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       |
|:-----------|-----------------:|-----------------:|---------:|-----------:|------------:|---------:|:--------|
| ANN1       |      1.43152e+06 | 148627           |  1580147 | 0.094059   | 1.05696e-07 | 0.466944 | Male    |
| ANN2       | 458291           |  47119           |   505410 | 0.0932293  | 3.2784e-07  | 0.504765 | Male    |
| ARD2       |      2.03287e+06 | 215559           |  2248431 | 0.0958709  | 7.55603e-08 | 0.48711  | Male    |
| ASH1       |      1.03226e+06 | 107663           |  1139924 | 0.0944475  | 1.47057e-07 | 0.472187 | Male    |
| ASH3       |      1.42389e+06 | 148629           |  1572521 | 0.0945164  | 1.06671e-07 | 0.484728 | Male    |
| AT1        |     30           |      1           |       31 | 0.0322581  | 0.00197375  | 0.546267 | Male?   |
| AT7        |     11           |      0           |       11 | 0          | 0           | 0.381503 | Male?   |
| BA342      |     99           |     10           |      109 | 0.0917431  | 0.00149834  | 0.735366 | Male?   |
| BA346      |     31           |      0           |       31 | 0          | 0           | 0.534078 | Male?   |
| BAL14      |     24           |      1           |       25 | 0.04       | 0.00301056  | 0.908812 | Female? |
| BAL3211    |    316           |     28           |      344 | 0.0813953  | 0.000426016 | 0.470497 | Male    |
| BAL329     |     32           |      4           |       36 | 0.111111   | 0.00537723  | 0.590216 | Male?   |
| BG72       |      1.53221e+06 | 156324           |  1688538 | 0.0925795  | 9.75144e-08 | 0.477186 | Male    |
| CAK16      |    264           |     14           |      278 | 0.0503597  | 0.000337174 | 0.663393 | Male?   |
| CAK375     |     25           |      2           |       27 | 0.0740741  | 0.00497892  | 0.598546 | Male?   |
| CAK530     |      2.41688e+06 |  14005           |  2430885 | 0.00576128 | 4.6185e-09  | 1.00497  | Female  |
| CAK531     |      1.09428e+06 | 111981           |  1206258 | 0.0928334  | 1.36838e-07 | 0.503982 | Male    |
| CAK532     |      2.29181e+06 | 233739           |  2525546 | 0.0925499  | 6.51778e-08 | 0.483846 | Male    |
| CAK533     |      3.81045e+06 |  22127           |  3832576 | 0.0057734  | 2.9355e-09  | 0.961289 | Female  |
| CAK534     |  54945           |   5171           |    60116 | 0.086017   | 2.56324e-06 | 0.501969 | Male    |
| CAK68      |      1.61588e+06 | 167546           |  1783423 | 0.0939463  | 9.35482e-08 | 0.480626 | Male    |
| CH448      |      1.66544e+06 | 173054           |  1838496 | 0.094128   | 9.09032e-08 | 0.473341 | Male    |
| GNM1007    |      1.1106e+06  | 109329           |  1219925 | 0.0896194  | 1.31084e-07 | 0.503133 | Male    |
| GNM1076    |      1.34721e+06 | 134057           |  1481263 | 0.0905018  | 1.08914e-07 | 0.507206 | Male    |
| GNM1141    |      7           |      1           |        8 | 0.125      | 0.0267969   | 1.03083  | Unknown |
| GNM1187    |    151           |     10           |      161 | 0.0621118  | 0.000709178 | 0.745357 | Male?   |
| GNM1217    |   1363           |    108           |     1471 | 0.0734194  | 9.06437e-05 | 0.649722 | Male?   |
| JP14       |      2.01764e+07 |      2.01782e+06 | 22194262 | 0.0909165  | 7.29898e-09 | 0.492038 | Male    |
| KGH6       |      1.29132e+06 | 131954           |  1423269 | 0.0927119  | 1.15838e-07 | 0.487972 | Male    |
| MB101      |    110           |     10           |      120 | 0.0833333  | 0.00124769  | 0.532166 | Male?   |
| MB4        |      7           |      0           |        7 | 0          | 0           | 0.521624 | Male?   |
| MB6        |      1.35799e+06 | 138390           |  1496376 | 0.0924834  | 1.09934e-07 | 0.475835 | Male    |
| MB9889     |     49           |      1           |       50 | 0.02       | 0.00076832  | 0.643447 | Male?   |
