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 |
|:-------|:------------------------------------------------------------------------------------|:-----------|:-------------|----:|:--------|--------:|------:|----------:|
| MNOI1  | Mini Hamburger Twins, I.W.                                                          | PIERRE     | 550          |  80 | 5.2 OZ  | 8940051 | 53.48 | 0.6685    |
| MNOI2  | SmartServe(R) Pub Steak Burger                                                      | ADVANCE    | 1-15-230     | 160 | 3 OZ    | 8942180 | 32.95 | 0.205937  |
| MNOI3  | Pub Style Steak Burger                                                              | ADVANCE    | CN1-15-230-2 | 160 | 3 OZ    | 8940039 | 33.52 | 0.2095    |
| MNOI5  | Our Deluxe Flamebroiled Beef Steak Burger Caramel Color Added                       | ADVANCE    | 1-15-320-09  | 250 | 2.01 OZ | 8942183 | 42.78 | 0.17112   |
| MNOI6  | Flamebroiled Steak Burger                                                           | ADVANCE    | 1-15-327-09  | 175 | 2.7 OZ  | 8942181 | 30.11 | 0.172057  |
| MNOI7  | Flamebroiled Steak Burger                                                           | ADVANCE    | 1-15-924-20  | 200 | 2.4 OZ  | 9010051 | 28.41 | 0.14205   |
| MNOI8  | Flamebroiled Steak Burger                                                           | ADVANCE    | 1-15-930-20  | 160 | 3 OZ    | 8954998 | 28.41 | 0.177563  |
| MNOI9  | Fully Cooked Flame Broiled Beef Patty Made With Applesauce Caramel Color Added      | ADVANCE    | 1-155-415-20 | 180 | 1.8 OZ  | 8868171 | 25.46 | 0.141444  |
| MNOI10 | A+ Flamebroiled Beef Pattie                                                         | ADVANCE    | 1-155-425-20 | 200 | 2.5 OZ  | 8958245 | 26.71 | 0.13355   |
| MNOI11 | Flamebroiled Beef Pattie                                                            | ADVANCE    | 1-155-525-20 | 200 | 2.5 OZ  | 8958220 | 23.64 | 0.1182    |
| MNOI12 | Chargrilled Beef Patty w/Soy                                                        | ADVANCE    | 1-155-820-20 | 250 | 1.95 OZ | 9011063 | 29.43 | 0.11772   |
| MNOI13 | Flamebroiled Beef Patties Caramel Color Added                                       | ADVANCE    | 1-155-825-20 | 200 | 2.5 OZ  | 8931242 | 22.61 | 0.11305   |
| MNOI14 | Flamebroiled Beef Salisbury Steak                                                   | ADVANCE    | 1-16-521-0   | 225 | 2.14 OZ | 8868175 | 42.17 | 0.187422  |
| MNOI15 | Salisbury Steak                                                                     | ADVANCE    | 1-16-530-0   | 170 | 3 OZ    | 8941443 | 27.22 | 0.160118  |
| MNOI16 | Deluxe Beef Charbroil Meatballs                                                     | ADVANCE    | 1-17-305-0   | 960 | .5 OZ   | 8925052 | 25.61 | 0.0266771 |
| MNOI17 | A+ Deluxe Beef Charbroil Meatball                                                   | ADVANCE    | 1-17-405-20  | 960 | .5 OZ   | 8868177 | 32.28 | 0.033625  |
| MNOI18 | Beef Charbroil Meatballs                                                            | ADVANCE    | 1-17-505-0   | 960 | .5 OZ   | 9011041 | 25.57 | 0.0266354 |
| MNOI19 | Whole Grain Breaded Steak Pattie                                                    | ADVANCE    | 1-234-20WG   | 130 | 3.8 OZ  | 8668102 | 37.17 | 0.285923  |
| MNOI20 | Chunky Applesauce Fruit Cup                                                         | ADVANCE    | 101041       |  96 | 4.6 OZ  | 8868181 | 40.17 | 0.418438  |
| MNOI21 | Cinnamon Applesauce Fruit Cup                                                       | ADVANCE    | 102041       |  96 | 4.6 OZ  | 8024000 | 40.19 | 0.418646  |
