Task: Arithmetic-Relationship (source dataset: Auto-Relate)

You are given a table with numerical values in multiple columns. Your task is to analyze the data and identify semantic relationships, expressed in arithmetic relationships, that exist between columns.

These relationships may involve any combination of the following operations: addition (+), subtraction (−), multiplication (*), and division (/). The expressions can involve two or more columns and may be nested (e.g., B = (A + C) / D).

Please only identify arithmetic relationships that hold semantically based on the data, and do not return relationships that are likely spurious, e.g., (A = B * 0), where A is an all 0 column. Please only return minimal atomic relationships, e.g., if A = B + C and D = E + F, then there is no need to return A = B + C + E + F - D.

No explanation, return all the formula(s) in JSON format: {"Arithmetic-Relationship": [<list-of-formulas>]}. If no relationship is found, return {"Arithmetic-Relationship": []}.

Input Table:
|    A |       B |     C |   D |      E |          F |        G |
|-----:|--------:|------:|----:|-------:|-----------:|---------:|
| 1104 | 3243.52 | 20.63 |  14 | 288.82 | -3.49719   |  12.1086 |
| 1108 | 3206.35 | 20.47 |  14 | 286.58 | -3.49266   |  12.1874 |
| 1112 | 3201.53 | 19.9  |  14 | 278.6  | -3.45184   |  12.3899 |
| 1116 | 3173.94 | 19.45 |  14 | 272.3  | -3.40194   |  12.4934 |
| 1120 | 3159.69 | 18.96 |  14 | 265.44 | -3.35658   |  12.6453 |
| 1124 | 3143.02 | 18.39 |  14 | 257.46 | -3.29308   |  12.7906 |
| 1128 | 3120.54 | 18    |  14 | 252    | -3.24772   |  12.8878 |
| 1132 | 3106.98 | 17.37 |  14 | 243.18 | -3.18875   |  13.1127 |
| 1136 | 3070.9  | 16.96 |  14 | 237.44 | -3.13886   |  13.2196 |
| 1140 | 3048.83 | 16.54 |  14 | 231.56 | -3.09803   |  13.379  |
| 1144 | 3025.3  | 16.04 |  14 | 224.56 | -3.05721   |  13.6142 |
| 1148 | 3004.3  | 15.64 |  14 | 218.96 | -3.00278   |  13.7138 |
| 1152 | 2979.37 | 15.19 |  14 | 212.66 | -2.93928   |  13.8215 |
| 1156 | 2953.53 | 14.71 |  14 | 205.94 | -2.88485   |  14.0082 |
| 1160 | 2936.83 | 14.33 |  14 | 200.62 | -2.84856   |  14.1988 |
| 1164 | 2914.06 | 13.93 |  14 | 195.02 | -2.78052   |  14.2576 |
| 1168 | 2883.22 | 13.57 |  14 | 189.98 | -2.76238   |  14.5403 |
| 1172 | 2861    | 13.1  |  14 | 183.4  | -2.6898    |  14.6663 |
| 1176 | 2847.43 | 12.7  |  14 | 177.8  | -2.64444   |  14.8731 |
| 1180 | 2814.56 | 12.4  |  14 | 173.6  | -2.59455   |  14.9455 |
| 1184 | 2802.26 | 11.9  |  14 | 166.6  | -2.52651   |  15.1651 |
| 1188 | 2776.19 | 11.6  |  14 | 162.4  | -2.49022   |  15.3339 |
| 1192 | 2739.63 | 11.3  |  14 | 158.2  | -2.45393   |  15.5116 |
| 1196 | 2704.73 | 11    |  14 | 154    | -2.40857   |  15.6401 |
| 1200 | 2697.09 | 10.6  |  14 | 148.4  | -2.34961   |  15.8329 |
| 1204 | 2658.7  | 10.36 |  14 | 145.04 | -2.336     |  16.1059 |
