{"abstract":"Backtracking steepens the rows instead of flattening them.","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].","evaluation_group":"w2-solar_tracker_geometry-gcr-backtracking","failed_approach":"A fixed negative correction is right in the afternoon only.","family":"w2-solar_tracker_geometry-gcr-backtracking-correction-direction","id":"FA-93376","implementations":{"attempt":{"sha256":"81fdad1306c9e0006db9fb94e13186d30b577122cddd6e8898ffe67dc8da0f58","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(ideal))) / gcr\n    if temp < 1:\n        corr = -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: correction direction', [45, 1.0], [0.0, True]],\n  ['regression: correction direction (partial repair)', [-70, 0.4], [-38.765, True]],\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: correction direction', [-70, 0.5], [-23.16, True]],\n  ['regression: correction direction (partial repair)', [-79.5, 0.4], [-16.603, True]],\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: correction direction', [-70, 0.4], [-38.765, True]],\n  ['regression: correction direction (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: correction direction', [-60, 1.0], [-0.0, True]],\n  ['regression: correction direction (partial repair)', [-80, 0.3], [-25.368, True]],\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: correction direction', [-69.5, 1.0], [0.0, True]],\n  ['regression: correction direction (partial repair)', [-60, 1.0], [-0.0, True]],\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":"d7309b56ffce110083df9efe348160e289e3a92571f16f113d30db3ad937e1ac","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(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: correction direction', [45, 1.0], [0.0, True]],\n  ['regression: correction direction (partial repair)', [-70, 0.4], [-38.765, True]],\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: correction direction', [-70, 0.5], [-23.16, True]],\n  ['regression: correction direction (partial repair)', [-79.5, 0.4], [-16.603, True]],\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: correction direction', [-70, 0.4], [-38.765, True]],\n  ['regression: correction direction (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: correction direction', [-60, 1.0], [-0.0, True]],\n  ['regression: correction direction (partial repair)', [-80, 0.3], [-25.368, True]],\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: correction direction', [-69.5, 1.0], [0.0, True]],\n  ['regression: correction direction (partial repair)', [-60, 1.0], [-0.0, True]],\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"},"fixed":{"sha256":"dddc2580226e6577d17c83fd0e4cfcb06b1d0056cd83bf6efa8dffd3024f3c5e","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(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: correction direction', [45, 1.0], [0.0, True]],\n  ['regression: correction direction (partial repair)', [-70, 0.4], [-38.765, True]],\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: correction direction', [-70, 0.5], [-23.16, True]],\n  ['regression: correction direction (partial repair)', [-79.5, 0.4], [-16.603, True]],\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: correction direction', [-70, 0.4], [-38.765, True]],\n  ['regression: correction direction (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: correction direction', [-60, 1.0], [-0.0, True]],\n  ['regression: correction direction (partial repair)', [-80, 0.3], [-25.368, True]],\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: correction direction', [-69.5, 1.0], [0.0, True]],\n  ['regression: correction direction (partial repair)', [-60, 1.0], [-0.0, True]],\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-correction-direction","generated_at":"2026-09-29T14:51:54.518760+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.","repair":"Correct toward flat with -sign(ideal).","root_cause":"The correction has the same sign as the ideal angle.","sha256":"e3e5a0b2f49c16385398c9f5ebc38aaf7b1d322be94f8ad2759b9dc9d8a85e17","title":"Ground-coverage-ratio backtracking: correction direction · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":39.827,"exit_code":1,"observations":[{"actual":[0,false],"check":"boundary: noon never backtracks","expected":[0,false],"passed":true},{"actual":[-124.681,true],"check":"normal: steep morning angle