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      |
|----:|:------------------------------|:--------------------|:---------|------:|--------:|----:|--------:|------:|:-------|
|   1 | strawberry                    | produce             | lb       |  3.28 |  1.7712 |  13 |  1.5088 | 0.46  | low    |
|   2 | apple_fuji                    | produce             | lb       |  1.44 |  0.432  |   2 |  1.008  | 0.7   | high   |
|   3 | orange                        | produce             | lb       |  1.02 |  0.3672 |   2 |  0.6528 | 0.64  | medium |
|   4 | clementines                   | produce             | lb       |  1.19 |  0.4403 |  44 |  0.7497 | 0.63  | medium |
|   5 | blood_orange                  | produce             | lb       |  3.86 |  1.6598 |  19 |  2.2002 | 0.57  | medium |
|   6 | blood_lime                    | produce             | lb       |  1.69 |  0.9126 |  10 |  0.7774 | 0.46  | low    |
|   7 | tayberry                      | produce             | lb       |  2.54 |  0.889  |  25 |  1.651  | 0.65  | medium |
|   8 | pluot                         | produce             | lb       |  3.99 |  1.4364 |  26 |  2.5536 | 0.64  | medium |
|   9 | tangelo                       | produce             | lb       |  0.96 |  0.5568 |  32 |  0.4032 | 0.42  | low    |
|  10 | pomello                       | produce             | lb       |  0.96 |  0.5664 |  33 |  0.3936 | 0.41  | low    |
|  11 | pineberry                     | produce             | lb       |  4.89 |  2.0049 |  42 |  2.8851 | 0.59  | medium |
|  12 | vegan_egg_substitute          | dairy               | oz       |  1.15 |  0.575  |  41 |  0.575  | 0.5   | low    |
|  13 | asparagus_water               | beverages           | fl_oz    |  0.38 |  0.2128 |  42 |  0.1672 | 0.44  | low    |
|  14 | falafel_chips                 | snacks              | oz       |  0.53 |  0.2862 |   2 |  0.2438 | 0.46  | low    |
|  15 | sweet_potato_hockey_pucks     | snacks              | oz       |  0.43 |  0.1677 |  35 |  0.2623 | 0.61  | medium |
|  16 | arugula_crisps                | snacks              | oz       |  2.43 |  1.1907 |  32 |  1.2393 | 0.51  | medium |
|  17 | bottled_organic_air           | other               | cubic_ft |  2.67 |  0.9612 |  38 |  1.7088 | 0.64  | medium |
|  18 | chia_seeds                    | dry_goods           | oz       |  0.67 |  0.3618 |  30 |  0.3082 | 0.46  | low    |
|  19 | all_natural_cheese_poofs      | snacks              | oz       |  0.41 |  0.164  |  13 |  0.246  | 0.6   | medium |
|  20 | sriracha_popcorn              | snacks              | oz       |  1.11 |  0.3663 |  26 |  0.7437 | 0.67  | high   |
|  21 | buttermilk_pancake_crunchies  | snacks              | oz       |  2.59 |  1.2432 |  21 |  1.3468 | 0.52  | medium |
|  22 | smoked_trout                  | meat                | lb       | 19.59 |  9.0114 |   3 | 10.5786 | 0.54  | medium |
|  23 | pine_nuts                     | dry_goods           | oz       |  0.91 |  0.3003 |  42 |  0.6097 | 0.67  | high   |
|  24 | dried_apricots                | dry_goods           | oz       |  0.56 |  0.2576 |  34 |  0.3024 | 0.54  | medium |
|  25 | smoked_salmon                 | meat                | lb       | 39.99 | 19.995  |   5 | 19.995  | 0.5   | low    |
|  26 | green_juice                   | beverages           | fl_oz    |  0.25 |  0.125  |  15 |  0.125  | 0.5   | low    |
|  27 | celery_foam                   | other               | fl_oz    |  6    |  4.29   |   7 |  1.71   | 0.285 | low    |
|  28 | protein_powder                | dry_goods           | oz       |  0.69 |  0.3312 |   2 |  0.3588 | 0.52  | medium |
