Comment #8 on issue 3826 by asmeu...@gmail.com: trigsimp can't reverse tan double angle formula
http://code.google.com/p/sympy/issues/detail?id=3826

Or better yet, if there is some heuristic that we can apply to functions that we will know that there is not a chance that we will get a better result from the full trigsimp, then just use the fast method. That way, it will stay fast for already simple expressions, but will become powerful for expressions that can be simplified a lot.

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