Equation 20 · How to Evaluate Codex Beyond SWE-bench and Vendor Scores
What does this equation mean?
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.
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.
Read it piece by piece
Symbol i
i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Symbol p_i
is one of the signed contributions combined to compute the quantity on the left.
Symbol v_i
the value of correctly completing task i , direct inference and infrastructure cost, human specification and review cost, and loss from an accepted failure.
Symbol C_i
is one of the signed contributions combined to compute the quantity on the left.
Symbol H_i
is one of the signed contributions combined to compute the quantity on the left.
Symbol L_i
is one of the signed contributions combined to compute the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
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.
Starting index or lower bound: i
This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.
How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Let be the value of correctly completing task i , direct inference and infrastructure cost, human specification and review cost, and loss from an accepted failure. Expected net value is . where is the probability a failure escapes detection and is accepted. A high resolve rate can have negative utility if it requires extreme review or creates rare, expensive escapes. A lower autonomous rate can be valuable if the system reliably identifies useful partial progress and makes review cheap.
For background, read the article’s source list.
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