|  29 | asiago_cheese                 | dairy               | oz       |  0.63 |  0.2457 |  20 |  0.3843 | 0.61  | medium |
|  30 | camembert_cheese              | dairy               | oz       |  0.91 |  0.5369 |  15 |  0.3731 | 0.41  | low    |
|  31 | almond_nut_thins              | snacks              | oz       |  0.61 |  0.2074 |  20 |  0.4026 | 0.66  | high   |
|  32 | arugula                       | produce             | lb       |  2.99 |  1.0465 |  10 |  1.9435 | 0.65  | medium |
|  33 | white_bean_and_basil_hummus   | canned_jarred_goods | oz       |  0.97 |  0.5529 |   2 |  0.4171 | 0.43  | low    |
|  34 | edamame_hummus                | canned_jarred_goods | oz       |  0.95 |  0.3515 |  13 |  0.5985 | 0.63  | medium |
|  35 | eggplant_caponata             | frozen              | oz       |  1.39 |  0.7367 |  25 |  0.6533 | 0.47  | low    |
|  36 | olive_tapanade                | canned_jarred_goods | oz       |  1.12 |  0.5712 |  36 |  0.5488 | 0.49  | low    |
|  37 | chocolate_ganache_torte       | frozen              | oz       |  3.52 |  1.0912 |  40 |  2.4288 | 0.69  | high   |
|  38 | pork_gyoza                    | frozen              | oz       |  1.19 |  0.6545 |  31 |  0.5355 | 0.45  | low    |
|  39 | table_wafers                  | snacks              | oz       |  0.59 |  0.2124 |  32 |  0.3776 | 0.64  | medium |
|  40 | vegetable_gyoza               | frozen              | oz       |  1.17 |  0.5967 |  28 |  0.5733 | 0.49  | low    |
|  41 | frozen_tamales                | frozen              | oz       |  1.09 |  0.5777 |  23 |  0.5123 | 0.47  | low    |
|  42 | porchini_mushrooms            | produce             | lb       |  5.99 |  3.4143 |  44 |  2.5757 | 0.43  | low    |
|  43 | garlic_naan                   | bread               | oz       |  0.99 |  0.3564 |  38 |  0.6336 | 0.64  | medium |
|  44 | frozen_clams                  | frozen              | oz       |  4.99 |  2.5449 |  39 |  2.4451 | 0.49  | low    |
|  45 | butter_chicken                | frozen              | oz       |  1.29 |  0.5676 |   4 |  0.7224 | 0.56  | medium |
|  46 | frozen_salmon                 | frozen              | oz       | 16.99 |  9.1746 |   5 |  7.8154 | 0.46  | low    |
|  47 | paneer                        | dairy               | oz       |  1.17 |  0.6552 |  43 |  0.5148 | 0.44  | low    |
|  48 | organic_mung_beans            | dry_goods           | oz       |  0.89 |  0.3115 |  17 |  0.5785 | 0.65  | medium |
|  49 | silken_tofu                   | dairy               | oz       |  0.67 |  0.3283 |  16 |  0.3417 | 0.51  | medium |
|  50 | white_cheddar                 | dairy               | oz       |  0.77 |  0.3619 |  24 |  0.4081 | 0.53  | medium |
|  51 | english_cheddar               | dairy               | oz       |  0.89 |  0.5251 |  15 |  0.3649 | 0.41  | low    |
|  52 | cranberry_infused_goat_cheese | dairy               | oz       |  1.79 |  0.716  |  15 |  1.074  | 0.6   | medium |
|  53 | black_pepper_goat_cheese      | dairy               | oz       |  1.69 |  0.6253 |  11 |  1.0647 | 0.63  | medium |
|  54 | aged_gouda                    | dairy               | oz       |  1.23 |  0.6888 |  38 |  0.5412 | 0.44  | low    |
|  55 | parmigiano_reggiano           | dairy               | oz       |  1.1  |  0.385  |  30 |  0.715  | 0.65  | medium |
|  56 | organic_glazed_walnuts        | dry_goods           | oz       |  0.86 |  0.4042 |  11 |  0.4558 | 0.53  | medium |
|  57 | Kumatos                       | produce             | lb       |  3.6  |  1.188  |  20 |  2.412  | 0.67  | high   |
