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      |
|:---------------------------------------|:-------------------------------------------------------------|-----:|----:|------:|----------:|----:|----:|:---------------------------------------------------|:-------|
| Fuze Juice Drink                       | Berry Punch (3% Juice)                                       | 20   | 2.5 | 125   |  50       |  50 |  50 | Marketed as Juice, Not 100% Juice                  | RED    |
| Fuze Juice Drink                       | Berry Punch (3% Juice)                                       | 33.8 | 4   | 320   |  75.7396  |  80 |  80 | Marketed as Juice, Not 100% Juice                  | RED    |
| Fuze Juice Drink                       | Strawberry Lemonade (3% Juice)                               | 20   | 2.5 | 157.5 |  63       |  63 |  19 | Marketed as Juice, Not 100% Juice                  | RED    |
| Fuze Juice Drink                       | Strawberry Lemonade (3% Juice)                               | 33.8 | 4   | 400   |  94.6746  | 100 |  30 | Marketed as Juice, Not 100% Juice                  | RED    |
| Hawaiian Punch                         | Fruit Juicy Red (5% Juice)                                   | 16   | 2   | 130   |  65       |  65 | 100 | Not 100% Juice, Flavored Punch Drink               | RED    |
| Hawaiian Punch                         | Green Berry Rush (5% Juice)                                  | 16   | 2   | 130   |  65       |  65 | 100 | Not 100% Juice, Flavored Punch Drink               | RED    |
| Hawaiian Punch                         | Polar Blast (5% Juice)                                       | 16   | 2   | 140   |  70       |  70 | 100 | Not 100% Juice, Flavored Punch Drink               | RED    |
| Izze                                   | Sparkling Blackberry (70% Juice)                             | 12   | 1   | 130   |  86.6667  | 130 |  25 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze                                   | Sparkling Blackberry (70% Juice)                             |  8.4 | 1   |  90   |  85.7143  |  90 |  20 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze                                   | Sparkling Blueberry (70% Juice)                              | 12   | 1   | 130   |  86.6667  | 130 |  30 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze                                   | Sparkling Clementine (70% Juice)                             | 16   | 1   | 160   |  80       | 160 |  30 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze                                   | Sparkling Clementine (70% Juice)                             | 12   | 1   | 120   |  80       | 120 |  25 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze                                   | Sparkling Clementine (70% Juice)                             |  8.4 | 1   |  90   |  85.7143  |  90 |  15 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze                                   | Sparkling Ginger (0% Juice)                                  | 12   | 1   | 120   |  80       | 120 |   5 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze                                   | Sparkling Grapefruit (70% Juice)                             | 16   | 1   | 160   |  80       | 160 |  25 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze                                   | Sparkling Grapefruit (70% Juice)                             | 12   | 1   | 120   |  80       | 120 |  20 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze                                   | Sparkling Grapefruit (70% Juice)                             |  8.4 | 1   |  90   |  85.7143  |  90 |  15 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze                                   | Sparkling Lemon (70% Juice)                                  | 12   | 1   | 130   |  86.6667  | 130 |  15 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze                                   | Sparkling Lemon Ginger (70% Juice)                           | 12   | 1   | 130   |  86.6667  | 130 |  20 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze                                   | Sparkling Peach (70% Juice)                                  | 12   | 1   | 130   |  86.6667  | 130 |  20 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze                                   | Sparkling Pomegranate (70% Juice)                            | 12   | 1   | 120   |  80       | 120 |  15 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze                                   | Sparkling Pomegranate (70% Juice)                            |  8.4 | 1   |  90   |  85.7143  |  90 |  10 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze Esque Low Calorie Sparkling Juice | Sparkling Black Raspberry (25% Juice)                        | 12   | 1   |  50   |  33.3333  |  50 |  10 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze Esque Low Calorie Sparkling Juice | Sparkling Limon (25% Juice)                                  | 12   | 1   |  50   |  33.3333  |  50 |  10 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze Esque Low Calorie Sparkling Juice | Sparkling Mandarin (25% Juice)                               | 12   | 1   |  50   |  33.3333  |  50 |  10 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Izze Esque Low Calorie Sparkling Juice | Sparkling Watermelon (25% Juice)                             | 12   | 1   |  50   |  33.3333  |  50 |  10 | Marketed as a Flavored Juice Blend, Not 100% Juice | RED    |
