Something slightly wrong with weapons NW (in General)

I present to you, the case of
An Elven Long Bow [6x5309] (+0) - $41,394,465

Blacksmith cost is $7798 per 1x
5,309 * $7,798 = $41,399,582
On top of the supposed $522 base NW, it should be $41,400,104
Sure, it's not missing much, but one can only assume it's the cause of several other measurement errors.
And I can only assume the rest of the weapons share a similar problem.

The reason for this is that I tried to find a formula for the PTH upgrade curve (for the ELBow in particular, but for all weapons in general), and I was hitting on quite a bit of discrepancies, especially in the lower ranges of PTH NW added.

Do remember base ELBs at 522 NW are x1 +0.

Oh... right... so it should be

(5,309-1) * $7,798 + $522 then...
= $41,392,306 calculated
still not quite
= $41,394,465 displayed

So you found a 2,159 difference, calculating this would become a 0.005% difference. big deal...

I think the difference is related to the change from exponential X to linear X prices.

The problem is when you calculate based on this and therefore display incorrect upgrade values of weapon PTH, thus making plotting a trend line (i.e. reverse-engineering the upgrade cost FORMULA) harder.
I guess it doesn't matter ALL that much... but still, the smallest discrepancy signals something.

Well, anyway, if you plot just the numbers you can see in the ELB PTH columns in the wiki, you will very soon notice that there are groups of PTH values which seem to go after a curve, then another group goes on a similar curve but either higher or lower, and there are several other points with "issues".
I guess that's mostly human error though, since they're LARGE discrepancies, not the puny ~2k CB$ I see on my weapon.

Still, it annoys me when I can't get a proper formula for something, especially when you KNOW there is a formula... with experimental data, it's something else, there you know the errors are from measurements or turbulences... here you know all results are precisely as output by a clear formula.

Why not grab any weapon without any + value and upgrade it point by point while noting the upgrade cost and NW it becomes. Should give you 100% true values...

Cashflow issues, obviously :)