\emph{Library learning} compresses a given corpus of programs by extracting common structure from the corpus into reusable library functions. Prior work on library learning suffers from two limitations that prevent it from scaling to larger, more complex inputs. First, it explores too many candidate library functions that are not useful for compression. Second, it is not robust to syntactic variation in the input.

We propose \emph{library learning modulo theory} (LLMT), a new library learning algorithm that additionally takes as input an equational theory for a given problem domain. LLMT uses e-graphs and equality saturation to compactly represent the space of programs equivalent modulo the theory, and
uses a novel \emph{e-graph anti-unification} technique to find common patterns in the corpus more directly and efficiently.

We implemented LLMT in a tool named \textsc{babble}. Our evaluation shows that \textsc{babble} achieves better compression orders of magnitude faster than the state of the art. We also provide a qualitative evaluation showing that \textsc{babble} learns reusable functions on inputs previously out of reach for library learning.