\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -709774825.857266784 \lor \neg \left(z \le 95573.78759798268\right):\\ \;\;\;\;x + \left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \end{array}\]

x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}

↓

\begin{array}{l}
\mathbf{if}\;z \le -709774825.857266784 \lor \neg \left(z \le 95573.78759798268\right):\\
\;\;\;\;x + \left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\

\end{array}

double f(double x, double y, double z) {
        double r416835 = x;
        double r416836 = y;
        double r416837 = z;
        double r416838 = 0.0692910599291889;
        double r416839 = r416837 * r416838;
        double r416840 = 0.4917317610505968;
        double r416841 = r416839 + r416840;
        double r416842 = r416841 * r416837;
        double r416843 = 0.279195317918525;
        double r416844 = r416842 + r416843;
        double r416845 = r416836 * r416844;
        double r416846 = 6.012459259764103;
        double r416847 = r416837 + r416846;
        double r416848 = r416847 * r416837;
        double r416849 = 3.350343815022304;
        double r416850 = r416848 + r416849;
        double r416851 = r416845 / r416850;
        double r416852 = r416835 + r416851;
        return r416852;
}

↓

double f(double x, double y, double z) {
        double r416853 = z;
        double r416854 = -709774825.8572668;
        bool r416855 = r416853 <= r416854;
        double r416856 = 95573.78759798268;
        bool r416857 = r416853 <= r416856;
        double r416858 = !r416857;
        bool r416859 = r416855 || r416858;
        double r416860 = x;
        double r416861 = 0.07512208616047561;
        double r416862 = y;
        double r416863 = r416862 / r416853;
        double r416864 = r416861 * r416863;
        double r416865 = 0.0692910599291889;
        double r416866 = r416865 * r416862;
        double r416867 = r416864 + r416866;
        double r416868 = 0.40462203869992125;
        double r416869 = 2.0;
        double r416870 = pow(r416853, r416869);
        double r416871 = r416862 / r416870;
        double r416872 = r416868 * r416871;
        double r416873 = r416867 - r416872;
        double r416874 = r416860 + r416873;
        double r416875 = r416853 * r416865;
        double r416876 = 0.4917317610505968;
        double r416877 = r416875 + r416876;
        double r416878 = r416877 * r416853;
        double r416879 = 0.279195317918525;
        double r416880 = r416878 + r416879;
        double r416881 = 6.012459259764103;
        double r416882 = r416853 + r416881;
        double r416883 = r416882 * r416853;
        double r416884 = 3.350343815022304;
        double r416885 = r416883 + r416884;
        double r416886 = r416880 / r416885;
        double r416887 = r416862 * r416886;
        double r416888 = r416860 + r416887;
        double r416889 = r416859 ? r416874 : r416888;
        return r416889;
}

Original	19.8
Target	0.2
Herbie	0.1

Derivation

Split input into 2 regimes
if z < -709774825.8572668 or 95573.78759798268 < z
1. Initial program 40.6
  \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
2. Taylor expanded around inf 0.0
  \[\leadsto x + \color{blue}{\left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)}\]
if -709774825.8572668 < z < 95573.78759798268
1. Initial program 0.1
  \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
2. Using strategy rm
3. Applied *-un-lft-identity0.1
  \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\color{blue}{1 \cdot \left(\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394\right)}}\]
4. Applied times-frac0.1
  \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}}\]
5. Simplified0.1
  \[\leadsto x + \color{blue}{y} \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
Recombined 2 regimes into one program.
Final simplification0.1
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -709774825.857266784 \lor \neg \left(z \le 95573.78759798268\right):\\ \;\;\;\;x + \left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \end{array}\]

Reproduce

herbie shell --seed 2020056 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (if (< z -8120153.652456675) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x)) (if (< z 657611897278737680000) (+ 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))))

Error

Try it out

Target

Derivation

`if z < -709774825.8572668 or 95573.78759798268 < z`

`if -709774825.8572668 < z < 95573.78759798268`

Reproduce

In
Out