Average Error: 0.3 → 0.3
Time: 11.0s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[{\left(\sqrt[3]{\sqrt[3]{e^{-w}}}\right)}^{5} \cdot \left({\ell}^{\left(e^{w}\right)} \cdot {\left(\sqrt[3]{\sqrt[3]{\sqrt{e^{-w}}} \cdot \sqrt[3]{\sqrt{e^{-w}}}}\right)}^{4}\right)\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
{\left(\sqrt[3]{\sqrt[3]{e^{-w}}}\right)}^{5} \cdot \left({\ell}^{\left(e^{w}\right)} \cdot {\left(\sqrt[3]{\sqrt[3]{\sqrt{e^{-w}}} \cdot \sqrt[3]{\sqrt{e^{-w}}}}\right)}^{4}\right)
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (*
  (pow (cbrt (cbrt (exp (- w)))) 5.0)
  (*
   (pow l (exp w))
   (pow (cbrt (* (cbrt (sqrt (exp (- w)))) (cbrt (sqrt (exp (- w)))))) 4.0))))
double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}
↓
double code(double w, double l) {
	return pow(cbrt(cbrt(exp(-w))), 5.0) * (pow(l, exp(w)) * pow(cbrt(cbrt(sqrt(exp(-w))) * cbrt(sqrt(exp(-w)))), 4.0));
}

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-cube-cbrt_binary640.3

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

  4. Applied associate-*l*_binary640.3

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

  5. Simplified0.3

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

  7. Applied add-cube-cbrt_binary640.3

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

  8. Applied associate-*r*_binary640.3

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

  9. Simplified0.3

    \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\sqrt[3]{e^{-w}}}\right)}^{5}} \cdot \sqrt[3]{\sqrt[3]{e^{-w}}}\right) \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \sqrt[3]{e^{-w}}\right)\]
  10. Using strategy rm

  11. Applied associate-*l*_binary640.3

    \[\leadsto \color{blue}{{\left(\sqrt[3]{\sqrt[3]{e^{-w}}}\right)}^{5} \cdot \left(\sqrt[3]{\sqrt[3]{e^{-w}}} \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \sqrt[3]{e^{-w}}\right)\right)}\]

  12. Simplified0.3

    \[\leadsto {\left(\sqrt[3]{\sqrt[3]{e^{-w}}}\right)}^{5} \cdot \color{blue}{\left({\ell}^{\left(e^{w}\right)} \cdot {\left(\sqrt[3]{\sqrt[3]{e^{-w}}}\right)}^{4}\right)}\]
  13. Using strategy rm

  14. Applied add-sqr-sqrt_binary640.3

    \[\leadsto {\left(\sqrt[3]{\sqrt[3]{e^{-w}}}\right)}^{5} \cdot \left({\ell}^{\left(e^{w}\right)} \cdot {\left(\sqrt[3]{\sqrt[3]{\color{blue}{\sqrt{e^{-w}} \cdot \sqrt{e^{-w}}}}}\right)}^{4}\right)\]

  15. Applied cbrt-prod_binary640.3

    \[\leadsto {\left(\sqrt[3]{\sqrt[3]{e^{-w}}}\right)}^{5} \cdot \left({\ell}^{\left(e^{w}\right)} \cdot {\left(\sqrt[3]{\color{blue}{\sqrt[3]{\sqrt{e^{-w}}} \cdot \sqrt[3]{\sqrt{e^{-w}}}}}\right)}^{4}\right)\]

  16. Final simplification0.3

    \[\leadsto {\left(\sqrt[3]{\sqrt[3]{e^{-w}}}\right)}^{5} \cdot \left({\ell}^{\left(e^{w}\right)} \cdot {\left(\sqrt[3]{\sqrt[3]{\sqrt{e^{-w}}} \cdot \sqrt[3]{\sqrt{e^{-w}}}}\right)}^{4}\right)\]

Reproduce

herbie shell --seed 2020219 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))