Average Error: 0.3 → 0.3
Time: 16.8s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[\left(\left(\sqrt[3]{\sqrt{e^{-w}}} \cdot \sqrt{\sqrt[3]{e^{-w}}}\right) \cdot \left(\sqrt[3]{\sqrt{e^{-w}}} \cdot \sqrt{\sqrt[3]{e^{-w}}}\right)\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right)\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\left(\left(\sqrt[3]{\sqrt{e^{-w}}} \cdot \sqrt{\sqrt[3]{e^{-w}}}\right) \cdot \left(\sqrt[3]{\sqrt{e^{-w}}} \cdot \sqrt{\sqrt[3]{e^{-w}}}\right)\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right)
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (*
  (*
   (* (cbrt (sqrt (exp (- w)))) (sqrt (cbrt (exp (- w)))))
   (* (cbrt (sqrt (exp (- w)))) (sqrt (cbrt (exp (- w))))))
  (* (cbrt (exp (- w))) (pow l (exp w)))))
double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}
↓
double code(double w, double l) {
	return ((cbrt(sqrt(exp(-w))) * sqrt(cbrt(exp(-w)))) * (cbrt(sqrt(exp(-w))) * sqrt(cbrt(exp(-w))))) * (cbrt(exp(-w)) * pow(l, 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 add-sqr-sqrt_binary64_7820.3

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

  8. Applied add-sqr-sqrt_binary64_7820.3

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

  9. Applied cbrt-prod_binary64_7910.3

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

  10. Applied unswap-sqr_binary64_7280.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2021015 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))