Average Error: 0.0 → 0.1
Time: 3.7s
Precision: binary64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(x \cdot \left(\sqrt[3]{e^{y \cdot y}} \cdot \sqrt[3]{e^{y \cdot y}}\right)\right) \cdot \sqrt[3]{e^{y \cdot y}}\]
x \cdot e^{y \cdot y}
↓
\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}}
double code(double x, double y) {
	return ((double) (x * ((double) exp(((double) (y * y))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (x * ((double) (((double) cbrt(((double) exp(((double) (y * y)))))) * ((double) cbrt(((double) exp(((double) (y * y)))))))))) * ((double) cbrt(((double) exp(((double) (y * y))))))));
}

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
Herbie0.1
\[x \cdot {\left(e^{y}\right)}^{y}\]

Derivation

  1. Initial program 0.0

    \[x \cdot e^{y \cdot y}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

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

  4. Applied associate-*r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020148 
(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))))