Average Error: 29.4 → 4.9
Time: 12.5s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -441648319598393860 \lor \neg \left(z \le 706881567136002.375\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]
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 -441648319598393860 \lor \neg \left(z \le 706881567136002.375\right):\\
\;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;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}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r299873 = x;
        double r299874 = y;
        double r299875 = z;
        double r299876 = 3.13060547623;
        double r299877 = r299875 * r299876;
        double r299878 = 11.1667541262;
        double r299879 = r299877 + r299878;
        double r299880 = r299879 * r299875;
        double r299881 = t;
        double r299882 = r299880 + r299881;
        double r299883 = r299882 * r299875;
        double r299884 = a;
        double r299885 = r299883 + r299884;
        double r299886 = r299885 * r299875;
        double r299887 = b;
        double r299888 = r299886 + r299887;
        double r299889 = r299874 * r299888;
        double r299890 = 15.234687407;
        double r299891 = r299875 + r299890;
        double r299892 = r299891 * r299875;
        double r299893 = 31.4690115749;
        double r299894 = r299892 + r299893;
        double r299895 = r299894 * r299875;
        double r299896 = 11.9400905721;
        double r299897 = r299895 + r299896;
        double r299898 = r299897 * r299875;
        double r299899 = 0.607771387771;
        double r299900 = r299898 + r299899;
        double r299901 = r299889 / r299900;
        double r299902 = r299873 + r299901;
        return r299902;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r299903 = z;
        double r299904 = -4.4164831959839386e+17;
        bool r299905 = r299903 <= r299904;
        double r299906 = 706881567136002.4;
        bool r299907 = r299903 <= r299906;
        double r299908 = !r299907;
        bool r299909 = r299905 || r299908;
        double r299910 = x;
        double r299911 = 3.13060547623;
        double r299912 = y;
        double r299913 = r299911 * r299912;
        double r299914 = t;
        double r299915 = r299914 * r299912;
        double r299916 = 2.0;
        double r299917 = pow(r299903, r299916);
        double r299918 = r299915 / r299917;
        double r299919 = r299913 + r299918;
        double r299920 = 36.527041698806414;
        double r299921 = r299912 / r299903;
        double r299922 = r299920 * r299921;
        double r299923 = r299919 - r299922;
        double r299924 = r299910 + r299923;
        double r299925 = 15.234687407;
        double r299926 = r299903 + r299925;
        double r299927 = r299926 * r299903;
        double r299928 = 31.4690115749;
        double r299929 = r299927 + r299928;
        double r299930 = r299929 * r299903;
        double r299931 = 11.9400905721;
        double r299932 = r299930 + r299931;
        double r299933 = r299932 * r299903;
        double r299934 = 0.607771387771;
        double r299935 = r299933 + r299934;
        double r299936 = r299903 * r299911;
        double r299937 = 11.1667541262;
        double r299938 = r299936 + r299937;
        double r299939 = r299938 * r299903;
        double r299940 = r299939 + r299914;
        double r299941 = r299940 * r299903;
        double r299942 = a;
        double r299943 = r299941 + r299942;
        double r299944 = r299943 * r299903;
        double r299945 = b;
        double r299946 = r299944 + r299945;
        double r299947 = r299935 / r299946;
        double r299948 = r299912 / r299947;
        double r299949 = r299910 + r299948;
        double r299950 = r299909 ? r299924 : r299949;
        return r299950;
}

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

Original29.4
Target1.2
Herbie4.9
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -4.4164831959839386e+17 or 706881567136002.4 < z

    1. Initial program 56.9

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

    2. Taylor expanded around inf 9.3

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

    if -4.4164831959839386e+17 < z < 706881567136002.4

    1. Initial program 0.5

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

    3. Applied associate-/l*0.2

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

  4. Final simplification4.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -441648319598393860 \lor \neg \left(z \le 706881567136002.375\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(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))))