{"id":"https://openalex.org/W4389814197","doi":"https://doi.org/10.48550/arxiv.2312.08472","title":"AutoNumerics-Zero: Automated Discovery of State-of-the-Art Mathematical Functions","display_name":"AutoNumerics-Zero: Automated Discovery of State-of-the-Art Mathematical Functions","publication_year":2023,"publication_date":"2023-12-13","ids":{"openalex":"https://openalex.org/W4389814197","doi":"https://doi.org/10.48550/arxiv.2312.08472"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2312.08472","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.08472","pdf_url":"https://arxiv.org/pdf/2312.08472","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2312.08472","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049581744","display_name":"Esteban Real","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Real, Esteban","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100687220","display_name":"Chen Yao","orcid":"https://orcid.org/0000-0003-4224-5535"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Yao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076545834","display_name":"Mirko Rossini","orcid":"https://orcid.org/0000-0002-5868-720X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rossini, Mirko","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037349956","display_name":"Connal de Souza","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"de Souza, Connal","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065357046","display_name":"Manav Garg","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Garg, Manav","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093510006","display_name":"Akhil Verghese","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Verghese, Akhil","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081794563","display_name":"Moritz Firsching","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Firsching, Moritz","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088551093","display_name":"Quoc V. Le","orcid":"https://orcid.org/0000-0002-1087-2844"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Le, Quoc V.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065360819","display_name":"Ekin D. Cubuk","orcid":"https://orcid.org/0000-0003-0524-2837"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cubuk, Ekin Dogus","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5085465832","display_name":"David H. Park","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Park, David H.","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":10,"corresponding_author_ids":["https://openalex.org/A5049581744"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9549999833106995,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9319999814033508,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/transcendental-function","display_name":"Transcendental function","score":0.776813805103302},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6989384293556213},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6587955355644226},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.5859926342964172},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5336654186248779},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5039958357810974},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.48849284648895264},{"id":"https://openalex.org/keywords/transcendental-number","display_name":"Transcendental number","score":0.4802734851837158},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45279064774513245},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.4473685622215271},{"id":"https://openalex.org/keywords/scratch","display_name":"Scratch","score":0.43759840726852417},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.43717435002326965},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4203990399837494},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4194665551185608},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3486423194408417},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2669796347618103},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.21498322486877441},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19664326310157776},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.12512525916099548}],"concepts":[{"id":"https://openalex.org/C43321923","wikidata":"https://www.wikidata.org/wiki/Q864333","display_name":"Transcendental function","level":2,"score":0.776813805103302},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6989384293556213},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6587955355644226},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.5859926342964172},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5336654186248779},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5039958357810974},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.48849284648895264},{"id":"https://openalex.org/C188370112","wikidata":"https://www.wikidata.org/wiki/Q173091","display_name":"Transcendental number","level":2,"score":0.4802734851837158},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45279064774513245},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.4473685622215271},{"id":"https://openalex.org/C2781235140","wikidata":"https://www.wikidata.org/wiki/Q275131","display_name":"Scratch","level":2,"score":0.43759840726852417},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.43717435002326965},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4203990399837494},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4194665551185608},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3486423194408417},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2669796347618103},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.21498322486877441},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19664326310157776},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.12512525916099548},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2312.08472","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.08472","pdf_url":"https://arxiv.org/pdf/2312.08472","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2312.08472","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2312.08472","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2312.08472","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.08472","pdf_url":"https://arxiv.org/pdf/2312.08472","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389814197.pdf","grobid_xml":"https://content.openalex.org/works/W4389814197.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1481108397","https://openalex.org/W2120451642","https://openalex.org/W2314977061","https://openalex.org/W3183290492","https://openalex.org/W1792497233","https://openalex.org/W4378448846","https://openalex.org/W4300089223","https://openalex.org/W4387814077","https://openalex.org/W2523571232","https://openalex.org/W3014029144"],"abstract_inverted_index":{"Computers":[0],"calculate":[1],"transcendental":[2,189],"functions":[3,190],"by":[4,34,73,79,135],"approximating":[5],"them":[6],"through":[7],"the":[8,32,38,53,93,127,172,184,196,200],"composition":[9],"of":[10,40,98,106,125,155,160,188,202],"a":[11,23,80,103,131,152],"few":[12,47],"limited-precision":[13],"instructions.":[14],"For":[15],"example,":[16],"an":[17],"exponential":[18,94],"can":[19,70,91],"be":[20,71],"calculated":[21],"with":[22],"Taylor":[24],"series.":[25],"These":[26],"approximation":[27,68],"methods":[28,69],"were":[29],"developed":[30],"over":[31,86,115,133],"centuries":[33],"mathematicians,":[35],"who":[36],"emphasized":[37],"attainability":[39],"arbitrary":[41],"precision.":[42],"Computers,":[43],"however,":[44],"operate":[45],"on":[46],"limited":[48,65],"precision":[49,101],"types,":[50],"such":[51],"as":[52],"popular":[54],"float32.":[55],"In":[56,84,144],"this":[57],"study,":[58],"we":[59],"show":[60],"that":[61,138,179,192],"when":[62,108],"aiming":[63],"for":[64,102,171],"precision,":[66,170],"existing":[67],"outperformed":[72],"programs":[74],"automatically":[75],"discovered":[76],"from":[77],"scratch":[78],"simple":[81],"evolutionary":[82],"algorithm.":[83],"particular,":[85],"real":[87],"numbers,":[88],"our":[89,193],"method":[90,129,194],"approximate":[92],"function":[95],"reaching":[96],"orders":[97],"magnitude":[99],"more":[100],"given":[104],"number":[105],"operations":[107],"compared":[109],"to":[110,120,162,168,198],"previous":[111],"approaches.":[112],"More":[113],"practically,":[114],"float32":[116],"numbers":[117],"and":[118],"constrained":[119],"less":[121],"than":[122],"1":[123],"ULP":[124],"error,":[126],"same":[128],"attains":[130],"speedup":[132],"baselines":[134],"generating":[136],"code":[137],"triggers":[139],"better":[140],"XLA/LLVM":[141],"compilation":[142],"paths.":[143],"other":[145],"words,":[146],"in":[147],"both":[148],"cases,":[149],"evolution":[150],"searched":[151],"vast":[153],"space":[154],"possible":[156],"programs,":[157],"without":[158],"knowledge":[159],"mathematics,":[161],"discover":[163],"previously":[164],"unknown":[165],"optimized":[166],"approximations":[167],"high":[169],"first":[173],"time.":[174],"We":[175],"also":[176],"give":[177],"evidence":[178],"these":[180],"results":[181],"extend":[182],"beyond":[183],"exponential.":[185],"The":[186],"ubiquity":[187],"suggests":[191],"has":[195],"potential":[197],"reduce":[199],"cost":[201],"scientific":[203],"computing":[204],"applications.":[205]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2023-12-16T00:00:00"}
