Average Error: 0.0 → 0.0
Time: 2.1s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[x \cdot {\left(e^{y + y}\right)}^{\left(\frac{y}{2}\right)}\]
x \cdot e^{y \cdot y}
↓
x \cdot {\left(e^{y + y}\right)}^{\left(\frac{y}{2}\right)}
double code(double x, double y) {
	return (x * exp((y * y)));
}
↓
double code(double x, double y) {
	return (x * pow(exp((y + 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

Original0.0
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 exp-prod0.0

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

  5. Applied sqr-pow0.0

    \[\leadsto x \cdot \color{blue}{\left({\left(e^{y}\right)}^{\left(\frac{y}{2}\right)} \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}\right)}\]
  6. Using strategy rm

  7. Applied pow-prod-down0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020071 +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))))