DeepSeek V4.1 Flash (Venice) (thinking on) on Dead reckoning, estimated position with current, and computed set and drift
DDeepSeek V4.1 Flash (Venice)thinking on · venice-mini-agent v1.3.1 · cloud · 2026-10-27 · by @bobsiopener
- Estimated cost
- $0.0073
- Wall time
- 23s
- Human step-ins
- 0
- Outcome
- Pass
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Summary
Exact prompt
# Dead reckoning, estimated position with current, and computed set and drift `input.json` (synthetic, not for navigation): `start` [lat, lon] in decimal degrees, `legs` (each `course` degrees true, `speed_kn` through the water, `minutes`), a forecast `current` (`set` = direction it flows TOWARD, degrees true; `drift_kn`), and a GPS `fix` [lat, lon] at the end of the last leg. Write `solve.py` (Python 3 standard library only); `python solve.py input.json answer.json` writes `answer.json` and `track.svg`. Fresh inputs are used too. ## Rules (plane sailing, 1 minute of latitude = 1 nm) 1. A move of n nm north and e nm east from (lat, lon): dlat = n / 60; mid = lat + dlat / 2; new lat = lat + dlat; new lon = lon + e / (60 * cos(mid)). 2. **DR**: per leg, distance = speed * hours along the course. **EP**: per leg, add the current vector (drift * hours toward set) to the leg's water vector, then move once. 3. Difference from point A to point B: north = (latB - latA) * 60, east = (lonB - lonA) * 60 * cos((latA + latB) / 2). 4. **Set/drift**: vector from the final DR position to the fix; set = atan2(east, north) in degrees mod 360; drift = length / total hours. `ep_error_nm` = distance from the final EP to the fix. **CMG/SMG**: same from `start` to the fix. 5. Round positions to 5 decimals, hours to 4, angles to 1, speeds and distances to 3. `dr` and `ep` list the start and the position after every leg. ## Visual output: track.svg Static, self-contained SVG (root `<svg>`, no scripts, images, links or external assets; renders headless) with `<polyline id="dr-track">`, `<polyline id="ep-track">` and `<circle id="fix">`. The drawing itself is not graded. ## answer.json `{"dr": [[lat, lon], ...], "ep": [...], "hours", "set_deg", "drift_kn", "ep_error_nm", "cmg_deg", "smg_kn"}` ## Scoring Hidden checks (partial credit; all must pass): `dr_positions`, `ep_positions`, `set_and_drift`, `course_speed_made_good`, `track_svg_static` (track.svg exists, follows the static rules, has the ids/tags above), `fresh_run_1`, `fresh_run_2`. Positions within 2e-5 degrees, angles within 0.11, speeds and distances within 0.002. 60-second limit per run.
Mid-latitude longitude scaling per leg, current applied per leg as a vector, 'set' as the direction the current flows toward, angle wrap, and positions checked at five decimals at high latitudes. Inspired by https://x.com/sm0rwo/status/2097955012949197155 Headless, offline run on a reproducible fixture. Cost shown is a list-price estimate (measured tokens x the site's price table).
Benchmark code for comparing AI models, not navigation or safety software.
Success criteria: 1. dr_positions 2. ep_positions 3. set_and_drift 4. course_speed_made_good 5. track_svg_static 6. fresh_run_1 7. fresh_run_2
Setup notes: Use Case Scout batch 10 case k06-dead-reckoning-set-drift (offline fixture). Prepared with the case's setup script; hidden key/tests kept outside the agent's work dir. Prompt = TASK.md verbatim. Scored automatically with the scout's scorer. Tools: list_files/read_file/write_file/run_shell (venice-mini-agent v1.3), web disabled. Single run, no retries. Visual output (track.svg) rendered offline to PNG with google-chrome headless, network blocked, 1280x800 at ~3 s after load. Harness: venice-mini-agent v1.3.1 via the Venice OpenAI-compatible API: same tool loop, system prompt and limits as the cases 02-25 Venice runs (max 25 turns, max 16,000 output tokens per call, temperature 0.2, Venice system prompt and web search off, per-run cost cap $0.05, thinking on (model default)). Same task text, work-dir layout and scorer as the Claude runs of this case. Cost = measured per-call tokens x Venice list price; paid from the Venice DIEM daily allowance. Harness: venice-mini-agent v1.3.1 via Venice OpenAI-compatible API (16000 max tokens/call, $0.05 run cap). Score: 7/7. Cost is an ESTIMATE: measured per-call tokens x the site's list-price table (paid from Venice DIEM allowance; Venice billing not itemized). input tokens include cached reads. Single run.
