  We prove that the group D^r(R) of C^r diffeomorphisms of the real line,
endowed with the compact-open and Whitney C^r topologies, is bihomeomorphic to
the group H(R) of homeomorphisms of the real line endowed with the compact-open
and Whitney topologies. This implies that the diffeomorphism group D^r(R)
endowed with the Whitney C^r topology is homeomorphic to the countable
box-power of the separable Hilbert space.
