  We present an update of our previous work, necessitated by availability of a
significantly improved dataset. The work is a model-independent analysis of the
cosmological supernova (Type Ia) data, where function families are fit to the
data in form of luminosity distance as function of redshift, that is,
$d_{L}(z)$; and subsequently time-derivatives of the scale function $a(t)$ are
$analytically$ derived, but as functions of $z$, without making assumptions
about of gravity or the contents of the universe. This gives, e.g. the redshift
value at which the universe goes over from deceleration to acceleration, as
$z_{t}=0.54 \pm 0.04$ for a flat universe. In the update, we switch to a more
modern fit criterion and also take into account the uncertainty in the
calibration of the SNIa luminosities.
  If a theory of gravity $is$ assumed, our results allow determination of the
density of the universe as function of $z$, from which conclusions about the
contents of the universe can be drawn. We update the previous work's result
where this was done for Einstein gravity, finding a lower-limit on the dark
energy fraction, $\Omega_{DE}>0.46$; and here we do this also for Starobinsky
gravity, where we can find a Starobinsky parameter that can eliminate the need
for dark energy.
