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 |
|:-----------------------------------------------------------|----:|-------:|----:|
| 1x4x8ft                                                    |   0 |   4.27 |   0 |
| 1x6x6ft                                                    |   0 |   3.07 |   0 |
| 2x2x8ft                                                    |   0 |   3.77 |   0 |
| 2x4x12ft                                                   |   0 |   7.27 |   0 |
| 2x4x8ft                                                    |   0 |   4.17 |   0 |
| 4x4x8ft                                                    |   0 |   8.98 |   0 |
| 2x4x10ft                                                   |   0 |   5.77 |   0 |
| 2x6x8ft                                                    |   0 |   6.27 |   0 |
| 2x6x10ft                                                   |   0 |   8.42 |   0 |
| 2x12x10ft                                                  |   0 |  19.77 |   0 |
| 2x6x12ft                                                   |   0 |  10.12 |   0 |
| 4x4x10ft                                                   |   0 |  12.57 |   0 |
| 4x4x12ft                                                   |   0 |  15.57 |   0 |
| 3x4ft Plexiglass Sheet                                     |   0 |  30.73 |   0 |
| 1/2"x4x8ft Plywood                                         |   0 |  24.75 |   0 |
| 1" Deck Screws (lbs)                                       |   0 |   6.98 |   0 |
| 2 ½" Deck Screws (lbs)                                     |   0 |   9.48 |   0 |
| 3/8" x 3 ½" Galvanized Carriage Bolts - 25-pack            |   0 |  16.87 |   0 |
| 3/8" Galvanized  Washers - 25-pack                         |   0 |   3.56 |   0 |
| 3/8" Galvanized Nuts - 25-pack                             |   0 |   3.98 |   0 |
| 6D Galvanized Nails (1-lbs)                                |   0 |   4.95 |   0 |
| 6" Galvanized Nails (30-lbs)                               |   0 |  59.97 |   0 |
| 0.5"x6" Galvanized Carriage Bolts                          |   0 |   1.94 |   0 |
| 0.5"x6" Lag Screws - 25-pack                               |   0 |  77.4  |   0 |
| 0.5"x8" Galvanized Carriage Bolts                          |   0 |   3.18 |   0 |
| 0.5"x8" Galvanized Screws - 10-pack                        |   0 |  17.91 |   0 |
| 0.5" Galvanized Washers                                    |   0 |   0.32 |   0 |
| 0.5" Galvanized Nuts                                       |   0 |   0.46 |   0 |
| 3" Lag Screws - each                                       |   0 |   0.42 |   0 |
| 3"Deck Screws 1lb box                                      |   0 |   9.48 |   0 |
| 1" Finishing Nails - 2lb box                               |   0 |   2.97 |   0 |
| 1 1/4" Exterior Philips Screws - 1lb Box                   |   0 |   8.97 |   0 |
| H2.5A Rafter Ties                                          |   0 |   0.34 |   0 |
| LS30-R Skewable Angle Braces                               |   0 |   1.96 |   0 |
| 1.5" N8 Nails - 2lb box                                    |   0 |   5.37 |   0 |
| Gate Latch                                                 |   0 |   4.8  |   0 |
| 3" Hinges                                                  |   0 |   7.42 |   0 |
| Corner Braces                                              |   0 |   2.45 |   0 |
| 80lb Bag Concrete                                          |   0 |   4.75 |   0 |
| Fill Dirt (1 Cubic Feet)                                   |   0 |   1.98 |   0 |
| Potting Soil (2 Cubic Feet)                                |   0 |  20    |   0 |
| Plants                                                     |   0 |   0    |   0 |
| Sod Pallet - 500 sq. ft.                                   |   0 | 449    |   0 |
| Homer Buckets                                              |   0 |   3.48 |   0 |
| Wood Glue                                                  |   0 |   5.97 |   0 |
| 4x8ft Lattice Pieces                                       |   0 |  15.98 |   0 |
| 8d Galvanized Nals - 2lb Box                               |   0 |  29.94 |   0 |
| 2" Deck Screws (lbs)                                       |   0 |   9.48 |   0 |
| 1¼” Galvanized Screws (lbs)                                |   0 |   8.97 |   0 |
| Marking Paint                                              |   0 |   5.98 |   0 |
| ¼”x4x8ft plywood                                           |   0 |  28.82 |   0 |
| ¾”x4x8ft plywood                                           |   0 |  24.98 |   0 |
| 1¼” Pocket Hole Screws (lbs)                               |   0 |   4.77 |   0 |
| 1x12x12ft                                                  |   0 |  34.42 |   0 |
| 1x3x8ft                                                    |   0 |   3.9  |   0 |
| 1x2x8ft                                                    |   0 |   1.98 |   0 |
| Wood Filler                                                |   0 |   5.58 |   0 |
| 1-5/8" Deck Screws (lbs)                                   |   0 |   9.48 |   0 |
| Spray Spar Polyurethane (can)                              |   0 |  10.28 |   0 |
| Set of Bean Bags                                           |   0 |  29.98 |   0 |
