> sym(0.0001575) - sym(1575)/sym(10000000)
That one tells us that the approximation of 0.0001575 by the symbolic toolbox is not the same as 1575/10000000 .
> fprintf('%.999g\n', 0.0001575)
... because the closest binary double precision representation to 0.0001575 is a number which is slightly larger than an exact fraction.
So if you use the symbolic toolbox carefully you can get the comparison to work out.
But the problem is not with "if": it has to do with the way that binary double precision numbers are represented. double() does not use decimal representation internally (IEEE has defined an equivalent decimal standard to the very common binary standard, but the only vendor that I know of that implements the decimal hardware, is IBM in their z90 series.)
This is a very common issue to have show up. When you compare two double precision numbers that have been calculated through different paths, you should always take into account precision limitations. For equality comparisons, use ismembertol() . Otherwise, instead of testing A <= B, test A <= B + tolerance