Average Error: 0.0 → 0.0
Time: 18.5s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\left(x + \left(\log \left(\sqrt{y}\right) \cdot y + \log \left(\sqrt{y}\right) \cdot y\right)\right) - z}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\left(x + \left(\log \left(\sqrt{y}\right) \cdot y + \log \left(\sqrt{y}\right) \cdot y\right)\right) - z}
double f(double x, double y, double z) {
        double r207030 = x;
        double r207031 = y;
        double r207032 = log(r207031);
        double r207033 = r207031 * r207032;
        double r207034 = r207030 + r207033;
        double r207035 = z;
        double r207036 = r207034 - r207035;
        double r207037 = exp(r207036);
        return r207037;
}
↓
double f(double x, double y, double z) {
        double r207038 = x;
        double r207039 = y;
        double r207040 = sqrt(r207039);
        double r207041 = log(r207040);
        double r207042 = r207041 * r207039;
        double r207043 = r207042 + r207042;
        double r207044 = r207038 + r207043;
        double r207045 = z;
        double r207046 = r207044 - r207045;
        double r207047 = exp(r207046);
        return r207047;
}

Error

Bits error versus x

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-sqr-sqrt0.0

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

  4. Applied log-prod0.0

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

  5. Applied distribute-lft-in0.0

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

  6. Simplified0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

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)))