A
licenseNot graded
qualityA
maintenanceProvides a token-efficient exact math engine for AI agents, enabling computation of derivatives, integrals, equations, and optimized Python/NumPy code via a single MCP tool.
4
MIT
Occam
by fit.occam
Server Details
Finds the simplest equation consistent with your data. SINDy and PySR symbolic regression via MCP.
If you are the author of this connector, you can claim ownership by verifying the domain or GitHub account it belongs to. Claimed connector authors can inspect health checks, view analytics, and manage their listing.
- Status
- Healthy
- Uptime
- 100.0% over 42 days
- Last Tested
- Transport
- Streamable HTTP · MCP 2025-11-25
- URL
TDQS
A4.8/5.0
Scored across 4 tools
Disambiguation5/5
Each tool has a clearly distinct purpose: pysr_run and sindy_run are explicitly cross-referenced to separate algebraic regression from differential equation discovery, pysr_uncertainty is a well-defined follow-up, and feature_request is a meta-tool. There is no realistic risk of an agent selecting the wrong tool.
Naming Consistency4/5
Compute tools follow a clear <method>_run/<method>_uncertainty pattern, but feature_request breaks the convention by leading with the object rather than a verb. Names are still lowercase snake_case and readable, so the deviation is minor.
Tool Count5/5
Four tools is a tight, well-scoped surface for a symbolic regression server: two core methods, one uncertainty companion, and one feedback channel. Each tool earns its place without redundancy.
Completeness5/5
The domain is covered end-to-end: algebraic regression via PySR, dynamical system discovery via SINDy, uncertainty quantification on PySR results, and a request mechanism for unsupported capabilities. No obvious missing operation is needed for the intended workflows.
Available Tools
4 toolsfeature_requestAInspect
Request a feature that Occam doesn't support yet.
Use this when you need a capability that Occam doesn't currently
offer. Requests are logged and used to prioritize development.
Rate limit: 5 requests/hour per IP, 50/hour global — stricter than
the compute tools' 10/hour to prevent log flooding. Descriptions
longer than 500 characters are truncated.
ParametersJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| description | Yes | A short description of the feature you need. Examples: 'LaTeX output for equations', 'support for ODE constraints', 'GPU-accelerated search', 'larger dataset limits'. Helps prioritize development. |
Output Schema
ParametersJSON Schema
| Name | Required | Description |
|---|---|---|
| ok | Yes | |
| message | Yes | |
| description | Yes |
TDQS
A4.7/5.0
Behavior5/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
The description provides significant behavioral context beyond the sparse annotations. It discloses that requests are logged and used for prioritization, implying a write side effect. It also details rate limits (5/hour per IP, 50/hour global) and the 500-character truncation rule, which are concrete constraints not derivable from annotations. This goes well beyond what structured fields offer.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is tight and front-loaded, leading with the purpose and then providing essential constraints. Every sentence adds value (usage condition, logging, rate limits, truncation). It uses clear line breaks for readability without fluff.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple one-parameter tool with an output schema, the description fully covers use case, side effects, limitations, and rate limits. The parameters are well-documented, and the behavior is transparent. No critical information is missing.
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 description covers 100% of the single parameter, including examples and purpose. The tool description adds the truncation limit, which is also parameter-relevant. Since the schema already does the heavy lifting, the extra note earns a score above baseline.
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's function with a specific verb and resource: "Request a feature that Occam doesn't support yet." It distinguishes itself from the sibling compute tools (pysr_run, etc.) by being focused on feature requests rather than scientific computation. The action is unambiguous.
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 explicitly states when to use the tool: "Use this when you need a capability that Occam doesn't currently offer." While it doesn't name alternative tools or exclusions, the context is clear given the unrelated siblings. It also adds practical constraints like rate limits and truncation behavior, which guide usage.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
pysr_runARead-onlyInspect
Evolutionary Symbolic Regression (PySR).
Discovers algebraic equations y = f(x1, x2, ...) from feature/target
data. Returns a Pareto front ranked by the complexity/accuracy
tradeoff. Slower than SINDy (10-60s); searches often terminate early
on convergence. For differential equations from time series, use
sindy_run instead.
Pricing: free tier up to 100 rows × 8 features, 60s timeout. Beyond
that, $0.25 + $0.03 per 100 extra rows + $0.01 per extra feature
squared, timeout up to 300s (5 min), via x402 (USDC on Base) or
MPP/Stripe. MPP/Stripe adds a flat $0.35 per-transaction fee (Stripe
processing), so the MPP challenge amount in a `payment_required`
response is $0.35 higher than the x402 amount for the same base
price; x402 gets the lower rate. Omit `payment` for free-tier
requests; paid requests without a valid credential receive a
`payment_required` result with pricing and accepted schemes. Full
pricing: occam://pricing
Advisory limits: jobs over 50,000 rows or 20 features are accepted
but may not converge; response carries a top-level `warning`.
Operators: fixed supported set only — custom operators (e.g.
'inv(x) = 1/x') are rejected. Unary: sin, cos, tan, exp, log, log2,
log10, sqrt, abs, sinh, cosh, tanh. Binary: +, -, *, /, ^.
