Average Error: 0.0 → 0.0
Time: 2.0s
Precision: binary64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(x \cdot {\left(e^{y \cdot y}\right)}^{0.8333333333333334}\right) \cdot \sqrt[3]{\sqrt{e^{y \cdot y}}}\]
x \cdot e^{y \cdot y}
↓
\left(x \cdot {\left(e^{y \cdot y}\right)}^{0.8333333333333334}\right) \cdot \sqrt[3]{\sqrt{e^{y \cdot y}}}
(FPCore (x y) :precision binary64 (* x (exp (* y y))))
↓
(FPCore (x y)
 :precision binary64
 (* (* x (pow (exp (* y y)) 0.8333333333333334)) (cbrt (sqrt (exp (* y y))))))
double code(double x, double y) {
	return x * exp(y * y);
}
↓
double code(double x, double y) {
	return (x * pow(exp(y * y), 0.8333333333333334)) * cbrt(sqrt(exp(y * y)));
}

Error

Bits error versus x

Bits error versus y

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Results

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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-cube-cbrt_binary64_209140.1

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

  4. Applied associate-*r*_binary64_208190.1

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

  6. Applied add-sqr-sqrt_binary64_209010.1

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

  7. Applied cbrt-prod_binary64_209100.1

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

  8. Applied associate-*r*_binary64_208190.1

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

  9. Simplified0.0

    \[\leadsto \color{blue}{\left(x \cdot {\left(e^{y \cdot y}\right)}^{0.8333333333333334}\right)} \cdot \sqrt[3]{\sqrt{e^{y \cdot y}}}\]

  10. Final simplification0.0

    \[\leadsto \left(x \cdot {\left(e^{y \cdot y}\right)}^{0.8333333333333334}\right) \cdot \sqrt[3]{\sqrt{e^{y \cdot y}}}\]

Reproduce

herbie shell --seed 2020355 
(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))))