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The passage around this formula

Computers represent real numbers with a finite number of bits, following a specification — IEEE 754 — that fixes the format and the rounding behavior of arithmetic exactly enough that different compliant hardware and software give reproducible results for the same operations [ 5 ] . The standard’s core guarantee is deceptively narrow: each individual elementary operation is correctly rounded , meaning the result is the closest representable floating-point number to the true mathematical result of that one operation. For a single addition or multiplication, this means $\mathrm{fl}(x \mathbin{\text{op}} y) = (x \mathbin{\text{op}} y)(1 + \delta), \qquad |\delta| \le u$. where u is the unit roundoff — roughly 10^{-16} for standard double precision — and $\mathrm{op}$ is…

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