| Lipton Brisk Diet Juice Drink          | Lemonade Sugar Free (1% Juice)                               | 12   | 1   |   5   |   3.33333 |   5 | 100 | Marketed as a Juice, Not 100% Juice                | RED    |
| Lipton Brisk Diet Juice Drink          | Lemonade Sugar Free (1% Juice)                               | 20   | 1   |  10   |   4       |  10 | 160 | Marketed as a Juice, Not 100% Juice                | RED    |
| Lipton Brisk Diet Juice Drink          | Lemonade Sugar Free (1% Juice)                               | 24   | 3   |  30   |  10       |  10 | 200 | Marketed as a Juice, Not 100% Juice                | RED    |
| Lipton Brisk Juice Drink               | Fruit Punch (1% Juice)                                       | 12   | 1   | 110   |  73.3333  | 110 |  80 | Marketed as a Juice, Not 100% Juice                | RED    |
| Lipton Brisk Juice Drink               | Fruit Punch (1% Juice)                                       | 20   | 1   | 180   |  72       | 180 | 135 | Marketed as a Juice, Not 100% Juice                | RED    |
| Lipton Brisk Juice Drink               | Fruit Punch (1% Juice)                                       | 24   | 3   | 210   |  70       |  70 |  55 | Marketed as a Juice, Not 100% Juice                | RED    |
| Lipton Brisk Juice Drink               | Lemonade (1% Juice)                                          | 12   | 1   | 110   |  73.3333  | 110 |  95 | Marketed as a Juice, Not 100% Juice                | RED    |
| Lipton Brisk Juice Drink               | Lemonade (1% Juice)                                          | 20   | 1   | 180   |  72       | 180 | 160 | Marketed as a Juice, Not 100% Juice                | RED    |
| Lipton Brisk Juice Drink               | Lemonade (1% Juice)                                          | 24   | 3   | 210   |  70       |  70 |  65 | Marketed as a Juice, Not 100% Juice                | RED    |
| Lipton Brisk Juice Drink               | Pink Lemonade (1% Juice)                                     | 12   | 1   | 100   |  66.6667  | 100 |  95 | Marketed as a Juice, Not 100% Juice                | RED    |
| Lipton Brisk Juice Drink               | Pink Lemonade (1% Juice)                                     | 20   | 1   | 170   |  68       | 170 | 160 | Marketed as a Juice, Not 100% Juice                | RED    |
| Lipton Brisk Juice Drink               | Pink Lemonade (1% Juice)                                     | 24   | 3   | 210   |  70       |  70 |  65 | Marketed as a Juice, Not 100% Juice                | RED    |
| Minute Maid                            | Apple Juice (100% Juice)                                     | 10   | 1   | 140   | 112       | 140 |  25 | 100% Juice, ≤ 12 oz.                               | GREEN  |
| Minute Maid                            | Apple Juice (100% Juice)                                     | 11.5 | 1   | 160   | 111.304   | 160 |  30 | 100% Juice, ≤ 12 oz.                               | GREEN  |
| Minute Maid                            | Apple Juice (100% Juice)                                     | 15.2 | 1   | 210   | 110.526   | 210 |  40 | 100% Juice, > 12 oz.                               | YELLOW |
| Minute Maid                            | Berry Blend (25% Juice)                                      | 15.2 | 1   | 130   |  68.4211  | 130 |  45 | Not 100% Juice                                     | RED    |
| Minute Maid                            | Cranberry Apple Cocktail (15% Juice)                         | 11.5 | 1   | 220   | 153.043   | 220 |  25 | Not 100% Juice                                     | RED    |
| Minute Maid                            | Cranberry Apple Raspberry (25% Juice)                        | 15.2 | 1   | 230   | 121.053   | 230 |  35 | Not 100% Juice                                     | RED    |
| Minute Maid                            | Cranberry Grape (25% Juice)                                  | 15.2 | 1   | 270   | 142.105   | 270 |  35 | Not 100% Juice                                     | RED    |
| Minute Maid                            | Grape (100% Juice)                                           | 10   | 1   | 150   | 120       | 150 |  25 | 100% Juice, ≤ 12 oz.                               | GREEN  |
| Minute Maid                            | Lemonade (3% Juice)                                          | 12   | 1   | 150   | 100       | 150 |  50 | Not 100% juice                                     | RED    |
| Minute Maid                            | Lemonade (3% Juice)                                          | 20   | 1   | 260   | 104       | 260 |  80 | Not 100% juice                                     | RED    |
| Minute Maid                            | Light Lemonade (3% Juice)                                    | 12   | 1   |   5   |   3.33333 |   5 |  50 | Not 100% juice                                     | RED    |
| Minute Maid                            | Mixed Berry (100% Juice)                                     | 10   | 1   | 150   | 120       | 150 |  25 | 100% Juice, ≤ 12 oz.                               | GREEN  |
