Average Error: 0.0 → 0.1
Time: 21.3s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[{\left(\sqrt{e^{\left(\left(\sqrt{y} \cdot \log y\right) \cdot \sqrt{y} + \left(x - z\right)\right) \cdot 3}} \cdot \sqrt{e^{\left(\left(\sqrt{y} \cdot \log y\right) \cdot \sqrt{y} + \left(x - z\right)\right) \cdot 3}}\right)}^{\frac{1}{3}}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
{\left(\sqrt{e^{\left(\left(\sqrt{y} \cdot \log y\right) \cdot \sqrt{y} + \left(x - z\right)\right) \cdot 3}} \cdot \sqrt{e^{\left(\left(\sqrt{y} \cdot \log y\right) \cdot \sqrt{y} + \left(x - z\right)\right) \cdot 3}}\right)}^{\frac{1}{3}}
double f(double x, double y, double z) {
        double r17399363 = x;
        double r17399364 = y;
        double r17399365 = log(r17399364);
        double r17399366 = r17399364 * r17399365;
        double r17399367 = r17399363 + r17399366;
        double r17399368 = z;
        double r17399369 = r17399367 - r17399368;
        double r17399370 = exp(r17399369);
        return r17399370;
}
↓
double f(double x, double y, double z) {
        double r17399371 = y;
        double r17399372 = sqrt(r17399371);
        double r17399373 = log(r17399371);
        double r17399374 = r17399372 * r17399373;
        double r17399375 = r17399374 * r17399372;
        double r17399376 = x;
        double r17399377 = z;
        double r17399378 = r17399376 - r17399377;
        double r17399379 = r17399375 + r17399378;
        double r17399380 = 3.0;
        double r17399381 = r17399379 * r17399380;
        double r17399382 = exp(r17399381);
        double r17399383 = sqrt(r17399382);
        double r17399384 = r17399383 * r17399383;
        double r17399385 = 0.3333333333333333;
        double r17399386 = pow(r17399384, r17399385);
        return r17399386;
}

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

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

  6. Applied pow1/30.1

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

  8. Applied add-sqr-sqrt0.1

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

  9. Applied associate-*l*0.1

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

  11. Applied add-sqr-sqrt0.1

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

  12. Final simplification0.1

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

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)))