Average Error: 0.0 → 0.0
Time: 9.3s
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 r38299000 = x;
        double r38299001 = y;
        double r38299002 = r38299001 * r38299001;
        double r38299003 = exp(r38299002);
        double r38299004 = r38299000 * r38299003;
        return r38299004;
}
↓
double f(double x, double y) {
        double r38299005 = y;
        double r38299006 = r38299005 * r38299005;
        double r38299007 = exp(r38299006);
        double r38299008 = sqrt(r38299007);
        double r38299009 = x;
        double r38299010 = r38299008 * r38299009;
        double r38299011 = r38299008 * r38299010;
        return r38299011;
}

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 
(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))))