Average Error: 0.2 → 0.7
Time: 20.0s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[\frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}{\sqrt{e^{w}}} \cdot \frac{{\left({\left(\sqrt{\ell}\right)}^{\left(\sqrt{e^{w}} \cdot \sqrt{\sqrt{e^{w}}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}}{\sqrt{e^{w}}}\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}{\sqrt{e^{w}}} \cdot \frac{{\left({\left(\sqrt{\ell}\right)}^{\left(\sqrt{e^{w}} \cdot \sqrt{\sqrt{e^{w}}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}}{\sqrt{e^{w}}}
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (*
  (/ (pow (sqrt l) (exp w)) (sqrt (exp w)))
  (/
   (pow
    (pow (sqrt l) (* (sqrt (exp w)) (sqrt (sqrt (exp w)))))
    (sqrt (sqrt (exp w))))
   (sqrt (exp w)))))
double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}
↓
double code(double w, double l) {
	return (pow(sqrt(l), exp(w)) / sqrt(exp(w))) * (pow(pow(sqrt(l), (sqrt(exp(w)) * sqrt(sqrt(exp(w))))), sqrt(sqrt(exp(w)))) / sqrt(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-sqr-sqrt_binary64_7720.2

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

  5. Applied add-sqr-sqrt_binary64_7720.6

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

  6. Applied unpow-prod-down_binary64_8270.6

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

  7. Applied times-frac_binary64_7570.6

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

  9. Applied add-sqr-sqrt_binary64_7720.7

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

  10. Applied pow-unpow_binary64_8250.7

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

  12. Applied add-sqr-sqrt_binary64_7720.7

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

  13. Applied pow-unpow_binary64_8250.7

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

  15. Applied pow-pow_binary64_8200.7

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

  16. Final simplification0.7

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

Reproduce

herbie shell --seed 2020281 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))