Average Error: 0.0 → 0.0
Time: 3.2s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(x \cdot \left(\left(\sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}} \cdot \sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\right) \cdot \sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\right)\right) \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}\]
x \cdot e^{y \cdot y}
↓
\left(x \cdot \left(\left(\sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}} \cdot \sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\right) \cdot \sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\right)\right) \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}
double f(double x, double y) {
        double r833871 = x;
        double r833872 = y;
        double r833873 = r833872 * r833872;
        double r833874 = exp(r833873);
        double r833875 = r833871 * r833874;
        return r833875;
}
↓
double f(double x, double y) {
        double r833876 = x;
        double r833877 = y;
        double r833878 = exp(r833877);
        double r833879 = 2.0;
        double r833880 = r833877 / r833879;
        double r833881 = pow(r833878, r833880);
        double r833882 = cbrt(r833881);
        double r833883 = r833882 * r833882;
        double r833884 = r833883 * r833882;
        double r833885 = r833876 * r833884;
        double r833886 = r833885 * r833881;
        return r833886;
}

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 sqr-pow0.0

    \[\leadsto x \cdot \color{blue}{\left({\left(e^{y}\right)}^{\left(\frac{y}{2}\right)} \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}\right)}\]

  7. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(x \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}\right) \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\]
  8. Using strategy rm

  9. Applied add-cube-cbrt0.0

    \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}} \cdot \sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\right) \cdot \sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\right)}\right) \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}\]

  10. Final simplification0.0

    \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}} \cdot \sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\right) \cdot \sqrt[3]{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\right)\right) \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}\]

Reproduce

herbie shell --seed 2020060 +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))))