pysr_run
Read-only
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
Input Schema
TableJSON 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
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| 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 |