  We present a new (and general) algorithm for deriving lattice Feynman rules
which is capable of handling actions as complex as the Highly Improved
Staggered Quark (HISQ) action. This enables us to perform a perturbative
calculation of the influence of dynamical HISQ fermions on the perturbative
improvement of the gluonic action in the same way as we have previously done
for asqtad fermions. We find the fermionic contributions to the radiative
corrections in the L\"uscher-Weisz gauge action to be somewhat larger for HISQ
fermions than for asqtad.
