Average Error: 0.0 → 0.0
Time: 4.3s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\left(x + \left(y \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + y \cdot \log \left(\sqrt[3]{y}\right)\right)\right) - z}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\left(x + \left(y \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + y \cdot \log \left(\sqrt[3]{y}\right)\right)\right) - z}
double f(double x, double y, double z) {
        double r379711 = x;
        double r379712 = y;
        double r379713 = log(r379712);
        double r379714 = r379712 * r379713;
        double r379715 = r379711 + r379714;
        double r379716 = z;
        double r379717 = r379715 - r379716;
        double r379718 = exp(r379717);
        return r379718;
}
↓
double f(double x, double y, double z) {
        double r379719 = x;
        double r379720 = y;
        double r379721 = 2.0;
        double r379722 = cbrt(r379720);
        double r379723 = log(r379722);
        double r379724 = r379721 * r379723;
        double r379725 = r379720 * r379724;
        double r379726 = r379720 * r379723;
        double r379727 = r379725 + r379726;
        double r379728 = r379719 + r379727;
        double r379729 = z;
        double r379730 = r379728 - r379729;
        double r379731 = exp(r379730);
        return r379731;
}

Error

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Bits error versus y

Bits error versus z

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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

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

  4. Applied log-prod0.0

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

  5. Applied distribute-lft-in0.0

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

  6. Simplified0.0

    \[\leadsto e^{\left(x + \left(\color{blue}{y \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right)} + y \cdot \log \left(\sqrt[3]{y}\right)\right)\right) - z}\]

  7. Final simplification0.0

    \[\leadsto e^{\left(x + \left(y \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + y \cdot \log \left(\sqrt[3]{y}\right)\right)\right) - z}\]

Reproduce

herbie shell --seed 2020062 
(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)))