Average Error: 0.1 → 0.1
Time: 3.3s
Precision: binary64
\[x \cdot e^{y \cdot y} \]
↓
\[x \cdot {\left(\sqrt{{\left(e^{y}\right)}^{y}}\right)}^{2} \]
x \cdot e^{y \cdot y}
↓
x \cdot {\left(\sqrt{{\left(e^{y}\right)}^{y}}\right)}^{2}

(FPCore (x y) :precision binary64 (* x (exp (* y y))))
↓
(FPCore (x y) :precision binary64 (* x (pow (sqrt (pow (exp y) y)) 2.0)))
double code(double x, double y) {
	return x * exp((y * y));
}
↓
double code(double x, double y) {
	return x * pow(sqrt(pow(exp(y), y)), 2.0);
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[x \cdot {\left(e^{y}\right)}^{y} \]

Derivation

  1. Initial program 0.1

    \[x \cdot e^{y \cdot y} \]

  2. Applied egg-rr0.1

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

  3. Applied egg-rr0.1

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

  4. Applied egg-rr0.1

    \[\leadsto x \cdot \color{blue}{{\left(\sqrt{{\left(e^{y}\right)}^{y}}\right)}^{2}} \]

  5. Final simplification0.1

    \[\leadsto x \cdot {\left(\sqrt{{\left(e^{y}\right)}^{y}}\right)}^{2} \]

Reproduce

herbie shell --seed 2022130 
(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))))