Average Error: 0.2 → 0.3
Time: 14.4s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[\sqrt{\sqrt{e^{-w}}} \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \left({\left(\sqrt{{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right)}^{-0.5}}\right)}^{3} \cdot {\left(\sqrt{{\left(\sqrt[3]{e^{w}}\right)}^{-0.5}}\right)}^{3}\right)\right)\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\sqrt{\sqrt{e^{-w}}} \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \left({\left(\sqrt{{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right)}^{-0.5}}\right)}^{3} \cdot {\left(\sqrt{{\left(\sqrt[3]{e^{w}}\right)}^{-0.5}}\right)}^{3}\right)\right)
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (*
  (sqrt (sqrt (exp (- w))))
  (*
   (pow l (exp w))
   (*
    (pow (sqrt (pow (* (cbrt (exp w)) (cbrt (exp w))) -0.5)) 3.0)
    (pow (sqrt (pow (cbrt (exp w)) -0.5)) 3.0)))))
double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}
↓
double code(double w, double l) {
	return sqrt(sqrt(exp(-w))) * (pow(l, exp(w)) * (pow(sqrt(pow((cbrt(exp(w)) * cbrt(exp(w))), -0.5)), 3.0) * pow(sqrt(pow(cbrt(exp(w)), -0.5)), 3.0)));
}

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 0.2

    \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt_binary64_16720.2

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

  4. Applied associate-*l*_binary64_17470.2

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

  5. Simplified0.2

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

  7. Applied add-sqr-sqrt_binary64_16720.2

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

  8. Applied associate-*l*_binary64_17470.2

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

  9. Simplified0.2

    \[\leadsto \sqrt{\sqrt{e^{-w}}} \cdot \color{blue}{\left({\ell}^{\left(e^{w}\right)} \cdot {\left(\sqrt{{\left(e^{w}\right)}^{-0.5}}\right)}^{3}\right)}\]
  10. Using strategy rm

  11. Applied add-cube-cbrt_binary64_16580.2

    \[\leadsto \sqrt{\sqrt{e^{-w}}} \cdot \left({\ell}^{\left(e^{w}\right)} \cdot {\left(\sqrt{{\color{blue}{\left(\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right) \cdot \sqrt[3]{e^{w}}\right)}}^{-0.5}}\right)}^{3}\right)\]

  12. Applied unpow-prod-down_binary64_16180.2

    \[\leadsto \sqrt{\sqrt{e^{-w}}} \cdot \left({\ell}^{\left(e^{w}\right)} \cdot {\left(\sqrt{\color{blue}{{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right)}^{-0.5} \cdot {\left(\sqrt[3]{e^{w}}\right)}^{-0.5}}}\right)}^{3}\right)\]

  13. Applied sqrt-prod_binary64_16660.2

    \[\leadsto \sqrt{\sqrt{e^{-w}}} \cdot \left({\ell}^{\left(e^{w}\right)} \cdot {\color{blue}{\left(\sqrt{{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right)}^{-0.5}} \cdot \sqrt{{\left(\sqrt[3]{e^{w}}\right)}^{-0.5}}\right)}}^{3}\right)\]

  14. Applied unpow-prod-down_binary64_16180.3

    \[\leadsto \sqrt{\sqrt{e^{-w}}} \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \color{blue}{\left({\left(\sqrt{{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right)}^{-0.5}}\right)}^{3} \cdot {\left(\sqrt{{\left(\sqrt[3]{e^{w}}\right)}^{-0.5}}\right)}^{3}\right)}\right)\]

  15. Final simplification0.3

    \[\leadsto \sqrt{\sqrt{e^{-w}}} \cdot \left({\ell}^{\left(e^{w}\right)} \cdot \left({\left(\sqrt{{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right)}^{-0.5}}\right)}^{3} \cdot {\left(\sqrt{{\left(\sqrt[3]{e^{w}}\right)}^{-0.5}}\right)}^{3}\right)\right)\]

Reproduce

herbie shell --seed 2020268 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))