Equation 1 · Part 4 · How Mathematics, Proof, and Scientific Computation Actually Work

Symbol u

\mathrm{fl}(x \mathbin{\text{op}} y) = (x \mathbin{\text{op}} y)(1 + \delta), \qquad |\delta| \le u,

u

What this part means

the unit roundoff — roughly 10^{-16} for standard double precision — and $\mathrm{op}$ is addition, subtraction, multiplication, or division.

Its job in the formula

u is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol uArticle meaning

Where the article explains it

where u is the unit roundoff — roughly 10^{-16} for standard double precision — and $\mathrm{op}$ is addition, subtraction, multiplication, or division.

The passage around this formula

…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 addition, subtraction, multiplication, or division. Each single step, in other words, is correct up to a tiny, precisely bounded relative error.

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

[5] IEEE 754-2019 — IEEE Standard for Floating-Point Arithmetic ↗

These citations provide research context; check each source for the exact claim it supports.