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 |
|------:|:----------------------------------------------|---------:|---------:|-------:|
|  1010 | Alcona Community Schools                      |  13484.5 |  1583.51 |  15068 |
|  2010 | AuTrain-Onota Public Schools                  |  10000   |     0    |  10000 |
|  2020 | Burt Township School District                 |  10000   |     0    |  10000 |
|  2070 | Munising Public Schools                       |  10000   |     0    |  10000 |
|  2080 | Superior Central School District              |  10000   |     0    |  10000 |
|  3010 | Plainwell Community Schools                   |  18117.3 |  2127.68 |  20245 |
|  3020 | Otsego Public Schools                         |  13020.3 |  1529.69 |  14550 |
|  3030 | Allegan Public Schools                        |  24128.1 |  2833.93 |  26962 |
|  3040 | Wayland Union Schools                         |  15808.4 |  1856.57 |  17665 |
|  3050 | Fennville Public Schools                      |  19138.6 |  2248.39 |  21387 |
|  3060 | Martin Public Schools                         |  10000   |     0    |  10000 |
|  3070 | Hopkins Public Schools                        |  10000   |     0    |  10000 |
|  3080 | Saugatuck Public Schools                      |  10000   |     0    |  10000 |
|  3100 | Hamilton Community Schools                    |  10000   |     0    |  10000 |
|  3900 | Innocademy Allegan Campus                     |  10000   |     0    |  10000 |
|  3902 | Outlook Academy                               |  10000   |     0    |  10000 |
|  4010 | Alpena Public Schools                         |  54667.2 |  6420.84 |  61088 |
|  5010 | Alba Public Schools                           |  10000   |     0    |  10000 |
|  5035 | Central Lake Public Schools                   |  10000   |     0    |  10000 |
|  5040 | Bellaire Public Schools                       |  10000   |     0    |  10000 |
|  5060 | Elk Rapids Schools                            |  11093.5 |  1303.47 |  12397 |
|  5065 | Ellsworth Community School                    |  10000   |     0    |  10000 |
|  5070 | Mancelona Public Schools                      |  17233.9 |  2024.13 |  19258 |
|  6010 | Arenac Eastern School District                |  10000   |     0    |  10000 |
|  6020 | Au Gres-Sims School District                  |  10000   |     0    |  10000 |
|  6050 | Standish-Sterling Community Schools           |  21494.6 |  2524.37 |  24019 |
|  7020 | Baraga Area Schools                           |  10000   |     0    |  10000 |
|  7040 | L'Anse Area Schools                           |  10000   |   338    |  10338 |
|  8010 | Delton Kellogg Schools                        |  13130.4 |  1542.6  |  14673 |
|  8030 | Hastings Area School District                 |  23647.3 |  2777.69 |  26425 |
|  8050 | Thornapple Kellogg School District            |  12404.2 |  1456.82 |  13861 |
|  9010 | Bay City School District                      | 147875   | 17369.2  | 165244 |
|  9030 | Bangor Township Schools                       |  27656.2 |  3248.81 |  30905 |
|  9050 | Essexville-Hampton Public Schools             |  10368.5 |  1217.48 |  11586 |
|  9090 | Pinconning Area Schools                       |  18665.3 |  2192.65 |  20858 |
|  9901 | Bay-Arenac Community High School              |  10000   |     0    |  10000 |
|  9902 | State Street Academy                          |  10000   |     0    |  10000 |
|  9903 | Bay City Academy                              |  10445.2 |  1226.81 |  11672 |
| 10015 | Benzie County Central Schools                 |  19405.4 |  2279.58 |  21685 |
| 10025 | Frankfort-Elberta Area Schools                |  10000   |     0    |  10000 |
| 11010 | Benton Harbor Area Schools                    | 256884   | 30173.6  | 287058 |
| 11020 | St. Joseph Public Schools                     |  12764.4 |  1499.57 |  14264 |
