  Star formation rate functions (SFRFs) give an instantaneous view of the
distribution of star formation rates (SFRs) in galaxies at different epochs.
They are a complementary and more stringent test for models than the galaxy
stellar mass function, which gives an integrated view of the past star
formation activity. However, the exploration of SFRFs has been limited thus far
due to difficulties in assessing the SFR from observed quantities and probing
the SFRF over a wide range of SFRs. We overcome these limitations thanks to an
original method that predicts the infrared luminosity from the rest-frame
UV/optical color of a galaxy and then its SFR over a wide range of stellar
masses and redshifts. We applied this technique to the deep imaging survey
HSC-CLAUDS combined with near-infrared and UV photometry. We provide the first
SFR functions with reliable measurements in the high- and low-SFR regimes up to
$z=2$ and compare our results with previous observations and four
state-of-the-art hydrodynamical simulations.
