Average Error: 0.0 → 0.0
Time: 5.0s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(\left(x \cdot {\left(e^{y \cdot y}\right)}^{\frac{1}{3}}\right) \cdot \sqrt{{\left(e^{y \cdot y}\right)}^{\frac{2}{3}}}\right) \cdot \sqrt[3]{e^{y \cdot y}}\]
x \cdot e^{y \cdot y}
↓
\left(\left(x \cdot {\left(e^{y \cdot y}\right)}^{\frac{1}{3}}\right) \cdot \sqrt{{\left(e^{y \cdot y}\right)}^{\frac{2}{3}}}\right) \cdot \sqrt[3]{e^{y \cdot y}}
double f(double x, double y) {
        double r4874 = x;
        double r4875 = y;
        double r4876 = r4875 * r4875;
        double r4877 = exp(r4876);
        double r4878 = r4874 * r4877;
        return r4878;
}
↓
double f(double x, double y) {
        double r4879 = x;
        double r4880 = y;
        double r4881 = r4880 * r4880;
        double r4882 = exp(r4881);
        double r4883 = 0.3333333333333333;
        double r4884 = pow(r4882, r4883);
        double r4885 = r4879 * r4884;
        double r4886 = 0.6666666666666666;
        double r4887 = pow(r4882, r4886);
        double r4888 = sqrt(r4887);
        double r4889 = r4885 * r4888;
        double r4890 = cbrt(r4882);
        double r4891 = r4889 * r4890;
        return r4891;
}

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-cube-cbrt0.0

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

  4. Applied associate-*r*0.0

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

  6. Applied pow1/30.0

    \[\leadsto \left(x \cdot \left(\sqrt[3]{e^{y \cdot y}} \cdot \color{blue}{{\left(e^{y \cdot y}\right)}^{\frac{1}{3}}}\right)\right) \cdot \sqrt[3]{e^{y \cdot y}}\]

  7. Applied pow1/30.0

    \[\leadsto \left(x \cdot \left(\color{blue}{{\left(e^{y \cdot y}\right)}^{\frac{1}{3}}} \cdot {\left(e^{y \cdot y}\right)}^{\frac{1}{3}}\right)\right) \cdot \sqrt[3]{e^{y \cdot y}}\]

  8. Applied pow-prod-up0.0

    \[\leadsto \left(x \cdot \color{blue}{{\left(e^{y \cdot y}\right)}^{\left(\frac{1}{3} + \frac{1}{3}\right)}}\right) \cdot \sqrt[3]{e^{y \cdot y}}\]

  9. Simplified0.0

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

  11. Applied add-sqr-sqrt0.0

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

  12. Applied associate-*r*0.0

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

  13. Simplified0.0

    \[\leadsto \left(\color{blue}{\left(x \cdot {\left(e^{y \cdot y}\right)}^{\frac{1}{3}}\right)} \cdot \sqrt{{\left(e^{y \cdot y}\right)}^{\frac{2}{3}}}\right) \cdot \sqrt[3]{e^{y \cdot y}}\]

  14. Final simplification0.0

    \[\leadsto \left(\left(x \cdot {\left(e^{y \cdot y}\right)}^{\frac{1}{3}}\right) \cdot \sqrt{{\left(e^{y \cdot y}\right)}^{\frac{2}{3}}}\right) \cdot \sqrt[3]{e^{y \cdot y}}\]

Reproduce

herbie shell --seed 2020025 +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))))