[問題] Codewars 6級數學題(可用Swift)

[pmove (熱臉迎人滿是傷)]

今天嘗試用Swift解難度6級的Floating-point Approximation (I)：
https://www.codewars.com/kata/58184387d14fc32f2b0012b2
結果只有測試資料Pass, 傳送過去就Fail了。
想了一個下午，最後只好看解答，
看了解答，我還是想不出來…為什麼？有人能明講，
這題解答的原理是什麼嗎？

題目很短，我順便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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→ pmove: 我想出來了，只用到簡單公式，（x+1) * (x-
→ pmove: 1) = x^2 - 1 ，討論區還有人說要用到泰勒
→ pmove: 展開式…笑死
→ pmove: 這題拿去問New Bing, 它可以解的出來喔，只
→ pmove: 是程式碼累贅了一點