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 | 2666.99 | 13.63 |  10 | 136.3 | -2.30425   |  16.9057 |
| 1108 | 2660.54 | 13.45 |  10 | 134.5 | -2.29518   |  17.0645 |
| 1112 | 2626.69 | 13.2  |  10 | 132   | -2.28157   |  17.2846 |
| 1116 | 2617.22 | 12.81 |  10 | 128.1 | -2.2226    |  17.3505 |
| 1120 | 2599.83 | 12.5  |  10 | 125   | -2.18178   |  17.4542 |
| 1124 | 2590    | 12.14 |  10 | 121.4 | -2.16363   |  17.8224 |
| 1128 | 2562.24 | 11.96 |  10 | 119.6 | -2.13188   |  17.8251 |
| 1132 | 2535.12 | 11.63 |  10 | 116.3 | -2.1092    |  18.1359 |
| 1136 | 2528.12 | 11.32 |  10 | 113.2 | -2.05477   |  18.1517 |
| 1140 | 2513.71 | 11    |  10 | 110   | -2.04116   |  18.556  |
| 1144 | 2484.17 | 10.8  |  10 | 108   | -1.98673   |  18.3957 |
| 1148 | 2471.72 | 10.45 |  10 | 104.5 | -1.95498   |  18.708  |
| 1152 | 2448.76 | 10.2  |  10 | 102   | -1.92777   |  18.8997 |
| 1156 | 2435.76 |  9.9  |  10 |  99   | -1.89148   |  19.1058 |
| 1160 | 2416.26 |  9.56 |  10 |  95.6 | -1.83705   |  19.216  |
| 1164 | 2395.29 |  9.29 |  10 |  92.9 | -1.80983   |  19.4815 |
| 1168 | 2370.82 |  9.1  |  10 |  91   | -1.79169   |  19.6889 |
| 1172 | 2344.27 |  8.8  |  10 |  88   | -1.7554    |  19.9477 |
| 1176 | 2332.12 |  8.5  |  10 |  85   | -1.71458   |  20.1715 |
| 1180 | 2305.96 |  8.3  |  10 |  83   | -1.68283   |  20.275  |
| 1184 | 2282.55 |  8.05 |  10 |  80.5 | -1.65107   |  20.5102 |
| 1188 | 2271.04 |  7.71 |  10 |  77.1 | -1.61932   |  21.0029 |
| 1192 | 2241.4  |  7.57 |  10 |  75.7 | -1.59211   |  21.0318 |
| 1196 | 2219.44 |  7.3  |  10 |  73   | -1.55582   |  21.3126 |
| 1200 | 2198.37 |  7.1  |  10 |  71   | -1.53768   |  21.6574 |
| 1204 | 2176.57 |  6.82 |  10 |  68.2 | -1.50139   |  22.0145 |
| 1208 | 2156.65 |  6.6  |  10 |  66   | -1.46964   |  22.2672 |
| 1212 | 2128.5  |  6.48 |  10 |  64.8 | -1.44242   |  22.2596 |
| 1216 | 2106.08 |  6.2  |  10 |  62   | -1.41067   |  22.7528 |
| 1220 | 2093.85 |  6    |  10 |  60   | -1.36078   |  22.6796 |
| 1224 | 2072.61 |  5.8  |  10 |  58   | -1.32902   |  22.9142 |
| 1228 | 2045.76 |  5.6  |  10 |  56   | -1.31995   |  23.5706 |
| 1232 | 2023.95 |  5.4  |  10 |  54   | -1.2882    |  23.8556 |
| 1236 | 2005.05 |  5.2  |  10 |  52   | -1.25645   |  24.1625 |
| 1240 | 1982.4  |  5    |  10 |  50   | -1.22016   |  24.4032 |
| 1244 | 1956.82 |  4.84 |  10 |  48.4 | -1.18841   |  24.5539 |
| 1248 | 1936.33 |  4.64 |  10 |  46.4 | -1.16573   |  25.1235 |
| 1252 | 1906.73 |  4.5  |  10 |  45   | -1.13852   |  25.3004 |
| 1256 | 1884.84 |  4.3  |  10 |  43   | -1.09769   |  25.5277 |
| 1260 | 1863.52 |  4.1  |  10 |  41   | -1.07501   |  26.2198 |
| 1264 | 1833.91 |  3.9  |  10 |  39   | -1.05687   |  27.0992 |
| 1268 | 1816.36 |  3.73 |  10 |  37.3 | -1.01605   |  27.2398 |
| 1272 | 1788.63 |  3.6  |  10 |  36   | -0.988831  |  27.4675 |
| 1276 | 1762.3  |  3.5  |  10 |  35   | -0.970687  |  27.7339 |
| 1280 | 1745.28 |  3.3  |  10 |  33   | -0.929864  |  28.1777 |
| 1284 | 1716.98 |  3.2  |  10 |  32   | -0.907184  |  28.3495 |
| 1288 | 1696.78 |  3    |  10 |  30   | -0.879968  |  29.3323 |
| 1292 | 1670.82 |  2.9  |  10 |  29   | -0.852753  |  29.4053 |
| 1296 | 1643.14 |  2.8  |  10 |  28   | -0.825537  |  29.4835 |
