  We consider the next-to-leading order QCD corrections to Higgs boson pair
production, using our recent calculation of the form factors in the high-energy
limit. We compute the virtual corrections to the partonic cross section,
applying Pad\'e approximations to extend the range of validity of the
high-energy expansion. This enables us to compare to the exact numerical
calculation in a significant part of the phase space and allows us to extend
the virtual matrix element grid, based on the exact numerical calculation, to
larger values of the (partonic) transverse momentum of the Higgs boson, which
is important for boosted Higgs studies. Improved predictions for hadron
colliders with centre-of-mass energies of $14\ \mathrm{TeV}$ and $100\
\mathrm{TeV}$ are presented. The updated grid is made publicly available.