Estimated cost List-price estimate; not actually billed.
Output
Metrics
- Estimated cost
- $0.0073
- Wall time
- 23s
- Human step-ins
- 0
- Turns
- 5
| Model | Input tok | Output tok | Cost |
|---|---|---|---|
| DDeepSeek V4.1 Flash (Venice)venice/deepseek-v4-1-flashthinking on | 13,914 | 3,541 | $0.0073 |
Reproduce this run
- Use the use case prompt on the use case page.
- Same setup: DeepSeek V4.1 Flash (Venice) (venice/deepseek-v4-1-flash, thinking on) via
venice-mini-agent v1.3.1, cloud. - It counts as a success only if it meets every success criterion: 1. dr_positions 2. ep_positions 3. set_and_drift 4. course_speed_made_good 5. track_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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"arguments": "{\"path\":\"solve.py\",\"content\":\"#!/usr/bin/env python3\\n\\\"\\\"\\\"Dead reckoning, estimated position with current, and computed set and drift.\\n\\nUsage: python solve.py input.json answer.json\\nWrites answer.json and track.svg (in the current directory).\\n\\\"\\\"\\\"\\nimport json\\nimport math\\nimport sys\\n\\n\\ndef move(lat, lon, n, e):\\n \\\"\\\"\\\"Move n nm north and e nm east from (lat, lon).\\\"\\\"\\\"\\n dlat = n / 60.0\\n mid = lat + dlat / 2.0\\n new_lat = lat + dlat\\n new_lon = lon + e / (60.0 * math.cos(math.radians(mid)))\\n return new_lat, new_lon\\n\\n\\ndef diff(a, b):\\n \\\"\\\"\\\"Difference from point A to point B: (north, east) in nm.\\\"\\\"\\\"\\n latA, lonA = a\\n latB, lonB = b\\n north = (latB - latA) * 60.0\\n east = (lonB - lonA) * 60.0 * math.cos(math.radians((latA + latB) / 2.0))\\n return north, east\\n\\n\\ndef bearing(north, east):\\n \\\"\\\"\\\"Direction in degrees true, mod 360.\\\"\\\"\\\"\\n return math.degrees(math.atan2(east, north)) % 360.0\\n\\n\\ndef main():\\n if len(sys.argv) < 3:\\n print(\\\"usage: python solve.py input.json answer.json\\\", file=sys.stderr)\\n return 1\\n in_path = sys.argv[1]\\n out_path = sys.argv[2]\\n\\n with open(in_path, \\\"r\\\") as f:\\n data = json.load(f)\\n\\n start = [float(data[\\\"start\\\"][0]), float(data[\\\"start\\\"][1])]\\n legs = data[\\\"legs\\\"]\\n current = data[\\\"current\\\"]\\n fix = [float(data[\\\"fix\\\"][0]), float(data[\\\"fix\\\"][1])]\\n\\n set_deg = float(current[\\\"set\\\"])\\n drift_kn = float(current[\\\"drift_kn\\\"])\\n\\n dr = [list(start)]\\n ep = [list(start)]\\n\\n dr_lat, dr_lon = start\\n ep_lat, ep_lon = start\\n\\n total_hours = 0.0\\n\\n for leg in legs:\\n course = float(leg[\\\"course\\\"])\\n speed = float(leg[\\\"speed_kn\\\"])\\n minutes = float(leg[\\\"minutes\\\"])\\n hours = minutes / 60.0\\n total_hours += hours\\n\\n # Water vector for this leg.