Average Error: 0.3 → 0.4
Time: 12.1s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[\frac{{\left({\left({\left({\ell}^{\left(\left|\sqrt[3]{e^{w}}\right|\right)}\right)}^{\left(\sqrt{\sqrt[3]{\sqrt{e^{w}}}}\right)}\right)}^{\left(\sqrt{\sqrt[3]{\sqrt{e^{w}}}}\right)}\right)}^{\left(\sqrt{e^{w}}\right)}}{e^{w}}\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\frac{{\left({\left({\left({\ell}^{\left(\left|\sqrt[3]{e^{w}}\right|\right)}\right)}^{\left(\sqrt{\sqrt[3]{\sqrt{e^{w}}}}\right)}\right)}^{\left(\sqrt{\sqrt[3]{\sqrt{e^{w}}}}\right)}\right)}^{\left(\sqrt{e^{w}}\right)}}{e^{w}}
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (/
  (pow
   (pow
    (pow (pow l (fabs (cbrt (exp w)))) (sqrt (cbrt (sqrt (exp w)))))
    (sqrt (cbrt (sqrt (exp w)))))
   (sqrt (exp w)))
  (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) pow(((double) pow(((double) pow(((double) pow(l, ((double) fabs(((double) cbrt(((double) exp(w)))))))), ((double) sqrt(((double) cbrt(((double) sqrt(((double) exp(w)))))))))), ((double) sqrt(((double) cbrt(((double) sqrt(((double) exp(w)))))))))), ((double) sqrt(((double) exp(w)))))) / ((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. Simplified0.3

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

  4. Applied add-sqr-sqrt_binary640.3

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

  5. Applied pow-unpow_binary640.3

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

  7. Applied add-cube-cbrt_binary640.4

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

  8. Applied sqrt-prod_binary640.4

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

  9. Applied pow-unpow_binary640.4

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

  10. Simplified0.4

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

  12. Applied add-sqr-sqrt_binary640.4

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

  13. Applied cbrt-prod_binary640.3

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

  14. Applied sqrt-prod_binary640.4

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

  15. Applied pow-unpow_binary640.4

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

  16. Final simplification0.4

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

Reproduce

herbie shell --seed 2020210 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))