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 |
|--------------:|:----------------------------------|----:|----------:|---------:|---------:|
|  100000000092 | ALT SCH-ADAMS/PIKE ROE   (Was 46) |   1 |  19098.5  |  9889.87 | 0.517833 |
|  100000000093 | SAFE SCH-ADAMS/PIKE ROE           |   1 |  19098.5  |  9889.87 | 0.517833 |
|  300000000092 | ALT SCH-BOND/EFFINGHAM/FAYETTE RO |   3 |  18151.7  |  8738.17 | 0.481398 |
|  300000000093 | SAFE SCH-BOND/EFFINGHAM/FAYETTE R |   3 |  18151.7  |  8738.17 | 0.481398 |
|  400000000092 | ALT SCH-BOONE/WINNEBAGO ROE       |   4 |  52169.9  | 30777.9  | 0.589955 |
|  400000000093 | SAFE SCH-BOONE/WINNEBAGO ROE      |   4 |  52169.9  | 30777.9  | 0.589955 |
|  400000000095 | ALOP-BOONE/WINNEBAGO ROE          |   4 |  52169.9  | 30777.9  | 0.589955 |
|  500000000093 | SAFE SCH-INTERMEDIATE SERVICE CEN |   5 | 143279    | 46267.7  | 0.32292  |
|  600000000093 | SAFE SCH-INTERMEDIATE SERVICE CEN |   6 |  88987.3  | 49842.7  | 0.560111 |
|  600000000095 | ALOP SCH-INTERMEDIATE SERVICE CEN |   6 |  88987.3  | 49842.7  | 0.560111 |
|  700000000093 | SAFE SCH-INTERMEDIATE SERVICE CEN |   7 | 133410    | 76768.9  | 0.575437 |
|  800000000092 | ALT SCH-CAROLL/JODAVIESS/STEPHENS |   8 |  11310.9  |  5743.07 | 0.507748 |
|  800000000093 | SAFE SCH-CARROLL/JO DAVIESS/STEPH |   8 |  11310.9  |  5743.07 | 0.507748 |
|  900000000093 | SAFE SCH-CHAMPAIGN/FORD ROE       |   9 |  26481.7  | 12934.7  | 0.488438 |
| 1100000000092 | ALT SCH-CLK/CLS/CMBN/DGLAS/EDGR/M |  11 |  20990.9  |  9883.63 | 0.470853 |
| 1100000000093 | SAFE SCH-CLK/CLS/CMBN/DGLAS/EDGR/ |  11 |  20990.9  |  9883.63 | 0.470853 |
| 1200000000092 | ALT SCH-CLAY/CWFORD/JSPER/LWRNCE/ |  12 |  10408.9  |  4825.48 | 0.463591 |
| 1200000000093 | SAFE SCH-CLAY/CWFORD/JSPER/LWRNCE |  12 |  10408.9  |  4825.48 | 0.463591 |
| 1300000000092 | ALT SCH-CLINTON/MARION/WASHINGTON |  13 |  18603.4  |  9086.68 | 0.488442 |
| 1300000000093 | SAFE SCH-CLINTON/MARION/WASHINGTO |  13 |  18603.4  |  9086.68 | 0.488442 |
| 1600000000093 | SAFE SCH-DE KALB ROE              |  16 |  16497.3  |  6662.61 | 0.403861 |
| 1700000000093 | SAFE SCH-DE WITT/LIVINGSTON/MCLEA |  17 |  35304.5  | 13694.6  | 0.3879   |
| 1700000000095 | ALOP-DE WITT/LIVINGSTON/MCLEAN    |  17 |  35304.5  | 13694.6  | 0.3879   |
| 1900000000093 | SAFE SCH-DU PAGE ROE              |  19 | 148953    | 43125.6  | 0.289524 |
| 1900000000095 | ALOP-DU PAGE ROE                  |  19 | 148953    | 43125.6  | 0.289524 |
| 2000000000092 | ALT SCH-EDWD/GLTN/HDIN/POP/SLNE/  |  20 |  13863.8  |  6979.81 | 0.503458 |
| 2000000000093 | SAFE SCH-EDWD/GLTN/HDIN/POP/SLNE/ |  20 |  13863.8  |  6979.81 | 0.503458 |
| 2100000000092 | ALT SCH-FRANKLIN/WILLIAMSON ROE   |  21 |  19752.7  | 10394.4  | 0.526226 |
| 2100000000093 | SAFE SCH-FRANKLIN/WILLIAMSON ROE  |  21 |  19752.7  | 10394.4  | 0.526226 |
| 2400000000092 | ALT SCH-GRUNDY/KENDALL ROE        |  24 |  39870.7  |  9653.99 | 0.242132 |
| 2400000000093 | SAFE SCH-GRUNDY/KENDALL ROE       |  24 |  39870.7  |  9653.99 | 0.242132 |
| 2600000000092 | ALT SCH-HANCOCK/MC DONOUGH ROE    |  26 |  11305.7  |  5197.49 | 0.459724 |
| 2600000000093 | SAFE SCH-HANCOCK/MC DONOUGH ROE   |  26 |  11305.7  |  5197.49 | 0.459724 |
| 2800000000093 | SAFE SCH-BUREAU/HENRY/STARK ROE   |  28 |  13533.7  |  5525.32 | 0.408265 |
