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.
{"title":"Synthesizing mathematical identities with e-graphs","authors":"Ian Briggs, P. Panchekha","doi":"10.1145/3520308.3534506","DOIUrl":"https://doi.org/10.1145/3520308.3534506","url":null,"abstract":"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.","PeriodicalId":230256,"journal":{"name":"Proceedings of the 1st ACM SIGPLAN International Symposium on E-Graph Research, Applications, Practices, and Human-factors","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114287336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Proceedings of the 1st ACM SIGPLAN International Symposium on E-Graph Research, Applications, Practices, and Human-factors","authors":"","doi":"10.1145/3520308","DOIUrl":"https://doi.org/10.1145/3520308","url":null,"abstract":"","PeriodicalId":230256,"journal":{"name":"Proceedings of the 1st ACM SIGPLAN International Symposium on E-Graph Research, Applications, Practices, and Human-factors","volume":"51 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131830884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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