← Mathematical compendium

Published equation contexts

p(t)=xp(t) = x

Why this formula appears here

with b > 0 , so predicted success falls as human-equivalent task length grows. The reported time horizon TxT_x at success level x is then the duration at which the fitted curve crosses that threshold, i.e. the t solving p(t) = x . Two things follow directly from this formulation that a single reported number obscures: the curve, not the crossing point, is the actual result, and a different chosen threshold x produces a different headline number from the identical underlying data.

Read the full article-specific guide →

Read the representative guide

How to interpret it

Read it with the definitions, units, and assumptions supplied by the article.

Research cited beside this formula

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

p(t)=xp(t) = x

Equation 7 · Foundation Models

What Claude's Capability Evaluations Actually Measure

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

with b > 0 , so predicted success falls as human-equivalent task length grows. The reported time horizon TxT_x at success level x is then the duration at which the fitted curve crosses that threshold, i.e. the t solving p(t) = x . Two things follow directly from this formulation that a single reported number obscures: the curve, not the crossing point, is the actual result, and a different chosen threshold x produces a different headline number from the identical underlying data.

Meanings in this article

  • xx: then the duration at which the fitted curve crosses that threshold, i.
Equation guide → · Article →