Catalyzes the conversion of 2-formylglutarate to (S)-2-hydroxymethylglutarate. Has very low activity with (S)-3-hydroxyisobutyrate. (S)-2-hydroxymethylglutarate + NAD(+) = 2-formylglutarate + H(+) + NADH Cofactor degradation; nicotinate degradation; propanoate and pyruvate from 6-hydroxynicotinate: step 3/8. Homotetramer. Belongs to the HIBADH-related family.