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 |
|:----------------------|--------:|-----------------:|-----------------:|----------:|-----------------:|------------:|----------:|
| Washington, D.C.      |  646449 |      2.23588e+08 |      1.69481e+08 | 262.173   |      5.41068e+07 |  83.6986    | 345.871   |
| Seattle               |  652405 |      1.94268e+08 |      1.16887e+08 | 179.163   |      7.73805e+07 | 118.608     | 297.771   |
| Arlington, Virginia   |  224906 |      5.59851e+07 |      3.62727e+07 | 161.279   |      1.97124e+07 |  87.6474    | 248.927   |
| Minneapolis           |  400070 |      9.19091e+07 |      7.07362e+07 | 176.809   |      2.11729e+07 |  52.9231    | 229.733   |
| San Francisco         |  837442 |      1.81309e+08 |      1.48377e+08 | 177.179   |      3.29321e+07 |  39.3246    | 216.503   |
| Irvine                |  236716 |      5.00428e+07 |      3.70428e+07 | 156.486   |      1.3e+07     |  54.9181    | 211.405   |
| Cincinnati            |  297517 |      5.24572e+07 |      4.18241e+07 | 140.577   |      1.06331e+07 |  35.7394    | 176.317   |
| St. Paul              |  294873 |      5.15646e+07 |      4.78586e+07 | 162.302   |      3.706e+06   |  12.5681    | 174.87    |
| Chicago               | 2718782 |      4.72103e+08 |      3.53744e+08 | 130.111   |      1.18359e+08 |  43.5337    | 173.645   |
| Long Beach            |  469428 |      7.86485e+07 |      4.9922e+07  | 106.347   |      2.87265e+07 |  61.1947    | 167.541   |
| San Jose              |  998537 |      1.62589e+08 |      6.16018e+07 |  61.692   |      1.00987e+08 | 101.135     | 162.827   |
| New York              | 8405837 |      1.36425e+09 |      9.41023e+08 | 111.949   |      4.23224e+08 |  50.3488    | 162.298   |
| Virginia Beach        |  448479 |      7.00804e+07 |      5.92838e+07 | 132.189   |      1.07966e+07 |  24.0738    | 156.262   |
| Raleigh               |  431746 |      6.70881e+07 |      4.69289e+07 | 108.696   |      2.01591e+07 |  46.6921    | 155.388   |
| Henderson             |  270811 |      4.02234e+07 |      3.36254e+07 | 124.166   |      6.59799e+06 |  24.3638    | 148.529   |
| Tampa                 |  352957 |      5.1334e+07  |      3.63116e+07 | 102.878   |      1.50225e+07 |  42.5618    | 145.44    |
| Portland              |  609456 |      8.59384e+07 |      7.37046e+07 | 120.935   |      1.22338e+07 |  20.0734    | 141.008   |
| Oakland               |  406253 |      5.70336e+07 |      4.13454e+07 | 101.773   |      1.56881e+07 |  38.6167    | 140.389   |
| St. Petersburg        |  249688 |      3.27216e+07 |      3.26465e+07 | 130.749   |  75095           |   0.300755  | 131.05    |
| Aurora                |  345803 |      4.52909e+07 |      3.55383e+07 | 102.77    |      9.75263e+06 |  28.2028    | 130.973   |
| Las Vegas             |  603488 |      7.55732e+07 |      5.85676e+07 |  97.0484  |      1.70056e+07 |  28.1789    | 125.227   |
| St. Louis             |  318416 |      3.96862e+07 |      3.13594e+07 |  98.4855  |      8.32683e+06 |  26.1508    | 124.636   |
| Boston                |  645966 |      7.98844e+07 |      5.65692e+07 |  87.573   |      2.33153e+07 |  36.0936    | 123.667   |
| Madison               |  243344 |      2.91114e+07 |      2.25628e+07 |  92.7197  |      6.54866e+06 |  26.9111    | 119.631   |
| Orlando               |  255483 |      3.01626e+07 |      2.90751e+07 | 113.805   |      1.08746e+06 |   4.25649   | 118.061   |
| Atlanta               |  447841 |      5.1969e+07  |      4.165e+07   |  93.0018  |      1.0319e+07  |  23.0417    | 116.043   |
| Kansas City           |  467007 |      5.36801e+07 |      4.00246e+07 |  85.7044  |      1.36556e+07 |  29.2406    | 114.945   |
| San Diego             | 1355896 |      1.51171e+08 |      1.38495e+08 | 102.143   |      1.26751e+07 |   9.34815   | 111.491   |
| Austin                |  885400 |      9.8281e+07  |      5.72384e+07 |  64.647   |      4.10425e+07 |  46.3548    | 111.002   |
| Cleveland             |  390113 |      4.2999e+07  |      3.41996e+07 |  87.666   |      8.79933e+06 |  22.5559    | 110.222   |
| Sacramento            |  479686 |      4.99963e+07 |      4.94043e+07 | 102.993   | 591968           |   1.23407   | 104.227   |
