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:
|   B | C                               |     D | E   |        F | G      |     H |         I | J      |     K |       L | M      |         N |
|----:|:--------------------------------|------:|:----|---------:|:-------|------:|----------:|:-------|------:|--------:|:-------|----------:|
|   1 | Aluminium chloride              | 500   | gm  |     1.8  | /-each |   900 |     2.7   | /-each |  1350 |     2.6 | /-each |   1300    |
|   2 | Glucose                         |   1   | Kg  |  1200    | /-each |  1200 |   360     | /-each |   360 |  1100   | /-each |   1100    |
|   3 | Hydrogen peroxide               |   1   | Lit |   900    | /-each |   900 |   300     | /-each |   300 |  1000   | /-each |   1000    |
|   4 | Iodine                          |   1   | kg  | 20800    | /-each | 20800 | 15000     | /-each | 15000 | 52600   | /-each |  52600    |
|   5 | Pthalic acid                    |   1   | kg  |  2400    | /-each |  2400 |  2400     | /-each |  2400 |  2400   | /-each |   2400    |
|   6 | Phenolphthalein                 | 100   | g   |   160    | /-each | 16000 |     6     | /-each |   600 |    17   | /-each |   1700    |
|   7 | Pepsin                          | 100   | g   |    40    | /-each |  4000 |    15     | /-each |  1500 |    65   | /-each |   6500    |
|   8 | Sodium benzoate                 |   1   | Kg  |  1400    | /-each |  1400 |   600     | /-each |   600 |  1700   | /-each |   1700    |
|   9 | Sodium nitrite                  |   1   | Kg  |  2400    | /-each |  2400 |   950     | /-each |   950 |  1700   | /-each |   1700    |
|  10 | Succinic acid                   | 500   | gm  |     2.7  | /-each |  1350 |     3.2   | /-each |  1600 |  1900   | /-each | 950000    |
|  11 | Sodium hydrogen phosphate       |   2   | Kg  |  1500    | /-each |  3000 |  1600     | /-each |  3200 |  1600   | /-each |   3200    |
|  12 | Disodium hydrogen phosphate     | 500   | g   |     2.6  | /-each |  1300 |     0.95  | /-each |   475 |     3.8 | /-each |   1900    |
|  13 | Silver nitrate                  |  50   | g   |    88    | /-each |  4400 |    84     | /-each |  4200 |   280   | /-each |  14000    |
|  14 | Zn sulphate                     |   2   | Kg  |  1250    | /-each |  2500 |   450     | /-each |   900 |  1800   | /-each |   3600    |
|  15 | Ethanol                         |  15   | Lit |   460    | /-each |  6900 |   600     | /-each |  9000 |  2200   | /-each |  33000    |
|  16 | Methanol                        |  15   | Lit |   300    | /-each |  4500 |   300     | /-each |  4500 |   400   | /-each |   6000    |
|  17 | n-Hexane                        |  15   | Lit |   720    | /-each | 10800 |   720     | /-each | 10800 |   875   | /-each |  13125    |
|  18 | Acetone                         |   1   | lit |   880    | /-each |   880 |   600     | /-each |   600 |  2200   | /-each |   2200    |
|  19 | Chloroform                      |   2.5 | Lit |   500    | /-each |  1250 |   300     | /-each |   750 |   962.5 | /-each |   2406.25 |
|  20 | Calcium Carbonate               | 500   | gm  |     1.6  | /-each |   800 |     0.7   | /-each |   350 |     1.1 | /-each |    550    |
|  21 | Calcium Hydroxid                | 500   | gm  |     1.8  | /-each |   900 |     0.7   | /-each |   350 |     1.4 | /-each |    700    |
|  22 | Na2CO3                          |   1   | Kg  |  1400    | /-each |  1400 |   750     | /-each |   750 |  1200   | /-each |   1200    |
|  23 | NaHCO3                          |   1   | Kg  |  1200    | /-each |  1200 |   450     | /-each |   450 |  1000   | /-each |   1000    |
|  24 | Oxalic acid                     |   1   | Kg  |  1100    | /-each |  1100 |   500     | /-each |   500 |  1800   | /-each |   1800    |
|  25 | Citric acid                     |   1   | Kg  |   900    | /-each |   900 |   450     | /-each |   450 |  2000   | /-each |   2000    |
|  26 | MgSO4                           | 900   | g   |     0.95 | /-each |   855 |     0.55  | /-each |   495 |     1.6 | /-each |   1440    |
|  27 | Sodium carboxy methyl cellulose | 500   | gm  |     7    | /-each |  3500 |     0.85  | /-each |   425 |     9   | /-each |   4500    |
|  28 | Bentonite                       | 500   | g   |     2.8  | /-each |  1400 |     0.9   | /-each |   450 |     2.4 | /-each |   1200    |
|  29 | Potassium dihydrogen phosphate  | 500   | g   |     1.3  | /-each |   650 |     1.5   | /-each |   750 |     1.8 | /-each |    900    |
