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The following photo is a part of a paper(Quicker than Quickhull by Nam-Du ̃ng Hoang et al) and it is about the orient operator of three points in a plain that uses the cross-product.

enter image description here

It is said that the numerical stability of (4) is worse than (2) and (3), in general. From the resources found on the Internet, I can expect as it is said, but I do not know why it is exactly.

Decimal point operation is not very accurate when it comes to computation by computers. Could anyone please explain (or compare the (2)~(4) equations) what exactly happens in terms of numerical stability?

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