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 |
|----:|:-----------------------|----------:|-----------:|--------:|--------:|----------:|
| 610 | Allan Hancock          |   7534.91 |    0       |  547.44 |  411.48 |   8493.83 |
| 620 | Antelope Valley        |  11613    |  319.57    |   43.96 |    0    |  11657    |
| 910 | Barstow                |   2464.42 |  114.402   |   32.55 |    0    |   2496.97 |
| 110 | Butte-Glenn            |   9656.1  |    7e-06   | 1177.11 |   32.15 |  10865.4  |
| 410 | Cabrillo               |   9184.82 |    0       |  182.39 |    0    |   9367.21 |
| 810 | Cerritos               |  17325    |  555.83    |  117.31 |  298.48 |  17740.8  |
| 480 | Chabot-Las Positas     |  17504.2  |  429.39    |  135.85 |    0    |  17640    |
| 920 | Chaffey                |  15489.4  | 1152.03    |  359.9  |    0    |  15849.3  |
| 820 | Citrus                 |  11378.5  |  261.81    |  272.26 |  132.19 |  11783    |
| 830 | Coast                  |  32335.1  |    0       |  288.66 |    0    |  32623.8  |
| 710 | Compton                |   5982.99 |   -7.2e-05 |   23.01 |    0    |   6006    |
| 310 | Contra Costa           |  29353.1  |  667.893   |  135.74 |    0    |  29488.8  |
| 970 | Copper Mountain        |   1397.72 |   -7.5e-05 |   82.1  |    2.46 |   1482.28 |
| 930 | Desert                 |   8435.03 | 1093.58    |   24.92 |  593.5  |   9053.45 |
| 720 | El Camino              |  19463.2  |  325.99    |   22.76 |    0    |  19486    |
| 120 | Feather River          |   1576.62 |   57.5786  |   43.26 |    0    |   1619.88 |
| 420 | Foothill-DeAnza        |  26757.6  |    0       |  215.89 |  169.43 |  27142.9  |
| 440 | Gavilan                |   4294.03 |    0       |  439.07 |   85.28 |   4818.38 |
| 730 | Glendale               |  11297.3  |    0       |  257.1  | 2538.98 |  14093.4  |
|  20 | Grossmont-Cuyamaca     |  18727.6  |  592.65    |   21.93 |    0    |  18749.5  |
| 450 | Hartnell               |   7276.54 |  250.306   |   17.8  |    0    |   7294.34 |
|  30 | Imperial               |   6770.48 |    0       |   24.72 |   16.7  |   6811.9  |
| 520 | Kern                   |  20732.1  |  936.992   |   61.47 |    0    |  20793.5  |
| 220 | Lake Tahoe             |   1620.22 |    0       |   36.4  |   22.09 |   1678.71 |
| 130 | Lassen                 |   1302.78 |    0       |   63.14 |    0    |   1365.92 |
| 840 | Long Beach             |  18622.6  |    0       |   64.72 |  389.99 |  19077.3  |
| 740 | Los Angeles            | 101464    | 2408.38    | 2034.51 | 4102.57 | 107601    |
| 230 | Los Rios               |  47527.5  |    0       |  251.75 |    0    |  47779.2  |
| 330 | Marin                  |   3566.03 |    0       |  240.72 |    0    |   3806.75 |
| 140 | Mendocino-Lake         |   2502.68 |    0       |   38.53 |   43.1  |   2584.31 |
| 530 | Merced                 |   8194.74 |    0       |  318.14 |  633.52 |   9146.4  |
|  50 | Mira Costa             |  10684.6  |  774.84    |  663.74 |    0    |  11348.3  |
| 460 | Monterey Peninsula     |   5789.88 |    0       |  355.9  |  115.98 |   6261.76 |
| 850 | Mt. San Antonio        |  25096.3  |  814.96    | 1644.62 | 4643.56 |  31384.5  |
| 940 | Mt. San Jacinto        |  11249.8  | 1259.06    |  323.88 |  315.98 |  11889.6  |
| 240 | Napa Valley            |   5036.74 |    0       |  539.61 |   13.89 |   5590.24 |
