Average Error: 0.0 → 0.0
Time: 2.3s
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 r307526 = x;
        double r307527 = y;
        double r307528 = r307526 * r307527;
        double r307529 = r307528 * r307527;
        double r307530 = exp(r307529);
        return r307530;
}
↓
double f(double x, double y) {
        double r307531 = x;
        double r307532 = y;
        double r307533 = 2.0;
        double r307534 = pow(r307532, r307533);
        double r307535 = r307531 * r307534;
        double r307536 = exp(r307535);
        double r307537 = 3.0;
        double r307538 = pow(r307536, r307537);
        double r307539 = 0.3333333333333333;
        double r307540 = pow(r307538, r307539);
        return r307540;
}

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 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))