Average Error: 0.0 → 0.0
Time: 11.9s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\left({\left(\sqrt[3]{e^{y}}\right)}^{y} \cdot x\right) \cdot {\left(\sqrt[3]{e^{y}} \cdot \sqrt[3]{e^{y}}\right)}^{y}\]
x \cdot e^{y \cdot y}
↓
\left({\left(\sqrt[3]{e^{y}}\right)}^{y} \cdot x\right) \cdot {\left(\sqrt[3]{e^{y}} \cdot \sqrt[3]{e^{y}}\right)}^{y}
double f(double x, double y) {
        double r641029 = x;
        double r641030 = y;
        double r641031 = r641030 * r641030;
        double r641032 = exp(r641031);
        double r641033 = r641029 * r641032;
        return r641033;
}
↓
double f(double x, double y) {
        double r641034 = y;
        double r641035 = exp(r641034);
        double r641036 = cbrt(r641035);
        double r641037 = pow(r641036, r641034);
        double r641038 = x;
        double r641039 = r641037 * r641038;
        double r641040 = r641036 * r641036;
        double r641041 = pow(r641040, r641034);
        double r641042 = r641039 * r641041;
        return r641042;
}

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. Simplified0.0

    \[\leadsto \color{blue}{{\left(e^{y}\right)}^{y} \cdot x}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt0.0

    \[\leadsto {\color{blue}{\left(\left(\sqrt[3]{e^{y}} \cdot \sqrt[3]{e^{y}}\right) \cdot \sqrt[3]{e^{y}}\right)}}^{y} \cdot x\]

  5. Applied unpow-prod-down0.0

    \[\leadsto \color{blue}{\left({\left(\sqrt[3]{e^{y}} \cdot \sqrt[3]{e^{y}}\right)}^{y} \cdot {\left(\sqrt[3]{e^{y}}\right)}^{y}\right)} \cdot x\]

  6. Applied associate-*l*0.0

    \[\leadsto \color{blue}{{\left(\sqrt[3]{e^{y}} \cdot \sqrt[3]{e^{y}}\right)}^{y} \cdot \left({\left(\sqrt[3]{e^{y}}\right)}^{y} \cdot x\right)}\]

  7. Final simplification0.0

    \[\leadsto \left({\left(\sqrt[3]{e^{y}}\right)}^{y} \cdot x\right) \cdot {\left(\sqrt[3]{e^{y}} \cdot \sqrt[3]{e^{y}}\right)}^{y}\]

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))))