " absolute error = 1.70974345792274100000000000000E-14 " " relative error = 1.1891376130890313000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8870000000000001 " " y[1] (closed_form) = -1.432943743203252 " " y[1] (numeric) = -1.4329437432032346 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 1.208664280527571900000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8880000000000001 " " y[1] (closed_form) = -1.428108166603418 " " y[1] (numeric) = -1.4281081666034008 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 1.2127568197684016000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8890000000000001 " " y[1] (closed_form) = -1.4232943229092072 " " y[1] (numeric) = -1.42329432290919 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 1.216858586827741000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8900000000000001 " " y[1] (closed_form) = -1.4185020901628294 " " y[1] (numeric) = -1.418502090162812 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 1.2209695920972767000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8910000000000001 " " y[1] (closed_form) = -1.4137313472268367 " " y[1] (numeric) = -1.4137313472268196 " " absolute error = 1.70974345792274100000000000000E-14 " " relative error = 1.2093835658921755000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8920000000000001 " " y[1] (closed_form) = -1.4089819737776954 " " y[1] (numeric) = -1.4089819737776779 " " absolute error = 1.754152378907747300000000000000E-14 " " relative error = 1.2449785813828389000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8930000000000001 " " y[1] (closed_form) = -1.4042538502994077 " " y[1] (numeric) = -1.4042538502993909 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 1.2017335733638398000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8940000000000001 " " y[1] (closed_form) = -1.3995468580772032 " " y[1] (numeric) = -1.3995468580771864 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 1.2057752748262382000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8950000000000001 " " y[1] (closed_form) = -1.3948608791912733 " " y[1] (numeric) = -1.3948608791912558 " " absolute error = 1.754152378907747300000000000000E-14 " " relative error = 1.257582318836548000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8960000000000001 " " y[1] (closed_form) = -1.3901957965105678 " " y[1] (numeric) = -1.3901957965105507 " " absolute error = 1.70974345792274100000000000000E-14 " " relative error = 1.229858025908471000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8970000000000001 " " y[1] (closed_form) = -1.3855514936866513 " " y[1] (numeric) = -1.3855514936866344 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 1.2179547314694625000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8980000000000001 " " y[1] (closed_form) = -1.380927855147605 " " y[1] (numeric) = -1.380927855147588 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 1.2220327015199936000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8990000000000001 " " y[1] (closed_form) = -1.3763247660919886 " " y[1] (numeric) = -1.376324766091971 " " absolute error = 1.754152378907747300000000000000E-14 " " relative error = 1.2745192284002727000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9000000000000001 " " y[1] (closed_form) = -1.3717421124828526 " " y[1] (numeric) = -1.3717421124828355 " " absolute error = 1.70974345792274100000000000000E-14 " " relative error = 1.2464029808256787000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9010000000000001 " " y[1] (closed_form) = -1.3671797810418103 " " y[1] (numeric) = -1.3671797810417927 " " absolute error = 1.754152378907747300000000000000E-14 " " relative error = 1.2830444124700693000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9020000000000001 " " y[1] (closed_form) = -1.3626376592431504 " " y[1] (numeric) = -1.3626376592431335 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 1.2384356075756393000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9030000000000001 " " y[1] (closed_form) = -1.3581156353080162 " " y[1] (numeric) = -1.3581156353079993 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 1.242559141179101100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9040000000000001 " " y[1] (closed_form) = -1.353613598198624 " " y[1] (numeric) = -1.3536135981986062 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.312307176704052800000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9050000000000001 " " y[1] (closed_form) = -1.349131437612536 " " y[1] (numeric) = -1.3491314376125187 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 1.2837503227114416000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9060000000000001 " " y[1] (closed_form) = -1.3446690439769917 " " y[1] (numeric) = -1.3446690439769744 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 1.2880105526136282000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9070000000000001 " " y[1] (closed_form) = -1.3402263084432766 " " y[1] (numeric) = -1.340226308443259 " " absolute error = 1.754152378907747300000000000000E-14 " " relative error = 1.3088478922229646000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9080000000000001 " " y[1] (closed_form) = -1.3358031228811487 " " y[1] (numeric) = -1.3358031228811311 " " absolute error = 1.754152378907747300000000000000E-14 " " relative error = 1.313181822126808000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9090000000000001 " " y[1] (closed_form) = -1.3313993798733115 " " y[1] (numeric) = -1.331399379873294 " " absolute error = 1.754152378907747300000000000000E-14 " " relative error = 1.3175253086528121000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9100000000000001 " " y[1] (closed_form) = -1.3270149727099367 " " y[1] (numeric) = -1.327014972709919 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.3386109998236867000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9110000000000001 " " y[1] (closed_form) = -1.3226497953832326 " " y[1] (numeric) = -1.3226497953832148 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.343028854350337100000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9120000000000001 " " y[1] (closed_form) = -1.3183037425820627 " " y[1] (numeric) = -1.318303742582045 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.3474564184434715000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9130000000000001 " " y[1] (closed_form) = -1.3139767096866095 " " y[1] (numeric) = -1.313976709686592 " " absolute error = 1.754152378907747300000000000000E-14 " " relative error = 1.3349950314767162000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9140000000000001 " " y[1] (closed_form) = -1.3096685927630873 " " y[1] (numeric) = -1.3096685927630696 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.3563407179617576000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9150000000000001 " " y[1] (closed_form) = -1.305379288558497 " " y[1] (numeric) = -1.3053792885584792 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.360797474703191000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9160000000000001 " " y[1] (closed_form) = -1.3011086944954313 " " y[1] (numeric) = -1.3011086944954136 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.3652639836436722000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9170000000000001 " " y[1] (closed_form) = -1.296856708666922 " " y[1] (numeric) = -1.296856708666905 " " absolute error = 1.70974345792274100000000000000E-14 " " relative error = 1.3183749958622937000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9180000000000001 " " y[1] (closed_form) = -1.292623229831336 " " y[1] (numeric) = -1.2926232298313185 " " absolute error = 1.754152378907747300000000000000E-14 " " relative error = 1.3570484719949158000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9190000000000002 " " y[1] (closed_form) = -1.2884081574073076 " " y[1] (numeric) = -1.2884081574072903 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 1.3442540769847977000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9200000000000002 " " y[1] (closed_form) = -1.2842113914687259 " " y[1] (numeric) = -1.2842113914687086 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 1.3486470606949308000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9210000000000002 " " y[1] (closed_form) = -1.2800328327397565 " " y[1] (numeric) = -1.2800328327397388 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.3877431843667418000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9220000000000002 " " y[1] (closed_form) = -1.2758723825899103 " " y[1] (numeric) = -1.2758723825898926 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.3922684303224747000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9230000000000002 " " y[1] (closed_form) = -1.2717299430291555 " " y[1] (numeric) = -1.271729943029138 " " absolute error = 1.754152378907747300000000000000E-14 " " relative error = 1.3793434592956907000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9240000000000002 " " y[1] (closed_form) = -1.2676054167030715 " " y[1] (numeric) = -1.2676054167030537 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.4013484133101892000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9250000000000002 " " y[1] (closed_form) = -1.2634987068880417 " " y[1] (numeric) = -1.2634987068880235 " " absolute error = 1.820765760385256700000000000000E-14 " " relative error = 1.4410507509499132000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9260000000000002 " " y[1] (closed_form) = -1.2594097174864913 " " y[1] (numeric) = -1.2594097174864731 " " absolute error = 1.820765760385256700000000000000E-14 " " relative error = 1.445729483506853200000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9270000000000002 " " y[1] (closed_form) = -1.255338353022166 " " y[1] (numeric) = -1.255338353022148 " " absolute error = 1.798561299892753600000000000000E-14 " " relative error = 1.4327303037964265000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9280000000000002 " " y[1] (closed_form) = -1.25128451863545 " " y[1] (numeric) = -1.2512845186354316 " " absolute error = 1.8429702208777599000000000000E-14 " " relative error = 1.472862641094253000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9290000000000002 " " y[1] (closed_form) = -1.2472481200787222 " " y[1] (numeric) = -1.247248120078704 " " absolute error = 1.820765760385256700000000000000E-14 " " relative error = 1.4598264219234390000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9300000000000002 " " y[1] (closed_form) = -1.243229063711759 " " y[1] (numeric) = -1.243229063711741 " " absolute error = 1.798561299892753600000000000000E-14 " " relative error = 1.4466853714978367000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9310000000000002 " " y[1] (closed_form) = -1.2392272564971691 " " y[1] (numeric) = -1.2392272564971507 " " absolute error = 1.8429702208777599000000000000E-14 " " relative error = 1.487193096516571000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9320000000000002 " " y[1] (closed_form) = -1.2352426059958712 " " y[1] (numeric) = -1.2352426059958526 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 1.5099662789452853000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9330000000000002 " " y[1] (closed_form) = -1.2312750203626102 " " y[1] (numeric) = -1.2312750203625917 " " absolute error = 1.8429702208777599000000000000E-14 " " relative error = 1.49679818919335000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9340000000000002 " " y[1] (closed_form) = -1.227324408341513 " " y[1] (numeric) = -1.2273244083414943 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 1.5197079669349028000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9350000000000002 " " y[1] (closed_form) = -1.223390679261677 " " y[1] (numeric) = -1.2233906792616585 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 1.524594483992559000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9360000000000002 " " y[1] (closed_form) = -1.2194737430328042 " " y[1] (numeric) = -1.2194737430327858 " " absolute error = 1.8429702208777599000000000000E-14 " " relative error = 1.5112832329577952000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9370000000000002 " " y[1] (closed_form) = -1.2155735101408665 " " y[1] (numeric) = -1.2155735101408474 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 1.5709322278123497000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9380000000000002 " " y[1] (closed_form) = -1.2116898916438068 " " y[1] (numeric) = -1.2116898916437882 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 1.5393168617094952000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9390000000000002 " " y[1] (closed_form) = -1.207822799167286 " " y[1] (numeric) = -1.2078227991672674 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 1.54424530043329000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9400000000000002 " " y[1] (closed_form) = -1.2039721449004548 " " y[1] (numeric) = -1.2039721449004361 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 1.5491842475512396000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9410000000000002 " " y[1] (closed_form) = -1.2001378415917683 " " y[1] (numeric) = -1.200137841591749 " " absolute error = 1.931788062847772400000000000000E-14 " " relative error = 1.6096384897634763000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9420000000000002 " " y[1] (closed_form) = -1.1963198025448316 " " y[1] (numeric) = -1.196319802544813 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 1.5590937117337955000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9430000000000002 " " y[1] (closed_form) = -1.19251794161429 " " y[1] (numeric) = -1.192517941614271 " " absolute error = 1.88737914186276600000000000000E-14 " " relative error = 1.5826840636945513000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9440000000000002 " " y[1] (closed_form) = -1.1887321732017389 " " y[1] (numeric) = -1.1887321732017198 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 1.6064035662566317000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9450000000000002 " " y[1] (closed_form) = -1.1849624122516809 " " y[1] (numeric) = -1.1849624122516624 " " absolute error = 1.8429702208777599000000000000E-14 " " relative error = 1.555298465016898000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9460000000000002 " " y[1] (closed_form) = -1.181208574247515 " " y[1] (numeric) = -1.181208574247496 " " absolute error = 1.88737914186276600000000000000E-14 " " relative error = 1.59783731934482000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9470000000000002 " " y[1] (closed_form) = -1.1774705752075507 " " y[1] (numeric) = -1.1774705752075323 " " absolute error = 1.8429702208777599000000000000E-14 " " relative error = 1.5651942899319610000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9480000000000002 " " y[1] (closed_form) = -1.1737483316810706 " " y[1] (numeric) = -1.1737483316810517 " " absolute error = 1.88737914186276600000000000000E-14 " " relative error = 1.6079930347245874000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9490000000000002 " " y[1] (closed_form) = -1.17004176074441 " " y[1] (numeric) = -1.1700417607443911 " " absolute error = 1.88737914186276600000000000000E-14 " " relative error = 1.6130869898711720000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9500000000000002 " " y[1] (closed_form) = -1.1663507799970831 " " y[1] (numeric) = -1.1663507799970645 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 1.5991541424398306000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9510000000000002 " " y[1] (closed_form) = -1.1626753075579352 " " y[1] (numeric) = -1.162675307557916 " " absolute error = 1.931788062847772400000000000000E-14 " " relative error = 1.661502614092037000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9520000000000002 " " y[1] (closed_form) = -1.1590152620613243 " " y[1] (numeric) = -1.159015262061305 " " absolute error = 1.931788062847772400000000000000E-14 " " relative error = 1.6667494605826513000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9530000000000002 " " y[1] (closed_form) = -1.1553705626533437 " " y[1] (numeric) = -1.1553705626533244 " " absolute error = 1.931788062847772400000000000000E-14 " " relative error = 1.6720073414466805000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9540000000000002 " " y[1] (closed_form) = -1.1517411289880677 " " y[1] (numeric) = -1.1517411289880486 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 