  This article reports an automated approach to the evaluation of higher-order
terms of QED perturbation to anomalous magnetic moments of charged leptons by
numerical means. We apply this approach to tenth-order correction due to a
particular subcollection of Feynman diagrams, which have no virtual lepton
loops. This set of diagrams is distinctive in that it grows factorially in
number as the order increases, and also each of the diagrams holds quite a
large number of subtraction terms to be treated along renormalization
procedure. Thus some automated scheme has long been required to evaluate
correctly this class of diagrams. We developed a fast algorithm and an
implementation which automates necessary steps to generate from the
representation of each Feynman diagram the FORTRAN codes for numerical
integration. Currently those diagrams of tenth order are being evaluated.
