  We present Rico, a code designed to compute the ionization fraction of the
Universe during the epoch of hydrogen and helium recombination with an
unprecedented combination of speed and accuracy. This is accomplished by
training the machine learning code Pico on the calculations of a multi-level
cosmological recombination code which self-consistently includes several
physical processes that were neglected previously. After training, Rico is used
to fit the free electron fraction as a function of the cosmological parameters.
While, for example at low redshifts (z<~900), much of the net change in the
ionization fraction can be captured by lowering the hydrogen fudge factor in
Recfast by about 3%, Rico provides a means of effectively using the accurate
ionization history of the full recombination code in the standard cosmological
parameter estimation framework without the need to add new or refined fudge
factors or functions to a simple recombination model. Within the new approach
presented here it is easy to update Rico whenever a more accurate full
recombination code becomes available. Once trained, Rico computes the
cosmological ionization history with negligible fitting error in ~10
milliseconds, a speed-up of at least 10^6 over the full recombination code that
was used here. Also Rico is able to reproduce the ionization history of the
full code to a level well below 0.1%, thereby ensuring that the theoretical
power spectra of CMB fluctuations can be computed to sufficient accuracy and
speed for analysis from upcoming CMB experiments like Planck. Furthermore it
will enable cross-checking different recombination codes across cosmological
parameter space, a comparison that will be very important in order to assure
the accurate interpretation of future cosmic microwave background data.
