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 |
|:--------|:----------------------------------------------------|:----|:----------------------|:------|:--------------------------------------------------------------------------|-------:|----------:|-----------------:|----:|
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC01Z | Assessment for Rehabilitation, Unidisciplinary                            |  32758 |  686.405  |      2.24852e+07 |   9 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC02Z | Assessment for Rehabilitation, Multidisciplinary, Non-Specialist          |   3823 |  357.221  |      1.36565e+06 |   3 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC03Z | Assessment for Rehabilitation, Multidisciplinary, Specialist              |  22425 |  115.195  |      2.58326e+06 |   9 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC04Z | Rehabilitation for Stroke                                                 |  98346 |  467.283  |      4.59555e+07 |  25 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC06Z | Rehabilitation for Brain Injuries                                         |  65636 |  572.203  |      3.75571e+07 |  29 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC08Z | Rehabilitation for Spinal Cord Injuries                                   |  36163 |  552.554  |      1.9982e+07  |  20 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC10Z | Rehabilitation for Pain Syndromes                                         |    698 |  476.29   | 332450           |   5 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC12Z | Rehabilitation for Other Neurological Disorders                           |  48223 |  547.533  |      2.64037e+07 |  27 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC14Z | Rehabilitation for Amputation of Limb                                     |    588 |  449.239  | 264152           |   8 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC16Z | Rehabilitation for Hip Fracture                                           |  22785 |  428.47   |      9.76269e+06 |  15 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC18Z | Rehabilitation for Joint Replacement                                      |   9510 |  397.345  |      3.77876e+06 |   9 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC20Z | Rehabilitation for Inflammatory Arthritis                                 |    870 |  418.433  | 364037           |   4 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC22Z | Rehabilitation for Non-Inflammatory Arthritis                             |    705 |  416.524  | 293649           |   8 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC24Z | Rehabilitation for Other Musculoskeletal Disorders                        |  24691 |  482.083  |      1.19031e+07 |  19 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC26Z | Rehabilitation for Drug or Alcohol Addiction                              |     13 | 1067.89   |  13882.6         |   1 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC28Z | Rehabilitation for Other Psychiatric Disorders                            |    383 |  661.54   | 253370           |   6 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC30Z | Rehabilitation for Burns                                                  |    246 |  463.397  | 113996           |   3 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC34Z | Rehabilitation following Other Reconstructive Surgery                     |    248 |  335.67   |  83246           |   5 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC36Z | Rehabilitation for Other Trauma                                           |  28590 |  500.276  |      1.43029e+07 |  20 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC38Z | Rehabilitation for Acute Myocardial Infarction or Other Cardiac Disorders |   6104 |  352.173  |      2.14966e+06 |  14 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC40Z | Rehabilitation for Respiratory Disorders                                  |  17469 |  379.794  |      6.63462e+06 |  13 |
| REHABL1 | Complex specialised rehabilitation services level 1 | APC | Admitted patient care | VC42Z | Rehabilitation for Other Disorders                                        | 192786 |  363.922  |      7.01591e+07 |  25 |
| REHABL1 | Complex specialised rehabilitation services level 1 | OP  | Outpatient            | VC01Z | Assessment for Rehabilitation, Unidisciplinary                            |   3386 |  203.802  | 690075           |   5 |
| REHABL1 | Complex specialised rehabilitation services level 1 | OP  | Outpatient            | VC02Z | Assessment for Rehabilitation, Multidisciplinary, Non-Specialist          |  22961 |  233.41   |      5.35933e+06 |   1 |
| REHABL1 | Complex specialised rehabilitation services level 1 | OP  | Outpatient            | VC03Z | Assessment for Rehabilitation, Multidisciplinary, Specialist              |  46012 |   82.3068 |      3.7871e+06  |   4 |
| REHABL1 | Complex specialised rehabilitation services level 1 | Oth | Other                 | VC03Z | Assessment for Rehabilitation, Multidisciplinary, Specialist              |      1 |  387.61   |    387.61        |   1 |
| REHABL1 | Complex specialised rehabilitation services level 1 | Oth | Other                 | VC04Z | Rehabilitation for Stroke                                                 |  14146 |  382.114  |      5.40538e+06 |   3 |
| REHABL1 | Complex specialised rehabilitation services level 1 | Oth | Other                 | VC06Z | Rehabilitation for Brain Injuries                                         |  18965 |  396.552  |      7.52061e+06 |   2 |
| REHABL1 | Complex specialised rehabilitation services level 1 | Oth | Other                 | VC08Z | Rehabilitation for Spinal Cord Injuries                                   |      1 | 1161.31   |   1161.31        |   1 |
