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Equation 15 · Building a Custom Evaluation Suite for a Production Agent

What does this equation mean?

Bday=k1n1c1+k2n2c2.B_{\text{day}} = k_1 n_1 c_1 + k_2 n_2 c_2 .

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

Inputs and operationsk_1 n_1 c_1 + k_2 n_2 c_2
Result or conditionB_day
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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BdayB_{\text{day}}

Symbol B_day

BdB_day is part of the quantity the equation computes from the expression on the right.

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k1k_1

Symbol k_1

k1k_1 is one of the signed contributions combined to compute the quantity on the left.

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n1n_1

Symbol n_1

n1n_1 is one of the signed contributions combined to compute the quantity on the left.

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c1c_1

Symbol c_1

c1c_1 is one of the signed contributions combined to compute the quantity on the left.

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k2k_2

Symbol k_2

k2k_2 is one of the signed contributions combined to compute the quantity on the left.

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n2n_2

Symbol n_2

n2n_2 is one of the signed contributions combined to compute the quantity on the left.

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c2c_2

Symbol c_2

c2c_2 is one of the signed contributions combined to compute the quantity on the left.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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addition

addition

Add the term after the plus sign to the term or group before it.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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How to interpret it

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What the article says around this equation

The practical answer most teams converge on is a tiered budget, and it is worth writing the tiering down as an explicit equation rather than an implicit habit, because an implicit habit is what quietly erodes into “we stopped running the full suite” a few months in. If every merge triggers a cheap smoke tier of n1n_1 tasks at unit cost c1c_1 , run k1k_1 times a day, and a slower, more thorough tier of n2n_2 tasks at unit cost c2c_2 , run only k2k_2 times a day, the daily evaluation bill is simply Bday=k1n1c1+k2n2c2B_{\text{day}} = k_1 n_1 c_1 + k_2 n_2 c_2 . The first term is the per-merge tax — it has to stay small enough that engineers do not start skipping it, which is the single most common way a CI gate quietly stops functioning. The…
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The practical answer most teams converge on is a tiered budget, and it is worth writing the tiering down as an explicit equation rather than an implicit habit, because an implicit habit is what quietly erodes into “we stopped running the full suite” a few months in. If every merge triggers a cheap smoke tier of n1n_1 tasks at unit cost c1c_1 , run k1k_1 times a day, and a slower, more thorough tier of n2n_2 tasks at unit cost c2c_2 , run only k2k_2 times a day, the daily evaluation bill is simply Bday=k1n1c1+k2n2c2B_{\text{day}} = k_1 n_1 c_1 + k_2 n_2 c_2 . The first term is the per-merge tax — it has to stay small enough that engineers do not start skipping it, which is the single most common way a CI gate quietly stops functioning. The second term is the trust budget — infrequent, thorough, and the number that should scale up before a release rather than on every keystroke. Braintrust’s continuous-evaluation documentation reports exactly this kind of tiering in its online-scoring guidance: score at somewhere between one and ten percent of traffic for high-volume applications, but score one hundred percent of traffic for flows judged critical enough that a missed regression is unacceptable [ 7 ] . That sampling rate is itself a budget decision made the same way — a cheap, wide net most of the time, and a full, expensive check only where the cost of missing something is highest. Writing the split down as two explicit numbers, rather than letting it happen ad hoc, is what keeps the fast tier fast enough to actually run on every change and the slow tier honest enough to actually catch what the fast tier cannot.

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