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:
| B                                         |     C |     D |     E |
|:------------------------------------------|------:|------:|------:|
| Rent                                      |  5000 |  5000 |     0 |
| Electricity Bill                          |  2000 |  1500 |   500 |
| Gas Bill                                  |  1000 |  1200 |  -200 |
| Water Bill                                |   500 |   450 |    50 |
| Phone Bill                                |   500 |   550 |   -50 |
| Cable TV Bill                             |   500 |   500 |     0 |
| Internet Bill                             |   500 |   500 |     0 |
| Furnishing Exp.                           |   600 |   750 |  -150 |
| Garden Maintainance                       |  1000 |  1000 |     0 |
| Home Supplies                             |  5000 |  4500 |   500 |
| Maintenance Exp.                          |  1000 |  1250 |  -250 |
| Groceries                                 |  8000 |  7800 |   200 |
| Clothing                                  |  2000 |  2200 |  -200 |
| Cleaning Services                         |  1000 |  1000 |     0 |
| Dining Out                                |   500 |   650 |  -150 |
| Laundry                                   |   500 |   450 |    50 |
| Children School Fee                       |   500 |   500 |     0 |
| Children School Transportation Exp.       |   500 |   500 |     0 |
| Children School Books and Stationery Exp. |   500 |   300 |   200 |
| Baby Sitting Exp.                         |   500 |     0 |   500 |
| Music / Dance / Art Class Fee             |   500 |     0 |   500 |
| Extra Activities Fee / Expenses           |   500 |   650 |  -150 |
| Toys / Games Exp.                         |   500 |   500 |     0 |
| Other Chiildren Expenses                  |   500 |     0 |   500 |
| Vehicle Fuel                              |  1500 |  1800 |  -300 |
| Vehilcle Repairs                          |  5000 |  3500 |  1500 |
| Vehicle Insurance                         |  1000 |  1000 |     0 |
| Bus/Taxi/Train Fare                       |   500 |  1200 |  -700 |
| Doctor/Dentist Fee                        |  2000 |  5000 | -3000 |
| Medicine Expenses                         |   500 |  2000 | -1500 |
| Medical Insurance                         |   200 |   200 |     0 |
| House Insurance                           |   200 |   200 |     0 |
| Life Insurance                            |   100 |   100 |     0 |
| Gifts Given                               |   500 |   200 |   300 |
| Donations and Charity                     |   500 |   600 |  -100 |
| Savings / Investment                      |  1500 |  1500 |     0 |
| Emergency Funds                           |   500 |   600 |  -100 |
| Loan - 1                                  |  1500 |  1500 |     0 |
| Loan - 2                                  |  1500 |  1500 |     0 |
| Loan - 3                                  |  1500 |  1500 |     0 |
| Credit Card - 1                           |   500 |   600 |  -100 |
| Credit Card - 2                           |  5000 |  5500 |  -500 |
| Movies / Theatre / Concerts / Play Exp.   |   500 |   800 |  -300 |
| Outdoor Recreation Exp.                   |  1500 |  2500 | -1000 |
| Club / Gym Membership                     |  2000 |  2500 |  -500 |
| Newspaper Subscription                    |   500 |   300 |   200 |
| Magazine Subscription                     |   500 |   350 |   150 |
| Pet's Food Exp.                           |     0 |     0 |     0 |
| Pet's Medical Exp.                        |     0 |     0 |     0 |
| Pet's Other Exp.                          |     0 |     0 |     0 |
| Vacation Travelling Exp.                  |  2000 |  2500 |  -500 |
| Postage Exp.                              |   500 |     0 |   500 |
| Other Misc. Exp.                          |   200 |     0 |   200 |
| Total Expenses                            | 65300 | 69200 | -3900 |



label: E=C-D
labeled_formulas: E=C-D
output: {"Arithmetic-Relationship": ["E=C-D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_506471___xlsx_257d38db292590085c9373507d6ed1a84afb21e6.xlsx___line_87