Average Error: 0.0 → 0.1
Time: 21.2s
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 r15256384 = x;
        double r15256385 = y;
        double r15256386 = log(r15256385);
        double r15256387 = r15256385 * r15256386;
        double r15256388 = r15256384 + r15256387;
        double r15256389 = z;
        double r15256390 = r15256388 - r15256389;
        double r15256391 = exp(r15256390);
        return r15256391;
}
↓
double f(double x, double y, double z) {
        double r15256392 = x;
        double r15256393 = z;
        double r15256394 = r15256392 - r15256393;
        double r15256395 = y;
        double r15256396 = log(r15256395);
        double r15256397 = sqrt(r15256395);
        double r15256398 = r15256396 * r15256397;
        double r15256399 = r15256398 * r15256397;
        double r15256400 = r15256394 + r15256399;
        double r15256401 = 3.0;
        double r15256402 = r15256400 * r15256401;
        double r15256403 = exp(r15256402);
        double r15256404 = sqrt(r15256403);
        double r15256405 = r15256404 * r15256404;
        double r15256406 = 0.3333333333333333;
        double r15256407 = pow(r15256405, r15256406);
        return r15256407;
}

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)))