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

Annotations already declare the operation as read-only, idempotent, and closed-world. The description adds useful behavioral context by noting that the change-of-base division is written out, which tells the agent what the output will include. It still omits domain constraints such as x needing to be positive, but the core behavioral gap beyond annotations is small.

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 front-loaded and compact: a single informative sentence followed by a short web-page link. The link is not essential for tool invocation, but it is brief and does not detract from the core content.

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 calculator with rich annotations and a full schema, the description covers the main operation and output detail. However, it does not warn that x must be positive for a logarithm or that a custom base must be greater than 0 and not equal to 1, despite schema ranges that permit invalid inputs. These edge-case gaps matter for correct invocation.

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 the baseline is 3. The description adds semantic meaning beyond the schema's terse labels by mapping the base enum values to 'common log (base 10)', 'natural log (ln)', and 'log base 2', and by giving a worked example log₃(81) = 4 that clarifies the custom-base use case.

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?

Names the tool as a log calculator and enumerates the supported bases (10, e, 2, custom), which clearly identifies the operation and distinguishes it from most siblings. It does not explicitly differentiate itself from the scientific_calculator, which can also compute logarithms, so it falls short of a 5.

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 says what the tool computes but gives no guidance on when to choose it over alternatives such as exponent_calculator or scientific_calculator. No prerequisites, exclusions, or when-not-to-use conditions are provided.

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