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 |   K |   L |     M |
|-----------:|:-----------|----:|:-------------|:-------|:-------------------------------|-------:|----:|----:|----:|----:|----:|------:|
| 4377000380 | 02936122G  | 355 | Series 6122  | S-029B | 6122 1/2 CPVC BV SLIP NSF NL   |   9.59 |   0 |   0 |  45 | 180 |   0 |  0.11 |
| 4377000390 | 02936122I  | 355 | Series 6122  | S-029B | 6122 3/4 CPVC BV SLIP NSF NL   |  13.15 |   0 |   0 |  25 | 100 |   0 |  0.18 |
| 4377000400 | 02936122K  | 355 | Series 6122  | S-029B | 6122 1 CPVC BV SLIP NSF NL     |  20.64 |   0 |   0 |  18 |  72 |   0 |  0.42 |
| 4377000590 | 02939521G  | 355 | Series 9521  | S-029C | 9521 1/2 WHITE PVC BV TE NL    |   4.98 |   0 |   0 |  24 |  96 |   0 |  0.2  |
| 4377000600 | 02939521I  | 355 | Series 9521  | S-029C | 9521 3/4 WHITE PVC BV TE NL    |   6.4  |   0 |   0 |  18 |  72 |   0 |  0.29 |
| 4377000610 | 02939521K  | 355 | Series 9521  | S-029C | 9521 1 WHITE PVC BV TE NL      |   8.81 |   0 |   0 |  20 |  80 |   0 |  0.62 |
| 4377000620 | 02939521L  | 355 | Series 9521  | S-029C | 9521 1-1/4 WHITE PVC BV TE NL  |  12.85 |   0 |   0 |  20 |  40 |   0 |  0.73 |
| 4377000630 | 02939521M  | 355 | Series 9521  | S-029C | 9521 1-1/2 WHITE PVC BV TE NL  |  18.08 |   0 |   0 |  14 |  28 |   0 |  0.97 |
| 4377000640 | 02939521N  | 355 | Series 9521  | S-029C | 9521 2 WHITE PVC BV TE NL      |  22.15 |   0 |   0 |   5 |  20 |   0 |  1.48 |
| 4377000650 | 02939522G  | 355 | Series 9522  | S-029C | 9522 1/2 WHITE PVC BV SLIP NL  |   4.98 |   0 |   0 |  24 |  96 |   0 |  0.22 |
| 4377000660 | 02939522I  | 355 | Series 9522  | S-029C | 9522 3/4 WHITE PVC BV SLIP NL  |   6.4  |   0 |   0 |  18 |  72 |   0 |  0.29 |
| 4377000670 | 02939522K  | 355 | Series 9522  | S-029C | 9522 1 WHITE PVC BV SLIP NL    |   8.81 |   0 |   0 |  20 |  80 |   0 |  0.62 |
| 4377000680 | 02939522L  | 355 | Series 9522  | S-029C | 9522 11/4 WHITE PVC BV SLIP NL |  12.85 |   0 |   0 |  20 |  40 |   0 |  0.73 |
| 4377000690 | 02939522M  | 355 | Series 9522  | S-029C | 9522 11/2 WHITE PVC BV SLIP NL |  18.08 |   0 |   0 |  14 |  28 |   0 |  0.97 |
| 4377000700 | 02939522N  | 355 | Series 9522  | S-029C | 9522 2 WHITE PVC BV SLIP NL    |  22.15 |   0 |   0 |   5 |  20 |   0 |  1.48 |
| 4377000710 | 02939541G  | 355 | Series 9541  | S-029C | 9541 1/2 GRAY PVC BV TE NL     |   4.98 |   0 |   0 |  24 |  96 |   0 |  0.17 |
| 4377000720 | 02939541I  | 355 | Series 9541  | S-029C | 9541 3/4 GRAY PVC BV TE NL     |   6.4  |   0 |   0 |  18 |  72 |   0 |  0.26 |
| 4377000730 | 02939541K  | 355 | Series 9541  | S-029C | 9541 1 GRAY PVC BV TE NL       |   8.72 |   0 |   0 |  20 |  80 |   0 |  0.42 |
| 4377000740 | 02939541L  | 355 | Series 9541  | S-029C | 9541 1-1/4 GRAY PVC BV TE NL   |  12.85 |   0 |   0 |  20 |  40 |   0 |  0.58 |
| 4377000750 | 02939541M  | 355 | Series 9541  | S-029C | 9541 1-1/2 GRAY PVC BV TE NL   |  18.08 |   0 |   0 |  14 |  28 |   0 |  0.87 |
