Average Error: 0.0 → 0.0
Time: 21.2s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\left(\left(x + \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot y\right) + \log \left(\sqrt[3]{y}\right) \cdot y\right) - z}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\left(\left(x + \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot y\right) + \log \left(\sqrt[3]{y}\right) \cdot y\right) - z}
double f(double x, double y, double z) {
        double r238824 = x;
        double r238825 = y;
        double r238826 = log(r238825);
        double r238827 = r238825 * r238826;
        double r238828 = r238824 + r238827;
        double r238829 = z;
        double r238830 = r238828 - r238829;
        double r238831 = exp(r238830);
        return r238831;
}
↓
double f(double x, double y, double z) {
        double r238832 = x;
        double r238833 = 2.0;
        double r238834 = y;
        double r238835 = cbrt(r238834);
        double r238836 = log(r238835);
        double r238837 = r238833 * r238836;
        double r238838 = r238837 * r238834;
        double r238839 = r238832 + r238838;
        double r238840 = r238836 * r238834;
        double r238841 = r238839 + r238840;
        double r238842 = z;
        double r238843 = r238841 - r238842;
        double r238844 = exp(r238843);
        return r238844;
}

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-rgt-in0.0

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

  6. Applied associate-+r+0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 
(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)))