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 |
|-------:|:-------------------------------------|-----------------:|----:|-----------------:|-----------------:|
| 101420 | Acad Engagement & Degree Completion  | 243851           |   0 |  22271           | 266122           |
| 101393 | Academic Budget & Resource Mgmt      | 213052           |   0 |   6579           | 219631           |
| 101338 | Academic Operations & Admin          | 338119           |   0 |  10174.9         | 348294           |
| 100331 | Academic Personnel                   | 124779           |   0 |   9900           | 134679           |
| 101358 | Accreditation, Assessmt, & Learning  | 242737           |   0 |  45224.5         | 287961           |
| 101316 | Admissions Operations Systems        | 302012           |   0 |  14893.8         | 316906           |
| 100192 | Aerospace Studies                    |  36316.8         |   0 |  11596           |  47912.8         |
| 100247 | Career Exploration and Development   | 601104           |   0 |  15363           | 616467           |
| 101475 | China Center                         |      0           |   0 | 350346           | 350346           |
| 101098 | Curriculum Services                  | 209957           |   0 |  50190           | 260147           |
| 101376 | Destination Kent State (3)           |  78034           |   0 | 656691           | 734725           |
| 101555 | Enrollment Management                | 185711           |   0 |      0           | 185711           |
| 101075 | EXCEL                                |  20092           |   0 |   8990           |  29082           |
| 100310 | Faculty Affairs                      | 240551           |   0 |   4763           | 245314           |
| 100207 | Faculty Senate                       |  36910           |   0 |  20407           |  57317           |
| 101289 | Graduate Studies Fellowship          |      0           |   0 |  55557.3         |  55557.3         |
| 101337 | Graduation Planning System           | 362961           |   0 |  11843.8         | 374805           |
| 100181 | Honors College                       |      1.09554e+06 |   0 |  70980.4         |      1.16652e+06 |
| 101474 | India Center                         |      0           |   0 | 194655           | 194655           |
| 101227 | Instructional Technology             |      0           |   0 | 854052           | 854052           |
| 101571 | International Agent Commissions      |      0           |   0 | 214353           | 214353           |
| 101369 | Invest/Subvention Pool - Provost     |      0           |   0 |      1.81497e+06 |      1.81497e+06 |
| 101430 | LaunchNET                            |  55000           |   0 |      0           |  55000           |
| 101197 | Library Collection Development       |      0           |   0 |      5.23518e+06 |      5.23518e+06 |
| 100340 | Liquid Crystal Institute (4)         | 704647           |   0 |  38292.9         | 742939           |
| 101415 | Math Emporium - Technology Costs     |      0           |   0 |  70000           |  70000           |
| 101213 | May 4 Commemoration (4)              |      0           |   0 |  10000           |  10000           |
| 100193 | Military Science                     |  39662.4         |   0 |  10560           |  50222.4         |
| 101113 | Off of Cont & Dist Educ Non Credit   |      0           |   0 |  18271.5         |  18271.5         |
| 100438 | Off of Continuing & Dist Educ        | 456906           |   0 |  40221.5         | 497127           |
| 101454 | Office of ACAA                       | 213553           |   0 |  19513           | 233066           |
| 100323 | Office of Global Education           | 291248           |   0 |  64182.6         | 355430           |
| 101556 | OGE - Non Center Recruitment         |      0           |   0 |  64197.8         |  64197.8         |
| 101579 | OGE Advancement                      |      0           |   0 |  15000.1         |  15000.1         |
| 101598 | OGE Assoc Provost Contingency        |      0           |   0 |  42019.1         |  42019.1         |
| 101583 | OGE Education Abroad                 | 230623           |   0 |  31555.9         | 262179           |
| 101581 | OGE Partnership & Marketing          | 226494           |   0 |  68678.1         | 295173           |
| 101205 | Provost Initiative Funding           |      0           |   0 | 200000           | 200000           |
| 100208 | Provost's Contingency                |      0           |   0 |     -1.47042e+06 |     -1.47042e+06 |
| 100301 | Provost's Office                     |      1.33232e+06 |   0 | 103700           |      1.43602e+06 |
| 100250 | Student Financial Aid Office         |      1.47559e+06 |   0 | 184159           |      1.65975e+06 |
| 100194 | Summer Sessions & Services           |      0           |   0 |  14250           |  14250           |
| 101064 | Teaching Assistant Orientation       |  40000           |   0 |  44350           |  84350           |
| 100203 | Teleproductions (4)                  | 519840           |   0 |      0           | 519840           |
| 101010 | The Kent State University Museum (4) | 398443           |   0 |      0           | 398443           |
| 101478 | Transfer Kent State (3)              |      0           |   0 |  46780           |  46780           |
| 101562 | UC Academic Diversity Success        | 129853           |   0 |   5271           | 135124           |
| 101572 | ULI One-Stop                         | 709370           |   0 |      0           | 709370           |
| 101141 | University College Dean              | 630094           |   0 |  19404           | 649498           |
| 101437 | University College Technology        | 212564           |   0 |  65970           | 278534           |
| 100210 | University Libraries                 |      5.18518e+06 |   0 | 408914           |      5.5941e+06  |
| 100434 | University Press                     | 431475           |   0 | 449449           | 880924           |
| 100243 | University Registrar's Office        | 917705           |   0 | 122707           |      1.04041e+06 |
| 101167 | University Teaching Council          | 128736           |   0 |  76832           | 205568           |



labeled_formulas: F=C+E
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_290564___xlsx_8b9c624d9dc64991c79d14f1c3548045ba26fa98.xlsx___line_486