Average Error: 0.3 → 1.6
Time: 11.8s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}} \cdot \left(\sqrt[3]{{\left(\sqrt{\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}}\right)}^{4}} \cdot \left(\sqrt[3]{{\left(\sqrt{\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}}\right)}^{4}} \cdot \sqrt[3]{{\left(\sqrt{\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}}\right)}^{4}}\right)\right)\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}} \cdot \left(\sqrt[3]{{\left(\sqrt{\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}}\right)}^{4}} \cdot \left(\sqrt[3]{{\left(\sqrt{\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}}\right)}^{4}} \cdot \sqrt[3]{{\left(\sqrt{\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}}\right)}^{4}}\right)\right)
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (*
  (cbrt (/ (pow l (exp w)) (exp w)))
  (*
   (cbrt (pow (sqrt (cbrt (/ (pow l (exp w)) (exp w)))) 4.0))
   (*
    (cbrt (pow (sqrt (cbrt (/ (pow l (exp w)) (exp w)))) 4.0))
    (cbrt (pow (sqrt (cbrt (/ (pow l (exp w)) (exp w)))) 4.0))))))
double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}
↓
double code(double w, double l) {
	return cbrt(pow(l, exp(w)) / exp(w)) * (cbrt(pow(sqrt(cbrt(pow(l, exp(w)) / exp(w))), 4.0)) * (cbrt(pow(sqrt(cbrt(pow(l, exp(w)) / exp(w))), 4.0)) * cbrt(pow(sqrt(cbrt(pow(l, exp(w)) / exp(w))), 4.0))));
}

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_binary641.3

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

  4. Simplified1.3

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

  5. Simplified1.3

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

  7. Applied add-cube-cbrt_binary641.6

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

  8. Simplified1.6

    \[\leadsto \left(\color{blue}{\left(\sqrt[3]{{\left(\sqrt{\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}}\right)}^{4}} \cdot \sqrt[3]{{\left(\sqrt{\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}}\right)}^{4}}\right)} \cdot \sqrt[3]{\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}} \cdot \sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}}\right) \cdot \sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}\]

  9. Simplified1.6

    \[\leadsto \left(\left(\sqrt[3]{{\left(\sqrt{\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}}\right)}^{4}} \cdot \sqrt[3]{{\left(\sqrt{\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}}\right)}^{4}}\right) \cdot \color{blue}{\sqrt[3]{{\left(\sqrt{\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}}\right)}^{4}}}\right) \cdot \sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}\]

  10. Final simplification1.6

    \[\leadsto \sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}} \cdot \left(\sqrt[3]{{\left(\sqrt{\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}}\right)}^{4}} \cdot \left(\sqrt[3]{{\left(\sqrt{\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}}\right)}^{4}} \cdot \sqrt[3]{{\left(\sqrt{\sqrt[3]{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}}\right)}^{4}}\right)\right)\]

Reproduce

herbie shell --seed 2020224 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))