  We consider the notion of information distance between two objects x and y
introduced by Bennett, G\'acs, Li, Vitanyi, and Zurek [1] as the minimal length
of a program that computes x from y as well as computing y from x, and study
different versions of this notion. It was claimed by Mahmud [11] that the
prefix version of information distance equals max(K(x|y), K(y|) + O(1) (this
equality with logarithmic precision was one of the main results of the paper by
Bennett, G\'acs, Li, Vitanyi, and Zurek). We show that this claim is false, but
does hold if the information distance is at least super logarithmic.
