Average Error: 0.0 → 0.0
Time: 9.3s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(x \cdot \sqrt{e^{y \cdot y}}\right) \cdot \sqrt{e^{y \cdot y}}\]
x \cdot e^{y \cdot y}
↓
\left(x \cdot \sqrt{e^{y \cdot y}}\right) \cdot \sqrt{e^{y \cdot y}}
double f(double x, double y) {
        double r52401337 = x;
        double r52401338 = y;
        double r52401339 = r52401338 * r52401338;
        double r52401340 = exp(r52401339);
        double r52401341 = r52401337 * r52401340;
        return r52401341;
}
↓
double f(double x, double y) {
        double r52401342 = x;
        double r52401343 = y;
        double r52401344 = r52401343 * r52401343;
        double r52401345 = exp(r52401344);
        double r52401346 = sqrt(r52401345);
        double r52401347 = r52401342 * r52401346;
        double r52401348 = r52401347 * r52401346;
        return r52401348;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[x \cdot {\left(e^{y}\right)}^{y}\]

Derivation

  1. Initial program 0.0

    \[x \cdot e^{y \cdot y}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

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

  4. Applied associate-*r*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Data.Number.Erf:$dmerfcx from erf-2.0.0.0"

  :herbie-target
  (* x (pow (exp y) y))

  (* x (exp (* y y))))