← Mathematical compendium

Published equation contexts

Ttotal=Tparent+∑i=1kTsubagenti,Tparent≪∑i=1kTsubagentiT_{\mathrm{total}} = T_{\mathrm{parent}} + \sum_{i=1}^{k} T_{\mathrm{subagent}_i}, \qquad T_{\mathrm{parent}} \ll \sum_{i=1}^{k} T_{\mathrm{subagent}_i}

Why this formula appears here

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…

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TtotalT_{\mathrm{total}}

Symbol T_total

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

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TparentT_{\mathrm{parent}}

Symbol T_parent

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

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ii

Symbol i

i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

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kk

Symbol k

k appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

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TsubagentiT_{\mathrm{subagent}_i}

Symbol T_subagent_i

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

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i=1i=1

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.

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kk

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.

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i=1i=1

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.

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kk

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.

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How to interpret it

Read it with the definitions, units, and assumptions supplied by the article.

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.

Ttotal=Tparent+∑i=1kTsubagenti,Tparent≪∑i=1kTsubagenti.T_{\mathrm{total}} = T_{\mathrm{parent}} + \sum_{i=1}^{k} T_{\mathrm{subagent}_i}, \qquad T_{\mathrm{parent}} \ll \sum_{i=1}^{k} T_{\mathrm{subagent}_i}.

Equation 1 · AI Agents & Systems

Why Claude Code Delegates to Subagents, and What That Actually Buys You

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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…

Equation guide → · Article →