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 |       L |        M |
|:-----------------|:---------------------------|---------:|---------:|---------:|----------------:|-----------------:|-----------------:|--------:|--------:|--------:|--------:|---------:|
| Arlington        | West Merrimack / Middlesex |  514.69  |  508.568 |  495.772 | 170167          | 170734           | 170211           | 330.62  | 335.716 | 343.325 |  42.754 | 0.92815  |
| Athol            | Central Massachusetts      |   88.22  |   90.075 |   87.23  |  27278.4        |  29074.9         |  26959.3         | 309.209 | 322.785 | 309.06  |   7.425 | 1.07768  |
| Attleboro        | Norwood / Attleboro        |  639.668 |  621.284 |  604.936 | 205689          | 205153           | 213061           | 321.556 | 330.208 | 352.204 |  51.204 | 0.966159 |
| Ayer             | West Merrimack / Middlesex |  339.852 |  328.208 |  322.153 | 107185          | 108027           | 111634           | 315.386 | 329.143 | 346.525 |  27.557 | 0.992662 |
| Beverly          | Lower North Shore          |  719.234 |  703.931 |  683.126 | 250319          | 248155           | 245412           | 348.035 | 352.527 | 359.248 |  59.447 | 0.983002 |
| Boston           | Metro Boston               | 3625.94  | 3592.76  | 3552.29  |      1.1946e+06 |      1.23157e+06 |      1.23732e+06 | 329.458 | 342.792 | 348.316 | 301.805 | 0.972277 |
| Brockton         | Metro South                | 1356.23  | 1318.38  | 1273.6   | 457877          | 456988           | 453744           | 337.609 | 346.628 | 356.268 | 108.222 | 1.06464  |
| Burlington       | West Merrimack / Middlesex |  147.885 |  143.63  |  140.629 |  51734.5        |  54924.7         |  52526.6         | 349.829 | 382.404 | 373.512 |  12.107 | 1.03575  |
| Cambridge        | Metro Boston               |  978.485 |  978.542 |  983.268 | 279773          | 285187           | 288714           | 285.925 | 291.441 | 293.627 |  82.661 | 0.807369 |
| Clinton          | Central Massachusetts      |   94.833 |   91.953 |   90.637 |  28598.5        |  28170.1         |  29921.3         | 301.567 | 306.354 | 330.122 |   7.713 | 1.0058   |
| Concord          | West Merrimack / Middlesex |  687.13  |  675.098 |  655.197 | 215400          | 225393           | 225083           | 313.477 | 333.866 | 343.534 |  56.199 | 0.92117  |
| Everett          | Metro Boston               |  144.957 |  142.912 |  140.266 |  48686.7        |  48026.5         |  52544.1         | 335.87  | 336.056 | 374.603 |  11.915 | 1.03222  |
| Fall River       | Fall River                 |  514.95  |  473.557 |  470.69  | 167714          | 162099           | 161350           | 325.689 | 342.3   | 342.796 |  39.793 | 1.07621  |
| Falmouth         | Cape and Islands           |  429.054 |  405.854 |  368.745 | 161892          | 160323           | 149884           | 377.323 | 395.027 | 406.471 |  31.267 | 1.07532  |
| Fitchburg        | Central Massachusetts      |  201.682 |  197.022 |  192.284 |  59701.6        |  59885.8         |  59853.9         | 296.018 | 303.955 | 311.279 |  16.374 | 0.967438 |
| Gardner          | Central Massachusetts      |  239.473 |  233.935 |  228.426 |  70684.6        |  73167.8         |  70581.1         | 295.167 | 312.77  | 308.989 |  19.403 | 0.985773 |
| Gloucester       | Lower North Shore          |  179.936 |  174.334 |  166.37  |  64870.8        |  65327.3         |  64466.3         | 360.521 | 374.725 | 387.488 |  14.201 | 1.07029  |
| Great Barrington | Berkshires                 |   46.067 |   45.345 |   41.938 |  18038.2        |  17804.8         |  17451.8         | 391.564 | 392.652 | 416.134 |   3.529 | 1.07967  |
| Greenfield       | Pioneer Valley / Franklin  |  178.484 |  171.722 |  161.352 |  51048.2        |  50477           |  44750           | 286.01  | 293.946 | 277.344 |  13.62  | 0.942201 |
| Haverhill        | East Merrimack             |  362.561 |  351.946 |  343.498 | 127073          | 124042           | 125436           | 350.488 | 352.447 | 365.172 |  29.392 | 1.04873  |
| Holyoke          | Pioneer Valley / Franklin  |  125.12  |  118.302 |  110.209 |  36550.2        |  34101.1         |  34823.1         | 292.121 | 288.255 | 315.973 |   9.364 | 1.03649  |
