  Progress in simulating QCD at nonzero baryon density requires, amongst
others, substantial numerical effort. Here we propose two different expansions
to all orders in the hopping parameter, preserving the full Yang-Mills action,
which are much cheaper to simulate. We carry out simulations using complex
Langevin dynamics, both in the hopping expansions and in the full theory, for
two flavours of Wilson fermions, and agreement is seen at sufficiently high
order in the expansion. These results provide support for the use of complex
Langevin dynamics to study QCD at nonzero density, both in the full and the
expanded theory, and for the convergence of the latter.
