GPT-6.1 Sol (effort default (no reasoning-effort override) · thinking on) on Tide prediction from harmonic constituents: extrema, wiggle removal, threshold crossings

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{"type": "item.completed", "item": {"id": "item_0", "type": "agent_message", "text": "I\u2019ll implement the analytic derivatives, root finding, wiggle removal, daily sampling, and static SVG, then check them with synthetic cases."}}
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{"type": "item.completed", "item": {"id": "item_2", "type": "command_execution", "command": "/bin/bash -lc 'cat input.json'", "aggregated_output": "{\n \"z0\": 3.839,\n \"constituents\": [\n  {\n   \"name\": \"M2\",\n   \"amp\": 1.131,\n   \"speed_deg_h\": 28.9841042,\n   \"phase_deg\": 163.1,\n   \"g_deg\": 296.42,\n   \"f\": 0.957\n  },\n  {\n   \"name\": \"S2\",\n   \"amp\": 0.334,\n   \"speed_deg_h\": 30.0,\n   \"phase_deg\": 165.98,\n   \"g_deg\": 40.57,\n   \"f\": 1.0307\n  },\n  {\n   \"name\": \"N2\",\n   \"amp\": 0.144,\n   \"speed_deg_h\": 28.4397295,\n   \"phase_deg\": 160.9,\n   \"g_deg\": 208.6,\n   \"f\": 1.0192\n  },\n  {\n   \"name\": \"K1\",\n   \"amp\": 0.254,\n   \"speed_deg_h\": 15.0410686,\n   \"phase_deg\": 71.94,\n   \"g_deg\": 334.98,\n   \"f\": 0.9643\n  },\n  {\n   \"name\": \"O1\",\n   \"amp\": 0.097,\n   \"speed_deg_h\": 13.9430356,\n   \"phase_deg\": 67.88,\n   \"g_deg\": 153.42,\n   \"f\": 1.0364\n  },\n  {\n   \"name\": \"M4\",\n   \"amp\": 0.415,\n   \"speed_deg_h\": 57.9682084,\n   \"phase_deg\": 317.92,\n   \"g_deg\": 323.11,\n   \"f\": 1.0167\n  },\n  {\n   \"name\": \"MS4\",\n   \"amp\": 0.081,\n   \"speed_deg_h\": 58.9841042,\n   \"phase_deg\": 185.85,\n   \"g_deg\": 121.33,\n   \"f\": 0.984\n  }\n ],\n \"start_h\": 2762.71,\n \"end_h\": 2834.71,\n \"min_range_m\": 0.15,\n \"threshold_m\": 3.02\n}", "exit_code": 0, "status": "completed"}}
{"type": "item.started", "item": {"id": "item_3", "type": "command_execution", "command": "/bin/bash -lc \"cat > solve.py <<'PY'\n#\"'!/usr/bin/env python3\n\"\"\"Predict a synthetic harmonic tide using only the Python standard library.\"\"\"\nimport json\nimport math\nimport sys\nfrom pathlib import Path\n\n\nclass Tide:\n    def __init__(self, data):\n        self.z0 = data['\"'z0']\n        self.terms = [(c['amp'] * c.get('f', 1.0),\n                       math.radians(c['speed_deg_h']),\n                       math.radians(c.get('phase_deg', 0) - c.get('g_deg', 0)))\n                      for c in data['constituents']]\n\n    def height(self, t):\n        return self.z0 + math.fsum(a * math.cos(w*t+p) for a, w, p in self.terms)\n\n    def derivative(self, t):\n        return math.fsum(-a*w * math.sin(w*t+p) for a, w, p in self.terms)\n\n    def second(self, t):\n        return math.fsum(-a*w*w * math.cos(w*t+p) for a, w, p in self.terms)\n\n\ndef roots(fn, start, end, step=0.1):\n    \\\"\\\"\\\"Bracket sign changes, including roots exactly on a scan boundary.