  Flame graphs are a popular way of representing profiling data. In this paper
we propose a possible mathematical definition of flame graphs. In doing so, we
gain some interesting algebraic properties almost for free, which in turn allow
us to define some operations that can allow to perform an in-depth performance
regression analysis. The typical documented use of a flame graph is via its
graphical representation, whereby one scans the picture for the largest
plateaux. Whilst this method is effective at finding the main sources of
performance issues, it leaves quite a large amount of data potentially unused.
By combining a mathematical precise definition of flame graphs with some
statistical methods we show how to generalise this visual procedure and make
the best of the full set of collected profiling data.
