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 |         N |         O |     P |          Q |     R |           S |     T |          U |          V |         W |          X |
|:---------------------|----------:|----------:|----------:|---------:|----------:|------:|------------:|------:|------------:|------:|------------:|----------:|----------:|----------:|------:|-----------:|------:|------------:|------:|-----------:|-----------:|----------:|-----------:|
| ALABAMA              |  492.766  |  455.808  |  322.762  | 150.269  |   59.95   | 43955 |   34.2796   | 44007 |  100.222    | 44015 |  645.879    |  392.543  |  8078.81  |  0.796613 | 43955 |   61.7033  | 44007 |  180.4      | 44015 | 1162.58    |   312.366  |  8078.81  |  0.633903  |
| ALASKA               |   75.9512 |   70.2549 |   49.748  |  14.1667 |   15.6667 | 43992 |    0        | 43993 |    0        | 44044 |    0        |   75.9512 |   864.303 |  1        | 43992 |    0       | 43993 |    0        | 44044 |    0       |    75.9512 |   864.303 |  1         |
| ARIZONA              |  901.713  |  834.085  |  590.622  | 115.194  |  208.433  | 43955 |   40.6381   | 43956 |   60.2425   | 43975 |  136.536    |  841.471  |  7027.52  |  0.933191 | 43955 |   73.1486  | 43956 |  108.436    | 43975 |  245.765   |   793.277  |  7027.52  |  0.879744  |
| ARKANSAS             |  323.513  |  299.25   |  211.901  |  60.25   |   30.4    | 43955 |    7.96226  | 43957 |   10.7171   | 43973 |   23.3234   |  312.796  |  3882.2   |  0.966873 | 43955 |   14.3321  | 43957 |   19.2907   | 43973 |   41.9821  |   304.223  |  3882.2   |  0.940371  |
| CALIFORNIA           | 3824.13   | 3537.32   | 2504.81   | 543.954  | 1161.06   | 43955 |  283.954    | 43955 |  360.735    | 43966 |  516.449    | 3463.4    | 40648.3   |  0.905669 | 43955 |  511.117   | 43955 |  649.323    | 43966 |  929.609   |  3174.81   | 40648.3   |  0.830204  |
| COLORADO             |  656.23   |  607.013  |  429.831  | 105.783  |  282.783  | 43955 |   70.8741   | 43955 |   88.6433   | 43955 |  122.913    |  567.586  |  5173.13  |  0.86492  | 43955 |  127.573   | 43955 |  159.558    | 43955 |  221.244   |   496.672  |  5173.13  |  0.756857  |
| CONNECTICUT          |  662.444  |  612.761  |  433.901  |  85.3333 |  216.5    | 43955 |  270.18     | 43955 |  327.477    | 43955 |  442.56     |  334.968  |  4467.15  |  0.505654 | 43955 |  486.324   | 43955 |  589.458    | 43955 |  796.609   |    72.9861 |  4467.15  |  0.110177  |
| DELAWARE             |  166.017  |  153.565  |  108.741  |  13.1167 |   76.6667 | 43955 |   30.4658   | 43955 |   44.8005   | 43974 |   89.8861   |  121.216  |  1316.72  |  0.730145 | 43955 |   54.8384  | 43955 |   80.6409   | 43974 |  161.795   |    85.3758 |  1316.72  |  0.51426   |
| DISTRICT OF COLUMBIA |  531.637  |  491.764  |  348.222  |  54.1667 |  144.493  | 43955 |   42.8023   | 43955 |   60.8019   | 43964 |  104.831    |  470.835  |  1736.89  |  0.885633 | 43955 |   77.0442  | 43955 |  109.444    | 43964 |  188.695   |   422.193  |  1736.89  |  0.794139  |
