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 |
|:--------------------------|:--------|-----:|-----:|-----:|
| Niagara Falls             | NFL     | 1550 | 1629 |  -79 |
| Lancaster                 | ECIC    | 1259 | 1292 |  -33 |
| Orchard Park              | ECIC    | 1046 | 1026 |   20 |
| Lockport                  | NFL     | 1022 |  957 |   65 |
| Clarence                  | ECIC    | 1016 | 1076 |  -60 |
| Jamestown                 | CCAA    | 1016 | 1002 |   14 |
| Jamestown                 | CCAA    | 1016 | 1002 |   14 |
| Frontier                  | ECIC    | 1013 |  978 |   35 |
| Williamsville North       | ECIC    |  992 | 1029 |  -37 |
| Hutchinson Tech           | Buffalo |  891 |  888 |    3 |
| Niagara-Wheatfield        | NFL     |  888 |  860 |   28 |
| West Seneca West          | ECIC    |  848 |  855 |   -7 |
| Kenmore West              | NFL     |  824 |  762 |   62 |
| Sweet Home                | ECIC    |  803 |  743 |   60 |
| North Tonawanda           | NFL     |  773 |  744 |   29 |
| Williamsville East        | ECIC    |  755 |  734 |   21 |
| Hamburg                   | ECIC    |  752 |  822 |  -70 |
| McKinley                  | Buffalo |  719 |  726 |   -7 |
| Starpoint                 | ECIC    |  681 |  686 |   -5 |
| Grand Island              | NFL     |  674 |  723 |  -49 |
| Kenmore East              | NFL     |  672 |  690 |  -18 |
| Williamsville South       | ECIC    |  668 |  677 |   -9 |
| Amherst                   | ECIC    |  653 |  641 |   12 |
| South Park                | Buffalo |  635 |  797 | -162 |
| Charter/ Applied Tech     | NFL     |  555 |  521 |   34 |
| West Seneca East          | ECIC    |  554 |  573 |  -19 |
| Iroquois                  | ECIC    |  498 |  548 |  -50 |
| Pioneer                   | ECIC    |  497 |  501 |   -4 |
| Lake Shore                | ECIC    |  489 |  453 |   36 |
| Lewiston Porter           | NFL     |  482 |  488 |   -6 |
| Maryvale                  | ECIC    |  480 |  482 |   -2 |
| Cheektowaga               | ECIC    |  479 |  531 |  -52 |
| Dunkirk                   | CCAA    |  479 |  473 |    6 |
| International Prep        | Buffalo |  455 |  495 |  -40 |
| City Honors               | Buffalo |  450 |  447 |    3 |
| Olean                     | CCAA    |  428 |  483 |  -55 |
| East Aurora               | ECIC    |  417 |  485 |  -68 |
| Albion                    | NO      |  411 |  411 |    0 |
| Lackawanna                | ECIC    |  392 |  369 |   23 |
| Depew                     | ECIC    |  389 |  384 |    5 |
| Tonawanda                 | ECIC    |  389 |  380 |    9 |
| Alden                     | ECIC    |  378 |  362 |   16 |
| Burgard                   | Buffalo |  371 |  407 |  -36 |
| Fredonia                  | CCAA    |  365 |  344 |   21 |
| Springville Griffith Inst | ECIC    |  360 |  381 |  -21 |
| Frederick Olmsted         | Buffalo |  335 |  330 |    5 |
| Medina                    | NO      |  354 |  318 |   36 |
| Akron                     | NO      |  342 |  362 |  -20 |
| Buffalo Arts Academy      | Buffalo |  341 |  339 |    2 |
| Southwestern              | CCAA    |  339 |  305 |   34 |
| Lafayette International   | Buffalo |  323 |  266 |   57 |
| Leonardo Da Vinci         | Buffalo |  323 |  297 |   26 |
| Eden                      | ECIC    |  318 |  323 |   -5 |
| Buffalo Culinary Arts     | Buffalo |  309 |  287 |   22 |
| Health Sciences Charter   | Indep.  |  306 |  293 |   13 |
| Cleveland Hill            | ECIC    |  305 |  299 |    6 |
| Emerson                   | Buffalo |  305 |  321 |  -16 |
| Lewis J Bennett           | Buffalo |  305 |  269 |   36 |
| Newfane                   | NO      |  297 |  360 |  -63 |
| Allegany-Limestone        | CCAA    |  296 |  315 |  -19 |
| Salamanca                 | CCAA    |  296 |  267 |   29 |
| Falconer                  | CCAA    |  294 |  267 |   27 |
| Royalton-Hartland         | NO      |  285 |  302 |  -17 |
| John F Kennedy            | ECIC    |  267 |  296 |  -29 |
| WNY Maritime Charter      | Indep.  |  266 |  306 |  -40 |
| Tapestry Charter School   | Indep.  |  264 |  254 |   10 |
| Middle Early College      | Buffalo |  254 |  237 |   17 |
| Bflo Acad Science         | Indep.  |  252 |  228 |   24 |
| East Community            | Buffalo |  252 |  291 |  -39 |
| MST Prep                  | Buffalo |  249 |  263 |  -14 |
| Riverside Academy         | Buffalo |  243 |  246 |   -3 |
| Portville                 | CCAA    |  240 |  237 |    3 |
| Silver Creek              | CCAA    |  237 |  227 |   10 |
| Wilson                    | NO      |  234 |  267 |  -33 |
| Global Concepts Charter   | Indep.  |  225 |  218 |    7 |
| Randolph                  | CCAA    |  213 |  189 |   24 |
| Frewsburg                 | CCAA    |  212 |  204 |    8 |
| Holland                   | ECIC    |  212 |  194 |   18 |
| Gowanda                   | CCAA    |  209 |  236 |  -27 |
| Cassadaga Valley          | CCAA    |  204 |  209 |   -5 |
| Cattaraugus-Little Valley | CCAA    |  188 |  191 |   -3 |
| Chautauqua Lake           | CCAA    |  185 |  186 |   -1 |
| Research Lab              | Buffalo |  153 |  135 |   18 |
| Westfield                 | CCAA    |  149 |  140 |    9 |
| Barker                    | NO      |  146 |  170 |  -24 |
| Maple Grove               | CCAA    |  141 |  159 |  -18 |
| Ellicottville             | CCAA    |  135 |  125 |   10 |
| Franklinville             | CCAA    |  125 |  131 |   -6 |
| Academy @4                | Buffalo |  122 |   89 |   33 |
| Forestville               | CCAA    |  119 |  108 |   11 |
| Brocton                   | CCAA    |  114 |  122 |   -8 |
| Pine Valley               | CCAA    |  114 |  129 |  -15 |
| North Collins             | CCAA    |  113 |  134 |  -21 |
| Panama                    | CCAA    |  105 |   93 |   12 |
| Sherman                   | CCAA    |  105 |   78 |   27 |
| Clymer                    | CCAA    |   93 |   96 |   -3 |
| Pathways                  | Buffalo |   80 |  143 |  -63 |
| West Valley               | CCAA    |   45 |   38 |    7 |



label: E=C-D
labeled_formulas: E=C-D
output: {"Arithmetic-Relationship": ["E=C-D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_303916___xlsx_ccefde514baf06d80f4821e09be11a4e906feb9b.xlsx___line_562