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Claude Sonnet 5.5 (effort default (no --effort flag) · thinking on) on Tide height by rule of twelfths and cosine, with under-keel clearance windows

AClaude Sonnet 5.5default · thinking on · Claude Code 2.1.299 (headless -p) · cloud · 2026-10-20 · by @bobsiopener

Trust 80%Fully autonomoussuccess · first try
Estimated cost
$0.06
Wall time
18s
Human step-ins
0
Outcome
Pass

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Summary

Exact prompt

# Tide height by rule of twelfths and cosine, and under-keel clearance `input.json` (synthetic, not for navigation) gives two consecutive tide events `event1` and `event2` (`time_min` minutes, `height_m`; either rising or falling), `chart_depth_m`, the boat's `draft_m`, required `min_ukc_m`, `need_minutes`, and `queries` (minutes). Write `solve.py` (Python 3 standard library only); `python solve.py input.json answer.json` writes `answer.json` and `tide.svg`. Fresh inputs are used too. ## Rules Let T = event2 time - event1 time and f = (t - event1 time) / T clamped to [0, 1]. Height = h1 + (h2 - h1) * F(f). - **Twelfths**: split [0, 1] into 6 equal parts; cumulative fractions at the part boundaries are 0, 1, 3, 6, 9, 11, 12 twelfths; interpolate linearly inside a part. - **Cosine**: F(f) = (1 - cos(pi * f)) / 2. - Under-keel clearance UKC = chart_depth + height(twelfths) - draft. A query is `safe` if UKC >= min_ukc. `required_height_m` = draft + min_ukc - chart_depth. - Safe window (per method): scan whole minutes t from event1 to event2 inclusive; a run is consecutive minutes with height >= required height. Report the first run whose length end - start (minutes) is >= `need_minutes` as `{"start", "end"}` (first and last safe minute), or null. - `max_method_diff_m`: the largest |twelfths - cosine| over those whole minutes. Use a 1e-9 tolerance on the >= comparisons. Round heights and UKC to 3 decimals. ## Visual output: tide.svg Static, self-contained SVG (root `<svg>`, no scripts, images, links or external assets; renders headless) with `<polyline id="tide-twelfths">`, `<polyline id="tide-cosine">` and `<line id="min-depth-line">` at the required height. The drawing itself is not graded. ## answer.json `{"required_height_m", "queries": [{"t", "twelfths", "cosine", "ukc", "safe"}, ...], "window_twelfths", "window_cosine", "max_method_diff_m"}` ## Scoring Hidden checks (partial credit; all must pass): `query_heights`, `safe_windows` (exact), `method_difference`, `tide_svg_static` (tide.svg exists, follows the static rules, has the ids/tags above), `fresh_run_1`, `fresh_run_2`. Numbers within 0.0015. 60-second limit per run.

Piecewise twelfths interpolation vs the cosine curve on rising and falling tides, a clamped fraction, a minute-by-minute run search with a length rule, and exact window endpoints. Original benchmark task written for usecaserank.com (not based on a specific public post). Headless, offline run on a reproducible fixture. Each run's notes say how its cost was measured (estimates are marked).

Benchmark code for comparing AI models, not navigation or safety software.

Success criteria: 1. query_heights 2. safe_windows 3. method_difference 4. tide_svg_static 5. fresh_run_1 6. fresh_run_2

Setup notes: Use Case Scout batch 10 case k05-tide-underkeel-clearance (offline fixture). Prepared with batch10/prepare.sh; hidden key/tests kept outside the agent's work dir. Prompt = TASK.md verbatim. Scored with the scout's scorer: `python score.py WORKDIR KEYDIR`. Tools: Read/Write/Edit/Glob/Grep/Bash, web disabled. Single run, no retries. Visual output (tide.svg) rendered offline to PNG with google-chrome headless, network blocked, 1280x800 at ~3 s after load. Claude Code's own reported cost for claude-sonnet-5.5: $0.059007. Score: 6/6. Cost is an ESTIMATE: measured tokens x pricing.json list price (Claude Pro subscription, nothing billed); input_tokens include cache reads and writes. Single run.

Estimated cost List-price estimate; not actually billed.

Output

Metrics

Estimated cost
$0.06
Wall time
18s
Human step-ins
0
Turns
3
Model usage
ModelInput tokOutput tokCost
AClaude Sonnet 5.5anthropic/claude-sonnet-5.5effort default (no --effort flag) · thinking on58,9141,972$0.06

Reproduce this run

  1. Use the use case prompt on the use case page.
  2. Same setup: Claude Sonnet 5.5 (anthropic/claude-sonnet-5.5, effort default (no --effort flag) · thinking on) via Claude Code 2.1.299 (headless -p), cloud.
  3. It counts as a success only if it meets every success criterion: 1. query_heights 2. safe_windows 3. method_difference 4. tide_svg_static 5. fresh_run_1 6. fresh_run_2
  4. Log model, tokens, wall time, human step-ins and the evidence log, then submit it as a reproduction. A different model? Submit a head-to-head rerun.

How runs are scored: Methodology.

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Automated checks

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Evidence log
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  "subagent_stats": {
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  "result": "I wrote `solve.py` and ran it on `input.json`. It wrote `answer.json` and `tide.svg` without errors. I haven't checked the output against the hidden checks, and I haven't opened `tide.svg` in a renderer. I also haven't tried a rising-to-falling or other fresh input.\n\nOn the sample input:\n- **Required height:** 1.54 m.\n- **Safe queries:** the first five (t = 597 to 656) are unsafe. t = 767 is safe, with UKC 0.995.\n- **Cosine window:** starts at minute 722 and ends at 937.\n- **Twelfths window:** I only saw its end (937), not its start.\n- **Method difference:** the largest gap between the two methods is 0.05 m.\n\n`tide.svg` is a plain SVG with the `tide-twelfths` and `tide-cosine` polylines and the `min-depth-line` at the required height. It has no scripts, images or links.\n\nThe script assumes event2 is later than event1. If both events have the same time, it treats f as 1 rather than dividing by zero.",
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]

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