| FLORIDA              | 2552.69   | 2361.24   | 1672.01   | 446.469  |  428.693  | 43955 |  155.263    | 43955 |  202.854    | 43999 |  630.012    | 2349.83   | 29513.9   |  0.920533 | 43955 |  279.473   | 43955 |  365.137    | 43999 | 1134.02    |  2187.55   | 29513.9   |  0.85696   |
| GEORGIA              | 1301.28   | 1203.69   |  852.341  | 174.812  |  289.537  | 43955 |  191.5      | 43979 |  329.447    | 43991 |  987.022    |  971.836  | 14492.2   |  0.746829 | 43955 |  344.701   | 43979 |  593.004    | 43991 | 1776.64    |   708.279  | 14492.2   |  0.544293  |
| HAWAII               |  210.636  |  194.838  |  137.966  |  25.2873 |   57.7833 | 43955 |    1.24444  | 43955 |    2.16216  | 43955 |    3.5683   |  208.474  |  1730.97  |  0.989735 | 43955 |    2.24    | 43955 |    3.89189  | 43955 |    6.42294 |   206.744  |  1730.97  |  0.981523  |
| IDAHO                |  231.15   |  213.814  |  151.403  |  32.0333 |   39.95   | 43955 |    4.22917  | 43955 |    4.97292  | 43955 |    5.81413  |  226.177  |  1446.39  |  0.978486 | 43955 |    7.6125  | 43955 |    8.95125  | 43955 |   10.4654  |   222.199  |  1446.39  |  0.961275  |
| ILLINOIS             | 1583.7    | 1464.92   | 1037.32   | 319.418  |  522.378  | 43955 |  400.456    | 43955 |  546.147    | 43975 |  890.453    | 1037.55   | 15180.7   |  0.655144 | 43955 |  720.821   | 43955 |  983.065    | 43975 | 1602.82    |   600.632  | 15180.7   |  0.379259  |
| INDIANA              |  934.203  |  864.138  |  611.903  | 149.525  |  230.928  | 43955 |  247.772    | 43956 |  386.54     | 43988 | 1765.13     |  547.663  |  8373.95  |  0.586235 | 43955 |  445.99    | 43956 |  695.772    | 43988 | 3177.24    |   238.431  |  8373.95  |  0.255224  |
| IOWA                 |  400.781  |  370.722  |  262.512  |  77.9179 |  101.261  | 43955 |   32.8125   | 43990 |   87.1111   | 44003 |  487.448    |  313.67   |  4199.34  |  0.782647 | 43955 |   59.0625  | 43990 |  156.8      | 44003 |  877.406   |   243.981  |  4199.34  |  0.608764  |
| KANSAS               |  389.018  |  359.842  |  254.807  | 109.875  |   73.35   | 43955 |    8.43816  | 43955 |   12.2785   | 43957 |   20.1522   |  376.739  |  4217.95  |  0.968437 | 43955 |   15.1887  | 43955 |   22.1013   | 43957 |   36.274   |   366.917  |  4217.95  |  0.943187  |
| KENTUCKY             |  588.737  |  544.582  |  385.623  | 103.226  |   88.8667 | 43955 |   27.8539   | 43955 |   36.6693   | 43962 |   60.5699   |  552.068  |  6786.5   |  0.937715 | 43955 |   50.1371  | 43955 |   66.0048   | 43962 |  109.026   |   522.732  |  6786.5   |  0.887887  |
| LOUISIANA            |  476.469  |  440.734  |  312.087  | 152.95   |  102.95   | 43955 |  170.886    | 43955 |  203.283    | 43955 |  257.641    |  273.186  |  6684.62  |  0.573355 | 43955 |  307.595   | 43955 |  365.91     | 43955 |  463.754   |   110.559  |  6684.62  |  0.232039  |
| MAINE                |  300.869  |  278.304  |  197.069  |  43.1583 |   76.2833 | 43955 |    4.40417  | 43955 |    5.45075  | 43955 |    9.28472  |  295.418  |  1923.94  |  0.981883 | 43955 |    7.9275  | 43955 |    9.81136  | 43955 |   16.7125  |   291.058  |  1923.94  |  0.96739   |
