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

Error

Bits error versus x

Bits error versus y

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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 add-cube-cbrt0.0

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

  7. Applied exp-prod0.0

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

  8. Applied pow-pow0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020162 
(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))))