Average Error: 0.0 → 0.1
Time: 20.4s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[{\left(\sqrt{e^{\left(\left(x - z\right) + \left(\log y \cdot \sqrt{y}\right) \cdot \sqrt{y}\right) \cdot 3}} \cdot \sqrt{e^{\left(\left(x - z\right) + \left(\log y \cdot \sqrt{y}\right) \cdot \sqrt{y}\right) \cdot 3}}\right)}^{\frac{1}{3}}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
{\left(\sqrt{e^{\left(\left(x - z\right) + \left(\log y \cdot \sqrt{y}\right) \cdot \sqrt{y}\right) \cdot 3}} \cdot \sqrt{e^{\left(\left(x - z\right) + \left(\log y \cdot \sqrt{y}\right) \cdot \sqrt{y}\right) \cdot 3}}\right)}^{\frac{1}{3}}
double f(double x, double y, double z) {
        double r16553615 = x;
        double r16553616 = y;
        double r16553617 = log(r16553616);
        double r16553618 = r16553616 * r16553617;
        double r16553619 = r16553615 + r16553618;
        double r16553620 = z;
        double r16553621 = r16553619 - r16553620;
        double r16553622 = exp(r16553621);
        return r16553622;
}
↓
double f(double x, double y, double z) {
        double r16553623 = x;
        double r16553624 = z;
        double r16553625 = r16553623 - r16553624;
        double r16553626 = y;
        double r16553627 = log(r16553626);
        double r16553628 = sqrt(r16553626);
        double r16553629 = r16553627 * r16553628;
        double r16553630 = r16553629 * r16553628;
        double r16553631 = r16553625 + r16553630;
        double r16553632 = 3.0;
        double r16553633 = r16553631 * r16553632;
        double r16553634 = exp(r16553633);
        double r16553635 = sqrt(r16553634);
        double r16553636 = r16553635 * r16553635;
        double r16553637 = 0.3333333333333333;
        double r16553638 = pow(r16553636, r16553637);
        return r16553638;
}

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
Herbie0.1
\[e^{\left(x - z\right) + \log y \cdot y}\]

Derivation

  1. Initial program 0.0

    \[e^{\left(x + y \cdot \log y\right) - z}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.1

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

  4. Simplified0.1

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

  6. Applied pow1/30.1

    \[\leadsto \color{blue}{{\left(e^{3 \cdot \left(\left(x - z\right) + \log y \cdot y\right)}\right)}^{\frac{1}{3}}}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt0.1

    \[\leadsto {\left(e^{3 \cdot \left(\left(x - z\right) + \log y \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right)}\right)}^{\frac{1}{3}}\]

  9. Applied associate-*r*0.1

    \[\leadsto {\left(e^{3 \cdot \left(\left(x - z\right) + \color{blue}{\left(\log y \cdot \sqrt{y}\right) \cdot \sqrt{y}}\right)}\right)}^{\frac{1}{3}}\]
  10. Using strategy rm

  11. Applied add-sqr-sqrt0.1

    \[\leadsto {\color{blue}{\left(\sqrt{e^{3 \cdot \left(\left(x - z\right) + \left(\log y \cdot \sqrt{y}\right) \cdot \sqrt{y}\right)}} \cdot \sqrt{e^{3 \cdot \left(\left(x - z\right) + \left(\log y \cdot \sqrt{y}\right) \cdot \sqrt{y}\right)}}\right)}}^{\frac{1}{3}}\]

  12. Final simplification0.1

    \[\leadsto {\left(\sqrt{e^{\left(\left(x - z\right) + \left(\log y \cdot \sqrt{y}\right) \cdot \sqrt{y}\right) \cdot 3}} \cdot \sqrt{e^{\left(\left(x - z\right) + \left(\log y \cdot \sqrt{y}\right) \cdot \sqrt{y}\right) \cdot 3}}\right)}^{\frac{1}{3}}\]

Reproduce

herbie shell --seed 2019163 
(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)))