作者pmove (热脸迎人满是伤)
看板MacDev
标题[问题] Codewars 6级数学题(可用Swift)
时间Tue Dec 13 19:23:39 2022
今天尝试用Swift解难度6级的Floating-point Approximation (I)：
https://www.codewars.com/kata/58184387d14fc32f2b0012b2
结果只有测试资料Pass, 传送过去就Fail了。
想了一个下午，最後只好看解答，
看了解答，我还是想不出来…为什麽？有人能明讲，
这题解答的原理是什麽吗？
题目很短，我顺便Po在下面：
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 neighborhood
of 0?
Note:
Don't round or truncate your results. See the testing function in Sample
Tests:.
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1F：→ pmove: 我想出来了，只用到简单公式，（x+1) * (x- 1.161.9.149 12/13 20:49
2F：→ pmove: 1) = x^2 - 1 ，讨论区还有人说要用到泰勒 1.161.9.149 12/13 20:49
3F：→ pmove: 展开式…笑死 1.161.9.149 12/13 20:49
4F：→ pmove: 这题拿去问New Bing, 它可以解的出来喔，只 1.161.38.179 03/26 10:12
5F：→ pmove: 是程式码累赘了一点 1.161.38.179 03/26 10:12