Abstract We present an application of the major new features of pySecDec, a program designed to numerically calculate multi-loop integrals. One important new feature is the ability to integrate weighted sums of integrals in a way which is optimised to reach a given accuracy goal on the sums rather than on the individual integrals. Another feature is the option to perform asymptotic expansions. These new assets of the program represent an important step towards the efficient evaluation of multi-loop amplitudes in a largely automated way. We will illustrate them in a pedagogical example, through the calculation of the one-loop amplitude for Higgs plus jet production in the gluon channel, mediated by a top quark loop. Numerical results in the heavy top limit, compared to their analytic counterparts, are shown as well.