[zmonx]

It is true that cancellation errors are often the source of wrong results.

However, computations involving IEEE floating point arithmetic can go horribly wrong even if there is no addition and no subtraction whatsoever, no divisions, and only a very small number of rounding errors. Here is one such example:

http://people.eecs.berkeley.edu/~wkahan/WrongR.pdf

Even professional users working in this domain will have a hard time to locate the cause of such problems involving IEEE floating point arithmetic. The format is extremely error-prone to use for casual users and experts alike.

[dragontamer]

Ehhh... I think that paper kinda "tricks" you with point #3.

> Only 257 algebraic operations, so no hordes of rounding errors

Rounding errors in Floating-point math grows exponentially in the common case. So 257 operations is more than enough to wipe out 53-bits of precision. Its not "hordes" of rounding errors that cause issues. Its the exponential nature of rounding errors, exponentially increasing every step of the way.

[zmonx]

Yes, that is true.