Efficient Symbolic Computation vis Hash Consing (2509.20534v1)

Abstract: Symbolic computation systems suffer from memory inefficiencies due to redundant storage of structurally identical subexpressions, commonly known as expression swell, which degrades performance in both classical computer algebra and emerging AI-driven mathematical reasoning tools. In this paper, we present the first integration of hash consing into JuliaSymbolics, a high-performance symbolic toolkit in Julia, by employing a global weak-reference hash table that canonicalizes expressions and eliminates duplication. This approach reduces memory consumption and accelerates key operations such as differentiation, simplification, and code generation, while seamlessly integrating with Julia's metaprogramming and just-in-time compilation infrastructure. Benchmark evaluations across different computational domains reveal substantial improvements: symbolic computations are accelerated by up to 3.2 times, memory usage is reduced by up to 2 times, code generation is up to 5 times faster, function compilation up to 10 times faster, and numerical evaluation up to 100 times faster for larger models. While certain workloads with fewer duplicate unknown-variable expressions show more modest gains or even slight overhead in initial computation stages, downstream processing consistently benefits significantly. These findings underscore the importance of hash consing in scaling symbolic computation and pave the way for future work integrating hash consing with e-graphs for enhanced equivalence-aware expression sharing in AI-driven pipelines.