Average Error: 0.0 → 0.0
Time: 1.8s
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 r210271 = x;
        double r210272 = y;
        double r210273 = r210271 * r210272;
        double r210274 = r210273 * r210272;
        double r210275 = exp(r210274);
        return r210275;
}
↓
double f(double x, double y) {
        double r210276 = x;
        double r210277 = y;
        double r210278 = r210276 * r210277;
        double r210279 = r210278 * r210277;
        double r210280 = cbrt(r210279);
        double r210281 = r210280 * r210280;
        double r210282 = r210281 * r210280;
        double r210283 = exp(r210282);
        return r210283;
}

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 2020001 +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)))