| MP18       |      8           |      2           |       10 | 0.2        | 0.03136     | 0.307328 | Male?   |
| NG10       |      2.33539e+07 |      2.35036e+06 | 25704275 | 0.0914387  | 6.33483e-09 | 0.496647 | Male    |
| NGZ1       |      1.48817e+06 |  11630           |  1499797 | 0.00775438 | 1.00552e-08 | 0.950745 | Female  |
| NGZ2       |    156           |     10           |      166 | 0.060241   | 0.000668431 | 0.576493 | Male?   |
| NM61       |     71           |      8           |       79 | 0.101266   | 0.002258    | 0.498448 | Male?   |
| PB1327     | 920851           |  93185           |  1014036 | 0.0918952  | 1.61299e-07 | 0.492875 | Male    |
| PB1794     |      1.34018e+06 |   8264           |  1348444 | 0.00612855 | 8.85341e-09 | 0.990557 | Female  |
| PB186      |      2.04622e+06 | 207945           |  2254161 | 0.0922494  | 7.28117e-08 | 0.4974   | Male    |
| PB2031     |      1.47495e+06 | 145378           |  1620324 | 0.0897216  | 9.87928e-08 | 0.494865 | Male    |
| PB357      |      5.33395e+06 |  28727           |  5362679 | 0.00535684 | 1.94738e-09 | 1.01383  | Female  |
| PB443      |      2.53126e+06 | 259643           |  2790908 | 0.0930317  | 5.92562e-08 | 0.488017 | Male    |
| PB581      |      2.00933e+06 | 205553           |  2214886 | 0.0928052  | 7.45037e-08 | 0.487891 | Male    |
| PB672      |      2.5858e+06  | 262045           |  2847846 | 0.0920152  | 5.75013e-08 | 0.503649 | Male    |
| PB675      |      2.06506e+07 |      2.05666e+06 | 22707280 | 0.0905725  | 7.10977e-09 | 0.491813 | Male    |
| PB754      |      1.25232e+06 |   8177           |  1260500 | 0.00648711 | 1.00216e-08 | 1.0024   | Female  |
| PB768      |      1.27002e+06 | 128606           |  1398622 | 0.0919519  | 1.17011e-07 | 0.481282 | Male    |
| PN02       |      1.37747e+06 | 140660           |  1518130 | 0.0926535  | 1.08538e-07 | 0.488818 | Male    |
| PN03       |      1.32961e+06 | 137395           |  1467003 | 0.0936569  | 1.13412e-07 | 0.484344 | Male    |
| PN04       |      1.36995e+06 | 142457           |  1512409 | 0.0941921  | 1.1057e-07  | 0.494088 | Male    |
| PN05       |      1.22734e+06 | 124680           |  1352023 | 0.0922174  | 1.21357e-07 | 0.495373 | Male    |
| PN06       |      1.27328e+06 | 130727           |  1404002 | 0.0931103  | 1.1788e-07  | 0.485812 | Male    |
| PN07       |      1.2708e+06  | 135002           |  1405807 | 0.0960317  | 1.21031e-07 | 0.471663 | Male    |
| PN10_PN113 |      4.95446e+06 |  30536           |  4984996 | 0.00612558 | 2.3937e-09  | 0.982524 | Female  |
| PN107      |      1.67578e+06 | 172691           |  1848468 | 0.0934239  | 8.98062e-08 | 0.51     | Male    |
| PN112      |      1.05685e+06 | 107903           |  1164757 | 0.0926399  | 1.41449e-07 | 0.499246 | Male    |
| PN12       |      1.03756e+06 | 103281           |  1140841 | 0.0905306  | 1.41454e-07 | 0.492727 | Male    |
| PN13       | 946685           |  95968           |  1042653 | 0.0920421  | 1.57097e-07 | 0.503289 | Male    |
| PN16       |      1.1981e+06  |   7523           |  1205618 | 0.00623995 | 1.00811e-08 | 0.979544 | Female  |
| PN19       |     72           |      6           |       78 | 0.0769231  | 0.00178425  | 0.484215 | Male?   |
| PN20       |     39           |      0           |       39 | 0          | 0           | 1.02065  | Female? |
| SI118      |    105           |     14           |      119 | 0.117647   | 0.00170975  | 0.764324 | Male?   |
| SRA62      |      1.38362e+07 |      1.43394e+06 | 15270179 | 0.0939043  | 1.09212e-08 | 0.500291 | Male    |



label: D=B+C
E=C/D
labeled_formulas: D=B+C
E=C/D
output: {"Arithmetic-Relationship": ["D=B+C", "E=C/D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_179825___xlsx_0814ed7d9e940524bed0f1628edd96e61fcff03c.xlsx___line_23