Average Error: 0.3 → 0.3
Time: 18.9s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
↓
\[\begin{array}{l} t_0 := \sqrt[3]{e^{-w}}\\ \left(t_0 \cdot t_0\right) \cdot \left(t_0 \cdot {\ell}^{\left(e^{w}\right)}\right) \end{array} \]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\begin{array}{l}
t_0 := \sqrt[3]{e^{-w}}\\
\left(t_0 \cdot t_0\right) \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 (cbrt (exp (- w))))) (* (* t_0 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 = cbrt(exp(-w));
	return (t_0 * 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 0.3

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

  2. Applied add-cube-cbrt_binary640.3

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}\right) \cdot \sqrt[3]{e^{-w}}\right)} \cdot {\ell}^{\left(e^{w}\right)} \]

  3. Applied associate-*l*_binary640.3

    \[\leadsto \color{blue}{\left(\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right)} \]

  4. Final simplification0.3

    \[\leadsto \left(\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

Reproduce

herbie shell --seed 2021329 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))