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 |
|----:|------:|:-------------------------|----:|--------:|-----------:|----:|
| 113 | 14005 | Aberdeen                 |   4 |  606.33 | 0.00659707 |   2 |
| 113 | 21226 | Adna                     |   1 |   66.33 | 0.0150761  |   2 |
| 189 | 29103 | Anacortes                |  10 |  328.89 | 0.0304053  |   4 |
| 189 | 31016 | Arlington                |  23 |  788.44 | 0.0291715  |   2 |
| 123 |  2420 | Asotin-Anatone           |   2 |   88.88 | 0.0225023  |   2 |
| 121 | 17408 | Auburn                   |  85 | 1949    | 0.0436121  |   4 |
| 121 | 18303 | Bainbridge Island        |  26 |  463.89 | 0.0560478  |   4 |
| 112 |  6119 | Battle Ground            |  48 | 1922.1  | 0.0249727  |   2 |
| 121 | 17405 | Bellevue                 | 150 | 1815.33 | 0.0826296  |   4 |
| 189 | 37501 | Bellingham               |  52 | 1667.11 | 0.0311917  |   4 |
| 121 | 27403 | Bethel                   |  67 | 2733.77 | 0.0245083  |   2 |
| 189 | 37503 | Blaine                   |   9 |  376    | 0.0239362  |   2 |
| 114 | 18100 | Bremerton                |  15 |  777.11 | 0.0193023  |   2 |
| 189 | 29100 | Burlington-Edison        |   7 |  532.33 | 0.0131497  |   2 |
| 112 |  6117 | Camas                    |  38 |  793.78 | 0.0478722  |   4 |
| 171 |  4222 | Cashmere                 |   4 |  205.78 | 0.0194382  |   2 |
| 112 |  8401 | Castle Rock              |   5 |  249.11 | 0.0200715  |   2 |
| 114 | 18401 | Central Kitsap           |  56 | 1770.67 | 0.0316264  |   4 |
| 101 | 32356 | Central Valley           |  24 | 2071    | 0.0115886  |   2 |
| 113 | 21401 | Centralia                |  15 |  585.33 | 0.0256266  |   2 |
| 113 | 21302 | Chehalis                 |   4 |  398.67 | 0.0100334  |   2 |
| 101 | 32360 | Cheney                   |   1 |  908.89 | 0.00110024 |   2 |
| 114 | 16049 | Chimacum                 |  10 |  134.56 | 0.0743163  |   4 |
| 121 | 27400 | Clover Park              |  74 | 2012.11 | 0.0367773  |   4 |
| 101 | 33115 | Colville                 |   6 |  319.22 | 0.0187958  |   2 |
| 189 | 29011 | Concrete                 |   7 |   94.22 | 0.0742942  |   4 |
| 189 | 15204 | Coupeville               |   1 |  143.67 | 0.0069604  |   2 |
| 105 | 19007 | Damman                   |   1 |    7    | 0.142857   |   6 |
| 189 | 31330 | Darrington               |   2 |   74.44 | 0.0268673  |   2 |
| 121 | 27343 | Dieringer                |   3 |  208.11 | 0.0144155  |   2 |
| 121 | 27404 | Eatonville               |   6 |  220.11 | 0.0272591  |   2 |
| 189 | 31015 | Edmonds                  |  41 | 3059.44 | 0.0134011  |   2 |
| 105 | 19401 | Ellensburg               |   5 |  459.12 | 0.0108904  |   2 |
| 113 | 14068 | Elma                     |   1 |  279.11 | 0.00358282 |   2 |
| 121 | 17216 | Enumclaw                 |  12 |  660.22 | 0.0181758  |   2 |
| 112 |  6701 | ESA 112                  |  78 | 2285.32 | 0.0341309  |   4 |
| 189 | 31002 | Everett                  |  93 | 2708.56 | 0.0343356  |   4 |
| 112 |  6114 | Evergreen 114            | 145 | 3531.55 | 0.0410585  |   4 |
| 121 | 17210 | Federal Way              | 146 | 3190.22 | 0.0457649  |   4 |
| 189 | 37502 | Ferndale                 |  21 |  741    | 0.0283401  |   2 |
| 121 | 27417 | Fife                     |   8 |  443.56 | 0.0180359  |   2 |
