Symbol q
q is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Read this term in its guide →Published equation contexts
Why this formula appears here
Holding = q constant across the trajectory — a simplification, since real failure rates are neither constant nor independent — the expected extra cost from retries is , and because increases with i , that extra cost is weighted toward the trajectory’s most expensive, latest steps rather than distributed evenly across it. A one-percent per-step retry rate is a rounding error at step five. Applied at step two hundred of an uncached or lightly cached loop, it is a rounding error on a much larger number.
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Symbol i
i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Read this term in its guide →Symbol c_i
is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Read this term in its guide →Denominator: 1-q
The complete quantity below the fraction bar; it must be nonzero for this division.
Read this term in its guide →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.
Read this term in its guide →How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction.
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.
Equation 31 · AI Agents & Systems
The Economics and Physical Limits of Running AI Agents at Scale
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Holding = q constant across the trajectory — a simplification, since real failure rates are neither constant nor independent — the expected extra cost from retries is , and because increases with i , that extra cost is weighted toward the trajectory’s most expensive, latest steps rather than distributed evenly across it. A one-percent per-step retry rate is a rounding error at step five. Applied at step two hundred of an uncached or lightly cached loop, it is a rounding error on a much larger number.
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