{"abstract":"Azimuth errors near the zenith are reported as huge.","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].","contract_signature":"cmd_az, cmd_el, sun_az, sun_el, tol","evaluation_group":"w2-solar_tracker_geometry-dual-axis-pointing-error","failed_approach":"Dropping the cos e factors lets azimuth error dominate at any elevation.","family":"w2-solar_tracker_geometry-dual-axis-pointing-error-elevation-trig-terms","id":"FA-93826","implementations":{"attempt":{"sha256":"dc39dc85d73026d175a0a05a7b911992b796f2745f4939e7ed89e1382f44bc12","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(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: elevation trig terms', [340, 45, 60, 80, 0.5], [44.136, False]],\n  ['regression: elevation trig terms (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: elevation trig terms', [200, 60, 60, 45, 5], [70.03, False]],\n  ['regression: elevation trig terms (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: elevation trig terms', [135, 60, 45, 45, 5], [52.239, False]],\n  ['regression: elevation trig terms (partial repair)', [270, 45, 340, 60, 5], [42.837, 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: elevation trig terms', [200, 30, 60, 80, 0.5], [67.839, False]],\n  ['regression: elevation trig terms (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: elevation trig terms', [270, 30, 250, 30, 5], [17.298, False]],\n  ['regression: elevation trig terms (partial repair)', [300, 30, 135, 60, 1], [89.155, 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":"12ae00c9fb9b2081c9f2c130adf51368905793ec0046c2f3d1f7936ccf7e2e47","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.cos(e1) * math.cos(e2) + math.sin(e1) * math.sin(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: elevation trig terms', [340, 45, 60, 80, 0.5], [44.136, False]],\n  ['regression: elevation trig terms (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: elevation trig terms', [200, 60, 60, 45, 5], [70.03, False]],\n  ['regression: elevation trig terms (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: elevation trig terms', [135, 60, 45, 45, 5], [52.239, False]],\n  ['regression: elevation trig terms (partial repair)', [270, 45, 340, 60, 5], [42.837, 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: elevation trig terms', [200, 30, 60, 80, 0.5], [67.839, False]],\n  ['regression: elevation trig terms (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: elevation trig terms', [270, 30, 250, 30, 5], [17.298, False]],\n  ['regression: elevation trig terms (partial repair)', [300, 30, 135, 60, 1], [89.155, 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-elevation-trig-terms","generated_at":"2026-09-29T14:51:58.743657+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":"Elevations are treated as zenith angles in the spherical law of cosines.","sha256":"d5720cbdadee442e0f4ba9470fe46900d95f99d5a1e9315add625f7686179dd2","title":"Dual-axis pointing error: elevation trig terms · 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":42.851,"exit_code":1,"observations":[{"actual":[0.0,true],"check":"normal: on target","expected":[0.0,true],"passed":true},{"actual":[0.0,true],"check":"boundary: across north","expected":[8.658,false],"passed":false},{"actual":[0.0,true],"check":"normal: elevation only","expected":[10.0,false],"passed":false},{"actual":[29.54,false],"check":"regression: elevation trig terms","expected":[44.136,false],"passed":false},{"actual":[45.927,false],"check":"regression: elevation trig terms (partial repair)","expected":[55.737,false],"passed":false},{"actual":[128.337,false],"check":"control 1","expected":[121.081,false],"passed":false},{"actual":[74.113,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\": [0.0, true], \"expected\": [8.658, false], \"passed\": false}, {\"check\": \"normal: elevation only\", \"actual\": [0.0, true], \"expected\": [10.0, false], \"passed\": false}, {\"check\": \"regression: elevation trig terms\", \"actual\": [29.54, false], \"expected\": [44.136, false], \"passed\": false}, {\"check\": \"regression: elevation trig terms (partial repair)\", \"actual\": [45.927, false], \"expected\": [55.737, false], \"passed\": false}, {\"check\": \"control 1\", \"actual\": [128.337, false], \"expected\": [121.081, false], \"passed\": false}, {\"check\": \"control 2\", \"actual\": [74.113, false], \"expected\": [49.874, false], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.823,"exit_code":1,"observations":[{"actual":[0.0,true],"check":"normal: on target","expected":[0.0,true],"passed":true},{"actual":[4.995,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":[75.894,false],"check":"regression: elevation trig terms","expected":[44.136,false],"passed":false},{"actual":[42.837,false],"check":"regression: elevation trig terms (partial repair)","expected":[55.737,false],"passed":false},{"actual":[37.676,false],"check":"control 1","expected":[121.081,false],"passed":false},{"actual":[99.876,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\": [4.995, false], \"expected\": [8.658, false], \"passed\": false}, {\"check\": \"normal: elevation only\", \"actual\": [10.0, false], \"expected\": [10.0, false], \"passed\": true}, {\"check\": \"regression: elevation trig terms\", \"actual\": [75.894, false], \"expected\": [44.136, false], \"passed\": false}, {\"check\": \"regression: elevation trig terms (partial repair)\", \"actual\": [42.837, false], \"expected\": [55.737, false], \"passed\": false}, {\"check\": \"control 1\", \"actual\": [37.676, false], \"expected\": [121.081, false], \"passed\": false}, {\"check\": \"control 2\", \"actual\": [99.876, false], \"expected\": [49.874, 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."}}