Average Error: 0.0 → 0.0
Time: 6.2s
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 r500809 = x;
        double r500810 = y;
        double r500811 = r500810 * r500810;
        double r500812 = exp(r500811);
        double r500813 = r500809 * r500812;
        return r500813;
}
↓
double f(double x, double y) {
        double r500814 = y;
        double r500815 = r500814 * r500814;
        double r500816 = exp(r500815);
        double r500817 = sqrt(r500816);
        double r500818 = exp(r500814);
        double r500819 = pow(r500818, r500814);
        double r500820 = sqrt(r500819);
        double r500821 = x;
        double r500822 = r500820 * r500821;
        double r500823 = r500817 * r500822;
        return r500823;
}

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

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

  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 
(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))))