  We establish a quantitative approximation formula of the Lyapunov exponent of
a rational function of degree more than one over an algebraically closed field
of characteristic $0$ that is complete with respect to a non-trivial and
possibly non-archimedean absolute value, in terms of the multipliers of
periodic points of the rational function. This quantifies both our former
convergence result over general fields and the one-dimensional version of
Berteloot--Dupont--Molino's one over archimedean fields.
