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 |
|:------|:-----------------------------------------------|:-------------|:-----------------------------------------------------------------------------------------------------|--------:|----------:|-----------------:|----:|
| CAMHS | Children and Adolescent Mental Health Services | CAMHSAPC     | Children and Adolescent Mental Health Services, Admitted Patients                                    |  180356 |  771.253  |      1.391e+08   |  39 |
| CAMHS | Children and Adolescent Mental Health Services | CAMHSAPCPICU | Children and Adolescent Mental Health Services, Admitted Patients, Psychiatric Intensive Care Unit   |    6849 | 1503.07   |      1.02946e+07 |   5 |
| CAMHS | Children and Adolescent Mental Health Services | CAMHSCC      | Children and Adolescent Mental Health Services, Community Contacts                                   | 2094938 |  221.419  |      4.63858e+08 |  51 |
| CAMHS | Children and Adolescent Mental Health Services | CAMHSCCCRHT  | Children and Adolescent Mental Health Services, Community Contacts, Crisis Resolution Home Treatment |   94074 |  247.404  |      2.32743e+07 |  17 |
| CAMHS | Children and Adolescent Mental Health Services | CAMHSDC      | Children and Adolescent Mental Health Services, Day Care Facilities                                  |    6702 |  595.23   |      3.98923e+06 |   7 |
| CAMHS | Children and Adolescent Mental Health Services | CAMHSOP      | Children and Adolescent Mental Health Services, Outpatient Attendances                               |  490085 |  282.275  |      1.38339e+08 |  28 |
| DAS   | Drug and Alcohol Services                      | ALCAAP       | Alcohol Services, Adult, Admitted Patient                                                            |   15477 |  498.964  |      7.72247e+06 |   8 |
| DAS   | Drug and Alcohol Services                      | ALCACC       | Alcohol Services, Adult, Community Contacts                                                          |  109058 |   91.4938 |      9.97813e+06 |  12 |
| DAS   | Drug and Alcohol Services                      | ALCAOP       | Alcohol Services, Adult, Outpatient Attendances                                                      |   38243 |   67.1371 |      2.56752e+06 |   3 |
| DAS   | Drug and Alcohol Services                      | ALCCCC       | Alcohol Services, Children and Adolescents, Community Contacts                                       |     857 |  313.017  | 268256           |   5 |
| DAS   | Drug and Alcohol Services                      | DRUAAP       | Drug Services, Adult, Admitted Patient                                                               |    7604 |  487.918  |      3.71013e+06 |   6 |
| DAS   | Drug and Alcohol Services                      | DRUACC       | Drug Services, Adult, Community Contacts                                                             |  449324 |  118.402  |      5.32009e+07 |  16 |
| DAS   | Drug and Alcohol Services                      | DRUAOP       | Drug Services, Adult, Outpatient Attendances                                                         |  170505 |  100.752  |      1.71787e+07 |   8 |
| DAS   | Drug and Alcohol Services                      | DRUCCC       | Drug Services, Children and Adolescents, Community Contacts                                          |    4946 |  146.856  | 726352           |   6 |
| MHST  | Mental Health Specialist Teams                 | MHSTAEA      | A&E Mental Health Liaison Services, Adult and Elderly                                                |  689538 |  216.974  |      1.49612e+08 |  39 |
| MHST  | Mental Health Specialist Teams                 | MHSTAEC      | A&E Mental Health Liaison Services, Children and Adolescents                                         |    6916 |  239.991  |      1.65978e+06 |   5 |
| MHST  | Mental Health Specialist Teams                 | MHSTCJA      | Criminal Justice Liaison Services, Adult and Elderly                                                 |  141966 |  254.992  |      3.62002e+07 |  37 |
| MHST  | Mental Health Specialist Teams                 | MHSTCJC      | Criminal Justice Liaison Services, Children and Adolescents                                          |    6133 |  400.055  |      2.45354e+06 |  11 |
| MHST  | Mental Health Specialist Teams                 | MHSTFA       | Forensic Community, Adult and Elderly                                                                |  168144 |  287.015  |      4.82598e+07 |  36 |
