Average Error: 0.0 → 0.0
Time: 10.4s
Precision: 64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[{\left(e^{\sqrt[3]{\left(x \cdot y\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y\right) \cdot y}}\right)}^{\left(\sqrt[3]{\left(x \cdot y\right) \cdot y}\right)}\]
e^{\left(x \cdot y\right) \cdot y}
↓
{\left(e^{\sqrt[3]{\left(x \cdot y\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y\right) \cdot y}}\right)}^{\left(\sqrt[3]{\left(x \cdot y\right) \cdot y}\right)}
double f(double x, double y) {
        double r4629780 = x;
        double r4629781 = y;
        double r4629782 = r4629780 * r4629781;
        double r4629783 = r4629782 * r4629781;
        double r4629784 = exp(r4629783);
        return r4629784;
}
↓
double f(double x, double y) {
        double r4629785 = x;
        double r4629786 = y;
        double r4629787 = r4629785 * r4629786;
        double r4629788 = r4629787 * r4629786;
        double r4629789 = cbrt(r4629788);
        double r4629790 = r4629789 * r4629789;
        double r4629791 = exp(r4629790);
        double r4629792 = pow(r4629791, r4629789);
        return r4629792;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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-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. Applied exp-prod0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  (exp (* (* x y) y)))