Average Error: 0.0 → 0.1
Time: 1.8s
Precision: binary64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(\sqrt[3]{{\left(e^{y}\right)}^{\left(y + y\right)}} \cdot x\right) \cdot \sqrt[3]{{e}^{\left(y \cdot y\right)}}\]
x \cdot e^{y \cdot y}
↓
\left(\sqrt[3]{{\left(e^{y}\right)}^{\left(y + y\right)}} \cdot x\right) \cdot \sqrt[3]{{e}^{\left(y \cdot y\right)}}
(FPCore (x y) :precision binary64 (* x (exp (* y y))))
↓
(FPCore (x y)
 :precision binary64
 (* (* (cbrt (pow (exp y) (+ y y))) x) (cbrt (pow E (* y y)))))
double code(double x, double y) {
	return ((double) (x * ((double) exp(((double) (y * y))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) cbrt(((double) pow(((double) exp(y)), ((double) (y + y)))))) * x)) * ((double) cbrt(((double) pow(((double) M_E), ((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-log-exp_binary640.0

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

  4. Applied exp-to-pow_binary640.0

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

  6. Applied add-cbrt-cube_binary640.1

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

  7. Simplified0.1

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

  9. Applied unpow3_binary640.1

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

  10. Applied cbrt-prod_binary640.1

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

  11. Applied associate-*r*_binary640.1

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

  12. Simplified0.1

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

  14. Applied *-un-lft-identity_binary640.1

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

  15. Applied exp-prod_binary640.1

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

  16. Applied pow-pow_binary640.1

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

  17. Final simplification0.1

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

Reproduce

herbie shell --seed 2020205 
(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))))