Average Error: 0.0 → 0.0
Time: 2.9s
Precision: binary64
\[x \cdot e^{y \cdot y} \]
↓
\[\begin{array}{l} t_0 := \sqrt{e^{y \cdot y}}\\ t_0 \cdot \left(x \cdot t_0\right) \end{array} \]
x \cdot e^{y \cdot y}
↓
\begin{array}{l}
t_0 := \sqrt{e^{y \cdot y}}\\
t_0 \cdot \left(x \cdot t_0\right)
\end{array}

(FPCore (x y) :precision binary64 (* x (exp (* y y))))
↓
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (sqrt (exp (* y y))))) (* t_0 (* x t_0))))
double code(double x, double y) {
	return x * exp(y * y);
}
↓
double code(double x, double y) {
	double t_0 = sqrt(exp(y * y));
	return t_0 * (x * t_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. Applied add-sqr-sqrt_binary640.1

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

  3. Applied associate-*r*_binary640.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2022068 
(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))))