| MHST  | Mental Health Specialist Teams                 | MHSTFC       | Forensic Community, Children and Adolescents                                                         |    3519 | 1313.43   |      4.62196e+06 |  11 |
| MHST  | Mental Health Specialist Teams                 | MHSTFLA      | Forensic liaison services, Adult and Elderly                                                         |    1478 |  534.023  | 789287           |   2 |
| MHST  | Mental Health Specialist Teams                 | MHSTFLC      | Forensic liaison services, Children and Adolescents                                                  |     454 |  898.32   | 407837           |   1 |
| MHST  | Mental Health Specialist Teams                 | MHSTIAPTC    | IAPT, Children and Adolescents                                                                       |   24541 |  267.645  |      6.56829e+06 |   4 |
| MHST  | Mental Health Specialist Teams                 | MHSTOTHA     | Other Mental Health Specialist Teams, Adult and Elderly                                              |  463438 |  154.847  |      7.17618e+07 |  33 |
| MHST  | Mental Health Specialist Teams                 | MHSTOTHC     | Other Mental Health Specialist Teams, Children and Adolescents                                       |   84509 |  170.294  |      1.43914e+07 |  11 |
| MHST  | Mental Health Specialist Teams                 | MHSTOTHPLA   | Other psychiatric liaison services, Adult and Elderly                                                |   80697 |  182.712  |      1.47443e+07 |  10 |
| MHST  | Mental Health Specialist Teams                 | MHSTOTHPLC   | Other psychiatric liaison services, Children and Adolescents                                         |    3007 |  233.165  | 701126           |   3 |
| MHST  | Mental Health Specialist Teams                 | MHSTPLA      | Psychiatric liaison – acute hospital/ Nursing Homes, Adult and Elderly                               |  174505 |  225.84   |      3.94101e+07 |  15 |
| MHST  | Mental Health Specialist Teams                 | MHSTPRIA     | Prison Health Adult and Elderly                                                                      |  156237 |  144.117  |      2.25164e+07 |   6 |
| MHST  | Mental Health Specialist Teams                 | MHSTPRIC     | Prison Health Children and Adolescents                                                               |   16576 |  149.555  |      2.47902e+06 |   2 |
| MHST  | Mental Health Specialist Teams                 | MHSTPSA      | Psycho – sexual services, Adult and Elderly                                                          |    6974 |  263.19   |      1.83548e+06 |   8 |
| MHST  | Mental Health Specialist Teams                 | MHSTPSC      | Psycho – sexual services, Children and Adolescents                                                   |     303 |  376.22   | 113995           |   1 |
| SCU   | Secure Mental Health Services                  | SCU02        | Child and Adolescent Low Secure Services                                                             |    5748 | 1455.35   |      8.36538e+06 |   3 |
| SCU   | Secure Mental Health Services                  | SCU03        | Child and Adolescent Medium Secure Services                                                          |   11040 | 1814.33   |      2.00302e+07 |   5 |
| SCU   | Secure Mental Health Services                  | SCU04        | High Dependency Secure Provision, Learning Disabilities                                              |     365 | 3203.95   |      1.16944e+06 |   1 |
| SCU   | Secure Mental Health Services                  | SCU05        | High Dependency Secure Provision, Mental Health or Psychosis                                         |    4015 |  809.02   |      3.24822e+06 |   1 |
| SCU   | Secure Mental Health Services                  | SCU06        | High Dependency Secure Provision, Personality Disorder                                               |    9356 |  710.149  |      6.64416e+06 |   2 |
| SPMHS | Specialist Mental Health Services              | SPHMSASDAPC  | Specialised Services For Asperger Syndrome and Autistic Spectrum Disorder, Admitted Patient          |    5956 | 1447.97   |      8.62411e+06 |   1 |
| SPMHS | Specialist Mental Health Services              | SPHMSASDCC   | Specialised Services For Asperger Syndrome and Autistic Spectrum Disorder, Community Contacts        |   32212 |  354.347  |      1.14142e+07 |  22 |
| SPMHS | Specialist Mental Health Services              | SPHMSASDOP   | Specialised Services For Asperger Syndrome and Autistic Spectrum Disorder, Outpatient Attendances    |    9370 |  292.651  |      2.74214e+06 |   8 |
