  One common approach for solving collisions between protoplanets in
simulations of planet formation is to employ analytical scaling laws. The most
widely used one was developed by Leinhardt & Stewart (2012) from a catalog of ~
180 N-body simulations of rubble-pile collisions. In this work, we use a new
catalogue of more than 20,000 SPH simulations to test the validity and the
prediction capability of Leinhardt & Stewart (2012) scaling laws. We find that
these laws overestimate the fragmentation efficiency in the merging regime and
they are not able to properly reproduce the collision outcomes in the
super-catastrophic regime. In the merging regime, we also notice a significant
dependence between the collision outcome, in terms of the largest remnant mass,
and the relative mass of the colliding protoplanets. Here, we present a new set
of scaling laws that are able to better predict the collision outcome in all
regimes and it is also able to reproduce the observed dependence on the mass
ratio. We compare our new scaling laws against a machine learning approach and
obtain similar prediction efficiency.
