Average Error: 20.1 → 0.1
Time: 4.9s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -175555486.192621917 \lor \neg \left(z \le 152068531.33662134\right):\\ \;\;\;\;x + \left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(\sqrt[3]{\left(z + 6.0124592597641033\right) \cdot z} \cdot \sqrt[3]{\left(z + 6.0124592597641033\right) \cdot z}\right) \cdot \sqrt[3]{\left(z + 6.0124592597641033\right) \cdot z} + 3.35034381502230394}\\ \end{array}\]
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 -175555486.192621917 \lor \neg \left(z \le 152068531.33662134\right):\\
\;\;\;\;x + \left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right)\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(\sqrt[3]{\left(z + 6.0124592597641033\right) \cdot z} \cdot \sqrt[3]{\left(z + 6.0124592597641033\right) \cdot z}\right) \cdot \sqrt[3]{\left(z + 6.0124592597641033\right) \cdot z} + 3.35034381502230394}\\

\end{array}
double f(double x, double y, double z) {
        double r310976 = x;
        double r310977 = y;
        double r310978 = z;
        double r310979 = 0.0692910599291889;
        double r310980 = r310978 * r310979;
        double r310981 = 0.4917317610505968;
        double r310982 = r310980 + r310981;
        double r310983 = r310982 * r310978;
        double r310984 = 0.279195317918525;
        double r310985 = r310983 + r310984;
        double r310986 = r310977 * r310985;
        double r310987 = 6.012459259764103;
        double r310988 = r310978 + r310987;
        double r310989 = r310988 * r310978;
        double r310990 = 3.350343815022304;
        double r310991 = r310989 + r310990;
        double r310992 = r310986 / r310991;
        double r310993 = r310976 + r310992;
        return r310993;
}
↓
double f(double x, double y, double z) {
        double r310994 = z;
        double r310995 = -175555486.19262192;
        bool r310996 = r310994 <= r310995;
        double r310997 = 152068531.33662134;
        bool r310998 = r310994 <= r310997;
        double r310999 = !r310998;
        bool r311000 = r310996 || r310999;
        double r311001 = x;
        double r311002 = 0.07512208616047561;
        double r311003 = y;
        double r311004 = r311003 / r310994;
        double r311005 = r311002 * r311004;
        double r311006 = 0.0692910599291889;
        double r311007 = r311006 * r311003;
        double r311008 = r311005 + r311007;
        double r311009 = r311001 + r311008;
        double r311010 = r310994 * r311006;
        double r311011 = 0.4917317610505968;
        double r311012 = r311010 + r311011;
        double r311013 = r311012 * r310994;
        double r311014 = 0.279195317918525;
        double r311015 = r311013 + r311014;
        double r311016 = 6.012459259764103;
        double r311017 = r310994 + r311016;
        double r311018 = r311017 * r310994;
        double r311019 = cbrt(r311018);
        double r311020 = r311019 * r311019;
        double r311021 = r311020 * r311019;
        double r311022 = 3.350343815022304;
        double r311023 = r311021 + r311022;
        double r311024 = r311015 / r311023;
        double r311025 = r311003 * r311024;
        double r311026 = r311001 + r311025;
        double r311027 = r311000 ? r311009 : r311026;
        return r311027;
}

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

Original20.1
Target0.2
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;z \lt -8120153.6524566747:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291888946\right) \cdot y - \left(\frac{0.404622038699921249 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z \lt 657611897278737680000:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)\right) \cdot \frac{1}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291888946\right) \cdot y - \left(\frac{0.404622038699921249 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -175555486.19262192 or 152068531.33662134 < z

    1. Initial program 40.7

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

    2. Taylor expanded around inf 0.0

      \[\leadsto \color{blue}{x + \left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right)}\]

    if -175555486.19262192 < z < 152068531.33662134

    1. Initial program 0.2

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

    3. Applied *-un-lft-identity0.2

      \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\color{blue}{1 \cdot \left(\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394\right)}}\]

    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

      \[\leadsto x + \color{blue}{y} \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
    6. Using strategy rm

    7. Applied add-cube-cbrt0.1

      \[\leadsto x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\color{blue}{\left(\sqrt[3]{\left(z + 6.0124592597641033\right) \cdot z} \cdot \sqrt[3]{\left(z + 6.0124592597641033\right) \cdot z}\right) \cdot \sqrt[3]{\left(z + 6.0124592597641033\right) \cdot z}} + 3.35034381502230394}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -175555486.192621917 \lor \neg \left(z \le 152068531.33662134\right):\\ \;\;\;\;x + \left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(\sqrt[3]{\left(z + 6.0124592597641033\right) \cdot z} \cdot \sqrt[3]{\left(z + 6.0124592597641033\right) \cdot z}\right) \cdot \sqrt[3]{\left(z + 6.0124592597641033\right) \cdot z} + 3.35034381502230394}\\ \end{array}\]

Reproduce

herbie shell --seed 2020024 
(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))))