Question: Approximating expressions

Hello,

concerning this question

http://www.mapleprimes.com/questions/137333-Making-Specific-Calculation-Computable

I want to describe the problem differently: I start with a rational function (polynomial/polynomial) B in two indeterminates x,y which is already quite lengthy (about 80 lines on my worksheet) and want to perform several (algebraic) operations on it. For example differentiating, taking euclidean norms, divide... (see first two blocks of code in the link above). The result is a function f which i plug into a differential equation that is solved numerically then. The problem is that the expressions become extremely lengthy, often resulting in a

"[Length of output exceeds limit of 1000000]"

Because the final result is a plot of a solution of the differential equation, no exact values are needed. So what possibilities are there to make the expression more manageable? Approximate? How?