| MNOI22 | Applesauce Fruit Cup                                                                | ADVANCE    | 110401       |  96 | 4.6 OZ  | 8650024 | 37.64 | 0.392083  |
| MNOI23 | Mini Twin Cheeseburger on a Whole Grain Bun                                         | ADVANCE    | 1171         | 192 | 2.35 OZ | 8868178 | 61.14 | 0.318437  |
| MNOI24 | Beef Taco Filling                                                                   | ADVANCE    | 32412328     |   6 | 5.5 LB  | 9911001 | 33.52 | 5.58667   |
| MNOI25 | Fully Cooked Taco Filling w/Beef and Soy Protein Product                            | ADVANCE    | 32432-328    | 220 | 2.4 OZ  | 8975110 | 40    | 0.181818  |
| MNOI26 | Spaghetti Sauce with Meat - Reduced Sodium                                          | ADVANCE    | 32433-328    |   6 | 5 LB    | 8868155 | 40.53 | 6.755     |
| MNOI27 | Chili Sauce with Beef-Reduced Sodium                                                | ADVANCE    | 32437-328    |   6 | 4.79 OZ | 8868154 | 43.84 | 7.30667   |
| MNOI28 | Fully Cooked Flame Broiled Beef Patties Caramel Color Added                         | Advance    | 3715         | 135 | 2.4 OZ  | 8868172 | 17.32 | 0.128296  |
| MNOI29 | Flame Broiled Salisbury Steaks Caramel Color Added                                  | ADVANCE    | 3721         | 140 | 2.6 OZ  | 8868179 | 27.05 | 0.193214  |
| MNOI30 | Pork Rib-B-Q                                                                        | PIERRE     | 3734         | 160 | 2.4 OZ  | 8931219 | 26.09 | 0.163062  |
| MNOI31 | Beef Teriyaki Dipper [3727]                                                         | ADVANCE    | 3740         | 572 | .7 OZ   | 8929151 | 29.83 | 0.0521503 |
| MNOI32 | Pork Sausage Patty [aprx. 2 1/2"]                                                   | PIERRE     | 3750         | 250 | 1.2 OZ  | 8931218 | 21.92 | 0.08768   |
| MNOI33 | Flame Broiled Rib Shaped Beef Patty with Honey BBQ Sauce Natural Smoke Flavor Added | ADVANCE    | 3753         | 100 | 3 OZ    | 8931234 | 28.41 | 0.2841    |
| MNOI34 | Pork Sausage Link                                                                   | Pierre     | 3755         | 250 | 1.2 OZ  | 9396958 | 24.62 | 0.09848   |
| MNOI35 | Flame Broiled Beef Steak                                                            | PIERRE     | 3760         | 140 | 2.3 OZ  | 8931210 | 14.16 | 0.101143  |
| MNOI36 | Beef Patty w/Onion [for 1788]                                                       | ADVANCE    | 3764         | 280 | 1.3 OZ  | 8868173 | 27.92 | 0.0997143 |
| MNOI38 | Beef and Onion Patty                                                                | ADVANCE    | 3779-150     | 200 | 1.85 OZ | 8868174 | 24.8  | 0.124     |
| MNOI39 | Beef & Onion Patty w/wrappers                                                       | PIERRE     | 3782         | 100 | 2.6 OZ  | 8931206 | 18.01 | 0.1801    |
| MNOI40 | Flame Broiled Rib Shaped Pork Patty Barbecue Sauce                                  | ADVANCE    | 3787         | 100 | 3 OZ    | 8868180 | 28.52 | 0.2852    |
| MNOI41 | Harvest Breaded Beef Patties                                                        | ADVANCE    | 69005        | 150 | 3.2 OZ  | 8952800 | 44.02 | 0.293467  |
| MNOI42 | Harvest Breaded Beef Patties- Sticks Shape                                          | ADVANCE    | 69006        | 620 | .80 OZ  | 8952801 | 45.43 | 0.0732742 |
| MNOI43 | Whole Grain Breaded Pork Patty                                                      | ADVANCE    | 69019        | 100 | 3.1 OZ  | 8868136 | 35.67 | 0.3567    |
| MNOI44 | Whole Grain Country Fried Breaded Beef Finger                                       | ADVANCE    | 69038        | 400 | 0.9 OZ  | 8868151 | 34.57 | 0.086425  |
