Average Error: 0.0 → 0.1
Time: 2.3s
Precision: binary64
\[x \cdot e^{y \cdot y}\]
↓
\[x \cdot \sqrt[3]{{\left({\left(e^{y}\right)}^{y}\right)}^{3}}\]
x \cdot e^{y \cdot y}
↓
x \cdot \sqrt[3]{{\left({\left(e^{y}\right)}^{y}\right)}^{3}}
double code(double x, double y) {
	return ((double) (x * ((double) exp(((double) (y * y))))));
}
↓
double code(double x, double y) {
	return ((double) (x * ((double) cbrt(((double) pow(((double) pow(((double) exp(y)), y)), 3.0))))));
}

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. Simplified0.0

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

  4. Applied add-cbrt-cube0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020179 
(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))))