\\\"\\\"\\\"\n    found = []\n\n    def add(t):\n        if not found or abs(t - found[-1]) > 1e-7:\n            found.append(t)\n\n    def is_crossing(t):\n        delta = 1e-5\n        return fn(t-delta) * fn(t+delta) < 0\n\n    left = start\n    fl = fn(left)\n    if fl == 0 and is_crossing(left):\n        add(left)\n    count = int(math.ceil((end-start)/step))\n    for i in range(1, count+1):\n        right = min(end, start+i*step)\n        fr = fn(right)\n        if fl * fr < 0:\n            lo, hi, flo = left, right, fl\n            for _ in range(60):\n                mid = (lo+hi)/2\n                fm = fn(mid)\n                if fm == 0 or hi-lo < 1e-10:\n                    lo = hi = mid\n                    break\n                if flo * fm < 0:\n                    hi = mid\n                else:\n                    lo, flo = mid, fm\n            add((lo+hi)/2)\n        elif fr == 0 and is_crossing(right):\n            add(right)\n        left, fl = right, fr\n    return found\n\n\ndef draw_svg(tide, start, end, threshold, extrema, path):\n    width, height, pad = 1000, 400, 40\n    n = max(2, min(10000, int((end-start)*60)+1))\n    samples = [(start+(end-start)*i/(n-1)) for i in range(n)]\n    levels = [tide.height(t) for t in samples]\n    low, high = min(levels+[threshold]), max(levels+[threshold])\n    margin = max((high-low)*0.1, 0.1)\n    low, high = low-margin, high+margin\n    def x(t):\n        return pad + (width-2*pad)*(t-start)/(end-start or 1)\n    def y(h):\n        return height-pad-(height-2*pad)*(h-low)/(high-low)\n    points = ' '.join(f'{x(t):.3f},{y(h):.3f}' for t, h in zip(samples, levels))\n    dots = ''.join(f'<circle cx=\\\"{x(t):.3f}\\\" cy=\\\"{y(h):.3f}\\\" r=\\\"4\\\" fill=\\\"{ \\\"#c34c38\\\" if kind == \\\"high\\\" else \\\"#247c65\\\"}\\\"/>'\n                   for t, h, kind in extrema)\n    path.write_text(f'''<svg xmlns=\\\"http://www.w3.org/2000/svg\\\" width=\\\"1000\\\" height=\\\"400\\\" viewBox=\\\"0 0 1000 400\\\">\n<title>Synthetic harmonic tide (not for navigation)</title>\n<rect width=\\\"1000\\\" height=\\\"400\\\" fill=\\\"white\\\"/>\n<line id=\\\"threshold-line\\\" x1=\\\"{pad}\\\" x2=\\\"{width-pad}\\\" y1=\\\"{y(threshold):.3f}\\\" y2=\\\"{y(threshold):.3f}\\\" stroke=\\\"#c34c38\\\" stroke-dasharray=\\\"6 4\\\"/>\n<polyline id=\\\"tide-curve\\\" points=\\\"{points}\\\" fill=\\\"none\\\" stroke=\\\"#126b9a\\\" stroke-width=\\\"2\\\"/>\n<g id=\\\"extrema\\\">{dots}</g>\n<text x=\\\"40\\\" y=\\\"22\\\" font-family=\\\"sans-serif\\\" font-size=\\\"15\\\">Synthetic harmonic tide \u2014 not for navigation</text>\n</svg>\\\\n''', encoding='utf-8')\n\n\ndef solve(data, output):\n    tide = Tide(data)\n    start, end = data['start_h'], data['end_h']\n    extrema = [(t, tide.height(t), 'high' if tide.second(t) < 0 else 'low')\n               for t in roots(tide.derivative, start, end)]\n    # Removing the first qualifying pair can expose a new qualifying pair.\n    i = 0\n    while i+1 < len(extrema):\n        if abs(extrema[i][1]-extrema[i+1][1]) < data['min_range_m']:\n            del extrema[i:i+2]\n            i = max(0, i-1)\n        else:\n            i += 1\n    threshold = data['threshold_m']\n    crossings = roots(lambda t: tide.height(t)-threshold, start, end)\n    day_count = max(1, math.ceil((end-start)/24 - 1e-12))\n    daily = {}\n    minutes = (end-start)*60\n    for minute in range(int(math.floor(minutes+1e-8))+1):\n        day = min(minute//1440, day_count-1)\n        h = tide.height(start+minute/60)\n        if day not in daily:\n            daily[day] = [h, h]\n        else:\n            daily[day][0] = max(daily[day][0], h)\n            daily[day][1] = min(daily[day][1], h)\n    answer = {\n        