Average Error: 20.1 → 0.1
Time: 5.3s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.81464760703818796 \cdot 10^{131} \lor \neg \left(z \le 26791.9880400715883\right):\\ \;\;\;\;x + \left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \end{array}\]
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 -1.81464760703818796 \cdot 10^{131} \lor \neg \left(z \le 26791.9880400715883\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 r334042 = x;
        double r334043 = y;
        double r334044 = z;
        double r334045 = 0.0692910599291889;
        double r334046 = r334044 * r334045;
        double r334047 = 0.4917317610505968;
        double r334048 = r334046 + r334047;
        double r334049 = r334048 * r334044;
        double r334050 = 0.279195317918525;
        double r334051 = r334049 + r334050;
        double r334052 = r334043 * r334051;
        double r334053 = 6.012459259764103;
        double r334054 = r334044 + r334053;
        double r334055 = r334054 * r334044;
        double r334056 = 3.350343815022304;
        double r334057 = r334055 + r334056;
        double r334058 = r334052 / r334057;
        double r334059 = r334042 + r334058;
        return r334059;
}
↓
double f(double x, double y, double z) {
        double r334060 = z;
        double r334061 = -1.814647607038188e+131;
        bool r334062 = r334060 <= r334061;
        double r334063 = 26791.98804007159;
        bool r334064 = r334060 <= r334063;
        double r334065 = !r334064;
        bool r334066 = r334062 || r334065;
        double r334067 = x;
        double r334068 = 0.07512208616047561;
        double r334069 = y;
        double r334070 = r334069 / r334060;
        double r334071 = r334068 * r334070;
        double r334072 = 0.0692910599291889;
        double r334073 = r334072 * r334069;
        double r334074 = r334071 + r334073;
        double r334075 = 0.40462203869992125;
        double r334076 = 2.0;
        double r334077 = pow(r334060, r334076);
        double r334078 = r334069 / r334077;
        double r334079 = r334075 * r334078;
        double r334080 = r334074 - r334079;
        double r334081 = r334067 + r334080;
        double r334082 = r334060 * r334072;
        double r334083 = 0.4917317610505968;
        double r334084 = r334082 + r334083;
        double r334085 = r334084 * r334060;
        double r334086 = 0.279195317918525;
        double r334087 = r334085 + r334086;
        double r334088 = 6.012459259764103;
        double r334089 = r334060 + r334088;
        double r334090 = r334089 * r334060;
        double r334091 = 3.350343815022304;
        double r334092 = r334090 + r334091;
        double r334093 = r334087 / r334092;
        double r334094 = r334069 * r334093;
        double r334095 = r334067 + r334094;
        double r334096 = r334066 ? r334081 : r334095;
        return r334096;
}

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 < -1.814647607038188e+131 or 26791.98804007159 < z

    1. Initial program 47.2

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

    2. 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 -1.814647607038188e+131 < z < 26791.98804007159

    1. Initial program 2.3

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

    3. Applied *-un-lft-identity2.3

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

    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

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.81464760703818796 \cdot 10^{131} \lor \neg \left(z \le 26791.9880400715883\right):\\ \;\;\;\;x + \left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291888946 \cdot y\right) - 0.404622038699921249 \cdot \frac{y}{{z}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 
(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))))