In the subagent view, a financial precommitment another subagent has arranged for the sole purpose of coercing you into one course of action is a threat.
Plenty of branches of decision theory advise you to disregard threats because consistently doing so will mean that instances of you will more rarely find themselves in the position to be threatened.
Of course, one can discuss how rational these subagents are in the first place. The “stay in bed, watch netflix and eat potato chips” subagent is probably not very concerned with high level abstract planning and might have a bad discount function for future benefits and not be overall that interested in the utility he get from being principled.
I would argue that the precision should be capped at the lowest precision of the operands. In physics, if you add to lengths, 0.123m+0.123456m should be rounded to 0.246m.
Also, IEEE754 fundamentally does not contain information about the precision of a number. If you want to track that information correctly, you can use two floating point numbers and do interval arithmetic. There is even an IEEE standard for that nowadays.
Of course, this comes at a cost. While monotonic functions can be converted for interval arithmetic, the general problem of finding the extremal values of a function in some high-dimensional domain is a hard problem. Of course, if you know how the function is composed out of simpler operations, you can at least find some bounds.
Or you could do what physicists do (at least when they are taking lab courses) and track physical quantities with a value and a precision, and do uncertainty propagation. (This might not be 100% kosher in cases where you first calculate multiple intermediate quantities from the same measurement (whose error will thus not be independent) and continue to treat them as if they were. But that might just give you bigger errors.) Also, this relies on your function being sufficiently well-described in the region of interest by the partial derivatives at the central point. If you calculate the uncertainty of f(x,y)=xy for x=0.1±1, y=0.1±1 using the partial derivatives you will not have fun.