| 121 | 27402 | Franklin Pierce          |  24 | 1173.45 | 0.0204525  |   2 |
| 171 | 13301 | Grand Coulee Dam         |   4 |  114.89 | 0.0348159  |   4 |
| 189 | 31332 | Granite Falls            |  29 |  375    | 0.0773333  |   4 |
| 113 | 23054 | Grapeview                |   1 |   26.11 | 0.0382995  |   4 |
| 121 | 27904 | Green Dot Destiny        |   2 |   30.22 | 0.0661813  |   4 |
| 121 | 17910 | Green Dot Rainier Valley |   3 |   39.44 | 0.0760649  |   4 |
| 121 | 17401 | Highline                 |  82 | 2788.67 | 0.0294047  |   2 |
| 112 |  6098 | Hockinson                |  11 |  176.89 | 0.0621855  |   4 |
| 121 | 17411 | Issaquah                 |  50 | 1676.67 | 0.029821   |   4 |
| 112 |  8458 | Kelso                    |  16 |  708.67 | 0.0225775  |   2 |
| 123 |  3017 | Kennewick                |  10 | 2309    | 0.00433088 |   2 |
| 121 | 17415 | Kent                     | 133 | 2915.24 | 0.0456223  |   4 |
| 112 |  6101 | La Center                |   8 |  220.45 | 0.0362894  |   4 |
| 189 | 29311 | La Conner                |   6 |   94.45 | 0.0635257  |   4 |
| 171 |  4129 | Lake Chelan              |   1 |  141.11 | 0.00708667 |   2 |
| 189 | 31004 | Lake Stevens             |  13 | 1496.33 | 0.00868792 |   2 |
| 121 | 17414 | Lake Washington          | 147 | 3277.66 | 0.0448491  |   4 |
| 189 | 31306 | Lakewood                 |  10 |  379.89 | 0.0263234  |   2 |
| 112 |  8122 | Longview                 |  33 | 1183.11 | 0.0278926  |   2 |
| 189 | 28144 | Lopez                    |   1 |   45.11 | 0.022168   |   2 |
| 189 | 37504 | Lynden                   |   7 |  540.44 | 0.0129524  |   2 |
| 105 | 39120 | Mabton                   |   2 |   98.89 | 0.0202245  |   2 |
| 113 | 23311 | Mary M Knight            |   4 |  272.45 | 0.0146816  |   2 |
| 189 | 31025 | Marysville               |  67 | 1751.23 | 0.0382588  |   4 |
| 121 | 17400 | Mercer Island            |  17 |  437.67 | 0.038842   |   4 |
| 189 | 37505 | Meridian                 |   2 |  199.56 | 0.010022   |   2 |
| 189 | 31103 | Monroe                   |  11 |  806.11 | 0.0136458  |   2 |
| 189 | 37507 | Mount Baker              |   4 |  355.44 | 0.0112537  |   2 |
| 189 | 29320 | Mount Vernon             |  51 |  955    | 0.0534031  |   4 |
| 189 | 31006 | Mukilteo                 |  57 | 2234.23 | 0.0255121  |   2 |
| 113 | 21014 | Napavine                 |   7 |  116    | 0.0603448  |   4 |
| 114 | 18400 | North Kitsap             |  57 |  823.22 | 0.0692403  |   4 |
| 114 | 23403 | North Mason              |   5 |  358.33 | 0.0139536  |   2 |
| 113 | 34003 | North Thurston           |  35 | 2148.44 | 0.0162909  |   2 |
| 121 | 17417 | Northshore               | 108 | 2911.34 | 0.0370963  |   4 |
| 189 | 15201 | Oak Harbor               |  10 |  999.55 | 0.0100045  |   2 |
| 113 | 34111 | Olympia                  |  73 | 1482.78 | 0.0492318  |   4 |
| 189 | 28137 | Orcas Island             |   7 |   95.11 | 0.073599   |   4 |
| 121 | 27344 | Orting                   |  12 |  413.77 | 0.0290016  |   2 |
| 113 | 21301 | Pe Ell                   |   1 |   53.22 | 0.0187899  |   2 |
| 121 | 27401 | Peninsula                |  18 | 1302.99 | 0.0138144  |   2 |
| 114 |  5121 | Port Angeles             |  13 |  568.67 | 0.0228604  |   2 |
| 114 | 16050 | Port Townsend            |   6 |  200.11 | 0.0299835  |   4 |
