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 |
|-------------:|:--------------------------------|----:|----:|---------:|-----:|
|  10100010000 | ALBANY CITY SD                  |  15 |  13 | 0.866667 | 0.15 |
| 270100010000 | AMSTERDAM CITY SD               |   6 |   5 | 0.833333 | 0.15 |
|  50100010000 | AUBURN CITY SD                  |   7 |   6 | 0.857143 | 0.15 |
|  30200010000 | BINGHAMTON CITY SD              |  10 |   9 | 0.9      | 0.15 |
|  62301040000 | BROCTON CSD                     |   2 |   0 | 0        | 0.05 |
| 580203020000 | BROOKHAVEN-COMSEWOGUE UFSD      |   6 |   0 | 0        | 0.05 |
| 490202040000 | BRUNSWICK CSD (BRITTONKILL)     |   2 |   1 | 0.5      | 0.1  |
| 161601040000 | BRUSHTON-MOIRA CSD              |   2 |   0 | 0        | 0.05 |
| 140600010000 | BUFFALO CITY SD                 |  56 |  35 | 0.625    | 0.12 |
| 222201060000 | CARTHAGE CSD                    |   5 |   1 | 0.2      | 0.05 |
|  60401040000 | CASSADAGA VALLEY CSD            |   2 |   0 | 0        | 0.05 |
| 190401060000 | CATSKILL CSD                    |   3 |   3 | 1        | 0.15 |
| 580513030000 | CENTRAL ISLIP UFSD              |   8 |   4 | 0.5      | 0.1  |
| 120401040000 | CHARLOTTE VALLEY CSD            |   1 |   1 | 1        | 0.15 |
| 110101040000 | CINCINNATUS CSD                 |   3 |   1 | 0.333333 | 0.06 |
| 650301040000 | CLYDE-SAVANNAH CSD              |   3 |   1 | 0.333333 | 0.06 |
|  10500010000 | COHOES CITY SD                  |   5 |   0 | 0        | 0.05 |
| 110200010000 | CORTLAND CITY SD                |   6 |   2 | 0.333333 | 0.06 |
| 610301060000 | DRYDEN CSD                      |   5 |   2 | 0.4      | 0.08 |
|  60800010000 | DUNKIRK CITY SD                 |   6 |   4 | 0.666667 | 0.13 |
| 500402060000 | EAST RAMAPO CSD (SPRING VALLEY) |  14 |   8 | 0.571429 | 0.11 |
| 180901040000 | ELBA CSD                        |   2 |   0 | 0        | 0.05 |
|  70600010000 | ELMIRA CITY SD                  |  11 |  11 | 1        | 0.15 |
| 590501060000 | FALLSBURG CSD                   |   2 |   1 | 0.5      | 0.1  |
|  21601040000 | FRIENDSHIP CSD                  |   1 |   1 | 1        | 0.15 |
| 460500010000 | FULTON CITY SD                  |   6 |   1 | 0.166667 | 0.05 |
| 430700010000 | GENEVA CITY SD                  |   4 |   3 | 0.75     | 0.15 |
|  81401040000 | GEORGETOWN-SOUTH OTSELIC CSD    |   1 |   1 | 1        | 0.15 |
| 630300010000 | GLENS FALLS CITY SD             |   5 |   1 | 0.2      | 0.05 |
| 630918080000 | GLENS FALLS COMN SD             |   1 |   0 | 0        | 0.05 |
| 170500010000 | GLOVERSVILLE CITY SD            |   6 |   4 | 0.666667 | 0.13 |
| 511101060000 | GOUVERNEUR CSD                  |   3 |   1 | 0.333333 | 0.06 |
|  42801060000 | GOWANDA CSD                     |   3 |   1 | 0.333333 | 0.06 |
|  10701030000 | GREEN ISLAND UFSD               |   1 |   1 | 1        | 0.15 |
| 610501040000 | GROTON CSD                      |   2 |   1 | 0.5      | 0.1  |
| 250701040000 | HAMILTON CSD                    |   2 |   0 | 0        | 0.05 |
| 460701040000 | HANNIBAL CSD                    |   3 |   3 | 1        | 0.15 |
| 230301040000 | HARRISVILLE CSD                 |   2 |   0 | 0        | 0.05 |
| 280201030000 | HEMPSTEAD UFSD                  |  10 |   7 | 0.7      | 0.14 |
| 511301040000 | HERMON-DEKALB CSD               |   1 |   1 | 1        | 0.15 |
|  61700010000 | JAMESTOWN CITY SD               |   9 |   5 | 0.555556 | 0.11 |
| 540901040000 | JEFFERSON CSD                   |   1 |   1 | 1        | 0.15 |
