Phylogenetic networks are increasingly being used to represent more complex evolutionary relationships, such as hybridization and horizontal gene transfer. Calculating distances between networks measures the discrepancies between networks built using different methodologies or reference networks, in the evaluation of construction methods. Here we are interested in the cherry distance, a network distance based on cherry operations. We describe refinements made to a cherry distance algorithm design that takes advantage of a network abstraction that maps reticulated elements between two inputs and performs a preprocessing step. We experimentally show, on a newly implemented and publicly available Rust package, both the improvements this design provides, as well as an exploration of when such an improvement is most effective vis-a-vis the input network topology. Next we present a heuristic strategy to calculate the cherry distance in a non-exact way, and experimentally show how it maintains a very high degree of accuracy while still providing large gains in the runtime efficiency. Finally, we explore particular characteristics of the cherry distance through experiments on real data from the Rose family using another rearrangement operation (rNNI). Specifically, we show how the cherry distance excels at reflecting how many taxa are impacted by changes in the network. We also show a higher degree of sensitivity in cherry distance when compared to a network adaptation of the ubiquitous RF distance on trees, the soft RF distance.