| Denver                |  649495 |      6.72366e+07 |      5.57014e+07 |  85.7611  |      1.15352e+07 |  17.7603    | 103.521   |
| Nashville/Davidson    |  658602 |      6.71529e+07 |      3.3927e+07  |  51.5136  |      3.3226e+07  |  50.4493    | 101.963   |
| Scottsdale            |  226918 |      2.268e+07   |      2.268e+07   |  99.948   |      0           |   0         |  99.948   |
| San Antonio           | 1409019 |      1.36788e+08 |      9.2035e+07  |  65.3185  |      4.47532e+07 |  31.7619    |  97.0804  |
| Milwaukee             |  599164 |      5.71371e+07 |      4.1244e+07  |  68.8359  |      1.58931e+07 |  26.5254    |  95.3613  |
| Columbus              |  822553 |      7.62272e+07 |      3.68139e+07 |  44.7557  |      3.94133e+07 |  47.9158    |  92.6715  |
| Arlington, Texas      |  379577 |      3.50099e+07 |      2.68286e+07 |  70.6802  |      8.1813e+06  |  21.5537    |  92.2339  |
| Plano                 |  274409 |      2.4828e+07  |      2.4828e+07  |  90.478   |      0           |   0         |  90.478   |
| Lincoln               |  268738 |      2.39756e+07 |      1.56569e+07 |  58.2609  |      8.31865e+06 |  30.9545    |  89.2154  |
| Fort Worth            |  792727 |      7.0331e+07  |      5.92813e+07 |  74.7815  |      1.10497e+07 |  13.9388    |  88.7203  |
| Tucson                |  526116 |      4.58391e+07 |      4.17109e+07 |  79.2808  |      4.12817e+06 |   7.8465    |  87.1273  |
| Bakersfield           |  363630 |      3.13997e+07 |      2.38321e+07 |  65.5394  |      7.56757e+06 |  20.8112    |  86.3506  |
| Phoenix               | 1513367 |      1.264e+08   |      1.07012e+08 |  70.711   |      1.93879e+07 |  12.8111    |  83.5221  |
| Lexington/Fayette     |  308428 |      2.5568e+07  |      2.3268e+07  |  75.4406  |      2.3e+06     |   7.45717   |  82.8978  |
| Los Angeles           | 3884307 |      3.17485e+08 |      2.57823e+08 |  66.3755  |      5.96623e+07 |  15.3598    |  81.7353  |
| New Orleans           |  378715 |      3.06424e+07 |      2.50479e+07 |  66.1392  |      5.59445e+06 |  14.7722    |  80.9114  |
| Miami                 |  417650 |      3.35561e+07 |      3.10616e+07 |  74.3724  |      2.49448e+06 |   5.97266   |  80.345   |
| Norfolk               |  246139 |      1.8579e+07  |      1.7206e+07  |  69.9035  |      1.373e+06   |   5.57815   |  75.4817  |
| Corpus Christi        |  316381 |      2.3791e+07  |      2.30029e+07 |  72.7063  | 788093           |   2.49096   |  75.1973  |
| Riverside             |  316619 |      2.37259e+07 |      2.10589e+07 |  66.5119  |      2.667e+06   |   8.42337   |  74.9352  |
| Durham                |  245475 |      1.83127e+07 |      1.25066e+07 |  50.9485  |      5.80616e+06 |  23.6528    |  74.6013  |
| Albuquerque           |  556495 |      4.06779e+07 |      2.16554e+07 |  38.914   |      1.90225e+07 |  34.1826    |  73.0966  |
| Omaha                 |  434353 |      3.08786e+07 |      2.4353e+07  |  56.0674  |      6.52559e+06 |  15.0237    |  71.0911  |
| Fort Wayne            |  256496 |      1.80004e+07 |      1.62939e+07 |  63.5251  |      1.7065e+06  |   6.65313   |  70.1782  |
| Anchorage             |  300950 |      2.09161e+07 |      1.88394e+07 |  62.5997  |      2.07672e+06 |   6.90054   |  69.5002  |
| Oklahoma City         |  610613 |      4.20643e+07 |      3.43524e+07 |  56.2588  |      7.71192e+06 |  12.6298    |  68.8886  |
| Mesa                  |  457587 |      3.11727e+07 |      2.33727e+07 |  51.0781  |      7.8e+06     |  17.0459    |  68.124   |
| Philadelphia          | 1553165 |      1.03278e+08 |      8.44367e+07 |  54.3643  |      1.88409e+07 |  12.1306    |  66.4949  |
| Colorado Springs      |  439886 |      2.89998e+07 |      2.27379e+07 |  51.6904  |      6.26195e+06 |  14.2354    |  65.9258  |
| Anaheim               |  345012 |      2.25095e+07 |      1.56069e+07 |  45.2359  |      6.90255e+06 |  20.0067    |  65.2426  |
| Greensboro            |  279639 |      1.82092e+07 |      1.82092e+07 |  65.1169  |      0           |   0         |  65.1169  |
| Tulsa                 |  398121 |      2.33232e+07 |      2.06157e+07 |  51.7826  |      2.70741e+06 |   6.80048   |  58.5831  |
