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

 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. 

NOTE:-

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Answers: 
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]] 
SEE COMPLETE ANSWER CLICK THE LINK 
https://matlabhelpers.com/questions/how-to-simplifying-a-very-long-symbolic-expression-by-automatically-introducing-temporal-variables-or-in-any-other-way.php

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