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 |
|:------|:-------------------------------------------------------------------------------------------------|--------:|---------:|-----------------:|----:|
| AA32Z | Neuropsychology Tests                                                                            |       1 | 189.32   |    189.32        |   1 |
| AA33C | Conventional EEG, EMG or Nerve Conduction Studies, 19 years and over                             |   46791 | 144.053  |      6.74039e+06 |  16 |
| AA33D | Conventional EEG, EMG or Nerve Conduction Studies, 18 years and under                            |     287 | 330.201  |  94767.8         |   6 |
| AA80Z | Complex Long-Term EEG Monitoring                                                                 |       2 | 228.47   |    456.94        |   1 |
| AA81Z | Standard Long-Term EEG Monitoring                                                                |     113 | 162.294  |  18339.2         |   2 |
| BZ89A | Digital Retinal Photography, 19 years and over                                                   |   21121 |  26.31   | 555694           |   1 |
| CA37A | Audiometry or Hearing Assessment, 19 years and over                                              |    4377 |  39.0616 | 170973           |   2 |
| CA37B | Audiometry or Hearing Assessment, between 5 and 18 years                                         |     350 |  83.9435 |  29380.2         |   2 |
| CA37C | Audiometry or Hearing Assessment, 4 years and under                                              |    6733 | 117.128  | 788624           |   2 |
| CA38A | Evoked Potential Recording, 19 years and over                                                    |      30 | 218.875  |   6566.25        |   2 |
| CA38B | Evoked Potential Recording, 18 years and under                                                   |     317 | 111.89   |  35469.2         |   2 |
| CA43Z | Balance Assessment                                                                               |     145 | 127.11   |  18431           |   1 |
| DAPF  | Direct Access Plain Film                                                                         | 5843232 |  30.588  |      1.78733e+08 | 145 |
| DZ30Z | Chest Physiotherapy                                                                              |     841 |  54.1464 |  45537.1         |   2 |
| DZ31Z | Cardiopulmonary Exercise Testing                                                                 |     792 |  90.0632 |  71330           |   6 |
| DZ32Z | Field Exercise Testing                                                                           |    4396 |  54.7562 | 240708           |   6 |
| DZ36Z | Bronchial Challenge Studies                                                                      |      24 |  45.2125 |   1085.1         |   2 |
| DZ37A | Non-Invasive Ventilation Support Assessment, 19 years and over                                   |    1608 |  49.7815 |  80048.6         |   5 |
| DZ38Z | Oxygen Assessment and Monitoring                                                                 |    2341 | 117.962  | 276148           |   4 |
| DZ45Z | Lung Volume Studies                                                                              |    1706 | 117.267  | 200058           |   4 |
| DZ49Z | Respiratory Nurse or AHP, Education or Support                                                   |     449 |  37.7758 |  16961.3         |   2 |
| DZ50Z | Respiratory Sleep Study                                                                          |    2076 |  84.5657 | 175558           |   6 |
| DZ52Z | Full Pulmonary Function Testing                                                                  |     117 |  65.4638 |   7659.27        |   5 |
| DZ55Z | Bronchodilator Studies                                                                           |     463 | 150.754  |  69799.3         |   4 |
| DZ56Z | Carbon Monoxide Transfer Factor Test                                                             |     677 |  59.7447 |  40447.1         |   3 |
| DZ57Z | Oximetry or Blood Gas Studies                                                                    |     829 |  94.7729 |  78566.8         |   6 |
| DZ58Z | Alveolar Carbon Monoxide Measurement or Smoking Cessation Support                                |       7 |  41.65   |    291.55        |   1 |
| DZ59Z | Airflow Studies                                                                                  |    3948 |  89.9526 | 355133           |   8 |
| DZ60Z | Hypoxic (Altitude) or Hyperoxic (Shunt) Assessment                                               |      28 | 113.398  |   3175.15        |   3 |
| DZ64C | Intermediate Thoracic Procedures, 19 years and over, with CC Score 0-2                           |       2 | 105.23   |    210.46        |   1 |
| EC21Z | Complex Echocardiogram for Congenital Heart Disease                                              |       3 |  65.19   |    195.57        |   1 |
| EC22Z | Electrocardiogram Monitoring or Stress Testing, for Congenital Heart Disease                     |    2690 | 110.172  | 296364           |   3 |
| EY02B | Implantation of Cardioverter Defibrillator with CC Score 0-8                                     |      10 |  89.22   |    892.2         |   1 |
| EY04B | Implantation of Biventricular Pacemaker with CC Score 0-5                                        |      26 |  86.55   |   2250.3         |   1 |
| EY08E | Implantation of Single-Chamber Pacemaker with CC Score 0-2                                       |      54 |  95.48   |   5155.92        |   1 |
