This is super slow:
>>> from pyca import *
>>> a = 417/(962*pi+80808)
>>> a**50 - a**51 * a**-1
Of course, it works well when increasing POW_LIMIT so that the powers get expanded algebraically:
>>> ctx = ca_ctx(pow_limit=100)
>>> a = ca(pi, context=ctx)
>>> a = 417 / (962 * ca(pi, context=ctx) + 80808)
>>> a**50 - a**51 * a**-1
But this shouldn't be necessary to get acceptable performance.