Thank you for the copy of the file. That went surprisingly smothly.
I am very glad I didn't try guess what kind of random file to show you.
For anyone who doesn't want to download the 52kbyte .rar compressed file which uncompresses to 20 mbytes, here is a sample of the head:
Element[{AV1, p, R, Rdot, \[Eta], etadot, \[Omega]}, Reals];
(0.` + 0.5` I) E^(I \[Eta]) etadot R + 0.5` E^(I \[Eta]) Rdot + (0.0005333333333` ((0.` + 0.5` I) E^(I \[Eta]) etadot R +
0.5` E^(I \[Eta])Rdot))/(-0.0005333333333` - (0.` + 1.` I) \[Omega])^2 + ((1.1001145919006453`*^9 + 0.` I) E^(
I \[Eta])p^4 R^3)/(((0.` - 0.0168942561` I) + 1.` \[Omega])^2 (-240.45040853881275` p^2 - (0.` +
244.26598709281276` I) p \[Omega] + 1.` \[Omega]^2)^2) + ((0.` + 2.0311153906021673` I) AV1 E^(
I \[Eta])p^2 R)/(((0.` - 0.0168942561` I) + 1.` \[Omega]) (-240.45040853881275` p^2 - (0.` +
244.26598709281276` I) p \[Omega] + 1.` \[Omega]^2)) - ((0.` + 1.2413088241018356`*^11 I) E^(
I \[Eta])p^7 R^3)/(((0.` - 0.00844712805` I) + 1.` \[Omega]) ((0.` + 0.0168942561` I) +
1.` \[Omega]) ((0.` - 121.63299354640638` I) p + 1.` \[Omega]) (-240.45040853881278` p^2 - (0.` +
244.26598709281276` I) p \[Omega] + 1.` \[Omega]^2)^2 (-240.45040853881275` p^2 + (0.` +
244.26598709281276` I) p \[Omega] + 1.` \[Omega]^2)) + ((8.817433435400575`*^10 + 0.` I) E^(
I \[Eta])p^6 R^3 \[Omega])/(((0.` - 0.00844712805` I) + 1.` \[Omega]) ((0.` + 0.0168942561` I) +
1.` \[Omega]) ((0.` - 121.63299354640638` I) p + 1.` \[Omega]) (-240.45040853881278` p^2 - (0.` +
244.26598709281276` I) p \[Omega] + 1.` \[Omega]^2)^2 (-240.45040853881275` p^2 + (0.` +
244.26598709281276` I) p \[Omega] + 1.` \[Omega]^2)) - ((0.` + 0.000010335972278911555` I) E^(
I \[Eta])p^5 R^3 \[Omega]^2)/(((0.` - 0.00844712805` I) + 1.` \[Omega]) ((0.` + 0.0168942561` I) +
1.` \[Omega]) ((0.` - 121.63299354640638` I) p + 1.` \[Omega]) (-240.45040853881278` p^2 - (0.` +
244.26598709281276` I) p \[Omega] + 1.` \[Omega]^2)^2 (-240.45040853881275` p^2 + (0.` +
244.26598709281276` I) p \[Omega] + 1.` \[Omega]^2)) + ((7.3419882135610845`*^-6 + 0.` I) E^(
I \[Eta])p^4 R^3 \[Omega]^3)/(((0.` - 0.00844712805` I) + 1.` \[Omega]) ((0.` + 0.0168942561` I) +
1.` \[Omega]) ((0.` - 121.63299354640638` I) p + 1.` \[Omega]) (-240.45040853881278` p^2 - (0.` +
244.26598709281276` I) p \[Omega] + 1.` \[Omega]^2)^2 (-240.45040853881275` p^2 + (0.` +
244.26598709281276` I) p \[Omega] + 1.` \[Omega]^2)) - ((0.` + 2.1516064511128958`*^-22 I) E^(
I \[Eta])p^3 R^3 \[Omega]^4)/(((0.` - 0.00844712805` I) + 1.` \[Omega]) ((0.` + 0.0168942561` I) +
1.` \[Omega]) ((0.` - 121.63299354640638` I) p + 1.` \[Omega]) (-240.45040853881278` p^2 - (0.` +
244.26598709281276` I) p \[Omega] + 1.` \[Omega]^2)^2 (-240.45040853881275` p^2 + (0.` +
244.26598709281276` I) p \[Omega] + 1.` \[Omega]^2)) + ((1.5283583177291376`*^-22 + 0.` I) E^(
I \[Eta])p^2 R^3 \[Omega]^5)/(((0.` - 0.00844712805` I) + 1.` \[Omega]) ((0.` + 0.0168942561` I) +
1.` \[Omega]) ((0.` - 121.63299354640638` I) p + 1.` \[Omega]) (-240.45040853881278` p^2 - (0.` +
244.26598709281276` I) p \[Omega] + 1.` \[Omega]^2)^2 (-240.45040853881275` p^2 + (0.` +
244.26598709281276` I) p \[Omega] + 1.` \[Omega]^2)) - ((0.` + 280.70399796437727` I) E^(I \[Eta])
p^6 R^3)/(((0.` - 0.0168942561` I) + 1.` \[Omega])^2 ((0.` + 0.0168942561` I) +
1.` \[Omega]) (-240.45040853881275` p^2 - (0.` + 244.26598709281276` I) p \[Omega] +
1.` \[Omega]^2)^2 (-240.45040853881275` p^2 + (0.` + 244.26598709281276` I) p \[Omega] +
1.` \[Omega]^2)) - ((2.2002291838012905`*^9 + 0.` I) E^(I \[Eta])p^4 R^3)/(((0.` - 0.0168942561` I) +
1.` \[Omega]) ((0.` + 0.0168942561` I) + 1.` \[Omega]) (-240.45040853881275` p^2 - (0.` +
244.26598709281276` I) p \[Omega] + 1.` \[Omega]^2) (-240.45040853881275` p^2 + (0.` +
244.26598709281276` I) p \[Omega] + 1.` \[Omega]^2)) - ((0.` + 3.610871796487759`*^8 I) E^(
I \[Eta])p^10 R^3)/(((0.` - 0.0168942561` I) + 1.` \[Omega]) (-240.45040853881275` p^2 - (0.` +
244.26598709281276` I) p \[Omega] + 1.` \[Omega]^2) (1.` p^4 +
1.0236710118812482` p^2 \[Omega]^2 + 0.000017296130818865636` \[Omega]^4)^2)
The rest of the twenty megabytes looks about the same as this.
ComplexExpand[Re[expression]] looks like it will probably roughly quadruple the size of the expression, octuple if you count the real and imaginary parts. Before and after is a forest of numerators and denominators of powers of powers of terms. There are a lot of identical denominators, but they are not all the same. For my little fragment Simplify was able to reduce the size by about a third and do that relatively quickly. But that is stacking up powers of variables even higher than they were originally and doesn't look promising when done with twenty megabytes and then hoping to equate terms and come up with the desired solution.
Hummm... The ability of rar to get a 400 fold compression ratio on the file says there is a stunning degree of repetition in that expression. If it were possible to get even 100 fold reduction in the size of that expression with Mathematica doing some delicate manipulation to take advantage of the repetition, but without putting the problem into a nearly insoluble form, then that might help dramatically. It might be interesting to see what the result of a Together done on each subset of the sum which shared a common denominator would be.
