Average Error: 0.3 → 0.3
Time: 11.6s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[e^{-w} \cdot {\left({\left({\left({\ell}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\right)}^{\left(\left|\sqrt[3]{e^{w}}\right|\right)}\right)}^{\left(\sqrt{\sqrt[3]{e^{w}}}\right)}\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
e^{-w} \cdot {\left({\left({\left({\ell}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\right)}^{\left(\left|\sqrt[3]{e^{w}}\right|\right)}\right)}^{\left(\sqrt{\sqrt[3]{e^{w}}}\right)}
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (*
  (exp (- w))
  (pow
   (pow
    (pow (pow l (sqrt (sqrt (exp w)))) (sqrt (sqrt (exp w))))
    (fabs (cbrt (exp w))))
   (sqrt (cbrt (exp w))))))
double code(double w, double l) {
	return ((double) (((double) exp(((double) -(w)))) * ((double) pow(l, ((double) exp(w))))));
}
↓
double code(double w, double l) {
	return ((double) (((double) exp(((double) -(w)))) * ((double) pow(((double) pow(((double) pow(((double) pow(l, ((double) sqrt(((double) sqrt(((double) exp(w)))))))), ((double) sqrt(((double) sqrt(((double) exp(w)))))))), ((double) fabs(((double) cbrt(((double) exp(w)))))))), ((double) sqrt(((double) cbrt(((double) 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-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

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

  7. Applied sqrt-prod_binary640.3

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

  8. Applied pow-unpow_binary640.3

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

  9. Simplified0.3

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

  11. Applied add-sqr-sqrt_binary640.3

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

  12. Applied sqrt-prod_binary640.3

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

  13. Applied pow-unpow_binary640.3

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

  14. Final simplification0.3

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

Reproduce

herbie shell --seed 2020205 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))