>>51
What I'm saying that f'(x) = f(f(x)) can often be computed to an equivalent that runs as fast as f(x) can, and if you believe
Each application of f cannot be performed until the input parameter is known.
holds in the vast majority of cases then you're in for a lot of surprises. Any commutative operation can be parallelized to log n time with log n CPUs via straightforward divide and conquer. Many that aren't can still be parallelized without much trouble (consider what's needed for division).