Average Error: 0.1 → 0.1
Time: 1.7s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[x \cdot {\left(e^{y}\right)}^{y}\]
x \cdot e^{y \cdot y}
↓
x \cdot {\left(e^{y}\right)}^{y}
double code(double x, double y) {
	return (x * exp((y * y)));
}
↓
double code(double x, double y) {
	return (x * pow(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

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

Derivation

  1. Initial program 0.1

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

  3. Applied add-log-exp0.1

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

  4. Applied exp-to-pow0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020102 +o rules:numerics
(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))))