Practical exponential time algorithms for polynomial-time solvable problems Inspired by this quote attributed to Alan Perlis: 


  For every polynomial-time algorithm you have, there is an exponential algorithm that I would rather run.


How I interpret this statement is that some exponential running times should be preferred over polynomial ones for realistic problem sizes. I have never actually seen such a case though.

I wonder if there are any problems for which exponential algorithms are known that are preferable to the best polynomial ones up to a nontrivial problem sizes?
The simplex method for linear programming has worst case exponential time complexity but is widely used in practice instead of the polynomial algorithms (which do exist).