| MARYLAND             |  629.318  |  582.119  |  412.203  |  61.25   |  182.01   | 43955 |  260.131    | 43955 |  338.422    | 43955 |  488.626    |  290.896  |  6695.75  |  0.46224  | 43955 |  468.236   | 43955 |  609.16     | 43955 |  879.527   |    20.1578 |  6695.75  |  0.0320311 |
| MASSACHUSETTS        | 1329.98   | 1230.24   |  871.14   | 122.367  |  229.028  | 43955 |  230.791    | 43955 |  315.58     | 43956 |  495.002    | 1014.4    |  8658.88  |  0.762719 | 43955 |  415.424   | 43955 |  568.045    | 43956 |  891.004   |   761.94   |  8658.88  |  0.572894  |
| MICHIGAN             | 1115.56   | 1031.89   |  730.69   | 356.833  |  188.65   | 43955 |  422.044    | 43955 |  542.059    | 43958 |  792.288    |  573.499  | 12926     |  0.514092 | 43955 |  759.679   | 43955 |  975.706    | 43958 | 1426.12    |   139.852  | 12926     |  0.125365  |
| MINNESOTA            |  907.621  |  839.55   |  594.492  | 144.492  |  120.45   | 43956 |   65.8299   | 43964 |  144.886    | 43977 |  416.534    |  762.736  |  7588.19  |  0.840368 | 43956 |  118.494   | 43964 |  260.795    | 43977 |  749.761   |   646.827  |  7588.19  |  0.712662  |
| MISSISSIPPI          |  297.965  |  275.617  |  195.167  |  59.3944 |   31.1167 | 43955 |   28.8451   | 43955 |   39.7938   | 43959 |   71.874    |  258.171  |  5409.69  |  0.866448 | 43955 |   51.9212  | 43955 |   71.6289   | 43959 |  129.373   |   226.336  |  5409.69  |  0.759606  |
| MISSOURI             |  912.256  |  843.837  |  597.528  | 126.162  |  257.683  | 43955 |   43.1234   | 43955 |   59.6934   | 44003 |  261.851    |  852.563  |  9406.34  |  0.934565 | 43955 |   77.6222  | 43955 |  107.448    | 44003 |  471.332   |   804.808  |  9406.34  |  0.882217  |
| MONTANA              |  209.226  |  193.534  |  137.043  |  26.3333 |   31.1667 | 43955 |    0.165278 | 43955 |    0.254314 | 43955 |    0.787986 |  208.972  |  1740.21  |  0.998785 | 43955 |    0.2975  | 43955 |    0.457765 | 43955 |    1.41838 |   208.768  |  1740.21  |  0.997812  |
| NEBRASKA             |  293.36   |  271.358  |  192.15   |  58.0833 |   34.6667 | 43955 |    9.87097  | 43967 |   27.9309   | 43979 |   81.8719   |  265.429  |  2878.73  |  0.90479  | 43955 |   17.7677  | 43967 |   50.2756   | 43979 |  147.369   |   243.084  |  2878.73  |  0.828621  |
| NEVADA               |  326.48   |  301.994  |  213.844  |  58.3333 |   55.3333 | 43955 |   31.6167   | 43955 |   39.6076   | 43960 |   56.5833   |  286.873  |  3869.79  |  0.878683 | 43955 |   56.91    | 43955 |   71.2937   | 43960 |  101.85    |   255.186  |  3869.79  |  0.781629  |
| NEW HAMPSHIRE        |  271.622  |  251.25   |  177.912  |  19.625  |   54.2667 | 43955 |   12.5611   | 43955 |   17.2042   | 43968 |   30.0028   |  254.418  |  1378.49  |  0.936661 | 43955 |   22.61    | 43955 |   30.9676   | 43968 |   54.005   |   240.654  |  1378.49  |  0.88599   |
| NEW JERSEY           |  925.071  |  855.69   |  605.921  | 206.31   |  172.171  | 43955 | 1015.05     | 43955 | 1303.79     | 43961 | 1963.71     | -378.72   | 11219.1   | -0.409396 | 43955 | 1827.1     | 43955 | 2346.82     | 43961 | 3534.67    | -1421.75   | 11219.1   | -1.53691   |
