Average Error: 0.0 → 0.0
Time: 8.9s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[{\left(e^{\sqrt[3]{\left(x + y \cdot \log y\right) - z} \cdot \sqrt[3]{\left(x + y \cdot \log y\right) - z}}\right)}^{\left(\sqrt[3]{\left(x + y \cdot \log y\right) - z}\right)}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
{\left(e^{\sqrt[3]{\left(x + y \cdot \log y\right) - z} \cdot \sqrt[3]{\left(x + y \cdot \log y\right) - z}}\right)}^{\left(\sqrt[3]{\left(x + y \cdot \log y\right) - z}\right)}
double f(double x, double y, double z) {
        double r220862 = x;
        double r220863 = y;
        double r220864 = log(r220863);
        double r220865 = r220863 * r220864;
        double r220866 = r220862 + r220865;
        double r220867 = z;
        double r220868 = r220866 - r220867;
        double r220869 = exp(r220868);
        return r220869;
}
↓
double f(double x, double y, double z) {
        double r220870 = x;
        double r220871 = y;
        double r220872 = log(r220871);
        double r220873 = r220871 * r220872;
        double r220874 = r220870 + r220873;
        double r220875 = z;
        double r220876 = r220874 - r220875;
        double r220877 = cbrt(r220876);
        double r220878 = r220877 * r220877;
        double r220879 = exp(r220878);
        double r220880 = pow(r220879, r220877);
        return r220880;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

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Target

Original0.0
Target0.0
Herbie0.0
\[e^{\left(x - z\right) + \log y \cdot y}\]

Derivation

  1. Initial program 0.0

    \[e^{\left(x + y \cdot \log y\right) - z}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.0

    \[\leadsto e^{\color{blue}{\left(\sqrt[3]{\left(x + y \cdot \log y\right) - z} \cdot \sqrt[3]{\left(x + y \cdot \log y\right) - z}\right) \cdot \sqrt[3]{\left(x + y \cdot \log y\right) - z}}}\]

  4. Applied exp-prod0.0

    \[\leadsto \color{blue}{{\left(e^{\sqrt[3]{\left(x + y \cdot \log y\right) - z} \cdot \sqrt[3]{\left(x + y \cdot \log y\right) - z}}\right)}^{\left(\sqrt[3]{\left(x + y \cdot \log y\right) - z}\right)}}\]

  5. Final simplification0.0

    \[\leadsto {\left(e^{\sqrt[3]{\left(x + y \cdot \log y\right) - z} \cdot \sqrt[3]{\left(x + y \cdot \log y\right) - z}}\right)}^{\left(\sqrt[3]{\left(x + y \cdot \log y\right) - z}\right)}\]

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (exp (+ (- x z) (* (log y) y)))

  (exp (- (+ x (* y (log y))) z)))