  We investigate nonlinear transport through quantum coherent metallic
conductors contacted to superconducting components. We find that in certain
geometries, the presence of superconductivity generates a large, finite-average
rectification effect. Specializing to Andreev interferometers, we show that the
direction and magnitude of rectification can be controlled by a magnetic flux
tuning the superconducting phase difference at two contacts. In particular,
this results in the breakdown of an Onsager reciprocity relation at finite
bias. The rectification current is macroscopic in that it scales with the
linear conductance, and we find that it exceeds 5% of the linear current at
sub-gap biases of few tens of \mu eV's.
