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 |
|-----------:|:-----------|----:|:-------------|:-------|:-------------------------------|--------:|----:|----:|----:|----:|----:|------:|
| 4347001270 | 01728155CL | 315 | Series 8155L | S-0LBA | 1/4   IPS BALL VALVE FP 600 NL |   17.04 |   0 |   0 |  10 | 160 |   0 |  0.3  |
| 4347001290 | 01728155EL | 315 | Series 8155L | S-0LBA | 3/8   IPS BALL VALVE FP 600 NL |   18.32 |   0 |   0 |  10 | 160 |   0 |  0.3  |
| 4347001310 | 01728155GL | 315 | Series 8155L | S-0LBA | 1/2   IPS BALL VALVE FP 600 NL |   19.5  |   0 |   0 |  10 | 120 |   0 |  0.5  |
| 4347001330 | 01728155IL | 315 | Series 8155L | S-0LBA | 3/4   IPS BALL VALVE FP 600 NL |   27.39 |   0 |   0 |  10 |  60 |   0 |  0.73 |
| 4347001350 | 01728155KL | 315 | Series 8155L | S-0LBA | 1     IPS BALL VALVE FP 600 NL |   41.57 |   0 |   0 |   6 |  60 |   0 |  1    |
| 4347001370 | 01728155LL | 315 | Series 8155L | S-0LBA | 1-1/4 IPS BALL VALVE FP 600 NL |   68.3  |   0 |   0 |   4 |  24 |   0 |  1.7  |
| 4347001390 | 01728155ML | 315 | Series 8155L | S-0LBA | 1-1/2 IPS BALL VALVE FP 600 NL |  100.09 |   0 |   0 |   4 |  16 |   0 |  2.27 |
| 4347001410 | 01728155NL | 315 | Series 8155L | S-0LBA | 2     IPS BALL VALVE FP 600 NL |  139.04 |   0 |   0 |   2 |  16 |   0 |  3.53 |
| 4347001610 | 01728156GL | 315 | Series 8156L | S-0LBA | 1/2   CXC BALL VALVE FP 600 NL |   19.5  |   0 |   0 |  10 | 120 |   0 |  0.42 |
| 4347001630 | 01728156IL | 315 | Series 8156L | S-0LBA | 3/4   CXC BALL VALVE FP 600 NL |   27.39 |   0 |   0 |  10 |  60 |   0 |  0.71 |
| 4347001650 | 01728156KL | 315 | Series 8156L | S-0LBA | 1     CXC BALL VALVE FP 600 NL |   41.57 |   0 |   0 |   6 |  60 |   0 |  0.92 |
| 4347001670 | 01728156LL | 315 | Series 8156L | S-0LBA | 1-1/4 CXC BALL VALVE FP 600 NL |   68.3  |   0 |   0 |   4 |  24 |   0 |  1.65 |
| 4347001690 | 01728156ML | 315 | Series 8156L | S-0LBA | 1-1/2 CXC BALL VALVE FP 600 NL |  100.09 |   0 |   0 |   4 |  16 |   0 |  2.29 |
| 4347001710 | 01728156NL | 315 | Series 8156L | S-0LBA | 2     CXC BALL VALVE FP 600 NL |  139.04 |   0 |   0 |   2 |  16 |   0 |  3.31 |
| 4347001430 | 01728155PL | 315 | Series 8155L | S-0LBB | 2-1/2 IPS BALL VALVE FP 600 NL |  332.59 |   0 |   0 |   1 |   0 |   0 |  9.04 |
| 4347001450 | 01728155QL | 315 | Series 8155L | S-0LBB | 3     IPS BALL VALVE FP 600 NL |  490.97 |   0 |   0 |   1 |   0 |   0 | 11.98 |
| 4347001470 | 01728155TL | 315 | Series 8155L | S-0LBB | 4     IPS BALL VALVE FP 600 NL |  814.6  |   0 |   0 |   1 |   0 |   0 | 21.61 |
