Average Error: 0.3 → 0.4
Time: 21.6s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
↓
\[\begin{array}{l} t_0 := \sqrt{e^{w}}\\ e^{-w} \cdot {\left({\ell}^{t_0}\right)}^{t_0} \end{array} \]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\begin{array}{l}
t_0 := \sqrt{e^{w}}\\
e^{-w} \cdot {\left({\ell}^{t_0}\right)}^{t_0}
\end{array}

(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (let* ((t_0 (sqrt (exp w)))) (* (exp (- w)) (pow (pow l t_0) t_0))))
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 exp(-w) * pow(pow(l, t_0), t_0);
}

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-sqr-sqrt_binary640.4

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

  3. Applied pow-unpow_binary640.4

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

  4. Applied pow1_binary640.4

    \[\leadsto e^{-w} \cdot {\left({\color{blue}{\left({\ell}^{1}\right)}}^{\left(\sqrt{e^{w}}\right)}\right)}^{\left(\sqrt{e^{w}}\right)} \]

  5. Applied pow-pow_binary640.4

    \[\leadsto e^{-w} \cdot {\color{blue}{\left({\ell}^{\left(1 \cdot \sqrt{e^{w}}\right)}\right)}}^{\left(\sqrt{e^{w}}\right)} \]

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2022088 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))