'extrema': [{'t_min': round((t-start)*60, 1), 'height_m': round(h, 3), 'kind': kind}\n                    for t, h, kind in extrema],\n        'crossings': [{'t_min': round((t-start)*60, 1),\n                       'direction': 'rising' if tide.derivative(t) > 0 else 'falling'}\n                      for t in crossings],\n        'daily': [{'day': d, 'max_m': round(v[0], 3), 'min_m': round(v[1], 3)}\n                  for d, v in sorted(daily.items())]\n    }\n    output.write_text(json.dumps(answer, indent=2)+'\\\\n', encoding='utf-8')\n    draw_svg(tide, start, end, threshold, extrema, output.parent/'tide.svg')\n\n\nif __name__ == '__main__':\n    if len(sys.argv) \"'!= 3:\n        raise SystemExit('\"'Usage: python solve.py input.json answer.json')\n    with open(sys.argv[1], encoding='utf-8') as source:\n        solve(json.load(source), Path(sys.argv[2]))\nPY\npython solve.py input.json answer.json\npython -m py_compile solve.py\"", "aggregated_output": "", "exit_code": null, "status": "in_progress"}}
{"type": "item.completed", "item": {"id": "item_3", "type": "command_execution", "command": "/bin/bash -lc \"cat > solve.py <<'PY'\n#\"'!/usr/bin/env python3\n\"\"\"Predict a synthetic harmonic tide using only the Python standard library.\"\"\"\nimport json\nimport math\nimport sys\nfrom pathlib import Path\n\n\nclass Tide:\n    def __init__(self, data):\n        self.z0 = data['\"'z0']\n        self.terms = [(c['amp'] * c.get('f', 1.0),\n                       math.radians(c['speed_deg_h']),\n                       math.radians(c.get('phase_deg', 0) - c.get('g_deg', 0)))\n                      for c in data['constituents']]\n\n    def height(self, t):\n        return self.z0 + math.fsum(a * math.cos(w*t+p) for a, w, p in self.terms)\n\n    def derivative(self, t):\n        return math.fsum(-a*w * math.sin(w*t+p) for a, w, p in self.terms)\n\n    def second(self, t):\n        return math.fsum(-a*w*w * math.cos(w*t+p) for a, w, p in self.terms)\n\n\ndef roots(fn, start, end, step=0.1):\n    \\\"\\\"\\\"Bracket sign changes, including roots exactly on a scan boundary.\\\"\\\"\\\"\n    found = []\n\n    def add(t):\n        if not found or abs(t - found[-1]) > 1e-7:\n            found.append(t)\n\n    def is_crossing(t):\n        delta = 1e-5\n        return fn(t-delta) * fn(t+delta) < 0\n\n    left = start\n    fl = fn(left)\n    if fl == 0 and is_crossing(left):\n        add(left)\n    count = int(math.ceil((end-start)/step))\n    for i in range(1, count+1):\n        right = min(end, start+i*step)\n        fr = fn(right)\n        if fl * fr < 0:\n            lo, hi, flo = left, right, fl\n            for _ in range(60):\n                mid = (lo+hi)/2\n                fm = fn(mid)\n                if fm == 0 or hi-lo < 1e-10:\n                    lo = hi = mid\n                    break\n                if flo * fm < 0:\n                    hi = mid\n                else:\n                    lo, flo = mid, fm\n            add((lo+hi)/2)\n        elif fr == 0 and is_crossing(right):\n            add(right)\n        left, fl = right, fr\n    return found\n\n\ndef draw_svg(tide, start, end, threshold, extrema, path):\n    width, height, pad = 1000, 400, 40\n    n = max(2, min(10000, int((end-start)*60)+1))\n    samples = [(start+(end-start)*i/(n-1)) for i in range(n)]\n    levels = [tide.height(t) for