\\n dist = speed * hours\\n n_w = dist * math.cos(math.radians(course))\\n e_w = dist * math.sin(math.radians(course))\\n\\n # DR: move along water vector only.\\n dr_lat, dr_lon = move(dr_lat, dr_lon, n_w, e_w)\\n dr.append([dr_lat, dr_lon])\\n\\n # EP: add current vector to the water vector, then move once.\\n c_dist = drift_kn * hours\\n n_c = c_dist * math.cos(math.radians(set_deg))\\n e_c = c_dist * math.sin(math.radians(set_deg))\\n ep_lat, ep_lon = move(ep_lat, ep_lon, n_w + n_c, e_w + e_c)\\n ep.append([ep_lat, ep_lon])\\n\\n # Set and drift: vector from final DR to the fix.\\n n_sd, e_sd = diff([dr_lat, dr_lon], fix)\\n set_val = bearing(n_sd, e_sd)\\n drift_val = math.hypot(n_sd, e_sd) / total_hours if total_hours else 0.0\\n\\n # EP error: distance from final EP to the fix.\\n n_ep, e_ep = diff([ep_lat, ep_lon], fix)\\n ep_error = math.hypot(n_ep, e_ep)\\n\\n # CMG / SMG: from start to the fix.\\n n_cm, e_cm = diff(start, fix)\\n cmg = bearing(n_cm, e_cm)\\n smg = math.hypot(n_cm, e_cm) / total_hours if total_hours else 0.0\\n\\n def rp(p):\\n return [round(p[0], 5), round(p[1], 5)]\\n\\n answer = {\\n \\\"dr\\\": [rp(p) for p in dr],\\n \\\"ep\\\": [rp(p) for p in ep],\\n \\\"hours\\\": round(total_hours, 4),\\n \\\"set_deg\\\": round(set_val, 1),\\n \\\"drift_kn\\\": round(drift_val, 3),\\n \\\"ep_error_nm\\\": round(ep_error, 3),\\n \\\"cmg_deg\\\": round(cmg, 1),\\n \\\"smg_kn\\\": round(smg, 3),\\n }\\n\\n with open(out_path, \\\"w\\\") as f:\\n json.dump(answer, f)\\n\\n write_svg(\\\"track.svg\\\", dr, ep, fix)\\n return 0\\n\\n\\ndef write_svg(path, dr, ep, fix):\\n pts = list(dr) + list(ep) + [list(fix)]\\n lats = [p[0] for p in pts]\\n lons = [p[1] for p in pts]\\n min_lat, max_lat = min(lats), max(lats)\\n min_lon, max_lon = min(lons), max(lons)\\n\\n width, height = 800.0, 600.0\\n pad = 40.0\\n span_lat = max(max_lat - min_lat, 1e-9)\\n span_lon = max(max_lon - min_lon, 1e-9)\\n scale = min((width - 2 * pad) / span_lon, (height - 2 * pad) / span_lat)\\n\\n def to_xy(p):\\n x = pad + (p[1] - min_lon) * scale\\n y = height - pad - (p[0] - min_lat) * scale\\n return x, y\\n\\n def polyline(pid, color, points):\\n coords = \\\" \\\".join(\\\"%.2f,%.2f\\\" % to_xy(p) for p in points)\\n return ('<polyline id=\\\"%s\\\" fill=\\\"none\\\" stroke=\\\"%s\\\" '\\n 'stroke-width=\\\"2\\\" points=\\\"%s\\\"/>' % (pid, color, coords))\\n\\n fx, fy = to_xy(fix)\\n parts = []\\n parts.append('<?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?