| 3000000000092 | ALT SCH-JACKSON/PERRY ROE         |  30 |  13696.7  |  7923.68 | 0.578511 |
| 3000000000093 | SAFE SCH-JACKSON/PERRY ROE        |  30 |  13696.7  |  7923.68 | 0.578511 |
| 3000000000095 | ALOP-JACKSON/PERRY ROE            |  30 |  13696.7  |  7923.68 | 0.578511 |
| 3100000000093 | SAFE SCH-KANE ROE                 |  31 | 115749    | 51858.2  | 0.448024 |
| 3100000000095 | ALOP-KANE ROE                     |  31 | 115749    | 51858.2  | 0.448024 |
| 3200000000092 | ALT SCH-IROQUOIS/KANKAKEE ROE     |  32 |  20898.3  | 10656.6  | 0.509926 |
| 3200000000093 | SAFE SCH-IROQUOIS/KANKAKEE ROE    |  32 |  20898.3  | 10656.6  | 0.509926 |
| 3300000000092 | ALT-HENDERSON/KNOX/MERCER/WARREN  |  33 |  11410.7  |  5917.12 | 0.518558 |
| 3300000000093 | SAFE SCH-KNOX ROE                 |  33 |  11410.7  |  5917.12 | 0.518558 |
| 3400000000093 | SAFE SCH-LAKE ROE                 |  34 | 130132    | 45775.6  | 0.351763 |
| 3400000000095 | ALOP SCH-LAKE ROE                 |  34 | 130132    | 45775.6  | 0.351763 |
| 3500000000093 | SAFE SCH-LA SALLE ROE             |  35 |  16973.5  |  8245.69 | 0.485799 |
| 3900000000092 | ALT SCH-MACON/PIATT ROE           |  39 |  18038.3  |  9610.26 | 0.532769 |
| 3900000000093 | SAFE SCH-MACON/PIATT ROE          |  39 |  18038.3  |  9610.26 | 0.532769 |
| 4000000000092 | ALT SCH-CALHOUN/GREENE/JERSY/MACO |  40 |  12583.8  |  5740.91 | 0.456216 |
| 4000000000093 | SAFE SCH-CALHOUN/GREENE/JERSY/MAC |  40 |  12583.8  |  5740.91 | 0.456216 |
| 4100000000093 | SAFE SCH-MADISON ROE              |  41 |  39105.7  | 17476.9  | 0.446915 |
| 4400000000093 | SAFE SCH-MC HENRY ROE             |  44 |  47717.3  | 13651.5  | 0.28609  |
| 4500000000092 | ALT SCH-MONROE/RANDOLPH ROE       |  45 |   9013.49 |  2616.54 | 0.290292 |
| 4500000000093 | SAFE SCH-MONROE/RANDOLPH ROE      |  45 |   9013.49 |  2616.54 | 0.290292 |
| 4700000000093 | SAFE SCH-LEE/OGLE ROE             |  47 |  21317.8  |  9303.13 | 0.436402 |
| 4700000000095 | ALOP-LEE/OGLE ROE                 |  47 |  21317.8  |  9303.13 | 0.436402 |
| 4800000000092 | ALT SCH-PEORIA ROE                |  48 |  27265.3  | 14943.4  | 0.548075 |
| 4800000000093 | SAFE SCH-PEORIA ROE               |  48 |  27265.3  | 14943.4  | 0.548075 |
| 4900000000093 | SAFE SCH-ROCK ISLAND ROE          |  49 |  22017.6  | 11888.9  | 0.539975 |
| 5000000000093 | SAFE SCH-ST CLAIR ROE             |  50 |  39427.9  | 19439.1  | 0.493027 |
| 5100000000092 | ALT SCH-SANGAMON ROE              |  51 |  30129.1  | 14248.4  | 0.472911 |
| 5100000000093 | SAFE SCH-SANGAMON ROE             |  51 |  30129.1  | 14248.4  | 0.472911 |
| 5300000000092 | ALT SCH-TAZEWELL ROE              |  53 |  29513.1  | 10257.7  | 0.347565 |
| 5300000000093 | SAFE SCH-TAZEWELL ROE             |  53 |  29513.1  | 10257.7  | 0.347565 |
| 5400000000093 | SAFE SCH-VERMILION ROE            |  54 |  12209.1  |  7676.82 | 0.628776 |
| 5600000000092 | ALT SCH-WILL ROE                  |  56 | 108356    | 39394.5  | 0.363566 |
| 5600000000093 | SAFE SCH-WILL ROE                 |  56 | 108356    | 39394.5  | 0.363566 |
| 5600000000095 | ALOP-WILL ROE                     |  56 | 108356    | 39394.5  | 0.363566 |



label: F=E/D
labeled_formulas: F=E/D
output: {"Arithmetic-Relationship": ["F=E/D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_362175___xlsx_22da949c6b037a5ea4d193bbeee9884f1f38aa96.xlsx___line_93