See also prompt `supported_operators`.
Loss metric: `loss` (in `pareto_front[].loss` and `best_loss`) is
mean squared error between model prediction and `y` on the full
training set — not RMSE, and not normalized by Var(y). A threshold
appropriate for one dataset scales with y's magnitude, so set
`loss_threshold` with that in mind (e.g. for y values near 1.0,
1e-6 is a tight fit; for y near 1000, the equivalent is 1.0).
Early termination: set `loss_threshold` to stop at your noise floor.
The server also stops when the search stalls (<1% improvement in the
last third of the budget); disable with `stall_detection=false`.
Response `stop_reason` is one of: loss_threshold, stall, timeout,
natural.
If `feature_names` is supplied, its length must equal the number of
columns in `X`; a mismatch is rejected with a validation error.
Follow-up: call `pysr_uncertainty` with a chosen expression and the
same dataset for bootstrap confidence intervals on its fit constants
and optional prediction bands.
Rate limit: 10 requests/hour per IP, 200/hour global, max queue
depth 20 (shared with sindy_run and pysr_uncertainty).
Response (success) includes `pareto_front[]` (each with `complexity`,
`loss`, `expression`, `expression_latex`), `best_expression`,
`best_expression_latex`, `best_loss`, `best_complexity`, `stop_reason`,
`elapsed_seconds`, `queue_seconds` (>0 = server saturated; use as
backoff signal), optional `warning`, optional `_meta` (MPP receipt).
Full response and payment-required schemas: occam://tool-schemas
Example request:
X=[[0.0], [1.0], [2.0], [3.0], [4.0]], y=[1.0, 3.0, 5.0, 7.0, 9.0],
feature_names=["x"], max_complexity=10, timeout_seconds=15
Policy: occam://privacy-policy — Citation: occam://citation-info
ParametersJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| X | Yes | 2D array of input features. Each row is an observation, each column is a feature. Minimum 5 rows. Free tier: 100 rows, 8 features. Paid tier: up to 50,000 rows, 20 features. | |
| y | Yes | Target values, one per row of X. | |
| payment | No | Payment credential. Accepts either a JSON object or a JSON-encoded string (FastMCP's transport pre-parses strings whose field annotation is non-bare-`str` into objects, so the object form is canonical; the string form is accepted for legacy callers). Required when the dataset exceeds the free tier (100 rows, 8 variables). Omit for free-tier requests. For x402: {"transaction":"0x...","network":"...","priceToken":"..."}. For MPP/Stripe: {"challenge":{...},"payload":"..."}. For prepaid API key: {"scheme":"prepaid","api_key":"occ_live_...","request_id":"<optional uuid>"}. | |
| populations | No | Number of evolutionary populations for the search. Default 15, max 20. | |
| feature_names | No | Names for each variable/feature column. Defaults to x0, x1, ... | |
| loss_threshold | No | Optional early-stop threshold on the best loss found. If set, the search terminates as soon as any Pareto-front member reaches a loss at or below this value, even if the timeout has not been reached. Useful when you know your noise floor. Default: None (no user threshold; the search runs until the stall detector or timeout). | |
| max_complexity | No | Maximum expression tree size. Higher allows more complex expressions. Default 20, max 25. | |
| stall_detection | No | When true (default), the server stops the search early if the best loss has not improved by more than 1% during the last third of the time budget. This reclaims compute once the search has converged. Set to false only if you want the search to run for the full timeout regardless of progress. | |
| timeout_seconds | No | Wall clock time limit in seconds. Free tier: max 60. Paid tier: max 300 (5 minutes). Default 60. | |
| unary_operators | No | Allowed unary operators, drawn from the fixed supported set: sin, cos, tan, exp, log, log2, log10, sqrt, abs, sinh, cosh, tanh. Custom operators (e.g. 'inv(x) = 1/x') are NOT supported — only the names listed are accepted. Default: sin, cos, exp, log, sqrt. Pass [] for none. | |
| binary_operators | No | Allowed binary operators, drawn from the fixed supported set: +, -, *, /, ^. Custom operators are NOT supported. Default: +, -, *, /. Pass [] for none. |
Output Schema
ParametersJSON Schema
| Name | Required | Description |
|---|---|---|
| warning | No | |
| best_loss | No | |
| stop_reason | No | |
| pareto_front | No | |
| queue_seconds | No | |
| best_complexity | No | |
| best_expression | No | |
| elapsed_seconds | No | |
| best_expression_latex | No |
TDQS
A4.9/5.0
Behavior5/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already declare readOnlyHint=true, destructiveHint=false, and idempotentHint=false, but the description adds substantial behavioral context: early termination via loss_threshold and stall detection, the exact definition of the loss metric (MSE not RMSE, not normalized), response stop_reason values, rate limits, and restrictions on custom operators. No contradiction with annotations; instead, it layers crucial operational details on top.
