  We carry out the enhanced group classification of a class of
(1+1)-dimensional nonlinear diffusion-reaction equations with
gradient-dependent diffusivity using the two-step version of the method of
furcate splitting. For simultaneously finding the equivalence groups of an
unnormalized class of differential equations and a collection of its
subclasses, we suggest an optimized version of the direct method. The
optimization includes the preliminary study of admissible transformations
within the entire class and the successive splitting of the corresponding
determining equations with respect to arbitrary elements and their derivatives
depending on auxiliary constraints associated with each of required subclasses.
In the course of applying the suggested technique to subclasses of the class
under consideration, we construct, for the first time, a nontrivial example of
finite-dimensional effective generalized equivalence group. Using the method of
Lie reduction and the generalized separation of variables, exact solutions of
some equations under consideration are found.
