Exercise 2.15.  Eva Lu Ator, another user, has also noticed the different 
intervals computed by different but algebraically equivalent expressions. She 
says that a formula to compute with intervals using Alyssa's system will 
produce tighter error bounds if it can be written in such a form that no 
variable that represents an uncertain number is repeated. Thus, she says, par2 
is a ``better'' program for parallel resistances than par1. Is she right? Why?

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Yes.

The correct lower bound of the result is the result of the calculation 
performed on the lower bounds of R₁ and R₂.
The correct upper bound of the result is the result of the calculation 
performed on the upper bounds of R₁ and R₂.

Analogous rules would hold for calculating any monotonically increasing 
function of a given parameter, regardless of how ofter that parameter 
might appear.

In this case, par2 happens to give the correct result.  Par1 goes wrong 
when it divides the upper bound of R₁R₂ by the lower bound of R₁+R₂, and 
vice-versa.  This is nonsense, as whatever the actual value of R₁ or R₂ 
might be, it cannot have more than one value at the same time.