Average Error: 0.3 → 0.3
Time: 15.0s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[e^{-w} \cdot {\left({\ell}^{\left(\sqrt{e^{w}}\right)}\right)}^{\left({\left(e^{\sqrt[3]{w} \cdot \sqrt[3]{w}}\right)}^{\left(\frac{\sqrt[3]{w}}{2}\right)}\right)}\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
e^{-w} \cdot {\left({\ell}^{\left(\sqrt{e^{w}}\right)}\right)}^{\left({\left(e^{\sqrt[3]{w} \cdot \sqrt[3]{w}}\right)}^{\left(\frac{\sqrt[3]{w}}{2}\right)}\right)}
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (*
  (exp (- w))
  (pow
   (pow l (sqrt (exp w)))
   (pow (exp (* (cbrt w) (cbrt w))) (/ (cbrt w) 2.0)))))
double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}
↓
double code(double w, double l) {
	return exp(-w) * pow(pow(l, sqrt(exp(w))), pow(exp(cbrt(w) * cbrt(w)), (cbrt(w) / 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. Using strategy rm

  3. Applied add-sqr-sqrt_binary640.3

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

  4. Applied pow-unpow_binary640.3

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

  6. Applied add-cube-cbrt_binary640.3

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

  7. Applied exp-prod_binary640.3

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

  8. Applied sqrt-pow1_binary640.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020231 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))