  We report on the advances in the calculation of the two-loop scattering
amplitudes for five-particle processes with one off-shell leg. Focusing on the
production of a Higgs boson in association with a bottom quark pair, we outline
how the newly developed technology allows us to overcome the computational
bottlenecks. In particular, we discuss the use of finite field arithmetic and
elucidate a convenient way to evaluate numerically the special functions
appearing in the amplitudes.