| EY11Z | Testing of Cardiac Pacemaker or Cardioverter Defibrillator                                       |    7965 |  66.9927 | 533596           |   8 |
| EY12B | Implantation of Electrocardiography Loop Recorder with CC Score 0-2                              |     129 |  98.0479 |  12648.2         |   2 |
| EY13Z | Removal of Electrocardiography Loop Recorder                                                     |      18 |  98.43   |   1771.74        |   1 |
| EY17B | Explantation or Attention to, Cardiac Pacemaker or Cardioverter Defibrillator, with CC Score 0-5 |       3 |  86.55   |    259.65        |   1 |
| EY23C | Standard Other Percutaneous Transluminal Repair of Acquired Defect of Heart with CC Score 0-4    |      12 | 101.61   |   1219.32        |   1 |
| EY41D | Standard Percutaneous Transluminal Coronary Angioplasty with CC Score 0-3                        |     626 |  90.54   |  56678           |   1 |
| EY50Z | Complex Echocardiogram                                                                           |   28610 |  84.819  |      2.42667e+06 |  16 |
| EY51Z | Electrocardiogram Monitoring or Stress Testing                                                   |  230902 |  48.7842 |      1.12644e+07 |  40 |
| FE10D | Endoscopic Insertion of Luminal Stent into Gastrointestinal Tract with CC Score 0                |       1 | 399.29   |    399.29        |   1 |
| FE22Z | Diagnostic Endoscopic Upper Gastrointestinal Tract Procedures, 19 years and over                 |       1 |  83.62   |     83.62        |   1 |
| FF22D | Major Small Intestine Procedures, 19 years and over, with CC Score 0-1                           |       3 | 145.19   |    435.57        |   1 |
| FF53A | Minor Therapeutic or Diagnostic, General Abdominal Procedures, 19 years and over                 |      13 |  35.83   |    465.79        |   1 |
| GB11Z | Diagnostic Endoscopic Retrograde Cholangiopancreatography                                        |       2 | 323.53   |    647.06        |   1 |
| HN14E | Intermediate Hip Procedures for Non-Trauma, 19 years and over, with CC Score 0                   |       1 | 145.19   |    145.19        |   1 |
| HN16A | Minimal Hip Procedures, 19 years and over                                                        |      41 | 157.08   |   6440.28        |   1 |
| HN56Z | Minimal Shoulder Procedures                                                                      |     108 | 157.08   |  16964.6         |   1 |
| HN93Z | Other Muscle, Tendon, Fascia or Ligament Procedures                                              |      90 | 118.52   |  10666.8         |   1 |
| JA43B | Unilateral Intermediate Breast Procedures with CC Score 0-2                                      |       4 | 203.59   |    814.36        |   1 |
| JA45Z | Unilateral Minor Breast Procedures                                                               |     139 |  35.83   |   4980.37        |   1 |
| LB42A | Dynamic Studies of Urinary Tract, 19 years and over                                              |      19 |  63.59   |   1208.21        |   1 |
| MA36Z | Transvaginal Ultrasound                                                                          |   46663 |  50.1761 |      2.34137e+06 |   7 |
| MC21Z | Collection of Sperm                                                                              |     597 |  85.19   |  50858.4         |   1 |
| NZ21Z | Ante-Natal Standard Routine Ultrasound Scan                                                      |   10545 |  26.01   | 274275           |   1 |
| NZ22Z | Ante-Natal Specialised Non-Routine Ultrasound Scan                                               |    4526 |  33.59   | 152028           |   1 |
| NZ72Z | Specialised Fetal Invasive Diagnostic Procedures                                                 |   37181 |  22.55   | 838432           |   1 |
| RD97Z | Same Day Diagnostic Imaging Admission or Attendance                                              |   97304 |  77.0016 |      7.49257e+06 |   3 |
| RD98Z | Admission or Attendance for Diagnostic Imaging under General Anaesthetic                         |      24 |   5.42   |    130.08        |   1 |
| RN97Z | Same Day Nuclear Medicine Admission or Attendance                                                |    9602 |  75.24   | 722454           |   1 |
| WH15Z | Special Screening, Examinations or Other Genetic Disorders                                       | 1190296 |  28.9619 |      3.44732e+07 |  35 |
| WH51Z | Admission Related to Donation, of Organ or Tissue                                                |    1007 |  49.26   |  49604.8         |   1 |
| YC01Z | Image Guided Core Needle Biopsy of Lesion of Neck                                                |       6 |  41.8    |    250.8         |   1 |
| YC02Z | Image Guided Fine Needle Aspiration of Lesion of Neck                                            |      11 |  35.83   |    394.13        |   1 |
| YD04Z | Percutaneous Drainage of Pleural Cavity                                                          |       1 |  53.74   |     53.74        |   1 |
| YF04C | Percutaneous Single Drainage of Abdominal Abscess, with CC Score 0-1                             |       2 |  38.72   |     77.44        |   1 |
| YG05B | Percutaneous Insertion of Single Other Stent, into Hepatic or Bile Duct, With CC Score 0-3       |       1 | 399.29   |    399.29        |   1 |
| YG12Z | Other Percutaneous Diagnostic, Hepatobiliary or Pancreatic Procedures                            |       1 | 160.98   |    160.98        |   1 |



label: D=E/C
labeled_formulas: D=E/C
output: {"Arithmetic-Relationship": ["D=E/C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_569644___xlsx_2a0660bf37fd14e87caa1993fb32590edcebd5ff.xlsx___line_177