Abstract Probabilistic logics, especially those based on logic programming (LP), are gaining popularity as modelling and reasoning tools, since they combine the power of logic to represent knowledge with the ability of probability theory to deal with uncertainty. In this paper, we propose a hybrid extension for probabilistic logic programming, which allows for exact inference for a much wider class of continuous distributions than existing extensions. At the same time, our extension allows one to compute approximations with bounded and arbitrarily small error. We propose a novel anytime algorithm exploiting the logical and continuous structure of distributions and experimentally show that our algorithm is, for typical relational problems, competitive with state-of-the-art sampling algorithms and outperforms them by far if rare events with deterministic structure are provided as evidence, despite the fact that it provides much stronger guarantees.