Average Error: 0.3 → 0.3
Time: 21.1s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
↓
\[\begin{array}{l} t_0 := \sqrt{e^{w}}\\ t_1 := \sqrt[3]{e^{-w}}\\ t_2 := \sqrt[3]{t_1}\\ t_3 := \sqrt[3]{t_2}\\ \left(\left(t_2 \cdot t_2\right) \cdot \left(\left(t_3 \cdot t_3\right) \cdot \left(t_1 \cdot t_3\right)\right)\right) \cdot \left(t_1 \cdot {\left({\ell}^{t_0}\right)}^{t_0}\right) \end{array} \]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\begin{array}{l}
t_0 := \sqrt{e^{w}}\\
t_1 := \sqrt[3]{e^{-w}}\\
t_2 := \sqrt[3]{t_1}\\
t_3 := \sqrt[3]{t_2}\\
\left(\left(t_2 \cdot t_2\right) \cdot \left(\left(t_3 \cdot t_3\right) \cdot \left(t_1 \cdot t_3\right)\right)\right) \cdot \left(t_1 \cdot {\left({\ell}^{t_0}\right)}^{t_0}\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_1 (cbrt (exp (- w))))
        (t_2 (cbrt t_1))
        (t_3 (cbrt t_2)))
   (*
    (* (* t_2 t_2) (* (* t_3 t_3) (* t_1 t_3)))
    (* t_1 (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));
	double t_1 = cbrt(exp(-w));
	double t_2 = cbrt(t_1);
	double t_3 = cbrt(t_2);
	return ((t_2 * t_2) * ((t_3 * t_3) * (t_1 * t_3))) * (t_1 * 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_binary640.3

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

  3. Applied pow-unpow_binary640.3

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

  4. Applied add-cube-cbrt_binary640.3

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

  5. Applied associate-*l*_binary640.3

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

  6. Applied add-cube-cbrt_binary640.3

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

  7. Applied associate-*l*_binary640.3

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

  8. Applied add-cube-cbrt_binary640.3

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

  9. Applied associate-*l*_binary640.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2022019 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))