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 |    G |      H |         I |         J |         K |
|------:|:--------------------------------|:----------------|----:|--------:|----------:|-----:|-------:|----------:|----------:|----------:|
| 12005 | Abraham Lincoln Memorial Hosp   | Critical Access |  33 | 3294.39 | 108715    | 1504 | 131.96 | 198468    | 307183    | 102394    |
|  5009 | Advocate Eureka Hospital        | Critical Access |   3 | 3294.39 |   9883.16 |  109 | 131.96 |  14383.6  |  24266.8  |   8088.93 |
|  8018 | Carle Hoopeston Region Hlth Ctr | Critical Access |   5 | 3294.39 |  16471.9  | 2335 | 131.96 | 308127    | 324599    | 108200    |
|  3007 | Carlinville Area Hospital       | Critical Access |  19 | 3294.39 |  62593.4  |  879 | 131.96 | 115993    | 178586    |  59528.7  |
|  6003 | Clay County Hospital            | Critical Access |  18 | 3294.39 |  59299    |  881 | 131.96 | 116257    | 175556    |  58518.6  |
| 19009 | Community Hospital of Staunton  | Critical Access |   6 | 3294.39 |  19766.3  |  544 | 131.96 |  71786.2  |  91552.6  |  30517.5  |
| 18014 | Crawford Memorial Hospital      | Critical Access | 139 | 3294.39 | 457920    | 1891 | 131.96 | 249536    | 707456    | 235819    |
|  6002 | Fairfield Memorial Hospital     | Critical Access |  41 | 3294.39 | 135070    | 1538 | 131.96 | 202954    | 338024    | 112675    |
| 22002 | Fayette County Hospital & LTC   | Critical Access |  18 | 3294.39 |  59299    | 1129 | 131.96 | 148983    | 208282    |  69427.3  |
|  5004 | Ferrell Hospital                | Critical Access |  35 | 3294.39 | 115304    | 1117 | 131.96 | 147399    | 262703    |  87567.6  |
|  2014 | Franklin Hospital District      | Critical Access |   3 | 3294.39 |   9883.16 |  960 | 131.96 | 126682    | 136565    |  45521.6  |
|  1001 | Genesis Medical Center          | Critical Access |  11 | 3294.39 |  36238.3  |  566 | 131.96 |  74689.4  | 110928    |  36975.9  |
|  7006 | Gibson Area Hosp & Hlth Servcs  | Critical Access |  39 | 3294.39 | 128481    | 1209 | 131.96 | 159540    | 288021    |  96006.9  |
| 13023 | Hamilton Memorial Hosp District | Critical Access |  19 | 3294.39 |  62593.4  |  547 | 131.96 |  72182.1  | 134775    |  44925.2  |
|  7004 | Hammond-Henry Hospital          | Critical Access |  18 | 3294.39 |  59299    | 1440 | 131.96 | 190022    | 249321    |  83107.1  |
| 18013 | Hardin County General Hospital  | Critical Access |  28 | 3294.39 |  92242.8  |  501 | 131.96 |  66112    | 158355    |  52784.9  |
|  8011 | Hillsboro Area Hospital         | Critical Access |  12 | 3294.39 |  39532.6  |  730 | 131.96 |  96330.8  | 135863    |  45287.8  |
|  8014 | Hopedale Medical Complex        | Critical Access |   0 | 3294.39 |      0    |   69 | 131.96 |   9105.24 |   9105.24 |   3035.08 |
| 12007 | HSHS St Francis Hospital        | Critical Access | 138 | 3294.39 | 454625    | 2005 | 131.96 | 264580    | 719205    | 239735    |
|  8009 | HSHS St Joseph's Hospital       | Critical Access |  42 | 3294.39 | 138364    |  783 | 131.96 | 103325    | 241689    |  80563    |
| 16009 | Illini Community Hospital       | Critical Access |  75 | 3294.39 | 247079    |  720 | 131.96 |  95011.2  | 342090    | 114030    |
| 13010 | Kirby Medical Center            | Critical Access |   0 | 3294.39 |      0    |  682 | 131.96 |  89996.7  |  89996.7  |  29998.9  |
| 12004 | Lawrence County Memorial Hosp   | Critical Access |  24 | 3294.39 |  79065.3  |  805 | 131.96 | 106228    | 185293    |  61764.4  |
|  4009 | Marshall Browning Hospital      | Critical Access |  20 | 3294.39 |  65887.7  |  716 | 131.96 |  94483.4  | 160371    |  53457    |
|  8015 | Mason District Hospital         | Critical Access |   7 | 3294.39 |  23060.7  | 1040 | 131.96 | 137238    | 160299    |  53433    |
