Comment #5 on issue 3826 by [email protected]: trigsimp can't reverse tan double angle formula
http://code.google.com/p/sympy/issues/detail?id=3826

How slow? The groebner algorithm is probably too slow to have on by default, but unless fu is just as bad, I think it should be enabled by default, especially if it is robust. Algorithms that aren't enabled by default might as well not even exist for the vast majority of users, because they will never bother to enable them. And furthermore, library code in SymPy itself that calls trigsimp will not benefit (including simplify()!), and it will be impossible for users to fix it.

Take heurisch as an example. It's ridiculously slow. In fact, if the expression is just a little too big, it might take literally days to finish (for all intents and purposes, it hangs). But it is also very powerful, and before meijerg or full risch, it was all we had. In fact, it is able to solve an integral that no other system can solve, and SymPy was for some time listed on the Wikipedia article for the Risch algorithm because of it. And even now there are a lot of integrals that SymPy can only do because of it, even some very simple ones. If it were disabled by default, SymPy would not be known for being able to do any integration, the code would have gotten stale (no one would ever have found bugs in it and tried to improve it), and there's even a decent chance that we would have never made the jump to the more complete integration algorithms we have today.

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