>')\\n parts.append('<svg xmlns=\\\"http://www.w3.org/2000/svg\\\" width=\\\"%d\\\" height=\\\"%d\\\" '\\n 'viewBox=\\\"0 0 %d %d\\\">' % (int(width), int(height), int(width), int(height)))\\n parts.append('<rect x=\\\"0\\\" y=\\\"0\\\" width=\\\"%d\\\" height=\\\"%d\\\" fill=\\\"white\\\"/>' % (int(width), int(height)))\\n parts.append(polyline(\\\"dr-track\\\", \\\"#1f77b4\\\", dr))\\n parts.append(polyline(\\\"ep-track\\\", \\\"#ff7f0e\\\", ep))\\n parts.append('<circle id=\\\"fix\\\" cx=\\\"%.2f\\\" cy=\\\"%.2f\\\" r=\\\"5\\\" fill=\\\"red\\\"/>' % (fx, fy))\\n parts.append('</svg>')\\n\\n with open(path, \\\"w\\\") as f:\\n f.write(\\\"\\\\n\\\".join(parts) + \\\"\\\\n\\\")\\n\\n\\nif __name__ == \\\"__main__\\\":\\n sys.exit(main())\\n\"}"
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"content": "#!/usr/bin/env python3\n\"\"\"Dead reckoning, estimated position with current, and computed set and drift.\n\nUsage: python solve.py input.json answer.json\nWrites answer.json and track.svg (in the current directory).\n\"\"\"\nimport json\nimport math\nimport sys\n\n\ndef move(lat, lon, n, e):\n \"\"\"Move n nm north and e nm east from (lat, lon).\"\"\"\n dlat = n / 60.0\n mid = lat + dlat / 2.0\n new_lat = lat + dlat\n new_lon = lon + e / (60.0 * math.cos(math.radians(mid)))\n return new_lat, new_lon\n\n\ndef diff(a, b):\n \"\"\"Difference from point A to point B: (north, east) in nm.\"\"\"\n latA, lonA = a\n latB, lonB = b\n north = (latB - latA) * 60.0\n east = (lonB - lonA) * 60.0 * math.cos(math.radians((latA + latB) / 2.0))\n return north, east\n\n\ndef bearing(north, east):\n \"\"\"Direction in degrees true, mod 360.\"\"\"\n return math.degrees(math.atan2(east, north)) % 360.0\n\n\ndef main():\n if len(sys.argv) < 3:\n print(\"usage: python solve.py input.json answer.json\", file=sys.stderr)\n return 1\n in_path = sys.argv[1]\n out_path = sys.argv[2]\n\n with open(in_path, \"r\") as f:\n data = json.load(f)\n\n start = [float(data[\"start\"][0]), float(data[\"start\"][1])]\n legs = data[\"legs\"]\n current = data[\"current\"]\n fix = [float(data[\"fix\"][0]), float(data[\"fix\"][1])]\n\n set_deg = float(current[\"set\"])\n drift_kn = float(current[\"drift_kn\"])\n\n dr = [list(start)]\n ep = [list(start)]\n\n dr_lat, dr_lon = start\n ep_lat, ep_lon = start\n\n total_hours = 0.0\n\n for leg in legs:\n course = float(leg[\"course\"])\n speed = float(leg[\"speed_kn\"])\n minutes = float(leg[\"minutes\"])\n hours = minutes / 60.0\n total_hours += hours\n\n # Water vector for this leg.\n dist = speed * hours\n n_w = dist * math.cos(math.radians(course))\n e_w = dist * math.sin(math.radians(course))\n\n # DR: move along water vector only.\n dr_lat, dr_lon = move(dr_lat, dr_lon, n_w, e_w)\n dr.append([dr_lat, dr_lon])\n\n # EP: add current vector to the water vector, then move once.\n c_dist = drift_kn * hours\n n_c = c_dist * math.cos(math.radians(set_deg))\n e_c = c_dist * math.sin(math.radians(set_deg))\n ep_lat, ep_lon = move(ep_lat, ep_lon, n_w + n_c, e_w + e_c)\n ep.append([ep_lat, ep_lon])\n\n # Set and drift: vector from final DR to the fix.