| Minute Maid                            | Orange Juice (100% Juice)                                    | 10   | 1   | 140   | 112       | 140 |  20 | 100% Juice, ≤ 12 oz.                               | GREEN  |
| Minute Maid                            | Orange Juice (100% Juice)                                    | 11.5 | 1   | 170   | 118.261   | 170 |  25 | 100% Juice, ≤ 12 oz.                               | GREEN  |
| Minute Maid                            | Orange Juice (100% Juice)                                    | 15.2 | 1   | 220   | 115.789   | 220 |  30 | 100% Juice, > 12 oz.                               | YELLOW |
| Minute Maid                            | Orangeade (3% Juice)                                         | 12   | 1   | 160   | 106.667   | 160 | 120 | Not 100% juice                                     | RED    |
| Minute Maid                            | Orangeade (3% Juice)                                         | 20   | 1   | 270   | 108       | 270 | 200 | Not 100% juice                                     | RED    |
| Minute Maid                            | Pineapple Orange (100% Juice)                                | 15.2 | 1   | 220   | 115.789   | 220 |  30 | 100% Juice, > 12 oz.                               | YELLOW |
| Minute Maid                            | Pink Lemonade (3% Juice)                                     | 12   | 1   | 150   | 100       | 150 |  50 | Not 100% juice                                     | RED    |
| Minute Maid                            | Pink Lemonade (3% Juice)                                     | 20   | 1   | 260   | 104       | 260 |  80 | Not 100% juice                                     | RED    |
| Minute Maid                            | Ruby Red Grapefruit (30% Juice)                              | 15.2 | 1   | 240   | 126.316   | 240 |  35 | Not 100% Juice                                     | RED    |
| Minute Maid                            | Strawberry Passion (25% Juice)                               | 15.2 | 1   | 310   | 163.158   | 310 |  35 | Not 100% Juice                                     | RED    |
| Minute Maid                            | Tropical Blend (25% Juice)                                   | 15.2 | 1   | 130   |  68.4211  | 130 |  55 | Not 100% Juice                                     | RED    |
| Naked                                  | "Boosted" Acai Machine (100% Juice)                          | 15.2 | 2   | 320   | 168.421   | 160 |  15 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | "Boosted" Blue Machine (100% Juice)                          | 15.2 | 2   | 340   | 178.947   | 170 |  10 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | "Boosted" Green Machine (100% Juice)                         | 15.2 | 2   | 280   | 147.368   | 140 |  15 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | "Boosted" Power -C Machine (100% Juice)                      | 15.2 | 2   | 240   | 126.316   | 120 |   0 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | "Boosted" Probiotic Machine Tropical Mango (100% Juice)      | 15.2 | 2   | 300   | 157.895   | 150 |   5 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | "Boosted" Red Machine (100% Juice)                           | 15.2 | 2   | 340   | 178.947   | 170 |  15 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | "Coconut Water" Peach Guava + Coconut Water (100% Juice)     | 15.2 | 2   | 200   | 105.263   | 100 |  40 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | "Coconut Water" Pineapple Mango + Coconut Water (100% Juice) | 15.2 | 2   | 200   | 105.263   | 100 |  45 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | "Protein" Banana Chocolate (88% Juice)                       | 15.2 | 2   | 500   | 263.158   | 250 | 170 | Juice Drink not 100% juice                         | RED    |
| Naked                                  | "Protein" Double Berry (93% Juice)                           | 15.2 | 2   | 440   | 231.579   | 220 | 130 | Juice Drink not 100% juice                         | RED    |
| Naked                                  | "Protein" Mango (93% Juice)                                  | 15.2 | 2   | 440   | 231.579   | 220 | 130 | Juice Drink not 100% juice                         | RED    |
| Naked                                  | "Protein" Protein Zone (90% Juice)                           | 15.2 | 2   | 440   | 231.579   | 220 | 140 | Juice Drink not 100% juice                         | RED    |
| Naked                                  | "Pure Fruit" Berry Blast (100% Juice)                        | 15.2 | 2   | 260   | 136.842   | 130 |  10 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | "Pure Fruit" Mighty Mango (100% Juice)                       | 15.2 | 2   | 300   | 157.895   | 150 |  10 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | "Pure Fruit" OJ (100% Juice)                                 | 15.2 | 2   | 220   | 115.789   | 110 |  15 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | "Pure Fruit" Orange Mango (100% Juice)                       | 15.2 | 2   | 260   | 136.842   | 130 |   5 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | "Pure Fruit" Pomegranate Acai (100% Juice)                   | 15.2 | 2   | 320   | 168.421   | 160 |  30 