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 | 3468.01 | 24.3  |  16 | 388.8  | -4.05058   |  10.4181 |
| 1108 | 3449.07 | 23.78 |  16 | 380.48 | -4.02336   |  10.5744 |
| 1112 | 3421.12 | 23.25 |  16 | 372    | -3.96439   |  10.657  |
| 1116 | 3409.95 | 22.64 |  16 | 362.24 | -3.90089   |  10.7688 |
| 1120 | 3394.78 | 22.07 |  16 | 353.12 | -3.86914   |  10.957  |
| 1124 | 3373.93 | 21.46 |  16 | 343.36 | -3.82378   |  11.1364 |
| 1128 | 3356.28 | 20.98 |  16 | 335.68 | -3.8011    |  11.3236 |
| 1132 | 3323.16 | 20.44 |  16 | 327.04 | -3.75121   |  11.4702 |
| 1136 | 3306.57 | 19.9  |  16 | 318.4  | -3.71492   |  11.6675 |
| 1140 | 3282.25 | 19.32 |  16 | 309.12 | -3.65595   |  11.827  |
| 1144 | 3247.62 | 18.74 |  16 | 299.84 | -3.58791   |  11.9661 |
| 1148 | 3223.24 | 18.11 |  16 | 289.76 | -3.51987   |  12.1475 |
| 1152 | 3207.09 | 17.53 |  16 | 280.48 | -3.45184   |  12.3069 |
| 1156 | 3176.96 | 17    |  16 | 272    | -3.3974    |  12.4905 |
| 1160 | 3152.96 | 16.45 |  16 | 263.2  | -3.31122   |  12.5806 |
| 1164 | 3111.45 | 15.96 |  16 | 255.36 | -3.25225   |  12.736  |
| 1168 | 3086.3  | 15.48 |  16 | 247.68 | -3.20236   |  12.9294 |
| 1172 | 3061.4  | 14.98 |  16 | 239.68 | -3.10711   |  12.9636 |
| 1176 | 3049.78 | 14.43 |  16 | 230.88 | -3.03907   |  13.163  |
| 1180 | 3003.32 | 14.04 |  16 | 224.64 | -2.99371   |  13.3267 |
| 1184 | 2987.73 | 13.55 |  16 | 216.8  | -2.93928   |  13.5575 |
| 1188 | 2952.33 | 13.1  |  16 | 209.6  | -2.86217   |  13.6554 |
| 1192 | 2918.2  | 12.74 |  16 | 203.84 | -2.82134   |  13.841  |
| 1196 | 2895.86 | 12.3  |  16 | 196.8  | -2.77145   |  14.0826 |
| 1200 | 2864.72 | 11.93 |  16 | 190.88 | -2.70794   |  14.1866 |
| 1204 | 2845.12 | 11.59 |  16 | 185.44 | -2.65805   |  14.3337 |
| 1208 | 2821.23 | 11.2  |  16 | 179.2  | -2.58094   |  14.4026 |
| 1212 | 2792.39 | 10.8  |  16 | 172.8  | -2.54919   |  14.7522 |
| 1216 | 2758.52 | 10.5  |  16 | 168    | -2.50836   |  14.9307 |
| 1220 | 2736.37 | 10.27 |  16 | 164.32 | -2.45393   |  14.9339 |
| 1224 | 2712.08 |  9.9  |  16 | 158.4  | -2.38136   |  15.0338 |
| 1228 | 2681.26 |  9.5  |  16 | 152    | -2.35414   |  15.4878 |
| 1232 | 2660.64 |  9.2  |  16 | 147.2  | -2.27703   |  15.469  |
| 1236 | 2629    |  8.9  |  16 | 142.4  | -2.23621   |  15.7037 |
| 1240 | 2598.64 |  8.6  |  16 | 137.6  | -2.19539   |  15.9548 |
| 1244 | 2575.93 |  8.2  |  16 | 131.2  | -2.11827   |  16.1454 |
| 1248 | 2547.87 |  7.9  |  16 | 126.4  | -2.08199   |  16.4714 |
| 1252 | 2517.32 |  7.57 |  16 | 121.12 | -2.02302   |  16.7026 |
| 1256 | 2482.17 |  7.19 |  16 | 115.04 | -1.97766   |  17.1911 |
| 1260 | 2440.17 |  6.89 |  16 | 110.24 | -1.94137   |  17.6104 |
| 1264 | 2418.69 |  6.53 |  16 | 104.48 | -1.85973   |  17.7998 |
| 1268 | 2369.48 |  6.29 |  16 | 100.64 | -1.81437   |  18.0283 |
| 1272 | 2345.45 |  6    |  16 |  96    | -1.76447   |  18.3799 |
| 1276 | 2306.38 |  5.75 |  16 |  92    | -1.70097   |  18.4888 |
| 1280 | 2277.85 |  5.5  |  16 |  88    | -1.66922   |  18.9684 |
| 1284 | 2248.15 |  5.3  |  16 |  84.8  | -1.61025   |  18.9888 |
| 1288 | 2222.36 |  5    |  16 |  80    | -1.55582   |  19.4478 |
| 1292 | 2198.72 |  4.8  |  16 |  76.8  | -1.515     |  19.7265 |
| 1296 | 2156.96 |  4.6  |  16 |  73.6  | -1.48778   |  20.2144 |
| 1300 | 2140.15 |  4.4  |  16 |  70.4  | -1.43789   |  20.4245 |
| 1304 | 2105.77 |  4.2  |  16 |  67.2  | -1.39706   |  20.7896 |
