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derivation_substitute

Substitute a variable in a formula with another expression to build complex formulas step by step, while documenting your reasoning and assumptions for transparent derivation.

Instructions

    代入操作(帶人類知識記錄)

    將公式中的變數替換為另一個表達式。
    這是組合公式的關鍵操作。

    ═══════════════════════════════════════════════════════════════════════
    ⚡ 每一步都可以加入人類知識!
    ═══════════════════════════════════════════════════════════════════════

    Args:
        variable: 要替換的變數名
        replacement: 替換的表達式
        in_formula: 在哪個公式中代入(預設為當前)
        description: 操作描述
        notes: 人類洞見(為什麼這樣做、觀察、警告)
        assumptions: 這步的假設條件
        limitations: 這步的限制

    Returns:
        代入結果(含記錄的知識)

    Example:
        derivation_substitute(
            variable="k",
            replacement="k_ref * exp(E_a/R * (1/T_ref - 1/T))",
            description="Apply Arrhenius equation for temperature dependence",
            notes="⚠️ 假設 V_max 遵循 Arrhenius,但酵素在 >42°C 會變性",
            assumptions=["Temperature range 32-42°C", "No enzyme denaturation"],
            limitations=["Not valid for high temperature"]
        )
    

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
notesNo
variableYes
in_formulaNo
session_idNo
assumptionsNo
descriptionNo
limitationsNo
replacementYes

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

Behavior3/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations provided, the description carries the full burden of behavioral disclosure. It mentions that every step can incorporate human knowledge and that the result includes 'recorded knowledge', implying persistence of a step. However, it does not state whether the operation mutates session state, whether it is reversible, or any side effects beyond the return value.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is well-structured with sections for explanation, callout, Args, Returns, and Example. The banner about human knowledge is visually prominent but somewhat gimmicky; otherwise, every sentence earns its place. Not overly long for an 8-parameter tool.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Description covers the operation, parameters, and return value sufficiently, and the example adds practical guidance. It does not explain session prerequisites or the precise return schema details, but an output schema exists and the description gives the essential context for invoking the tool correctly.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The schema has zero descriptions, so the description's Args section adds substantial meaning to 7 of the 8 parameters (e.g., variable, replacement, in_formula, notes, assumptions, limitations). It omits session_id entirely, which is a minor gap, but the provided example showcases all documented parameters in a realistic use case.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool replaces variables in a formula with another expression, which is a specific verb+resource operation. It also mentions 'with human knowledge recording' and 'key operation for combining formulas', which positions it distinctly from sibling operations like simplify or integrate.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description gives a clear context: 'This is the key operation for combining formulas', which tells the user when it is appropriate to use. It does not explicitly mention alternatives or when not to use it, but the context is clear enough for a derivation workflow.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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