Average Error: 28.8 → 1.1
Time: 21.1s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.895393240846026 \cdot 10^{+34}:\\ \;\;\;\;\left(y \cdot \left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{36.527041698806414 \cdot y}{z}\right) + x\\ \mathbf{elif}\;z \le 3.866410402714096 \cdot 10^{+43}:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot \left(a + z \cdot \left(z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right) + t\right)\right)}{0.607771387771 + \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{36.527041698806414 \cdot y}{z}\right) + x\\ \end{array}\]
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.895393240846026 \cdot 10^{+34}:\\
\;\;\;\;\left(y \cdot \left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{36.527041698806414 \cdot y}{z}\right) + x\\

\mathbf{elif}\;z \le 3.866410402714096 \cdot 10^{+43}:\\
\;\;\;\;x + y \cdot \frac{b + z \cdot \left(a + z \cdot \left(z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right) + t\right)\right)}{0.607771387771 + \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right) \cdot z}\\

\mathbf{else}:\\
\;\;\;\;\left(y \cdot \left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{36.527041698806414 \cdot y}{z}\right) + x\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r18375827 = x;
        double r18375828 = y;
        double r18375829 = z;
        double r18375830 = 3.13060547623;
        double r18375831 = r18375829 * r18375830;
        double r18375832 = 11.1667541262;
        double r18375833 = r18375831 + r18375832;
        double r18375834 = r18375833 * r18375829;
        double r18375835 = t;
        double r18375836 = r18375834 + r18375835;
        double r18375837 = r18375836 * r18375829;
        double r18375838 = a;
        double r18375839 = r18375837 + r18375838;
        double r18375840 = r18375839 * r18375829;
        double r18375841 = b;
        double r18375842 = r18375840 + r18375841;
        double r18375843 = r18375828 * r18375842;
        double r18375844 = 15.234687407;
        double r18375845 = r18375829 + r18375844;
        double r18375846 = r18375845 * r18375829;
        double r18375847 = 31.4690115749;
        double r18375848 = r18375846 + r18375847;
        double r18375849 = r18375848 * r18375829;
        double r18375850 = 11.9400905721;
        double r18375851 = r18375849 + r18375850;
        double r18375852 = r18375851 * r18375829;
        double r18375853 = 0.607771387771;
        double r18375854 = r18375852 + r18375853;
        double r18375855 = r18375843 / r18375854;
        double r18375856 = r18375827 + r18375855;
        return r18375856;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r18375857 = z;
        double r18375858 = -2.895393240846026e+34;
        bool r18375859 = r18375857 <= r18375858;
        double r18375860 = y;
        double r18375861 = 3.13060547623;
        double r18375862 = t;
        double r18375863 = r18375857 * r18375857;
        double r18375864 = r18375862 / r18375863;
        double r18375865 = r18375861 + r18375864;
        double r18375866 = r18375860 * r18375865;
        double r18375867 = 36.527041698806414;
        double r18375868 = r18375867 * r18375860;
        double r18375869 = r18375868 / r18375857;
        double r18375870 = r18375866 - r18375869;
        double r18375871 = x;
        double r18375872 = r18375870 + r18375871;
        double r18375873 = 3.866410402714096e+43;
        bool r18375874 = r18375857 <= r18375873;
        double r18375875 = b;
        double r18375876 = a;
        double r18375877 = 11.1667541262;
        double r18375878 = r18375861 * r18375857;
        double r18375879 = r18375877 + r18375878;
        double r18375880 = r18375857 * r18375879;
        double r18375881 = r18375880 + r18375862;
        double r18375882 = r18375857 * r18375881;
        double r18375883 = r18375876 + r18375882;
        double r18375884 = r18375857 * r18375883;
        double r18375885 = r18375875 + r18375884;
        double r18375886 = 0.607771387771;
        double r18375887 = 11.9400905721;
        double r18375888 = 31.4690115749;
        double r18375889 = 15.234687407;
        double r18375890 = r18375889 + r18375857;
        double r18375891 = r18375857 * r18375890;
        double r18375892 = r18375888 + r18375891;
        double r18375893 = r18375857 * r18375892;
        double r18375894 = r18375887 + r18375893;
        double r18375895 = r18375894 * r18375857;
        double r18375896 = r18375886 + r18375895;
        double r18375897 = r18375885 / r18375896;
        double r18375898 = r18375860 * r18375897;
        double r18375899 = r18375871 + r18375898;
        double r18375900 = r18375874 ? r18375899 : r18375872;
        double r18375901 = r18375859 ? r18375872 : r18375900;
        return r18375901;
}

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

Original28.8
Target1.0
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.895393240846026e+34 or 3.866410402714096e+43 < z

    1. Initial program 58.2

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]

    2. Taylor expanded around inf 8.0

      \[\leadsto x + \color{blue}{\left(\left(\frac{t \cdot y}{{z}^{2}} + 3.13060547623 \cdot y\right) - 36.527041698806414 \cdot \frac{y}{z}\right)}\]

    3. Simplified1.5

      \[\leadsto x + \color{blue}{\left(3.13060547623 \cdot y + \left(\frac{t}{z} \cdot \frac{y}{z} - 36.527041698806414 \cdot \frac{y}{z}\right)\right)}\]

    4. Taylor expanded around 0 8.0

      \[\leadsto x + \color{blue}{\left(\left(\frac{t \cdot y}{{z}^{2}} + 3.13060547623 \cdot y\right) - 36.527041698806414 \cdot \frac{y}{z}\right)}\]

    5. Simplified2.6

      \[\leadsto x + \color{blue}{\left(\frac{y \cdot \left(\frac{t}{z} - 36.527041698806414\right)}{z} + y \cdot 3.13060547623\right)}\]

    6. Taylor expanded around 0 8.0

      \[\leadsto x + \color{blue}{\left(\left(\frac{t \cdot y}{{z}^{2}} + 3.13060547623 \cdot y\right) - 36.527041698806414 \cdot \frac{y}{z}\right)}\]

    7. Simplified1.4

      \[\leadsto x + \color{blue}{\left(y \cdot \left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{y \cdot 36.527041698806414}{z}\right)}\]

    if -2.895393240846026e+34 < z < 3.866410402714096e+43

    1. Initial program 1.4

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity1.4

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771\right)}}\]

    4. Applied times-frac0.7

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}}\]

    5. Simplified0.7

      \[\leadsto x + \color{blue}{y} \cdot \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.895393240846026 \cdot 10^{+34}:\\ \;\;\;\;\left(y \cdot \left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{36.527041698806414 \cdot y}{z}\right) + x\\ \mathbf{elif}\;z \le 3.866410402714096 \cdot 10^{+43}:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot \left(a + z \cdot \left(z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right) + t\right)\right)}{0.607771387771 + \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{36.527041698806414 \cdot y}{z}\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"

  :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))))