EGRAPHS '22: "Synthesizing Mathematical ..."
Synthesizing Mathematical Identities with E-Graphs
Ian Briggs
and Pavel Panchekha (University of Utah, USA)
Identities compactly describe properties of a mathematical expression and can be leveraged into faster and more accurate function implementations. However, identities must currently be discovered manually, which requires a lot of expertise. We propose a two-phase synthesis and deduplication pipeline that discovers these identities automatically. In the synthesis step, a set of rewrite rules is composed, using an e-graph, to discover candidate identities. However, most of these candidates are duplicates, which a secondary de-duplication step discards using integer linear programming and another e-graph. Applied to a set of 61 benchmarks, the synthesis phase generates 7215 candidate identities which the de-duplication phase then reduces down to 125 core identities.
@InProceedings{EGRAPHS22p1,
author = {Ian Briggs and Pavel Panchekha},
title = {Synthesizing Mathematical Identities with E-Graphs},
booktitle = {Proc.\ EGRAPHS},
publisher = {ACM},
pages = {1--6},
doi = {10.1145/3520308.3534506},
year = {2022},
}
Publisher's Version
EGRAPHS '22: "Synthesizing Mathematical ..."
Synthesizing Mathematical Identities with E-Graphs
Ian Briggs
and Pavel Panchekha (University of Utah, USA)
Identities compactly describe properties of a mathematical expression and can be leveraged into faster and more accurate function implementations. However, identities must currently be discovered manually, which requires a lot of expertise. We propose a two-phase synthesis and deduplication pipeline that discovers these identities automatically. In the synthesis step, a set of rewrite rules is composed, using an e-graph, to discover candidate identities. However, most of these candidates are duplicates, which a secondary de-duplication step discards using integer linear programming and another e-graph. Applied to a set of 61 benchmarks, the synthesis phase generates 7215 candidate identities which the de-duplication phase then reduces down to 125 core identities.
@InProceedings{EGRAPHS22p1,
author = {Ian Briggs and Pavel Panchekha},
title = {Synthesizing Mathematical Identities with E-Graphs},
booktitle = {Proc.\ EGRAPHS},
publisher = {ACM},
pages = {1--6},
doi = {10.1145/3520308.3534506},
year = {2022},
}
Publisher's Version