{"abstract":"Small commanded offsets across north read as nearly 360 degrees of error.","category":"Solar tracker geometry","checks":7,"contract":"Pointing error is the great-circle angle between the commanded direction and the sun: cos(err) = sin e1 sin e2 + cos e1 cos e2 cos(az1 - az2), clamped to [-1, 1]. Return [err degrees rounded 3, err <= tol].","evaluation_group":"w2-solar_tracker_geometry-dual-axis-pointing-error","failed_approach":"A planar hypotenuse still ignores azimuth wrap and convergence toward the zenith.","family":"w2-solar_tracker_geometry-dual-axis-pointing-error-angular-distance-metric","id":"FA-93831","implementations":{"attempt":{"sha256":"e2bd277b4a5ebedcaa8ba44bfddbb86e4b56537472e3f0d0530d83f1ef3e5849","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(cmd_az, cmd_el, sun_az, sun_el, tol):\n    e1 = math.radians(cmd_el)\n    e2 = math.radians(sun_el)\n    d = math.radians(cmd_az - sun_az)\n    c = math.sin(e1) * math.sin(e2) + math.cos(e1) * math.cos(e2) * math.cos(d)\n    c = max(-1.0, min(1.0, c))\n    err = math.hypot(cmd_az - sun_az, cmd_el - sun_el)\n    return [round(err, 3), err <= tol]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['normal: on target', [180, 45, 180, 45, 1], [0.0, True]],\n  ['boundary: across north', [355, 30, 5, 30, 1], [8.658, False]],\n  ['normal: elevation only', [90, 30, 90, 40, 5], [10.0, False]],\n  ['regression: angular distance metric', [340, 45, 60, 80, 0.5], [44.136, False]],\n  ['regression: angular distance metric (partial repair)', [340, 30, 270, 45, 1], [55.737, False]],\n  ['control 1', [90, 10, 225, 30, 0.5], [121.081, False]],\n  ['control 2', [340, 80, 225, 45, 0.5], [49.874, False]]],\n [['normal: on target', [180, 45, 180, 45, 1], [0.0, True]],\n  ['boundary: across north', [355, 30, 5, 30, 1], [8.658, False]],\n  ['normal: elevation only', [90, 30, 90, 40, 5], [10.0, False]],\n  ['regression: angular distance metric', [200, 60, 60, 45, 5], [70.03, False]],\n  ['regression: angular distance metric (partial repair)', [180, 60, 0, 60, 0.5], [60.0, False]],\n  ['control 1', [180, 80, 200, 10, 5], [70.628, False]],\n  ['control 2', [45, 60, 60, 80, 1], [20.49, False]]],\n [['normal: on target', [180, 45, 180, 45, 1], [0.0, True]],\n  ['boundary: across north', [355, 30, 5, 30, 1], [8.658, False]],\n  ['normal: elevation only', [90, 30, 90, 40, 5], [10.0, False]],\n  ['regression: angular distance metric', [135, 60, 45, 45, 5], [52.239, False]],\n  ['regression: angular distance metric (partial repair)', [270, 30, 0, 80, 5], [60.501, False]],\n  ['control 1', [135, 80, 60, 60, 5], [28.915, False]],\n  ['control 2', [60, 30, 315, 10, 0.5], [97.696, False]]],\n [['normal: on target', [180, 45, 180, 45, 1], [0.0, True]],\n  ['boundary: across north', [355, 30, 5, 30, 1], [8.658, False]],\n  ['normal: elevation only', [90, 30, 90, 40, 5], [10.0, False]],\n  ['regression: angular distance metric', [200, 30, 60, 80, 0.5], [67.839, False]],\n  ['regression: angular distance metric (partial repair)', [0, 45, 250, 60, 2], [60.564, False]],\n  ['control 1', [180, 45, 45, 60, 1], [68.754, False]],\n  ['control 2', [300, 10, 135, 45, 5], [123.357, False]]],\n [['normal: on target', [180, 45, 180, 45, 1], [0.0, True]],\n  ['boundary: across north', [355, 30, 5, 30, 1], [8.658, False]],\n  ['normal: elevation only', [90, 30, 90, 40, 5], [10.0, False]],\n  ['regression: angular distance metric', [300, 30, 135, 60, 1], [89.155, False]],\n  ['regression: angular distance metric (partial repair)', [270, 30, 250, 30, 5], [17.298, False]],\n  ['control 1', [270, 10, 250, 60, 0.5], [52.187, False]],\n  ['control 2', [300, 30, 180, 30, 2], [97.181, 