I'm not a fan of this approach. I care that the values are close to what they should be. Sure, computing the interpolation by hand and putting those values in will allow me to be much tighter with the numbers, but what if we change the interpolation scheme in the future and therefore the numbers become meaningless - at least with using expected *exact* values, we know our interpolation is close...

I can see benefit to what you're suggesting, but I'm just not convinced that the exact value from bilinear interpolation is a better solution than the exact analytical value.