Light field microscopy can capture 3D volume datasets in a snapshot, making it a valuable tool for high-speed 3D imaging of dynamic biological events. However, subsequent computational reconstruction of the raw data into a human-interpretable 3D+time image is very time-consuming, limiting the technique's utility as a routine imaging tool. Here we derive improved equations for 3D volume reconstruction from light field microscopy datasets, leading to dramatic speedups. We characterize our open-source Python implementation of these algorithms and demonstrate real-world reconstruction speedups of more than an order of magnitude compared with established approaches. The scale of this performance improvement opens up new possibilities for studying large timelapse datasets in light field microscopy.