| REHABL1 | Complex specialised rehabilitation services level 1 | Oth | Other                 | VC12Z | Rehabilitation for Other Neurological Disorders                           |     77 |  904.06   |  69612.6         |   1 |
| REHABL1 | Complex specialised rehabilitation services level 1 | Oth | Other                 | VC14Z | Rehabilitation for Amputation of Limb                                     |   3894 |  777.85   |      3.02895e+06 |   1 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC01Z | Assessment for Rehabilitation, Unidisciplinary                            |     11 |  361.12   |   3972.32        |   1 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC02Z | Assessment for Rehabilitation, Multidisciplinary, Non-Specialist          |      8 |  448.934  |   3591.47        |   2 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC03Z | Assessment for Rehabilitation, Multidisciplinary, Specialist              |  11206 |  458.849  |      5.14186e+06 |   5 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC04Z | Rehabilitation for Stroke                                                 | 136393 |  428.632  |      5.84623e+07 |  35 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC06Z | Rehabilitation for Brain Injuries                                         |  37700 |  514.759  |      1.94064e+07 |  30 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC08Z | Rehabilitation for Spinal Cord Injuries                                   |   8500 |  459.968  |      3.90973e+06 |  23 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC10Z | Rehabilitation for Pain Syndromes                                         |    228 |  384.51   |  87668.4         |   4 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC12Z | Rehabilitation for Other Neurological Disorders                           |  59301 |  467.367  |      2.77154e+07 |  34 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC14Z | Rehabilitation for Amputation of Limb                                     |   4031 |  416.997  |      1.68092e+06 |  13 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC16Z | Rehabilitation for Hip Fracture                                           |  12083 |  398.494  |      4.815e+06   |  13 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC18Z | Rehabilitation for Joint Replacement                                      |   6824 |  385.991  |      2.634e+06   |   9 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC20Z | Rehabilitation for Inflammatory Arthritis                                 |     11 |  511.19   |   5623.09        |   1 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC22Z | Rehabilitation for Non-Inflammatory Arthritis                             |    501 |  417.839  | 209337           |   8 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC24Z | Rehabilitation for Other Musculoskeletal Disorders                        |  17574 |  407.675  |      7.16448e+06 |  18 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC26Z | Rehabilitation for Drug or Alcohol Addiction                              |    503 |  323.652  | 162797           |   8 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC28Z | Rehabilitation for Other Psychiatric Disorders                            |    647 |  454.387  | 293988           |   5 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC32Z | Rehabilitation following Head and Neck Reconstructive Surgery             |      9 |  470.829  |   4237.46        |   3 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC34Z | Rehabilitation following Other Reconstructive Surgery                     |    235 |  355.422  |  83524.1         |   5 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC36Z | Rehabilitation for Other Trauma                                           |   2357 |  486.638  |      1.14701e+06 |  18 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC38Z | Rehabilitation for Acute Myocardial Infarction or Other Cardiac Disorders |   2087 |  379.188  | 791365           |  14 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC40Z | Rehabilitation for Respiratory Disorders                                  |   8133 |  392.877  |      3.19526e+06 |  11 |
| REHABL2 | Specialist rehabilitation services level 2          | APC | Admitted patient care | VC42Z | Rehabilitation for Other Disorders                                        | 123228 |  404.579  |      4.98555e+07 |  29 |
| REHABL2 | Specialist rehabilitation services level 2          | OP  | Outpatient            | VC01Z | Assessment for Rehabilitation, Unidisciplinary                            |   1646 |  257.696  | 424168           |   2 |
| REHABL2 | Specialist rehabilitation services level 2          | Oth | Other                 | VC08Z | Rehabilitation for Spinal Cord Injuries                                   |  10666 |  477.47   |      5.0927e+06  |   1 |
| REHABL2 | Specialist rehabilitation services level 2          | Oth | Other                 | VC10Z | Rehabilitation for Pain Syndromes                                         |   4775 |  163.358  | 780036           |   2 |
