Average Error: 0.0 → 0.0
Time: 9.7s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\sqrt{e^{y \cdot y}} \cdot \left(\sqrt{{\left(e^{y}\right)}^{y}} \cdot x\right)\]
x \cdot e^{y \cdot y}
↓
\sqrt{e^{y \cdot y}} \cdot \left(\sqrt{{\left(e^{y}\right)}^{y}} \cdot x\right)
double f(double x, double y) {
        double r472695 = x;
        double r472696 = y;
        double r472697 = r472696 * r472696;
        double r472698 = exp(r472697);
        double r472699 = r472695 * r472698;
        return r472699;
}
↓
double f(double x, double y) {
        double r472700 = y;
        double r472701 = r472700 * r472700;
        double r472702 = exp(r472701);
        double r472703 = sqrt(r472702);
        double r472704 = exp(r472700);
        double r472705 = pow(r472704, r472700);
        double r472706 = sqrt(r472705);
        double r472707 = x;
        double r472708 = r472706 * r472707;
        double r472709 = r472703 * r472708;
        return r472709;
}

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. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +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))))