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":"ef5e92e27a4962b0de412891d0d2cdd1ec1d73de00d09ad641799bc775bb5391","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(cmd_az, cmd_el, sun_az, sun_el, tol):\n    e1 = math.radians(cmd_el)\n    e2 = math.radians(sun_el)\n    d = math.radians(cmd_az - sun_az)\n    c = math.sin(e1) * math.sin(e2) + math.cos(e1) * math.cos(e2) * math.cos(d)\n    c = max(-1.0, min(1.0, c))\n    err = abs(cmd_az - sun_az) + abs(cmd_el - sun_el)\n    return [round(err, 3), err <= tol]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['normal: on target', [180, 45, 180, 45, 1], [0.0, True]],\n  ['boundary: across north', [355, 30, 5, 30, 1], [8.658, False]],\n  ['normal: elevation only', [90, 30, 90, 40, 5], [10.0, False]],\n  ['regression: angular distance metric', [340, 45, 60, 80, 0.5], [44.136, False]],\n  ['regression: angular distance metric (partial repair)', [340, 30, 270, 45, 1], [55.737, False]],\n  ['control 1', [90, 10, 225, 30, 0.5], [121.081, False]],\n  ['control 2', [340, 80, 225, 45, 0.5], [49.874, False]]],\n [['normal: on target', [180, 45, 180, 45, 1], [0.0, True]],\n  ['boundary: across north', [355, 30, 5, 30, 1], [8.658, False]],\n  ['normal: elevation only', [90, 30, 90, 40, 5], [10.0, False]],\n  ['regression: angular distance metric', [200, 60, 60, 45, 5], [70.03, False]],\n  ['regression: angular distance metric (partial repair)', [180, 60, 0, 60, 0.5], [60.0, False]],\n  ['control 1', [180, 80, 200, 10, 5], [70.628, False]],\n  ['control 2', [45, 60, 60, 80, 1], [20.49, False]]],\n [['normal: on target', [180, 45, 180, 45, 1], [0.0, True]],\n  ['boundary: across north', [355, 30, 5, 30, 1], [8.658, False]],\n  ['normal: elevation only', [90, 30, 90, 40, 5], [10.0, False]],\n  ['regression: angular distance metric', [135, 60, 45, 45, 5], [52.239, False]],\n  ['regression: angular distance metric (partial repair)', [270, 30, 0, 80, 5], [60.501, False]],\n  ['control 1', [135, 80, 60, 60, 5], [28.915, False]],\n  ['control 2', [60, 30, 315, 10, 0.5], [97.696, False]]],\n [['normal: on target', [180, 45, 180, 45, 1], [0.0, True]],\n  ['boundary: across north', [355, 30, 5, 30, 1], [8.658, False]],\n  ['normal: elevation only', [90, 30, 90, 40, 5], [10.0, False]],\n  ['regression: angular distance metric', [200, 30, 60, 80, 0.5], [67.839, False]],\n  ['regression: angular distance metric (partial repair)', [0, 45, 250, 60, 2], [60.564, False]],\n  ['control 1', [180, 45, 45, 60, 1], [68.754, False]],\n  ['control 2', [300, 10, 135, 45, 5], [123.357, False]]],\n [['normal: on target', [180, 45, 180, 45, 1], [0.0, True]],\n  ['boundary: across north', [355, 30, 5, 30, 1], [8.658, False]],\n  ['normal: elevation only', [90, 30, 90, 40, 5], [10.0, False]],\n  ['regression: angular distance metric', [300, 30, 135, 60, 1], [89.155, False]],\n  ['regression: angular distance metric (partial repair)', [270, 30, 250, 30, 5], [17.298, False]],\n  ['control 1', [270, 10, 250, 60, 0.5], [52.187, False]],\n  ['control 2', [300, 30, 180, 30, 2], [97.181, 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":"12bb03d0c21a4981b67e4921fe29bc28d7681b5910c06e863cbd6311c1471a8e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(cmd_az, cmd_el, sun_az, sun_el, tol):\n    e1 = math.radians(cmd_el)\n    e2 = math.radians(sun_el)\n    d = math.radians(cmd_az - sun_az)\n    c = math.sin(e1) * math.sin(e2) + math.cos(e1) * math.cos(e2) * math.cos(d)\n    c = max(-1.0, min(1.0, c))\n    err = math.degrees(math.acos(c))\n    return [round(err, 3), err <= tol]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['normal: on target', [180, 45, 180, 45, 1], [0.0, True]],\n  ['boundary: across north', [355, 30, 5, 30, 1], [8.658, False]],\n  ['normal: elevation only', [90, 30, 90, 40, 5], [10.0, False]],\n  ['regression: angular distance metric', [340, 45, 60, 80, 