Simplifying a very long symbolic expression by automatically introducing temporal variables or in any other way

Question

After attempting to solve a symbolic math problem, I got an expression with about 17000 characters. I am using the symbolic toolbox for Matlab, but I am open to any suggestion (Mathematica, whatever).

For obvious reasons, I won't copy-paste the expression straight into the question. Here is a link instead.

Running the Matlab commands simplify and simple, and even attempts to collect didn't improve the situation (Some got it worse).

But I am wondering, I don't care if the expression is evaluated in steps, with temporal parameters. Something like:

 z1 = a^2*y1;
 %Now the expression can be simplified by using z1 as alias!
 z1+z1^2 ....

Is there an automatic method to get such a step-by-step simplification with temporal variables? Also, any other method that you can think of is plausible.

Answer 1

Might try common subexpression elimination (CSE). Here is an example cribbed from

Get mathematica to simplify expression with another equation

InputForm[Experimental`OptimizeExpression[(3 + 3*a^2 + Sqrt[5 + 6*a + 5*a^2] +
      a*(4 + Sqrt[5 + 6*a + 5*a^2]))/6]]

==>

Out[206]//InputForm=
Experimental`OptimizedExpression[Block[{Compile`$1, Compile`$3, Compile`$4, 
   Compile`$5, Compile`$6}, Compile`$1 = a^2; Compile`$3 = 6*a; 
   Compile`$4 = 5*Compile`$1; Compile`$5 = 5 + Compile`$3 + Compile`$4; 
   Compile`$6 = Sqrt[Compile`$5]; (3 + 3*Compile`$1 + Compile`$6 + 
     a*(4 + Compile`$6))/6]]