If we were to evaluate \( x\sim \pi \), then the second expression for \( f(x) \) can lead to potential losses of precision due to cancellations of nearly equal numbers.
This simple example demonstrates the loss of numerical precision due to roundoff errors, where the number of leading digits is lost in a subtraction of two near equal numbers. The lesson to be drawn is that we cannot blindly compute a function. We will always need to carefully analyze our algorithm in the search for potential pitfalls. There is no magic recipe however, the only guideline is an understanding of the fact that a machine cannot represent correctly all numbers.