Average Error: 0.0 → 0.0
Time: 3.3s
Precision: binary64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(x \cdot {\left(\sqrt[3]{e^{y}} \cdot \sqrt[3]{e^{y}}\right)}^{y}\right) \cdot {\left(\sqrt[3]{e^{y}}\right)}^{y}\]
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}
(FPCore (x y) :precision binary64 (* x (exp (* y y))))
↓
(FPCore (x y)
 :precision binary64
 (* (* x (pow (* (cbrt (exp y)) (cbrt (exp y))) y)) (pow (cbrt (exp y)) y)))
double code(double x, double y) {
	return x * exp(y * y);
}
↓
double code(double x, double y) {
	return (x * pow((cbrt(exp(y)) * cbrt(exp(y))), y)) * pow(cbrt(exp(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
Herbie0.0
\[x \cdot {\left(e^{y}\right)}^{y}\]

Derivation

  1. Initial program 0.0

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

  3. Applied add-log-exp_binary64_198950.0

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

  4. Applied exp-to-pow_binary64_199180.0

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

  6. Applied add-cube-cbrt_binary64_198910.0

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

  7. Applied unpow-prod-down_binary64_199350.0

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

  8. Applied associate-*r*_binary64_197960.0

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

  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 2021043 
(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))))