Examples of problems where exponential algorithms run faster than polynomial algorithms for practical sizes? Do you know of any problems (preferably at least somewhat well known), where, for a practical problem size, an exponential algorithm runs much faster than a best-known polynomial time counterpart.

For example, suppose a problem has a practical size* of $n = 100$ and there are two known algorithms: One is $2^n$ and the other is $n^c$ for some constant $c$. Clearly for any $c &gt; 15$, the exponential algorithm is preferred.

*I guess practical size would mean something commonly found in the real world. Like the number of trains on a network.
How bout the simplex algorithm for linear programming?
In many occasions it is used in practice.
Edited to add:
I think it's more of a &quot;worse-case exponential algorithm&quot; which runs efficiently on practical instances/distributions rather than runs faster on practical sized adversarial instances.