| REHABL2 | Specialist rehabilitation services level 2          | Oth | Other                 | VC42Z | Rehabilitation for Other Disorders                                        |  22765 |  477.813  |      1.08774e+07 |   3 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC01Z | Assessment for Rehabilitation, Unidisciplinary                            |    777 |  375.264  | 291580           |   4 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC02Z | Assessment for Rehabilitation, Multidisciplinary, Non-Specialist          |     13 |  301.156  |   3915.03        |   2 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC03Z | Assessment for Rehabilitation, Multidisciplinary, Specialist              |      8 |  392.409  |   3139.27        |   2 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC04Z | Rehabilitation for Stroke                                                 | 160782 |  423.051  |      6.8019e+07  |  38 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC06Z | Rehabilitation for Brain Injuries                                         |  11025 |  398.071  |      4.38873e+06 |  33 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC08Z | Rehabilitation for Spinal Cord Injuries                                   |   2221 |  373.344  | 829198           |  15 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC10Z | Rehabilitation for Pain Syndromes                                         |   1316 |  400.958  | 527661           |   5 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC12Z | Rehabilitation for Other Neurological Disorders                           |  19663 |  446.76   |      8.78464e+06 |  32 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC14Z | Rehabilitation for Amputation of Limb                                     |   6144 |  358.014  |      2.19964e+06 |  20 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC16Z | Rehabilitation for Hip Fracture                                           |  75507 |  336.852  |      2.54347e+07 |  32 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC18Z | Rehabilitation for Joint Replacement                                      |  30988 |  365.597  |      1.13291e+07 |  29 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC20Z | Rehabilitation for Inflammatory Arthritis                                 |    596 |  371.423  | 221368           |   9 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC22Z | Rehabilitation for Non-Inflammatory Arthritis                             |   3458 |  337.445  |      1.16689e+06 |  19 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC24Z | Rehabilitation for Other Musculoskeletal Disorders                        | 146276 |  320.044  |      4.68147e+07 |  35 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC26Z | Rehabilitation for Drug or Alcohol Addiction                              |    309 |  345.598  | 106790           |   9 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC28Z | Rehabilitation for Other Psychiatric Disorders                            |   1518 |  359.763  | 546120           |   9 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC30Z | Rehabilitation for Burns                                                  |    355 |  339.709  | 120597           |   8 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC32Z | Rehabilitation following Head and Neck Reconstructive Surgery             |    267 |  382.837  | 102217           |   3 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC34Z | Rehabilitation following Other Reconstructive Surgery                     |   1621 |  362.083  | 586937           |  12 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC36Z | Rehabilitation for Other Trauma                                           |  15025 |  326.167  |      4.90066e+06 |  28 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC38Z | Rehabilitation for Acute Myocardial Infarction or Other Cardiac Disorders |  15709 |  343.442  |      5.39513e+06 |  27 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC40Z | Rehabilitation for Respiratory Disorders                                  |  58105 |  350.883  |      2.0388e+07  |  30 |
| REHABL3 | Non-specialist rehabilitation services level 3      | APC | Admitted patient care | VC42Z | Rehabilitation for Other Disorders                                        | 440337 |  341.25   |      1.50265e+08 |  41 |
| REHABL3 | Non-specialist rehabilitation services level 3      | OP  | Outpatient            | VC01Z | Assessment for Rehabilitation, Unidisciplinary                            |  20640 |   69.1763 |      1.4278e+06  |   2 |
| REHABL3 | Non-specialist rehabilitation services level 3      | Oth | Other                 | VC02Z | Assessment for Rehabilitation, Multidisciplinary, Non-Specialist          |   7234 |  150.01   |      1.08517e+06 |   1 |
| REHABL3 | Non-specialist rehabilitation services level 3      | Oth | Other                 | VC04Z | Rehabilitation for Stroke                                                 |  12474 |  124.301  |      1.55053e+06 |   2 |
| REHABL3 | Non-specialist rehabilitation services level 3      | Oth | Other                 | VC12Z | Rehabilitation for Other Neurological Disorders                           |  10540 |   89.1629 | 939777           |   2 |
| REHABL3 | Non-specialist rehabilitation services level 3      | Oth | Other                 | VC16Z | Rehabilitation for Hip Fracture                                           |     36 |  110.85   |   3990.6         |   1 |
| REHABL3 | Non-specialist rehabilitation services level 3      | Oth | Other                 | VC18Z | Rehabilitation for Joint Replacement                                      |   1987 |   26.68   |  53013.2         |   1 |
| REHABL3 | Non-specialist rehabilitation services level 3      | Oth | Other                 | VC38Z | Rehabilitation for Acute Myocardial Infarction or Other Cardiac Disorders |   7221 |   48.43   | 349713           |   1 |
| REHABL3 | Non-specialist rehabilitation services level 3      | Oth | Other                 | VC40Z | Rehabilitation for Respiratory Disorders                                  |  11724 |   79.4245 | 931173           |   3 |
| REHABL3 | Non-specialist rehabilitation services level 3      | Oth | Other                 | VC42Z | Rehabilitation for Other Disorders                                        |  40206 |   96.3001 |      3.87184e+06 |   3 |



label: H=I/G
labeled_formulas: H=I/G
output: {"Arithmetic-Relationship": ["H=I/G"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_569641___xlsx_2a0660bf37fd14e87caa1993fb32590edcebd5ff.xlsx___line_174