Average Error: 0.0 → 0.0
Time: 8.0s
Precision: 64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[e^{\left(\sqrt[3]{\left(x \cdot y\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y\right) \cdot y}}\]
e^{\left(x \cdot y\right) \cdot y}
↓
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 r142874 = x;
        double r142875 = y;
        double r142876 = r142874 * r142875;
        double r142877 = r142876 * r142875;
        double r142878 = exp(r142877);
        return r142878;
}
↓
double f(double x, double y) {
        double r142879 = x;
        double r142880 = y;
        double r142881 = r142879 * r142880;
        double r142882 = r142881 * r142880;
        double r142883 = cbrt(r142882);
        double r142884 = r142883 * r142883;
        double r142885 = r142884 * r142883;
        double r142886 = exp(r142885);
        return r142886;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied add-cube-cbrt0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019350 +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)))