Symbol x
x is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Read this term in its guide →Published equation contexts
Why this formula appears here
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 . where u is the unit roundoff — roughly 10^{-16} for standard double precision — and is…
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Symbol y
y is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Read this term in its guide →Symbol delta
delta is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol u
the unit roundoff — roughly 10^{-16} for standard double precision — and is addition, subtraction, multiplication, or division.
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Read it with the definitions, units, and assumptions supplied by the article.
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Published contexts (1)
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Equation 1 · Mathematics
How Mathematics, Proof, and Scientific Computation Actually Work
This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.
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 . where u is the unit roundoff — roughly 10^{-16} for standard double precision — and is…
Meanings in this article
- : the unit roundoff — roughly 10^{-16} for standard double precision — and is addition, subtraction, multiplication, or division.