| NEW MEXICO           |  282.877  |  261.662  |  185.285  |  35.6429 |   35.2667 | 43955 |   22.4965   | 43955 |   36.0304   | 43984 |   88.3188   |  246.847  |  1788.05  |  0.872629 | 43955 |   40.4937  | 43955 |   64.8546   | 43984 |  158.974   |   218.023  |  1788.05  |  0.770732  |
| NEW YORK             | 2422.09   | 2240.44   | 1586.47   | 318.393  |  664.967  | 43955 |  885.485    | 43955 | 1095.67     | 43955 | 1528.99     | 1326.42   | 32337.8   |  0.547636 | 43955 | 1593.87    | 43955 | 1972.2      | 43955 | 2752.18    |   449.89   | 32337.8   |  0.185744  |
| NORTH CAROLINA       | 1534.34   | 1419.27   | 1004.99   | 121.975  |  271.45   | 43955 |   76.1196   | 43955 |  107.525    | 43967 |  196.988    | 1426.82   | 12659.6   |  0.929921 | 43955 |  137.015   | 43955 |  193.545    | 43967 |  354.578   |  1340.8    | 12659.6   |  0.873858  |
| NORTH DAKOTA         |  138.477  |  128.092  |   90.7027 |  14.6429 |   49.0333 | 43955 |    2.14715  | 43955 |    3.40783  | 43960 |    6.58219  |  135.07   |  1604.45  |  0.975391 | 43955 |    3.86487 | 43955 |    6.1341   | 43960 |   11.8479  |   132.343  |  1604.45  |  0.955703  |
| OHIO                 | 1684.53   | 1558.19   | 1103.36   | 262.043  |  388.383  | 43955 |  199.678    | 43955 |  275.922    | 43956 |  422.153    | 1408.6    | 15628     |  0.836202 | 43955 |  359.42    | 43955 |  496.66     | 43956 |  759.876   |  1187.87   | 15628     |  0.705163  |
| OKLAHOMA             |  411.8    |  380.915  |  269.729  |  79.5333 |   40.0333 | 43955 |   23.7686   | 43955 |   32.5839   | 43964 |   52.7503   |  379.216  |  5071.45  |  0.920874 | 43955 |   42.7836  | 43955 |   58.6511   | 43964 |   94.9506  |   353.149  |  5071.45  |  0.857574  |
| OREGON               |  647.11   |  598.577  |  423.857  |  46.1667 |  123.683  | 43955 |   10.5856   | 43955 |   15.0286   | 43957 |   24.1998   |  632.081  |  3762.15  |  0.976776 | 43955 |   19.054   | 43955 |   27.0514   | 43957 |   43.5597  |   620.058  |  3762.15  |  0.958197  |
| PENNSYLVANIA         | 1917.19   | 1773.4    | 1255.76   | 387.635  |  503.383  | 43955 |  504.868    | 43955 |  720.263    | 43968 | 1353.35     | 1196.93   | 18826.8   |  0.624314 | 43955 |  908.762   | 43955 | 1296.47     | 43968 | 2436.03    |   620.719  | 18826.8   |  0.323764  |
| RHODE ISLAND         |  155.983  |  144.285  |  102.169  |  24.5    |   17.4167 | 43955 |   34.055    | 43955 |   45.4873   | 43955 |   70.427    |  110.496  |  1283.99  |  0.708383 | 43955 |   61.299   | 43955 |   81.8772   | 43955 |  126.769   |    74.1061 |  1283.99  |  0.47509   |
| SOUTH CAROLINA       |  663.625  |  613.854  |  434.675  |  82.0429 |   70.6167 | 43955 |   62.8961   | 43957 |   96.9479   | 43976 |  246.475    |  566.678  |  6279.57  |  0.853912 | 43955 |  113.213   | 43957 |  174.506    | 43976 |  443.656   |   489.119  |  6279.57  |  0.737041  |
