Star formation rate function at redshifts z ∼ 0, 1, 2, 3, 4, and 5. The data points with error bars include the data from VVDS (blue squares; Cucciati et al. 2012), Herschel PEP/HerMES (orange rhombuses; Gruppioni et al. 2013), PEP and HerMES (green circles; Gruppioni et al. 2015), CIGALE (red triangles; Lyon et al. 2024), Herschel-PACS (purple triangles; Magnelli et al. 2013), GALEX (brown arrows; Wyder et al. 2005), ALCS (pink pluses; Fujimoto et al. 2024), ALMA-ALPINE (grey pentagons; Gruppioni et al. 2020), SCUBA-2 (yellow stars; Koprowski et al. 2017), A³COSMOS (cyan rhombuses; Traina et al. 2024), HST (blue crosses, purple, orange and green hexagons; Alavi et al. 2014; Bouwens et al. 2015, 2021, 2022), Herschel-ATLAS (red stars; Lapi et al. 2011), Herschel+LOFAR (brown hexagons; Wang et al. 2021), JWST-CEERS (pink squares; Ling et al. 2024) and WUDS (grey rhombuses; Pelló et al. 2018). The black solid lines and shaded areas show our fit to Equation (2) and 1σ uncertainty.