{"abstract":"Backtracking switches on and off erratically through the day.","category":"Solar tracker geometry","checks":7,"contract":"Horizontal single-axis rows with ground coverage ratio gcr in (0, 1]. temp = |cos(ideal)|/gcr. When temp < 1 the rows would shade each other and the angle is corrected by -sign(ideal)*acos(temp) degrees (backtracking, flag True). gcr <= 0 disables backtracking. Return [angle rounded to 3, backtracking flag].","contract_signature":"ideal, gcr","evaluation_group":"w2-solar_tracker_geometry-gcr-backtracking","failed_approach":"Shifting by 90 degrees uses the sine, treating the rotation as an elevation.","family":"w2-solar_tracker_geometry-gcr-backtracking-cosine-argument-units","id":"FA-93381","implementations":{"attempt":{"sha256":"482dfaf21008f7ef5ee4c62adf8c04881bf3f2925171fea4e45fb30011d9d42e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(ideal, gcr):\n    if gcr <= 0:\n        return [round(ideal, 3), False]\n    temp = abs(math.cos(math.radians(abs(ideal) - 90))) / gcr\n    if temp < 1:\n        corr = -math.copysign(1, ideal) * math.degrees(math.acos(temp))\n        return [round(ideal + corr, 3), True]\n    return [round(ideal, 3), False]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['boundary: continuous rows', [60, 1.0], [0.0, True]],\n  ['regression: cosine argument units', [45, 1.0], [0.0, True]],\n  ['regression: cosine argument units (partial repair)', [-10, 0.4], [-10, False]],\n  ['control 1', [30, 0.25], [30, False]], ['control 2', [-29.5, 0.5], [-29.5, False]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['boundary: continuous rows', [60, 1.0], [0.0, True]],\n  ['regression: cosine argument units', [-29.5, 0.5], [-29.5, False]],\n  ['regression: cosine argument units (partial repair)', [-10, 0.5], [-10, False]],\n  ['control 1', [-80, 0.35], [-19.745, True]], ['control 2', [85.5, 1.0], [0.0, True]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['boundary: continuous rows', [60, 1.0], [0.0, True]],\n  ['regression: cosine argument units', [-70, 0.4], [-38.765, True]],\n  ['regression: cosine argument units (partial repair)', [-79.5, 0.3], [-26.905, True]],\n  ['control 1', [0, 0.25], [0, False]], ['control 2', [10.5, 0], [10.5, False]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['boundary: continuous rows', [60, 1.0], [0.0, True]],\n  ['regression: cosine argument units', [-60, 1.0], [-0.0, True]],\n  ['regression: cosine argument units (partial repair)', [10, 0.35], [10, False]],\n  ['control 1', [-59.5, 1.0], [0.0, True]], ['control 2', [-45, 0.5], [-45, False]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['boundary: continuous rows', [60, 1.0], [0.0, True]],\n  ['regression: cosine argument units', [-69.5, 1.0], [0.0, True]],\n  ['regression: cosine argument units (partial repair)', [-9.5, 0.35], [-9.5, False]],\n  ['control 1', [10, 0.35], [10, False]], ['control 2', [-60, 0.3], [-60, False]]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"d30a51a9a0825d891a6fd7920e9a70163543a18c51901e5155eaabe0e98f6525","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(ideal, gcr):\n    if gcr <= 0:\n        return [round(ideal, 3), False]\n    temp = abs(math.cos(ideal)) / gcr\n    if temp < 1:\n        corr = -math.copysign(1, ideal) * math.degrees(math.acos(temp))\n        return [round(ideal + corr, 3), True]\n    return [round(ideal, 3), False]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['boundary: continuous rows', [60, 1.0], [0.0, True]],\n  ['regression: cosine argument units', [45, 1.0], [0.0, True]],\n  ['regression: cosine argument units (partial repair)', [-10, 0.4], [-10, False]],\n  ['control 1', [30, 0.25], [30, False]], ['control 2', [-29.5, 0.5], [-29.5, False]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['boundary: continuous rows', [60, 1.0], [0.0, True]],\n  ['regression: cosine argument units', [-29.5, 0.5], [-29.5, False]],\n  ['regression: cosine argument units (partial repair)', [-10, 0.5], [-10, False]],\n  ['control 1', [-80, 0.35], [-19.745, True]], ['control 2', [85.5, 1.0], [0.0, True]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['boundary: continuous rows', [60, 1.0], [0.0, True]],\n  ['regression: cosine argument units', [-70, 0.4], [-38.765, True]],\n  ['regression: cosine argument units (partial repair)', [-79.5, 0.3], [-26.905, True]],\n  ['control 1', [0, 0.25], [0, False]], ['control 2', [10.5, 0], [10.5, False]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['boundary: continuous rows', [60, 1.0], [0.0, True]],\n  ['regression: cosine argument units', [-60, 1.0], [-0.0, True]],\n  ['regression: cosine argument units (partial repair)', [10, 