| SOUTH DAKOTA         |  156.552  |  144.811  |  102.542  |  40.5833 |   18      | 43965 |    3.79142  | 44002 |   17.2149   | 44014 |  106.712    |  139.337  |  2065.24  |  0.890037 | 43965 |    6.82456 | 44002 |   30.9868   | 44014 |  192.082   |   125.566  |  2065.24  |  0.802067  |
| TENNESSEE            |  870.524  |  805.235  |  570.193  | 163.529  |  198.66   | 43955 |   16.44     | 43956 |   26.8746   | 43986 |   69.0566   |  843.65   | 10521     |  0.969128 | 43955 |   29.5921  | 43956 |   48.3743   | 43986 |  124.302   |   822.15   | 10521     |  0.944431  |
| TEXAS                | 2852.34   | 2638.41   | 1868.28   | 528.126  |  602.983  | 43955 |  140.716    | 43979 |  206.539    | 43994 |  720.9      | 2645.8    | 31325.6   |  0.92759  | 43955 |  253.289   | 43979 |  371.77     | 43994 | 1297.62    |  2480.57   | 31325.6   |  0.869661  |
| UTAH                 |  237.151  |  219.365  |  155.334  |  37.1667 |   54.1667 | 43956 |    6.67941  | 43955 |   11.0794   | 43956 |   21.6035   |  226.072  |  2483.87  |  0.953281 | 43956 |   12.0229  | 43955 |   19.9429   | 43956 |   38.8863  |   217.208  |  2483.87  |  0.915906  |
| VERMONT              |  121.126  |  112.042  |   79.3377 |  16.5    |   17      | 43955 |    1.69142  | 43955 |    2.81988  | 43955 |    4.77361  |  118.306  |   653.191 |  0.976719 | 43955 |    3.04456 | 43955 |    5.07579  | 43955 |    8.5925  |   116.05   |   653.191 |  0.958095  |
| VIRGINIA             |  994.443  |  919.86   |  651.36   | 120.285  |  194.693  | 43955 |  107.248    | 43955 |  147.69     | 43961 |  227.482    |  846.753  | 10237.7   |  0.851485 | 43955 |  193.046   | 43955 |  265.842    | 43961 |  409.467   |   728.602  | 10237.7   |  0.732673  |
| WASHINGTON           | 1174.02   | 1085.96   |  768.98   | 104.893  |  265.811  | 43955 |   59.6824   | 43955 |   68.3412   | 43955 |   80.8891   | 1105.67   |  7163.95  |  0.941788 | 43955 |  107.428   | 43955 |  123.014    | 43955 |  145.6     |  1051      |  7163.95  |  0.895219  |
| WEST VIRGINIA        |  274.956  |  254.335  |  180.096  |  71.829  |   56.3444 | 43955 |    4.86111  | 43955 |    8.11368  | 43991 |   22.2483   |  266.843  |  3282.06  |  0.970491 | 43955 |    8.75    | 43955 |   14.6046   | 43991 |   40.047   |   260.352  |  3282.06  |  0.946884  |
| WISCONSIN            |  913.761  |  845.229  |  598.513  |  98.425  |  232.183  | 43955 |   34.5137   | 43955 |   44.5995   | 43966 |   65.2118   |  869.161  |  5954.78  |  0.951191 | 43955 |   62.1247  | 43955 |   80.2791   | 43966 |  117.381   |   833.482  |  5954.78  |  0.912144  |
| WYOMING              |   89.2135 |   82.5225 |   58.4348 |  19.1667 |   12.7833 | 43956 |    0.233333 | 43956 |    0.358789 | 43956 |    0.495833 |   88.8547 |   801.807 |  0.995978 | 43956 |    0.42    | 43956 |    0.64582  | 43956 |    0.8925  |    88.5677 |   801.807 |  0.992761  |



label: M=B-J
O=M/B
V=B-S
X=V/B
labeled_formulas: M=B-J
O=M/B
V=B-S
X=V/B
output: {"Arithmetic-Relationship": ["M=B-J", "O=M/B", "V=B-S", "X=V/B"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_105172___xlsx_073bbb0e9742a5f40bafa274e286009518a73988.xlsx___line_17