| 1208 | 2658.2  |  9.93 |  14 | 139.02 | -2.25889   |  16.2487 |
| 1212 | 2619.43 |  9.67 |  14 | 135.38 | -2.20446   |  16.2835 |
| 1216 | 2598.21 |  9.33 |  14 | 130.62 | -2.17724   |  16.6685 |
| 1220 | 2565.53 |  9    |  14 | 126    | -2.11827   |  16.8117 |
| 1224 | 2543.29 |  8.7  |  14 | 121.8  | -2.05477   |  16.87   |
| 1228 | 2503.75 |  8.4  |  14 | 117.6  | -2.02756   |  17.2411 |
| 1232 | 2482.3  |  8    |  14 | 112    | -1.98673   |  17.7387 |
| 1236 | 2452.4  |  7.7  |  14 | 107.8  | -1.90962   |  17.7145 |
| 1240 | 2418.4  |  7.4  |  14 | 103.6  | -1.89148   |  18.2575 |
| 1244 | 2404.79 |  7.04 |  14 |  98.56 | -1.8189    |  18.4548 |
| 1248 | 2365.92 |  6.8  |  14 |  95.2  | -1.76447   |  18.5344 |
| 1252 | 2330.73 |  6.5  |  14 |  91    | -1.71911   |  18.8914 |
| 1256 | 2302.44 |  6.29 |  14 |  88.06 | -1.68283   |  19.11   |
| 1260 | 2271.3  |  6    |  14 |  84    | -1.63293   |  19.4397 |
| 1264 | 2246.36 |  5.77 |  14 |  80.78 | -1.5785    |  19.5407 |
| 1268 | 2220.63 |  5.5  |  14 |  77    | -1.56489   |  20.3233 |
| 1272 | 2193.77 |  5.34 |  14 |  74.76 | -1.51953   |  20.3255 |
| 1276 | 2170.6  |  5.1  |  14 |  71.4  | -1.47871   |  20.7102 |
| 1280 | 2139.34 |  4.9  |  14 |  68.6  | -1.44242   |  21.0266 |
| 1284 | 2116.44 |  4.7  |  14 |  65.8  | -1.4016    |  21.3009 |
| 1288 | 2081.06 |  4.5  |  14 |  63    | -1.36985   |  21.7436 |
| 1292 | 2055.76 |  4.29 |  14 |  60.06 | -1.32449   |  22.0528 |
| 1296 | 2022.58 |  4.1  |  14 |  57.4  | -1.28367   |  22.3635 |
| 1300 | 1994.8  |  3.9  |  14 |  54.6  | -1.23831   |  22.6796 |
| 1304 | 1959.18 |  3.7  |  14 |  51.8  | -1.19295   |  23.0299 |
| 1308 | 1930.36 |  3.5  |  14 |  49    | -1.16573   |  23.7904 |
| 1312 | 1896.19 |  3.3  |  14 |  46.2  | -1.12491   |  24.3487 |
| 1316 | 1872.9  |  3.2  |  14 |  44.8  | -1.08862   |  24.2996 |
| 1320 | 1838.11 |  3    |  14 |  42    | -1.05233   |  25.0556 |
| 1324 | 1813.29 |  2.9  |  14 |  40.6  | -1.01605   |  25.0258 |
| 1328 | 1784.61 |  2.7  |  14 |  37.8  | -0.984295  |  26.0395 |
| 1332 | 1754.27 |  2.5  |  14 |  35    | -0.952543  |  27.2155 |
| 1336 | 1724.22 |  2.3  |  14 |  32.2  | -0.916256  |  28.4552 |
| 1340 | 1688.58 |  2.2  |  14 |  30.8  | -0.884504  |  28.7177 |
| 1344 | 1658.74 |  2    |  14 |  28    | -0.848217  |  30.2935 |
| 1348 | 1624.8  |  1.9  |  14 |  26.6  | -0.807394  |  30.3531 |
| 1352 | 1589.51 |  1.7  |  14 |  23.8  | -0.76657   |  32.2088 |
| 1356 | 1552.32 |  1.6  |  14 |  22.4  | -0.739355  |  33.0069 |
| 1360 | 1523.47 |  1.5  |  14 |  21    | -0.703068  |  33.4794 |
| 1364 | 1487.32 |  1.4  |  14 |  19.6  | -0.680388  |  34.7137 |
| 1368 | 1455.15 |  1.3  |  14 |  18.2  | -0.648637  |  35.6394 |
| 1372 | 1420.91 |  1.2  |  14 |  16.8  | -0.621421  |  36.9893 |
| 1376 | 1375.31 |  1.1  |  14 |  15.4  | -0.585134  |  37.9957 |
| 1380 | 1340.81 |  1    |  14 |  14    | -0.548846  |  39.2033 |
