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.