backtracks","expected":[-25.319,true],"passed":false},{"actual":[0.0,true],"check":"boundary: continuous rows","expected":[0.0,true],"passed":true},{"actual":[0.0,true],"check":"regression: correction direction","expected":[0.0,true],"passed":true},{"actual":[-101.235,true],"check":"regression: correction direction (partial repair)","expected":[-38.765,true],"passed":false},{"actual":[30,false],"check":"control 1","expected":[30,false],"passed":true},{"actual":[-29.5,false],"check":"control 2","expected":[-29.5,false],"passed":true}],"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\": [-124.681, true], \"expected\": [-25.319, true], \"passed\": false}, {\"check\": \"boundary: continuous rows\", \"actual\": [0.0, true], \"expected\": [0.0, true], \"passed\": true}, {\"check\": \"regression: correction direction\", \"actual\": [0.0, true], \"expected\": [0.0, true], \"passed\": true}, {\"check\": \"regression: correction direction (partial repair)\", \"actual\": [-101.235, true], \"expected\": [-38.765, true], \"passed\": false}, {\"check\": \"control 1\", \"actual\": [30, false], \"expected\": [30, false], \"passed\": true}, {\"check\": \"control 2\", \"actual\": [-29.5, false], \"expected\": [-29.5, false], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.34,"exit_code":1,"observations":[{"actual":[0,false],"check":"boundary: noon never backtracks","expected":[0,false],"passed":true},{"actual":[-124.681,true],"check":"normal: steep morning angle backtracks","expected":[-25.319,true],"passed":false},{"actual":[120.0,true],"check":"boundary: continuous rows","expected":[0.0,true],"passed":false},{"actual":[90.0,true],"check":"regression: correction direction","expected":[0.0,true],"passed":false},{"actual":[-101.235,true],"check":"regression: correction direction (partial repair)","expected":[-38.765,true],"passed":false},{"actual":[30,false],"check":"control 1","expected":[30,false],"passed":true},{"actual":[-29.5,false],"check":"control 2","expected":[-29.5,false],"passed":true}],"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\": [-124.681, true], \"expected\": [-25.319, true], \"passed\": false}, {\"check\": \"boundary: continuous rows\", \"actual\": [120.0, true], \"expected\": [0.0, true], \"passed\": false}, {\"check\": \"regression: correction direction\", \"actual\": [90.0, true], \"expected\": [0.0, true], \"passed\": false}, {\"check\": \"regression: correction direction (partial repair)\", \"actual\": [-101.235, true], \"expected\": [-38.765, true], \"passed\": false}, {\"check\": \"control 1\", \"actual\": [30, false], \"expected\": [30, false], \"passed\": true}, {\"check\": \"control 2\", \"actual\": [-29.5, false], \"expected\": [-29.5, false], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":38.805,"exit_code":0,"observations":[{"actual":[0,false],"check":"boundary: noon never backtracks","expected":[0,false],"passed":true},{"actual":[-25.319,true],"check":"normal: steep morning angle backtracks","expected":[-25.319,true],"passed":true},{"actual":[0.0,true],"check":"boundary: continuous rows","expected":[0.0,true],"passed":true},{"actual":[0.0,true],"check":"regression: correction direction","expected":[0.0,true],"passed":true},{"actual":[-38.765,true],"check":"regression: correction direction (partial repair)","expected":[-38.765,true],"passed":true},{"actual":[30,false],"check":"control 1","expected":[30,false],"passed":true},{"actual":[-29.5,false],"check":"control 2","expected":[-29.5,false],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"boundary: noon never backtracks\", \"actual\": [0, false], \"expected\": [0, false], \"passed\": true}, {\"check\": \"normal: steep morning angle backtracks\", \"actual\": [-25.319, true], \"expected\": [-25.319, true], \"passed\": true}, {\"check\": \"boundary: continuous rows\", \"actual\": [0.0, true], \"expected\": [0.0, true], \"passed\": true}, {\"check\": \"regression: correction direction\", \"actual\": [0.0, true], \"expected\": [0.0, true], \"passed\": true}, {\"check\": \"regression: correction direction (partial repair)\", \"actual\": [-38.765, true], \"expected\": [-38.765, true], \"passed\": true}, {\"check\": \"control 1\", \"actual\": [30, false], \"expected\": [30, false], \"passed\": true}, {\"check\": \"control 2\", \"actual\": [-29.5, false], \"expected\": [-29.5, false], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}