| 11030 | Lakeshore School District (Berrien)           |  14720.2 |  1728.76 |  16449 |
| 11033 | River Valley School District                  |  10664.2 |  1252.78 |  11917 |
| 11200 | New Buffalo Area Schools                      |  12816.4 |  1505.61 |  14322 |
| 11210 | Brandywine Community Schools                  |  17134.5 |  2012.55 |  19147 |
| 11240 | Berrien Springs Public Schools                |  29336.8 |  3446.19 |  32783 |
| 11250 | Eau Claire Public Schools                     |  26909.3 |  3160.67 |  30070 |
| 11300 | Niles Community Schools                       |  57705.5 |  6778.5  |  64484 |
| 11310 | Buchanan Community Schools                    |  21395.8 |  2513.15 |  23909 |
| 11320 | Watervliet School District                    |  14739.6 |  1731.44 |  16471 |
| 11330 | Coloma Community Schools                      |  46060.6 |  5410.42 |  51471 |
| 11340 | Bridgman Public Schools                       |  10000   |   151    |  10151 |
| 11670 | Hagar Township S/D #6                         |  10000   |     0    |  10000 |
| 11830 | Sodus Township S/D #5                         |  10000   |     0    |  10000 |
| 11901 | Countryside Academy                           |  20817.6 |  2445.42 |  23263 |
| 11903 | Benton Harbor Charter School Academy          |  19927.7 |  2340.34 |  22268 |
| 11904 | Mildred C. Wells Preparatory Academy          |  10000   |     0    |  10000 |
| 12010 | Coldwater Community Schools                   |  44989.1 |  5284.9  |  50274 |
| 12020 | Bronson Community School District             |  20171   |  2369.04 |  22540 |
| 12040 | Quincy Community Schools                      |  25595.2 |  3006.82 |  28602 |
| 12901 | Pansophia Academy                             |  16678.9 |  1959.15 |  18638 |
| 13020 | Battle Creek Public Schools                   | 187547   | 22029.3  | 209576 |
| 13050 | Athens Area Schools                           |  10000   |     0    |  10000 |
| 13070 | Harper Creek Community Schools                |  19542   |  2295.01 |  21837 |
| 13080 | Homer Community School District               |  10000   |   647    |  10647 |
| 13090 | Lakeview Sch. District (Calhoun)              |  34840.4 |  4092.56 |  38933 |
| 13095 | Mar Lee School District                       |  10000   |     0    |  10000 |
| 13110 | Marshall Public Schools                       |  59815.4 |  7025.63 |  66841 |
| 13120 | Pennfield Schools                             |  14648.1 |  1720.92 |  16369 |
| 13130 | Tekonsha Community Schools                    |  10000   |   265    |  10265 |
| 13135 | Union City Community Schools                  |  12426.8 |  1459.21 |  13886 |
| 13900 | Battle Creek Montessori Academy               |  10000   |     0    |  10000 |
| 13901 | Arbor Academy                                 |  10000   |     0    |  10000 |
| 13902 | Endeavor Charter Academy                      |  16929   |  1988.99 |  18918 |
| 13903 | Marshall Academy                              |  10000   |     0    |  10000 |
| 13904 | Battle Creek Area Learning Center             |  10000   |     0    |  10000 |
| 13905 | Lakeside Charter School - Albion              |      0   | 10000    |  10000 |
| 14010 | Cassopolis Public Schools                     |  16998.6 |  1996.36 |  18995 |
| 14020 | Dowagiac Union School District                |  47485.5 |  5577.49 |  53063 |
| 14030 | Edwardsburg Public Schools                    |  12713   |  1493.02 |  14206 |
| 14050 | Marcellus Community Schools                   |  10000   |     0    |  10000 |
| 15010 | Beaver Island Community School                |  10000   |     0    |  10000 |
| 15020 | Boyne City Public Schools                     |  10205.7 |  1198.3  |  11404 |
| 15030 | Boyne Falls Public School District            |  10000   |     0    |  10000 |
