Average Error: 0.3 → 0.3
Time: 12.9s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[\frac{{\ell}^{\left(e^{w}\right)} \cdot {\left(\sqrt{{\left(e^{w}\right)}^{-0.3333333333333333}}\right)}^{5}}{\sqrt{\sqrt[3]{e^{w}}}}\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\frac{{\ell}^{\left(e^{w}\right)} \cdot {\left(\sqrt{{\left(e^{w}\right)}^{-0.3333333333333333}}\right)}^{5}}{\sqrt{\sqrt[3]{e^{w}}}}
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (/
  (* (pow l (exp w)) (pow (sqrt (pow (exp w) -0.3333333333333333)) 5.0))
  (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) pow(l, ((double) exp(w)))) * ((double) pow(((double) sqrt(((double) pow(((double) exp(w)), -0.3333333333333333)))), 5.0)))) / ((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-cube-cbrt0.3

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

  4. Applied associate-*l*0.3

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

  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-sqrt0.3

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

  8. Applied associate-*r*0.3

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

  9. Simplified0.3

    \[\leadsto \left(\color{blue}{{\left(\sqrt{{\left(e^{w}\right)}^{-0.3333333333333333}}\right)}^{3}} \cdot \sqrt{\sqrt[3]{e^{-w}}}\right) \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \sqrt[3]{e^{-w}}\right)\]
  10. Using strategy rm

  11. Applied exp-neg0.3

    \[\leadsto \left({\left(\sqrt{{\left(e^{w}\right)}^{-0.3333333333333333}}\right)}^{3} \cdot \sqrt{\sqrt[3]{\color{blue}{\frac{1}{e^{w}}}}}\right) \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \sqrt[3]{e^{-w}}\right)\]

  12. Applied cbrt-div0.3

    \[\leadsto \left({\left(\sqrt{{\left(e^{w}\right)}^{-0.3333333333333333}}\right)}^{3} \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{1}}{\sqrt[3]{e^{w}}}}}\right) \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \sqrt[3]{e^{-w}}\right)\]

  13. Applied sqrt-div0.3

    \[\leadsto \left({\left(\sqrt{{\left(e^{w}\right)}^{-0.3333333333333333}}\right)}^{3} \cdot \color{blue}{\frac{\sqrt{\sqrt[3]{1}}}{\sqrt{\sqrt[3]{e^{w}}}}}\right) \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \sqrt[3]{e^{-w}}\right)\]

  14. Applied associate-*r/0.3

    \[\leadsto \color{blue}{\frac{{\left(\sqrt{{\left(e^{w}\right)}^{-0.3333333333333333}}\right)}^{3} \cdot \sqrt{\sqrt[3]{1}}}{\sqrt{\sqrt[3]{e^{w}}}}} \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \sqrt[3]{e^{-w}}\right)\]

  15. Applied associate-*l/0.3

    \[\leadsto \color{blue}{\frac{\left({\left(\sqrt{{\left(e^{w}\right)}^{-0.3333333333333333}}\right)}^{3} \cdot \sqrt{\sqrt[3]{1}}\right) \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \sqrt[3]{e^{-w}}\right)}{\sqrt{\sqrt[3]{e^{w}}}}}\]

  16. Simplified0.3

    \[\leadsto \frac{\color{blue}{{\ell}^{\left(e^{w}\right)} \cdot {\left(\sqrt{{\left(e^{w}\right)}^{-0.3333333333333333}}\right)}^{5}}}{\sqrt{\sqrt[3]{e^{w}}}}\]

  17. Final simplification0.3

    \[\leadsto \frac{{\ell}^{\left(e^{w}\right)} \cdot {\left(\sqrt{{\left(e^{w}\right)}^{-0.3333333333333333}}\right)}^{5}}{\sqrt{\sqrt[3]{e^{w}}}}\]

Reproduce

herbie shell --seed 2020198 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))