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 long but well-structured with clear sections (pricing, advisory limits, operators, loss metric, early termination, follow-up, rate limits, response, example). Every paragraph adds essential information; there is no fluff or redundancy. It could be slightly more compact, but given the number of distinct operational aspects it must cover, the length is justified.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
The description is exhaustive for a tool with 11 parameters, an output schema, and payment complexity. It covers pricing, rate limits, operator constraints, loss semantics, stop reasons, pagination/queue hints, example request, and response fields (including optional warning and _meta). The follow-up tool and full schema links are provided. An agent has everything needed to call this tool correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters5/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100% (baseline 3), but the description goes well beyond schema descriptions. For example, it explains that loss_threshold scales with y's magnitude, that feature_names length must match X columns or be rejected, that unary/binary operators are restricted to a fixed set with custom operators rejected, and that payment accepts three distinct forms. This meaningfully compensates for any ambiguity in the schema.
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 states a specific verb ('discovers algebraic equations'), resource ('from feature/target data'), and method ('evolutionary symbolic regression (PySR)'). It explicitly contrasts with a sibling ('For differential equations from time series, use sindy_run instead'), making it easy to distinguish from other tools without inspecting schemas.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines5/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
Provides clear when-to-use guidance: it names the alternative `sindy_run` for differential equations and tells the user to use `pysr_uncertainty` for follow-up confidence intervals. It also details conditions for free vs. paid tiers and how to handle payment-required responses, leaving nothing to inference.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
pysr_uncertaintyARead-onlyInspect
Bootstrap confidence intervals for the numeric constants of a frozen expression, plus optional prediction bands on an x-grid.
Typical flow: call pysr_run, pick an expression from the response
(best_expression or a pareto_front entry), pass it back here with
the same dataset to get CIs on its fit constants.
Returns frequentist bootstrap confidence intervals, not Bayesian
credible intervals — posterior inference over expression structures
is an open research problem. This tool freezes the expression
chosen by the caller and bootstraps only its numeric constants;
uncertainty about *which* expression is correct is not quantified.
Bootstrap semantics:
- If y_sigma is supplied, uses parametric bootstrap
(y_b = y + Normal(0, y_sigma)). CI reflects user-stated
measurement noise.
- Otherwise uses residual bootstrap: fit once, resample residuals.
CI reflects estimated-from-residuals noise.
Only Float constants in the expression become free parameters.
Integers stay structural (the 2 in x**2 is a function-class choice,
not a fit constant). Expressions with no Float constants
(e.g. "x + y") will be rejected with a validation error.
Expression grammar: the `expression` string is parsed by sympy.
Accepted operators are the same set pysr_run emits: unary `sin`,
`cos`, `tan`, `exp`, `log`, `log2`, `log10`, `sqrt`, `abs`, `sinh`,
`cosh`, `tanh`; binary `+`, `-`, `*`, `/`, `^` (or `**`). Whitespace
and parenthesization are free. Every free symbol in the expression
must correspond to an entry in `feature_names` — an unrecognised
symbol is silently treated as a fresh sympy Symbol and the fit will
fail downstream rather than reject early. Parse failures (syntax
errors, malformed operators) surface as tool errors.
If `feature_names` is supplied, its length must equal the number of
columns in `X`; a mismatch is rejected with a validation error.
Pricing: always free, regardless of dataset size. This tool has no
`payment` parameter and is never subject to the x402/Stripe gate.
Large bootstrap jobs still count against the shared rate limit
below, so budget `n_resamples` accordingly.
Rate limit: 10 requests/hour per IP, 200/hour global, max queue
depth 20 (shared with sindy_run and pysr_run).
ParametersJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| X | Yes | 2D array of input features. Each row is an observation, each column is a feature. Minimum 5 rows. Free tier: 100 rows, 8 features. Paid tier: up to 50,000 rows, 20 features. | |
| y | Yes | Target values, one per row of X. | |
| alpha | No | Significance level. 0.05 → 95%% CI. Default 0.05. | |
| x_grid | No | Optional 2D grid of feature values at which to report a prediction band. Must have the same number of columns as X. Omit to skip prediction-band computation. | |
| y_sigma | No | Optional per-point measurement standard deviations, or a single scalar applied to all points. When supplied, the helper uses parametric bootstrap (y_b = y + Normal(0, y_sigma)); otherwise it uses residual bootstrap. Supplying y_sigma also improves the initial weighted fit. | |
| expression | Yes | The expression to bootstrap, as returned by pysr_run (`best_expression` or a `pareto_front[i].expression`). Only numeric Float constants are treated as free parameters — integers in the expression (e.g. the 2 in x**2) stay structural. | |
| n_resamples | No | Number of bootstrap resamples. Higher = tighter CIs, more compute. Default 100. | |
| feature_names | No | Names for each variable/feature column. Defaults to x0, x1, ... |
Output Schema
ParametersJSON Schema
| Name | Required | Description |
|---|---|---|
| note | Yes | |
| alpha | Yes | |
| coefficients | Yes | |
| prediction_ci | No | |
| bootstrap_method | Yes | |
| n_requested_resamples | Yes | |
| n_successful_resamples | Yes |
TDQS
A4.7/5.0
Behavior5/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
The description goes far beyond the readOnlyHint annotation. It discloses the parametric vs. residual bootstrap semantics, the rule that only Float constants become free parameters, validation errors for expressions without Float constants, the silent treatment of unrecognized symbols as fresh sympy Symbols, pricing, rate limits, and the absence of a payment gate. This is rich behavioral context with no contradiction to the annotations.