| 15050 | Charlevoix Public Schools                     |  12021.2 |  1411.75 |  13433 |
| 15060 | East Jordan Public Schools                    |  13837.8 |  1625.25 |  15463 |
| 15901 | Concord Academy - Boyne                       |  10000   |     0    |  10000 |
| 15902 | Charlevoix Montessori Academy for the Arts    |  10000   |     0    |  10000 |
| 16015 | Cheboygan Area Schools                        |  34026.6 |  3996.44 |  38023 |
| 16050 | Inland Lakes Schools                          |  15341.9 |  1802.1  |  17144 |
| 16070 | Mackinaw City Public Schools                  |  10000   |     0    |  10000 |
| 16100 | Wolverine Community School District           |  10000   |     0    |  10000 |
| 17010 | Sault Ste. Marie Area Schools                 |  38276.9 |  4496.1  |  42773 |
| 17050 | DeTour Area Schools                           |  10000   |     0    |  10000 |
| 17090 | Pickford Public Schools                       |  10000   |     0    |  10000 |
| 17110 | Rudyard Area Schools                          |  23093.7 |  2712.31 |  25806 |
| 17140 | Brimley Area Schools                          |  10000   |     0    |  10000 |
| 17160 | Whitefish Township Schools                    |  10000   |     0    |  10000 |
| 17901 | Joseph K. Lumsden Bahweting Anishnabe Academy |  10041.6 |  1179.45 |  11221 |
| 17902 | Ojibwe Charter School                         |  10000   |     0    |  10000 |
| 17903 | DeTour Arts and Technology Academy            |  10000   |     0    |  10000 |
| 18010 | Clare Public Schools                          |  25294.5 |  2971.48 |  28266 |
| 18020 | Farwell Area Schools                          |  34190.5 |  4016.48 |  38207 |
| 18060 | Harrison Community Schools                    |  59624   |  7003.04 |  66627 |
| 19010 | DeWitt Public Schools                         |  10000   |     0    |  10000 |
| 19070 | Fowler Public Schools                         |  10000   |     0    |  10000 |
| 19100 | Bath Community Schools                        |  10000   |     0    |  10000 |
| 19120 | Ovid-Elsie Area Schools                       |  14787.3 |  1736.74 |  16524 |
| 19125 | Pewamo-Westphalia Community Schools           |  10000   |     0    |  10000 |
| 19140 | St. Johns Public Schools                      |  16930.5 |  1988.53 |  18919 |
| 19900 | Michigan International Prep School            |  10000   |     0    |  10000 |
| 20015 | Crawford AuSable Schools                      |  35307.5 |  4147.45 |  39455 |
| 21010 | Escanaba Area Public Schools                  |  38548.1 |  4527.91 |  43076 |
| 21025 | Gladstone Area Schools                        |  10000   |   813    |  10813 |
| 21060 | Rapid River Public Schools                    |  10000   |     0    |  10000 |
| 21065 | Big Bay De Noc School District                |  10000   |     0    |  10000 |
| 21090 | Bark River-Harris School District             |  10000   |     0    |  10000 |
| 21135 | Mid Peninsula School District                 |  10000   |     0    |  10000 |
| 22010 | Iron Mountain Public Schools                  |  13679.3 |  1606.74 |  15286 |
| 22025 | Norway-Vulcan Area Schools                    |  10000   |     0    |  10000 |
| 22030 | Breitung Township School District             |  10036.5 |  1178.47 |  11215 |
| 22045 | North Dickinson County Schools                |  10000   |     0    |  10000 |
| 23010 | Bellevue Community Schools                    |  13468.2 |  1581.77 |  15050 |
| 23030 | Charlotte Public Schools                      |  24139.2 |  2835.75 |  26975 |
| 23050 | Eaton Rapids Public Schools                   |  21599.1 |  2536.87 |  24136 |
| 23060 | Grand Ledge Public Schools                    |  27433.3 |  3222.72 |  30656 |
| 23065 | Maple Valley Schools                          |  20730   |  2434.96 |  23165 |
