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 |
|------:|:---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|----:|-----:|----:|----:|----:|----:|----:|
| 80048 | Basic metabolic panel (Calcium, total) This panel must include the following: Calcium, total (82310), Carbon dioxide (82374), Chloride (82435), Creatinine (82565), Glucose (82947), Potassium (84132), Sodium (84295), Urea nitrogen (BUN) (84520)                                                                                                                                                                                                            |  21 | 12.6 |   6 |   8 |   7 |   8 |   6 |
| 80050 | General health panel This panel must include the following: Comprehensive metabolic panel (80053), Blood count, complete (CBC), automated and automated differential WBC count (85025 or 85027 and 85004), OR, Blood count, complete (CBC), automated (85027) and appropriate manual differential WBC count (85007 or 85009), Thyroid stimulating hormone (TSH) (84443)                                                                                        |  87 | 52.2 |  25 |  35 |  25 |  35 |  25 |
| 80053 | Comprehensive metabolic panel This panel must include the following: Albumin (82040), Bilirubin, total (82247), Calcium, total (82310), Carbon dioxide (bicarbonate) (82374), Chloride (82435), Creatinine (82565), Glucose (82947), Phosphatase, alkaline (84075), Potassium (84132), Protein, total (84155), Sodium (84295), Transferase, alanine amino (ALT) (SGPT) (84460), Transferase, aspartate amino (AST) (SGOT) (84450), Urea nitrogen (BUN) (84520) |  26 | 15.6 |   8 |  11 |   9 |  11 |   8 |
| 80061 | Lipid panel This panel must include the following: Cholesterol, serum, total (82465), Lipoprotein, direct measurement, high density cholesterol (HDL cholesterol) (83718), Triglycerides (84478)                                                                                                                                                                                                                                                               |  33 | 19.8 |  10 |  12 |  10 |  12 |  10 |
| 80074 | Acute hepatitis panel This panel must include the following: Hepatitis A antibody (HAAb), IgM antibody (86709), Hepatitis B core antibody (HBcAb), IgM antibody (86705), Hepatitis B surface antigen (HBsAg) (87340), Hepatitis C antibody (86803)                                                                                                                                                                                                             | 118 | 70.8 |  34 |  47 |  39 |  47 |  34 |
| 80076 | Hepatic function panel This panel must include the following: Albumin (82040), Bilirubin, total (82247), Bilirubin, direct (82248), Phosphatase, alkaline (84075), Protein, total (84155), Transferase, alanine amino (ALT) (SGPT) (84460), Transferase, aspartate amino (AST) (SGOT) (84450)                                                                                                                                                                  |  20 | 12   |   6 |   8 |   7 |   8 |   6 |
| 80158 | Cyclosporine                                                                                                                                                                                                                                                                                                                                                                                                                                                   |  45 | 27   |  13 |  18 |  15 |  18 |  13 |
| 80162 | Digoxin                                                                                                                                                                                                                                                                                                                                                                                                                                                        |  33 | 19.8 |  10 |  13 |  11 |  13 |  10 |
| 80164 | Dipropylacetic acid (valproic acid)                                                                                                                                                                                                                                                                                                                                                                                                                            |  33 | 19.8 |  10 |  13 |  11 |  13 |  10 |
| 80175 | HC DRUG SCREEN QUANT LAMOTRIGINE                                                                                                                                                                                                                                                                                                                                                                                                                               |  33 | 19.8 |  10 |  13 |  11 |  13 |  10 |
| 80202 | Vancomycin                                                                                                                                                                                                                                                                                                                                                                                                                                                     |  33 | 19.8 |  10 |  13 |  11 |  13 |  10 |
| 80306 | HC DRUG TEST(S) PRSMV INSTRUMENT                                                                                                                                                                                                                                                                                                                                                                                                                               |  41 | 24.6 |  12 |  16 |  12 |  16 |  12 |
| 81001 | Urinalysis, by dip stick or tablet reagent for bilirubin, glucose, hemoglobin, ketones, leukocytes, nitrite, pH, protein, specific gravity, urobilinogen, any number of these constituents; automated, with microscopy                                                                                                                                                                                                                                         |   8 |  4.8 |   2 |   3 |   3 |   3 |   2 |
| 81003 | Urinalysis, by dip stick or tablet reagent for bilirubin, glucose, hemoglobin, ketones, leukocytes, nitrite, pH, protein, specific gravity, urobilinogen, any number of these constituents; automated, without microscopy                                                                                                                                                                                                                                      |   6 |  3.6 |   2 |   2 |   2 |   2 |   2 |
| 82043 | Albumin; urine, microalbumin, quantitative                                                                                                                                                                                                                                                                                                                                                                                                                     |  14 |  8.4 |   4 |   6 |   5 |   6 |   4 |
| 82140 | Ammonia                                                                                                                                                                                                                                                                                                                                                                                                                                                        |  36 | 21.6 |  11 |  14 |  12 |  14 |  11 |
| 82150 | Amylase                                                                                                                                                                                                                                                                                                                                                                                                                                                        |  16 |  9.6 |   5 |   6 |   5 |   6 |   5 |
| 82247 | Bilirubin; total                                                                                                                                                                                                                                                                                                                                                                                                                                               |  12 |  7.2 |   4 |   5 |   4 |   5 |   4 |
