  Given a set of quantum gates and a target unitary operation, the most
elementary task of quantum compiling is the identification of a sequence of the
gates that approximates the target unitary to a determined precision
$\varepsilon$. Solovay-Kitaev theorem provides an elegant solution which is
based on the construction of successively tighter `nets' around the unity
comprised by successively longer sequences of gates. The procedure for the
construction of the nets, according to this theorem, requires accessibility to
the inverse of the gates as well. In this work, we propose a method for
constructing nets around unity without this requirement. The algorithmic
procedure is applicable to sets of gates which are diffusive enough, in the
sense that sequences of moderate length cover the space of unitary matrices in
a uniform way. We prove that the number of gates sufficient for reaching a
precision $\varepsilon$ scales as $ \log (1/\varepsilon )^{\log 3 / log 2} $
while the pre-compilation time is increased as compared to thatof the
Solovay-Kitaev algorithm by the exponential factor 3/2.