\n n_sd, e_sd = diff([dr_lat, dr_lon], fix)\n set_val = bearing(n_sd, e_sd)\n drift_val = math.hypot(n_sd, e_sd) / total_hours if total_hours else 0.0\n\n # EP error: distance from final EP to the fix.\n n_ep, e_ep = diff([ep_lat, ep_lon], fix)\n ep_error = math.hypot(n_ep, e_ep)\n\n # CMG / SMG: from start to the fix.\n n_cm, e_cm = diff(start, fix)\n cmg = bearing(n_cm, e_cm)\n smg = math.hypot(n_cm, e_cm) / total_hours if total_hours else 0.0\n\n def rp(p):\n return [round(p[0], 5), round(p[1], 5)]\n\n answer = {\n \"dr\": [rp(p) for p in dr],\n \"ep\": [rp(p) for p in ep],\n \"hours\": round(total_hours, 4),\n \"set_deg\": round(set_val, 1),\n \"drift_kn\": round(drift_val, 3),\n \"ep_error_nm\": round(ep_error, 3),\n \"cmg_deg\": round(cmg, 1),\n \"smg_kn\": round(smg, 3),\n }\n\n with open(out_path, \"w\") as f:\n json.dump(answer, f)\n\n write_svg(\"track.svg\", dr, ep, fix)\n return 0\n\n\ndef write_svg(path, dr, ep, fix):\n pts = list(dr) + list(ep) + [list(fix)]\n lats = [p[0] for p in pts]\n lons = [p[1] for p in pts]\n min_lat, max_lat = min(lats), max(lats)\n min_lon, max_lon = min(lons), max(lons)\n\n width, height = 800.0, 600.0\n pad = 40.0\n span_lat = max(max_lat - min_lat, 1e-9)\n span_lon = max(max_lon - min_lon, 1e-9)\n scale = min((width - 2 * pad) / span_lon, (height - 2 * pad) / span_lat)\n\n def to_xy(p):\n x = pad + (p[1] - min_lon) * scale\n y = height - pad - (p[0] - min_lat) * scale\n return x, y\n\n def polyline(pid, color, points):\n coords = \" \".join(\"%.2f,%.2f\" % to_xy(p) for p in points)\n return ('<polyline id=\"%s\" fill=\"none\" stroke=\"%s\" '\n 'stroke-width=\"2\" points=\"%s\"/>' % (pid, color, coords))\n\n fx, fy = to_xy(fix)\n parts = []\n parts.append('<?xml version=\"1.0\" encoding=\"UTF-8\"?>')\n parts.append('<svg xmlns=\"http://www.w3.org/2000/svg\" width=\"%d\" height=\"%d\" '\n 'viewBox=\"0 0 %d %d\">' % (int(width), int(height), int(width), int(height)))\n parts.append('<rect x=\"0\" y=\"0\" width=\"%d\" height=\"%d\" fill=\"white\"/>' % (int(width), int(height)))\n parts.append(polyline(\"dr-track\", \"#1f77b4\", dr))\n parts.append(polyline(\"ep-track\", \"#ff7f0e\", ep))\n parts.append('<circle id=\"fix\" cx=\"%.2f\" cy=\"%.2f\" r=\"5\" fill=\"red\"/>' % (fx, fy))\n parts.append('</svg>')\n\n with open(path, \"w\") as f:\n f.write(\"\\n\".join(parts) + \"\\n\")\n\n\nif __name__ == \"__main__\":\n sys.exit(main())\n"
},
"result": "wrote 4910 chars"
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"turn": 3,
"tool": "run_shell",
"args": {
"command": "cd . && python3 solve.py input.json answer.json && cat answer.json && echo && cat track.svg"
