--- title: [2603.21852] All elementary functions from a single... description: A research paper introduces a single binary operator eml(x,y)=exp(x)-ln(y) that, combined with the constant 1, can generate all elementary functions used in... canonical: https://daily.dev/posts/2603-21852-all-elementary-functions-from-a-single-binary-operator-kwaenwkg3 twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: [2603.21852] All elementary functions from a single binary operator | daily.dev og:description: A research paper introduces a single binary operator eml(x,y)=exp(x)-ln(y) that, combined with the constant 1, can generate all elementary functions used in... og:url: https://daily.dev/posts/2603-21852-all-elementary-functions-from-a-single-binary-operator-kwaenwkg3 og:image: https://api.daily.dev/og/posts/KwaEnWKG3.png og:image:alt: [2603.21852] All elementary functions from a single binary operator og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # [2603.21852] All elementary functions from a single binary operator **[Hacker News](https://daily.dev/sources/hn)** · 3 min read · 0 upvotes · 0 comments ## Summary A research paper introduces a single binary operator eml(x,y)=exp(x)-ln(y) that, combined with the constant 1, can generate all elementary functions used in scientific computing — including sin, cos, sqrt, log, arithmetic operations, and transcendental functions. Analogous to how NAND/NOR gates suffice for all Boolean logic, this EML operator provides a universal primitive for continuous mathematics. Discovered via exhaustive search, every expression in EML form becomes a binary tree of identical nodes with a trivially simple grammar (S -> 1 | eml(S,S)). The paper also demonstrates that this uniform structure enables gradient-based symbolic regression using EML trees as trainable circuits with the Adam optimizer, allowing exact recovery of closed-form elementary functions from numerical data at shallow tree depths. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: ## Similar posts on daily.dev - [Not all elementary functions can be expressed with exp-minus-log](https://daily.dev/posts/not-all-elementary-functions-can-be-expressed-with-exp-minus-log-klshz3zx5) · Hacker News · 0 upvotes · 0 comments - [A Neighborhood of Infinity: Logarithms and exponentials of functions](https://daily.dev/posts/a-neighborhood-of-infinity-logarithms-and-exponentials-of-functions-kexsxdrbj) · Planet Haskell · 0 upvotes · 0 comments - [On the Expectation-Maximization \(EM\) algorithm and regression models](https://daily.dev/posts/on-the-expectation-maximization-em-algorithm-and-regression-models-s0tbinrws) · R-bloggers · 0 upvotes · 0 comments - [How LLMs Can Be Assisted To Do Arithmetic Correctly](https://daily.dev/posts/how-llms-can-be-assisted-to-do-arithmetic-correctly-04arkfsu0) · Hackaday · 1 upvotes · 0 comments --- [View this post on daily.dev](https://daily.dev/posts/2603-21852-all-elementary-functions-from-a-single-binary-operator-kwaenwkg3) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} {"@context":"https://schema.org","@type":"TechArticle","headline":"[2603.21852] All elementary functions from a single binary operator","url":"https://daily.dev/posts/2603-21852-all-elementary-functions-from-a-single-binary-operator-kwaenwkg3","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/2603-21852-all-elementary-functions-from-a-single-binary-operator-kwaenwkg3"},"datePublished":"2026-04-13T04:36:06.022Z","dateModified":"2026-04-13T04:36:30.441Z","description":"A research paper introduces a single binary operator eml(x,y)=exp(x)-ln(y) that, combined with the constant 1, can generate all elementary functions used in...","image":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/1fed0de190485cbbb37a86fdf656d71b?_a=AQAEuop","thumbnailUrl":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/1fed0de190485cbbb37a86fdf656d71b?_a=AQAEuop","isAccessibleForFree":true,"articleSection":"Hacker News","inLanguage":"en","publisher":{"@type":"Organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180}},"author":{"@type":"Organization","name":"Hacker News","logo":"https://media.daily.dev/image/upload/t_logo,f_auto/v1/logos/hn","url":"https://daily.dev/sources/hn"},"commentCount":0,"discussionUrl":"https://daily.dev/posts/2603-21852-all-elementary-functions-from-a-single-binary-operator-kwaenwkg3","interactionStatistic":[{"@type":"InteractionCounter","interactionType":{"@type":"LikeAction"},"userInteractionCount":0},{"@type":"InteractionCounter","interactionType":{"@type":"CommentAction"},"userInteractionCount":0}],"keywords":"","timeRequired":"PT3M"} {"@context":"https://schema.org","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://daily.dev"},{"@type":"ListItem","position":2,"name":"Hacker News","item":"https://daily.dev/sources/hn"},{"@type":"ListItem","position":3,"name":"[2603.21852] All elementary functions from a single binary operator"}]} ```