Equation 2 · Part 9 · What Claude's Capability Evaluations Actually Measure

Denominator: 1 + exp(a + b log t)

p(t) = \frac{1}{1 + \exp\left(a + b \log t\right)},

1 + \exp\left(a + b \log t\right)

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

1 + exp(a + b log t) occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Full expressionDenominator: 1 + exp(a + b log t)Article meaning

The passage around this formula

The method is a curve fit, not a lookup table, and stating it plainly exposes the assumption it rests on. For a task of human-expert duration t , METR fits a logistic curve to the model’s observed success rate across many tasks of varying length: $p(t) = \frac{1}{1 + \exp\left(a + b \log t\right)}$ . with b > 0 , so predicted success falls as human-equivalent task length grows. The reported time horizon $T_x$ 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…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

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