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 long but well-structured with clear sections and bullet points. It front-loads the core purpose and typical flow before diving into semantics. Some content, like the full operator grammar and rate-limit figures, could arguably live elsewhere, but it is dense and useful. It earns points for organization but loses a little for overall length.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity, an output schema exists, and the description covers all non-obvious aspects: bootstrap method selection, expression grammar, constant typing, validation failures, rate limits, and pricing. An agent has enough context to invoke the tool correctly and anticipate failure modes without needing to inspect the output schema.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters5/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Although schema coverage is 100%, the description adds substantial meaning beyond the schema. It explains that y_sigma switches between parametric and residual bootstrap, that integers in the expression are structural while Floats are free parameters, that feature_names must match X columns, and that x_grid controls prediction bands. This materially improves an agent's ability to set parameters correctly.
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 opens with a specific verb and resource: 'Bootstrap confidence intervals for the numeric constants of a frozen expression, plus optional prediction bands on an x-grid.' It clearly distinguishes this from pysr_run by emphasizing that the expression is frozen and only its numeric constants are bootstrapped. The purpose is immediately identifiable and not confused with sibling tools.
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 'Typical flow' section gives explicit guidance: call pysr_run, select an expression, pass it back with the same dataset. It also states what this tool does not do — posterior/Bayesian inference over expression structures — which helps an agent avoid misuse. However, it stops short of explicitly naming alternatives or stating exact conditions for when a sibling tool would be preferable, so it is clear but not fully exhaustive.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
sindy_runARead-onlyIdempotentInspect
Sparse Identification of Nonlinear Dynamics (SINDy).
Recovers governing differential equations (dx/dt = f(x)) from time
series data. Returns human-readable sparse expressions. Fast (seconds).
For algebraic y = f(x) relationships without time structure, use
pysr_run instead.
Pricing: free tier up to 100 rows and 8 variables. Beyond that,
$0.05 + $0.01 per 100 extra rows + $0.01 per extra variable squared,
via x402 (USDC on Base) or MPP/Stripe. MPP/Stripe adds a flat $0.35
per-transaction fee (Stripe processing), so the MPP challenge amount
in a `payment_required` response is $0.35 higher than the x402 amount
for the same base price; x402 gets the lower rate. Omit `payment`
for free-tier requests; paid requests without a valid credential
receive a `payment_required` result with pricing and accepted schemes.
Full pricing table as structured JSON: occam://pricing
Advisory limits: jobs over 500,000 rows or 50 variables are accepted
but may not converge within the time budget; the response carries a
top-level `warning` the agent should surface and treat as tentative.
If `feature_names` is supplied, its length must equal the number of
data columns; a mismatch is rejected with a validation error.
Rate limit: 10 requests/hour per IP, 200/hour global, max queue
depth 20 (shared with pysr_run and pysr_uncertainty).
Response (success) includes `equations[]` (each with `variable`,
`equation`, `expression`, `expression_latex`, `r2`), `library_terms`,
`nonzero_terms`, `elapsed_seconds`, `canonical_match` (dict with
`system`, `form`, `variable_map`, `parameter_map`, `confidence` if
the discovered system matches one of Lorenz / Lotka-Volterra /
Van der Pol / Duffing; `null` otherwise), optional `warning`,
optional `_meta` (MPP receipt on paid calls). Full response and
payment-required schemas: occam://tool-schemas
Example request:
data=[[1.0, 0.0], [0.95, -0.31], [0.81, -0.59]], t=[0.0, 0.1, 0.2],
feature_names=["x", "y"], poly_degree=2, threshold=0.1
Policy: occam://privacy-policy — Citation: occam://citation-info
ParametersJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| t | Yes | Timestamps corresponding to each row of data. Length must match row count. | |
| data | Yes | 2D array of time series data. Each row is a timestep, each column is a state variable. Minimum 3 rows (finite-difference derivative). Free tier: 100 rows, 8 variables. Paid tier: up to 500,000 rows, 50 variables. | |
| payment | No | Payment credential. Accepts either a JSON object or a JSON-encoded string (FastMCP's transport pre-parses strings whose field annotation is non-bare-`str` into objects, so the object form is canonical; the string form is accepted for legacy callers). Required when the dataset exceeds the free tier (100 rows, 8 variables). Omit for free-tier requests. For x402: {"transaction":"0x...","network":"...","priceToken":"..."}. For MPP/Stripe: {"challenge":{...},"payload":"..."}. For prepaid API key: {"scheme":"prepaid","api_key":"occ_live_...","request_id":"<optional uuid>"}. | |
| max_iter | No | Maximum STLSQ optimizer iterations. Default 20. | |
| threshold | No | STLSQ sparsity threshold. Higher values produce sparser equations. Default 0.1. | |
| poly_degree | No | Polynomial library degree for SINDy candidate functions. Default 2. | |
| feature_names | No | Names for each variable/feature column. Defaults to x0, x1, ... |
Output Schema
ParametersJSON Schema
| Name | Required | Description |
|---|---|---|
| warning | No | |
| equations | No | |
| library_terms | No | |
| nonzero_terms | No | |
| canonical_match | No | |
| elapsed_seconds | No |
TDQS
A4.8/5.0
Behavior5/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already establish read-only, idempotent, non-destructive behavior. The description adds substantial behavioral context: pricing tiers and payment schemes, rate limits, advisory convergence warnings, validation errors (feature_names mismatch), and the structure of success and payment_required responses. Nothing contradicts annotations; the description enriches them.
