Average Error: 0.2 → 0.2
Time: 16.8s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
↓
\[\begin{array}{l} t_0 := \sqrt{e^{-w}}\\ t_0 \cdot \left(t_0 \cdot {\ell}^{\left(e^{w}\right)}\right) \end{array} \]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\begin{array}{l}
t_0 := \sqrt{e^{-w}}\\
t_0 \cdot \left(t_0 \cdot {\ell}^{\left(e^{w}\right)}\right)
\end{array}

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

Error

Bits error versus w

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
  2. Using strategy rm

  3. Applied add-sqr-sqrt_binary640.3

    \[\leadsto \color{blue}{\left(\sqrt{e^{-w}} \cdot \sqrt{e^{-w}}\right)} \cdot {\ell}^{\left(e^{w}\right)} \]

  4. Applied associate-*l*_binary640.2

    \[\leadsto \color{blue}{\sqrt{e^{-w}} \cdot \left(\sqrt{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right)} \]

  5. Simplified0.2

    \[\leadsto \sqrt{e^{-w}} \cdot \color{blue}{\left({\ell}^{\left(e^{w}\right)} \cdot \sqrt{e^{-w}}\right)} \]
  6. Using strategy rm

  7. Applied *-commutative_binary640.2

    \[\leadsto \sqrt{e^{-w}} \cdot \color{blue}{\left(\sqrt{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right)} \]

  8. Final simplification0.2

    \[\leadsto \sqrt{e^{-w}} \cdot \left(\sqrt{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

Reproduce

herbie shell --seed 2021210 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))