Claude Opus 5.5 (effort default (no --effort flag) · thinking on) on Great-circle vs rhumb-line passage plan with ETAs

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

Trust 80%Fully autonomoussuccess · first tryCompare

Estimated cost: $0.22
Wall time: 46s
Human step-ins: 0
Outcome: Pass

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Exact prompt

# Great-circle vs rhumb-line passage plan with ETAs `input.json` (synthetic; not for navigation): `waypoints` ([lat, lon] decimal degrees, legs may cross the 180° meridian), `speed_kn`, `depart_utc` ("YYYY-MM-DDTHH:MM:SSZ"). Write `solve.py` (Python 3 standard library only); `python solve.py input.json answer.json` writes `answer.json` and `route.svg`. Fresh inputs are used too. ## Rules (sphere, R = 3440.065 nm) - Longitude difference dlon is always wrapped into [-180°, 180°). - **Great circle**: haversine distance; initial course = atan2(sin dlon * cos lat2, cos lat1 * sin lat2 - sin lat1 * cos lat2 * cos dlon) mod 360. - **Rhumb line**: dpsi = ln(tan(pi/4 + lat2/2) / tan(pi/4 + lat1/2)); q = dlat / dpsi, or cos(lat1) when |dpsi| <= 1e-12; distance = sqrt(dlat^2 + q^2 * dlon^2) * R (radians); course = atan2(dlon, dpsi) mod 360. - The boat sails the **rhumb** legs at `speed_kn`; leg ETA = departure + cumulative rhumb distance / speed, rounded to the nearest minute (half a minute rounds up), formatted "YYYY-MM-DDTHH:MMZ". - `rhumb_extra_pct` = (total rhumb - total GC) / total GC * 100. Round distances to 2 decimals, courses to 1, the percentage to 3. ## Visual output: route.svg Static, self-contained SVG (root `<svg>`, no scripts, images, links or external assets; renders headless) with `<polyline id="route-gc">`, `<polyline id="route-rhumb">` and an element `id="waypoints"`. The drawing (projection etc.) is not graded. ## answer.json `{"legs": [{"gc_nm", "gc_initial_course", "rhumb_nm", "rhumb_course", "eta_utc"}, ...], "total_gc_nm", "total_rhumb_nm", "rhumb_extra_pct", "arrival_utc"}` ## Scoring Hidden checks (partial credit; all must pass): `great_circle_legs`, `rhumb_legs` (first four legs; distances within 0.011, courses within 0.11), `totals`, `etas` (exact strings), `route_svg_static` (route.svg exists, follows the static rules, has the ids/tags above), `fresh_run_1`, `fresh_run_2` (all keys, within 0.02). 60-second limit per run.

Antimeridian wrap on both methods, the due east/west rhumb leg where dpsi is zero, initial great-circle course, and minute-rounded UTC ETAs that drift if per-leg rounding is used. 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. great_circle_legs 2. rhumb_legs 3. totals 4. etas 5. route_svg_static 6. fresh_run_1 7. fresh_run_2

Setup notes: Use Case Scout batch 10 case k09-passage-gc-vs-rhumb (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 (route.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-opus-5.5: $0.224311. Score: 7/7. 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

Claude Opus 5.5 (effort default (no --effort flag) · thinking on) on Great-circle vs rhumb-line passage plan with ETAsSuccess

Metrics

Estimated cost: $0.22
Wall time: 46s
Human step-ins: 0
Turns: 6

Model usage
Model	Input tok	Output tok	Cost
AClaude Opus 5.5anthropic/claude-opus-5.5effort default (no --effort flag) · thinking on	84,261	5,551	$0.22

Reproduce this run

Use the use case prompt on the use case page.
Same setup: Claude Opus 5.5 (anthropic/claude-opus-5.5, effort default (no --effort flag) · thinking on) via Claude Code 2.1.299 (headless -p), cloud.
It counts as a success only if it meets every success criterion: 1. great_circle_legs 2. rhumb_legs 3. totals 4. etas 5. route_svg_static 6. fresh_run_1 7. fresh_run_2
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

Trust 80% comes from these checks (how Trust % works).

Run date is not in the future : passed
Model is in the dated pricing table : passed
Cost recomputed from tokens matches : passed
Cached tokens are consistent : passed
Output throughput is plausible : passed
Autonomy matches step-ins : passed
Step-ins do not exceed turns : passed
Retries agree with first-try result : passed
Evidence log SHA-256 matches : passed
Evidence log is substantial : passed

Evidence log

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    "contextWindow": 1000000,
    "maxOutputTokens": 128000,
    "thinkingTokens": 410,
    "canonicalModel": "claude-opus-5-5",
    "provider": "firstParty",
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  },
  "permission_denials": [],
  "terminal_reason": "completed",
  "fast_mode_state": "off",
  "fast_mode_disabled_reason": "sdk_opt_in_required",
  "subagent_stats": {
   "spawned": 0,
   "requested": {
    "background": 0,
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   "started_in_background": 0,
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  "subtype": "success",
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  "result": "I've written `solve.py`. I ran it once on the provided `input.json` and it wrote both `answer.json` and `route.svg`. I haven't run it on any other inputs, and there's no answer key here, so the numbers below aren't checked against the hidden grader.\n\n| Leg | GC nm / course | Rhumb nm / course | ETA |\n|---|---|---|---|\n| 1 | 232.74 / 156.1\u00b0 | 232.75 / 155.6\u00b0 | 2026-11-21T21:12Z |\n| 2 | 604.32 / 41.6\u00b0 | 604.44 / 39.5\u00b0 | 2026-11-24T21:10Z |\n| 3 (crosses 180\u00b0) | 770.53 / 93.4\u00b0 | 770.98 / 90.0\u00b0 | 2026-11-28T16:57Z |\n| 4 | 375.27 / 149.8\u00b0 | 375.29 / 148.9\u00b0 | 2026-11-30T13:38Z |\n| 5 | 122.30 / 125.9\u00b0 | 122.31 / 125.3\u00b0 | 2026-12-01T04:11Z |\n\n**Totals:** 2105.17 nm great circle against 2105.77 nm rhumb, so `rhumb_extra_pct` is 0.028. Arrival is 2026-12-01T04:11Z.\n\nLeg 3 starts and ends at the same latitude, so it runs due east (90.0\u00b0) and uses the `cos(lat1)` fallback from your rules. It also crosses the 180\u00b0 meridian, which the longitude wrapping handles.\n\nA few choices I made where the spec left room:\n- **Totals:** the totals and the percentage are worked out from unrounded leg distances and only rounded at the end.\n- **ETA rounding:** for half-up rounding to the minute, I add a 1e-9 tolerance so a value sitting exactly on half a minute isn't pushed down by floating-point error.\n- **`route.svg` location:** the spec doesn't say where it goes, so it's written next to `answer.json` and also in the current directory.\n\n**`route.svg`:** it's plain static SVG with no scripts, images, links or external assets. It contains the `route-gc` and `route-rhumb` polylines and a `<g id=\"waypoints\">` group. The drawing uses a Mercator-style projection with longitudes kept continuous, so the leg across 180\u00b0 draws as one line.",
  "ttft_ms": 2262,
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  "uuid": "[REDACTED]",
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  "time_to_request_ms": 227,
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 }
]