I thought that it might, for a small set of inputs. The overhead of creating and populating the hash, as well as assignments to two new lexicals would only be overcome with a significantly larger data set.

I wonder, though. Yep. Changing it to this:

{
my %cache;
sub memoized {
    ( $cache{$a} ||= substr($a, -(19+20), 19) )
    cmp ( $cache{$b} ||= substr($b, -(19+20), 19) );
}
}
[download]

gives a slight increase in speed (but my benchmarks are varying wildly right now. Maintaining ranking, but % differences are all over the board.)

            Rate       st memoized    naive      grt
st       10281/s       --      -6%     -51%     -54%
memoized 10930/s       6%       --     -48%     -51%
naive    20942/s     104%      92%       --      -5%
grt      22143/s     115%     103%       6%       --
[download]