The energy variance extrapolation method consists in relating the approximate
energies in many-body calculations to the corresponding energy variances and
inferring eigenvalues by extrapolating to zero variance. The method needs a
fast evaluation of the energy variances. For many-body methods that expand the
nuclear wave functions in terms of deformed Slater determinants, the best
available method for the evaluation of energy variances scales with the sixth
power of the number of single-particle states. We propose a new method which
depends on the number of single-particle orbits and the number of particles
rather than the number of single-particle states. We discuss as an example the
case of 4He using the chiral N3LO interaction in a basis consisting up to
184 single-particle states.Comment: 16 pages, 2 figure