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 |
|-----:|----:|:-------------------------------------|---------:|----------:|--------:|
| 2022 | 800 | Acceleration Day and Evening Academy |   528.55 |   3173766 | 6004.67 |
| 2022 | 102 | Alexander City                       |  2853.45 |  15614790 | 5472.25 |
| 2022 | 104 | Andalusia City                       |  1724.2  |   9916550 | 5751.39 |
| 2022 | 105 | Anniston City                        |  1738.75 |   9795688 | 5633.75 |
| 2022 | 109 | Attalla City                         |  1440.35 |   9042663 | 6278.1  |
| 2022 |   3 | Barbour County                       |   646.7  |   3148181 | 4868.07 |
| 2022 | 113 | Bessemer City                        |  3229.1  |  17113648 | 5299.82 |
| 2022 |   4 | Bibb County                          |  3052.15 |  19042924 | 6239.18 |
| 2022 | 114 | Birmingham City                      | 20818.8  | 105370289 | 5061.32 |
| 2022 |   5 | Blount County                        |  7612.05 |  46104088 | 6056.72 |
| 2022 | 115 | Boaz City                            |  2337.45 |  14270001 | 6104.94 |
| 2022 |   6 | Bullock County                       |  1386.5  |   8552322 | 6168.28 |
| 2022 |   7 | Butler County                        |  2825.3  |  16333086 | 5781.01 |
| 2022 |   8 | Calhoun County                       |  7817.05 |  46950255 | 6006.13 |
| 2022 |  10 | Cherokee County                      |  3686.15 |  21770064 | 5905.91 |
| 2022 | 121 | Chickasaw City                       |  2691.3  |  15818104 | 5877.5  |
| 2022 |  11 | Chilton County                       |  7396.95 |  42414794 | 5734.09 |
| 2022 |  12 | Choctaw County                       |  1070.75 |   4797483 | 4480.49 |
| 2022 |  14 | Clay County                          |  1794.95 |  10887222 | 6065.47 |
| 2022 |  15 | Cleburne County                      |  2436.1  |  15557774 | 6386.34 |
| 2022 |  16 | Coffee County                        |  2569.95 |  14760302 | 5743.42 |
| 2022 |  17 | Colbert County                       |  2498.65 |  12875988 | 5153.18 |
| 2022 |  20 | Covington County                     |  2755.1  |  16030086 | 5818.33 |
| 2022 |  22 | Cullman County                       |  9185.05 |  56013578 | 6098.34 |
| 2022 |  23 | Dale County                          |  3381.4  |  20804082 | 6152.51 |
| 2022 | 126 | Daleville City                       |  1084.85 |   6545338 | 6033.4  |
| 2022 |  24 | Dallas County                        |  2738.3  |  16469127 | 6014.36 |
| 2022 | 127 | Decatur City                         |  8520.35 |  46916521 | 5506.41 |
| 2022 |  25 | DeKalb County                        |  8332.75 |  50838253 | 6101.02 |
| 2022 | 128 | Demopolis City                       |  2052.95 |  12425159 | 6052.34 |
| 2022 | 130 | Dothan City                          |  8049.6  |  41637261 | 5172.59 |
| 2022 | 131 | Elba City                            |   612.3  |   3878267 | 6333.93 |
| 2022 | 137 | Fairfield City                       |  1534.15 |   9186923 | 5988.28 |
| 2022 |  29 | Fayette County                       |  2126    |  12715750 | 5981.07 |
| 2022 | 141 | Florence City                        |  4476.75 |  24723734 | 5522.7  |
| 2022 | 143 | Fort Payne City                      |  3353.5  |  19776344 | 5897.22 |
| 2022 |  30 | Franklin County                      |  3490.65 |  21604943 | 6189.38 |
| 2022 | 144 | Gadsden City                         |  4824.95 |  27980332 | 5799.09 |
| 2022 |  31 | Geneva County                        |  2538.85 |  15811378 | 6227.77 |
| 2022 |  32 | Greene County                        |   913.05 |   5070540 | 5553.41 |
| 2022 |  33 | Hale County                          |  2270.95 |  13840220 | 6094.46 |
| 2022 | 155 | Haleyville City                      |  1573.9  |   9609492 | 6105.53 |
| 2022 |  35 | Houston County                       |  6177.6  |  33779840 | 5468.12 |
| 2022 | 805 | i3 Academy                           |   512.3  |   3313118 | 6467.14 |
| 2022 |  37 | Jefferson County                     | 34576.1  | 190678303 | 5514.74 |
| 2022 |  38 | Lamar County                         |  2190.55 |  13397922 | 6116.24 |
