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 |
|:------------|:-----------------------------------|-----:|----:|---------:|
| Coffee      | Iced Coffee - Grande               | 2.75 | 165 |  60      |
| Coffee      | Blonde Roast - Short               | 1.85 | 180 |  97.2973 |
| Espresso    | Carmel Macchiato - Short           | 3.85 |  75 |  19.4805 |
| Espresso    | Iced Carmel Macchiato - Grande     | 4.75 | 150 |  31.5789 |
| Espresso    | Latte Macchiato - Short            | 3.85 | 150 |  38.961  |
| Espresso    | Caffe Mocha - Short                | 3.65 |  90 |  24.6575 |
| Espresso    | Flat White - Grande                | 4.75 | 195 |  41.0526 |
| Espresso    | Iced Caffe Americano - Grande      | 3.25 | 225 |  69.2308 |
| Frappuccino | Carmel Frappuccino - Grande        | 4.75 | 100 |  21.0526 |
| Frappuccino | Mocha Frappuccino - Grande         | 4.75 | 110 |  23.1579 |
| Frappuccino | Java Chip Frappuccino - Grande     | 4.75 | 110 |  23.1579 |
| Coffee      | Dark Roast - Short                 | 1.85 | 160 |  86.4865 |
| Coffee      | Medium Roast - Short               | 1.85 | 155 |  83.7838 |
| Espresso    | Espresso - Solo                    | 1.95 |  75 |  38.4615 |
| Espresso    | Doubleshot on Ice - Tall           | 2.95 | 150 |  50.8475 |
| Espresso    | Caffe Americano - Short            | 2.25 |  75 |  33.3333 |
| Espresso    | Cappuccino - Short                 | 3.15 |  75 |  23.8095 |
| Coffee      | Narino Cold Brewed Coffee - Tall   | 2.95 | 155 |  52.5424 |
| Espresso    | Caffe Latte - Short                | 3.15 |  75 |  23.8095 |
| Espresso    | Caffe Latte - Tall                 | 3.25 |  75 |  23.0769 |
| Espresso    | Caffe Latte - Grande               | 3.95 | 150 |  37.9747 |
| Coffee      | Narino Cold Brewed Coffee - Grande | 3.45 | 205 |  59.4203 |
| Coffee      | Narino Cold Brewed Coffee - Trenta | 3.95 | 360 |  91.1392 |
| Espresso    | Cappuccino - Tall                  | 3.25 |  75 |  23.0769 |
| Espresso    | Cappuccino - Grande                | 3.95 | 150 |  37.9747 |
| Espresso    | Caffe Americano - Tall             | 2.45 | 150 |  61.2245 |
| Espresso    | Caffe Americano - Grande           | 3.25 | 225 |  69.2308 |
| Espresso    | Doubleshot on Ice - Grande         | 3.75 | 225 |  60      |
| Espresso    | Espresso - Doppio                  | 2.25 | 150 |  66.6667 |
| Espresso    | Espresso - Triple                  | 2.65 | 225 |  84.9057 |
| Espresso    | Flat White - Tall                  | 3.95 | 130 |  32.9114 |
| Espresso    | Flat White - Short                 | 3.85 | 130 |  33.7662 |
| Coffee      | Blonde Roast - Tall                | 1.95 | 270 | 138.462  |
| Coffee      | Blonde Roast - Grande              | 2.25 | 360 | 160      |
| Coffee      | Dark Roast - Tall                  | 1.95 | 195 | 100      |
| Coffee      | Dark Roast - Grande                | 2.25 | 260 | 115.556  |
| Coffee      | Medium Roast - Tall                | 1.95 | 235 | 120.513  |
| Coffee      | Medium Roast - Grande              | 2.25 | 310 | 137.778  |
| Espresso    | Latte Macchiato - Tall             | 3.95 | 150 |  37.9747 |
| Espresso    | Latte Macchiato - Grande           | 4.75 | 225 |  47.3684 |
| Espresso    | Carmel Macchiato - Tall            | 3.95 |  75 |  18.9873 |
| Espresso    | Carmel Macchiato - Grande          | 4.75 | 150 |  31.5789 |
| Espresso    | Caffe Mocha - Tall                 | 3.75 |  95 |  25.3333 |
| Espresso    | Caffe Mocha - Grande               | 4.45 | 175 |  39.3258 |
| Coffee      | Iced Coffee - Tall                 | 2.45 | 120 |  48.9796 |
| Coffee      | Iced Coffee - Trenta               | 3.65 | 280 |  76.7123 |
| Coffee      | Iced Carmel Macchiato - Tall       | 3.95 |  75 |  18.9873 |
| Coffee      | Iced Caffe Americano - Tall        | 2.45 | 150 |  61.2245 |
| Frappuccino | Carmel Frappuccino - Tall          | 3.95 |  70 |  17.7215 |
| Frappuccino | Mocha Frappuccino - Tall           | 3.95 |  75 |  18.9873 |
| Frappuccino | Java Chip Frappuccino - Tall       | 3.95 |  75 |  18.9873 |



label: E=D/C
labeled_formulas: E=D/C
output: {"Arithmetic-Relationship": ["E=D/C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_41459___xlsx_0160f9b81b4fd47936081fc19ceb12b7e6363132.xlsx___line_5