| 82272 | Blood, occult, by peroxidase activity (eg, guaiac), qualitative, feces, 1-3 simultaneous determinations, performed for other than colorectal neoplasm screening                                                                                                                                                                                                                                                                                                |   8 |  4.8 |   2 |   3 |   3 |   3 |   2 |
| 82306 | Vitamin D; 25 hydroxy, includes fraction(s), if performed                                                                                                                                                                                                                                                                                                                                                                                                      |  73 | 43.8 |  21 |  31 |  25 |  31 |  21 |
| 82553 | Creatine kinase (CK), (CPK); MB fraction only                                                                                                                                                                                                                                                                                                                                                                                                                  |  29 | 17.4 |   8 |  12 |  10 |  12 |   8 |
| 82607 | Cyanocobalamin (Vitamin B-12);                                                                                                                                                                                                                                                                                                                                                                                                                                 |  37 | 22.2 |  11 |  15 |  13 |  15 |  11 |
| 82670 | Estradiol                                                                                                                                                                                                                                                                                                                                                                                                                                                      |  69 | 41.4 |  20 |  27 |  23 |  27 |  20 |
| 82728 | Ferritin                                                                                                                                                                                                                                                                                                                                                                                                                                                       |  34 | 20.4 |  10 |  14 |  11 |  14 |  10 |
| 82746 | Folic acid; serum                                                                                                                                                                                                                                                                                                                                                                                                                                              |  36 | 21.6 |  11 |  14 |  11 |  14 |  11 |
| 82941 | Gastrin                                                                                                                                                                                                                                                                                                                                                                                                                                                        |  44 | 26.4 |  13 |  17 |  15 |  17 |  13 |
| 83001 | Gonadotropin; follicle stimulating hormone (FSH)                                                                                                                                                                                                                                                                                                                                                                                                               |  46 | 27.6 |  13 |  19 |  16 |  19 |  13 |
| 83002 | Gonadotropin; luteinizing hormone (LH)                                                                                                                                                                                                                                                                                                                                                                                                                         |  46 | 27.6 |  13 |  19 |  16 |  19 |  13 |
| 83036 | Hemoglobin; glycosylated (A1C)                                                                                                                                                                                                                                                                                                                                                                                                                                 |  24 | 14.4 |   7 |  10 |   8 |  10 |   7 |
| 83090 | Homocysteine                                                                                                                                                                                                                                                                                                                                                                                                                                                   |  42 | 25.2 |  12 |  17 |  14 |  17 |  12 |
| 83525 | Insulin; total                                                                                                                                                                                                                                                                                                                                                                                                                                                 |  28 | 16.8 |   8 |  11 |   9 |  11 |   8 |
| 83540 | Iron                                                                                                                                                                                                                                                                                                                                                                                                                                                           |  16 |  9.6 |   5 |   6 |   5 |   6 |   5 |
| 83690 | Lipase                                                                                                                                                                                                                                                                                                                                                                                                                                                         |  17 | 10.2 |   5 |   7 |   6 |   7 |   5 |
| 83735 | Magnesium                                                                                                                                                                                                                                                                                                                                                                                                                                                      |  17 | 10.2 |   5 |   7 |   6 |   7 |   5 |
| 84132 | Potassium; serum, plasma or whole blood                                                                                                                                                                                                                                                                                                                                                                                                                        |  11 |  6.6 |   3 |   4 |   4 |   4 |   3 |
| 84134 | Prealbumin                                                                                                                                                                                                                                                                                                                                                                                                                                                     |  36 | 21.6 |  11 |  14 |  12 |  14 |  11 |
