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 |      H |      I |         J |         K |
|:------------------|-------:|-------:|----------:|-------:|-------:|----------:|-------:|-------:|----------:|----------:|
| yw                |  427.2 | 1605.5 | 0.266085  |  686.9 | 1577.3 | 0.435491  | 2345   | 1206.4 | 1.9438    | 0.881792  |
| yw                |  428.4 |  579.4 | 0.739386  |  415.6 |  644.2 | 0.645141  |  511.1 |  427.2 | 1.1964    | 0.860307  |
| yw                |  417.9 |  534.6 | 0.781706  |  383.1 |  738.3 | 0.518895  |  254.8 |  558.4 | 0.456304  | 0.585635  |
| yw                |  257.9 |  900.3 | 0.28646   |  251.8 |  167   | 1.50778   |  175.2 |  983.2 | 0.178194  | 0.657479  |
| yw                |  448.7 |  657.9 | 0.682019  |  480.3 |  938.4 | 0.511829  |  345   |  869.7 | 0.396689  | 0.530179  |
| yw                | 1465.8 | 2343   | 0.625608  | 2237   | 1581   | 1.41493   |  340.1 | 1581.4 | 0.215063  | 0.751866  |
| yw                |  257.1 |  237.4 | 1.08298   |  220.3 |  174.3 | 1.26391   |  177   |  161.6 | 1.0953    | 1.1474    |
| yw                |  398   |  497   | 0.800805  |  785   |  647.6 | 1.21217   |  440   |  582.9 | 0.754846  | 0.922606  |
| yw                | 3895   | 2988   | 1.30355   | 1578.7 | 1782.1 | 0.885865  | 1808.9 | 1870   | 0.967326  | 1.05225   |
| yw                |  565.4 | 1138.9 | 0.496444  |  506.4 |  705.5 | 0.717789  |  532   |  770.4 | 0.69055   | 0.634928  |
| yw                |  343.5 | 1754.6 | 0.195771  |  346   | 1547.6 | 0.223572  |  484.4 | 1878.2 | 0.257907  | 0.22575   |
| yw                |  882.9 | 1757.7 | 0.502304  |  478   | 1099   | 0.434941  |  515.1 | 1002.5 | 0.513815  | 0.483687  |
| yw                |  668.6 | 1869.4 | 0.357655  |  990.9 | 1853.9 | 0.534495  |  546.9 | 1317   | 0.415262  | 0.435804  |
| yw                |  401.7 | 3372.2 | 0.119121  |  235.3 | 1998.5 | 0.117738  |  217.9 | 2245.7 | 0.0970299 | 0.111296  |
| fascin-/-         | 1174   |  419.4 | 2.79924   | 1018.4 |  467.6 | 2.17793   |  994   |  507   | 1.96055   | 2.31257   |
| fascin-/-         |  842.8 |  736.8 | 1.14387   |  609   |  443.6 | 1.37286   |  939.6 |  723.4 | 1.29887   | 1.27186   |
| fascin-/-         | 1355   | 1076   | 1.25929   | 1512.9 | 1359.4 | 1.11292   | 1737.8 |  927.6 | 1.87344   | 1.41522   |
| fascin-/-         | 1868.9 |  780.5 | 2.39449   | 1220.5 |  560.2 | 2.17869   | 2553   |  703.5 | 3.629     | 2.73406   |
| fascin-/-         |  871.1 |   89.1 | 9.77666   |   67.6 |  127   | 0.532283  |  768.7 |   98.4 | 7.81199   | 6.04031   |
| fascin-/-         |  407.9 |  198.3 | 2.05698   | 1154.7 |  280.3 | 4.11951   | 1767.5 |  471.2 | 3.75106   | 3.30919   |
