SICP Exercise 2.15

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?

 SOLUTION

 Eva Lu Ator is right. We can see in the solution to exercise 2.14 that the system will produce tighter error bounds if we minimize the repetition of intervals. So par2 is a better program than par1.

We can also see from the examples in the solution to exercise 2.14 that expressions that use the same interval everywhere also produce larger error bounds with more repetitions of the interval.

In real-world engineering problems that involve complex arithmetic expressions, it may not always be possible to avoid repeating variables which represent uncertain numbers.

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