Average Error: 0.3 → 0.3
Time: 11.9s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[\left(\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}\right) \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \left(\left(\sqrt[3]{\sqrt{\sqrt{e^{-w}}}} \cdot \sqrt[3]{\sqrt{\sqrt{e^{-w}}}}\right) \cdot \left(\sqrt[3]{\sqrt{\sqrt{e^{-w}}}} \cdot \sqrt[3]{\sqrt{\sqrt{e^{-w}}}}\right)\right)\right)\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\left(\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}\right) \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \left(\left(\sqrt[3]{\sqrt{\sqrt{e^{-w}}}} \cdot \sqrt[3]{\sqrt{\sqrt{e^{-w}}}}\right) \cdot \left(\sqrt[3]{\sqrt{\sqrt{e^{-w}}}} \cdot \sqrt[3]{\sqrt{\sqrt{e^{-w}}}}\right)\right)\right)
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (*
  (* (cbrt (exp (- w))) (cbrt (exp (- w))))
  (*
   (pow l (exp w))
   (*
    (* (cbrt (sqrt (sqrt (exp (- w))))) (cbrt (sqrt (sqrt (exp (- w))))))
    (* (cbrt (sqrt (sqrt (exp (- w))))) (cbrt (sqrt (sqrt (exp (- w))))))))))
double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}
↓
double code(double w, double l) {
	return (cbrt(exp(-w)) * cbrt(exp(-w))) * (pow(l, exp(w)) * ((cbrt(sqrt(sqrt(exp(-w)))) * cbrt(sqrt(sqrt(exp(-w))))) * (cbrt(sqrt(sqrt(exp(-w)))) * cbrt(sqrt(sqrt(exp(-w)))))));
}

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-sqr-sqrt_binary640.3

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

  8. Applied cbrt-prod_binary640.3

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

  10. Applied add-sqr-sqrt_binary640.3

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

  11. Applied cbrt-prod_binary640.3

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

  13. Applied add-sqr-sqrt_binary640.3

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

  14. Applied cbrt-prod_binary640.3

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

  15. Final simplification0.3

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

Reproduce

herbie shell --seed 2020232 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))