  As a key step towards a complete automation of the finite element method, we
present a new algorithm for automatic and efficient evaluation of multilinear
variational forms. The algorithm has been implemented in the form of a
compiler, the FEniCS Form Compiler FFC. We present benchmark results for a
series of standard variational forms, including the incompressible
Navier-Stokes equations and linear elasticity. The speedup compared to the
standard quadrature-based approach is impressive; in some cases the speedup is
as large as a factor 1000.
