…t sum (#3)

computeEnhancedStats emitted one segment per tool/agent and summed their
durations. When tools or subagents are fanned out in a single assistant turn
(e.g. a 5-agent review panel, or parallel Read/Bash calls), those segments
overlap in wall-clock time, so summing double-counts the concurrency — the
'Subagents' bar reported cumulative agent-seconds, not real elapsed time, and
the active-time percentages could sum to >100% (e.g. 109%).

Aggregate toolExec and subagent by wall-clock interval UNION instead:
  - subagent = time with >=1 subagent open
  - toolExec = busy-with-a-tool time NOT already counted as subagent
    (subagent wins the rare cross-kind overlap, e.g. Agent + Bash in one turn)
claudeThink / planning / humanWait / humanAway are emitted as sequential,
non-overlapping slices and are still summed (unchanged).

On a fan-out-heavy session this dropped reported subagent time from ~53m
(sum of 19 overlapping agents) to ~38m (true elapsed), and the breakdown now
sums to ~100% instead of 109%. The per-call 'Tools' latency table (avg/p50/p95)
is computed separately and is intentionally unchanged.

Tests: 3 cases (parallel agents → union not sum; parallel non-agent tools →
union; sequential agents still add up). 90/90 tests pass.

Time accounting must aggregate possibly-overlapping phase spans by wall-clock
UNION, not SUM — parallel tool/subagent spans (two tool_use in one assistant
message share the same start) overlap, so a naive sum overcounts and can exceed
the session's wall-clock. This adds a regression guard:

- union(enhancedSegments) ≤ (max endTime − min startTime), always
- a parallel-tools scenario where naiveSum > span (proves the overlap is real,
  so the invariant is non-vacuous) while union ≤ span
- each segment is a valid non-negative interval (endTime ≥ startTime,
  durationMs === endTime − startTime)

Pure test addition (no src change). Full suite 89 passing; tsc clean. Came out
of an independent wall/active/away recompute that used exactly this union-vs-sum
cross-check to reconcile against the live tool.

Co-authored-by: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

)

Surfaces the value of fanning out: the subagent phase is aggregated by
wall-clock union (correct elapsed time), but sum−union = time saved by running
agents concurrently and sum/union = effective concurrency. Adds an Insights
line shown only when ≥2 subagents actually overlapped (saved >1s), so
sequential sessions get no spurious line. Exports unionMs from analyzer for
reuse. +3 formatter tests. 102 pass; tsc clean.