Why Except is so slow as compared to equivalent RegularExpression?

Question

When comparing performance of the solutions suggested for this question I discovered that StringExpression involving Except is two orders of magnitude slower for large strings as compared to equivalent RegularExpression. Here is a simplified example demonstrating the problem:

With[{str = StringRepeat["a", 10^6] <> "b"}, {
  AbsoluteTiming[StringMatchQ[str, Except["b"] .. ~~ "b"]][[1]],
  AbsoluteTiming[StringMatchQ[str, RegularExpression["[^b]+b"]]][[1]]}]

Divide @@ %

{0.719855, 0.00323316}
222.648

The string pattern is 220 times slower than pure regex! But the regular expression [^x]+x is the direct semantic translation of the string pattern Except["x"] .. ~~ "x", and this translation is unique and unambiguous. Why then the latter is so insanely slow?

Answer 1

Using StringPattern`PatternConvert we can find the regexp into which Mathematica converts the original string expression:

StringPattern`PatternConvert[Except["b"] .. ~~ "b"][[1]]

"(?ms)(?:[^b])+b"

The only difference as compared to the direct semantic translation is that the negated character class [^b] is enclosed by redundant non-capturing group (?: … ). Since this group is non-capturing, one would expect that it can't introduce noticeable overhead. But is it so in practice? Let us check:

With[{str = StringRepeat["a", 10^6] <> "b"}, {
  AbsoluteTiming[StringMatchQ[str, Except["b"] .. ~~ "b"]][[1]],
  AbsoluteTiming[StringMatchQ[str, RegularExpression["(?:[^b])+b"]]][[1]],
  AbsoluteTiming[StringMatchQ[str, RegularExpression["[^b]+b"]]][[1]]}]

{0.721896, 0.717353, 0.00325354}

We see that this redundant non-capturing group is responsible for all the slowdown we observe.

It is interesting that the overhead isn't constant but grows step-wise with the length of the string up to approximately 95000 characters:

PrintTemporary[Dynamic[n]];

timings = Transpose[Table[With[{str = StringRepeat["a", n] <> "b"},
     {{n, AbsoluteTiming[StringMatchQ[str, RegularExpression[".+b"]]][[1]]},
      {n, AbsoluteTiming[StringMatchQ[str, RegularExpression["(?:.)+b"]]][[1]]}}],
    {n, 100, 100000, 100}]];

ListPlot[timings, PlotRange -> All, Frame -> True, Axes -> False, ImageSize -> 600, 
 FrameLabel -> {"string length", "seconds"}]

(evaluated with Mathematica 11.1.0 on Windows 7 x64.)