Average Error: 0.3 → 0.3
Time: 15.2s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[\left(\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}\right) \cdot \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\left(\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}\right) \cdot \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (*
  (* (cbrt (exp (- w))) (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(exp(-w)) * 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_binary640.3

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

  4. Applied associate-*l*_binary640.3

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

  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-exp-log_binary640.3

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

  8. Applied pow-to-exp_binary644.7

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

  9. Applied prod-exp_binary644.7

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

  10. Simplified4.7

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

  11. Taylor expanded around 0 4.7

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

  12. Simplified0.3

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

  13. Final simplification0.3

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

Alternatives

Reproduce

herbie shell --seed 2021118 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))