We show that far-from-equilibrium relativistic fluid dynamics may be systematically defined, for arbitrary flow profiles, in terms of a generalized tensorial expansion with transport coefficients that contain an all order resummation in gradients. In this formulation, the transport coefficients of far-from-equilibrium fluid dynamics depend not only on the microscopic properties of the system but also on the nonlinear properties of the underlying state of the fluid itself. In contrast to previous works, no additional assumptions about the symmetries of the flow are necessary. A concrete example of this proposal is constructed using the slow-roll expansion in conformal Israel-Stewart theory. In this case, the novel resummed shear viscosity and relaxation time coefficients decrease with increasing Knudsen number according to formulas that can be readily investigated in current numerical simulations of the quark-gluon plasma formed in ultrarelativistic heavy ion collisions.