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 long but well-structured: it leads with the core purpose, then pricing, advisories, validation, rate limits, response schema, and an example. While verbose, each section carries necessary operational detail for a commercial tool. It is front-loaded and organized, though could be tightened without losing information.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Despite having an output schema, the description goes beyond it to explain response contents (equations, canonical_match, warnings, _meta), payment-required behavior, validation errors, rate limits, and pricing. Combined with the schema, an agent has virtually everything needed to call the tool correctly, including edge cases and failure modes.
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?
Schema description coverage is 100%, so parameters are already documented. The description adds value beyond the schema by explaining free-tier limits on the 'data' parameter, the exact validation rule for 'feature_names', and the full semantics of the 'payment' parameter (x402 vs MPP/Stripe formats and pricing implications). This goes beyond the schema's basic type/description info.
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 recovers governing differential equations from time series data via SINDy, and explicitly contrasts with pysr_run for algebraic relationships. It names the specific method and output, making it immediately distinguishable from siblings.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines5/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
It provides explicit when-to-use guidance (time series data for differential equations), explicitly directs users to pysr_run for non-time-structured algebraic problems, and includes detailed free/paid tier rules, rate limits, and advisory limits. Alternatives and exclusions are unambiguous.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Tool Schema Changelog
Recent tool additions, removals, and schema changes observed during successful MCP inspections.
3 tool updates
- Changed
pysr_run5 fields changed- changed
Input schema / properties / X / descriptionPrevious value: -"2D array of input features. Each row is an observation, each column is a feature. Free tier: 100 rows, 8 features. Paid tier: up to 50,000 rows, 20 features."New value: +"2D array of input features. Each row is an observation, each column is a feature. Minimum 5 rows. Free tier: 100 rows, 8 features. Paid tier: up to 50,000 rows, 20 features." - added
Input schema / properties / X / examplesAdded value: +[ + [ + [ + 0 + ], + [ + 1 + ], + [ + 2 + ], + [ + 3 + ], + [ + 4 + ] + ] +] - added
Input schema / properties / X / minItemsAdded value: +5 - added
Input schema / properties / y / examplesAdded value: +[ + [ + 1.02, + 2.97, + 5.01, + 7.03, + 8.98 + ] +] - added
Input schema / properties / y / minItemsAdded value: +5
- Changed
pysr_uncertainty6 fields changed- changed
Input schema / properties / X / descriptionPrevious value: -"2D array of input features. Each row is an observation, each column is a feature. Free tier: 100 rows, 8 features. Paid tier: up to 50,000 rows, 20 features."New value: +"2D array of input features. Each row is an observation, each column is a feature. Minimum 5 rows. Free tier: 100 rows, 8 features. Paid tier: up to 50,000 rows, 20 features." - added
Input schema / properties / X / examplesAdded value: +[ + [ + [ + 0 + ], + [ + 1 + ], + [ + 2 + ], + [ + 3 + ], + [ + 4 + ] + ] +] - added
Input schema / properties / X / minItemsAdded value: +5 - added
Input schema / properties / expression / examplesAdded value: +[ + "2.0*x0 + 1.0" +] - added
Input schema / properties / y / examplesAdded value: +[ + [ + 1.02, + 2.97, + 5.01, + 7.03, + 8.98 + ] +] - added
Input schema / properties / y / minItemsAdded value: +5
- Changed
sindy_run5 fields changed- changed
Input schema / properties / data / descriptionPrevious value: -"2D array of time series data. Each row is a timestep, each column is a state variable. Free tier: 100 rows, 8 variables. Paid tier: up to 500,000 rows, 50 variables."New value: +"2D array of time series data. Each row is a timestep, each column is a state variable. Minimum 3 rows (finite-difference derivative). Free tier: 100 rows, 8 variables. Paid tier: up to 500,000 rows, 50 variables." - added
Input schema / properties / data / examplesAdded value: +[ + [ + [ + 1, + 0 + ], + [ + 0.9553, + -0.2955 + ], + [ + 0.8253, + -0.5646 + ], + [ + 0.6216, + -0.7833 + ], + [ + 0.3624, + -0.932 + ], + [ + 0.0707, + -0.9975 + ], + [ + -0.2272, + -0.9738 + ], + [ + -0.5048, + -0.8632 + ], + [ + -0.7374, + -0.6755 + ], + [ + -0.9041, + -0.4274 + ], + [ + -0.99, + -0.1411 + ], + [ + -0.9875, + 0.1577 + ] + ] +] - added
Input schema / properties / data / minItemsAdded value: +3 - added
