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PySR and Eureqa, free and open-source symbolic regression tools, are used for discovering simple and accurate approximate formulas. Three approaches are used: (1) brute force of computing power, which provides results based on raw input data; (2) an improved method where input parameters are transformed through the Lambert W-function; (3) a method where the results are based on inputs and the Colebrook equation transformed through new suitable dimensionless groups. The discovered models were simplified by the WolframAlpha simplify tool and\/or the equivalent Matlab Symbolic toolbox. Novel models make iterative calculus redundant; they are simple for computer coding while the relative error remains lower compared with the solution through nomograms. The symbolic-regression solutions discovered by brute force computing power discard the kinematic viscosity of the fluid as an input parameter, implying that it has the least influence.<\/jats:p>","DOI":"10.3390\/axioms12090850","type":"journal-article","created":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T11:45:51Z","timestamp":1693482351000},"page":"850","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Symbolic Regression Approaches for the Direct Calculation of Pipe Diameter"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2502-0601","authenticated-orcid":false,"given":"Dejan","family":"Brki\u0107","sequence":"first","affiliation":[{"name":"Faculty of Electronic Engineering, University of Ni\u0161, 18000 Ni\u0161, Serbia"},{"name":"IT4Innovations, VSB\u2014Technical University of Ostrava, 708 00 Ostrava, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3913-7800","authenticated-orcid":false,"given":"Pavel","family":"Praks","sequence":"additional","affiliation":[{"name":"IT4Innovations, VSB\u2014Technical University of Ostrava, 708 00 Ostrava, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7510-4723","authenticated-orcid":false,"given":"Ren\u00e1ta","family":"Praksov\u00e1","sequence":"additional","affiliation":[{"name":"IT4Innovations, VSB\u2014Technical University of Ostrava, 708 00 Ostrava, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tom\u00e1\u0161","family":"Kozubek","sequence":"additional","affiliation":[{"name":"IT4Innovations, VSB\u2014Technical University of Ostrava, 708 00 Ostrava, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Brown, G.O. 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