| fascin-/-         |  579.5 |  200.4 | 2.89172   |  588.2 |  305.7 | 1.92411   | 1098.1 |  222.6 | 4.93306   | 3.24963   |
| fascin-/-         |  253.7 | 1075   | 0.236     | 1154.4 | 1521.6 | 0.758675  |  106   | 1132   | 0.0936396 | 0.362772  |
| fascin-/-  y27632 |  535   |  937   | 0.570971  |  559.6 | 1575.7 | 0.355144  |  720.6 | 1759.2 | 0.409618  | 0.445244  |
| fascin-/-  y27633 |  482.3 | 1341.6 | 0.359496  |  734.4 | 1285.8 | 0.571162  |  523.2 | 1621.7 | 0.322624  | 0.417761  |
| fascin-/-  y27634 |  458.3 | 1184.3 | 0.38698   |  362.8 |  962.6 | 0.376896  |  469.2 | 1299.2 | 0.361145  | 0.375007  |
| fascin-/-  y27635 | 1275   | 2032.7 | 0.627245  | 1297   |  736   | 1.76223   | 1243   |  479   | 2.59499   | 1.66149   |
| fascin-/-  y27636 |  874   | 1813.5 | 0.481941  | 1256.4 | 2051.5 | 0.61243   | 1325.1 | 1493.8 | 0.887067  | 0.660479  |
| fascin-/-  y27637 |  347.3 | 1950.9 | 0.17802   |  362   | 1665.9 | 0.2173    |  460.9 | 1723.6 | 0.267405  | 0.220909  |
| fascin-/-  y27638 |  591.8 |  882.5 | 0.670595  |  373.3 |  977   | 0.382088  |  251.2 |  621.4 | 0.404248  | 0.485644  |
| fascin-/-  y27639 |  692.7 | 1808.6 | 0.383003  |  575.3 |  724.1 | 0.794504  |  519.3 | 1240.9 | 0.418487  | 0.531998  |
| fascin-/-  y27640 | 1038   | 1942   | 0.534501  |  864.3 | 1513.2 | 0.571174  |  590.6 | 1361.5 | 0.433786  | 0.513153  |
| fascin-/-  y27641 |  220   | 1799.8 | 0.122236  |  206.5 | 1034.1 | 0.199691  |  274.4 | 1417.7 | 0.193553  | 0.171826  |
| fascin-/-  y27642 |  197.6 | 1466.3 | 0.134761  |  332.7 | 1735   | 0.191758  |  249.5 | 1422.1 | 0.175445  | 0.167321  |
| fascin-/-  y27643 |  225   | 1241.9 | 0.181174  |  139.8 | 1976   | 0.070749  |  194.3 | 1275.8 | 0.152297  | 0.13474   |
| fascin-/-  y27644 |  182   | 1779.8 | 0.102259  |  157   | 2470   | 0.0635628 |  196   | 2574   | 0.0761461 | 0.0806558 |
| fascin-/-  y27645 |  576.5 |  743.5 | 0.775387  |  502.4 |  694.9 | 0.722982  |  976.1 | 1950.4 | 0.500461  | 0.666277  |
| fascin-/-  y27646 |  851.6 | 3539.8 | 0.240579  |  884.6 | 3302   | 0.267898  |  688.5 | 2815   | 0.244583  | 0.25102   |
| fascin-/-  y27647 |  246   | 2188.4 | 0.112411  |  224.8 | 2033   | 0.110576  |  254.6 | 1610.7 | 0.158068  | 0.127018  |
| fascin-/-  y27648 |  384.3 | 2342.3 | 0.16407   |  270.8 | 3760   | 0.0720213 |  433.3 | 3163.9 | 0.136951  | 0.124347  |
| fascin-/-  y27649 |  159.6 | 2186   | 0.0730101 |  310.1 | 2221.6 | 0.139584  |  280   | 1722   | 0.162602  | 0.125065  |
| fascin-/-  y27650 |  200.4 | 1140.9 | 0.175651  |  154.8 | 1181.3 | 0.131042  |  194.5 |  905.7 | 0.214751  | 0.173815  |
| fascin-/-  y27651 |  345   |  812   | 0.424877  |  319   |  748.9 | 0.425958  |  265.9 |  776.6 | 0.34239   | 0.397742  |
