  We give an algorithm for reversion of formal power series, based on an
efficient way to implement the Lagrange inversion formula. Our algorithm
requires $O(n^{1/2}(M(n) + MM(n^{1/2})))$ operations where $M(n)$ and $MM(n)$
are the costs of polynomial and matrix multiplication respectively. This
matches the asymptotic complexity of an algorithm of Brent and Kung, but we
achieve a constant factor speedup whose magnitude depends on the polynomial and
matrix multiplication algorithms used. Benchmarks confirm that the algorithm
performs well in practice.
