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 |
|-------:|:--------------------------|---------:|----------:|--------:|
| 100300 | Barbour County            |   646.7  |   2990560 | 4624.34 |
| 100420 | Blount County             |  7612.05 |  44501693 | 5846.22 |
| 100480 | Bullock County            |  1386.5  |   8358327 | 6028.36 |
| 100510 | Butler County             |  2825.3  |  15824613 | 5601.04 |
| 100630 | Cherokee County           |  3686.15 |  21398029 | 5804.98 |
| 100660 | Chilton County            |  7396.95 |  42280015 | 5715.87 |
| 100690 | Choctaw County            |  1070.75 |   5197308 | 4853.89 |
| 100750 | Clay County               |  1794.95 |  11049112 | 6155.67 |
| 100780 | Cleburne County           |  2436.1  |  15171092 | 6227.61 |
| 100810 | Coffee County             |  2569.95 |  14301358 | 5564.84 |
| 100840 | Colbert County            |  2498.65 |  13027470 | 5213.8  |
| 100930 | Covington County          |  2755.1  |  16313072 | 5921.05 |
| 101020 | Cullman County            |  9185.05 |  53858883 | 5863.76 |
| 101050 | Dale County               |  3381.4  |  20284382 | 5998.81 |
| 101140 | DeKalb County             |  8332.75 |  51464102 | 6176.12 |
| 101470 | Fayette County            |  2126    |  12654895 | 5952.44 |
| 101660 | Geneva County             |  2538.85 |  15723305 | 6193.08 |
| 101680 | Greene County             |   913.05 |   5006997 | 5483.81 |
| 101710 | Hale County               |  2270.95 |  13669194 | 6019.15 |
| 101770 | Houston County            |  6177.6  |  33410070 | 5408.26 |
| 101920 | Jefferson County          | 34576.1  | 193459257 | 5595.17 |
| 101950 | Lamar County              |  2190.55 |  13160486 | 6007.85 |
| 102070 | Lee County                |  9065.7  |  50723328 | 5595.08 |
| 102160 | Lowndes County            |  1306.05 |   7625627 | 5838.69 |
| 102190 | Macon County              |  1897.15 |  11519743 | 6072.13 |
| 102250 | Marengo County            |   912.15 |   5135982 | 5630.63 |
| 102310 | Marion County             |  3190.85 |  18585384 | 5824.59 |
| 100006 | Marshall County           |  5528.45 |  32356456 | 5852.72 |
| 102370 | Mobile County             | 51299.8  | 273470885 | 5330.84 |
| 102430 | Montgomery County         | 27503.9  | 147258770 | 5354.11 |
| 102480 | Morgan County             |  7271.7  |  38538076 | 5299.73 |
| 102670 | Perry County              |  1123.15 |   6455816 | 5747.96 |
| 102730 | Pickens County            |  2311.45 |  14345659 | 6206.35 |
| 102790 | Pike County               |  2102.3  |  12345885 | 5872.56 |
| 102820 | Randolph County           |  1987    |  11668672 | 5872.51 |
| 102880 | Russell County            |  3396.95 |  18768350 | 5525.06 |
| 103090 | Sumter County             |  1138.25 |   6372522 | 5598.53 |
| 103180 | Talladega County          |  6827.3  |  37108153 | 5435.26 |
| 103210 | Tallapoosa County         |  2684.55 |  12798311 | 4767.4  |
| 103390 | Tuscaloosa County         | 18165.5  | 100306154 | 5521.81 |
| 103450 | Walker County             |  6938.7  |  40211377 | 5795.23 |
| 103480 | Washington County         |  2520.75 |  12946856 | 5136.11 |
| 103510 | Wilcox County             |  1324.1  |   7795244 | 5887.2  |
| 103580 | Winston County            |  2186.95 |  12819596 | 5861.86 |
| 100030 | Alexander City            |  2853.45 |  15921063 | 5579.58 |
| 100060 | Andalusia City            |  1724.2  |   9813128 | 5691.41 |
| 100090 | Anniston City             |  1738.75 |   8726387 | 5018.77 |
| 100180 | Attalla City              |  1440.35 |   9011232 | 6256.28 |
| 100330 | Bessemer City             |  3229.1  |  18483155 | 5723.93 |
| 100390 | Birmingham City           | 20818.8  | 110772236 | 5320.79 |
| 100012 | Boaz City                 |  2337.45 |  13842471 | 5922.04 |
| 100188 | Chickasaw City            |  2691.3  |   7479273 | 2779.06 |
| 101080 | Daleville City            |  1084.85 |   6150070 | 5669.05 |
| 101170 | Decatur City              |  8520.35 |  46048271 | 5404.5  |
| 101200 | Demopolis City            |  2052.95 |  12546738 | 6111.57 |
| 101230 | Dothan City               |  8049.6  |  43562792 | 5411.8  |
| 101260 | Elba City                 |   612.3  |   3728277 | 6088.97 |
| 101440 | Fairfield City            |  1534.15 |   9784294 | 6377.66 |
| 101560 | Fort Payne City           |  3353.5  |  18224242 | 5434.39 |
| 101620 | Gadsden City              |  4824.95 |  28270859 | 5859.31 |
| 101720 | Haleyville City           |  1573.9  |   9463688 | 6012.89 |
| 101980 | Lanett City               |   943.15 |   5580250 | 5916.61 |
| 102130 | Linden City               |   478.4  |   3140419 | 6564.42 |
| 102350 | Midfield City             |  1013.4  |   6109338 | 6028.56 |
| 102580 | Opelika City              |  4688.3  |  23757924 | 5067.49 |
| 102610 | Opp City                  |  1227.95 |   7612844 | 6199.64 |
| 102635 | Oxford City               |  4050.1  |  21961713 | 5422.51 |
| 102640 | Ozark City                |  1947    |  11803754 | 6062.53 |
| 102700 | Phenix City               |  7073.6  |  42486633 | 6006.37 |
| 102760 | Piedmont City             |  1096.4  |   6577761 | 5999.42 |
| 102910 | Russellville City         |  2442.05 |  14956940 | 6124.75 |
| 102970 | Selma City                |  2674.2  |  16409141 | 6136.09 |
| 103000 | Sheffield City            |   979.1  |   5688829 | 5810.26 |
| 103120 | Sylacauga City            |  2011    |  11265028 | 5601.7  |
| 103150 | Talladega City            |  1803.55 |  11137943 | 6175.57 |
| 103240 | Tallassee City            |  1614.45 |   9584462 | 5936.67 |
| 103300 | Thomasville City          |  1064.4  |   6608456 | 6208.62 |
| 103420 | Tuscumbia City            |  1429.75 |   8725792 | 6103.02 |
| 100197 | Accel Academy             |   328.55 |   2028574 | 6174.32 |
| 100199 | University Charter School |   478    |   2623594 | 5488.69 |
| 100203 | Lead Academy              |   453.15 |   2207578 | 4871.63 |
| 100201 | Legacy Prep               |   252.7  |    981497 | 3884.04 |
| 100204 | I3 Academy                |   412.3  |   2896167 | 7024.42 |



label: E=D/C
labeled_formulas: E=D/C
output: {"Arithmetic-Relationship": ["E=D/C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_733923___xlsx_cbb8798c98f56e7a14f804853ae7e879bffd1911.xlsx___line_559