| 13019 | Massac Memorial Hospital        | Critical Access |  21 | 3294.39 |  69182.1  | 1008 | 131.96 | 133016    | 202198    |  67399.3  |
|  3010 | Memorial Hospital               | Critical Access |  41 | 3294.39 | 135070    |  544 | 131.96 |  71786.2  | 206856    |  68952    |
|  3091 | Memorial Hospital               | Critical Access |  12 | 3294.39 |  39532.6  |  327 | 131.96 |  43150.9  |  82683.6  |  27561.2  |
|  8005 | Mercyhealth Hosp-Harvard Campus | Critical Access |  21 | 3294.39 |  69182.1  |  494 | 131.96 |  65188.2  | 134370    |  44790.1  |
|  7009 | Midwest Medical Center          | Critical Access |   0 | 3294.39 |      0    |  470 | 131.96 |  62021.2  |  62021.2  |  20673.7  |
| 13012 | Morrison Community Hospital     | Critical Access |   0 | 3294.39 |      0    |  232 | 131.96 |  30614.7  |  30614.7  |  10204.9  |
| 19028 | NW Med Valley West Hospital     | Critical Access |  39 | 3294.39 | 128481    |  887 | 131.96 | 117049    | 245530    |  81843.2  |
| 13009 | OSF Holy Family Medical Center  | Critical Access |   0 | 3294.39 |      0    |  382 | 131.96 |  50408.7  |  50408.7  |  16802.9  |
| 11004 | OSF Saint Luke Medical Center   | Critical Access |  17 | 3294.39 |  56004.6  |  745 | 131.96 |  98310.2  | 154315    |  51438.3  |
| 13005 | OSF Saint Paul Medical Center   | Critical Access |   0 | 3294.39 |      0    |  314 | 131.96 |  41435.4  |  41435.4  |  13811.8  |
| 16001 | Pana Community Hospital         | Critical Access |   6 | 3294.39 |  19766.3  |  818 | 131.96 | 107943    | 127710    |  42569.9  |
| 16002 | Paris Community Hospital        | Critical Access |  35 | 3294.39 | 115304    | 1538 | 131.96 | 202954    | 318258    | 106086    |
| 16011 | Perry Memorial Hospital         | Critical Access |  20 | 3294.39 |  65887.7  | 1038 | 131.96 | 136974    | 202862    |  67620.7  |
| 16012 | Pinckneyville Community Hosp    | Critical Access |   6 | 3294.39 |  19766.3  |  421 | 131.96 |  55555.2  |  75321.5  |  25107.2  |
| 18001 | Red Bud Regional Hospital       | Critical Access |  17 | 3294.39 |  56004.6  |  498 | 131.96 |  65716.1  | 121721    |  40573.6  |
| 18004 | Rochelle Community Hospital     | Critical Access |  33 | 3294.39 | 108715    |  730 | 131.96 |  96330.8  | 205046    |  68348.5  |
| 19001 | Salem Township Hospital         | Critical Access |  15 | 3294.39 |  49415.8  | 1199 | 131.96 | 158220    | 207636    |  69211.9  |
| 18010 | Sarah D Culbertson Mem Hosp     | Critical Access |   4 | 3294.39 |  13177.5  |  577 | 131.96 |  76140.9  |  89318.5  |  29772.8  |
| 19023 | Sparta Community Hospital       | Critical Access |  24 | 3294.39 |  79065.3  | 1097 | 131.96 | 144760    | 223825    |  74608.5  |
| 13024 | St Joseph Memorial Hospital     | Critical Access |  27 | 3294.39 |  88948.5  | 2585 | 131.96 | 341117    | 430065    | 143355    |
| 20001 | Taylorville Memorial Hospital   | Critical Access |  16 | 3294.39 |  52710.2  | 1366 | 131.96 | 180257    | 232968    |  77655.8  |
|  3009 | Thomas H Boyd Memorial Hospital | Critical Access |  14 | 3294.39 |  46121.4  |  320 | 131.96 |  42227.2  |  88348.6  |  29449.5  |
|  1006 | Union County Hospital           | Critical Access |  74 | 3294.39 | 243785    | 1123 | 131.96 | 148191    | 391976    | 130659    |
| 13013 | Wabash General Hospital         | Critical Access |  37 | 3294.39 | 121892    | 1263 | 131.96 | 166665    | 288558    |  96185.9  |
|  3062 | Warner Hospital & Health Srvcs  | Critical Access |   0 | 3294.39 |      0    |  702 | 131.96 |  92635.9  |  92635.9  |  30878.6  |
| 14003 | Washington County Hospital      | Critical Access |   0 | 3294.39 |      0    |  254 | 131.96 |  33517.8  |  33517.8  |  11172.6  |



label: F=E*D
I=G*H
J=I+F
labeled_formulas: F=E*D
I=G*H
J=I+F
output: {"Arithmetic-Relationship": ["F=E*D", "I=G*H", "J=I+F"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_331582___xlsx_bb2a563fa305dc142e03a02be099c9d8f5bfa53e.xlsx___line_762