maxima is 100 times slower than maple



Another speed up:  load(lrats) an replace subst with lratsubst.  Since ratsubst knows a  bit more about the meaning of expressions than
does subst, you'll need to decide it that's OK.
 
--Barton

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Using CRE expressions reduces the run time for the big loop in your code by a factor of about 3.  To do this, insert something
like

    f : rat(f)
   C[0] : rat(1/(2*pi^(3/2)*sqrt(rho[0, 0]*d)*m*sigma));

into your code
--Barton

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F