1.6579972307084753000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9550000000000002 " " y[1] (closed_form) = -1.1481268812238337 " " y[1] (numeric) = -1.1481268812238146 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 1.6632165256158526000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9560000000000002 " " y[1] (closed_form) = -1.1445277400195524 " " y[1] (numeric) = -1.1445277400195335 " " absolute error = 1.88737914186276600000000000000E-14 " " relative error = 1.6490462186880010000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9570000000000002 " " y[1] (closed_form) = -1.1409436265310517 " " y[1] (numeric) = -1.1409436265310329 " " absolute error = 1.88737914186276600000000000000E-14 " " relative error = 1.6542264648089514000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9580000000000002 " " y[1] (closed_form) = -1.1373744624074487 " " y[1] (numeric) = -1.1373744624074293 " " absolute error = 1.931788062847772400000000000000E-14 " " relative error = 1.6984626670435440000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9590000000000002 " " y[1] (closed_form) = -1.1338201697875516 " " y[1] (numeric) = -1.1338201697875323 " " absolute error = 1.931788062847772400000000000000E-14 " " relative error = 1.7037869975533590000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9600000000000002 " " y[1] (closed_form) = -1.1302806712962958 " " y[1] (numeric) = -1.1302806712962763 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.7287675291299828000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9610000000000002 " " y[1] (closed_form) = -1.126755890041204 " " y[1] (numeric) = -1.1267558900411843 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 1.7538820975326888000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9620000000000002 " " y[1] (closed_form) = -1.1232457496088786 " " y[1] (numeric) = -1.123245749608859 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.7395948518128543000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9630000000000002 " " y[1] (closed_form) = -1.1197501740615246 " " y[1] (numeric) = -1.1197501740615052 " " absolute error = 1.931788062847772400000000000000E-14 " " relative error = 1.7251955905850394000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9640000000000002 " " y[1] (closed_form) = -1.1162690879334987 " " y[1] (numeric) = -1.116269087933479 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 1.7703589620055035000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9650000000000002 " " y[1] (closed_form) = -1.1128024162278853 " " y[1] (numeric) = -1.1128024162278662 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 1.716013170449672000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9660000000000002 " " y[1] (closed_form) = -1.10935008441311 " " y[1] (numeric) = -1.1093500844130901 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 1.7814006701755156000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9670000000000002 " " y[1] (closed_form) = -1.1059120184195657 " " y[1] (numeric) = -1.1059120184195461 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.7668607364740307000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9680000000000002 " " y[1] (closed_form) = -1.1024881446362838 " " y[1] (numeric) = -1.1024881446362638 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 1.812628511288495000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9690000000000002 " " y[1] (closed_form) = -1.0990783899076182 " " y[1] (numeric) = -1.0990783899075982 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 1.818251966989593000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9700000000000002 " " y[1] (closed_form) = -1.095682681529967 " " y[1] (numeric) = -1.095682681529947 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 1.823887041396688700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9710000000000002 " " y[1] (closed_form) = -1.0923009472485148 " " y[1] (numeric) = -1.0923009472484948 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 1.8295337465001904000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9720000000000002 " " y[1] (closed_form) = -1.0889331152540043 " " y[1] (numeric) = -1.0889331152539845 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 1.8148010710206122000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9730000000000002 " " y[1] (closed_form) = -1.0855791141795355 " " y[1] (numeric) = -1.0855791141795157 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 1.8204080734607345000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9740000000000002 " " y[1] (closed_form) = -1.082238873097388 " " y[1] (numeric) = -1.0822388730973678 " " absolute error = 2.02060590481778500000000000000E-14 " " relative error = 1.8670609188475856000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9750000000000002 " " y[1] (closed_form) = -1.0789123215158707 " " y[1] (numeric) = -1.0789123215158511 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.8110762889378426000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9760000000000002 " " y[1] (closed_form) = -1.0755993893762024 " " y[1] (numeric) = -1.0755993893761826 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 1.8372983504377785000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9770000000000002 " " y[1] (closed_form) = -1.0723000070494066 " " y[1] (numeric) = -1.0723000070493869 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 1.842951572172959000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9780000000000002 " " y[1] (closed_form) = -1.0690141053332431 " " y[1] (numeric) = -1.0690141053332232 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 1.8693873489183957000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9790000000000002 " " y[1] (closed_form) = -1.0657416154491575 " " y[1] (numeric) = -1.0657416154491377 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 1.8542927809006587000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9800000000000002 " " y[1] (closed_form) = -1.0624824690392602 " " y[1] (numeric) = -1.06248246903924 " " absolute error = 2.02060590481778500000000000000E-14 " " relative error = 1.901778112767261700000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9810000000000002 " " y[1] (closed_form) = -1.0592365981633245 " " y[1] (numeric) = -1.0592365981633047 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 1.865680422352691000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9820000000000002 " " y[1] (closed_form) = -1.0560039352958164 " " y[1] (numeric) = -1.0560039352957964 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 1.892418557858379000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9830000000000002 " " y[1] (closed_form) = -1.0527844133229414 " " y[1] (numeric) = -1.052784413322921 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 1.9403881169388634000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9840000000000002 " " y[1] (closed_form) = -1.0495779655397186 " " y[1] (numeric) = -1.0495779655396982 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 1.9463159787846965000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9850000000000002 " " y[1] (closed_form) = -1.04638452564708 " " y[1] (numeric) = -1.0463845256470603 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 1.8885953828595717000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9860000000000002 " " y[1] (closed_form) = -1.043204027748993 " " y[1] (numeric) = -1.043204027748973 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 1.915638160099321000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9870000000000002 " " y[1] (closed_form) = -1.0400364063495995 " " y[1] (numeric) = -1.0400364063495793 " " absolute error = 2.02060590481778500000000000000E-14 " " relative error = 1.942822282452462000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9880000000000002 " " y[1] (closed_form) = -1.0368815963503883 " " y[1] (numeric) = -1.0368815963503686 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 1.9059041946434277000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9890000000000002 " " y[1] (closed_form) = -1.0337395330473855 " " y[1] (numeric) = -1.0337395330473655 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 1.933176956514516300000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9900000000000002 " " y[1] (closed_form) = -1.0306101521283642 " " y[1] (numeric) = -1.0306101521283442 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 1.939046923027377000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9910000000000002 " " y[1] (closed_form) = -1.0274933896700826 " " y[1] (numeric) = -1.027493389670063 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.901708120932712000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9920000000000002 " " y[1] (closed_form) = -1.0243891821355435 " " y[1] (numeric) = -1.024389182135524 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.9074708689004197000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9930000000000002 " " y[1] (closed_form) = -1.0212974663712702 " " y[1] (numeric) = -1.0212974663712509 " " absolute error = 1.931788062847772400000000000000E-14 " " relative error = 1.891503823769904000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9940000000000002 " " y[1] (closed_form) = -1.0182181796046117 " " y[1] (numeric) = -1.0182181796045924 " " absolute error = 1.931788062847772400000000000000E-14 " " relative error = 1.89722409356108000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9950000000000002 " " y[1] (closed_form) = -1.0151512594410643 " " y[1] (numeric) = -1.0151512594410452 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 1.8810828283921688000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9960000000000002 " " y[1] (closed_form) = -1.0120966438616188 " " y[1] (numeric) = -1.0120966438615993 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.9306382796457922000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9970000000000002 " " y[1] (closed_form) = -1.009054271220123 " " y[1] (numeric) = -1.0090542712201034 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.936459295670546000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9980000000000002 " " y[1] (closed_form) = -1.0060240802406728 " " y[1] (numeric) = -1.0060240802406537 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 1.898149000467699000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9990000000000002 " " y[1] (closed_form) = -1.0030060100150204 " " y[1] (numeric) = -1.003006010015001 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.9481364057938333000000000000E-12 "%" Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -1.000E-3 " " "Finished!" "diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; " Iterations = 300 "Total Elapsed Time "= 7 Seconds "Elapsed Time(since restart) "= 7 Seconds "Expected Time Remaining "= 0 Seconds "Optimized Time Remaining "= 0 Seconds "Expected Total Time "= 7 Seconds "Time to Timeout "= 2 Minutes 52 Seconds Percent Done = 0.0 "%" (%o255) temp/diffeq.sing5_back.max