|  58 | pumpkin_spice_pumpkin_seeds   | dry_goods           | oz       |  0.96 |  0.4512 |  19 |  0.5088 | 0.53  | medium |
|  59 | medjool_dates                 | produce             | oz       |  4.29 |  1.3728 |  21 |  2.9172 | 0.68  | high   |
|  60 | satsuma_oranges               | produce             | lb       |  2.06 |  0.8652 |  39 |  1.1948 | 0.58  | medium |
|  61 | grapefruits                   | produce             | lb       |  0.55 |  0.22   |  15 |  0.33   | 0.6   | medium |
|  62 | goji_berries                  | dry_goods           | oz       |  1.17 |  0.5616 |  19 |  0.6084 | 0.52  | medium |
|  63 | organic_garlic                | produce             | lb       |  3.57 |  1.3209 |  24 |  2.2491 | 0.63  | medium |
|  64 | white_onions                  | produce             | lb       |  1.22 |  0.4392 |   2 |  0.7808 | 0.64  | medium |
|  65 | purple_onions                 | produce             | lb       |  1.32 |  0.4488 |  20 |  0.8712 | 0.66  | high   |
|  66 | yellow_onions                 | produce             | lb       |  1.12 |  0.4368 |  11 |  0.6832 | 0.61  | medium |
|  67 | barberries                    | dry_goods           | oz       |  1.74 |  0.87   |  34 |  0.87   | 0.5   | low    |
|  68 | salmonberries                 | produce             | lb       |  0.67 |  0.2881 |  11 |  0.3819 | 0.57  | medium |
|  69 | wholewheat_couscous           | dry_goods           | oz       |  0.27 |  0.0864 |  20 |  0.1836 | 0.68  | high   |
|  70 | orzo                          | dry_goods           | oz       |  0.19 |  0.095  |   3 |  0.095  | 0.5   | low    |
|  71 | autumn_pilaf                  | dry_goods           | oz       |  0.24 |  0.1104 |  42 |  0.1296 | 0.54  | medium |
|  72 | wild_rice                     | dry_goods           | oz       |  0.27 |  0.162  |  12 |  0.108  | 0.4   | low    |
|  73 | cheddar_corn_sticks           | snacks              | oz       |  0.69 |  0.3243 |  14 |  0.3657 | 0.53  | medium |
|  74 | poppy_onion_sesame_sticks     | snacks              | oz       |  0.75 |  0.3975 |  44 |  0.3525 | 0.47  | low    |
|  75 | rice_crackers                 | snacks              | oz       |  0.57 |  0.2964 |   0 |  0.2736 | 0.48  | low    |
|  76 | cheddar_whales                | snacks              | oz       |  0.69 |  0.2415 |  35 |  0.4485 | 0.65  | medium |
|  77 | sugar_snap_peas               | produce             | lb       |  2.67 |  1.5219 |  11 |  1.1481 | 0.43  | low    |
|  78 | garam_masala                  | dry_goods           | oz       |  1.44 |  0.4896 |  40 |  0.9504 | 0.66  | high   |
|  79 | darjeeling_black_tea          | dry_goods           | oz       |  3.3  |  1.386  |  15 |  1.914  | 0.58  | medium |
|  80 | rooibos_tea                   | dry_goods           | oz       |  3.49 |  1.8497 |   0 |  1.6403 | 0.47  | low    |
|  81 | irish_breakfast_black_tea     | dry_goods           | oz       |  2.99 |  1.7043 |  40 |  1.2857 | 0.43  | low    |
|  82 | mango_black_tea               | dry_goods           | oz       |  3.08 |  1.2936 |  22 |  1.7864 | 0.58  | medium |
|  83 | soy_ginger_trail_mix          | snacks              | oz       |  0.39 |  0.2223 |  30 |  0.1677 | 0.43  | low    |
|  84 | buckwheat_flour               | dry_goods           | lb       |  2.59 |  1.2173 |   2 |  1.3727 | 0.53  | medium |
|  85 | cranberry_milk                | beverages           | fl_oz    |  0.08 |  0.0416 |  36 |  0.0384 | 0.48  | low    |



label: H=E-F
labeled_formulas: H=E-F
output: {"Arithmetic-Relationship": ["H=E-F"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_131297___xlsx_810ce72541bdda7afb1e73c63aeff30aff2fd4dc.xlsx___line_587