Criterion for applying variable substitution

The following enumerates a few of the points to be considered when designing a variable substitution scheme.

1. Minimize the number of levels of substitution. Ideally this should not be more than [tex2html_wrap5808].
2. Avoid unnecessary substitutions. In eq:integral, substituting a variable for the entire right-hand side is redundant.
3. Use a complexity measure that determines when an expression is sufficiently complex to warrant variable substitution. This measure should capture the following properties of an expression:
   1. Complexity of a math object considered by itself.
   2. Relative complexity of an expression with respect to its parent.