| Hyannis          | Cape and Islands           |  576.576 |  545.809 |  489.862 | 232198          | 230496           | 210555           | 402.719 | 422.302 | 429.825 |  41.502 | 1.17765  |
| Lawrence         | East Merrimack             |  543.277 |  522.339 |  517.769 | 171922          | 168337           | 163895           | 316.453 | 322.276 | 316.541 |  44.097 | 0.930054 |
| Leominster       | Central Massachusetts      |  165.402 |  163.41  |  160.86  |  50868.4        |  50821.5         |  50428           | 307.544 | 311.006 | 313.49  |  13.728 | 0.981971 |
| Lowell           | West Merrimack / Middlesex | 1382.71  | 1359.16  | 1313.82  | 444794          | 437404           | 438224           | 321.683 | 321.82  | 333.549 | 115.949 | 1.00658  |
| Ludlow           | Pioneer Valley / Franklin  |   57.921 |   56.391 |   53.105 |  15566.1        |  17840.4         |  16117.5         | 268.748 | 316.37  | 303.502 |   4.461 | 1.00895  |
| Lynn             | Lower North Shore          |  408.404 |  400.31  |  390.52  | 140883          | 151163           | 145241           | 344.961 | 377.616 | 371.916 |  33.36  | 1.04338  |
| Malden           | Metro Boston               |  250.923 |  243.394 |  235.448 |  85410.4        |  82585.5         |  82205.7         | 340.385 | 339.308 | 349.146 |  19.948 | 0.99179  |
| Marlborough      | Metro West                 |  310.197 |  301.266 |  290.184 |  99758.3        |  99936.3         | 101403           | 321.597 | 331.721 | 349.443 |  24.811 | 1.0159   |
| Medford          | Metro Boston               |  292.231 |  285.967 |  279.248 |  99652.3        | 103640           | 105891           | 341.005 | 362.419 | 379.2   |  23.805 | 1.07494  |
| Melrose          | Metro Boston               |  475.256 |  467.512 |  452.107 | 166237          | 173683           | 170459           | 349.785 | 371.504 | 377.033 |  38.573 | 1.05958  |
| Methuen          | East Merrimack             |  226.021 |  215.138 |  212.352 |  77302.9        |  73741.5         |  79155.4         | 342.016 | 342.764 | 372.756 |  18.076 | 1.05788  |
| Milton           | Metro Boston               |  190.846 |  187.684 |  183.202 |  64374.9        |  61433.2         |  65966.2         | 337.313 | 327.322 | 360.074 |  15.484 | 1.0124   |
| Nantucket        | Cape and Islands           |   62.738 |   60.386 |   58.921 |  26500.7        |  22694.3         |  26697.9         | 422.402 | 375.821 | 453.113 |   4.923 | 0.910237 |
| Natick           | Metro West                 | 1438.7   | 1405.93  | 1368.29  | 483117          | 506693           | 492235           | 335.8   | 360.398 | 359.744 | 116.282 | 1.00273  |
| Needham          | Metro Boston               |  217.191 |  213.66  |  209.897 |  72619.2        |  74911.5         |  79558.5         | 334.356 | 350.611 | 379.036 |  17.788 | 0.955181 |
| New Bedford      | New Bedford                |  629.49  |  561.679 |  549.697 | 207025          | 188408           | 188494           | 328.878 | 335.438 | 342.906 |  46.937 | 1.04566  |
| Newburyport      | Upper North Shore          |  365.445 |  353.908 |  342.442 | 125556          | 125310           | 128223           | 343.57  | 354.076 | 374.436 |  29.093 | 1.05431  |
| Newton           | Metro Boston               |  604.11  |  597.851 |  588.905 | 203798          | 207110           | 207307           | 337.352 | 346.425 | 352.021 |  49.531 | 0.929179 |
| Norfolk          | Norwood / Attleboro        |  333.249 |  322.597 |  314.652 | 103684          | 102564           | 104595           | 311.13  | 317.932 | 332.413 |  26.662 | 0.944951 |
| North Adams      | Berkshires                 |  118.818 |  116.185 |  111.595 |  41334.3        |  40148.9         |  40765.1         | 347.879 | 345.56  | 365.295 |   9.189 | 1.07688  |
| Northampton      | Pioneer Valley / Franklin  |  252.11  |  244.309 |  236.097 |  79243.4        |  75310.3         |  76449.3         | 314.321 | 308.258 | 323.805 |  19.944 | 1.01023  |
| Norwood          | Norwood / Attleboro        |  801.985 |  784.378 |  767.189 | 269247          | 275203           | 274518           | 335.725 | 350.855 | 357.823 |  64.982 | 1.01123  |
| Oak Bluffs       | Cape and Islands           |   90.667 |   86.969 |   82.344 |  41664.4        |  44572.4         |  41593.4         | 459.532 | 512.509 | 505.118 |   6.992 | 1.04926  |