| 84145 | Procalcitonin (PCT)                                                                                                                                                                                                                                                                                                                                                                                                                                            |  66 | 39.6 |  19 |  26 |  23 |  26 |  19 |
| 84146 | Prolactin                                                                                                                                                                                                                                                                                                                                                                                                                                                      |  48 | 28.8 |  14 |  19 |  16 |  19 |  14 |
| 84153 | Prostate specific antigen (PSA); total                                                                                                                                                                                                                                                                                                                                                                                                                         |  45 | 27   |  13 |  18 |  15 |  18 |  13 |
| 84402 | Testosterone; free                                                                                                                                                                                                                                                                                                                                                                                                                                             |  63 | 37.8 |  18 |  25 |  21 |  25 |  18 |
| 84403 | Testosterone; total                                                                                                                                                                                                                                                                                                                                                                                                                                            |  64 | 38.4 |  19 |  25 |  22 |  25 |  19 |
| 84410 | HC TESTOSTERONE BIOAVAILABLE                                                                                                                                                                                                                                                                                                                                                                                                                                   | 127 | 76.2 |  37 |  50 |  43 |  50 |  37 |
| 84439 | Thyroxine; free                                                                                                                                                                                                                                                                                                                                                                                                                                                |  22 | 13.2 |   6 |   9 |   8 |   9 |   6 |
| 84443 | Thyroid stimulating hormone (TSH)                                                                                                                                                                                                                                                                                                                                                                                                                              |  42 | 25.2 |  12 |  18 |  14 |  18 |  12 |
| 84466 | Transferrin                                                                                                                                                                                                                                                                                                                                                                                                                                                    |  32 | 19.2 |   9 |  13 |  11 |  13 |   9 |
| 84481 | Triiodothyronine T3; free                                                                                                                                                                                                                                                                                                                                                                                                                                      |  42 | 25.2 |  12 |  17 |  14 |  17 |  12 |
| 84482 | Triiodothyronine T3; reverse                                                                                                                                                                                                                                                                                                                                                                                                                                   |  39 | 23.4 |  11 |  15 |  13 |  15 |  11 |
| 84484 | Troponin, quantitative                                                                                                                                                                                                                                                                                                                                                                                                                                         |  25 | 15   |   7 |  10 |   8 |  10 |   7 |
| 84550 | Uric acid; blood                                                                                                                                                                                                                                                                                                                                                                                                                                               |  11 |  6.6 |   3 |   4 |   4 |   4 |   3 |
| 85025 | Blood count; complete (CBC), automated (Hgb, Hct, RBC, WBC and platelet count) and automated differential WBC count                                                                                                                                                                                                                                                                                                                                            |  19 | 11.4 |   6 |   8 |   7 |   8 |   6 |
| 85045 | Blood count; reticulocyte, automated                                                                                                                                                                                                                                                                                                                                                                                                                           |  10 |  6   |   3 |   4 |   3 |   4 |   3 |
| 85378 | Fibrin degradation products, D-dimer; qualitative or semiquantitative                                                                                                                                                                                                                                                                                                                                                                                          |  19 | 11.4 |   6 |   8 |   6 |   8 |   6 |
| 85610 | Prothrombin time;                                                                                                                                                                                                                                                                                                                                                                                                                                              |  10 |  6   |   3 |   4 |   3 |   4 |   3 |
| 85651 | Sedimentation rate, erythrocyte; non-automated                                                                                                                                                                                                                                                                                                                                                                                                                 |   9 |  5.4 |   3 |   4 |   3 |   4 |   3 |
| 85730 | Thromboplastin time, partial (PTT); plasma or whole blood                                                                                                                                                                                                                                                                                                                                                                                                      |  15 |  9   |   4 |   6 |   5 |   6 |   4 |
| 86003 | Allergen specific IgE; quantitative or semiquantitative, each allergen                                                                                                                                                                                                                                                                                                                                                                                         |  52 | 31.2 |  15 |  21 |  18 |  21 |  15 |
| 86038 | Antinuclear antibodies (ANA);                                                                                                                                                                                                                                                                                                                                                                                                                                  |  30 | 18   |   9 |  12 |  10 |  12 |   9 |
| 86140 | C-reactive protein;                                                                                                                                                                                                                                                                                                                                                                                                                                            |  13 |  7.8 |   4 |   5 |   4 |   5 |   4 |
| 86200 | Cyclic citrullinated peptide (CCP), antibody                                                                                                                                                                                                                                                                                                                                                                                                                   |  32 | 19.2 |   9 |  13 |  11 |  13 |   9 |
| 86376 | Microsomal antibodies (eg, thyroid or liver-kidney), each                                                                                                                                                                                                                                                                                                                                                                                                      |  36 | 21.6 |  11 |  14 |  12 |  14 |  11 |
| 86431 | Rheumatoid factor; quantitative                                                                                                                                                                                                                                                                                                                                                                                                                                |  14 |  8.4 |   4 |   6 |   5 |   6 |   4 |
| 86592 | Syphilis test, non-treponemal antibody; qualitative (eg, VDRL, RPR, ART)                                                                                                                                                                                                                                                                                                                                                                                       |  11 |  6.6 |   3 |   4 |   4 |   4 |   3 |
| 86617 | Antibody; Borrelia burgdorferi (Lyme disease) confirmatory test (eg, Western Blot or immunoblot)                                                                                                                                                                                                                                                                                                                                                               |  76 | 45.6 |  22 |  30 |  26 |  30 |  22 |
| 86618 | Antibody; Borrelia burgdorferi (Lyme disease)                                                                                                                                                                                                                                                                                                                                                                                                                  |  84 | 50.4 |  25 |  33 |  29 |  33 |  25 |
| 86644 | Antibody; cytomegalovirus (CMV)                                                                                                                                                                                                                                                                                                                                                                                                                                |  36 | 21.6 |  11 |  14 |  12 |  14 |  11 |
| 86645 | Antibody; cytomegalovirus (CMV), IgM                                                                                                                                                                                                                                                                                                                                                                                                                           |  42 | 25.2 |  12 |  17 |  14 |  17 |  12 |
| 86677 | Antibody; Helicobacter pylori                                                                                                                                                                                                                                                                                                                                                                                                                                  |  36 | 21.6 |  11 |  14 |  12 |  14 |  11 |
| 86694 | Antibody; herpes simplex, non-specific type test                                                                                                                                                                                                                                                                                                                                                                                                               |  36 | 21.6 |  11 |  14 |  12 |  14 |  11 |
| 86695 | Antibody; herpes simplex, type 1                                                                                                                                                                                                                                                                                                                                                                                                                               |  33 | 19.8 |  10 |  13 |  11 |  13 |  10 |
| 86696 | Antibody; herpes simplex, type 2                                                                                                                                                                                                                                                                                                                                                                                                                               |  48 | 28.8 |  14 |  19 |  16 |  19 |  14 |
| 86706 | Hepatitis B surface antibody (HBsAb)                                                                                                                                                                                                                                                                                                                                                                                                                           |  27 | 16.2 |   8 |  11 |   8 |  11 |   8 |
| 86747 | Antibody; parvovirus                                                                                                                                                                                                                                                                                                                                                                                                                                           |  74 | 44.4 |  22 |  29 |  25 |  29 |  22 |
| 86757 | Antibody; Rickettsia                                                                                                                                                                                                                                                                                                                                                                                                                                           |  96 | 57.6 |  28 |  38 |  33 |  38 |  28 |
