To make the problem short let's say I want to compute expression: a / (b - c) on float's.

To make sure the result is meaningful, I can check if 'b' and 'c' are inequal:

float eps = std::numeric_limits<float>::epsilon();
if ((b - c) > EPS || (c - b) > EPS)
{
    return a / (b - c);
}

but my tests show it is not enough to guarantee either meaningful results nor not failing to provide a result if it is possible.

Case 1: a = 1.0f; b = 0.00000003f; c = 0.00000002f;

Result: The if condition is NOT met, but the expression would produce a correct result 100000008 (as for the floats' precision).

Case 2: a = 1e33f; b = 0.000003; c = 0.000002;

Result: The if condition is met, but the expression produces not a meaningful result +1.#INF00.

I found it much more reliable to check the result, not the arguments:

const float INF = numeric_limits<float>::infinity();
float x = a / (b - c);
if (-INF < x && x < INF)
{
     return x;
}

But what for is the epsilon then and why is everyone saying epsilon is good to use?