|  30 | Lactose                         |   3   | Kg  |  1700    | /-each |  5100 |   650     | /-each |  1950 |  1300   | /-each |   3900    |
|  31 | Zinc oxide                      | 500   | g   |     3.2  | /-each |  1600 |     0.7   | /-each |   350 |     1.8 | /-each |    900    |
|  32 | Gelatin powder                  |   1   | k g |  2200    | /-each |  2200 |   700     | /-each |   700 |  3400   | /-each |   3400    |
|  33 | Mg Sterate                      |   1   | Kg  |  3400    | /-each |  3400 |   600     | /-each |   600 |  2800   | /-each |   2800    |
|  34 | Steric acid                     | 800   | g   |     3    | /-each |  2400 |     0.625 | /-each |   500 |     1.8 | /-each |   1440    |
|  35 | Tartaric acid                   | 500   | g   |     4.2  | /-each |  2100 |     0.8   | /-each |   400 |     3.5 | /-each |   1750    |
|  36 | Liquid paraffin                 |   5   | Lit |  1850    | /-each |  9250 |   260     | /-each |  1300 |  1200   | /-each |   6000    |
|  37 | Acetic acid                     |   5   | kg  |   440    | /-each |  2200 |   260     | /-each |  1300 |   450   | /-each |   2250    |
|  38 | HCl                             |  10   | Lit |  1280    | /-each | 12800 |   180     | /-each |  1800 |  3000   | /-each |  30000    |
|  39 | HNO3                            |   7.5 | Lit |   460    | /-each |  3450 |   360     | /-each |  2700 |  5400   | /-each |  40500    |
|  40 | H2SO4                           |   7.5 | Lit |  1280    | /-each |  9600 |   480     | /-each |  3600 |     2.3 | /-each |  17250    |
|  42 | Sodium oxalate                  | 500   | g   |     3.2  | /-each |  1600 |     0.9   | /-each |   450 |     2.4 | /-each |   1200    |
|  43 | Lead acetate                    | 500   | g   |     2.2  | /-each |  1100 |     1.3   | /-each |   650 |     2.9 | /-each |   1450    |
|  44 | Ferrous sulphate                |   1   | kg  |  1150    | /-each |  1150 |   450     | /-each |   450 |  1100   | /-each |   1100    |
|  45 | 4-Amino benzoic acid            |  50   | g   |    11.6  | /-each |   580 |    30     | /-each |  1500 |     9.8 | /-each |    490    |
|  46 | Methyl red                      |  25   | g   |    36    | /-each |   900 |    32     | /-each |   800 |    52   | /-each |   1300    |
|  47 | Barium chloride                 |   1   | Kg  |   900    | /-each |   900 |   650     | /-each |   650 |  1900   | /-each |   1900    |
|  48 | Methyl cellulose                |   1   | Kg  |  8400    | /-each |  8400 |  2900     | /-each |  2900 | 15600   | /-each |  15600    |
|  49 | Ammonium chloride               |   1   | Kg  |  1100    | /-each |  1100 |   250     | /-each |   250 |  1100   | /-each |   1100    |
|  50 | Poly vinyl pyrrolidone          |   1   | kg  |  8800    | /-each |  8800 |  1400     | /-each |  1400 | 10600   | /-each |  10600    |
|  51 | Butanol                         |   5   | Lit |   480    | /-each |  2400 |   720     | /-each |  3600 |  1200   | /-each |   6000    |
|  52 | Xylene                          |   2.5 | Lit |   560    | /-each |  1400 |   380     | /-each |   950 |   675   | /-each |   1687.5  |
|  53 | Phenol red                      |  50   | g   |    38    | /-each |  1900 |    48     | /-each |  2400 |    96   | /-each |   4800    |
|  54 | Nutrient Agar                   | 500   | g   |    10.4  | /-each |  5200 |     8.8   | /-each |  4400 |     9   | /-each |   4500    |
|  55 | Crystal Violet                  |  25   | g   |    32    | /-each |   800 |    30     | /-each |   750 |    40   | /-each |   1000    |
|  56 | Safranine                       |  25   | g   |    50    | /-each |  1250 |    96     | /-each |  2400 |    72   | /-each |   1800    |
|  57 | Chloral hydrate                 | 500   | g   |     5.6  | /-each |  2800 |     1.8   | /-each |   900 |    12.8 | /-each |   6400    |
|  58 | Methylene blue                  |  25   | g   |    34    | /-each |   850 |    22     | /-each |   550 |    76   | /-each |   1900    |
|  59 | Lactic acid                     | 600   | gm  |     2.8  | /-each |  1680 |     0.95  | /-each |   570 |     2.4 | /-each |   1440    |
|  60 | Benzoin                         | 500   | g   |    13.6  | /-each |  6800 |     0.55  | /-each |   275 |     4.3 | /-each |   2150    |



label: H=F*D
K=D*I
labeled_formulas: H=F*D
K=D*I
output: {"Arithmetic-Relationship": ["H=F*D", "K=D*I"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_2454___xlsx_8b84a50e1401d1e942c4d58c9fba4330d97afa80.xlsx___line_447