ComplexityFunction

ComplexityFunction
is an option for Simplify and other functions which gives a function to rank the complexity of different forms of an expression.

With the default setting ComplexityFunction->Automatic, forms are ranked primarily according to their LeafCount, with corrections to treat integers with more digits as more complex.

Simplify applies f to each intermediate expression generated by Simplify, treating the one which yields the smallest numerical value as simplest.

The default ComplexityFunction counts the subexpressions and digits of integers:

LeafCount counts only the number of subexpressions:

By default this expression is not simplified:

This complexity function makes ChebyshevT more expensive than other functions:

The default ComplexityFunction counts the subexpressions and digits of integers:

Out[1]=

LeafCount counts only the number of subexpressions:

Out[2]=

By default this expression is not simplified:

Out[1]=

This complexity function makes ChebyshevT more expensive than other functions:

Out[3]=

With the default ComplexityFunction, Abs[x] is simpler than the FullForm of -x:

This complexity function counts characters in the InputForm of the expression:

Now -x is simpler than Abs[x]:

The automatic complexity function: