Color error associated with an image rendered by a rendering device is calculated in the no more than N−1 dimensions of an associated color sensor color space. The color error is assumed to be small. A differential of a mapping from an N dimensional rendering device color space to the associated color sensor color space is used to calculate a colorant error in the N dimensions of the rendering device color space. Where necessary, appropriate assumptions are used to constrain an underdetermined system of equations. Where calculated colorant error is unreasonable, the calculated colorant error is clipped and colorant error is recalculated based on the clipped value.