Catalyzes the oxydation of D-erythritol 1-phosphate to D-erythrulose 1-phosphate. D-erythritol 1-phosphate + NADP(+) = D-erythrulose 1-phosphate + H(+) + NADPH Carbohydrate metabolism; erythritol degradation. Induced by erythritol and repressed by EryD. Belongs to the FAD-dependent glycerol-3-phosphate dehydrogenase family.