| 23080 | Olivet Community Schools                      |  10000   |   551    |  10551 |
| 23090 | Potterville Public Schools                    |  10000   |     0    |  10000 |
| 23900 | LifeTech Academy                              |  10000   |     0    |  10000 |
| 23901 | Island City Academy                           |  10000   |     0    |  10000 |
| 23902 | Relevant Academy of Eaton County              |  10000   |     0    |  10000 |
| 23903 | Insight School of Michigan                    |  18849.4 |  2214.56 |  21064 |
| 24020 | Harbor Springs School District                |  10000   |     0    |  10000 |
| 24030 | Alanson Public Schools                        |  10000   |     0    |  10000 |
| 24040 | Pellston Public Schools                       |  10741.6 |  1261.4  |  12003 |
| 24070 | Public Schools of Petoskey                    |  17190.9 |  2019.14 |  19210 |
| 24901 | Concord Academy - Petoskey                    |  10000   |     0    |  10000 |
| 25010 | Flint, School District of the City of         | 745542   | 87572.6  | 833115 |
| 25030 | Grand Blanc Community Schools                 |  48066.6 |  5646.42 |  53713 |
| 25040 | Mt. Morris Consolidated Schools               |  53720.8 |  6310.18 |  60031 |
| 25050 | Goodrich Area Schools                         |  10000   |     0    |  10000 |
| 25060 | Bendle Public Schools                         |  29514.8 |  3467.19 |  32982 |
| 25070 | Genesee School District                       |  10448.8 |  1227.19 |  11676 |
| 25080 | Carman-Ainsworth Community Schools            | 106412   | 12499.2  | 118911 |
| 25100 | Fenton Area Public Schools                    |  16882.1 |  1982.93 |  18865 |
| 25110 | Kearsley Community School District            |  36066   |  4236.03 |  40302 |
| 25120 | Flushing Community Schools                    |  30933.3 |  3633.73 |  34567 |
| 25130 | Atherton Community Schools                    |  18399.6 |  2161.44 |  20561 |
| 25140 | Davison Community Schools                     |  39234.5 |  4608.46 |  43843 |
| 25150 | Clio Area School District                     |  31070.3 |  3649.71 |  34720 |
| 25180 | Swartz Creek Community Schools                |  33699   |  3957.98 |  37657 |
| 25200 | Lake Fenton Community Schools                 |  10000   |     0    |  10000 |
| 25210 | Westwood Heights Schools                      |  34076   |  4002.95 |  38079 |
| 25230 | Bentley Community School District             |  12461.7 |  1464.27 |  13926 |
| 25240 | Beecher Community School District             | 109595   | 12873    | 122468 |
| 25250 | Linden Community Schools                      |  19108.4 |  2244.63 |  21353 |
| 25260 | Montrose Community Schools                    |  16463.6 |  1933.44 |  18397 |
| 25280 | LakeVille Community School District           |  21374.3 |  2510.75 |  23885 |
| 25900 | Genesee STEM Academy                          |  11316.2 |  1328.82 |  12645 |
| 25902 | Woodland Park Academy                         |  10573.6 |  1242.43 |  11816 |
| 25903 | Grand Blanc Academy                           |  14101.3 |  1656.68 |  15758 |
| 25904 | Northridge Academy                            |  14807.9 |  1739.09 |  16547 |
| 25905 | International Academy of Flint                |  32037.8 |  3763.22 |  35801 |
| 25907 | Linden Charter Academy                        |  29805.4 |  3500.62 |  33306 |
| 25909 | Burton Glen Charter Academy                   |  27521.9 |  3233.1  |  30755 |
| 25910 | Richfield Public School Academy               |  25618.9 |  3009.12 |  28628 |
| 25911 | Madison Academy                               |  12055.4 |  1415.64 |  13471 |



label: D=E-C
labeled_formulas: D=E-C
output: {"Arithmetic-Relationship": ["D=E-C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_196605___xlsx_ca7016825df7cb38ef32a7acbebafb63f9e99448.xlsx___line_514