  We compute the cosmological reduction of general string theories, including
bosonic, heterotic and type II string theory to order $\alpha'^{3}$, i.e., with
up to eight derivatives. To this end we refine recently introduced methods that
allow one to bring the reduced theory in one dimension to a canonical form with
only first-order time derivatives. The resulting theories are compatible with a
continuous $O(d,d,\mathbb{R})$ invariance, which in turn fixes the B-field
couplings.