| 4347001730 | 01728156PL | 315 | Series 8156L | S-0LBB | 2-1/2 CXC BALL VALVE FP 600 NL |  332.59 |   0 |   0 |   2 |   6 |   0 |  9.34 |
| 4347001750 | 01728156QL | 315 | Series 8156L | S-0LBB | 3     CXC BALL VALVE FP 600 NL |  490.97 |   0 |   0 |   2 |   4 |   0 | 12.18 |
| 4347001770 | 01728156TL | 315 | Series 8156L | S-0LBB | 4     CXC BALL VALVE FP 600 NL |  814.6  |   0 |   0 |   1 |   0 |   0 | 21.81 |
| 4347001010 | 01728145CL | 315 | Series 8145L | S-0LBC | 1/4   IPS BALL VLV FP 600  NL  |   12.89 |   0 |   0 |  12 | 120 |   0 |  0.35 |
| 4347001030 | 01728145EL | 315 | Series 8145L | S-0LBC | 3/8   IPS BALL VLV FP 600  NL  |   12.89 |   0 |   0 |  12 | 120 |   0 |  0.31 |
| 4347001050 | 01728145GL | 315 | Series 8145L | S-0LBC | 1/2   IPS BALL VLV FP 600  NL  |   13.69 |   0 |   0 |   8 |  96 |   0 |  0.38 |
| 4347001070 | 01728145IL | 315 | Series 8145L | S-0LBC | 3/4   IPS BALL VLV FP 600  NL  |   20.99 |   0 |   0 |   6 |  72 |   0 |  0.61 |
| 4347001090 | 01728145KL | 315 | Series 8145L | S-0LBC | 1     IPS BALL VLV FP 600  NL  |   34.63 |   0 |   0 |   6 |  36 |   0 |  0.91 |
| 4347001110 | 01728145LL | 315 | Series 8145L | S-0LBC | 1-1/4 IPS BALL VLV FP 600  NL  |   49.53 |   0 |   0 |   6 |  24 |   0 |  1.35 |
| 4347001130 | 01728145ML | 315 | Series 8145L | S-0LBC | 1-1/2 IPS BALL VLV FP 600  NL  |   79.67 |   0 |   0 |   2 |  16 |   0 |  2.05 |
| 4347001150 | 01728145NL | 315 | Series 8145L | S-0LBC | 2     IPS BALL VLV FP 600  NL  |  117.34 |   0 |   0 |   2 |  12 |   0 |  3.07 |
| 4347001200 | 01728146GL | 315 | Series 8146L | S-0LBC | 1/2   CXC BALL VLV FP 600  NL  |   13.69 |   0 |   0 |   8 |  96 |   0 |  0.38 |
| 4347001210 | 01728146IL | 315 | Series 8146L | S-0LBC | 3/4   CXC BALL VLV FP 600  NL  |   20.99 |   0 |   0 |   6 |  72 |   0 |  0.58 |
| 4347001220 | 01728146KL | 315 | Series 8146L | S-0LBC | 1     CXC BALL VLV FP 600  NL  |   34.63 |   0 |   0 |   6 |  36 |   0 |  0.91 |
| 4347001230 | 01728146LL | 315 | Series 8146L | S-0LBC | 1-1/4 CXC BALL VLV FP 600  NL  |   49.53 |   0 |   0 |   6 |  24 |   0 |  1.35 |
| 4347001240 | 01728146ML | 315 | Series 8146L | S-0LBC | 1-1/2 CXC BALL VLV FP 600  NL  |   79.67 |   0 |   0 |   2 |  16 |   0 |  2.05 |
| 4347001250 | 01728146NL | 315 | Series 8146L | S-0LBC | 2     CXC BALL VLV FP 600  NL  |  117.34 |   0 |   0 |   1 |   0 |   0 |  3.55 |
| 4347002200 | 01728170CL | 315 | Series 8170L | S-0LBD | 1/4   IPS BALL FP 600 NL       |   19.48 |   0 |   0 |  10 | 160 |   0 |  0.36 |