| 1384 | 1306.67 |  0.9  |  14 |  12.6  | -0.517095  |  41.0393 |
| 1388 | 1267.97 |  0.8  |  14 |  11.2  | -0.489879  |  43.7392 |
| 1392 | 1232.99 |  0.8  |  14 |  11.2  | -0.462664  |  41.3093 |
| 1396 | 1187.7  |  0.7  |  14 |   9.8  | -0.426376  |  43.5078 |
| 1400 | 1149.61 |  0.6  |  14 |   8.4  | -0.399161  |  47.5192 |
| 1404 | 1105.72 |  0.5  |  14 |   7    | -0.371945  |  53.1351 |
| 1408 | 1063.81 |  0.5  |  14 |   7    | -0.349266  |  49.8951 |
| 1412 | 1017.51 |  0.4  |  14 |   5.6  | -0.317514  |  56.699  |
| 1416 |  974.07 |  0.4  |  14 |   5.6  | -0.285763  |  51.0291 |
| 1420 |  929.01 |  0.3  |  14 |   4.2  | -0.258547  |  61.5589 |
| 1424 |  885.8  |  0.3  |  14 |   4.2  | -0.235868  |  56.159  |
| 1428 |  834.28 |  0.2  |  14 |   2.8  | -0.208652  |  74.5187 |
| 1432 |  786.35 |  0.2  |  14 |   2.8  | -0.185973  |  66.4188 |
| 1436 |  734.96 |  0.2  |  14 |   2.8  | -0.163293  |  58.319  |
| 1440 |  682.97 |  0.11 |  14 |   1.54 | -0.145149  |  94.2529 |
| 1444 |  627.5  |  0.1  |  14 |   1.4  | -0.12247   |  87.4785 |
| 1448 |  574.57 |  0.1  |  14 |   1.4  | -0.0997902 |  71.2787 |
| 1452 |  517.91 |  0.05 |  14 |   0.7  | -0.0816466 | 116.638  |
| 1456 |  462.63 |  0.05 |  14 |   0.7  | -0.0680388 |  97.1983 |
| 1460 |  400.48 |  0.05 |  14 |   0.7  | -0.0453592 |  64.7989 |
| 1464 |  341.53 |  0.05 |  14 |   0.7  | -0.0317514 |  45.3592 |
| 1468 |    0    |  0    |  14 |   0    |  0         |   0      |
| 1472 |    0    |  0    |  14 |   0    |  0         |   0      |
| 1476 |    0    |  0    |  14 |   0    |  0         |   0      |
| 1480 |    0    |  0    |  14 |   0    |  0         |   0      |
| 1484 |    0    |  0    |  14 |   0    |  0         |   0      |
| 1488 |    0    |  0    |  14 |   0    |  0         |   0      |
| 1492 |    0    |  0    |  14 |   0    |  0         |   0      |
| 1496 |    0    |  0    |  14 |   0    |  0         |   0      |
| 1500 |    0    |  0    |  14 |   0    |  0         |   0      |
| 1504 |    0    |  0    |  14 |   0    |  0         |   0      |
| 1508 |    0    |  0    |  14 |   0    |  0         |   0      |
| 1512 |    0    |  0    |  14 |   0    |  0         |   0      |
| 1516 |    0    |  0    |  14 |   0    |  0         |   0      |
| 1520 |    0    |  0    |  14 |   0    |  0         |   0      |
| 1524 |    0    |  0    |  14 |   0    |  0         |   0      |
| 1528 |    0    |  0    |  14 |   0    |  0         |   0      |
| 1532 |    0    |  0    |  14 |   0    |  0         |   0      |
| 1536 |  344.26 |  0.05 |  14 |   0.7  |  0.0453592 |  64.7989 |
| 1540 |  399.1  |  0.05 |  14 |   0.7  |  0.0635029 |  90.7184 |
| 1544 |  460.93 |  0.05 |  14 |   0.7  |  0.0816466 | 116.638  |



label: E=C*D
labeled_formulas: E=C*D
output: {"Arithmetic-Relationship": ["E=C*D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_705652___xlsx_35750e3b17a55b3b82949caebf97ac6eb8f4ed6a.xlsx___line_202