},
"result": "exit=0\nstdout:\n{\"dr\": [[-16.7478, 90.7095], [-16.75963, 90.7974], [-16.70891, 90.82922], [-16.71498, 90.79944], [-16.78977, 90.83259], [-16.83918, 90.81681], [-16.7936, 90.93466]], \"ep\": [[-16.7478, 90.7095], [-16.77379, 90.77279], [-16.7278, 90.79641], [-16.73858, 90.75841], [-16.82046, 90.77926], [-16.87931, 90.74706], [-16.84317, 90.84851]], \"hours\": 5.25, \"set_deg\": 248.8, \"drift_kn\": 0.889, \"ep_error_nm\": 1.42, \"cmg_deg\": 117.3, \"smg_kn\": 1.84}\n<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<svg xmlns=\"http://www.w3.org/2000/svg\" width=\"800\" height=\"600\" viewBox=\"0 0 800 600\">\n<rect x=\"0\" y=\"0\" width=\"800\" height=\"600\" fill=\"white\"/>\n<polyline id=\"dr-track\" fill=\"none\" stroke=\"#1f77b4\" stroke-width=\"2\" points=\"40.00,158.67 308.26,194.77 405.37,40.00 314.47,58.51 415.64,286.75 367.49,437.53 727.12,298.44\"/>\n<polyline id=\"ep-track\" fill=\"none\" stroke=\"#ff7f0e\" stroke-width=\"2\" points=\"40.00,158.67 233.14,238.00 305.22,97.63 189.27,130.55 252.89,380.40 154.61,560.00 464.23,449.73\"/>\n<circle id=\"fix\" cx=\"495.93\" cy=\"384.19\" r=\"5\" fill=\"red\"/>\n</svg>\n\nstderr:\n"
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"turn": 4,
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"arguments": "{\"command\":\"cd . && cat > /tmp/in2.json <<'EOF'\\n{\\\"start\\\":[10.0,-20.0],\\\"legs\\\":[{\\\"course\\\":0,\\\"speed_kn\\\":6,\\\"minutes\\\":60},{\\\"course\\\":90,\\\"speed_kn\\\":6,\\\"minutes\\\":60}],\\\"current\\\":{\\\"set\\\":180,\\\"drift_kn\\\":1},\\\"fix\\\":[10.1,-19.9]}\\nEOF\\npython3 solve.py /tmp/in2.json /tmp/out2.json && cat /tmp/out2.json && echo && python3 -c \\\"import xml.dom.minidom,sys; xml.dom.minidom.parse('track.svg'); print('svg ok')\\\"\"}"
}
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],
"role": "assistant",
"reasoning_content": "Let me verify the calculations manually for a couple of legs.\n\nLeg 1: course 98, speed 3.4, 90 min = 1.5 h. dist = 5.1 nm. n = 5.1*cos(98\u00b0) = 5.1*(-0.13917) = -0.70978. e = 5.1*sin(98\u00b0) = 5.1*0.99027 = 5.05038.\n\ndlat = -0.70978/60 = -0.0118297. mid = -16.7478 + (-0.0059148) = -16.7537148. new lat = -16.7596297 \u2192 -16.75963 \u2713. new lon = 90.7095 + 5.05038/(60*cos(-16.7537\u00b0)). cos(16.7537\u00b0)=0.95755. 60*0.95755=57.453. 5.05038/57.453=0.087904. lon = 90.797404 \u2192 90.7974 \u2713.\n\nGood. Everything looks consistent.\n\nLet me double-check the SVG static rules: root svg, no scripts/images/links/external assets. We have xmlns which is fine. Good.\n\nLet me verify the answer keys match spec exactly. Yes.\n\nLet me test with a fresh synthetic input to make sure it runs."
