  We study the resummation of soft gluon emission corrections to the production
of a top-antitop pair in association with a Higgs boson at the Large Hadron
Collider. Starting from a soft-gluon resummation formula derived in previous
work, we develop a bespoke parton-level Monte Carlo program which can be used
to calculate the total cross section along with differential distributions. We
use this tool to study the phenomenological impact of the resummation to
next-to-next-to-leading logarithmic (NNLL) accuracy, finding that these
corrections increase the total cross section and the differential distributions
with respect to NLO calculations of the same observables.
