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 |
|-----:|:-----------------------------------------|-----:|----------:|-------:|
| 2009 | Bowie State University                   |  706 |  497.024  | 0.704  |
| 2009 | Coppin State University                  |  566 |  341.864  | 0.604  |
| 2009 | Frostburg State University               | 1031 |  760.878  | 0.738  |
| 2009 | Salisbury University                     | 1279 | 1029.6    | 0.805  |
| 2009 | Towson University                        | 2398 | 2031.11   | 0.847  |
| 2009 | University of Baltimore                  |  174 |  132.936  | 0.764  |
| 2009 | University of Maryland, Baltimore County | 1524 | 1271.02   | 0.834  |
| 2009 | University of Maryland, College Park     | 4211 | 3992.03   | 0.948  |
| 2009 | University of Maryland Eastern Shore     |  876 |  564.144  | 0.644  |
| 2009 | Morgan State University                  | 1263 |  852.525  | 0.675  |
| 2009 | St. Mary's College of Maryland           |  488 |  426.024  | 0.873  |
| 2010 | Bowie State University                   |  671 |  493.185  | 0.735  |
| 2010 | Coppin State University                  |  525 |  333.9    | 0.636  |
| 2010 | Frostburg State University               | 1028 |  727.824  | 0.708  |
| 2010 | Salisbury University                     | 1253 | 1027.46   | 0.82   |
| 2010 | Towson University                        | 2428 | 2046.8    | 0.843  |
| 2010 | University of Baltimore                  |  163 |  125.999  | 0.773  |
| 2010 | University of Maryland, Baltimore County | 1499 | 1253.16   | 0.836  |
| 2010 | University of Maryland, College Park     | 3925 | 3697.35   | 0.942  |
| 2010 | University of Maryland Eastern Shore     |  944 |  641.92   | 0.68   |
| 2010 | Morgan State University                  | 1234 |  899.586  | 0.729  |
| 2010 | St. Mary's College of Maryland           |  442 |  385.866  | 0.873  |
| 2011 | Bowie State University                   |  623 |  444.199  | 0.713  |
| 2011 | Coppin State University                  |  486 |  317.844  | 0.654  |
| 2011 | Frostburg State University               |  825 |  594.825  | 0.721  |
| 2011 | Salisbury University                     | 1252 | 1040.41   | 0.831  |
| 2011 | Towson University                        | 2545 | 2175.97   | 0.855  |
| 2011 | University of Baltimore                  |  155 |  112.995  | 0.729  |
| 2011 | University of Maryland, Baltimore County | 1427 | 1191.54   | 0.835  |
| 2011 | University of Maryland, College Park     | 3990 | 3738.63   | 0.937  |
| 2011 | University of Maryland Eastern Shore     |  748 |  513.876  | 0.687  |
| 2011 | Morgan State University                  | 1068 |  765.756  | 0.717  |
| 2011 | St. Mary's College of Maryland           |  455 |  389.025  | 0.855  |
| 2012 | Bowie State University                   |  477 |  334.854  | 0.702  |
| 2012 | Coppin State University                  |  430 |  264.02   | 0.614  |
| 2012 | Frostburg State University               |  814 |  625.152  | 0.768  |
| 2012 | Salisbury University                     | 1231 |  977.414  | 0.794  |
| 2012 | Towson University                        | 2463 | 2118.18   | 0.86   |
| 2012 | University of Baltimore                  |  215 |  144.91   | 0.674  |
| 2012 | University of Maryland, Baltimore County | 1553 | 1324.71   | 0.853  |
| 2012 | University of Maryland, College Park     | 3896 | 3677.82   | 0.944  |
| 2012 | University of Maryland Eastern Shore     |  882 |  597.996  | 0.678  |
| 2012 | Morgan State University                  | 1017 |  733.257  | 0.721  |
| 2012 | St. Mary's College of Maryland           |  419 |  377.1    | 0.9    |
| 2013 | Bowie State University                   |  625 |  463.125  | 0.741  |
| 2013 | Coppin State University                  |  355 |  242.11   | 0.682  |
| 2013 | Frostburg State University               |  889 |  664.972  | 0.748  |
| 2013 | Salisbury University                     | 1249 | 1022.93   | 0.819  |
| 2013 | Towson University                        | 2747 | 2345.94   | 0.854  |
| 2013 | University of Baltimore                  |  236 |  185.968  | 0.788  |
| 2013 | University of Maryland, Baltimore County | 1666 | 1472.74   | 0.884  |
| 2013 | University of Maryland, College Park     | 4012 | 3835.47   | 0.956  |
| 2013 | University of Maryland Eastern Shore     |  604 |  439.712  | 0.728  |
| 2013 | Morgan State University                  |  886 |  667.158  | 0.753  |
| 2013 | St. Mary's College of Maryland           |  387 |  328.176  | 0.848  |
