Average Error: 0.0 → 0.0
Time: 2.1s
Precision: 64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[{\left({\left(e^{x \cdot {y}^{2}}\right)}^{3}\right)}^{\frac{1}{3}}\]
e^{\left(x \cdot y\right) \cdot y}
↓
{\left({\left(e^{x \cdot {y}^{2}}\right)}^{3}\right)}^{\frac{1}{3}}
double f(double x, double y) {
        double r233807 = x;
        double r233808 = y;
        double r233809 = r233807 * r233808;
        double r233810 = r233809 * r233808;
        double r233811 = exp(r233810);
        return r233811;
}
↓
double f(double x, double y) {
        double r233812 = x;
        double r233813 = y;
        double r233814 = 2.0;
        double r233815 = pow(r233813, r233814);
        double r233816 = r233812 * r233815;
        double r233817 = exp(r233816);
        double r233818 = 3.0;
        double r233819 = pow(r233817, r233818);
        double r233820 = 0.3333333333333333;
        double r233821 = pow(r233819, r233820);
        return r233821;
}

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-cbrt-cube0.0

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

  4. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(e^{x \cdot {y}^{2}}\right)}^{3}}}\]
  5. Using strategy rm

  6. Applied pow1/30.0

    \[\leadsto \color{blue}{{\left({\left(e^{x \cdot {y}^{2}}\right)}^{3}\right)}^{\frac{1}{3}}}\]

  7. Final simplification0.0

    \[\leadsto {\left({\left(e^{x \cdot {y}^{2}}\right)}^{3}\right)}^{\frac{1}{3}}\]

Reproduce

herbie shell --seed 2020065 +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)))