| 1300 | 1615.06 |  2.6  |  10 |  26   | -0.798322  |  30.7047 |
| 1304 | 1591.35 |  2.4  |  10 |  24   | -0.780178  |  32.5074 |
| 1308 | 1562.13 |  2.3  |  10 |  23   | -0.752963  |  32.7375 |
| 1312 | 1539    |  2.1  |  10 |  21   | -0.721211  |  34.3434 |
| 1316 | 1515.73 |  2    |  10 |  20   | -0.698532  |  34.9266 |
| 1320 | 1487.76 |  1.9  |  10 |  19   | -0.671316  |  35.3324 |
| 1324 | 1460.76 |  1.8  |  10 |  18   | -0.653172  |  36.2874 |
| 1328 | 1439.6  |  1.7  |  10 |  17   | -0.630493  |  37.0878 |
| 1332 | 1411.47 |  1.6  |  10 |  16   | -0.612349  |  38.2718 |
| 1336 | 1382.01 |  1.5  |  10 |  15   | -0.580598  |  38.7065 |
| 1340 | 1347.15 |  1.4  |  10 |  14   | -0.553382  |  39.5273 |
| 1344 | 1320.39 |  1.3  |  10 |  13   | -0.530703  |  40.8233 |
| 1348 | 1293.77 |  1.2  |  10 |  12   | -0.512559  |  42.7132 |
| 1352 | 1264.77 |  1.2  |  10 |  12   | -0.485343  |  40.4453 |
| 1356 | 1239.06 |  1.1  |  10 |  11   | -0.4672    |  42.4727 |
| 1360 | 1199.94 |  1    |  10 |  10   | -0.44452   |  44.452  |
| 1364 | 1173.63 |  0.9  |  10 |   9   | -0.421841  |  46.8712 |
| 1368 | 1141.91 |  0.8  |  10 |   8   | -0.399161  |  49.8951 |
| 1372 | 1113.95 |  0.8  |  10 |   8   | -0.381017  |  47.6272 |
| 1376 | 1079.74 |  0.7  |  10 |   7   | -0.353802  |  50.5431 |
| 1380 | 1047.69 |  0.7  |  10 |   7   | -0.335658  |  47.9512 |
| 1384 | 1015.58 |  0.6  |  10 |   6   | -0.312978  |  52.1631 |
| 1388 |  985.54 |  0.5  |  10 |   5   | -0.294835  |  58.967  |
| 1392 |  948.45 |  0.5  |  10 |   5   | -0.276691  |  55.3382 |
| 1396 |  916.27 |  0.4  |  10 |   4   | -0.249476  |  62.3689 |
| 1400 |  882.74 |  0.4  |  10 |   4   | -0.235868  |  58.967  |
| 1404 |  845.2  |  0.4  |  10 |   4   | -0.213188  |  53.2971 |
| 1408 |  813.07 |  0.3  |  10 |   3   | -0.19958   |  66.5268 |
| 1412 |  773.62 |  0.22 |  10 |   2.2 | -0.181437  |  82.4713 |
| 1416 |  739.5  |  0.2  |  10 |   2   | -0.163293  |  81.6466 |
| 1420 |  700.67 |  0.2  |  10 |   2   | -0.154221  |  77.1106 |
| 1424 |  664.03 |  0.2  |  10 |   2   | -0.136078  |  68.0388 |
| 1428 |  624.21 |  0.2  |  10 |   2   | -0.117934  |  58.967  |
| 1432 |  584.37 |  0.1  |  10 |   1   | -0.0997902 |  99.7902 |
| 1436 |  544.9  |  0.1  |  10 |   1   | -0.0861825 |  86.1825 |
| 1440 |  504.09 |  0.1  |  10 |   1   | -0.0725747 |  72.5747 |
| 1444 |  462    |  0.05 |  10 |   0.5 | -0.0635029 | 127.006  |
| 1448 |  421.48 |  0.05 |  10 |   0.5 | -0.054431  | 108.862  |
| 1452 |  377.18 |  0.05 |  10 |   0.5 | -0.0453592 |  90.7184 |
| 1456 |  334.68 |  0.05 |  10 |   0.5 | -0.0317514 |  63.5029 |
| 1460 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1464 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1468 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1472 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1476 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1480 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1484 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1488 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1492 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1496 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1500 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1504 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1508 