|  31502060000 | JOHNSON CITY CSD                |   4 |   2 | 0.5      | 0.1  |
| 620600010000 | KINGSTON CITY SD                |  10 |   4 | 0.4      | 0.08 |
| 420807040000 | LAFAYETTE CSD                   |   3 |   0 | 0        | 0.05 |
| 590901060000 | LIBERTY CSD                     |   2 |   2 | 1        | 0.15 |
| 161501060000 | MALONE CSD                      |   5 |   2 | 0.4      | 0.08 |
| 121401040000 | MARGARETVILLE CSD               |   1 |   1 | 1        | 0.15 |
| 541001040000 | MIDDLEBURGH CSD                 |   2 |   1 | 0.5      | 0.1  |
|  51301040000 | MORAVIA CSD                     |   2 |   0 | 0        | 0.05 |
| 240901040000 | MT MORRIS CSD                   |   2 |   1 | 0.5      | 0.1  |
| 660900010000 | MT VERNON SCHOOL DISTRICT       |  16 |  10 | 0.625    | 0.12 |
| 650101060000 | NEWARK CSD                      |   5 |   2 | 0.4      | 0.08 |
| 441600010000 | NEWBURGH CITY SD                |  12 |   6 | 0.5      | 0.1  |
| 400800010000 | NIAGARA FALLS CITY SD           |  11 |   7 | 0.636364 | 0.12 |
| 651501060000 | NORTH ROSE-WOLCOTT CSD          |   3 |   1 | 0.333333 | 0.06 |
| 170901040000 | NORTHVILLE CSD                  |   2 |   1 | 0.5      | 0.1  |
| 411504020000 | NY MILLS UFSD                   |   2 |   0 | 0        | 0.05 |
| 550101040000 | ODESSA-MONTOUR CSD              |   3 |   0 | 0        | 0.05 |
| 661500010000 | PEEKSKILL CITY SD               |   6 |   3 | 0.5      | 0.1  |
| 680601060000 | PENN YAN CSD                    |   3 |   1 | 0.333333 | 0.06 |
|  91200010000 | PLATTSBURGH CITY SD             |   5 |   2 | 0.4      | 0.08 |
| 441800050000 | PORT JERVIS CITY SD             |   4 |   1 | 0.25     | 0.05 |
| 131500010000 | POUGHKEEPSIE CITY SD            |   7 |   6 | 0.857143 | 0.15 |
| 580602040000 | RIVERHEAD CSD                   |   7 |   6 | 0.857143 | 0.15 |
| 261600010000 | ROCHESTER CITY SD               |  51 |  41 | 0.803922 | 0.15 |
|  43200050000 | SALAMANCA CITY SD               |   3 |   2 | 0.666667 | 0.13 |
| 161201040000 | SALMON RIVER CSD                |   4 |   1 | 0.25     | 0.05 |
| 530600010000 | SCHENECTADY CITY SD             |  17 |  14 | 0.823529 | 0.15 |
| 121601060000 | SIDNEY CSD                      |   3 |   0 | 0        | 0.05 |
|  61501040000 | SILVER CREEK CSD                |   3 |   0 | 0        | 0.05 |
| 651201060000 | SODUS CSD                       |   3 |   1 | 0.333333 | 0.06 |
| 421800010000 | SYRACUSE CITY SD                |  33 |  24 | 0.727273 | 0.14 |
| 491700010000 | TROY CITY SD                    |   7 |   2 | 0.285714 | 0.05 |
| 412300010000 | UTICA CITY SD                   |  13 |   7 | 0.538462 | 0.1  |
| 121901040000 | WALTON CSD                      |   3 |   2 | 0.666667 | 0.13 |
| 600101060000 | WAVERLY CSD                     |   5 |   1 | 0.2      | 0.05 |
| 280401030000 | WESTBURY UFSD                   |   6 |   1 | 0.166667 | 0.05 |
| 262001040000 | WHEATLAND-CHILI CSD             |   2 |   0 | 0        | 0.05 |
| 170301020000 | WHEELERVILLE UFSD               |   1 |   1 | 1        | 0.15 |
| 472506040000 | WORCESTER CSD                   |   1 |   1 | 1        | 0.15 |
| 580109020000 | WYANDANCH UFSD                  |   4 |   4 | 1        | 0.15 |
| 662300010000 | YONKERS CITY SD                 |  39 |  10 | 0.25641  | 0.05 |



label: E=D/C
labeled_formulas: E=D/C
output: {"Arithmetic-Relationship": ["E=D/C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_48257___xlsx_faea7804c2914f4bb70a8d95dd40482368f98b82.xlsx___line_721