Average Error: 0.0 → 0.0
Time: 13.4s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(x \cdot {\left(\sqrt[3]{e^{y}} \cdot \sqrt[3]{e^{y}}\right)}^{y}\right) \cdot {\left(\sqrt[3]{e^{y}}\right)}^{y}\]
x \cdot e^{y \cdot y}
↓
\left(x \cdot {\left(\sqrt[3]{e^{y}} \cdot \sqrt[3]{e^{y}}\right)}^{y}\right) \cdot {\left(\sqrt[3]{e^{y}}\right)}^{y}
double f(double x, double y) {
        double r592606 = x;
        double r592607 = y;
        double r592608 = r592607 * r592607;
        double r592609 = exp(r592608);
        double r592610 = r592606 * r592609;
        return r592610;
}
↓
double f(double x, double y) {
        double r592611 = x;
        double r592612 = y;
        double r592613 = exp(r592612);
        double r592614 = cbrt(r592613);
        double r592615 = r592614 * r592614;
        double r592616 = pow(r592615, r592612);
        double r592617 = r592611 * r592616;
        double r592618 = pow(r592614, r592612);
        double r592619 = r592617 * r592618;
        return r592619;
}

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-log-exp0.0

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

  4. Applied exp-to-pow0.0

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

  6. Applied add-cube-cbrt0.0

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

  7. Applied unpow-prod-down0.0

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

  8. Applied associate-*r*0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (x y)
  :name "Data.Number.Erf:$dmerfcx from erf-2.0.0.0"
  :precision binary64

  :herbie-target
  (* x (pow (exp y) y))

  (* x (exp (* y y))))