Equation 1 · Why Claude Code Delegates to Subagents, and What That Actually Buys You
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 T_total
otal is part of the quantity the equation computes from the expression on the right.
Symbol T_parent
arent is one of the signed contributions combined to compute the quantity on the left.
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 k
k appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Symbol T_subagent_i
ubagen 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 →Starting index or lower bound: i=1
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.
Ending index or upper bound: k
This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.
Starting index or lower bound: i=1
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.
Ending index or upper bound: k
This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.
How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
This is the specific problem a subagent is built to solve, and Claude Code’s own documentation gives a concrete, numeric illustration of the effect rather than an abstract claim about it. In a worked session example, a subagent delegated to research a piece of session-timeout handling reads three files totalling 6,100 tokens of raw source, entirely inside its own isolated window — “None of this touches your main context,” the documentation notes of the reads — and returns a single 420-token summary to the parent conversation, which the documentation flags directly: “That’s the context savings” [ 2 ] . The parent’s window absorbs an addition roughly a fourteenth the size of what was actually…
Read the full surrounding passage
This is the specific problem a subagent is built to solve, and Claude Code’s own documentation gives a concrete, numeric illustration of the effect rather than an abstract claim about it. In a worked session example, a subagent delegated to research a piece of session-timeout handling reads three files totalling 6,100 tokens of raw source, entirely inside its own isolated window — “None of this touches your main context,” the documentation notes of the reads — and returns a single 420-token summary to the parent conversation, which the documentation flags directly: “That’s the context savings” [ 2 ] . The parent’s window absorbs an addition roughly a fourteenth the size of what was actually read. Put as a simple accounting identity, isolation does not shrink the total amount of computation a system performs; it relocates where that computation’s output lands: . The parent conversation’s occupied share of its own window, , stays small and bounded even as the total work performed across k delegated subagents grows without bound. That inequality is the real content behind the phrase “context savings” — the saving is measured in the one window that has to keep attending to everything else in the task, not in total tokens billed.
Sources cited in the surrounding passage
These citations give research context. Read each source to check which claims it supports.
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