| SPMHS | Specialist Mental Health Services              | SPHMSDAAPC   | Specialist Mental Health Services For Deaf Adults, Admitted Patient                                  |   14089 |  502.914  |      7.08556e+06 |   3 |
| SPMHS | Specialist Mental Health Services              | SPHMSDACC    | Specialist Mental Health Services For Deaf Adults, Community Contacts                                |    1750 |  474.866  | 831016           |   5 |
| SPMHS | Specialist Mental Health Services              | SPHMSDAOP    | Specialist Mental Health Services For Deaf Adults, Outpatient Attendances                            |    4346 |  401.666  |      1.74564e+06 |   3 |
| SPMHS | Specialist Mental Health Services              | SPHMSDCAPC   | Mental Health Services for Deaf Children And Adolescents, Admitted Patient                           |    1033 | 1722.84   |      1.77969e+06 |   1 |
| SPMHS | Specialist Mental Health Services              | SPHMSDCCC    | Mental Health Services for Deaf Children And Adolescents, Community Contacts                         |    4081 |  590.817  |      2.41113e+06 |   3 |
| SPMHS | Specialist Mental Health Services              | SPHMSDCOP    | Mental Health Services for Deaf Children And Adolescents, Outpatient Attendances                     |    4288 |  670.173  |      2.8737e+06  |   3 |
| SPMHS | Specialist Mental Health Services              | SPHMSEDSAAPC | Adult Specialist Eating Disorder Services, Admitted Patient                                          |   74913 |  532.319  |      3.98776e+07 |  17 |
| SPMHS | Specialist Mental Health Services              | SPHMSEDSACC  | Adult Specialist Eating Disorder Services, Community Contacts                                        |   82273 |  184.361  |      1.5168e+07  |  17 |
| SPMHS | Specialist Mental Health Services              | SPHMSEDSAOP  | Adult Specialist Eating Disorder Services, Outpatient Attendances                                    |   62213 |  192.306  |      1.19639e+07 |  12 |
| SPMHS | Specialist Mental Health Services              | SPHMSEDSCAPC | Child and Adolescent Eating Disorder Services, Admitted Patient                                      |   11937 |  787.108  |      9.39571e+06 |   5 |
| SPMHS | Specialist Mental Health Services              | SPHMSEDSCCC  | Child and Adolescent Eating Disorder Services, Community Contacts                                    |  105369 |  199.362  |      2.10065e+07 |  23 |
| SPMHS | Specialist Mental Health Services              | SPHMSEDSCOP  | Child and Adolescent Eating Disorder Services, Outpatient Attendances                                |   43693 |  206.237  |      9.01111e+06 |   9 |
| SPMHS | Specialist Mental Health Services              | SPHMSGIDCC   | Gender Identity Disorder Services, Community Contacts                                                |   25413 |  246.704  |      6.26948e+06 |   6 |
| SPMHS | Specialist Mental Health Services              | SPHMSGIDOP   | Gender Identity Disorder Services, Outpatient Attendances                                            |    9956 |  126.87   |      1.26312e+06 |   1 |
| SPMHS | Specialist Mental Health Services              | SPHMSMBUAPC  | Specialist Perinatal Mental Health Services, Admitted Patient                                        |   35837 |  839.636  |      3.009e+07   |  17 |
| SPMHS | Specialist Mental Health Services              | SPHMSMBUCC   | Specialist Perinatal Mental Health Services, Community Contacts                                      |  163062 |  232.225  |      3.78672e+07 |  39 |
| SPMHS | Specialist Mental Health Services              | SPHMSMBUOP   | Specialist Perinatal Mental Health Services, Outpatient Attendances                                  |   24289 |  349.686  |      8.49353e+06 |  12 |
| SPMHS | Specialist Mental Health Services              | SPHMSMVCC    | Mental Health Services For Veterans, Community Contacts                                              |   11239 |  264.761  |      2.97565e+06 |   9 |
| SPMHS | Specialist Mental Health Services              | SPHMSMVOP    | Mental Health Services For Veterans, Outpatient Attendances                                          |    9237 |  371.028  |      3.42719e+06 |   4 |
| SPMHS | Specialist Mental Health Services              | SPHMSOTHAPC  | Other Specialist Mental Health Services, Admitted Patient                                            |   95764 |  407.882  |      3.90604e+07 |  13 |



label: F=G/E
labeled_formulas: F=G/E
output: {"Arithmetic-Relationship": ["F=G/E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_569652___xlsx_2a0660bf37fd14e87caa1993fb32590edcebd5ff.xlsx___line_185