nearexact

Nearexact is a term used in numerical computation to describe a value that is not exactly equal to another value but is equal within a specified tolerance. It reflects that exact equality is often unattainable due to finite precision, rounding, and measurement error.

The term is a portmanteau of near and exact. It is not a formal standard; usage varies by field and the tolerance that is defined for comparisons.

A common formalization is |a - b| <= tol, with tol chosen as an absolute tolerance, a relative tolerance, tol_rel, or a combination. Relative tolerance uses tol_rel * max(|a|, |b|) to account for scale.

Applications include approximate equality tests in programming (for example, Python's isclose) and in numerical simulations where convergence is determined by a near-exact criterion. Data analysis and measurement workflows also rely on near-exact comparisons under noise.

Choosing a tolerance depends on units, scale, and the acceptable risk of incorrect decisions. Edge cases, NaN or infinity handling, and cross-platform floating-point behavior must be considered. The term remains informal; some see it as a synonym for isclose or tolerance-based matching.

Related concepts include isclose, epsilon, floating-point arithmetic, numerical tolerance, and approximate matching.