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1512 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1516 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1520 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1524 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1528 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1532 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1536 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1540 |    0    |  0    |  10 |   0   |  0         |   0      |
| 1544 |  332.34 |  0.05 |  10 |   0.5 |  0.0408233 |  81.6466 |
| 1548 |  373.31 |  0.05 |  10 |   0.5 |  0.054431  | 108.862  |
| 1552 |  417.31 |  0.05 |  10 |   0.5 |  0.0680388 | 136.078  |
| 1556 |  458.76 |  0.1  |  10 |   1   |  0.0771106 |  77.1106 |
| 1560 |  500.1  |  0.1  |  10 |   1   |  0.0907184 |  90.7184 |
| 1564 |  540.3  |  0.1  |  10 |   1   |  0.108862  | 108.862  |
| 1568 |  582.31 |  0.1  |  10 |   1   |  0.127006  | 127.006  |
| 1572 |  621    |  0.2  |  10 |   2   |  0.145149  |  72.5747 |
| 1576 |  657.13 |  0.2  |  10 |   2   |  0.163293  |  81.6466 |
| 1580 |  694.76 |  0.2  |  10 |   2   |  0.181437  |  90.7184 |
| 1584 |  732.6  |  0.2  |  10 |   2   |  0.204116  | 102.058  |
| 1588 |  766    |  0.3  |  10 |   3   |  0.22226   |  74.0867 |
| 1592 |  804.51 |  0.3  |  10 |   3   |  0.24494   |  81.6466 |
| 1596 |  835.96 |  0.4  |  10 |   4   |  0.263083  |  65.7708 |
| 1600 |  872.57 |  0.4  |  10 |   4   |  0.290299  |  72.5747 |
| 1604 |  905.53 |  0.47 |  10 |   4.7 |  0.312978  |  66.5912 |
| 1608 |  937.84 |  0.5  |  10 |   5   |  0.335658  |  67.1316 |
| 1612 |  974.06 |  0.5  |  10 |   5   |  0.362874  |  72.5747 |
| 1616 | 1006.56 |  0.6  |  10 |   6   |  0.385553  |  64.2589 |
| 1620 | 1035.16 |  0.7  |  10 |   7   |  0.412769  |  58.967  |
| 1624 | 1066.46 |  0.7  |  10 |   7   |  0.44452   |  63.5029 |
| 1628 | 1100.71 |  0.8  |  10 |   8   |  0.4672    |  58.4    |
| 1632 | 1128.87 |  0.83 |  10 |   8.3 |  0.494415  |  59.5681 |
| 1636 | 1159.42 |  0.94 |  10 |   9.4 |  0.521631  |  55.4926 |
| 1640 | 1187.81 |  1    |  10 |  10   |  0.548846  |  54.8846 |
| 1644 | 1219.22 |  1.1  |  10 |  11   |  0.580598  |  52.7816 |
| 1648 | 1250.46 |  1.2  |  10 |  12   |  0.607813  |  50.6511 |
| 1652 | 1278.23 |  1.3  |  10 |  13   |  0.639565  |  49.1973 |
| 1656 | 1303.26 |  1.4  |  10 |  14   |  0.684924  |  48.9231 |
| 1660 | 1330.15 |  1.5  |  10 |  15   |  0.703068  |  46.8712 |
| 1664 | 1362.78 |  1.5  |  10 |  15   |  0.725747  |  48.3831 |
| 1668 | 1391.56 |  1.6  |  10 |  16   |  0.762035  |  47.6272 |
| 1672 | 1417.83 |  1.8  |  10 |  18   |  0.798322  |  44.3512 |
| 1676 | 1445.47 |  1.9  |  10 |  19   |  0.825537  |  43.4493 |
| 1680 | 1473.43 |  2    |  10 |  20   |  0.852753  |  42.6376 |
| 1684 | 1495.93 |  2.1  |  10 |  21   |  0.88904   |  42.3353 |
| 1688 | 1518.95 |  2.2  |  10 |  22   |  0.920792  |  41.8542 |
| 1692 | 1541.94 |  2.3  |  10 |  23   |  0.948007  |  41.2177 |
| 1696 | 1570.74 |  2.43 |  10 |  24.3 |  0.975223  |  40.1326 |
| 1700 | 1596    |  2.7  |  10 |  27   |  0.970687  |  35.9514 |
| 1704 | 1621.63 |  2.8  |  10 |  28   |  1.0478    |  37.4213 |
| 1708 | 1650.43 |  2.9  |  10 |  29   |  1.07501   |  37.0694 |
