Average Error: 0.0 → 0.0
Time: 2.1s
Precision: 64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[\sqrt{e^{\left(x \cdot y\right) \cdot y}} \cdot \sqrt{e^{\left(\sqrt[3]{\left(x \cdot y\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y\right) \cdot y}}}\]
e^{\left(x \cdot y\right) \cdot y}
↓
\sqrt{e^{\left(x \cdot y\right) \cdot y}} \cdot \sqrt{e^{\left(\sqrt[3]{\left(x \cdot y\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y\right) \cdot y}}}
double f(double x, double y) {
        double r235288 = x;
        double r235289 = y;
        double r235290 = r235288 * r235289;
        double r235291 = r235290 * r235289;
        double r235292 = exp(r235291);
        return r235292;
}
↓
double f(double x, double y) {
        double r235293 = x;
        double r235294 = y;
        double r235295 = r235293 * r235294;
        double r235296 = r235295 * r235294;
        double r235297 = exp(r235296);
        double r235298 = sqrt(r235297);
        double r235299 = cbrt(r235296);
        double r235300 = r235299 * r235299;
        double r235301 = r235300 * r235299;
        double r235302 = exp(r235301);
        double r235303 = sqrt(r235302);
        double r235304 = r235298 * r235303;
        return r235304;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

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

  3. Applied add-sqr-sqrt0.0

    \[\leadsto \color{blue}{\sqrt{e^{\left(x \cdot y\right) \cdot y}} \cdot \sqrt{e^{\left(x \cdot y\right) \cdot y}}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.0

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

  6. Final simplification0.0

    \[\leadsto \sqrt{e^{\left(x \cdot y\right) \cdot y}} \cdot \sqrt{e^{\left(\sqrt[3]{\left(x \cdot y\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y\right) \cdot y}}}\]

Reproduce

herbie shell --seed 2020056 +o rules:numerics
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))