  We present a method to accelerate the numerical evaluation of spatial
integrals of Feynman diagrams when expressed on the real frequency axis. This
can be realized through use of a renormalized perturbation expansion with a
constant but complex renormalization shift. The complex shift acts as a
regularization parameter for the numerical integration of otherwise sharp
functions. This results in an exponential speed up of stochastic numerical
integration at the expense of evaluating additional counter-term diagrams. We
provide proof of concept calculations within a difficult limit of the
half-filled 2D Hubbard model on a square lattice.
