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

With no annotations, the description carries the full behavioral burden and discloses the key side effect: text is written to a local log only and never transmitted elsewhere. It does not cover log location, permissions, or return behavior, but the critical data-handling trait is stated.

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 efficient sentences. The primary purpose and trigger conditions are front-loaded, and the second sentence adds essential behavioral context without waste.

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 simple two-parameter feedback tool with no output schema and no annotations, the description covers purpose, usage triggers, and data handling adequately. It could be slightly more complete by clarifying whether feedback should also be given when verify finds issues, but the core context is sufficient.

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%, and the schema already documents both context and message thoroughly. The description adds no parameter-specific syntax, format, or constraints beyond what the schema provides, so the baseline of 3 is appropriate.

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 and target: reporting a problem to the operator. It also specifies the exact triggering conditions tied to the sibling tool solve, making it easy to distinguish from computational siblings like solve, verify, and poly_roots.

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?

It clearly says when to use the tool: when solve hits a dead end, returns an error, or produces something believed wrong. It does not state when not to use it or name explicit alternatives, but the contextual guidance is strong and actionable.

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 load and does well: it discloses determinism/reproducibility, the Krawczyk certification with strict error boxes, exclusion of complex roots, and the honorPaid licensing declaration. It omits failure behavior for malformed or non-polynomial input and does not explain that honorPaid is not present in the declared input schema, which is a notable gap.

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?

Front-loaded with the core purpose and scope, then the coefficient-ordering convention and the licensing note. Four sentences with little waste, though the honorPaid sentence is longer than the information warrants.

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?

No output schema exists, so the description must cover returns; it explains the certificate and error box but not the shape of the result (list of roots? objects with bounds?). It also never reconciles the honorPaid parameter with a schema that lacks it, leaving the agent unsure how to satisfy the licensing requirement.

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% and the schema already documents coefficients ordering and tolerance defaults, so the description's repetition of the [1,-2,-5,6] example adds no new meaning. The only novel parameter information is honorPaid, which is not in the schema at all, creating ambiguity rather than usable semantics.

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 – returning all real roots of a polynomial – plus the scope qualifier that complex roots are excluded and roots are certified by Krawczyk with a strict error box. It does not explicitly compare itself to siblings like solve or verify, so an agent still has to infer the boundary between this and a general solver.

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?

It advises use 'instead of letting a general language model estimate roots', which implies when to reach for it, but gives no when-not guidance and never names the sibling solve/verify tools it should be preferred over or combined with. Requirements and prerequisites for input are not stated.

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 supplied, so the description carries full burden and does so richly: determinism/reproducibility ('identical input always returns an identical output, so caching and retries are safe'), hard limits, error taxonomy (invalid_input/internal_error), truncated semantics, and payment behavior. This is exactly the behavioral disclosure a mutation-free but complex tool needs.

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?

Front-loaded with purpose, then INPUT/HARD LIMITS/OUTPUT/PAYMENT headers that make scanning easy; each block is substantive rather than filler. It is long, and the OUTPUT block is verbose because no output schema exists, but the payment paragraph is the only portion that could be trimmed.

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 nested options/domain objects, the description supplies the return contract itself (resultType enum, solutions[].tier/certified, truncated, error.type), so an agent knows what it will get back. Nothing material is missing for correct invocation or interpretation.

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 already 100%, so the schema handles per-parameter meaning; the description still adds constraints the schema does not encode (max 6 variables, 1-64 equations, equation count >= variable count, 100KB cap, 6-decimal fixed output, domain defaulting to +/1e6). It stops short of explaining options.budget/maxDepth or fastMode, which the schema also leaves thin.

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+resource ('deterministic solver for systems of real equations') and immediately separates itself from siblings by naming what it is not: not symbolic algebra, not an ODE solver, not a language model. An agent can distinguish it from poly_roots/verify without opening any 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?

Explicitly frames when to use it ('verifiable, reproducible numeric answer for algebraic equations or common transcendentals') and when not ('Not suitable for symbolic algebra, closed-form proofs, initial-value ODEs, or mandatory integer equality'), plus it routes failures to give_feedback. This is the full when/when-not/alternative pattern.

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 carries the full burden, and it does well: it discloses the certified-kernel neighbourhood search, determinism and reproducibility, the refutation branch returning the nearest certified root, and a pricing/usage declaration via honorPaid. It omits failure modes such as malformed equation or non-convergence behaviour.

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 core behaviour and input forms are front-loaded in the first two sentences, and every sentence carries information. It runs slightly long, with the honorPaid pricing clause appended as a trailing sentence that is easy to skim past.

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 4-parameter tool with no annotations and no output schema, the description covers both outcomes (verified with error box vs refuted with nearest certified root) so the agent knows what it will receive. It stops short of describing invalid-input or timeout behaviour, which is a minor gap.

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 baseline is 3, but the description adds meaning beyond the schema by explaining that the candidate is evaluated within a neighbourhood of the supplied value ('the same certified kernel runs in a neighbourhood around the candidate'), which contextualises what tolerance actually does.

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 object ('Check whether a claimed answer is correct') and frames the tool as a verifier of a supplied candidate rather than a solver, which cleanly separates it from siblings solve and poly_roots. An agent can select it 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?

Gives clear context for use: supply an equation plus a candidate value, and the tool certifies or refutes it. It does not explicitly say when not to use it (e.g. use solve/poly_roots when no candidate exists), so routing to alternatives is left to inference.

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