0.5], [44.136, False]],\n  ['regression: angular distance metric (partial repair)', [340, 30, 270, 45, 1], [55.737, False]],\n  ['control 1', [90, 10, 225, 30, 0.5], [121.081, False]],\n  ['control 2', [340, 80, 225, 45, 0.5], [49.874, False]]],\n [['normal: on target', [180, 45, 180, 45, 1], [0.0, True]],\n  ['boundary: across north', [355, 30, 5, 30, 1], [8.658, False]],\n  ['normal: elevation only', [90, 30, 90, 40, 5], [10.0, False]],\n  ['regression: angular distance metric', [200, 60, 60, 45, 5], [70.03, False]],\n  ['regression: angular distance metric (partial repair)', [180, 60, 0, 60, 0.5], [60.0, False]],\n  ['control 1', [180, 80, 200, 10, 5], [70.628, False]],\n  ['control 2', [45, 60, 60, 80, 1], [20.49, False]]],\n [['normal: on target', [180, 45, 180, 45, 1], [0.0, True]],\n  ['boundary: across north', [355, 30, 5, 30, 1], [8.658, False]],\n  ['normal: elevation only', [90, 30, 90, 40, 5], [10.0, False]],\n  ['regression: angular distance metric', [135, 60, 45, 45, 5], [52.239, False]],\n  ['regression: angular distance metric (partial repair)', [270, 30, 0, 80, 5], [60.501, False]],\n  ['control 1', [135, 80, 60, 60, 5], [28.915, False]],\n  ['control 2', [60, 30, 315, 10, 0.5], [97.696, False]]],\n [['normal: on target', [180, 45, 180, 45, 1], [0.0, True]],\n  ['boundary: across north', [355, 30, 5, 30, 1], [8.658, False]],\n  ['normal: elevation only', [90, 30, 90, 40, 5], [10.0, False]],\n  ['regression: angular distance metric', [200, 30, 60, 80, 0.5], [67.839, False]],\n  ['regression: angular distance metric (partial repair)', [0, 45, 250, 60, 2], [60.564, False]],\n  ['control 1', [180, 45, 45, 60, 1], [68.754, False]],\n  ['control 2', [300, 10, 135, 45, 5], [123.357, False]]],\n [['normal: on target', [180, 45, 180, 45, 1], [0.0, True]],\n  ['boundary: across north', [355, 30, 5, 30, 1], [8.658, False]],\n  ['normal: elevation only', [90, 30, 90, 40, 5], [10.0, False]],\n  ['regression: angular distance metric', [300, 30, 135, 60, 1], [89.155, False]],\n  ['regression: angular distance metric (partial repair)', [270, 30, 250, 30, 5], [17.298, False]],\n  ['control 1', [270, 10, 250, 60, 0.5], [52.187, False]],\n  ['control 2', [300, 30, 180, 30, 2], [97.181, 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-dual-axis-pointing-error-angular-distance-metric","generated_at":"2026-09-29T14:51:58.747760+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":"Use the great-circle angle.","root_cause":"The error adds raw azimuth and elevation differences.","sha256":"0cc9f01ee04ef8584ae09770c2c41980ea48c8357979d18e9e7d27df6e9580ed","title":"Dual-axis pointing error: angular distance metric · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":39.065,"exit_code":1,"observations":[{"actual":[0.0,true],"check":"normal: on target","expected":[0.0,true],"passed":true},{"actual":[350.0,false],"check":"boundary: across north","expected":[8.658,false],"passed":false},{"actual":[10.0,false],"check":"normal: elevation only","expected":[10.0,false],"passed":true},{"actual":[282.179,false],"check":"regression: angular distance metric","expected":[44.136,false],"passed":false},{"actual":[71.589,false],"check":"regression: angular distance metric (partial repair)","expected":[55.737,false],"passed":false},{"actual":[136.473,false],"check":"control 1","expected":[121.081,false],"passed":false},{"actual":[120.208,false],"check":"control 2","expected":[49.874,false],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"normal: on target\", \"actual\": [0.0, true], \"expected\": [0.0, true], \"passed\": true}, {\"check\": \"boundary: across north\", \"actual\": [350.0, false], \"expected\": [8.658, false], \"passed\": false}, {\"check\": \"normal: elevation