0.35], [10, False]],\n  ['control 1', [-59.5, 1.0], [0.0, True]], ['control 2', [-45, 0.5], [-45, False]]],\n [['boundary: noon never backtracks', [0, 0.4], [0, False]],\n  ['normal: steep morning angle backtracks', [-75, 0.4], [-25.319, True]],\n  ['boundary: continuous rows', [60, 1.0], [0.0, True]],\n  ['regression: cosine argument units', [-69.5, 1.0], [0.0, True]],\n  ['regression: cosine argument units (partial repair)', [-9.5, 0.35], [-9.5, False]],\n  ['control 1', [10, 0.35], [10, False]], ['control 2', [-60, 0.3], [-60, False]]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"Deterministic stipulated toy contract for teaching; no claim of conformance with any standard, vendor protocol or production controller. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-solar_tracker_geometry-gcr-backtracking-cosine-argument-units","generated_at":"2026-09-29T14:51:54.607569+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Single-axis and dual-axis solar trackers turn a sun direction into actuator commands; a sign, frame or limit mistake points a whole plant away from the sun or into a mechanical stop.","root_cause":"The ideal angle in degrees is passed to cos as radians.","sha256":"f9e4a7fbdf939accb5b56b66a24d12edb4948bef93040e790eb5c02234568e57","title":"Ground-coverage-ratio backtracking: cosine argument units · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":37.612,"exit_code":1,"observations":[{"actual":[-90.0,true],"check":"boundary: noon never backtracks","expected":[0,false],"passed":false},{"actual":[-75,false],"check":"normal: steep morning angle backtracks","expected":[-25.319,true],"passed":false},{"actual":[30.0,true],"check":"boundary: continuous rows","expected":[0.0,true],"passed":false},{"actual":[0.0,true],"check":"regression: cosine argument units","expected":[0.0,true],"passed":true},{"actual":[54.271,true],"check":"regression: cosine argument units (partial repair)","expected":[-10,false],"passed":false},{"actual":[30,false],"check":"control 1","expected":[30,false],"passed":true},{"actual":[-19.513,true],"check":"control 2","expected":[-29.5,false],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"boundary: noon never backtracks\", \"actual\": [-90.0, true], \"expected\": [0, false], \"passed\": false}, {\"check\": \"normal: steep morning angle backtracks\", \"actual\": [-75, false], \"expected\": [-25.319, true], \"passed\": false}, {\"check\": \"boundary: continuous rows\", \"actual\": [30.0, true], \"expected\": [0.0, true], \"passed\": false}, {\"check\": \"regression: cosine argument units\", \"actual\": [0.0, true], \"expected\": [0.0, true], \"passed\": true}, {\"check\": \"regression: cosine argument units (partial repair)\", \"actual\": [54.271, true], \"expected\": [-10, false], \"passed\": false}, {\"check\": \"control 1\", \"actual\": [30, false], \"expected\": [30, false], \"passed\": true}, {\"check\": \"control 2\", \"actual\": [-19.513, true], \"expected\": [-29.5, false], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.941,"exit_code":1,"observations":[{"actual":[0,false],"check":"boundary: noon never backtracks","expected":[0,false],"passed":true},{"actual":[-75,false],"check":"normal: steep morning angle backtracks","expected":[-25.319,true],"passed":false},{"actual":[42.253,true],"check":"boundary: continuous rows","expected":[0.0,true],"passed":false},{"actual":[-13.31,true],"check":"regression: cosine argument units","expected":[0.0,true],"passed":false},{"actual":[-10,false],"check":"regression: cosine argument units (partial repair)","expected":[-10,false],"passed":true},{"actual":[-21.902,true],"check":"control 1","expected":[30,false],"passed":false},{"actual":[17.918,true],"check":"control 2","expected":[-29.5,false],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"boundary: noon never backtracks\", \"actual\": [0, false], \"expected\": [0, false], \"passed\": true}, {\"check\": \"normal: steep morning angle backtracks\", \"actual\": [-75, false], \"expected\": [-25.319, true], \"passed\": false}, {\"check\": \"boundary: continuous rows\", \"actual\": [42.253, true], \"expected\": [0.0, true], \"passed\": false}, {\"check\": \"regression: cosine argument units\", \"actual\": [-13.31, true], \"expected\": [0.0, true], \"passed\": false}, {\"check\": \"regression: cosine argument units (partial repair)\", \"actual\": [-10, false], \"expected\": [-10, false], \"passed\": true}, {\"check\": \"control 1\", \"actual\": [-21.902, true], \"expected\": [30, false], \"passed\": false}, {\"check\": \"control 2\", \"actual\": [17.918, true], \"expected\": [-29.5, false], \"passed\": false}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}