OK, the problem was a logical error in solve_linear that only showed
up because it of the order terms were being processed in an
expression. Since dummy variables were being used, sometimes the x
would get processed before the y in something like x + y + sqrt(x) and
sometimes the y would get processed first. The logical error was in
the processing that occurred after the linear term was identified.

Conclusion: hashing affected the ordering of terms which helped to
bring to the surface a logical error in the code.

The problem has now been fixed. With this fixed, 1694 offers a solver
that is more robust in single equations and systems of equations. See
issue 1694 for more details.

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