only\", \"actual\": [10.0, false], \"expected\": [10.0, false], \"passed\": true}, {\"check\": \"regression: angular distance metric\", \"actual\": [282.179, false], \"expected\": [44.136, false], \"passed\": false}, {\"check\": \"regression: angular distance metric (partial repair)\", \"actual\": [71.589, false], \"expected\": [55.737, false], \"passed\": false}, {\"check\": \"control 1\", \"actual\": [136.473, false], \"expected\": [121.081, false], \"passed\": false}, {\"check\": \"control 2\", \"actual\": [120.208, false], \"expected\": [49.874, false], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.832,"exit_code":1,"observations":[{"actual":[0,true],"check":"normal: on target","expected":[0.0,true],"passed":true},{"actual":[350,false],"check":"boundary: across north","expected":[8.658,false],"passed":false},{"actual":[10,false],"check":"normal: elevation only","expected":[10.0,false],"passed":true},{"actual":[315,false],"check":"regression: angular distance metric","expected":[44.136,false],"passed":false},{"actual":[85,false],"check":"regression: angular distance metric (partial repair)","expected":[55.737,false],"passed":false},{"actual":[155,false],"check":"control 1","expected":[121.081,false],"passed":false},{"actual":[150,false],"check":"control 2","expected":[49.874,false],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"normal: on target\", \"actual\": [0, true], \"expected\": [0.0, true], \"passed\": true}, {\"check\": \"boundary: across north\", \"actual\": [350, false], \"expected\": [8.658, false], \"passed\": false}, {\"check\": \"normal: elevation only\", \"actual\": [10, false], \"expected\": [10.0, false], \"passed\": true}, {\"check\": \"regression: angular distance metric\", \"actual\": [315, false], \"expected\": [44.136, false], \"passed\": false}, {\"check\": \"regression: angular distance metric (partial repair)\", \"actual\": [85, false], \"expected\": [55.737, false], \"passed\": false}, {\"check\": \"control 1\", \"actual\": [155, false], \"expected\": [121.081, false], \"passed\": false}, {\"check\": \"control 2\", \"actual\": [150, false], \"expected\": [49.874, false], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":41.478,"exit_code":0,"observations":[{"actual":[0.0,true],"check":"normal: on target","expected":[0.0,true],"passed":true},{"actual":[8.658,false],"check":"boundary: across north","expected":[8.658,false],"passed":true},{"actual":[10.0,false],"check":"normal: elevation only","expected":[10.0,false],"passed":true},{"actual":[44.136,false],"check":"regression: angular distance metric","expected":[44.136,false],"passed":true},{"actual":[55.737,false],"check":"regression: angular distance metric (partial repair)","expected":[55.737,false],"passed":true},{"actual":[121.081,false],"check":"control 1","expected":[121.081,false],"passed":true},{"actual":[49.874,false],"check":"control 2","expected":[49.874,false],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"normal: on target\", \"actual\": [0.0, true], \"expected\": [0.0, true], \"passed\": true}, {\"check\": \"boundary: across north\", \"actual\": [8.658, false], \"expected\": [8.658, false], \"passed\": true}, {\"check\": \"normal: elevation only\", \"actual\": [10.0, false], \"expected\": [10.0, false], \"passed\": true}, {\"check\": \"regression: angular distance metric\", \"actual\": [44.136, false], \"expected\": [44.136, false], \"passed\": true}, {\"check\": \"regression: angular distance metric (partial repair)\", \"actual\": [55.737, false], \"expected\": [55.737, false], \"passed\": true}, {\"check\": \"control 1\", \"actual\": [121.081, false], \"expected\": [121.081, false], \"passed\": true}, {\"check\": \"control 2\", \"actual\": [49.874, false], \"expected\": [49.874, false], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}