| 2014 | Bowie State University                   |  594 |  419.958  | 0.707  |
| 2014 | Coppin State University                  |  267 |  185.031  | 0.693  |
| 2014 | Frostburg State University               |  957 |  734.976  | 0.768  |
| 2014 | Salisbury University                     | 1144 |  935.792  | 0.818  |
| 2014 | Towson University                        | 2711 | 2323.33   | 0.857  |
| 2014 | University of Baltimore                  |  227 |  160.035  | 0.705  |
| 2014 | University of Maryland, Baltimore County | 1625 | 1395.88   | 0.859  |
| 2014 | University of Maryland, College Park     | 4129 | 3934.94   | 0.953  |
| 2014 | University of Maryland Eastern Shore     |  756 |  511.056  | 0.676  |
| 2014 | Morgan State University                  | 1058 |  794.558  | 0.751  |
| 2014 | St. Mary's College of Maryland           |  378 |  323.946  | 0.857  |
| 2015 | Bowie State University                   |  564 |  420.744  | 0.746  |
| 2015 | Coppin State University                  |  244 |  149.084  | 0.611  |
| 2015 | Frostburg State University               |  931 |  714.077  | 0.767  |
| 2015 | Salisbury University                     | 1186 |  976.078  | 0.823  |
| 2015 | Towson University                        | 2708 | 2307.22   | 0.852  |
| 2015 | University of Baltimore                  |  137 |   99.051  | 0.723  |
| 2015 | University of Maryland, Baltimore County | 1551 | 1313.7    | 0.847  |
| 2015 | University of Maryland, College Park     | 3936 | 3735.26   | 0.949  |
| 2015 | University of Maryland Eastern Shore     | 1009 |  584.211  | 0.579  |
| 2015 | Morgan State University                  | 1159 |  817.095  | 0.705  |
| 2015 | St. Mary's College of Maryland           |  393 |  339.945  | 0.865  |
| 2016 | Bowie State University                   |  964 |  681.548  | 0.707  |
| 2016 | Coppin State University                  |  383 |  243.971  | 0.637  |
| 2016 | Frostburg State University               |  829 |  610.973  | 0.737  |
| 2016 | Salisbury University                     | 1328 | 1099.58   | 0.828  |
| 2016 | Towson University                        | 2750 | 2329.25   | 0.847  |
| 2016 | University of Baltimore                  |  138 |   92.046  | 0.667  |
| 2016 | University of Maryland, Baltimore County | 1524 | 1295.4    | 0.85   |
| 2016 | University of Maryland, College Park     | 4559 | 4349.29   | 0.954  |
| 2016 | University of Maryland Eastern Shore     |  698 |  445.324  | 0.638  |
| 2016 | Morgan State University                  | 1123 |  829.897  | 0.739  |
| 2016 | St. Mary's College of Maryland           |  334 |  290.914  | 0.871  |
| 2017 | Bowie State University                   | 1079 |  728.972  | 0.6756 |
| 2017 | Coppin State University                  |  383 |  239.988  | 0.6266 |
| 2017 | Frostburg State University               |  777 |  596.037  | 0.7671 |
| 2017 | Salisbury University                     | 1326 | 1093.95   | 0.825  |
| 2017 | Towson University                        | 2735 | 2316      | 0.8468 |
| 2017 | University of Baltimore                  |  107 |   80.0039 | 0.7477 |
| 2017 | University of Maryland, Baltimore County | 1773 | 1474.96   | 0.8319 |
| 2017 | University of Maryland, College Park     | 5187 | 4906.9    | 0.946  |
| 2017 | University of Maryland Eastern Shore     |  560 |  348.992  | 0.6232 |
| 2017 | Morgan State University                  | 1192 |  855.022  | 0.7173 |
| 2017 | St. Mary's College of Maryland           |  341 |  279.006  | 0.8182 |
| 2018 | Bowie State University                   |  898 |  622.045  | 0.6927 |
| 2018 | Coppin State University                  |  389 |  271.016  | 0.6967 |
| 2018 | Frostburg State University               |  735 |  538.976  | 0.7333 |
| 2018 | Salisbury University                     | 1285 | 1010.01   | 0.786  |
| 2018 | Towson University                        | 2990 | 2572      | 0.8602 |
| 2018 | University of Baltimore                  |   76 |   62.0008 | 0.8158 |
| 2018 | University of Maryland, Baltimore County | 1786 | 1467.91   | 0.8219 |
| 2018 | University of Maryland, College Park     | 6038 | 5689      | 0.9422 |
| 2018 | University of Maryland Eastern Shore     |  501 |  306.011  | 0.6108 |
| 2018 | Morgan State University                  | 1326 |  927.935  | 0.6998 |
| 2018 | St. Mary's College of Maryland           |  376 |  313.998  | 0.8351 |



label: D=C*E
labeled_formulas: D=C*E
output: {"Arithmetic-Relationship": ["D=C*E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_682245___xlsx_84888262f0a2c160f026de46ec63ea17761b9805.xlsx___line_411