Average Error: 0.0 → 0.0
Time: 2.6s
Precision: binary64
\[x \cdot e^{y \cdot y} \]
↓
\[\begin{array}{l} t_0 := \sqrt{e^{y}}\\ x \cdot {\left(t_0 \cdot t_0\right)}^{y} \end{array} \]
x \cdot e^{y \cdot y}
↓
\begin{array}{l}
t_0 := \sqrt{e^{y}}\\
x \cdot {\left(t_0 \cdot t_0\right)}^{y}
\end{array}

(FPCore (x y) :precision binary64 (* x (exp (* y y))))
↓
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (sqrt (exp y)))) (* x (pow (* t_0 t_0) y))))
double code(double x, double y) {
	return x * exp(y * y);
}
↓
double code(double x, double y) {
	double t_0 = sqrt(exp(y));
	return x * pow((t_0 * t_0), y);
}

Error

Bits error versus x

Bits error versus y

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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-log-exp_binary640.0

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

  3. Applied exp-to-pow_binary640.0

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

  4. Applied add-sqr-sqrt_binary640.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2022081 
(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))))