},
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{
"turn": 4,
"tool": "run_shell",
"args": {
"command": "cd . && cat > /tmp/in2.json <<'EOF'\n{\"start\":[10.0,-20.0],\"legs\":[{\"course\":0,\"speed_kn\":6,\"minutes\":60},{\"course\":90,\"speed_kn\":6,\"minutes\":60}],\"current\":{\"set\":180,\"drift_kn\":1},\"fix\":[10.1,-19.9]}\nEOF\npython3 solve.py /tmp/in2.json /tmp/out2.json && cat /tmp/out2.json && echo && python3 -c \"import xml.dom.minidom,sys; xml.dom.minidom.parse('track.svg'); print('svg ok')\""
},
"result": "exit=0\nstdout:\n{\"dr\": [[10.0, -20.0], [10.1, -20.0], [10.1, -19.89843]], \"ep\": [[10.0, -20.0], [10.08333, -20.0], [10.06667, -19.89843]], \"hours\": 2.0, \"set_deg\": 270.0, \"drift_kn\": 0.046, \"ep_error_nm\": 2.002, \"cmg_deg\": 44.6, \"smg_kn\": 4.21}\nsvg ok\n\nstderr:\n"
},
{
"turn": 5,
"response": {
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"choices": [
{
"index": 0,
"message": {
"content": "Both the sample and a fresh synthetic input produce correct results, and the SVG parses as valid XML.\n\n**Summary**\n\nCreated `solve.py` (Python 3 stdlib only) that reads the input JSON and writes `answer.json` plus `track.svg`.\n\nImplementation details:\n- **`move`**: plane-sailing step using `dlat = n/60`, `mid = lat + dlat/2`, `lon += e/(60\u00b7cos(mid))`.\n- **`diff`**: north/east between two points using the mid-latitude formula.\n- **DR**: each leg advances by the water vector (`speed\u00b7hours` along `course`).\n- **EP**: each leg advances once by the water vector plus the current vector (`drift\u00b7hours` toward `set`).\n- **Set/drift**: vector from final DR to the fix \u2192 `set = atan2(east, north) mod 360`, `drift = length/total_hours`; `ep_error_nm` = final EP\u2192fix distance.\n- **CMG/SMG**: start\u2192fix bearing and distance/total_hours.\n- Rounding: positions 5 dp, hours 4 dp, angles 1 dp, speeds/distances 3 dp; `dr`/`ep` include start plus one entry per leg.\n- **`track.svg`**: self-contained static SVG with `<polyline id=\"dr-track\">`, `<polyline id=\"ep-track\">`, and `<circle id=\"fix\">`, no scripts/images/links/external assets.\n\nVerified against the provided input and a fresh synthetic case (hand-checked values match).",
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"reasoning_content": "Let me verify the logic manually for the simple case.\n\nLeg 1: course 0, speed 6, 1 hour \u2192 6 nm north. DR: lat 10 + 6/60 = 10.1, lon -20. \u2713\nLeg 2: course 90, 6 nm east. mid = 10.1, new lon = -20 + 6/(60*cos(10.1\u00b0)) = -20 + 6/(60*0.9845) = -20 + 0.10157 = -19.89843. \u2713\n\nEP leg1: water 6 north + current 1 toward 180 (south) = 5 north \u2192 10.08333. \u2713\nEP leg2: water 6 east + current 1 toward 180 = 1 south. Move 6 east, 1 south from (10.08333,-20). dlat=-1/60=-0.016667 \u2192 lat 10.06667. mid=10.075. lon = -20 + 6/(60*cos(10.075)) = -19.89843. \u2713\n\nSet/drift from final DR (10.1,-19.89843) to fix (10.1,-19.9): north=0, east=(-19.9+19.89843)*60*cos(10.1)= -0.00157*60*0.9845 = -0.0927. bearing atan2(-0.0927,0) = -90 \u2192 270. drift = 0.0927/2 = 0.046. \u2713\n\nCMG from start (10,-20) to fix (10.1,-19.9): north=6, east=0.1*60*cos(10.05)=5.907. bearing=atan2(5.907,6)=44.6. smg=hypot(6,5.907)/2=8.42/2=4.21. \u2713\n\nAll good. The SVG is valid XML. Everything works.\n\nLet me double check the SVG static rules: root svg, no scripts/images/links/external assets. We have xmlns which is fine. Good.\n\nDone."
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