Math Tools

Why this matters

LLMs cannot reliably compute standard deviations, fit regression lines, or produce consistent numeric sequences. Math tools handle the full lifecycle: generate data, compute statistics, detect trends, measure correlation — all deterministically. When reproducibility matters — audit trails, regression tests, financial models — pass a seed and the output is identical across runs, servers, and time.

Generation

• ✓math.range — Evenly-spaced sequences from start to stop with exact step arithmetic
• ✓math.linspace — Exactly N points between start and stop (NumPy-style)
• ✓math.sequence — Named sequences: fibonacci, primes, triangular, square, geometric, powers
• ✓math.sample — Draw from uniform, normal, or exponential distributions with optional seed
• ✓math.interpolate — Lerp, clamp, remap, smoothstep, and 12 easing functions with batch support

Analysis

• ✓math.describe — Full descriptive statistics: mean, median, std, variance, percentiles (p5/p25/p50/p75/p95), skewness, and binned histogram for distribution shape
• ✓math.window — Sliding window operations: moving average, moving sum, cumulative sum, first differences, percentage change, lag, and EWMA
• ✓math.correlate — Pearson and Spearman pairwise correlation with r-squared, interpretation labels, and scatter-ready paired records
• ✓math.trend — Regression fitting: linear, polynomial (degree 2–5), exponential, and logarithmic models with r-squared, equation strings, fitted values, and forecasting
• ✓math.normalize — Scale data using z-score (mean=0, std=1), min-max (to [0,1] or custom range), or percentile rank (0–100)
• ✓math.outliers — Detect anomalies via IQR or z-score methods; returns outlier indices, threshold bounds, and a cleaned array
• ✓math.rank — Rank values using ordinal, dense, average, or percentile methods with tie detection

Use cases

• ◆Test data generation — Reproducible datasets for QA pipelines: seeded samples that don't change between runs
• ◆Animation and UI — Easing curves, smoothstep transitions, interpolated color ramps for agent-generated interfaces
• ◆Financial modeling — Time series with moving averages, trend detection, correlation between metrics, Monte Carlo inputs
• ◆Data quality — Outlier detection with math.outliers, distribution profiling with math.describe, change-point detection with pct_change and first differences
• ◆Scientific computation — Linspace grids, regression fits, correlation analysis, exact step arithmetic without floating-point drift
• ◆Quantitative analysis — Moving averages for smoothing, EWMA for signal extraction, trend lines for forecasting, correlation for portfolio analysis

Example: generate and ease

// Generate data, clean outliers, normalize, and fit a polynomial trend
{ "name": "data-grout@1/math.sample@1",
  "arguments": { "distribution": "normal", "count": 200, "mean": 50, "std": 15, "seed": 42 }
}

// Detect and remove outliers using IQR method
{ "name": "data-grout@1/math.outliers@1",
  "arguments": { "cache_ref": "$sample._meta.cache_ref", "method": "iqr" }
}

// Normalize cleaned data to [0, 1] range
{ "name": "data-grout@1/math.normalize@1",
  "arguments": { "payload": "$outliers.clean_values", "method": "minmax" }
}

// Fit a quadratic trend with 10-point forecast
{ "name": "data-grout@1/math.trend@1",
  "arguments": { "cache_ref": "$normalize._meta.cache_ref", "model": "polynomial", "degree": 2, "forecast": 10 }
}

Output is chart-ready — pass records directly to prism.chart for visualization.