Pick the best option from a set of variants (Multi-Armed Bandit: UCB1, Thompson sampling, or ε-greedy). Use this when you have N options with observed reward history and need to choose the next one with optimal explore/exploit tradeoff (A/B test arm selection, ad/email variant routing, recommendation ranking). For context-dependent selection (different best option per user/situation), use optimize_contextual instead. For continuous parameter tuning, use optimize_cmaes. Returns the selected arm + score breakdown in <1ms.

Pick the best option given a situational context vector (LinUCB contextual bandit). Use when the best option depends on features that vary per call (user demographics, time of day, weather, market regime). Pass observed history so the model can learn per-context preferences. If you have no per-call context features, use optimize_bandit instead. Returns selected arm with expected reward + confidence width.

[Premium] Continuous black-box optimization via CMA-ES (Covariance Matrix Adaptation Evolution Strategy). Use for tuning N continuous parameters when the objective is non-convex, noisy, or has no gradient — hyperparameter search, simulator calibration, control policy tuning. 10-100x fewer evaluations than grid search. For discrete combinatorial problems, use optimize_evolve. For LP/MIP problems with linear constraints, use solve_constraints. Stochastic init means re-runs with the same input may differ slightly. Requires ORACLAW_API_KEY.

[Premium] Solve linear / mixed-integer / quadratic programs (HiGHS solver). Use when the objective and constraints are linear (or quadratic) and you need a provably optimal solution: budget allocation across line items, supply chain optimization, capacity planning with integer counts, portfolio construction with hard caps. For continuous black-box objectives, use optimize_cmaes. For task→slot scheduling, use solve_schedule. Returns variable assignments + objective value. Requires ORACLAW_API_KEY.

Assign tasks to time slots maximizing productivity, matching task energy requirements with slot energy levels. Use specifically for task→slot assignment with energy matching (deep-work scheduling, shift planning, exercise scheduling). For general resource allocation with arbitrary linear constraints, use solve_constraints. For sequence/route problems, use plan_pathfind. Deterministic.

[Premium] Compute structural properties of a directed graph: PageRank centrality, Louvain community detection, shortest critical path between two nodes, and bottleneck identification. Use to surface influential nodes, community clusters, or chokepoints in dependency graphs, knowledge graphs, supply chains, social networks. For pathfinding alone (single source→goal route), use plan_pathfind — it's faster and free. Requires ORACLAW_API_KEY.

[Premium] Compute portfolio Value-at-Risk (VaR) and Conditional VaR (Expected Shortfall) from historical asset return series, accounting for cross-asset correlation. Use for portfolio risk attribution, regulatory capital sizing, drawdown scenario analysis. Returns are matrix [asset][time] of period returns. For simulating outcomes from a parametric distribution rather than historical data, use simulate_montecarlo. Requires ORACLAW_API_KEY.

Score how much multiple independent sources agree on a probability estimate, weighting by recency, volume, and confidence. Use to fuse signals from polling, prediction markets, model ensembles, or any source emitting a 0..1 probability. Returns an aggregate convergence score, the consensus probability, and per-pair disagreement so you can see which sources are outliers. Free tier. For comparing pre-binned distributions, prefer this over simulate_montecarlo.

[Premium] Project future values from a univariate time series using ARIMA or Holt-Winters (additive seasonal). Use for short-to-medium horizon point forecasts with confidence bands: demand planning, KPI projection, capacity forecasting. ARIMA suits non-seasonal trend data; Holt-Winters handles repeating seasonality (set seasonLength). Needs at least ~20 observations for stable fit. For point-anomaly flags rather than projection, use detect_anomaly. Requires ORACLAW_API_KEY.

[Premium] Flag outlier points in a numeric series using Z-score (parametric, assumes ~normal) or IQR (robust to skew). Use for monitoring metrics, fraud signals, sensor noise, quality control. Z-score is faster and tighter on near-normal data; IQR is the right default when the distribution has heavy tails or known outliers. Returns indices + values + the underlying statistics. For projecting a series forward, use predict_forecast. Requires ORACLAW_API_KEY.

Find the shortest (or k-shortest) path between two nodes in a weighted graph using A* + Yen's algorithm. Use for routing, dependency resolution, project critical-path discovery, or 'how do I get from X to Y' questions on graphs. Set kPaths>1 to also return alternatives. For full graph structure analysis (centrality, communities), use analyze_graph. For task-to-time-slot assignment, use solve_schedule. Free.

Sample N draws from a parametric distribution and return summary statistics + percentiles + histogram. Use to quantify uncertainty around a single random factor: project NPV with uncertain growth rate, estimate latency tail percentiles, size insurance reserves. Supports normal/lognormal/uniform/triangular/beta/exponential. For multi-asset portfolio risk with correlations, use analyze_risk. Each call re-samples (non-idempotent). Capped at 2000 iterations on the free tier.

Score how well-calibrated a set of probability predictions are against observed binary outcomes using Brier score and log score. Use to evaluate forecaster accuracy, model calibration, prediction-market fairness. Lower Brier/log score = better. predictions[i] is the probability assigned to event i; outcomes[i] is 1 if it happened, 0 otherwise. For comparing multiple forecasters' agreement, use score_convergence instead. Free.

Update a prior probability with weighted evidence using a Beta-Bayesian posterior. Use for incremental belief revision: starting from a baseline probability, fold in new signals (each with a value in [0,1] and a weight) and get an updated posterior plus calibration score. Suited to fraud-risk scoring, A/B test stopping decisions, diagnostic probability stacking. For combining N independent model predictions, use predict_ensemble. For full distribution sampling, use simulate_montecarlo. Free.

Combine N model predictions into a single consensus value using weighted voting, stacking, or Bayesian model averaging. Returns the consensus, decomposed uncertainty (epistemic vs aleatoric), agreement score, weight share per model, and Shannon entropy of the weight distribution. Use to fuse outputs from heterogeneous predictors (statistical + ML + human forecasters). For fusing source-agreement on a probability of one event, use score_convergence. Free.

Genetic algorithm for combinatorial / discrete optimization with optional Pareto frontier for multi-objective problems. Use when the search space is discrete or mixed (binary feature selection, integer allocation, permutation problems like TSP), or when you want to explore multiple non-dominated solutions. For continuous black-box parameters, use optimize_cmaes — it converges faster on smooth objectives. Stochastic: same input gives different best chromosome each run. Free.

Compare named what-if scenarios against a base case, returning per-scenario outcome delta plus a sensitivity ranking showing which input variables move the outcome most across scenarios. Use for budget sensitivity analysis, deal what-ifs, capacity planning under multiple demand assumptions. The default outcome metric is the sum of input variables — supply scenarios that vary individual drivers to isolate their impact. For random sampling from a distribution, use simulate_montecarlo. Free.