Average Error: 29.0 → 1.1
Time: 10.2s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.27109209614237641 \cdot 10^{59} \lor \neg \left(z \le 4.6361017995721538 \cdot 10^{51}\right):\\ \;\;\;\;x + y \cdot \left(\left(\frac{t}{{z}^{2}} + 3.13060547622999996\right) - 36.527041698806414 \cdot \frac{1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.27109209614237641 \cdot 10^{59} \lor \neg \left(z \le 4.6361017995721538 \cdot 10^{51}\right):\\
\;\;\;\;x + y \cdot \left(\left(\frac{t}{{z}^{2}} + 3.13060547622999996\right) - 36.527041698806414 \cdot \frac{1}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r417824 = x;
        double r417825 = y;
        double r417826 = z;
        double r417827 = 3.13060547623;
        double r417828 = r417826 * r417827;
        double r417829 = 11.1667541262;
        double r417830 = r417828 + r417829;
        double r417831 = r417830 * r417826;
        double r417832 = t;
        double r417833 = r417831 + r417832;
        double r417834 = r417833 * r417826;
        double r417835 = a;
        double r417836 = r417834 + r417835;
        double r417837 = r417836 * r417826;
        double r417838 = b;
        double r417839 = r417837 + r417838;
        double r417840 = r417825 * r417839;
        double r417841 = 15.234687407;
        double r417842 = r417826 + r417841;
        double r417843 = r417842 * r417826;
        double r417844 = 31.4690115749;
        double r417845 = r417843 + r417844;
        double r417846 = r417845 * r417826;
        double r417847 = 11.9400905721;
        double r417848 = r417846 + r417847;
        double r417849 = r417848 * r417826;
        double r417850 = 0.607771387771;
        double r417851 = r417849 + r417850;
        double r417852 = r417840 / r417851;
        double r417853 = r417824 + r417852;
        return r417853;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r417854 = z;
        double r417855 = -2.2710920961423764e+59;
        bool r417856 = r417854 <= r417855;
        double r417857 = 4.636101799572154e+51;
        bool r417858 = r417854 <= r417857;
        double r417859 = !r417858;
        bool r417860 = r417856 || r417859;
        double r417861 = x;
        double r417862 = y;
        double r417863 = t;
        double r417864 = 2.0;
        double r417865 = pow(r417854, r417864);
        double r417866 = r417863 / r417865;
        double r417867 = 3.13060547623;
        double r417868 = r417866 + r417867;
        double r417869 = 36.527041698806414;
        double r417870 = 1.0;
        double r417871 = r417870 / r417854;
        double r417872 = r417869 * r417871;
        double r417873 = r417868 - r417872;
        double r417874 = r417862 * r417873;
        double r417875 = r417861 + r417874;
        double r417876 = r417854 * r417867;
        double r417877 = 11.1667541262;
        double r417878 = r417876 + r417877;
        double r417879 = r417878 * r417854;
        double r417880 = r417879 + r417863;
        double r417881 = r417880 * r417854;
        double r417882 = a;
        double r417883 = r417881 + r417882;
        double r417884 = r417883 * r417854;
        double r417885 = b;
        double r417886 = r417884 + r417885;
        double r417887 = 15.234687407;
        double r417888 = r417854 + r417887;
        double r417889 = r417888 * r417854;
        double r417890 = 31.4690115749;
        double r417891 = r417889 + r417890;
        double r417892 = r417891 * r417854;
        double r417893 = 11.9400905721;
        double r417894 = r417892 + r417893;
        double r417895 = r417894 * r417854;
        double r417896 = 0.607771387771;
        double r417897 = r417895 + r417896;
        double r417898 = r417886 / r417897;
        double r417899 = r417862 * r417898;
        double r417900 = r417861 + r417899;
        double r417901 = r417860 ? r417875 : r417900;
        return r417901;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.0
Target1.1
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.2710920961423764e+59 or 4.636101799572154e+51 < z

    1. Initial program 61.6

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity61.6

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004\right)}}\]

    4. Applied times-frac60.1

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}}\]

    5. Simplified60.1

      \[\leadsto x + \color{blue}{y} \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]

    6. Taylor expanded around inf 0.8

      \[\leadsto x + y \cdot \color{blue}{\left(\left(\frac{t}{{z}^{2}} + 3.13060547622999996\right) - 36.527041698806414 \cdot \frac{1}{z}\right)}\]

    if -2.2710920961423764e+59 < z < 4.636101799572154e+51

    1. Initial program 2.9

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity2.9

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004\right)}}\]

    4. Applied times-frac1.3

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}}\]

    5. Simplified1.3

      \[\leadsto x + \color{blue}{y} \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.27109209614237641 \cdot 10^{59} \lor \neg \left(z \le 4.6361017995721538 \cdot 10^{51}\right):\\ \;\;\;\;x + y \cdot \left(\left(\frac{t}{{z}^{2}} + 3.13060547622999996\right) - 36.527041698806414 \cdot \frac{1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (if (< z -6.499344996252632e+53) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1))) (if (< z 7.066965436914287e+59) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771) (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)))) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1)))))

  (+ x (/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))