You seem to be thinking about handling a line at a time. In that context, checking for an x at the beginning would be much faster than looking for an x anywher

You seem to be thinking about handling a line at a time. In that context, checking for an x at the beginning would be much faster than looking for an x anywhere in the line. However, for anything fast you're going to be handling a large buffer at a time, if not the entire memory-mapped file. In that context, there's no difference between ^x and yx, except that ^x also needs to match at start-of-file (so if anything it should be marginally slower). Finding just x is probably faster than finding yx - longer patterns can be faster when you can skip looking at some fraction of the input (as per TFA) but I expect 2 characters isn't enough to allow that.