| 2x2x6ft                                                    |   0 |   8.81 |   0 |
| Fertilizer - lbs                                           |   0 |  15.98 |   0 |
| 1.5" N8 Nails - 1lb box                                    |   0 |   5.37 |   0 |
| Miter Saw                                                  |   0 | 219    |   0 |
| Circular Saw                                               |   0 |  99    |   0 |
| Jig Saw                                                    |   0 | 159    |   0 |
| Chalk Line                                                 |   0 |   9.97 |   0 |
| Pencil                                                     |   0 |   0.19 |   0 |
| Tape Measure                                               |   0 |   8.7  |   0 |
| Safety Glasses                                             |   0 |   2.99 |   0 |
| Carpenter's Square                                         |   0 |  11.97 |   0 |
| Utility Knife                                              |   0 |   4.48 |   0 |
| Drill                                                      |   0 |  69    |   0 |
| Screwdriver Bit                                            |   0 |  29.97 |   0 |
| 9/64" Drill Bit                                            |   0 |   9.97 |   0 |
| 1/8" Drill Bit                                             |   0 |   9.97 |   0 |
| 1/4" Long Drill Bit                                        |   0 |   9.97 |   0 |
| 3/8" Long Drill Bit                                        |   0 |   9.97 |   0 |
| 1/2" Long Drill Bit                                        |   0 |   9.97 |   0 |
| Level                                                      |   0 |   8.47 |   0 |
| Hammer                                                     |   0 |  25.97 |   0 |
| Ladder                                                     |   0 |  79.97 |   0 |
| Sanding Sponge                                             |   0 |   7.97 |   0 |
| Post Hole Digger                                           |   0 |  49.98 |   0 |
| Lawn Roller                                                |   0 | 129    |   0 |
| Kreg Jig                                                   |   0 |  39.97 |   0 |
| 4" hole saw attachment                                     |   0 |  23.97 |   0 |
| Paint Brush/Roller Multipack                               |   0 |  10.97 |   0 |
| Shovel                                                     |   0 |  23.98 |   0 |
| Landscaping Rake                                           |   0 |  28.98 |   0 |
| Cresent Wrench Set                                         |   0 |  26.55 |   0 |
| 1-1/4" Finishing Nails                                     |   0 |   8.22 |   0 |
| 2x12x8ft                                                   |   0 |  15.77 |   0 |
| 2" Finishing Nails - 1 lbs                                 |   0 |   5.98 |   0 |
| 5/32" Drill Bit                                            |   0 |   9.97 |   0 |
| 2-1/2" 8D galvanized nails - 10lbs                         |   0 |  29.94 |   0 |
| 7" Carriage Bolt                                           |   0 |   3.42 |   0 |
| 1x12x6ft                                                   |   0 |  14.91 |   0 |
| 1x12x8ft                                                   |   0 |  21.42 |   0 |
| 1x12x10ft                                                  |   0 |  28.68 |   0 |
| 2" Trim Srews - 100-pack                                   |   0 |  10.47 |   0 |
| 3/4" Brad Nails - 1000-pack                                |   0 |   5.98 |   0 |
| 48" Barn Door Hardware Kit                                 |   0 |  99.44 |   0 |
| Brad Nailer                                                |   0 |  84    |   0 |
| 2-3/4" Self-tapping Wood Screws - 100-pack                 |   0 |  13.47 |   0 |
| Watco Danish Oil                                           |   0 |   8.98 |   0 |
| 1x8x8ft                                                    |   0 |   7.98 |   0 |
| roll of 1/4" hardware cloth 50x24"                         |   0 |  36.46 |   0 |
| Wood Stain                                                 |   0 |  44.97 |   0 |
| Cushion                                                    |   0 |  55.89 |   0 |
| 12’ x 26" standard corrugated plastic greenhouse panels    |   0 |  22.47 |   0 |
| 8’ x 26" wide standard corrugated plastic greenhouse panel |   0 |  15.96 |   0 |
| 12’ tin panels                                             |   0 |  21.55 |   0 |
| 8’ tin panel                                               |   0 |  14.36 |   0 |
| Tin screws - 300-pack                                      |   0 |   7.98 |   0 |
| 4' long ribbing strips - 100-pack                          |   0 |   5.98 |   0 |
| L flashing (optional for the corners)                      |   0 |   0.37 |   0 |
| metal gussets                                              |   0 |   0.34 |   0 |
| 5/32" Countersink Drill Bit                                |   0 |   7.99 |   0 |



label: E=C*D
labeled_formulas: E=C*D
output: {"Arithmetic-Relationship": ["E=C*D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_636272___xlsx_3769fccaf658888c190736f9e20fba8cc1b20b93.xlsx___line_242