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 |
|------:|:------------------------------------|----:|----:|----:|----:|----:|----:|----:|----:|
| 30    | Adults & Pediatrics                 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 31    | Intensive Care Unit                 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 31.01 | Neonatal Intensive Care             |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 40    | Subprovider - IPF                   |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 41    | Subprovider - IRF                   |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 43    | Nursery                             |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 50    | Operating Room                      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 51    | Recovery Room                       |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 52    | Delivery & Labor                    |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 53    | Anesthesia                          |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 54    | Radiology-Diagnostic                |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 57    | CT Scan                             |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 58    | MRI                                 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 59    | Cardiac Cath                        |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 60    | Laboratory                          |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 62    | Whole Blood & Packed Red Blood Cell |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 65    | Respiratory Therapy                 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 66    | Physical Therapy                    |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 67    | Occupational Therapy                |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 68    | Speech Therapy                      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 69    | Electrocardiology                   |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 70    | Electroencephalography              |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90    | Clinic                              |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.01 | Other Clinic 1                      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.02 | Other Clinic 2                      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.03 | Other Clinic 3                      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.04 | Other Clinic 4                      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.05 | Other Clinic 5                      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.06 | Other Clinic 6                      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.07 | Other Clinic 7                      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.08 | Other Clinic 8                      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.09 | Other Clinic 9                      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.1  | Other Clinic 10                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.11 | Other Clinic 11                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.12 | Other Clinic 12                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.13 | Other Clinic 13                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.14 | Other Clinic 14                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.15 | Other Clinic 15                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.16 | Other Clinic 16                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.17 | Other Clinic 17                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.18 | Other Clinic 18                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.19 | Other Clinic 19                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.2  | Other Clinic 20                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.21 | Other Clinic 21                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.22 | Other Clinic 22                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.23 | Other Clinic 23                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.24 | Other Clinic 24                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.25 | Other Clinic 25                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.26 | Other Clinic 26                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.27 | Other Clinic 27                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.28 | Other Clinic 28                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.29 | Other Clinic 29                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.3  | Other Clinic 30                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.31 | Other Clinic 31                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.32 | Other Clinic 32                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.33 | Other Clinic 33                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.34 | Other Clinic 34                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 90.35 | Other Clinic 35                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 91    | Emergency Room                      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 93    | Family Practice                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |



label: J=H-I
labeled_formulas: J=H-I
output: {"Arithmetic-Relationship": ["J=H-I"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_627589___xlsx_c0613e053971e7323466349ad27fcc4983000495.xlsx___line_544