Comment #18 on issue 2607 by asmeurer: as_numer_denom() is too slow http://code.google.com/p/sympy/issues/detail?id=2607
There is a fifth method, which is to cancel stuff, as discussed in comments 4 and 5. I've pushed that as as_numer_denom5() in my branch. For the example expressions I've posted here, it is the fastest (by far).
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