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Updates last float exercise

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Andrew Cumming 2023-09-05 12:17:06 -04:00
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@ -62,9 +62,9 @@ The size of the roundoff error is set by the number of bits that we have availab
Consider the two forms of the function
$$f(x) = {1\over\sqrt{1+x^2}-x} = \sqrt{1+x^2}+x$$
$$f(x) = \sqrt{1+x^2}-x = {1\over \sqrt{1+x^2}+x}$$
One of these involves a subtraction, and one doesn't. Try evaluating and plotting these two expressions as a function of $x$. Which is more accurate? Do you see the effects of roundoff error at large values of $x$?
One of these involves a subtraction, and one doesn't. Try evaluating and plotting these two expressions as a function of $x$. Which is more accurate? Do you see the effects of roundoff error at large values of $x$? How do you explain the size of $x$ where roundoff error appears?
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