t in samples]\n    low, high = min(levels+[threshold]), max(levels+[threshold])\n    margin = max((high-low)*0.1, 0.1)\n    low, high = low-margin, high+margin\n    def x(t):\n        return pad + (width-2*pad)*(t-start)/(end-start or 1)\n    def y(h):\n        return height-pad-(height-2*pad)*(h-low)/(high-low)\n    points = ' '.join(f'{x(t):.3f},{y(h):.3f}' for t, h in zip(samples, levels))\n    dots = ''.join(f'<circle cx=\\\"{x(t):.3f}\\\" cy=\\\"{y(h):.3f}\\\" r=\\\"4\\\" fill=\\\"{ \\\"#c34c38\\\" if kind == \\\"high\\\" else \\\"#247c65\\\"}\\\"/>'\n                   for t, h, kind in extrema)\n    path.write_text(f'''<svg xmlns=\\\"http://www.w3.org/2000/svg\\\" width=\\\"1000\\\" height=\\\"400\\\" viewBox=\\\"0 0 1000 400\\\">\n<title>Synthetic harmonic tide (not for navigation)</title>\n<rect width=\\\"1000\\\" height=\\\"400\\\" fill=\\\"white\\\"/>\n<line id=\\\"threshold-line\\\" x1=\\\"{pad}\\\" x2=\\\"{width-pad}\\\" y1=\\\"{y(threshold):.3f}\\\" y2=\\\"{y(threshold):.3f}\\\" stroke=\\\"#c34c38\\\" stroke-dasharray=\\\"6 4\\\"/>\n<polyline id=\\\"tide-curve\\\" points=\\\"{points}\\\" fill=\\\"none\\\" stroke=\\\"#126b9a\\\" stroke-width=\\\"2\\\"/>\n<g id=\\\"extrema\\\">{dots}</g>\n<text x=\\\"40\\\" y=\\\"22\\\" font-family=\\\"sans-serif\\\" font-size=\\\"15\\\">Synthetic harmonic tide \u2014 not for navigation</text>\n</svg>\\\\n''', encoding='utf-8')\n\n\ndef solve(data, output):\n    tide = Tide(data)\n    start, end = data['start_h'], data['end_h']\n    extrema = [(t, tide.height(t), 'high' if tide.second(t) < 0 else 'low')\n               for t in roots(tide.derivative, start, end)]\n    # Removing the first qualifying pair can expose a new qualifying pair.\n    i = 0\n    while i+1 < len(extrema):\n        if abs(extrema[i][1]-extrema[i+1][1]) < data['min_range_m']:\n            del extrema[i:i+2]\n            i = max(0, i-1)\n        else:\n            i += 1\n    threshold = data['threshold_m']\n    crossings = roots(lambda t: tide.height(t)-threshold, start, end)\n    day_count = max(1, math.ceil((end-start)/24 - 1e-12))\n    daily = {}\n    minutes = (end-start)*60\n    for minute in range(int(math.floor(minutes+1e-8))+1):\n        day = min(minute//1440, day_count-1)\n        h = tide.height(start+minute/60)\n        if day not in daily:\n            daily[day] = [h, h]\n        else:\n            daily[day][0] = max(daily[day][0], h)\n            daily[day][1] = min(daily[day][1], h)\n    answer = {\n        'extrema': [{'t_min': round((t-start)*60, 1), 'height_m': round(h, 3), 'kind': kind}\n                    for t, h, kind in extrema],\n        'crossings': [{'t_min': round((t-start)*60, 1),\n                       'direction': 'rising' if tide.derivative(t) > 0 else 'falling'}\n                      for t in crossings],\n        'daily': [{'day': d, 'max_m': round(v[0], 3), 'min_m': round(v[1], 3)}\n                  for d, v in sorted(daily.items())]\n    }\n    output.write_text(json.dumps(answer, indent=2)+'\\\\n', encoding='utf-8')\n    draw_svg(tide, start, end, threshold, extrema, output.parent/'tide.svg')\n\n\nif __name__ == '__main__':\n    if len(sys.argv) \"'!= 3:\n        raise SystemExit('\"'Usage: python solve.py input.json answer.json')\n    with open(sys.argv[1], encoding='utf-8') as source:\n        solve(json.load(source), Path(sys.argv[2]))\nPY\npython solve.py input.json answer.json\npython -m py_compile solve.py\"", "aggregated_output": "/bin/bash: line 137: python: command not found\n/bin/bash: line 138: python: command not found\n", "exit_code": 127, "status": "failed"}}