| Gilbert               |  229972 |      1.3307e+07  |      1.27919e+07 |  55.6237  | 515079           |   2.23975   |  57.8634  |
| Baltimore             |  622104 |      3.54774e+07 |      3.54774e+07 |  57.028   |      0           |   0         |  57.028   |
| Pittsburgh            |  305841 |      1.66363e+07 |      1.50863e+07 |  49.3272  |      1.55e+06    |   5.06799   |  54.3952  |
| Honolulu              |  347884 |      1.87106e+07 |      9.22572e+06 |  26.5195  |      9.48489e+06 |  27.2645    |  53.784   |
| Buffalo               |  258959 |      1.37677e+07 |      7.48822e+06 |  28.9166  |      6.27948e+06 |  24.2489    |  53.1655  |
| Chesapeake            |  230571 |      1.2092e+07  |      1.19005e+07 |  51.613   | 191494           |   0.830521  |  52.4436  |
| Memphis               |  653450 |      3.42179e+07 |      2.67425e+07 |  40.9252  |      7.47539e+06 |  11.4399    |  52.365   |
| Santa Ana             |  334227 |      1.71094e+07 |      1.2186e+07  |  36.4603  |      4.92333e+06 |  14.7305    |  51.1908  |
| Dallas                | 1257676 |      6.30433e+07 |      6.12991e+07 |  48.74    |      1.74423e+06 |   1.38687   |  50.1269  |
| Wichita               |  386552 |      1.91626e+07 |      1.64869e+07 |  42.6513  |      2.67568e+06 |   6.9219    |  49.5732  |
| Baton Rouge           |  229426 |      1.12055e+07 |      1.09025e+07 |  47.5208  | 303034           |   1.32084   |  48.8417  |
| Lubbock               |  239538 |      1.11406e+07 |      9.56433e+06 |  39.9282  |      1.57632e+06 |   6.58068   |  46.5089  |
| Reno                  |  233294 |      1.0284e+07  |      9.86349e+06 |  42.2792  | 420468           |   1.80231   |  44.0815  |
| Toledo                |  282313 |      1.23992e+07 |      1.15655e+07 |  40.9669  | 833654           |   2.95294   |  43.9199  |
| Chula Vista           |  256780 |      1.09613e+07 |      1.0336e+07  |  40.2523  | 625256           |   2.43499   |  42.6873  |
| Winston-Salem         |  236441 |      9.87929e+06 |      8.90654e+06 |  37.6692  | 972751           |   4.11414   |  41.7833  |
| Charlotte/Mecklenburg |  990977 |      3.97208e+07 |      3.31208e+07 |  33.4223  |      6.6e+06     |   6.66009   |  40.0824  |
| El Paso               |  674433 |      2.58692e+07 |      2.58587e+07 |  38.3414  |  10500           |   0.0155686 |  38.357   |
| Houston               | 2195914 |      8.21038e+07 |      6.95807e+07 |  31.6864  |      1.25231e+07 |   5.70291   |  37.3893  |
| Glendale              |  234632 |      8.54878e+06 |      8.54878e+06 |  36.4349  |      0           |   0         |  36.4349  |
| Fremont               |  224922 |      7.80603e+06 |      7.54629e+06 |  33.5507  | 259740           |   1.1548    |  34.7055  |
| Louisville/Jefferson  |  756832 |      2.61924e+07 |      2.09136e+07 |  27.6331  |      5.27875e+06 |   6.97479   |  34.6079  |
| Jacksonville          |  842583 |      2.3124e+07  |      2.23486e+07 |  26.524   | 775333           |   0.920186  |  27.4441  |
| Newark                |  278427 |      7.04131e+06 |      2.13048e+06 |   7.65185 |      4.91083e+06 |  17.6378    |  25.2896  |
| Indianapolis          |  843393 |      2.00405e+07 |      1.65608e+07 |  19.6359  |      3.47969e+06 |   4.12582   |  23.7617  |
| Fresno                |  509924 |      1.18601e+07 |      9.96306e+06 |  19.5383  |      1.897e+06   |   3.72016   |  23.2585  |
| Jersey City           |  257342 |      5.75e+06    |      3.75e+06    |  14.572   |      2e+06       |   7.77176   |  22.3438  |
| Detroit               |  688701 |      1.1652e+07  |      1.1289e+07  |  16.3917  | 363000           |   0.527079  |  16.9188  |
| Stockton              |  298118 |      4.08888e+06 |      3.73037e+06 |  12.5131  | 358505           |   1.20256   |  13.7156  |
| Hialeah               |  233394 | 817676           | 817676           |   3.50341 |      0           |   0         |   3.50341 |



label: E=D/B
G=F/B
H=C/B
labeled_formulas: E=D/B
G=F/B
H=C/B
output: {"Arithmetic-Relationship": ["E=D/B", "G=F/B", "H=C/B"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_480537___xlsx_180f0b1fe7ae66ca5dac1762b47b134a3150e244.xlsx___line_140