Plays a central role in assimilation of carbon. It converts hydroxypyruvate to glycerate as a key step in the serine cycle, and may also play an important role in C2 reactions, by interconverting glyoxylate and glycolate. (R)-glycerate + NAD(+) = 3-hydroxypyruvate + H(+) + NADH One-carbon metabolism; formaldehyde assimilation via serine pathway. Homodimer. Uses both NAD and NADP. Belongs to the D-isomer specific 2-hydroxyacid dehydrogenase family.