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 |
| 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 |
| 54.01 | Ultrasound                          |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 54.02 | Nuclear Medicine-Diagnostic         |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 55    | Radiology-Therapeutic               |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 56    | Radioisotope                        |   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 |
| 60.01 | Blood Laboratory                    |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 62    | Whole Blood & Packed Red Blood Cell |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 63    | Blood Storing, Processing & Trans.  |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 64    | IV Therapy                          |   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 |
| 71    | Med Supplies Charged to Patients    |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 72    | Imp. Dev Charge to Patient          |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 73    | Drugs Charged to Patients           |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 74    | Renal Dialysis                      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 75    | ASC (Non-Distinct Part)             |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 76    | Endoscopy                           |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 76.01 | Prosthetic Devices                  |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 76.02 | Inpatient Care                      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 76.03 | NICU Professional Services          |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 76.04 | PICU Professional Services          |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 76.05 | Outpatient Observation Unit         |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 76.06 | Intensivists Professional Services  |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 76.07 | Cardiac Rehab                       |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 88    | Rural Health Clinic                 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 89    | Federally Qualified Health Center   |   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 |
| 91    | Emergency Room                      |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 92    | Observation Beds                    |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 93    | Family Practice                     |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |
| 94    | Home Program Dialysis               |   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_404127___xlsx_980d67392d1b5ce9f24ddf7e25e8814a8aa47d82.xlsx___line_348