Average Error: 0.0 → 0.0
Time: 22.5s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \log y\right) \cdot \sqrt[3]{y} - \left(z - x\right)}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \log y\right) \cdot \sqrt[3]{y} - \left(z - x\right)}
double f(double x, double y, double z) {
        double r18893547 = x;
        double r18893548 = y;
        double r18893549 = log(r18893548);
        double r18893550 = r18893548 * r18893549;
        double r18893551 = r18893547 + r18893550;
        double r18893552 = z;
        double r18893553 = r18893551 - r18893552;
        double r18893554 = exp(r18893553);
        return r18893554;
}
↓
double f(double x, double y, double z) {
        double r18893555 = y;
        double r18893556 = cbrt(r18893555);
        double r18893557 = r18893556 * r18893556;
        double r18893558 = log(r18893555);
        double r18893559 = r18893557 * r18893558;
        double r18893560 = r18893559 * r18893556;
        double r18893561 = z;
        double r18893562 = x;
        double r18893563 = r18893561 - r18893562;
        double r18893564 = r18893560 - r18893563;
        double r18893565 = exp(r18893564);
        return r18893565;
}

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-exp-log0.0

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

  4. Simplified0.0

    \[\leadsto e^{\color{blue}{\log y \cdot y - \left(z - x\right)}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.0

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

  7. Applied associate-*r*0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"

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

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