Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\left(x + \left(y \cdot \log \left(\sqrt{y}\right) + y \cdot \log \left(\sqrt{y}\right)\right)\right) - z}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\left(x + \left(y \cdot \log \left(\sqrt{y}\right) + y \cdot \log \left(\sqrt{y}\right)\right)\right) - z}
double f(double x, double y, double z) {
        double r298991 = x;
        double r298992 = y;
        double r298993 = log(r298992);
        double r298994 = r298992 * r298993;
        double r298995 = r298991 + r298994;
        double r298996 = z;
        double r298997 = r298995 - r298996;
        double r298998 = exp(r298997);
        return r298998;
}
↓
double f(double x, double y, double z) {
        double r298999 = x;
        double r299000 = y;
        double r299001 = sqrt(r299000);
        double r299002 = log(r299001);
        double r299003 = r299000 * r299002;
        double r299004 = r299003 + r299003;
        double r299005 = r298999 + r299004;
        double r299006 = z;
        double r299007 = r299005 - r299006;
        double r299008 = exp(r299007);
        return r299008;
}

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. Final simplification0.0

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

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)))