  Binary population synthesis (BPS) modelling is a very effective tool to study
the evolution and properties of close binary systems. The uncertainty in the
parameters of the model and their effect on a population can be tested in a
statistical way, which then leads to a deeper understanding of the underlying
physical processes involved. To understand the predictive power of BPS codes,
we study the similarities and differences in the predicted populations of four
different BPS codes for low- and intermediate-mass binaries. We investigate
whether the differences are caused by different assumptions made in the BPS
codes or by numerical effects. To simplify the complex problem of comparing BPS
codes, we equalise the inherent assumptions as much as possible. We find that
the simulated populations are similar between the codes. Regarding the
population of binaries with one WD, there is very good agreement between the
physical characteristics, the evolutionary channels that lead to the birth of
these systems, and their birthrates. Regarding the double WD population, there
is a good agreement on which evolutionary channels exist to create double WDs
and a rough agreement on the characteristics of the double WD population.
Regarding which progenitor systems lead to a single and double WD system and
which systems do not, the four codes agree well. Most importantly, we find that
for these two populations, the differences in the predictions from the four
codes are not due to numerical differences, but because of different inherent
assumptions. We identify critical assumptions for BPS studies that need to be
studied in more detail.
