  The partition function of the symmetric (zero electric field) eight-vertex
model on a square lattice can be formulated either in the original "electric"
vertex format or in an equivalent "magnetic" Ising-spin format. In this paper,
both electric and magnetic versions of the model are studied numerically by
using the Corner Transfer Matrix Renormalization Group method which provides
reliable data. The emphasis is put on the calculation of four specific critical
exponents, related by two scaling relations, and of the central charge. The
numerical method is first tested in the magnetic format, the obtained
dependencies of critical exponents on model's parameters agree with Baxter's
exact solution and weak universality is confirmed within the accuracy of the
method due to the finite size of the system. In particular, the critical
exponents $\eta$ and $\delta$ are constant as required by weak universality. On
the other hand, in the electric format, analytic formulas based on the scaling
relations are derived for the critical exponents $\eta_{\rm e}$ and
$\delta_{\rm e}$ which agree with our numerical data. These exponents depend on
model's parameters which is an evidence for the full non-universality of the
symmetric eight-vertex model in the original electric formulation.
