feat: add StatVar for numerically stable statistics in audit and logs commands

[Copilot]

Summary

Adds a pkg/stats.StatVar statistical variable type and uses it throughout the audit and logs commands to compute richer, more statistically correct metrics.

Changes

New: pkg/stats.StatVar

• Accumulates float64 observations incrementally
• Uses Welford's online algorithm for numerically stable mean and variance (avoids catastrophic cancellation with large, tightly-clustered values)
• Computes: count, sum, min, max, mean, population variance/stddev, sample variance/stddev (Bessel's correction), and exact median
• Memory usage is documented: suitable for tens–hundreds of observations (typical agentic workflow scale)

pkg/workflow/metrics.go — LogMetrics

• Added MedianTimeBetweenTurns time.Duration
• Added StdDevTimeBetweenTurns time.Duration (sample stddev)

pkg/cli/copilot_events_jsonl.go

• Replaced manual TBT accumulation loop with stats.StatVar
• Now sets AvgTimeBetweenTurns, MaxTimeBetweenTurns, MedianTimeBetweenTurns, and StdDevTimeBetweenTurns

pkg/cli/audit_cross_run.go — MetricsTrendData

• Added MedianCost, StdDevCost, MedianTokens, StdDevTokens, MedianTurns, StdDevTurns, MedianDurationNs, StdDevDurationNs
• buildMetricsTrend() now uses StatVar for all four metric dimensions (cost, tokens, turns, duration), replacing verbose manual min/max/sum loops

pkg/cli/health_metrics.go

• CalculateWorkflowHealth() now uses StatVar internally for duration, token, and cost averages

Test coverage

• pkg/stats/statvar_test.go: 9 test cases covering empty, single, two-observation, odd/even count, known variance (Wikipedia example), numerical stability, median idempotency, and all-identical inputs

[Copilot]

Pull request overview

Introduces a new pkg/stats.StatVar utility for numerically stable, incremental descriptive statistics (Welford) and wires it into CLI audit/log health metrics to compute richer aggregates (median/stddev in addition to avg/min/max).

Changes:

• Added pkg/stats.StatVar (mean/variance/stddev + exact median) with unit tests.
• Extended workflow.LogMetrics with median + sample stddev for time-between-turns and populated these in copilot_events_jsonl parsing.
• Refactored cross-run audit and workflow health computations to use StatVar for cost/tokens/turns/duration aggregation.

Show a summary per file

File	Description
pkg/stats/statvar.go	New streaming stats accumulator (Welford) + exact median support.
pkg/stats/statvar_test.go	Unit tests for StatVar behavior and numerical stability.
pkg/workflow/metrics.go	Adds median/stddev fields for time-between-turns in LogMetrics.
pkg/cli/copilot_events_jsonl.go	Uses StatVar to compute avg/max/median/stddev TBT from timestamps.
pkg/cli/audit_cross_run.go	Uses StatVar to compute cross-run avg/median/stddev for key metrics.
pkg/cli/health_metrics.go	Uses StatVar internally to compute workflow health averages.

Copilot's findings

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• Files reviewed: 6/6 changed files
• Comments generated: 3

[Copilot]

totalDuration is accumulated but never used in this function (there is no TotalDuration field on WorkflowHealth). This will fail compilation due to an unused variable. Remove totalDuration and the totalDuration += run.Duration line, or add a corresponding output field if the total duration is intended to be reported.

[Copilot]

The doc comment says NaN and ±Inf "will propagate through all derived statistics", but Min()/Max() may not propagate when NaN is added after initial finite values (comparisons with NaN are false, leaving min/max unchanged). Either update the comment to reflect actual behavior, or explicitly detect NaN/Inf in Add and set min/max accordingly (e.g., if math.IsNaN(v) then force min/max to NaN).

Suggested change

	if v < s.min {
	s.min = v
	}
	if v > s.max {
	s.max = v
	if math.IsNaN(v) {
	s.min = v
	s.max = v
	} else {
	if v < s.min {
	s.min = v
	}
	if v > s.max {
	s.max = v
	}

[Copilot]

The MetricsTrendData type comment is duplicated twice back-to-back, which makes the docs noisy and harder to read. Remove one of the duplicate two-line blocks so the doc comment appears only once.

Suggested change

	// MetricsTrendData contains aggregated cost, token, turn, and duration statistics
	// across multiple runs, with spike detection for anomalous runs.

[pelikhan]

@copilot review all comments

[Copilot]

@copilot review all comments

Addressed all three review comments in 39f35b1:

1. health_metrics.go — removed unused totalDuration variable and accumulation line
2. audit_cross_run.go — removed the duplicate MetricsTrendData comment block
3. statvar.go — updated the Add() doc comment to accurately state that NaN will propagate through sum/mean/variance but that Min/Max may not update correctly for NaN inputs due to IEEE 754 comparison semantics, and notes that in practice all inputs are finite (time.Duration, token counts, costs)