| 860 | North Orange County    |  30332.1  | 1645.43    | 2724.79 | 2777.81 |  35834.7  |
| 430 | Ohlone                 |   7065.28 |    0       |    0    |    0    |   7065.28 |
| 950 | Palo Verde             |   1948.66 |  203.951   |  108.07 |    0    |   2056.73 |
|  60 | Palomar                |  15801.9  |    0       |  280.2  |  520.71 |  16602.8  |
| 770 | Pasadena Area          |  22282.7  | 1187.95    |  183.34 | 1036.18 |  23502.2  |
| 340 | Peralta                |  19409.3  |    0       |  119.13 |    0    |  19528.5  |
| 870 | Rancho Santiago        |  22274.1  |  -91.69    |  702.14 | 5925.41 |  28901.6  |
| 160 | Redwoods               |   3549.91 |    0       |   54.32 |   31.68 |   3635.91 |
| 880 | Rio Hondo              |  12503.3  |  111.9     |  365.21 |   37.38 |  12905.9  |
| 960 | Riverside              |  28599.6  | 1716.81    |   82.8  |    0    |  28682.4  |
| 980 | San Bernardino         |  15275.7  | 1087.12    |   67.08 |    0    |  15342.7  |
|  70 | San Diego              |  34919    | 1507.74    | 2077.72 | 6289.53 |  43286.3  |
| 360 | San Francisco          |  15012.2  |    0       | 2110.73 | 4806.76 |  21929.7  |
| 550 | San Joaquin Delta      |  16165.3  |  476.91    |  171.42 |    0    |  16336.7  |
| 470 | San Jose-Evergreen     |  11493.1  |    0       |   87.43 |    0    |  11580.5  |
| 640 | San Luis Obispo County |   8036.95 |   -6.8e-05 |  109.19 |  173.86 |   8320    |
| 370 | San Mateo County       |  17216.7  |    0       |   87.46 |    0    |  17304.1  |
| 650 | Santa Barbara          |  12675    |    0       |  147.59 |  387.68 |  13210.3  |
| 660 | Santa Clarita          |  15566.4  |  729.436   |  246.74 |  181.64 |  15994.8  |
| 780 | Santa Monica           |  21263.9  |  360.63    |  597.29 |  167.26 |  22028.4  |
| 560 | Sequoias               |   8921.49 |  463.98    |  339.26 |  169.53 |   9430.28 |
| 170 | Shasta-Tehama-Trinity  |   5907.72 |    0       |  177.17 |   34.34 |   6119.23 |
| 270 | Sierra                 |  14578.9  |  177.29    |  296.83 |    0    |  14875.7  |
| 180 | Siskiyou               |   2354.38 |  195.941   |   63.79 |  401.67 |   2819.84 |
| 280 | Solano County          |   8272.73 |    0       |   15.12 |    0    |   8287.85 |
| 260 | Sonoma County          |  16518.8  |   -9.9e-05 | 2303.55 |  592.23 |  19414.6  |
| 890 | South Orange County    |  21433.6  |    0       | 2030.21 |  169.1  |  23632.9  |
|  90 | Southwestern           |  13509.5  |    0       |  220.62 |   37.32 |  13767.4  |
| 570 | State Center           |  28765.4  | 1757.88    |  270.64 |  158.08 |  29194.2  |
| 680 | Ventura County         |  26405.2  |  561.99    |   61.88 |    0    |  26467    |
| 990 | Victor Valley          |   9141.67 |    3.82442 |   70.88 |    0    |   9212.55 |
| 580 | West Hills             |   4934.96 |  209.99    |  346.65 |    0    |   5281.61 |
| 690 | West Kern              |   2519.69 |   50.4596  |   44.69 |    0    |   2564.38 |
| 490 | West Valley-Mission    |  12344.3  |    0       | 1087.3  |    0    |  13431.6  |
| 590 | Yosemite               |  16226.9  |    0       |  175.66 |  168.85 |  16571.4  |
| 290 | Yuba                   |   7484.81 |    0       |  141.61 |    0    |   7626.42 |



label: G=C+E+F
labeled_formulas: G=C+E+F
output: {"Arithmetic-Relationship": ["G=C+E+F"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_641546___xlsx_30d6841814df39d2c2454335276a006ae5ca3e12.xlsx___line_133