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:
|   BD | BE                                                                   |   BF |   BG |   BH |
|-----:|:---------------------------------------------------------------------|-----:|-----:|-----:|
|    1 | Member Months                                                        |    0 |    0 |    0 |
|    2 | Specialized Behavioral Health Revenue from MCO                       |    0 |    0 |    0 |
|    3 | Other income                                                         |    0 |    0 |    0 |
|    4 | TOTAL REVENUES                                                       |    0 |    0 |    0 |
|    5 | Distinct Part Psychiatric Inpatient Hospital (DPP)                   |    0 |    0 |    0 |
|    6 | Psychiatric Residential Treatment Facility (PRTF)                    |    0 |    0 |    0 |
|    7 | Freestanding Psychiatric Hospital (IMD)                              |    0 |    0 |    0 |
|    8 | Total Inpatient Expenses                                             |    0 |    0 |    0 |
|    9 | Outpatient Hospital                                                  |    0 |    0 |    0 |
|   10 | Total Outpatient Expenses                                            |    0 |    0 |    0 |
|   11 | Psychiatrist                                                         |    0 |    0 |    0 |
|   12 | Federally Qualified Health Center (FQHC), Rural Health Center (RHC)* |    0 |    0 |    0 |
|   13 | Medical or Licensed Psychologists                                    |    0 |    0 |    0 |
|   14 | Licensed Clinical Social Workers (LCSWs)                             |    0 |    0 |    0 |
|   15 | Licensed Professional Counselors (LPCs)                              |    0 |    0 |    0 |
|   16 | Licensed Marriage and Family Therapists (LMFTs)                      |    0 |    0 |    0 |
|   17 | Advanced Practice Registered Nurses (APRNs)**                        |    0 |    0 |    0 |
|   18 | Other Licensed Mental Health Practitioner (LMHP)                     |    0 |    0 |    0 |
|   19 | Total Professional Expenses                                          |    0 |    0 |    0 |
|   20 | Addiction services: Residential                                      |    0 |    0 |    0 |
|   21 | Addiction services: Outpatient                                       |    0 |    0 |    0 |
|   22 | Addiction services: Intensive Outpatient                             |    0 |    0 |    0 |
|   23 | Licensed Addiction Counselors (LACs)                                 |    0 |    0 |    0 |
|   24 | Total Addiction Services Expenses                                    |    0 |    0 |    0 |
|   25 | Lab Services***                                                      |    0 |    0 |    0 |
|   26 | Crisis Intervention                                                  |    0 |    0 |    0 |
|   27 | Crisis Stabilization                                                 |    0 |    0 |    0 |
|   28 | Diagnostic Services (Psych)                                          |    0 |    0 |    0 |
|   29 | Community Psychiatric Support and Treatment (CPST)                   |    0 |    0 |    0 |
|   30 | Multisystemic Therapy (MST)                                          |    0 |    0 |    0 |
|   31 | Functional Family Therapy (FFT)                                      |    0 |    0 |    0 |
|   32 | Therapeutic Group Home (TGH)****                                     |    0 |    0 |    0 |
|   33 | Homebuilders                                                         |    0 |    0 |    0 |
|   34 | Assertive Community Treatment (ACT)                                  |    0 |    0 |    0 |
|   35 | Psychosocial Rehabilitation (including peer support services)        |    0 |    0 |    0 |
|   36 | Reserved for future use                                              |    0 |    0 |    0 |
|   37 | Other expenses (Describe in Supplemental Working Area)               |    0 |    0 |    0 |
|   38 | Specialized Behavioral Health Change in Current Period IBNR          |    0 |    0 |    0 |
|   39 | Specialized Behavioral Health Change in Prior Period IBNR            |    0 |    0 |    0 |
|   40 | Total Other Expenses                                                 |    0 |    0 |    0 |
|   41 | TOTAL COVERED SPECIALIZED BEHAVIORAL HEALTH EXPENSES                 |    0 |    0 |    0 |
|   42 | Reinsurance premiums                                                 |    0 |    0 |    0 |
|   43 | Reinsurance recoveries                                               |    0 |    0 |    0 |
|   44 | Cost of Reinsurance net of recoveries                                |    0 |    0 |    0 |
|   45 | Third party liability subrogation                                    |    0 |    0 |    0 |
|   46 | Fraud and abuse recoveries                                           |    0 |    0 |    0 |
|   47 | Other Recoveries                                                     |    0 |    0 |    0 |
|   48 | TOTAL COVERED NET MEDICAL EXPENSES                                   |    0 |    0 |    0 |
|   49 | Health Care Quality Improvement                                      |    0 |    0 |    0 |
|   50 | Other Administrative Costs                                           |    0 |    0 |    0 |
|   51 | TOTAL ADMINISTRATIVE EXPENSES                                        |    0 |    0 |    0 |
|   52 | Encounter Member Value-Added Services                                |    0 |    0 |    0 |
|   53 | Non-Encounter Member Value-Added Services                            |    0 |    0 |    0 |
|   54 | TOTAL MEMBER VALUE-ADDED SERVICES                                    |    0 |    0 |    0 |
|   55 | TOTAL SPECIALIZED BEHAVIORAL HEALTH EXPENSES                         |    0 |    0 |    0 |



label: BH=BF-BG
labeled_formulas: BH=BF-BG
output: {"Arithmetic-Relationship": ["BH=BF-BG"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_764560___xlsx_4998d6956cbe9e39eecdcf76d6707ffaf75a4585.xlsx___line_308