  Tree-level double-color-ordered amplitudes are computed using Berends--Giele
recursion relations applied to the bi-adjoint cubic scalar theory. The standard
notion of Berends--Giele currents is generalized to double-currents and their
recursions are derived from a perturbiner expansion of linearized fields that
solve the non-linear field equations. Two applications are given. Firstly, we
prove that the entries of the inverse KLT matrix are equal to Berends--Giele
double-currents (and are therefore easy to compute). And secondly, a simple
formula to generate tree-level BCJ-satisfying numerators for arbitrary
multiplicity is proposed by evaluating the field-theory limit of tree-level
string amplitudes for various color orderings using double-color-ordered
amplitudes.
