This can be considerably more efficient, because the two methods
sometimes share a considerable amount of code.

The prime example for this is the energy density of a degraded
elastic material with a spectral split.  In that situation,
both the gradient and the Hesse matrix implementations need
an eigenvector decomposition of the strain, which is quite
expensive.  With the new code, the eigenvector decomposition
is computed only once and used for both the gradient and
the Hesse matrix.