## Abstract

Term Rewriting Systems (TRSs) are used in compilers to simplify and prove expressions. State-of-The-Art TRSs in compilers use a greedy algorithm that applies a set of rewriting rules in a predefined order (where some of the rules are not axiomatic). This leads to a loss of the ability to simplify certain expressions. E-graphs and equality saturation sidestep this issue by representing the different equivalent expressions in a compact manner from which the optimal expression can be extracted. While an e-graph-based TRS can be more powerful than a TRS that uses a greedy algorithm, it is slower because expressions may have a large or sometimes infinite number of equivalent expressions. Accelerating e-graph construction is crucial for making the use of e-graphs practical in compilers. In this paper, we present Caviar, an e-graph-based TRS for proving expressions within compilers. The main advantage of Caviar is its speed. It can prove expressions much faster than base e-graph TRSs. It relies on three techniques: 1) a technique that stops e-graphs from growing when the goal is reached, called Iteration Level Check; 2) a mechanism that balances exploration and exploitation in the equality saturation algorithm, called Pulsing Caviar; 3) a technique to stop e-graph construction before reaching saturation when a non-provable pattern is detected, called Non-Provable Patterns Detection (NPPD). We evaluate caviar on Halide, an optimizing compiler that relies on a greedy-Algorithm-based TRS to simplify and prove its expressions. The proposed techniques allow Caviar to accelerate e-graph expansion for the task of proving expressions. They also allow Caviar to prove expressions that Halide's TRS cannot prove while being only 0.68x slower. Caviar is publicly available at: <a>https://github.com/caviar-Trs/caviar</a>.

Original language | English (US) |
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Title of host publication | CC 2022 - Proceedings of the 31st ACM SIGPLAN International Conference on Compiler Construction |

Editors | Bernhard Egger, Aaron Smith |

Publisher | Association for Computing Machinery, Inc |

Pages | 54-64 |

Number of pages | 11 |

ISBN (Electronic) | 9781450391832 |

DOIs | |

State | Published - Sep 19 2022 |

Event | 31st ACM SIGPLAN International Conference on Compiler Construction, CC 2022 - Virtual, Online, Korea, Republic of Duration: Apr 2 2022 → Apr 3 2022 |

### Publication series

Name | CC 2022 - Proceedings of the 31st ACM SIGPLAN International Conference on Compiler Construction |
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### Conference

Conference | 31st ACM SIGPLAN International Conference on Compiler Construction, CC 2022 |
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Country/Territory | Korea, Republic of |

City | Virtual, Online |

Period | 4/2/22 → 4/3/22 |

## Keywords

- Algebraic expressions simplification
- Equality Graphs
- Equality Saturation
- Term Rewriting Systems

## ASJC Scopus subject areas

- Hardware and Architecture
- Signal Processing
- Software