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One obvious thing is that the wall time is considerably longer than the cpu-time. That can mean your process didn't get 100% of the CPU time or that Sage called out to a different process (maxima?) to get some results. Indeed, if you run:
import cProfile
S=sum(k*x^k,k,0,10)
cProfile.run("mydiff(S)")
you'll find 4995 calls to
maxima.py:722(_eval_line)
indicating that there were 4995 calls to another process. There are also various calls to various "simplify" routines, so either in construction or in comparison of symbolic expressions, Sage did feel the need to simplify things.
In short: If you want to do pattern matching on symbolic expressions, do not use "==". It is apparently already reserved for a fairly expensive equality test.
I am surprised that this program still triggers calls out to maxima. I don't think it's "reduce", since that only receives 18 calls and takes negligible time in the profile. All the other operations, including "==" should really map to straight pynac operations.