{"type": "item.started", "item": {"id": "item_4", "type": "command_execution", "command": "/bin/bash -lc \"python3 solve.py input.json answer.json\npython3 - <<'PY'\nimport json, math, tempfile\nfrom pathlib import Path\nimport xml.etree.ElementTree as ET\nfrom solve import solve, roots\nwith tempfile.TemporaryDirectory() as d:\n    p=Path(d)/'answer.json'\n    data=dict(z0=0, constituents=[dict(amp=1,speed_deg_h=30,phase_deg=0,g_deg=0,f=1)],start_h=0,end_h=25,min_range_m=0.1,threshold_m=0)\n    solve(data,p)\n    a=json.loads(p.read_text())\n    assert [e['t_min'] for e in a['extrema']]==[0,360,720,1080,1440], a\n    assert [c['t_min'] for c in a['crossings']]==[180,540,900,1260], a\n    assert a['daily'][0]==dict(day=0,max_m=1.0,min_m=-1.0)\n    svg=ET.parse(Path(d)/'tide.svg').getroot()\n    assert {e.get('id') for e in svg.iter()} >= {'tide-curve','threshold-line','extrema'}\n    data['min_range_m']=3\n    solve(data,p)\n    assert len(json.loads(p.read_text())['extrema'])==1\n    assert roots(lambda t:(t-1)**2,0,2)==[]\na=json.load(open('answer.json'))\nprint('Checks passed; supplied input:',len(a['extrema']),'extrema,',len(a['crossings']),'crossings,',len(a['daily']),'days')\nPY\"", "aggregated_output": "", "exit_code": null, "status": "in_progress"}}
{"type": "item.completed", "item": {"id": "item_4", "type": "command_execution", "command": "/bin/bash -lc \"python3 solve.py input.json answer.json\npython3 - <<'PY'\nimport json, math, tempfile\nfrom pathlib import Path\nimport xml.etree.ElementTree as ET\nfrom solve import solve, roots\nwith tempfile.TemporaryDirectory() as d:\n    p=Path(d)/'answer.json'\n    data=dict(z0=0, constituents=[dict(amp=1,speed_deg_h=30,phase_deg=0,g_deg=0,f=1)],start_h=0,end_h=25,min_range_m=0.1,threshold_m=0)\n    solve(data,p)\n    a=json.loads(p.read_text())\n    assert [e['t_min'] for e in a['extrema']]==[0,360,720,1080,1440], a\n    assert [c['t_min'] for c in a['crossings']]==[180,540,900,1260], a\n    assert a['daily'][0]==dict(day=0,max_m=1.0,min_m=-1.0)\n    svg=ET.parse(Path(d)/'tide.svg').getroot()\n    assert {e.get('id') for e in svg.iter()} >= {'tide-curve','threshold-line','extrema'}\n    data['min_range_m']=3\n    solve(data,p)\n    assert len(json.loads(p.read_text())['extrema'])==1\n    assert roots(lambda t:(t-1)**2,0,2)==[]\na=json.load(open('answer.json'))\nprint('Checks passed; supplied input:',len(a['extrema']),'extrema,',len(a['crossings']),'crossings,',len(a['daily']),'days')\nPY\"", "aggregated_output": "Checks passed; supplied input: 12 extrema, 12 crossings, 3 days\n", "exit_code": 0, "status": "completed"}}
{"type": "item.completed", "item": {"id": "item_5", "type": "agent_message", "text": "Created [solve.py](solve.py), [answer.json](answer.json), and [tide.svg](tide.svg).\n\nVerified analytic extrema, threshold crossings, wiggle removal, daily samples, and SVG structure using synthetic checks. The supplied input produces 12 extrema, 12 crossings, and 3 daily records.\n\nRun with `python3 solve.py input.json answer.json` (`python` is unavailable here)."}}
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