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:
| K                          |     L |                M |        N |
|:---------------------------|------:|-----------------:|---------:|
| Albury                     | 10788 | 131292           | 12.1702  |
| Armidale-Dumaresq          |  9421 | 325820           | 34.5844  |
| Ashfield                   |  7712 | 187463           | 24.308   |
| Auburn                     | 19842 | 359246           | 18.1053  |
| Balranald                  |   387 |   8506.68        | 21.9811  |
| Bankstown                  | 27156 | 707352           | 26.0477  |
| Bathurst                   | 11088 | 231704           | 20.8968  |
| Bega Valley                |  6952 |  98585.1         | 14.1808  |
| Berrigan                   |  2495 |  57078.2         | 22.877   |
| Blacktown                  | 48454 | 990573           | 20.4436  |
| Bland                      |  3138 |  47948           | 15.2798  |
| Blue Mountains             | 18489 | 310082           | 16.7712  |
| Botany Bay                 |  8485 | 227910           | 26.8604  |
| Bourke                     |  3237 |  44297.4         | 13.6847  |
| Broken Hill                |  3947 |  49573           | 12.5597  |
| Burwood                    | 10966 | 172863           | 15.7636  |
| Camden                     |  7779 | 188789           | 24.2691  |
| Campbelltown               | 18236 | 550022           | 30.1614  |
| Canada Bay                 | 12441 | 406483           | 32.6728  |
| Canterbury                 | 25373 | 504520           | 19.8841  |
| Central Murray             |  3682 |  42519.8         | 11.548   |
| Central Northern           | 33542 | 438021           | 13.0589  |
| Central West               |  8840 | 300265           | 33.9666  |
| Cessnock                   | 11263 | 221821           | 19.6946  |
| Clarence                   | 16515 | 302420           | 18.3119  |
| Cobar                      |  2756 |  26416           |  9.58491 |
| Coffs Harbour              | 11141 | 211131           | 18.9508  |
| Eurobodalla                |  8637 | 180579           | 20.9076  |
| Fairfield                  | 33366 | 756420           | 22.6704  |
| Glen Innes Severn          |  2474 |  70056.3         | 28.317   |
| Gosford                    | 34213 | 645325           | 18.862   |
| Goulburn Mulwaree          |  4710 | 136157           | 28.9081  |
| Great Lakes                |  8002 | 200998           | 25.1185  |
| Greater Taree              | 11674 | 240658           | 20.6149  |
| Grenfell                   |  1123 |  20324           | 18.098   |
| Gunnedah                   |  2091 |  41033.4         | 19.6238  |
| Guyra                      |  1397 |  47454.2         | 33.9687  |
| Hawkesbury                 | 13892 | 268568           | 19.3326  |
| Hills, The                 | 24258 | 594473           | 24.5063  |
| Holroyd                    | 10161 | 451178           | 44.4029  |
| Hornsby                    | 44756 | 654232           | 14.6178  |
| Hurstville                 | 16851 | 366693           | 21.7609  |
| Inverell                   |  4499 |  90855.8         | 20.1947  |
| Kempsey                    |  6125 | 117701           | 19.2165  |
| Kiama                      |  3325 | 105447           | 31.7134  |
| Kogarah                    | 13934 | 272777           | 19.5763  |
| Ku-Ring-Gai                | 24570 | 661705           | 26.9314  |
| Lachlan                    |  1797 |  28808.8         | 16.0316  |
| Lake Macquarie             | 45278 | 751998           | 16.6085  |
| Lane Cove                  | 20675 | 316563           | 15.3114  |
| Leeton                     |  4428 |  58180.9         | 13.1393  |
| Leichhardt                 | 27877 | 380128           | 13.6359  |
| Lithgow                    |  6350 |  99900.1         | 15.7323  |
| Liverpool                  | 37783 | 983284           | 26.0245  |
| Macquarie                  | 13663 | 285469           | 20.8935  |
| Maitland                   | 18245 | 279364           | 15.3118  |
| Manly                      | 11708 | 304483           | 26.0064  |
| Marrickville               | 13894 | 332987           | 23.9662  |
| Mid-Western                |  5640 | 139376           | 24.7121  |
| Monaro                     |  5378 | 115226           | 21.4255  |
| Mosman                     |  8573 | 304516           | 35.5204  |
| Nambucca                   |  2605 |  67433.1         | 25.886   |
| Newcastle                  | 79923 |      1.38576e+06 | 17.3387  |
| North Sydney               | 18177 | 376509           | 20.7135  |
| North West Slopes & Plains |  6650 | 133707           | 20.1063  |
| North Western              |  6132 | 144191           | 23.5145  |
| Oberon                     |  1139 |  26545           | 23.3055  |
| Parkes                     |  4259 |  80880           | 18.9904  |
| Parramatta                 | 43507 | 965739           | 22.1973  |
| Penrith                    | 36464 | 985092           | 27.0155  |
| Pittwater                  | 13320 | 291522           | 21.886   |
| Port Macquarie-Hastings    | 16946 | 284901           | 16.8123  |
| Queanbeyan                 | 10531 | 336632           | 31.9658  |
| Randwick                   | 21487 | 458378           | 21.3328  |
| Richmond-Tweed             | 54017 | 702664           | 13.0082  |
| Richmond-Upper Clarence    |  5910 |  93926.5         | 15.8928  |
| Riverina                   | 26268 | 512929           | 19.5268  |
| Rockdale                   | 22187 | 466028           | 21.0046  |
| Ryde                       | 23010 | 576720           | 25.0639  |
| Shellharbour               | 15560 | 274129           | 17.6176  |
| Shoalhaven                 | 14848 | 388478           | 26.1637  |
| Singleton                  |  6283 |  82870           | 13.1896  |
| South West                 |  3151 |  55817.2         | 17.7141  |
| Strathfield                |  6866 | 102362           | 14.9085  |
| Sutherland                 | 39691 |      1.14102e+06 | 28.7477  |
| Sydney                     | 47929 |      1.28035e+06 | 26.7135  |
| Tenterfield                |  2302 |  29319.2         | 12.7364  |
| Upper Hunter Network       | 10713 | 120318           | 11.231   |
| Upper Lachlan              |  2354 |  33557.1         | 14.2554  |
| Upper Murray               | 10706 | 151083           | 14.112   |
| Wakool                     |  1353 |  18884.5         | 13.9575  |
| Warringah                  | 32211 | 501101           | 15.5568  |
| Waverley                   | 10287 | 381784           | 37.1133  |
| Wentworth                  |  2795 |  49477.3         | 17.7021  |
| Western Riverina           | 13467 | 204771           | 15.2054  |
| Willoughby                 | 31453 | 429558           | 13.6571  |
| Wingecarribee              |  8431 | 123992           | 14.7067  |
| Wollondilly                |  3684 |  90316.6         | 24.5159  |
| Wollongong                 | 48003 |      1.24142e+06 | 25.8614  |
| Woollahra                  | 17134 | 509373           | 29.7288  |
| Wyong                      | 24465 | 514331           | 21.0232  |
| Yass Valley                |  2952 |  69306.4         | 23.4778  |



label: N=M/L
labeled_formulas: N=M/L
output: {"Arithmetic-Relationship": ["N=M/L"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_194022___xlsx_b401c25a1ac559c1553bc0c17f1792dcadbd498d.xlsx___line_470