Average Error: 0.0 → 0.0
Time: 1.3s
Precision: 64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[\left(\sqrt[3]{e^{\left(x \cdot y\right) \cdot y}} \cdot \sqrt[3]{e^{\left(x \cdot y\right) \cdot y}}\right) \cdot \sqrt[3]{e^{\left(x \cdot y\right) \cdot y}}\]
e^{\left(x \cdot y\right) \cdot y}
↓
\left(\sqrt[3]{e^{\left(x \cdot y\right) \cdot y}} \cdot \sqrt[3]{e^{\left(x \cdot y\right) \cdot y}}\right) \cdot \sqrt[3]{e^{\left(x \cdot y\right) \cdot y}}
double f(double x, double y) {
        double r217940 = x;
        double r217941 = y;
        double r217942 = r217940 * r217941;
        double r217943 = r217942 * r217941;
        double r217944 = exp(r217943);
        return r217944;
}
↓
double f(double x, double y) {
        double r217945 = x;
        double r217946 = y;
        double r217947 = r217945 * r217946;
        double r217948 = r217947 * r217946;
        double r217949 = exp(r217948);
        double r217950 = cbrt(r217949);
        double r217951 = r217950 * r217950;
        double r217952 = r217951 * r217950;
        return r217952;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020033 +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)))