| 86787 | Antibody; varicella-zoster                                                                                                                                                                                                                                                                                                                                                                                                                                     |  32 | 19.2 |   9 |  13 |  11 |  13 |   9 |
| 87040 | Culture, bacterial; blood, aerobic, with isolation and presumptive identification of isolates (includes anaerobic culture, if appropriate)                                                                                                                                                                                                                                                                                                                     |  50 | 30   |  15 |  20 |  17 |  20 |  15 |
| 87045 | Culture, bacterial; stool, aerobic, with isolation and preliminary examination (eg, KIA, LIA), Salmonella and Shigella species                                                                                                                                                                                                                                                                                                                                 |  23 | 13.8 |   7 |   9 |   8 |   9 |   7 |
| 87046 | Culture, bacterial; stool, aerobic, additional pathogens, isolation and presumptive identification of isolates, each plate                                                                                                                                                                                                                                                                                                                                     |  23 | 13.8 |   7 |   9 |   8 |   9 |   7 |
| 87070 | Culture, bacterial; any other source except urine, blood or stool, aerobic, with isolation and presumptive identification of isolates                                                                                                                                                                                                                                                                                                                          |  21 | 12.6 |   6 |   8 |   7 |   8 |   6 |
| 87077 | Culture, bacterial; aerobic isolate, additional methods required for definitive identification, each isolate                                                                                                                                                                                                                                                                                                                                                   |  20 | 12   |   6 |   8 |   7 |   8 |   6 |
| 87086 | Culture, bacterial; quantitative colony count, urine                                                                                                                                                                                                                                                                                                                                                                                                           |  20 | 12   |   6 |   8 |   7 |   8 |   6 |
| 87186 | Susceptibility studies, antimicrobial agent; microdilution or agar dilution (minimum inhibitory concentration [MIC] or breakpoint), each multi-antimicrobial, per plate                                                                                                                                                                                                                                                                                        |  21 | 12.6 |   6 |   8 |   7 |   8 |   6 |
| 87205 | Smear, primary source with interpretation; Gram or Giemsa stain for bacteria, fungi, or cell types                                                                                                                                                                                                                                                                                                                                                             |  11 |  6.6 |   3 |   4 |   4 |   4 |   3 |
| 87210 | Smear, primary source with interpretation; wet mount for infectious agents (eg, saline, India ink, KOH preps)                                                                                                                                                                                                                                                                                                                                                  |  12 |  7.2 |   4 |   5 |   4 |   5 |   4 |
| 87324 | Infectious agent antigen detection by enzyme immunoassay technique, qualitative or semiquantitative, multiple-step method; Clostridium difficile toxin(s)                                                                                                                                                                                                                                                                                                      |  30 | 18   |   9 |  12 |   9 |  12 |   9 |
| 87328 | Infectious agent antigen detection by enzyme immunoassay technique, qualitative or semiquantitative, multiple-step method; cryptosporidium                                                                                                                                                                                                                                                                                                                     |  30 | 18   |   9 |  12 |   9 |  12 |   9 |
| 87329 | Infectious agent antigen detection by enzyme immunoassay technique, qualitative or semiquantitative, multiple-step method; giardia                                                                                                                                                                                                                                                                                                                             |  30 | 18   |   9 |  12 |   9 |  12 |   9 |
| 87425 | Infectious agent antigen detection by enzyme immunoassay technique, qualitative or semiquantitative, multiple-step method; rotavirus                                                                                                                                                                                                                                                                                                                           |  30 | 18   |   9 |  12 |   9 |  12 |   9 |
| 87426 | HC CORONAVIRUS AG IA                                                                                                                                                                                                                                                                                                                                                                                                                                           |  80 | 48   |  23 |  32 |  31 |  32 |  23 |
| 87427 | Infectious agent antigen detection by enzyme immunoassay technique, qualitative or semiquantitative, multiple-step method; Shiga-like toxin                                                                                                                                                                                                                                                                                                                    |  30 | 18   |   9 |  12 |   9 |  12 |   9 |
| 87449 | Infectious agent antigen detection by enzyme immunoassay technique qualitative or semiquantitative; multiple step method, not otherwise specified, each organism                                                                                                                                                                                                                                                                                               |  30 | 18   |   9 |  12 |   9 |  12 |   9 |
| 89055 | Leukocyte assessment, fecal, qualitative or semiquantitative                                                                                                                                                                                                                                                                                                                                                                                                   |  11 |  6.6 |   3 |   4 |   4 |   4 |   3 |



labeled_formulas: I=(E+F)-H
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_724443___xlsx_3c2e810cb61d88e1cadddbee87deb4ad50bf357b.xlsx___line_189