Average Error: 0.0 → 0.0
Time: 9.0s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\sqrt{e^{y \cdot y}} \cdot \left(\sqrt{e^{y \cdot y}} \cdot x\right)\]
x \cdot e^{y \cdot y}
↓
\sqrt{e^{y \cdot y}} \cdot \left(\sqrt{e^{y \cdot y}} \cdot x\right)
double f(double x, double y) {
        double r34267369 = x;
        double r34267370 = y;
        double r34267371 = r34267370 * r34267370;
        double r34267372 = exp(r34267371);
        double r34267373 = r34267369 * r34267372;
        return r34267373;
}
↓
double f(double x, double y) {
        double r34267374 = y;
        double r34267375 = r34267374 * r34267374;
        double r34267376 = exp(r34267375);
        double r34267377 = sqrt(r34267376);
        double r34267378 = x;
        double r34267379 = r34267377 * r34267378;
        double r34267380 = r34267377 * r34267379;
        return r34267380;
}

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

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

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))))