Average Error: 0.3 → 0.3
Time: 13.1s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[\frac{1}{\sqrt[3]{\sqrt[3]{e^{w}}} \cdot {\left(\sqrt[3]{\sqrt[3]{e^{w}}}\right)}^{5}} \cdot \left(\frac{1}{{\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{e^{w}}}} \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{e^{w}}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{e^{w}}}}\right)\right)}^{2}} \cdot \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{\sqrt[3]{e^{w}}}}\right)\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\frac{1}{\sqrt[3]{\sqrt[3]{e^{w}}} \cdot {\left(\sqrt[3]{\sqrt[3]{e^{w}}}\right)}^{5}} \cdot \left(\frac{1}{{\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{e^{w}}}} \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{e^{w}}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{e^{w}}}}\right)\right)}^{2}} \cdot \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{\sqrt[3]{e^{w}}}}\right)
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (*
  (/ 1.0 (* (cbrt (cbrt (exp w))) (pow (cbrt (cbrt (exp w))) 5.0)))
  (*
   (/
    1.0
    (pow
     (*
      (cbrt (cbrt (cbrt (exp w))))
      (* (cbrt (cbrt (cbrt (exp w)))) (cbrt (cbrt (cbrt (exp w))))))
     2.0))
   (/ (pow l (exp w)) (cbrt (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) ((1.0 / ((double) (((double) cbrt(((double) cbrt(((double) exp(w)))))) * ((double) pow(((double) cbrt(((double) cbrt(((double) exp(w)))))), 5.0))))) * ((double) ((1.0 / ((double) pow(((double) (((double) cbrt(((double) cbrt(((double) cbrt(((double) exp(w)))))))) * ((double) (((double) cbrt(((double) cbrt(((double) cbrt(((double) exp(w)))))))) * ((double) cbrt(((double) cbrt(((double) cbrt(((double) exp(w)))))))))))), 2.0))) * (((double) pow(l, ((double) exp(w)))) / ((double) cbrt(((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 Error: 0.3 bits

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

  2. SimplifiedError: 0.3 bits

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

  4. Applied add-cube-cbrtError: 0.3 bits

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

  5. Applied *-un-lft-identityError: 0.3 bits

    \[\leadsto \frac{{\color{blue}{\left(1 \cdot \ell\right)}}^{\left(e^{w}\right)}}{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right) \cdot \sqrt[3]{e^{w}}}\]

  6. Applied unpow-prod-downError: 0.3 bits

    \[\leadsto \frac{\color{blue}{{1}^{\left(e^{w}\right)} \cdot {\ell}^{\left(e^{w}\right)}}}{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right) \cdot \sqrt[3]{e^{w}}}\]

  7. Applied times-fracError: 0.3 bits

    \[\leadsto \color{blue}{\frac{{1}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}} \cdot \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}}\]

  8. SimplifiedError: 0.3 bits

    \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}} \cdot \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}\]
  9. Using strategy rm

  10. Applied add-cube-cbrtError: 0.3 bits

    \[\leadsto \frac{1}{\sqrt[3]{e^{w}} \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{e^{w}}} \cdot \sqrt[3]{\sqrt[3]{e^{w}}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{w}}}\right)}} \cdot \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}\]

  11. Applied associate-*r*Error: 0.3 bits

    \[\leadsto \frac{1}{\color{blue}{\left(\sqrt[3]{e^{w}} \cdot \left(\sqrt[3]{\sqrt[3]{e^{w}}} \cdot \sqrt[3]{\sqrt[3]{e^{w}}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{e^{w}}}}} \cdot \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}\]

  12. SimplifiedError: 0.3 bits

    \[\leadsto \frac{1}{\color{blue}{{\left(\sqrt[3]{\sqrt[3]{e^{w}}}\right)}^{5}} \cdot \sqrt[3]{\sqrt[3]{e^{w}}}} \cdot \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}\]
  13. Using strategy rm

  14. Applied add-cube-cbrtError: 0.3 bits

    \[\leadsto \frac{1}{{\left(\sqrt[3]{\sqrt[3]{e^{w}}}\right)}^{5} \cdot \sqrt[3]{\sqrt[3]{e^{w}}}} \cdot \frac{{\ell}^{\left(e^{w}\right)}}{\color{blue}{\left(\sqrt[3]{\sqrt[3]{e^{w}}} \cdot \sqrt[3]{\sqrt[3]{e^{w}}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{w}}}}}\]

  15. Applied *-un-lft-identityError: 0.3 bits

    \[\leadsto \frac{1}{{\left(\sqrt[3]{\sqrt[3]{e^{w}}}\right)}^{5} \cdot \sqrt[3]{\sqrt[3]{e^{w}}}} \cdot \frac{{\color{blue}{\left(1 \cdot \ell\right)}}^{\left(e^{w}\right)}}{\left(\sqrt[3]{\sqrt[3]{e^{w}}} \cdot \sqrt[3]{\sqrt[3]{e^{w}}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{w}}}}\]

  16. Applied unpow-prod-downError: 0.3 bits

    \[\leadsto \frac{1}{{\left(\sqrt[3]{\sqrt[3]{e^{w}}}\right)}^{5} \cdot \sqrt[3]{\sqrt[3]{e^{w}}}} \cdot \frac{\color{blue}{{1}^{\left(e^{w}\right)} \cdot {\ell}^{\left(e^{w}\right)}}}{\left(\sqrt[3]{\sqrt[3]{e^{w}}} \cdot \sqrt[3]{\sqrt[3]{e^{w}}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{w}}}}\]

  17. Applied times-fracError: 0.3 bits

    \[\leadsto \frac{1}{{\left(\sqrt[3]{\sqrt[3]{e^{w}}}\right)}^{5} \cdot \sqrt[3]{\sqrt[3]{e^{w}}}} \cdot \color{blue}{\left(\frac{{1}^{\left(e^{w}\right)}}{\sqrt[3]{\sqrt[3]{e^{w}}} \cdot \sqrt[3]{\sqrt[3]{e^{w}}}} \cdot \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{\sqrt[3]{e^{w}}}}\right)}\]

  18. SimplifiedError: 0.3 bits

    \[\leadsto \frac{1}{{\left(\sqrt[3]{\sqrt[3]{e^{w}}}\right)}^{5} \cdot \sqrt[3]{\sqrt[3]{e^{w}}}} \cdot \left(\color{blue}{\frac{1}{{\left(\sqrt[3]{\sqrt[3]{e^{w}}}\right)}^{2}}} \cdot \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{\sqrt[3]{e^{w}}}}\right)\]
  19. Using strategy rm

  20. Applied add-cube-cbrtError: 0.3 bits

    \[\leadsto \frac{1}{{\left(\sqrt[3]{\sqrt[3]{e^{w}}}\right)}^{5} \cdot \sqrt[3]{\sqrt[3]{e^{w}}}} \cdot \left(\frac{1}{{\color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{e^{w}}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{e^{w}}}}\right) \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{e^{w}}}}\right)}}^{2}} \cdot \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{\sqrt[3]{e^{w}}}}\right)\]

  21. Final simplificationError: 0.3 bits

    \[\leadsto \frac{1}{\sqrt[3]{\sqrt[3]{e^{w}}} \cdot {\left(\sqrt[3]{\sqrt[3]{e^{w}}}\right)}^{5}} \cdot \left(\frac{1}{{\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{e^{w}}}} \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{e^{w}}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{e^{w}}}}\right)\right)}^{2}} \cdot \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{\sqrt[3]{e^{w}}}}\right)\]

Reproduce

herbie shell --seed 2020203 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))