| 4347002210 | 01728170EL | 315 | Series 8170L | S-0LBD | 3/8   IPS BALL FP 600 NL       |   20.05 |   0 |   0 |  10 | 160 |   0 |  0.33 |
| 4347002220 | 01728170GL | 315 | Series 8170L | S-0LBD | 1/2   IPS BALL FP 600 NL       |   21.26 |   0 |   0 |  10 | 120 |   0 |  0.5  |
| 4347002230 | 01728170IL | 315 | Series 8170L | S-0LBD | 3/4   IPS BALL FP 600 NL       |   29.98 |   0 |   0 |   6 |  72 |   0 |  0.73 |
| 4347002240 | 01728170KL | 315 | Series 8170L | S-0LBD | 1    IPS BALL FP 600 NL        |   45.94 |   0 |   0 |   4 |  48 |   0 |  1    |
| 4347002250 | 01728170LL | 315 | Series 8170L | S-0LBD | 1-1/4 IPS BALL FP 600 NL       |   90.2  |   0 |   0 |   4 |  24 |   0 |  1.7  |
| 4347002260 | 01728170ML | 315 | Series 8170L | S-0LBD | 1-1/2 IPS BALL FP 600 NL       |  127.61 |   0 |   0 |   6 |  18 |   0 |  2.27 |
| 4347002270 | 01728170NL | 315 | Series 8170L | S-0LBD | 2     IPS BALL FP 600 NL       |  192.13 |   0 |   0 |   4 |   8 |   0 |  3.53 |
| 4347002400 | 01728171GL | 315 | Series 8171L | S-0LBD | 1/2   CXC BALL FP 600 NL       |   21.55 |   0 |   0 |  10 | 120 |   0 |  0.37 |
| 4347002410 | 01728171IL | 315 | Series 8171L | S-0LBD | 3/4   CXC BALL FP 600 NL       |   29.98 |   0 |   0 |  10 |  60 |   0 |  0.79 |
| 4347002420 | 01728171KL | 315 | Series 8171L | S-0LBD | 1     CXC BALL FP 600 NL       |   45.94 |   0 |   0 |   4 |  48 |   0 |  1.15 |
| 4347002430 | 01728171LL | 315 | Series 8171L | S-0LBD | 1-1/4 CXC BALL FP 600 NL       |   91.56 |   0 |   0 |   4 |  24 |   0 |  1.89 |
| 4347002440 | 01728171ML | 315 | Series 8171L | S-0LBD | 1-1/2 CXC BALL FP 600 NL       |  127.61 |   0 |   0 |   6 |  18 |   0 |  2.67 |
| 4347002450 | 01728171NL | 315 | Series 8171L | S-0LBD | 2     CXC BALL FP 600 NL       |  192.13 |   0 |   0 |   4 |   8 |   0 |  4.33 |
| 4347002280 | 01728170PL | 315 | Series 8170L | S-0LBE | 2-1/2  IPS BALL FP 600 NL      |  484.56 |   0 |   0 |   1 |   0 |   0 |  8    |
| 4347002290 | 01728170QL | 315 | Series 8170L | S-0LBE | 3  IPS BALL FP 600 NL          |  639.84 |   0 |   0 |   1 |   0 |   0 | 12    |
| 4347002300 | 01728170TL | 315 | Series 8170L | S-0LBE | 4  IPS BALL FP 600 NL          | 1348.57 |   0 |   0 |   1 |   0 |   0 | 23    |
| 4347000710 | 01728135CL | 315 | Series 8135L | S-0LBF | 1/4   IPS BALL VALVE SP 400 NL |   13.85 |   0 |   0 |  12 | 120 |   0 |  0.33 |
| 4347000730 | 01728135EL | 315 | Series 8135L | S-0LBF | 3/8   IPS BALL VALVE SP 400 NL |   12.61 |   0 |   0 |  12 | 120 |   0 |  0.3  |
| 4347000750 | 01728135GL | 315 | Series 8135L | S-0LBF | 1/2   IPS BALL VALVE SP 400 NL |   14.59 |   0 |   0 |  12 | 120 |   0 |  0.36 |
