I would just like to mention that the main benefit of my formulae is that it does work for fermenting wort. For the well-attenuated beer, Terrill's and my result aren't too different. I would say they're within an experimental error.
I find the opposite to be true. I brew only Trappist style ales and my attenuation is routinely > 85%. Your calculations seem to overshoot my actuals by a wide margin, in some cases as high as -0.006 S.G. Points from actual. I’m fairly confident I have entered the calculations faithfully in my spreadsheet, as they match the calculators that use your equations.
For me, Terrill Cubic is king above 82% AA, and Terrill Linear for 78-82% AA.
I’ll also say that the above is true for values 4-6 points above final gravity as well, which is important for me as I use spunding.
Well, I have never seen so large difference between the two methods for fully-attenuated beers. Can you provide me with some of your data, I would like to check that out? The data that were used to get my formulae was from hundreds of samples, although the strongest was 18 P, therefore it is possible that for stronger beer it can be less accurate. Or it can be simply because of wort correction factor. What kind of value do you use?
In many cases, and I'm not saying it is your case, people misuse the refractometer and hydrometer. The wort correction factor is good example. I was quite lucky and my factor is 1.00, although it vary a lot, and I have friends that have 0.90 or even 1.1. If someone is using in good belief standard value of 1.04 it can be pretty far from the reality. A friend of mine has also a refractometer that he must calibrate on the water every single time before measurement. I just want to say that that cheap refractometers can be quite tricky to use accurately.
The accuracy itself is another issue. The hydrometer should be used with decarbonated wort only but not all of as do that. That can make difference order of 0.001 SG. Then there is a temperature, +-10F from calibration temperature can make +-0.001 SG. In case of the refractometer, they have usually accuracy around 0.2 Bx (0.001 SG) and into formulae you're feeding it twice. For beer before bottling it is often even worse, and the sample can be pretty fuzzy on refractometer's glass. So I would say, that you cannot expect the accuracy of FG from formulae to be better than 0.001-0.002 depending on particular circumstances, sometimes worse.
So, if all of these aspects are not ideal in some particular case, there is no point in chasing which formulae is better. In some cases, even worse formulae can give you better results if the input is not ideal it can cancel out some of that "non-ideality".
My formula is actually quite connected to Balling's formula that is widely used for its overall accuracy, although there could be cases when beer deviates from that formula, and there is no doubt about that even if it's less common than the other case.