Average Error: 19.4 → 0.1
Time: 43.5s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -273974326636.0899:\\ \;\;\;\;\left(0.0692910599291889 \cdot y + \left(0.07512208616047561 \cdot \frac{y}{z} - \frac{0.40462203869992125}{z} \cdot \frac{y}{z}\right)\right) + x\\ \mathbf{elif}\;z \le 727958.1035308853:\\ \;\;\;\;\frac{\left(0.279195317918525 + z \cdot \left(0.4917317610505968 + 0.0692910599291889 \cdot z\right)\right) \cdot y}{z \cdot \left(6.012459259764103 + z\right) + 3.350343815022304} + x\\ \mathbf{else}:\\ \;\;\;\;\left(0.0692910599291889 \cdot y + \left(0.07512208616047561 \cdot \frac{y}{z} - \frac{0.40462203869992125}{z} \cdot \frac{y}{z}\right)\right) + x\\ \end{array}\]
x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}
↓
\begin{array}{l}
\mathbf{if}\;z \le -273974326636.0899:\\
\;\;\;\;\left(0.0692910599291889 \cdot y + \left(0.07512208616047561 \cdot \frac{y}{z} - \frac{0.40462203869992125}{z} \cdot \frac{y}{z}\right)\right) + x\\

\mathbf{elif}\;z \le 727958.1035308853:\\
\;\;\;\;\frac{\left(0.279195317918525 + z \cdot \left(0.4917317610505968 + 0.0692910599291889 \cdot z\right)\right) \cdot y}{z \cdot \left(6.012459259764103 + z\right) + 3.350343815022304} + x\\

\mathbf{else}:\\
\;\;\;\;\left(0.0692910599291889 \cdot y + \left(0.07512208616047561 \cdot \frac{y}{z} - \frac{0.40462203869992125}{z} \cdot \frac{y}{z}\right)\right) + x\\

\end{array}
double f(double x, double y, double z) {
        double r32251902 = x;
        double r32251903 = y;
        double r32251904 = z;
        double r32251905 = 0.0692910599291889;
        double r32251906 = r32251904 * r32251905;
        double r32251907 = 0.4917317610505968;
        double r32251908 = r32251906 + r32251907;
        double r32251909 = r32251908 * r32251904;
        double r32251910 = 0.279195317918525;
        double r32251911 = r32251909 + r32251910;
        double r32251912 = r32251903 * r32251911;
        double r32251913 = 6.012459259764103;
        double r32251914 = r32251904 + r32251913;
        double r32251915 = r32251914 * r32251904;
        double r32251916 = 3.350343815022304;
        double r32251917 = r32251915 + r32251916;
        double r32251918 = r32251912 / r32251917;
        double r32251919 = r32251902 + r32251918;
        return r32251919;
}
↓
double f(double x, double y, double z) {
        double r32251920 = z;
        double r32251921 = -273974326636.0899;
        bool r32251922 = r32251920 <= r32251921;
        double r32251923 = 0.0692910599291889;
        double r32251924 = y;
        double r32251925 = r32251923 * r32251924;
        double r32251926 = 0.07512208616047561;
        double r32251927 = r32251924 / r32251920;
        double r32251928 = r32251926 * r32251927;
        double r32251929 = 0.40462203869992125;
        double r32251930 = r32251929 / r32251920;
        double r32251931 = r32251930 * r32251927;
        double r32251932 = r32251928 - r32251931;
        double r32251933 = r32251925 + r32251932;
        double r32251934 = x;
        double r32251935 = r32251933 + r32251934;
        double r32251936 = 727958.1035308853;
        bool r32251937 = r32251920 <= r32251936;
        double r32251938 = 0.279195317918525;
        double r32251939 = 0.4917317610505968;
        double r32251940 = r32251923 * r32251920;
        double r32251941 = r32251939 + r32251940;
        double r32251942 = r32251920 * r32251941;
        double r32251943 = r32251938 + r32251942;
        double r32251944 = r32251943 * r32251924;
        double r32251945 = 6.012459259764103;
        double r32251946 = r32251945 + r32251920;
        double r32251947 = r32251920 * r32251946;
        double r32251948 = 3.350343815022304;
        double r32251949 = r32251947 + r32251948;
        double r32251950 = r32251944 / r32251949;
        double r32251951 = r32251950 + r32251934;
        double r32251952 = r32251937 ? r32251951 : r32251935;
        double r32251953 = r32251922 ? r32251935 : r32251952;
        return r32251953;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original19.4
Target0.2
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;z \lt -8120153.652456675:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z \lt 6.576118972787377 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -273974326636.0899 or 727958.1035308853 < z

    1. Initial program 40.3

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]

    2. Taylor expanded around inf 0.0

      \[\leadsto x + \color{blue}{\left(\left(0.0692910599291889 \cdot y + 0.07512208616047561 \cdot \frac{y}{z}\right) - 0.40462203869992125 \cdot \frac{y}{{z}^{2}}\right)}\]

    3. Simplified0.0

      \[\leadsto x + \color{blue}{\left(0.0692910599291889 \cdot y + \left(0.07512208616047561 \cdot \frac{y}{z} - \frac{0.40462203869992125}{z} \cdot \frac{y}{z}\right)\right)}\]

    if -273974326636.0899 < z < 727958.1035308853

    1. Initial program 0.2

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -273974326636.0899:\\ \;\;\;\;\left(0.0692910599291889 \cdot y + \left(0.07512208616047561 \cdot \frac{y}{z} - \frac{0.40462203869992125}{z} \cdot \frac{y}{z}\right)\right) + x\\ \mathbf{elif}\;z \le 727958.1035308853:\\ \;\;\;\;\frac{\left(0.279195317918525 + z \cdot \left(0.4917317610505968 + 0.0692910599291889 \cdot z\right)\right) \cdot y}{z \cdot \left(6.012459259764103 + z\right) + 3.350343815022304} + x\\ \mathbf{else}:\\ \;\;\;\;\left(0.0692910599291889 \cdot y + \left(0.07512208616047561 \cdot \frac{y}{z} - \frac{0.40462203869992125}{z} \cdot \frac{y}{z}\right)\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"

  :herbie-target
  (if (< z -8120153.652456675) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x)) (if (< z 6.576118972787377e+20) (+ x (* (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (/ 1 (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x))))

  (+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))