Average Error: 0.2 → 0.3
Time: 16.9s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[\frac{{\left({\left({\ell}^{\left({\left(e^{w}\right)}^{0.6666666666666666}\right)}\right)}^{\left(\sqrt[3]{{\left(e^{w}\right)}^{0.6666666666666666}}\right)}\right)}^{\left(\sqrt[3]{\sqrt[3]{e^{w}}}\right)}}{e^{w}}\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\frac{{\left({\left({\ell}^{\left({\left(e^{w}\right)}^{0.6666666666666666}\right)}\right)}^{\left(\sqrt[3]{{\left(e^{w}\right)}^{0.6666666666666666}}\right)}\right)}^{\left(\sqrt[3]{\sqrt[3]{e^{w}}}\right)}}{e^{w}}
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (/
  (pow
   (pow
    (pow l (pow (exp w) 0.6666666666666666))
    (cbrt (pow (exp w) 0.6666666666666666)))
   (cbrt (cbrt (exp w))))
  (exp w)))
double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}
↓
double code(double w, double l) {
	return pow(pow(pow(l, pow(exp(w), 0.6666666666666666)), cbrt(pow(exp(w), 0.6666666666666666))), cbrt(cbrt(exp(w)))) / 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 0.2

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

  2. Simplified0.2

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

  4. Applied add-cube-cbrt_binary640.4

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

  5. Applied pow-unpow_binary640.3

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

  7. Applied add-cube-cbrt_binary640.3

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

  8. Applied cbrt-prod_binary640.4

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

  9. Applied pow-unpow_binary640.4

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

  10. Simplified0.3

    \[\leadsto \frac{{\color{blue}{\left({\left({\ell}^{\left({\left(e^{w}\right)}^{0.6666666666666666}\right)}\right)}^{\left(\sqrt[3]{{\left(e^{w}\right)}^{0.6666666666666666}}\right)}\right)}}^{\left(\sqrt[3]{\sqrt[3]{e^{w}}}\right)}}{e^{w}}\]

  11. Final simplification0.3

    \[\leadsto \frac{{\left({\left({\ell}^{\left({\left(e^{w}\right)}^{0.6666666666666666}\right)}\right)}^{\left(\sqrt[3]{{\left(e^{w}\right)}^{0.6666666666666666}}\right)}\right)}^{\left(\sqrt[3]{\sqrt[3]{e^{w}}}\right)}}{e^{w}}\]

Reproduce

herbie shell --seed 2020253 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))