  We compare performances of well-known numerical time-stepping methods that
are widely used to compute solutions of the doubly-infinite
Fermi-Pasta-Ulam-Tsingou (FPUT) lattice equations. The methods are benchmarked
according to (1) their accuracy in capturing the soliton peaks and (2) in
capturing highly-oscillatory parts of the solutions of the Toda lattice
resulting from a variety of initial data. The numerical inverse scattering
transform method is used to compute a reference solution with high accuracy. We
find that benchmarking a numerical method on pure-soliton initial data can lead
one to overestimate the accuracy of the method.