| 1308 | 2081.37 |  3.98 |  16 |  63.68 | -1.34717   |  21.1553 |
| 1312 | 2039.83 |  3.7  |  16 |  59.2  | -1.30181   |  21.99   |
| 1316 | 2001.27 |  3.58 |  16 |  57.28 | -1.25645   |  21.9352 |
| 1320 | 1968.2  |  3.39 |  16 |  54.24 | -1.20202   |  22.1611 |
| 1324 | 1935.5  |  3.2  |  16 |  51.2  | -1.1612    |  22.6796 |
| 1328 | 1902.76 |  3    |  16 |  48    | -1.12037   |  23.3411 |
| 1332 | 1869.56 |  2.84 |  16 |  45.44 | -1.10223   |  24.2568 |
| 1336 | 1839.98 |  2.7  |  16 |  43.2  | -1.05233   |  24.3596 |
| 1340 | 1807.39 |  2.4  |  16 |  38.4  | -1.02058   |  26.5777 |
| 1344 | 1773.08 |  2.3  |  16 |  36.8  | -0.979759  |  26.6239 |
| 1348 | 1737.6  |  2.1  |  16 |  33.6  | -0.943471  |  28.0795 |
| 1352 | 1704.96 |  2    |  16 |  32    | -0.902648  |  28.2078 |
| 1356 | 1667.06 |  1.9  |  16 |  30.4  | -0.870897  |  28.6479 |
| 1360 | 1630.35 |  1.7  |  16 |  27.2  | -0.821002  |  30.1839 |
| 1364 | 1589.17 |  1.6  |  16 |  25.6  | -0.784714  |  30.6529 |
| 1368 | 1553.88 |  1.5  |  16 |  24    | -0.743891  |  30.9955 |
| 1372 | 1518.54 |  1.4  |  16 |  22.4  | -0.716675  |  31.9944 |
| 1376 | 1481.78 |  1.3  |  16 |  20.8  | -0.680388  |  32.711  |
| 1380 | 1448.45 |  1.2  |  16 |  19.2  | -0.648637  |  33.7832 |
| 1384 | 1409.65 |  1.1  |  16 |  17.6  | -0.616885  |  35.0503 |
| 1388 | 1362.08 |  1    |  16 |  16    | -0.580598  |  36.2874 |
| 1392 | 1324.67 |  0.9  |  16 |  14.4  | -0.539774  |  37.4843 |
| 1396 | 1284.84 |  0.8  |  16 |  12.8  | -0.512559  |  40.0437 |
| 1400 | 1246.14 |  0.7  |  16 |  11.2  | -0.480808  |  42.9292 |
| 1404 | 1199.38 |  0.66 |  16 |  10.56 | -0.44452   |  42.0947 |
| 1408 | 1152.94 |  0.56 |  16 |   8.96 | -0.417305  |  46.5742 |
| 1412 | 1112.71 |  0.5  |  16 |   8    | -0.385553  |  48.1942 |
| 1416 | 1064.11 |  0.4  |  16 |   6.4  | -0.353802  |  55.2815 |
| 1420 | 1016.48 |  0.4  |  16 |   6.4  | -0.32205   |  50.3204 |
| 1424 |  969.68 |  0.37 |  16 |   5.92 | -0.294835  |  49.8032 |
| 1428 |  916.03 |  0.3  |  16 |   4.8  | -0.258547  |  53.864  |
| 1432 |  868.6  |  0.2  |  16 |   3.2  | -0.235868  |  73.7087 |
| 1436 |  809.94 |  0.2  |  16 |   3.2  | -0.208652  |  65.2039 |
| 1440 |  758.15 |  0.2  |  16 |   3.2  | -0.181437  |  56.699  |
| 1444 |  697.28 |  0.1  |  16 |   1.6  | -0.149685  |  93.5533 |
| 1448 |  641.26 |  0.1  |  16 |   1.6  | -0.127006  |  79.3786 |
| 1452 |  577.81 |  0.1  |  16 |   1.6  | -0.104326  |  65.2039 |
| 1456 |  513.25 |  0.05 |  16 |   0.8  | -0.0861825 | 107.728  |
| 1460 |  449.5  |  0.05 |  16 |   0.8  | -0.0680388 |  85.0485 |
| 1464 |  388.48 |  0.05 |  16 |   0.8  | -0.0498951 |  62.3689 |
| 1468 |  317.17 |  0.05 |  16 |   0.8  | -0.0362874 |  45.3592 |
| 1472 |    0    |  0    |  16 |   0    |  0         |   0      |
| 1476 |    0    |  0    |  16 |   0    |  0         |   0      |
| 1480 |    0    |  0    |  16 |   0    |  0         |   0      |
| 1484 |    0    |  0    |  16 |   0    |  0         |   0      |
| 1488 |    0    |  0    |  16 |   0    |  0         |   0      |
| 1492 |    0    |  0    |  16 |   0    |  0         |   0      |
| 1496 |    0    |  0    |  16 |   0    |  0         |   0      |



label: E=D*C
labeled_formulas: E=D*C
output: {"Arithmetic-Relationship": ["E=D*C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_705653___xlsx_35750e3b17a55b3b82949caebf97ac6eb8f4ed6a.xlsx___line_203