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | "Pure Fruit" Pomegranate Blueberry (100% Juice)              | 15.2 | 2   | 300   | 157.895   | 150 |  20 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | "Pure Fruit" Strawberry Banana (100% Juice)                  | 15.2 | 2   | 260   | 136.842   | 130 |   5 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | "Veggies"  Berry Veggie                                      | 15.2 | 2   | 260   | 136.842   | 130 |  70 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | "Veggies"  Orange Carrot                                     | 15.2 | 2   | 240   | 126.316   | 120 |  25 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | "Veggies"  Tomato Kick                                       | 15.2 | 2   | 120   |  63.1579  |  60 | 200 | 100% Juice per nutrition fact label, > 12 oz.      | YELLOW |
| Naked                                  | Coconut Water with Mango Peach Juice (100% Juice)            | 11.2 | 1   |  80   |  57.1429  |  80 | 150 | 100% Juice - No added sugar, ≤ 12 oz.              | GREEN  |
| Naked                                  | Cocunut Water with Pineapple Juice (100% Juice)              | 11.2 | 1   |  80   |  57.1429  |  80 | 150 | 100% Juice - No added sugar, ≤ 12 oz.              | GREEN  |
| Naked                                  | Coconut Water (100% Juice)                                   | 11.2 | 1   |  50   |  35.7143  |  50 |  85 | 100% Juice - No added sugar, ≤ 12 oz.              | GREEN  |
| Ocean Spray                            | Apple Juice (100% Juice)                                     | 15.2 | 1   | 210   | 110.526   | 210 |  20 | 100% Juice, > 12 oz.                               | YELLOW |
| Ocean Spray                            | Cran-Apple (15% Juice)                                       | 15.2 | 1   | 230   | 121.053   | 230 |  85 | Not 100% Juice                                     | RED    |
| Ocean Spray                            | Cranberry Juice Cocktail (27% Juice)                         | 15.2 | 1   | 240   | 126.316   | 240 |  70 | Not 100% Juice                                     | RED    |
| Ocean Spray                            | Cran-Grape (15% Juice)                                       | 15.2 | 1   | 240   | 126.316   | 240 | 150 | Not 100% Juice                                     | RED    |
| Ocean Spray                            | Cran-Lemonade (11% Juice)                                    | 15.2 | 1   | 210   | 110.526   | 210 | 240 | Not 100% Juice                                     | RED    |
| Ocean Spray                            | Diet Cranberry (7% Juice)                                    | 15.2 | 1   |  15   |   7.89474 |  15 |  35 | Not 100% Juice                                     | RED    |
| Ocean Spray                            | Orange Juice (100% Juice)                                    | 15.2 | 1   | 210   | 110.526   | 210 |  30 | 100% Juice, > 12 oz.                               | YELLOW |
| Ocean Spray                            | Pineapple Peach Mango (100% Juice)                           | 15.2 | 1   | 240   | 126.316   | 240 |  25 | 100% Juice, > 12 oz.                               | YELLOW |
| Ocean Spray                            | Ruby Red (30% Juice)                                         | 15.2 | 1   | 210   | 110.526   | 210 | 125 | Not 100% Juice                                     | RED    |
| Ocean Spray                            | Strawberry Kiwi (25% Juice)                                  | 15.2 | 1   | 230   | 121.053   | 230 |  80 | Not 100% Juice                                     | RED    |
| Snapple                                | Apple Juice (10% Juice)                                      | 16   | 1   | 200   | 100       | 200 |  10 | Not 100% Juice                                     | RED    |
| Sunny D                                | Blue Raspberry (5% Juice)                                    | 16   | 1   | 120   |  60       | 120 | 330 | Not 100% Juice                                     | RED    |
| Sunny D                                | Cherry Limeade (5% Juice)                                    | 16   | 1   | 120   |  60       | 120 | 320 | Not 100% Juice                                     | RED    |
| Sunny D                                | Grape (5% Juice)                                             | 16   | 1   | 120   |  60       | 120 | 320 | Not 100% Juice                                     | RED    |
| Sunny D                                | Orange (5% Juice)                                            | 16   | 1   | 110   |  55       | 110 | 320 | Not 100% Juice                                     | RED    |
| Sunny D                                | Orange Mango (5% Juice)                                      | 16   | 1   | 110   |  55       | 110 | 330 | Not 100% Juice                                     | RED    |
| Sunny D                                | Orange Strawberry (No Juice)                                 | 16   | 1   | 110   |  55       | 110 | 320 | Not 100% Juice                                     | RED    |



label: E=D*G
labeled_formulas: E=D*G
output: {"Arithmetic-Relationship": ["E=D*G"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_362137___xlsx_17cc7b1e95caf5d53b6742996d39ab24b84e0571.xlsx___line_73