  Field-theoretical calculations performed in an approximation scheme often
present a spurious dependence of physical quantities on some unphysical
parameters associated with the details of the calculation setup (such as, the
renormalization scheme or, in perturbation theory, the resummation procedure).
In the present article, we propose to reduce this dependence by invoking
conformal invariance. Using as a benchmark the three-dimensional Ising model,
we show that, within the derivative expansion at order 4, performed in the
nonperturbative renormalization group formalism, the identity associated with
this symmetry is not exactly satisfied. The calculations which best satisfy
this identity are shown to yield critical exponents which coincide to a high
accuracy with those obtained by the conformal bootstrap.
