feat: add cache compounding savings to rtk gain

[sahilmgandhi]

I think more importantly than just the immediate savings of rtk, it also offers compounding savings in the form of less cache thrashing. This is helpful both from a monetary perspective (cache writes/reads cost money) and also from a time perspective (fewer tokens from cache => less thinking => less time for output** (potentially))

Summary

• Adds a "Cache Compounding Effect" section to rtk gain showing how direct token savings multiply through Claude Code's prompt caching
• Scans JSONL session files to compute average session length, then applies the multiplier: 1.25 + 0.1 × avg_remaining_turns
• Includes optional dollar amounts when ccusage is installed
• Adds cache_compounding field to JSON/CSV export

How it works

When RTK removes tokens from command output, those tokens:

1. Never get written to cache (avoids 1.25x input cost)
2. Never get re-read from cache on every subsequent turn (avoids 0.1x per turn)

For a session with 336 avg turns (median position = 168 remaining), the multiplier is 1.25 + 0.1 × 168 = 18.06x.

Example output

Cache Compounding Effect
target/release/rtk gain
RTK Token Savings (Global Scope)
════════════════════════════════════════════════════════════

Total commands:    684
Input tokens:      2.0M
Output tokens:     255.4K
Tokens saved:      1.7M (87.1%)
Total exec time:   16m2s (avg 1.4s)
Efficiency meter: █████████████████████░░░ 87.1%

By Command
────────────────────────────────────────────────────────────────────────
  #  Command                   Count   Saved    Avg%    Time  Impact
────────────────────────────────────────────────────────────────────────
 1.  rtk go test ./server/...      2  866.3K  100.0%   41.9s  ██████████
 2.  rtk go test ./server/...      1  393.4K  100.0%   27.3s  █████░░░░░
 3.  rtk cargo clippy --al...     26  144.2K   92.9%   693ms  ██░░░░░░░░
 4.  rtk cargo test                8   62.2K   99.6%    2.3s  █░░░░░░░░░
 5.  rtk cargo test --all          5   38.2K   99.8%    1.6s  ░░░░░░░░░░
 6.  rtk find                    167   30.9K   79.1%     1ms  ░░░░░░░░░░
 7.  rtk git diff b0378a62...      4   26.7K   76.6%    53ms  ░░░░░░░░░░
 8.  rtk go test -run Test...      2   13.7K   99.9%   15.1s  ░░░░░░░░░░
 9.  rtk cargo test -- --n...      1    8.6K   99.9%    1.1s  ░░░░░░░░░░
10.  rtk ls                       34    8.3K   61.5%     7ms  ░░░░░░░░░░
────────────────────────────────────────────────────────────────────────

Cache Compounding Effect
──────────────────────────────────────────────────────────────
Direct savings:    1.7M
Avg session turns: 337 (from 48 sessions)
Avg remaining:     169
Cache multiplier:  18.12x  (1.25 + 0.1 x 169)
  ┌─────────────────────────────────────────────────────────┐
  │ Effective savings:   31.2M tokens  ($153.13)            │
  └─────────────────────────────────────────────────────────┘
How: Saved tokens avoid 1.25x cache write + 0.1x per
subsequent turn. Longer sessions = bigger multiplier.
How: Saved tokens avoid 1.25x cache write + 0.1x per
subsequent turn. Longer sessions = bigger multiplier.

Graceful degradation

• No Claude Code sessions found → uses fallback estimate of 20 turns with "(model estimate)" label
• No ccusage installed → omits dollar amount, shows install tip
• Any failure → section silently omitted

Files changed

File	Change
src/session_stats.rs	NEW — session stats + compounding logic (8 unit tests)
src/cc_economics.rs	Export WEIGHT_* constants as pub(crate), remove dead BILLION
src/main.rs	Register mod session_stats
src/gain.rs	Add display + JSON/CSV export, consolidate color helpers

Test plan

• cargo fmt --all --check — clean
• cargo clippy --all-targets — no new warnings
• cargo test --all — 422 passed, 2 ignored
• Manual: rtk gain shows new section with real session data
• Manual: rtk gain --format json includes cache_compounding field