Average Error: 0.0 → 0.0
Time: 1.6s
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 r214118 = x;
        double r214119 = y;
        double r214120 = r214118 * r214119;
        double r214121 = r214120 * r214119;
        double r214122 = exp(r214121);
        return r214122;
}
↓
double f(double x, double y) {
        double r214123 = x;
        double r214124 = y;
        double r214125 = r214123 * r214124;
        double r214126 = r214125 * r214124;
        double r214127 = cbrt(r214126);
        double r214128 = r214127 * r214127;
        double r214129 = r214128 * r214127;
        double r214130 = exp(r214129);
        return r214130;
}

Error

Bits error versus x

Bits error versus y

Try it out

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)))