Equation 11 · 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 p_ir
r is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Symbol α
α is one of the signed contributions combined to compute the quantity on the left.
Symbol u_r
is one of the signed contributions combined to compute the quantity on the left.
Symbol β^top
β^top is one of the signed contributions combined to compute the quantity on the left.
Symbol x_ir
r is one of the signed contributions combined to compute the quantity on the left.
Symbol N
N is one of the signed contributions combined to compute the quantity on the left.
Symbol sigma_r^2
sigm 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 →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.
superscript
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
See an illustrated explanation →How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
A hierarchical model can represent repository effects: . where r indexes repositories and task characteristics. The estimate can then expose between-repository variance rather than hiding it inside a global mean. Bootstrap intervals should resample at relevant task-family or repository levels when generalization across those units is the target.
For background, read the article’s source list.
Return to How to Evaluate Codex Beyond SWE-bench and Vendor Scores