HMMT November 2014 U6

In the octagon COMPUTER exhibited below, all interior angles are either $90^{\circ}$ or $270^{\circ}$ and we have $C O=O M=M P=P U=U T=T E=1$.

Point $D$ (not to scale in the diagram) is selected on segment $R E$ so that polygons COMPUTED and $C D R$ have the same area. Find $D R$.