It is shown that the accuracy of quantum dynamics calculations obtained according to the Herman-Kluk (HK) semiclassical initial value representation (SC-IVR) is significantly improved when the time evolution operator is computed by concatenating finite time propagators. This approach results in an approximate calculation of a real-time path-integral in a discrete coherent-state representation, which becomes exact in the limit of sufficiently short time-slice intervals. The efficiency of the computational method is optimized by devising a compact coherent-state basis set that obviates the need for calculating the inverse overlap matrix. Quantitative agreement with full quantum mechanical results is verified in the description of tunneling between disjoint classically allowed regions in one- and two-dimensional systems, in the treatment of long-time dynamics, and in nonadiabatic dynamics in a model system with two coupled one-dimensional potential energy surfaces.