  We present an efficient implementation of dynamically pruned quantum
dynamics, both in coordinate space and in phase space. We combine the ideas
behind the biorthogonal von Neumann basis (PvB) with the orthogonalized
momentum-symmetrized Gaussians (Weylets) to create a new basis, projected
Weylets, that takes the best from both methods. We benchmark pruned dynamics
using phase-space-localized PvB, projected Weylets, and
coordinate-space-localized DVR bases, with real-world examples in up to six
dimensions. We show that coordinate-space localization is most important for
efficient pruning and that pruned dynamics is much faster compared to unpruned,
exact dynamics. Phase-space localization is useful for more demanding dynamics
where many basis functions are required. There, projected Weylets offer a more
compact representation than pruned DVR bases.