| MNOI45 | Whole Grain Country Fried Breaded Beef Pattie                                       | ADVANCE    | 69039        |  85 | 3.85 OZ | 8868153 | 32.09 | 0.377529  |
| MNOI46 | Peach Fruit Cup                                                                     | ADVANCE    | 801401       |  96 | 4.75 OZ | 8650026 | 66.03 | 0.687813  |
| MNOI47 | Pear Fruit Cup                                                                      | ADVANCE    | 802401       |  96 | 4.75 OZ | 8024012 | 64.88 | 0.675833  |
| MNOI48 | Peanut Butter & Jelly Cup                                                           | Pierre     | 90017        | 100 | 2.8 OZ  | 8024013 | 47.66 | 0.4766    |
| MNOI49 | Peanut Butter & Grape Jamwich on Wheat                                              | PIERRE     | 92123        |  72 | 2.8 OZ  | 9911065 | 35.78 | 0.496944  |
| MNOI50 | Peanut Butter & Strawberry Jamwich on Wheat                                         | PIERRE     | 92127        |  72 | 2.8 OZ  | 4535354 | 35.9  | 0.498611  |
| MNOI51 | Fully Cooked Pork Sausage Patties Caramel Color Added                               | ADVANCE    | 9467         | 250 | 1.2 OZ  | 8925451 | 22.5  | 0.09      |
| MNOI53 | PB & GRAPE JELLY ON GRAHAM WAFER WHOLE GRAIN                                        | PIERRE     | A1290        | 160 | 2.2 OZ  | 4531212 | 59.75 | 0.373437  |
| MNOI54 | SAUSAGE PATTY PORK PC                                                               | PIERRE     | 3750         | 250 | 1.2 OZ  | 8931218 | 21.92 | 0.08768   |
| MNOI55 | PORK RIB PATTIE CN                                                                  | PIERRE     | 3734         | 160 | 2.4 OZ  | 8931219 | 26.09 | 0.163062  |
| MNOI56 | PORK BITES HONEY BBQ COMMODI                                                        | PIERRE     | 3722         | 400 | .8 OZ   | 8931225 | 37.63 | 0.094075  |
| MNOI57 | PATTY, PORK BRD FC COMMODITY                                                        | ADVANCE    | 69019        | 100 | 3.1 OZ  | 8868136 | 35.67 | 0.3567    |
| MNOI58 | Pork Sausage Link CN                                                                | Pierre     | 3755         | 250 | 1.2 OZ  | 9396958 | 24.62 | 0.09848   |
| MNOI59 | BEEF CRUMBLE CN FC REDCD FAT                                                        | ADVANCE    | 1-320400-20  |   6 | 5 LB    | 8931087 | 27.84 | 4.64      |
| MNOI60 | Teriyaki Beef Blasters with Sauce, 10% APP C16070GLZ                                | Integrated | C16070GLZ    | 100 | 3.3 OZ  | 9995850 | 34.58 | 0.3458    |
| MNOI61 | BEEF PATTIES F/C MESQ.FLAV                                                          | JTM        | CP5664       |   6 | 5 LB    | 8931006 | 31.67 | 5.27833   |
| MNOI62 | Jalapeno PepperJack Beef Patty                                                      | JTM        | CP5673       | 200 | 2.4 OZ  | 9404192 | 36.89 | 0.18445   |
| MNOI63 | JTM Culinary RF / RS Beef Tips and Gravy                                            | JTM        | CP5840       |   4 | 8 LB    | 8931128 | 39.84 | 9.96      |
| MNOI64 | Glazed Teriyaki Beef Nuggets (4 ct)                                                 | JTM        | CP5850       |   6 | 5 LB    | 8931003 | 37.65 | 6.275     |
| MNOI65 | Cooked Ground Beef (100%) Drained and Rinsed                                        | JTM        | CP5872       |   6 | 5 LB    | 8931095 | 22.09 | 3.68167   |



label: I=H/E
labeled_formulas: I=H/E
output: {"Arithmetic-Relationship": ["I=H/E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_306049___xlsx_5118b82126ab00c0d0e6e8f97ef8767db934597c.xlsx___line_182