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Why is the machine error/epsilon higher between a pair of two lower numbers than a pair of two high numbers? For example, between the two smallest numbers possible in 5 bit mantissa and the two largest numbers possible in a 5 bit mantissa. The error for the smallest pair is nearly twice as much as the largest pair?

Another way to phrase this question is why does the machine error differ across an interval?

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The potential error is the same in absolute terms for the same exponent.

But since the smaller numbers are about half the size of the larger numbers, the relative error is about twice as high for the smaller numbers.

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