SICP Workout (2.15) Solution Summary: In-depth thinking interval error

SICP 2.15 is followed by the topic 2.14 , the topic 2.14 mentioned in the Alyssa design of the interval calculation module in the parallel resistor calculation will be faulted, The problem was discovered by Lem.

Then, a person called Eva also found the problem. At the same time she had more in-depth thinking.

Eva thinks. Suppose a formula can be written in a form in which a variable with non-accuracy does not recur. Then the Alyssa system will produce a tighter gauge of the interval.

Thus, she arguesthat the formula "1/(1/R1 + 1/r2)" is betterthan the formula "(R1*R2)/(R1 + R2)" When calculating parallel resistors.

The title asks us to see what Eva says is incorrect.

It's a little difficult to understand the meaning of the topic. The main thing is that I don't know what the "variable with non-accuracy" means here.

It's just that we can make an intuitive judgment based on the phenomena we observed in exercise 2.14.

We found in exercise 2.14 that the interval division of Alyssa would fail. Dividing the two intervals will enlarge the error.

Just, one noteworthy is that. When the formula "1/(1/R1 + 1/r2)" is implemented, Lem defines a range called one, with a value of (1 1). This is a definite interval. There is no error. Using it in Interval division is not an issue that will cause errors to widen.

For example one/(100 200). It is

(1 1)/(100 200)

+ (1 1) * (1/100 1/200)

+ (1/100 1/200)

The further calculation of one/(one/(100 200)) is

(1 1)/(1/100 1/200)

(1 1) * (100 200)

(100 200)

In other words, if we have defined interval one as (1 1), then one/(one/a) or a will not cause the problem of the interval error to become larger.

So, as mentioned in topic 2.15, using the one program Part2 is a better program.

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SICP Workout (2.15) Solution Summary: In-depth thinking interval error