  Aims. We present further development of the rolling root mean square (rRMS)
algorithm. These improvements consist of an increase in computational speed and
an estimation of the uncertainty on the recovered diagnostics. This improvement
is named the cross root mean square (xRMS) algorithm.
  Methods. We used the quantile method to recover the statistics of the line
profiles in order to study the evolution of the prominence observed by IRIS on
1 October 2019. We then introduced the improvements to rRMS. These improvements
greatly increased the computational speed, and this increase in speed allowed
us to use a large model grid. Thus, we utilised a grid of 23 940 models to
recover the thermodynamic diagnostics. We used the 'good' (but not 'best')
fitting models to recover an estimate of the uncertainty on the recovered
diagnostics.
  Results. The maximum line-of-sight (LOS) velocities were found to be 70 km/s.
The line widths were mostly 0.4 {\AA} with the asymmetries of most pixels
around zero. The central temperature of the prominence was found to range from
10 kK to 20 kK, with uncertainties of approximately +/-5 to +/-15 kK. The
central pressure was around 0.2 dyn/cm2, with uncertainties of +/-0.2 to +/-0.3
dyn/cm2. The ionisation degree ranged from 1 to 1000, with uncertainties mostly
in the range +/-10 to +/-100. The electron density was mostly 10^10 /cm3, with
uncertainties of mostly +/-10^9.
  Conclusions. The new xRMS algorithm finds an estimation of the errors of the
recovered thermodynamic properties. To our knowledge, this is the first attempt
at systematically determining the errors from forward modelling. The large
range of errors found may hint at the degeneracies present when using a single
ion and/or species from forward modelling. In the future, co-aligned
observations of more than one ion and/or species should be used to attempt to
constrain this problem.