Input schema / properties / t / examplesAdded value: +[ + [ + 0, + 0.3, + 0.6, + 0.9, + 1.2, + 1.5, + 1.8, + 2.1, + 2.4, + 2.7, + 3, + 3.3 + ] +] - added
Input schema / properties / t / minItemsAdded value: +3
2 tool updates
- Changed
pysr_run2 fields changed- changed
Input schema / properties / payment / anyOfPrevious value: -[ - { - "type": "string" - }, - { - "type": "null" - } -]New value: +[ + { + "additionalProperties": true, + "type": "object" + }, + { + "type": "string" + }, + { + "type": "null" + } +] - changed
Input schema / properties / payment / descriptionPrevious value: -"Payment credential as a JSON string. Required when the dataset exceeds the free tier (100 rows, 8 variables). Omit for free-tier requests. For x402: {\"transaction\":\"0x...\",\"network\":\"...\",\"priceToken\":\"...\"}. For MPP/Stripe: {\"challenge\":{...},\"payload\":\"...\"}."New value: +"Payment credential. Accepts either a JSON object or a JSON-encoded string (FastMCP's transport pre-parses strings whose field annotation is non-bare-`str` into objects, so the object form is canonical; the string form is accepted for legacy callers). Required when the dataset exceeds the free tier (100 rows, 8 variables). Omit for free-tier requests. For x402: {\"transaction\":\"0x...\",\"network\":\"...\",\"priceToken\":\"...\"}. For MPP/Stripe: {\"challenge\":{...},\"payload\":\"...\"}. For prepaid API key: {\"scheme\":\"prepaid\",\"api_key\":\"occ_live_...\",\"request_id\":\"<optional uuid>\"}."
- Changed
sindy_run2 fields changed- changed
Input schema / properties / payment / anyOfPrevious value: -[ - { - "type": "string" - }, - { - "type": "null" - } -]New value: +[ + { + "additionalProperties": true, + "type": "object" + }, + { + "type": "string" + }, + { + "type": "null" + } +] - changed
Input schema / properties / payment / descriptionPrevious value: -"Payment credential as a JSON string. Required when the dataset exceeds the free tier (100 rows, 8 variables). Omit for free-tier requests. For x402: {\"transaction\":\"0x...\",\"network\":\"...\",\"priceToken\":\"...\"}. For MPP/Stripe: {\"challenge\":{...},\"payload\":\"...\"}."New value: +"Payment credential. Accepts either a JSON object or a JSON-encoded string (FastMCP's transport pre-parses strings whose field annotation is non-bare-`str` into objects, so the object form is canonical; the string form is accepted for legacy callers). Required when the dataset exceeds the free tier (100 rows, 8 variables). Omit for free-tier requests. For x402: {\"transaction\":\"0x...\",\"network\":\"...\",\"priceToken\":\"...\"}. For MPP/Stripe: {\"challenge\":{...},\"payload\":\"...\"}. For prepaid API key: {\"scheme\":\"prepaid\",\"api_key\":\"occ_live_...\",\"request_id\":\"<optional uuid>\"}."
4 tool updates
- Changed
feature_request1 field changed- changed
Output schema / (root)Previous value: -nullNew value: +{ + "additionalProperties": false, + "properties": { + "description": { + "title": "Description", + "type": "string" + }, + "message": { + "title": "Message", + "type": "string" + }, + "ok": { + "title": "Ok", + "type": "boolean" + } + }, + "required": [ + "ok", + "message", + "description" + ], + "title": "FeatureRequestResult", + "type": "object" +}
- Changed
pysr_run1 field changed- changed
Output schema / (root)Previous value: -nullNew value: +{ + "$defs": { + "PySRParetoEntry": { + "additionalProperties": true, + "properties": { + "complexity": { + "title": "Complexity", + "type": "integer" + }, + "expression": { + "title": "Expression", + "type": "string" + }, + "expression_latex": { + "anyOf": [ + { + "type": "string" + }, + { + "type": "null" + } + ], + "title": "Expression Latex" + }, + "loss": { + "title": "Loss", + "type": "number" + } + }, + "required": [ + "complexity", + "loss", + "expression", + "expression_latex" + ], + "title": "PySRParetoEntry", + "type": "object" + } + }, + "additionalProperties": true, + "properties": { + "best_complexity": { + "anyOf": [ + { + "type": "integer" + }, + { + "type": "null" + } + ], + "default": null, + "title": "Best Complexity" + }, + "best_expression": { + "anyOf": [ + { + "type": "string" + }, + { + "type": "null" + } + ], + "default": null, + "title": "Best Expression" + }, + "best_expression_latex": { + "anyOf": [ + { + "type": "string" + }, + { + "type": "null" + } + ], + "default": null, + "title": "Best Expression Latex" + }, + "best_loss": { + "anyOf": [ + { + "type": "number" + }, + { + "type": "null" + } + ], + "default": null, + "title": "Best Loss" + }, + "elapsed_seconds": { + "anyOf": [ + { + "type": "number" + }, + { + "type": "null" + } + ], + "default": null, + "title": "Elapsed Seconds" + }, + "pareto_front": { + "anyOf": [ + { + "items": { + "$ref": "#/$defs/PySRParetoEntry" + }, + "type": "array" + }, + { + "type": "null" + } + ], + "default": null, + "title": "Pareto Front" + }, + "queue_seconds": { + "anyOf": [ + { + "type": "number" + }, + { + "type": "null" + } + ], + "default": null, + "title": "Queue Seconds" + }, + "stop_reason": { + "anyOf": [ + { + "type": "string" + }, + { + "type": "null" + } + ], + "default": null, + "title": "Stop Reason" + }, + "warning": { + "anyOf": [ + { + "type": "string" + }, + { + "type": "null" + } + ], + "default": null, + "title": "Warning" + } + }, + "title": "PySRRunResult", + "type": "object" +}
