Not what you ask for, and I didn't completely solve it when I saw it a few days ago, but I think it's reasonably solvable by hand. I would first make the search space a lot smaller by assuming that b/c and gh/i are integers (hm, I think they must be, as you cannot end up with an integer by adding just two fractions that have different integer denominators)

And of course, simplify -11 ... -10 to -21. Then, taking out a factor of 12 might help:

  a + 13 * b / c + d + 12 * e - f - 11 + g * h / i - 10
  = 12 * (b/c + e - 2) + (a + b/c + d - f + g * h / i + 3)
  = 12 * x + y

Now I would guess that y is positive (may be not too hard to prove) and x equals 4 or 5. If that leads to a dead end, work your way down for values of x.