  We present a general method to optimize the evaluation of Feynman
diagrammatic expansions, which requires the automated symbolic assignment of
momentum/energy conserving variables to each diagram. With this symbolic
representation, we utilize the pole structure of each diagram to automatically
sort the Feynman diagrams into groups that are likely to contain nearly equal
or nearly cancelling diagrams, and we show that for some systems this
cancellation is exact. This allows for a potentially massive cancellation
during the numerical integration of internal momenta variables, leading to an
optimal suppression of the `sign problem' and hence reducing the computational
cost. Although we define these groups using a frequency space representation,
the equality or cancellation of diagrams within the group remains valid in
other representations such as imaginary time used in standard diagrammatic
Monte Carlo. As an application of the approach we apply this method, combined
with algorithmic Matsubara integration (AMI) [Phys. Rev. B 99, 035120 (2019)]
and Monte Carlo methods, to the Hubbard model self-energy expansion on a 2D
square lattice up to sixth order which we evaluate and compare with existing
benchmarks.