- Changed
pysr_uncertainty1 field changed- changed
Output schema / (root)Previous value: -nullNew value: +{ + "$defs": { + "UncertaintyCoefficient": { + "additionalProperties": true, + "properties": { + "ci": { + "maxItems": 2, + "minItems": 2, + "prefixItems": [ + { + "type": "number" + }, + { + "type": "number" + } + ], + "title": "Ci", + "type": "array" + }, + "estimate": { + "title": "Estimate", + "type": "number" + }, + "initial": { + "title": "Initial", + "type": "number" + }, + "name": { + "title": "Name", + "type": "string" + } + }, + "required": [ + "name", + "initial", + "estimate", + "ci" + ], + "title": "UncertaintyCoefficient", + "type": "object" + }, + "UncertaintyPredictionPoint": { + "additionalProperties": true, + "properties": { + "ci": { + "maxItems": 2, + "minItems": 2, + "prefixItems": [ + { + "type": "number" + }, + { + "type": "number" + } + ], + "title": "Ci", + "type": "array" + }, + "estimate": { + "title": "Estimate", + "type": "number" + }, + "x": { + "items": { + "type": "number" + }, + "title": "X", + "type": "array" + } + }, + "required": [ + "x", + "estimate", + "ci" + ], + "title": "UncertaintyPredictionPoint", + "type": "object" + } + }, + "additionalProperties": true, + "description": "Always a success shape — pysr_uncertainty is never paid.", + "properties": { + "alpha": { + "title": "Alpha", + "type": "number" + }, + "bootstrap_method": { + "title": "Bootstrap Method", + "type": "string" + }, + "coefficients": { + "items": { + "$ref": "#/$defs/UncertaintyCoefficient" + }, + "title": "Coefficients", + "type": "array" + }, + "n_requested_resamples": { + "title": "N Requested Resamples", + "type": "integer" + }, + "n_successful_resamples": { + "title": "N Successful Resamples", + "type": "integer" + }, + "note": { + "title": "Note", + "type": "string" + }, + "prediction_ci": { + "anyOf": [ + { + "items": { + "$ref": "#/$defs/UncertaintyPredictionPoint" + }, + "type": "array" + }, + { + "type": "null" + } + ], + "default": null, + "title": "Prediction Ci" + } + }, + "required": [ + "coefficients", + "n_requested_resamples", + "n_successful_resamples", + "bootstrap_method", + "alpha", + "note" + ], + "title": "PySRUncertaintyResult", + "type": "object" +}
- Changed
sindy_run1 field changed- changed
Output schema / (root)Previous value: -nullNew value: +{ + "$defs": { + "CanonicalMatch": { + "additionalProperties": true, + "properties": { + "confidence": { + "title": "Confidence", + "type": "number" + }, + "form": { + "title": "Form", + "type": "string" + }, + "parameter_map": { + "additionalProperties": { + "type": "number" + }, + "title": "Parameter Map", + "type": "object" + }, + "system": { + "title": "System", + "type": "string" + }, + "variable_map": { + "additionalProperties": { + "type": "string" + }, + "title": "Variable Map", + "type": "object" + } + }, + "required": [ + "system", + "form", + "variable_map", + "parameter_map", + "confidence" + ], + "title": "CanonicalMatch", + "type": "object" + }, + "SindyEquation": { + "additionalProperties": true, + "properties": { + "equation": { + "title": "Equation", + "type": "string" + }, + "expression": { + "title": "Expression", + "type": "string" + }, + "expression_latex": { + "anyOf": [ + { + "type": "string" + }, + { + "type": "null" + } + ], + "title": "Expression Latex" + }, + "r2": { + "title": "R2", + "type": "number" + }, + "variable": { + "title": "Variable", + "type": "string" + } + }, + "required": [ + "variable", + "equation", + "expression", + "expression_latex", + "r2" + ], + "title": "SindyEquation", + "type": "object" + } + }, + "additionalProperties": true, + "properties": { + "canonical_match": { + "anyOf": [ + { + "$ref": "#/$defs/CanonicalMatch" + }, + { + "type": "null" + } + ], + "default": null + }, + "elapsed_seconds": { + "anyOf": [ + { + "type": "number" + }, + { + "type": "null" + } + ], + "default": null, + "title": "Elapsed Seconds" + }, + "equations": { + "anyOf": [ + { + "items": { + "$ref": "#/$defs/SindyEquation" + }, + "type": "array" + }, + { + "type": "null" + } + ], + "default": null, + "title": "Equations" + }, + "library_terms": { + "anyOf": [ + { + "items": { + "type": "string" + }, + "type": "array" + }, + { + "type": "null" + } + ], + "default": null, + "title": "Library Terms" + }, + "nonzero_terms": { + "anyOf": [ + { + "type": "integer" + }, + { + "type": "null" + } + ], + "default": null, + "title": "Nonzero Terms" + }, + "warning": { + "anyOf": [ + { + "type": "string" + }, + { + "type": "null" + } + ], + "default": null, + "title": "Warning" + } + }, + "title": "SindyRunResult", + "type": "object" +}
