You say 1/0 = INF, but the 754 standard says negative zero is different, and 1/(-0) = -INF. Yet it says -0 is numerically equal to 0. It also specifies that the square root of -0 is -0. This is neither straightforward nor common sense.

They also do not round to the nearest representable rational number. If you double MAXREAL, it will round to INF, even though MAXREAL is infinitely closer to 2*MAXREAL than INF is.

Despite efforts in the 2008 update to the 754 Standard, there still is no guarantee that the Standard will produce reproducible, bitwise identical results. The Standards committee admits this. It is important for everyone to understand the shortcomings of the Standard.