The ability to calculate analytic full-colour two-to-three two-loop helicity
amplitudes in massless QCD has been a recent triumph of the field, driving
phenomenology towards one percent precision. In this contribution, we focus on
the virtual correction of diphoton-plus-jet production via gluon fusion, gg→gγγ. We outline state-of-the-art strategies to optimise the
reconstruction over finite fields of the rational coefficients of the
amplitude. We also present an updated performance analysis of our
publicly-available C++ implementation of the amplitude, demonstrating its
typical speed and stability, and study its stability in infrared regions of
phase space. These results are relevant for improving predictions in Higgs
physics at hadron colliders.Comment: 6 pages, 2 figures, Proceedings of the 21th International Workshop on
Advanced Computing and Analysis Techniques in Physics Research (ACAT 2022)
[v3: minor edits to address referee comments