| 4377000760 | 02939541N  | 355 | Series 9541  | S-029C | 9541 2 GRAY PVC BV TE NL       |  22.15 |   0 |   0 |   5 |  20 |   0 |  1.46 |
| 4377000770 | 02939542G  | 355 | Series 9542  | S-029C | 9542 1/2 GRAY PVC BV SLIP NL   |   4.98 |   0 |   0 |  24 |  96 |   0 |  0.16 |
| 4377000780 | 02939542I  | 355 | Series 9542  | S-029C | 9542 3/4 GRAY PVC BV SLIP NL   |   6.4  |   0 |   0 |  18 |  72 |   0 |  0.24 |
| 4377000790 | 02939542K  | 355 | Series 9542  | S-029C | 9542 1 GRAY PVC BV SLIP NL     |   8.81 |   0 |   0 |  20 |  80 |   0 |  0.39 |
| 4377000800 | 02939542L  | 355 | Series 9542  | S-029C | 9542 1-1/4 GRAY PVC BV SLIP NL |  12.85 |   0 |   0 |  20 |  40 |   0 |  0.55 |
| 4377000810 | 02939542M  | 355 | Series 9542  | S-029C | 9542 1-1/2 GRAY PVC BV SLIP NL |  18.08 |   0 |   0 |  14 |  28 |   0 |  0.83 |
| 4377000820 | 02939542N  | 355 | Series 9542  | S-029C | 9542 2 GRAY PVC BV SLIP NL     |  22.15 |   0 |   0 |   5 |  20 |   0 |  1.37 |
| 4347000200 | 01718501CL | 334 | Series 8501L | S-0LAA | 8501L 1/4 GATE VLV BRS TE NL   |  20.76 |   0 |   0 |  12 |  72 |   0 |  0.55 |
| 4347000210 | 01718501EL | 334 | Series 8501L | S-0LAA | 8501L 3/8 GATE VLV BRS TE NL   |  20.76 |   0 |   0 |  12 |  72 |   0 |  0.54 |
| 4347000220 | 01718501GL | 334 | Series 8501L | S-0LAA | 8501L 1/2 GATE VLV BRS TE NL   |  20.88 |   0 |   0 |  12 |  72 |   0 |  0.58 |
| 4347000230 | 01718501IL | 334 | Series 8501L | S-0LAA | 8501L 3/4 GATE VLV BRS TE NL   |  28.13 |   0 |   0 |  14 |  56 |   0 |  0.81 |
| 4347000240 | 01718501KL | 334 | Series 8501L | S-0LAA | 8501L 1 GATE VLV BRS TE 200 NL |  42.17 |   0 |   0 |   5 |  40 |   0 |  1.15 |
| 4347000250 | 01718501LL | 334 | Series 8501L | S-0LAA | 8501L 1-1/4 GATE VLV BRS TE NL |  59.4  |   0 |   0 |   3 |  18 |   0 |  1.77 |
| 4347000260 | 01718501ML | 334 | Series 8501L | S-0LAA | 8501L 1-1/2 GATE VLV BRS TE NL |  75.56 |   0 |   0 |   6 |  24 |   0 |  2.19 |
| 4347000270 | 01718501NL | 334 | Series 8501L | S-0LAA | 8501L 2 GATE VLV BRS TE 200 NL | 108.3  |   0 |   0 |   4 |  16 |   0 |  3.3  |
| 4347000400 | 01718502EL | 334 | Series 8502L | S-0LAA | 8502L 3/8 CXC GATE VLV BRS NL  |  20.76 |   0 |   0 |  14 |  84 |   0 |  0.53 |
| 4347000410 | 01718502GL | 334 | Series 8502L | S-0LAA | 8502L 1/2 CXC GATE VLV BRS NL  |  20.88 |   0 |   0 |  12 |  72 |   0 |  0.52 |
| 4347000420 | 01718502IL | 334 | Series 8502L | S-0LAA | 8502L 3/4 CXC GATE VLV BRS NL  |  28.13 |   0 |   0 |  14 |  56 |   0 |  0.73 |
| 4347000430 | 01718502KL | 334 | Series 8502L | S-0LAA | 8502L 1 CXC GATE VLV BRS NL    |  42.17 |   0 |   0 |   8 |  32 |   0 |  1.08 |
| 4347000440 | 01718502LL | 334 | Series 8502L | S-0LAA | 8502L 11/4 CXC GATE VLV BRS NL |  59.4  |   0 |   0 |   4 |  16 |   0 |  1.62 |
| 4347000450 | 01718502ML | 334 | Series 8502L | S-0LAA | 8502L 11/2 CXC GATE VLV BRS NL |  75.56 |   0 |   0 |   4 |  16 |   0 |  2    |
| 4347000460 | 01718502NL | 334 | Series 8502L | S-0LAA | 8502L 2 CXC GATE VLV BRS NL    | 108.3  |   0 |   0 |   2 |  12 |   0 |  3.3  |