| fascin-/-  y27652 |  130.3 | 1303.1 | 0.0999923 |  183   | 1790   | 0.102235  |  181.2 | 1572.5 | 0.115231  | 0.105819  |
| fascin-/-  y27653 |  197.9 |  865.4 | 0.22868   |  222.1 | 1165.1 | 0.190627  |  214.4 |  921.7 | 0.232614  | 0.217307  |
| fascin-/-  y27654 |  171.2 | 1053.6 | 0.162491  |  229.5 | 1097.1 | 0.209188  |  192.6 |  914.4 | 0.21063   | 0.194103  |
| fascin-/- bleb    | 1328.4 | 1251.8 | 1.06119   | 1301.7 | 1397.9 | 0.931182  | 1326.1 | 1224.5 | 1.08297   | 1.02512   |
| fascin-/- bleb    |  634.9 |  547.5 | 1.15963   |  618.2 |  525.7 | 1.17596   |  448   |  363.3 | 1.23314   | 1.18958   |
| fascin-/- bleb    | 1255.9 | 2534.1 | 0.4956    | 1310.6 | 1974.4 | 0.663797  | 1424.6 | 2068.1 | 0.688845  | 0.61608   |
| fascin-/- bleb    | 1956.1 | 1950.1 | 1.00308   | 1424   | 1756   | 0.810934  | 1096   | 1496.4 | 0.732424  | 0.848812  |
| fascin-/- bleb    |  668   | 3634.6 | 0.183789  |  617   | 3486   | 0.176994  |  597.6 | 3626.4 | 0.164792  | 0.175191  |
| fascin-/- bleb    |  450.3 | 1920.4 | 0.234482  |  425.1 | 2041.3 | 0.20825   |  858.8 | 1875.9 | 0.457807  | 0.30018   |
| fascin-/- bleb    |  246.8 |  791.5 | 0.311813  |  418.1 |  813.1 | 0.514205  |  392.5 |  773.8 | 0.507237  | 0.444418  |
| fascin-/- bleb    |  607.8 | 1506.3 | 0.403505  |  682   | 2138   | 0.31899   |  548.3 | 1646.3 | 0.33305   | 0.351848  |
| fascin-/- bleb    | 1233.1 | 1439.9 | 0.856379  |  659   |  944   | 0.698093  |  520.3 | 1855   | 0.280485  | 0.611652  |
| fascin-/- bleb    |  447.3 | 3681.2 | 0.121509  |  422   | 3938   | 0.107161  |  537   | 3910   | 0.13734   | 0.122003  |
| fascin-/- bleb    |  292.2 | 3220.8 | 0.0907228 |  432.7 |  839.1 | 0.515672  |  231.7 |  922.2 | 0.251247  | 0.28588   |
| fascin-/- bleb    |  318.9 | 2443.1 | 0.130531  |  386.4 | 3004   | 0.128628  |  442   | 4095   | 0.107937  | 0.122365  |
| fascin-/- bleb    |  348   | 2147.8 | 0.162026  |  302   | 1151.4 | 0.262289  |  344.8 | 2945.2 | 0.117072  | 0.180462  |
| fascin-/- bleb    |  299   | 1838.9 | 0.162597  |  369.4 | 1566.6 | 0.235797  |  309.2 | 1460.1 | 0.211766  | 0.203387  |
| fascin-/- bleb    |  487   | 1919.2 | 0.253752  |  535.1 | 1454.6 | 0.367867  |  341.6 | 1558.7 | 0.219157  | 0.280259  |
| fascin-/- bleb    | 1268.8 |  430.8 | 2.94522   | 1174.7 | 1052.8 | 1.11579   |  612   |  501   | 1.22156   | 1.76085   |
| fascin-/- bleb    |  403.3 |  452   | 0.892257  |  430.8 |  606   | 0.710891  |  388.1 |  660.4 | 0.587674  | 0.730274  |



label: D=B/C
G=E/F
J=H/I
labeled_formulas: D=B/C
G=E/F
J=H/I
output: {"Arithmetic-Relationship": ["D=B/C", "G=E/F", "J=H/I"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_185571___xlsx_342d128ecfd851d91f821bf0813fd58cf42e1198.xlsx___line_219