| Palmer           | Pioneer Valley / Franklin  |   60.509 |   57.853 |   49.68  |  20113.5        |  20367.5         |  16823.1         | 332.405 | 352.056 | 338.629 |   4.571 | 1.02374  |
| Pittsfield       | Berkshires                 |  239.962 |  232.025 |  217.318 |  83267.3        |  84492.1         |  81833.3         | 347.002 | 364.151 | 376.56  |  18.4   | 1.02117  |
| Plymouth         | South Shore                |  581.653 |  565.459 |  549.824 | 198398          | 195068           | 198141           | 341.094 | 344.972 | 360.372 |  46.436 | 1.06276  |
| Providence       | Norwood / Attleboro        |   86.861 |   83.286 |   83.267 |  26547.2        |  25856.3         |  27169.4         | 305.629 | 310.452 | 326.292 |   7.033 | 0.963788 |
| Quincy           | South Shore                |  352.332 |  340.724 |  338.892 | 117479          | 117899           | 122242           | 333.432 | 346.026 | 360.709 |  28.818 | 1.08252  |
| Salem            | Lower North Shore          |  656.04  |  636.365 |  609.991 | 239157          | 241599           | 235275           | 364.547 | 379.654 | 385.703 |  54.155 | 1.01371  |
| Somerville       | Metro Boston               |  358.766 |  355.424 |  349.318 |  96648.9        | 102764           | 106944           | 269.393 | 289.131 | 306.152 |  29.707 | 0.885241 |
| South Weymouth   | South Shore                | 1464.05  | 1422.26  | 1391.48  | 482874          | 481600           | 483547           | 329.821 | 338.616 | 347.506 | 117.828 | 1.04278  |
| Southbridge      | Central Massachusetts      |  188.105 |  178.985 |  173.356 |  58071.3        |  58573.5         |  55539.7         | 308.717 | 327.254 | 320.379 |  14.851 | 0.958937 |
| Springfield      | Pioneer Valley / Franklin  |  493.67  |  469.164 |  434.361 | 139422          | 131979           | 132474           | 282.419 | 281.306 | 304.987 |  36.844 | 1.0131   |
| Stoneham         | West Merrimack / Middlesex |  131.848 |  129.287 |  125.14  |  50861.7        |  49146.7         |  49470.3         | 385.76  | 380.136 | 395.32  |  10.67  | 1.07149  |
| Stoughton        | Metro South                |  151.345 |  144.638 |  140.213 |  54529.8        |  52089.1         |  52188.5         | 360.302 | 360.134 | 372.209 |  11.892 | 1.10462  |
| Taunton          | Metro South                |  613.547 |  586.135 |  564.72  | 201111          | 193766           | 197175           | 327.784 | 330.582 | 349.156 |  48.164 | 1.03392  |
| Waltham          | Metro Boston               |  375.108 |  372.711 |  369.895 | 136813          | 142948           | 144833           | 364.729 | 383.536 | 391.551 |  30.767 | 1.08017  |
| Ware             | Pioneer Valley / Franklin  |  121.009 |  117.807 |  112.265 |  35298.7        |  33369.8         |  34204.6         | 291.703 | 283.259 | 304.677 |   9.564 | 0.958976 |
| Wareham          | New Bedford                |  152.169 |  139.276 |  133.749 |  54543.6        |  52532.7         |  48117.2         | 358.441 | 377.184 | 359.758 |  11.343 | 1.08608  |
| Webster          | Central Massachusetts      |   93.873 |   91.858 |   92.062 |  32749.7        |  30865.2         |  30482.2         | 348.873 | 336.01  | 331.105 |   7.904 | 1.02763  |
| Westfield        | Pioneer Valley / Franklin  |  144.599 |  134.538 |  126.131 |  41401.2        |  39011.3         |  37206.9         | 286.317 | 289.965 | 294.986 |  10.691 | 1.04183  |
| Winchester       | West Merrimack / Middlesex |  784.858 |  772.712 |  756.242 | 265568          | 268477           | 275251           | 338.364 | 347.448 | 363.972 |  65.019 | 1.01028  |
| Winthrop         | Metro Boston               |   86.756 |   85.365 |   83.985 |  33913          |  38035.5         |  34687.6         | 390.901 | 445.563 | 413.021 |   7.123 | 1.11324  |
| Woonsocket       | Metro West                 |  150.64  |  145.487 |  139.926 |  52817.2        |  52129.4         |  51073.7         | 350.619 | 358.31  | 365.005 |  11.866 | 1.0141   |
| Worcester        | Central Massachusetts      | 1927.34  | 1834.04  | 1790.87  | 585489          | 583961           | 582972           | 303.782 | 318.402 | 325.525 | 154.245 | 0.94178  |



label: I=F/C
J=G/D
K=H/E
labeled_formulas: I=F/C
J=G/D
K=H/E
output: {"Arithmetic-Relationship": ["I=F/C", "J=G/D", "K=H/E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_299585___xlsx_fdb576f62408f377b44b72c6a4e3b90e49769d68.xlsx___line_706