Consider the function
f: x -> sqrt(1 + x) - 1 at x = 1e-15.
We get:
f(x) = 4.44089209850062616e-16
or something around that, depending on the language.
This function involves the subtraction of a pair of similar numbers when x is near 0
and the results are significantly erroneous in this region. Using pow instead of sqrt
doesn't give better results.
A "good" answer is 4.99999999999999875... * 1e-16.
Can you modify f(x) to give a good approximation of f(x) in the neighbourhood of 0?
Note:
Don't round or truncate your results. See the testing function in Sample Tests:.