[ollyfg]

Wow, this makes a lot of sense. In what ways is this different to the way I was taught through school and university (that for a+-b * c+-d, the answer was (ab)+-sqrt( (b/a)^2) + (d/c)^2 )?

I can see that ((a-b) (c-d)+(a+b) * (c+d))/2 is different to a*b, and that makes sense when you think about it, but the second part is confusing me a bit.

Also, I'm a bit confused by your suggestion to break it down into cases, do you mean if an uncertainty is negative? Because at the moment I'm making all uncertainties positive, but if there are cases where negative ones are correct, I need to fix that up.

[spacehome]

The formula you cite is a back-of-the-envelope approximation that only works so long as c and d have much smaller magnitudes than a and b. (Try to derive that formula yourself. You'll find it pop up in a limit, but it's certainly not generally true.)

You also need to clear up your own confusion about what exactly you mean by "uncertainty". You seem to go back and forth between several different measures.

Uncertainties aren't negative. But solve the rest of the issues, and what I meant by cases should become more clear.