Why IDL have different value in same expression?

I'm doing some image processing with IDL, and it required a high-precision. But when I debug my colleague's program, I find some thing strange:

IDL> lat,y_res
   45.749001
   0.00026999999
IDL> lat - findgen(10)*y_res + y_res * 0.5 + findgen(10)*y_res + y_res * 0.5
   45.749268       45.749268       45.749268       45.749268 ...      45.749268
IDL> lat - (findgen(10)*y_res + y_res * 0.5) + (findgen(10)*y_res + y_res * 0.5)
   45.749001       45.749001       45.749001       45.749001 ...

Just as code above, I don't know why the two results have different value? My IDL version is 8.3 with ENVI package.

Solution

TriskalJM is correct. If you look at your parentheses in the second expression, you are grouping your terms differently. This will always happen with floating-point arithmetic in any computer language, just due to roundoff errors. If you want a more information, you could consult: http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

In the meantime, I would recommend that you switch to double-precision:

lat - dindgen(10)*y_res + y_res * 0.5 + dindgen(10)*y_res + y_res * 0.5