| 2022 | 165 | Lanett City                          |   943.15 |   5866087 | 6219.68 |
| 2022 | 802 | LEAD Academy                         |   501.15 |   3231379 | 6447.93 |
| 2022 |  41 | Lee County                           |  9065.7  |  51299615 | 5658.65 |
| 2022 | 803 | Legacy Prep                          |   302.7  |   2008308 | 6634.65 |
| 2022 | 168 | Linden City                          |   478.4  |   3312362 | 6923.83 |
| 2022 |  43 | Lowndes County                       |  1306.05 |   7774928 | 5953.01 |
| 2022 |  44 | Macon County                         |  1897.15 |  12242932 | 6453.33 |
| 2022 |  46 | Marengo County                       |   912.15 |   5051127 | 5537.61 |
| 2022 |  47 | Marion County                        |  3190.85 |  19091579 | 5983.23 |
| 2022 |  48 | Marshall County                      |  5528.45 |  32718895 | 5918.28 |
| 2022 | 171 | Midfield City                        |  1013.4  |   6315048 | 6231.55 |
| 2022 |  49 | Mobile County                        | 51299.8  | 271166530 | 5285.92 |
| 2022 |  50 | Monroe County                        |  3056.6  |  17024992 | 5569.91 |
| 2022 |  51 | Montgomery County                    | 27503.9  | 151548473 | 5510.07 |
| 2022 |  52 | Morgan County                        |  7271.7  |  39338372 | 5409.79 |
| 2022 | 179 | Opelika City                         |  4688.3  |  24549408 | 5236.31 |
| 2022 | 180 | Opp City                             |  1227.95 |   7752174 | 6313.1  |
| 2022 | 181 | Oxford City                          |  4050.1  |  22296631 | 5505.21 |
| 2022 | 182 | Ozark City                           |  1947    |  11606699 | 5961.32 |
| 2022 |  53 | Perry County                         |  1123.15 |   6600603 | 5876.87 |
| 2022 | 184 | Phenix City                          |  7073.6  |  42706690 | 6037.48 |
| 2022 |  54 | Pickens County                       |  2311.45 |  13985000 | 6050.31 |
| 2022 | 185 | Piedmont City                        |  1096.4  |   7144969 | 6516.75 |
| 2022 |  55 | Pike County                          |  2102.3  |  12438155 | 5916.45 |
| 2022 |  56 | Randolph County                      |  1987    |  11344346 | 5709.28 |
| 2022 |  57 | Russell County                       |  3396.95 |  18939223 | 5575.36 |
| 2022 | 189 | Russellville City                    |  2442.05 |  15062339 | 6167.91 |
| 2022 | 191 | Selma City                           |  2674.2  |  16169356 | 6046.43 |
| 2022 | 192 | Sheffield City                       |   972.1  |   5745691 | 5910.6  |
| 2022 |  60 | Sumter County                        |  1138.25 |   6527235 | 5734.45 |
| 2022 | 193 | Sylacauga City                       |  2011    |  11601797 | 5769.17 |
| 2022 | 194 | Talladega City                       |  1803.55 |  11051568 | 6127.67 |
| 2022 |  61 | Talladega County                     |  6827.3  |  35575127 | 5210.72 |
| 2022 |  62 | Tallapoosa County                    |  2684.55 |  12516078 | 4662.26 |
| 2022 | 195 | Tallassee City                       |  1614.45 |   9978672 | 6180.85 |
| 2022 | 198 | Thomasville City                     |  1064.4  |   6708634 | 6302.74 |
| 2022 | 199 | Troy City                            |  1645.6  |   8860803 | 5384.54 |
| 2022 | 200 | Tuscaloosa City                      | 10275.6  |  51434508 | 5005.5  |
| 2022 |  63 | Tuscaloosa County                    | 18165.5  |  98651508 | 5430.72 |
| 2022 | 201 | Tuscumbia City                       |  1429.75 |   8993773 | 6290.45 |
| 2022 | 801 | University Charter School            |   538    |   3597148 | 6686.15 |
| 2022 |  64 | Walker County                        |  6938.7  |  40236997 | 5798.92 |
| 2022 |  65 | Washington County                    |  2520.75 |  13642468 | 5412.07 |
| 2022 |  66 | Wilcox County                        |  1324.1  |   7385171 | 5577.5  |
| 2022 |  67 | Winston County                       |  2186.95 |  13136865 | 6006.93 |



label: F=E/D
labeled_formulas: F=E/D
output: {"Arithmetic-Relationship": ["F=E/D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_733924___xlsx_cbb8798c98f56e7a14f804853ae7e879bffd1911.xlsx___line_560