I guess you'll find much of what you would like to know in these notes.

We give the first formal definition of the concept of simplification for general expressions in the context of Computer Algebra Systems. The main mathematical tool is an adaptation of the theory of Minimum Description Length, which is closely related to various theories of complexity, such as Kolmogorov Complexity and Algorithmic Information Theory. In particular, we show how this theory can justify the use of various “magic constants” for deciding between some equivalent representations of an expression, as found in implementations of simplification routines.

I guess you'll find much of what you would like to know in this 2004 paper by Jacques Carette (published here):

We give the first formal definition of the concept of simplification for general expressions in the context of Computer Algebra Systems. The main mathematical tool is an adaptation of the theory of Minimum Description Length, which is closely related to various theories of complexity, such as Kolmogorov Complexity and Algorithmic Information Theory. In particular, we show how this theory can justify the use of various “magic constants” for deciding between some equivalent representations of an expression, as found in implementations of simplification routines.