1 tool update
- Added
pysr_uncertainty
1 tool update
- Changed
pysr_run2 fields changed- changed
Input schema / properties / binary_operators / descriptionPrevious value: -"Allowed binary operators. Options: +, -, *, /, ^. Default: +, -, *, /."New value: +"Allowed binary operators, drawn from the fixed supported set: +, -, *, /, ^. Custom operators are NOT supported. Default: +, -, *, /. Pass [] for none." - changed
Input schema / properties / unary_operators / descriptionPrevious value: -"Allowed unary operators. Options: sin, cos, tan, exp, log, log2, log10, sqrt, abs, sinh, cosh, tanh. Default: sin, cos, exp, log, sqrt."New value: +"Allowed unary operators, drawn from the fixed supported set: sin, cos, tan, exp, log, log2, log10, sqrt, abs, sinh, cosh, tanh. Custom operators (e.g. 'inv(x) = 1/x') are NOT supported — only the names listed are accepted. Default: sin, cos, exp, log, sqrt. Pass [] for none."
2 tool updates
- Changed
pysr_run4 fields changed- changed
Input schema / properties / X / descriptionPrevious value: -"2D array of input features. Each row is an observation, each column is a feature. Max 1,000 rows, 10 features."New value: +"2D array of input features. Each row is an observation, each column is a feature. Free tier: 100 rows, 8 features. Paid tier: up to 50,000 rows, 20 features." - added
Input schema / properties / paymentAdded value: +{ + "anyOf": [ + { + "type": "string" + }, + { + "type": "null" + } + ], + "default": null, + "description": "Payment credential as a JSON string. Required when the dataset exceeds the free tier (100 rows, 8 variables). Omit for free-tier requests. For x402: {\"transaction\":\"0x...\",\"network\":\"...\",\"priceToken\":\"...\"}. For MPP/Stripe: {\"challenge\":{...},\"payload\":\"...\"}.", + "title": "Payment" +} - changed
Input schema / properties / timeout_seconds / descriptionPrevious value: -"Wall clock time limit in seconds. Default 60, max 60."New value: +"Wall clock time limit in seconds. Free tier: max 60. Paid tier: max 300 (5 minutes). Default 60." - changed
Input schema / properties / timeout_seconds / maximumPrevious value: -60New value: +300
- Changed
sindy_run2 fields changed- changed
Input schema / properties / data / descriptionPrevious value: -"2D array of time series data. Each row is a timestep, each column is a state variable. Max 10,000 rows, 20 variables."New value: +"2D array of time series data. Each row is a timestep, each column is a state variable. Free tier: 100 rows, 8 variables. Paid tier: up to 500,000 rows, 50 variables." - added
Input schema / properties / paymentAdded value: +{ + "anyOf": [ + { + "type": "string" + }, + { + "type": "null" + } + ], + "default": null, + "description": "Payment credential as a JSON string. Required when the dataset exceeds the free tier (100 rows, 8 variables). Omit for free-tier requests. For x402: {\"transaction\":\"0x...\",\"network\":\"...\",\"priceToken\":\"...\"}. For MPP/Stripe: {\"challenge\":{...},\"payload\":\"...\"}.", + "title": "Payment" +}
1 tool update
- Changed
pysr_run2 fields changed- added
Input schema / properties / loss_thresholdAdded value: +{ + "anyOf": [ + { + "exclusiveMinimum": 0, + "type": "number" + }, + { + "type": "null" + } + ], + "default": null, + "description": "Optional early-stop threshold on the best loss found. If set, the search terminates as soon as any Pareto-front member reaches a loss at or below this value, even if the timeout has not been reached. Useful when you know your noise floor. Default: None (no user threshold; the search runs until the stall detector or timeout).", + "title": "Loss Threshold" +} - added
Input schema / properties / stall_detectionAdded value: +{ + "default": true, + "description": "When true (default), the server stops the search early if the best loss has not improved by more than 1% during the last third of the time budget. This reclaims compute once the search has converged. Set to false only if you want the search to run for the full timeout regardless of progress.", + "title": "Stall Detection", + "type": "boolean" +}
6 tool updates
- Added
feature_request - Removed
feature.request - Added
pysr_run - Removed
pysr.run - Added
sindy_run - Removed
sindy.run
6 tool updates
- Added
feature.request - Added
pysr.run - Removed
request_feature - Removed
run_pysr_tool - Removed
run_sindy_tool - Added
sindy.run
3 tool updates
- First observed
request_feature - First observed
run_pysr_tool - First observed
run_sindy_tool
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