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Apparently substituting variables with RIF numbers does not give Sage an easier time solving equations.

The trouble is that Sage uses Maxima for solving equations (by default).

The traceback shows that Sage has a problem converting RIF numbers into Maxima objects.

Here is a more self-contained example:

sage: var('x')
sage: solve(x + RIF(0.999,1.001) == 0, x)

I reported this as trac ticket #27314.