| 1712 | 1673.75 |  3.1  |  10 |  31   |  1.1113    |  35.8484 |
| 1716 | 1695.56 |  3.3  |  10 |  33   |  1.16573   |  35.3252 |
| 1720 | 1720.07 |  3.4  |  10 |  34   |  1.18388   |  34.8199 |
| 1724 | 1747.39 |  3.5  |  10 |  35   |  1.20655   |  34.473  |
| 1728 | 1764.86 |  3.7  |  10 |  37   |  1.23831   |  33.4677 |
| 1732 | 1793.13 |  3.84 |  10 |  38.4 |  1.27459   |  33.1925 |
| 1736 | 1818.93 |  4    |  10 |  40   |  1.31088   |  32.772  |
| 1740 | 1833.08 |  4.2  |  10 |  42   |  1.35624   |  32.2914 |
| 1744 | 1860.28 |  4.4  |  10 |  44   |  1.41067   |  32.0607 |
| 1748 | 1889.11 |  4.5  |  10 |  45   |  1.42881   |  31.7514 |
| 1752 | 1910.68 |  4.7  |  10 |  47   |  1.47871   |  31.4619 |
| 1756 | 1933.17 |  4.9  |  10 |  49   |  1.52407   |  31.1035 |
| 1760 | 1961.66 |  5.1  |  10 |  51   |  1.54675   |  30.3284 |
| 1764 | 1983.53 |  5.3  |  10 |  53   |  1.5785    |  29.783  |
| 1768 | 2004.48 |  5.5  |  10 |  55   |  1.62386   |  29.5247 |
| 1772 | 2026.86 |  5.7  |  10 |  57   |  1.65561   |  29.0458 |
| 1776 | 2052.48 |  5.9  |  10 |  59   |  1.6919    |  28.6762 |
| 1780 | 2075.09 |  6.09 |  10 |  60.9 |  1.72819   |  28.3774 |
| 1784 | 2092.78 |  6.3  |  10 |  63   |  1.77354   |  28.1515 |
| 1788 | 2118.09 |  6.5  |  10 |  65   |  1.80076   |  27.704  |
| 1792 | 2139.65 |  6.73 |  10 |  67.3 |  1.84612   |  27.4312 |
| 1796 | 2160.17 |  6.9  |  10 |  69   |  1.87787   |  27.2155 |
| 1800 | 2178.68 |  7.13 |  10 |  71.3 |  1.91416   |  26.8465 |
| 1804 | 2199.9  |  7.4  |  10 |  74   |  1.99127   |  26.909  |
| 1808 | 2225.32 |  7.6  |  10 |  76   |  1.9958    |  26.2606 |
| 1812 | 2245.42 |  7.9  |  10 |  79   |  2.05931   |  26.0672 |
| 1816 | 2273.47 |  8.1  |  10 |  81   |  2.09106   |  25.8155 |
| 1820 | 2293.24 |  8.33 |  10 |  83.3 |  2.12281   |  25.4839 |
| 1824 | 2307.25 |  8.64 |  10 |  86.4 |  2.16817   |  25.0946 |
| 1828 | 2332.74 |  8.89 |  10 |  88.9 |  2.21353   |  24.8991 |
| 1832 | 2353    |  9.14 |  10 |  91.4 |  2.2725    |  24.8632 |
| 1836 | 2377.84 |  9.4  |  10 |  94   |  2.30425   |  24.5133 |
| 1840 | 2398    |  9.7  |  10 |  97   |  2.36321   |  24.363  |
| 1844 | 2410.17 | 10    |  10 | 100   |  2.40857   |  24.0857 |
| 1848 | 2435.89 | 10.2  |  10 | 102   |  2.45393   |  24.0582 |
| 1852 | 2453.29 | 10.5  |  10 | 105   |  2.48115   |  23.63   |
| 1856 | 2481    | 10.79 |  10 | 107.9 |  2.55372   |  23.6675 |
| 1860 | 2499.34 | 11.04 |  10 | 110.4 |  2.58094   |  23.3781 |
| 1864 | 2522.36 | 11.35 |  10 | 113.5 |  2.61723   |  23.0593 |
| 1868 | 2542.85 | 11.6  |  10 | 116   |  2.64898   |  22.836  |
| 1872 | 2558.17 | 11.9  |  10 | 119   |  2.68526   |  22.5652 |
| 1876 | 2574.59 | 12.28 |  10 | 122.8 |  2.73516   |  22.2733 |
| 1880 | 2601.92 | 12.44 |  10 | 124.4 |  2.77145   |  22.2785 |
| 1884 | 2612.65 | 12.8  |  10 | 128   |  2.82134   |  22.0417 |
| 1888 | 2632.98 | 13.13 |  10 | 131.3 |  2.87577   |  21.9023 |
| 1892 | 2657.24 | 13.4  |  10 | 134   |  2.89392   |  21.5964 |
| 1896 | 2664.79 | 13.62 |  10 | 136.2 |  2.9166    |  21.4141 |



label: E=D*C
labeled_formulas: E=D*C
output: {"Arithmetic-Relationship": ["E=D*C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_705650___xlsx_35750e3b17a55b3b82949caebf97ac6eb8f4ed6a.xlsx___line_200