Average Error: 0.3 → 0.3
Time: 16.7s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{e^{w}} \cdot \left(\sqrt[3]{\sqrt[3]{e^{w}}} \cdot \left(\sqrt[3]{\sqrt[3]{e^{w}}} \cdot \sqrt[3]{\sqrt[3]{e^{w}}}\right)\right)} \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \sqrt[3]{e^{-w}}\right)\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{e^{w}} \cdot \left(\sqrt[3]{\sqrt[3]{e^{w}}} \cdot \left(\sqrt[3]{\sqrt[3]{e^{w}}} \cdot \sqrt[3]{\sqrt[3]{e^{w}}}\right)\right)} \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \sqrt[3]{e^{-w}}\right)
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (*
  (/
   (* (cbrt 1.0) (cbrt 1.0))
   (*
    (cbrt (exp w))
    (* (cbrt (cbrt (exp w))) (* (cbrt (cbrt (exp w))) (cbrt (cbrt (exp w)))))))
  (* (pow l (exp w)) (cbrt (exp (- w))))))
double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}
↓
double code(double w, double l) {
	return ((cbrt(1.0) * cbrt(1.0)) / (cbrt(exp(w)) * (cbrt(cbrt(exp(w))) * (cbrt(cbrt(exp(w))) * cbrt(cbrt(exp(w))))))) * (pow(l, exp(w)) * cbrt(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_binary64_7950.3

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

  4. Applied associate-*l*_binary64_7010.3

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

  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 neg-sub0_binary64_7550.3

    \[\leadsto \left(\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{\color{blue}{0 - w}}}\right) \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \sqrt[3]{e^{-w}}\right)\]

  8. Applied exp-diff_binary64_8080.3

    \[\leadsto \left(\sqrt[3]{e^{-w}} \cdot \sqrt[3]{\color{blue}{\frac{e^{0}}{e^{w}}}}\right) \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \sqrt[3]{e^{-w}}\right)\]

  9. Applied cbrt-div_binary64_7920.3

    \[\leadsto \left(\sqrt[3]{e^{-w}} \cdot \color{blue}{\frac{\sqrt[3]{e^{0}}}{\sqrt[3]{e^{w}}}}\right) \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \sqrt[3]{e^{-w}}\right)\]

  10. Applied neg-sub0_binary64_7550.3

    \[\leadsto \left(\sqrt[3]{e^{\color{blue}{0 - w}}} \cdot \frac{\sqrt[3]{e^{0}}}{\sqrt[3]{e^{w}}}\right) \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \sqrt[3]{e^{-w}}\right)\]

  11. Applied exp-diff_binary64_8080.3

    \[\leadsto \left(\sqrt[3]{\color{blue}{\frac{e^{0}}{e^{w}}}} \cdot \frac{\sqrt[3]{e^{0}}}{\sqrt[3]{e^{w}}}\right) \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \sqrt[3]{e^{-w}}\right)\]

  12. Applied cbrt-div_binary64_7920.3

    \[\leadsto \left(\color{blue}{\frac{\sqrt[3]{e^{0}}}{\sqrt[3]{e^{w}}}} \cdot \frac{\sqrt[3]{e^{0}}}{\sqrt[3]{e^{w}}}\right) \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \sqrt[3]{e^{-w}}\right)\]

  13. Applied frac-times_binary64_7700.3

    \[\leadsto \color{blue}{\frac{\sqrt[3]{e^{0}} \cdot \sqrt[3]{e^{0}}}{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}} \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \sqrt[3]{e^{-w}}\right)\]

  14. Simplified0.3

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

  16. Applied add-cube-cbrt_binary64_7950.3

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

  17. Final simplification0.3

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

Reproduce

herbie shell --seed 2020295 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))