| 121 | 27003 | Puyallup                 |  69 | 2851    | 0.024202   |   2 |
| 171 | 13144 | Quincy                   |   5 |  425.45 | 0.0117523  |   2 |
| 121 | 17403 | Renton                   |  90 | 2286.23 | 0.0393661  |   4 |
| 123 |  3400 | Richland                 |   9 | 1599.44 | 0.00562697 |   2 |
| 112 |  6122 | Ridgefield               |  22 |  358.44 | 0.0613771  |   4 |
| 121 | 17407 | Riverview                |   1 |  352.78 | 0.00283463 |   2 |
| 113 | 34401 | Rochester                |  10 |  340    | 0.0294118  |   2 |
| 121 | 17001 | Seattle                  | 161 | 7656.34 | 0.0210283  |   2 |
| 189 | 29101 | Sedro-Woolley            |  35 |  816.44 | 0.042869   |   4 |
| 105 | 39119 | Selah                    |   1 |  492    | 0.00203252 |   2 |
| 113 | 23309 | Shelton                  |  15 |  733.11 | 0.0204608  |   2 |
| 121 | 17412 | Shoreline                |  42 | 1126.99 | 0.0372674  |   4 |
| 189 | 31201 | Snohomish                |  40 | 1280.88 | 0.0312285  |   4 |
| 121 | 17410 | Snoqualmie Valley        |  17 |  788.77 | 0.0215525  |   2 |
| 114 | 18402 | South Kitsap             |  43 | 1481.45 | 0.0290256  |   2 |
| 189 | 15206 | South Whidbey            |   6 |  208.55 | 0.0287701  |   2 |
| 101 | 32081 | Spokane                  |  44 | 4951.89 | 0.0088855  |   2 |
| 189 | 31401 | Stanwood-Camano          |  20 |  678.34 | 0.0294837  |   2 |
| 121 | 27001 | Steilacoom Hist.         |   7 |  415.11 | 0.016863   |   2 |
| 189 | 31311 | Sultan                   |   3 |  330.56 | 0.00907551 |   2 |
| 121 | 27320 | Sumner                   |  34 | 1221.55 | 0.0278335  |   2 |
| 121 | 27010 | Tacoma                   | 125 | 4368    | 0.0286172  |   2 |
| 121 | 17409 | Tahoma                   |  65 | 1073.21 | 0.060566   |   4 |
| 113 | 34402 | Tenino                   |   2 |  187.33 | 0.0106763  |   2 |
| 113 | 21237 | Toledo                   |   3 |  128.11 | 0.0234174  |   2 |
| 121 | 17406 | Tukwila                  |   4 |  355.22 | 0.0112606  |   2 |
| 121 | 27083 | University Place         |   7 |  607.56 | 0.0115215  |   2 |
| 101 | 33070 | Valley                   |   1 |   96    | 0.0104167  |   2 |
| 112 |  6037 | Vancouver                | 113 | 2988.67 | 0.0378095  |   4 |
| 121 | 17402 | Vashon Island            |   9 |  183.89 | 0.0489423  |   4 |
| 112 | 34975 | WA State CCDHL           |   3 |  102    | 0.0294118  |   2 |
| 112 |  6112 | Washougal                |  25 |  454.34 | 0.0550249  |   4 |
| 171 |  4246 | Wenatchee                |  14 |  945.89 | 0.0148009  |   2 |
| 105 | 39208 | West Valley 208          |   9 |  749.89 | 0.0120018  |   2 |
| 101 | 32363 | West Valley 363          |   4 |  509.11 | 0.00785685 |   2 |
| 121 | 27416 | White River              |   1 |  544.66 | 0.00183601 |   2 |
| 113 | 21232 | Winlock                  |   3 |  158.89 | 0.018881   |   2 |
| 112 |  8404 | Woodland                 |  22 |  344.66 | 0.063831   |   4 |
| 105 | 39007 | Yakima                   |   4 | 2214.45 | 0.00180632 |   2 |
| 113 | 34002 | Yelm                     |   5 |  802.32 | 0.00623193 |   2 |



label: F=D/E
labeled_formulas: F=D/E
output: {"Arithmetic-Relationship": ["F=D/E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_705270___xlsx_f16eba1f11c93d382cab19a5200caed6ea809c7b.xlsx___line_709