Average Error: 0.3 → 0.3
Time: 23.5s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
↓
\[\begin{array}{l} t_0 := \sqrt[3]{{\left(e^{w}\right)}^{0.1111111111111111}}\\ \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}} \cdot {\left({\left(t_0 \cdot {\left({\left(\sqrt[3]{t_0}\right)}^{2}\right)}^{3}\right)}^{3}\right)}^{2}} \end{array} \]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\begin{array}{l}
t_0 := \sqrt[3]{{\left(e^{w}\right)}^{0.1111111111111111}}\\
\frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}} \cdot {\left({\left(t_0 \cdot {\left({\left(\sqrt[3]{t_0}\right)}^{2}\right)}^{3}\right)}^{3}\right)}^{2}}
\end{array}

(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (let* ((t_0 (cbrt (pow (exp w) 0.1111111111111111))))
   (/
    (pow l (exp w))
    (*
     (cbrt (exp w))
     (pow (pow (* t_0 (pow (pow (cbrt t_0) 2.0) 3.0)) 3.0) 2.0)))))
double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}
↓
double code(double w, double l) {
	double t_0 = cbrt(pow(exp(w), 0.1111111111111111));
	return pow(l, exp(w)) / (cbrt(exp(w)) * pow(pow((t_0 * pow(pow(cbrt(t_0), 2.0), 3.0)), 3.0), 2.0));
}

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. Simplified0.3

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

  3. Applied egg-rr0.3

    \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{\color{blue}{\sqrt[3]{e^{w}} \cdot {\left(\sqrt[3]{e^{w}}\right)}^{2}}} \]

  4. Applied egg-rr0.3

    \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}} \cdot {\color{blue}{\left({\left(\sqrt[3]{\sqrt[3]{e^{w}}}\right)}^{3}\right)}}^{2}} \]

  5. Applied egg-rr0.3

    \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}} \cdot {\left({\color{blue}{\left({\left({\left(\sqrt[3]{\sqrt[3]{{\left(e^{w}\right)}^{0.1111111111111111}}}\right)}^{2}\right)}^{3} \cdot \sqrt[3]{{\left(e^{w}\right)}^{0.1111111111111111}}\right)}}^{3}\right)}^{2}} \]

  6. Final simplification0.3

    \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}} \cdot {\left({\left(\sqrt[3]{{\left(e^{w}\right)}^{0.1111111111111111}} \cdot {\left({\left(\sqrt[3]{\sqrt[3]{{\left(e^{w}\right)}^{0.1111111111111111}}}\right)}^{2}\right)}^{3}\right)}^{3}\right)}^{2}} \]

Reproduce

herbie shell --seed 2022130 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))