math-to-code-mcp

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

With no annotations, the description carries the behavioral disclosure burden. It usefully discloses the numerical method and supported functions, and distinguishes signed integral from geometric area. It does not describe the return type, numerical accuracy, error behavior for unsupported inputs, or invalid intervals.

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

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

The description is two sentences and front-loads the purpose and method. The second sentence duplicates schema information, but it functions as a useful supported-function constraint rather than filler.

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

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

For a low-complexity computation tool with full schema coverage, the description is minimum viable. Because there are no annotations and no output schema, it should say more about the returned value, precision, and error handling for unsupported functions or invalid interval counts.

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

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

Schema description coverage is 100%, so the baseline is 3. The description repeats the supported function list and names Simpson's 1/3 rule, which implicitly relates to the intervals parameter, but it adds little meaning beyond the schema.

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

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

The description states a specific verb (Calculate), resource (definite integral / geometric area under a curve), and method (Simpson's 1/3 rule). It also lists supported functions, so the tool's scope is immediately clear. The sibling tools are unrelated, so explicit sibling differentiation is not necessary here.

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

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

The supported function list and signed-vs-geometric distinction give implied usage constraints. However, there is no explicit statement of when to use this tool versus alternatives or when not to use it, and no prerequisites are mentioned.

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

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

No annotations exist, so the description bears the full burden. It discloses the algorithmic behavior via the formula and names what is returned (base, offsets, terms, result), but says nothing about edge cases, negative integers, or error conditions. Adequate but incomplete for a computation tool.

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

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

Two compact sentences that lead with the purpose and pack the formula and return contents efficiently. Slightly dense but no wasted words.

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

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

With no output schema, the description usefully enumerates the return contents (base, offsets, terms, exact result), which is the key missing piece. The method and parameters are covered, though edge-case behavior remains unstated.

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

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

Schema coverage is 100%, so all three parameters are already documented. The description reinforces the meaning of N, a, b through the formula, adding marginal value, but does not add syntax or constraint detail beyond the schema. Baseline 3 applies.

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

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

States a specific verb and resource ('Multiply two integers') and names the exact method used, fully distinguishing it from siblings like prime_analyze and generate_java_algorithm. An agent can identify the operation without opening the schema.

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

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

The description explains what the tool does but gives no guidance on when to choose it over a plain multiplication or the sibling analytical tools. No exclusions, prerequisites, or alternative-selection criteria are provided.

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

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

No annotations are provided, so the description carries the full burden. It does disclose one genuinely non-obvious behavioral trait – that it returns fixed, reviewed templates and does not execute generated code – but says nothing about the return form (text vs. file), whether it can fail, or any auth/preconditions.

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

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

Two short sentences, both of which earn their place: the first states purpose, the second states the key behavioral caveat. Front-loaded with the action and free of filler.

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

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

With no output schema and no annotations, the description should clarify what is actually returned (a code string? a file? a path?) and any limits. It gestures at this ('returns fixed, reviewed templates') but leaves the return shape ambiguous, which is a meaningful gap for a generator tool.

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

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

With one parameter at 100% schema description coverage ('Algorithm identifier: gcd, is_prime, or factorial'), the schema already fully documents the input. The description only restates the bounded set ('supported mathematical algorithm') without adding format or fallback semantics, so the baseline 3 applies.

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

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

States a specific verb and resource ('Generate a Java implementation of a supported mathematical algorithm'), and the word 'supported' signals a bounded set matching the schema's values. It does not explicitly differentiate itself from siblings like common_base_multiply or prime_analyze, but the purpose is unambiguous.

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

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

There is no when-to-use guidance, no statement of when this tool is preferable to the sibling tools, and no prerequisites. The agent must infer the trigger condition entirely from the tool name and the schema's enumerated values.

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

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

With no annotations, the description carries the full behavioral burden. It usefully discloses domain boundaries beyond the schema — the supported range and that prime status is only defined for n >= 2 — which is genuinely additive. But it is silent on what happens for out-of-range inputs or n < 2 (e.g., is 1 prime? error?), and says nothing about performance for large composites.

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

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

Two tight sentences with zero waste. The core capability is front-loaded, and the domain constraint follows immediately as supporting detail.

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

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

There is no output schema, so the description must carry return-value semantics — and it only partially does. It says it returns the prime factorization, but leaves ambiguous what is returned for composite inputs, for n < 2, or for out-of-range values. Adequate for the core case but with a real gap for a tool whose output shape is undocumented.

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

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

Schema description coverage is 100% with a single integer parameter, so the schema already fully documents the accepted range. The description merely restates that range, adding no syntax or format detail beyond structured data. Baseline 3 applies when the schema does the heavy lifting.

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

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

The description states a specific verb+resource: 'Check whether an integer is prime and return its prime factorization.' An agent immediately knows this is a primality test plus factorization tool. The sibling tools (common_base_multiply, generate_java_algorithm) are unrelated, so no differentiation is needed.

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

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

Usage is implied by the description ('check whether an integer is prime'), and the domain constraints (range -10^12 to 10^12, prime status only for n >= 2) effectively define when the tool is applicable. However, there is no explicit when-to-use or when-not-to-use guidance and no alternatives to route to, since the siblings are unrelated.

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