| 4347000280 | 01718501PL | 334 | Series 8501L | S-0LAB | 8501L 2-1/2 GATE VLV BRS TE NL | 207.98 |   0 |   0 |   1 |   0 |   0 |  6.42 |
| 4347000290 | 01718501QL | 334 | Series 8501L | S-0LAB | 8501L 3 GATE VLV BRS TE 200 NL | 286.1  |   0 |   0 |   1 |   6 |   0 |  9.75 |
| 4347000300 | 01718501TL | 334 | Series 8501L | S-0LAB | 8501L 4 GATE VLV BRS TE 200 NL | 490.93 |   0 |   0 |   1 |   4 |   0 | 17    |
| 4347000470 | 01718502PL | 334 | Series 8502L | S-0LAB | 8502L 21/2 CXC GATE VLV BRS NL | 207.98 |   0 |   0 |   1 |   6 |   0 |  5.83 |
| 4347000480 | 01718502QL | 334 | Series 8502L | S-0LAB | 8502L 3 CXC GATE VLV BRS NL    | 286.1  |   0 |   0 |   1 |   6 |   0 |  9.12 |
| 4347000500 | 01719101GL | 334 | Series 9101L | S-0LAC | 9101L 1/2 GATE VLV BRZ TE NL   |  35.29 |   0 |   0 |  12 |  72 |   0 |  0.64 |
| 4347000510 | 01719101IL | 334 | Series 9101L | S-0LAC | 9101L 3/4 GATE VLV BRZ TE NL   |  44    |   0 |   0 |  14 |  56 |   0 |  1.92 |
| 4347000520 | 01719101KL | 334 | Series 9101L | S-0LAC | 9101L 1 GATE VLV BRZ TE NL     |  64.14 |   0 |   0 |   5 |  40 |   0 |  1.28 |
| 4347000530 | 01719101LL | 334 | Series 9101L | S-0LAC | 9101L 1-1/4 GATE VLV BRZ TE NL |  83.56 |   0 |   0 |   3 |  18 |   0 |  1.92 |
| 4347000540 | 01719101ML | 334 | Series 9101L | S-0LAC | 9101L 1-1/2 GATE VLV BRZ TE NL | 114.62 |   0 |   0 |   6 |  24 |   0 |  2.34 |
| 4347000550 | 01719101NL | 334 | Series 9101L | S-0LAC | 9101L 2 GATE VLV BRZ TE NL     | 178.81 |   0 |   0 |   4 |  16 |   0 |  3.55 |
| 4347000000 | 01718103GL | 334 | Series 8103L | S-0LAD | 8103L 1/2 GATE VLV BRS TE NL   |  32.18 |   0 |   0 |  12 |  72 |   0 |  0.72 |
| 4347000010 | 01718103IL | 334 | Series 8103L | S-0LAD | 8103L 3/4 GATE VLV BRS TE NL   |  49.68 |   0 |   0 |  14 |  56 |   0 |  1.18 |
| 4347000020 | 01718103KL | 334 | Series 8103L | S-0LAD | 8103L 1 GATE VLV BRS TE NL     |  71.6  |   0 |   0 |   8 |  32 |   0 |  1.26 |
| 4347000030 | 01718104GL | 334 | Series 8104L | S-0LAD | 8104L 1/2 CXC GATE VLV BRS NL  |  29.46 |   0 |   0 |  12 |  72 |   0 |  0.68 |
| 4347000040 | 01718104IL | 334 | Series 8104L | S-0LAD | 8104L 3/4 CXC GATE VLV BRS NL  |  47.33 |   0 |   0 |  14 |  56 |   0 |  0.93 |
| 4347000050 | 01718104KL | 334 | Series 8104L | S-0LAD | 8104L 1 CXC GATE VLV BRS NL    |  75.17 |   0 |   0 |   8 |  32 |   0 |  1.18 |
| 4347000060 | 01718130GL | 334 | Series 8130L | S-0LAE | 8130L 1/2 GATE VLV BRS COMP NL |  23.41 |   0 |   0 |  10 |  60 |   0 |  0.79 |
| 4347000070 | 01718130IL | 334 | Series 8130L | S-0LAE | 8130L 3/4 GATE VLV BRS COMP NL |  33.56 |   0 |   0 |  10 |  40 |   0 |  1.05 |
| 4347000080 | 01718130KL | 334 | Series 8130L | S-0LAE | 8130L 1 GATE VLV BRS COMP NL   |  47.82 |   0 |   0 |   8 |  32 |   0 |  1.37 |



label: I=G*H
labeled_formulas: I=G*H
output: {"Arithmetic-Relationship": ["I=G*H"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_705677___xlsx_3c2014e36d0458d76de4687ac743214a23521516.xlsx___line_213