| 4347000770 | 01728135IL | 315 | Series 8135L | S-0LBF | 3/4   IPS BALL VALVE SP 400 NL |   19.23 |   0 |   0 |   8 |  96 |   0 |  0.49 |
| 4347000790 | 01728135KL | 315 | Series 8135L | S-0LBF | 1  IPS BALL VALVE SP 400 NL    |   35.78 |   0 |   0 |   8 |  48 |   0 |  0.86 |
| 4347000810 | 01728135LL | 315 | Series 8135L | S-0LBF | 1-1/4 IPS BALL VALVE SP 400 NL |   48.99 |   0 |   0 |   8 |  32 |   0 |  1.15 |
| 4347000830 | 01728135ML | 315 | Series 8135L | S-0LBF | 1-1/2 IPS BALL VALVE SP 400 NL |   70.89 |   0 |   0 |   4 |  24 |   0 |  1.66 |
| 4347000850 | 01728135NL | 315 | Series 8135L | S-0LBF | 2  IPS BALL VALVE SP 400 NL    |  107.63 |   0 |   0 |   2 |  16 |   0 |  2.4  |
| 4347002000 | 01728160AL | 315 | Series 8160L | S-0LBG | 1/8 BV FP NICKEL PLT IPS NL    |   18.13 |   0 |   0 |  10 | 160 |   0 |  0.3  |
| 4347002010 | 01728160CL | 315 | Series 8160L | S-0LBG | 1/4 BV FP NICKEL PLT IPS NL    |   18.13 |   0 |   0 |  10 | 160 |   0 |  0.3  |
| 4347002020 | 01728160EL | 315 | Series 8160L | S-0LBG | 3/8 BV FP NICKEL PLT IPS NL    |   18.13 |   0 |   0 |  10 | 160 |   0 |  0.3  |
| 4347002030 | 01728160GL | 315 | Series 8160L | S-0LBG | 1/2 BV FP NICKEL PLT IPS NL    |   21.13 |   0 |   0 |  10 | 120 |   0 |  0.5  |
| 4347002040 | 01728160IL | 315 | Series 8160L | S-0LBG | 3/4 BV FP NICKEL PLT IPS NL    |   31.84 |   0 |   0 |  10 |  60 |   0 |  0.73 |
| 4347002050 | 01728160KL | 315 | Series 8160L | S-0LBG | 1 BV FP NICKEL PLT IPS NL      |   45.26 |   0 |   0 |   6 |  60 |   0 |  1    |
| 4347002060 | 01728160LL | 315 | Series 8160L | S-0LBG | 1-1/4 BV FP NICKEL PLT IPS NL  |   74.64 |   0 |   0 |   4 |  24 |   0 |  1.7  |
| 4347002070 | 01728160ML | 315 | Series 8160L | S-0LBG | 1-1/2 BV FP NICKEL PLT IPS NL  |  107.38 |   0 |   0 |   4 |  16 |   0 |  2.27 |
| 4347002080 | 01728160NL | 315 | Series 8160L | S-0LBG | 2 BV FP NICKEL PLT IPS NL      |  152.05 |   0 |   0 |   2 |  16 |   0 |  3.53 |
| 4347002500 | 01728175GL | 315 | Series 8175L | S-0LBH | 1/2   IPS BALL FP W DRAIN NL   |   21.43 |   0 |   0 |  10 | 100 |   0 |  0.46 |
| 4347002510 | 01728175IL | 315 | Series 8175L | S-0LBH | 3/4   IPS BALL FP W DRAIN NL   |   32.11 |   0 |   0 |   8 |  48 |   0 |  0.85 |
| 4347002520 | 01728175KL | 315 | Series 8175L | S-0LBH | 1     IPS BALL FP W DRAIN NL   |   52.63 |   0 |   0 |   5 |  30 |   0 |  1.19 |
| 4347002530 | 01728176GL | 315 | Series 8176L | S-0LBH | 1/2   CXC BALL FP W DRAIN NL   |   21.43 |   0 |   0 |  10 | 100 |   0 |  0.38 |
| 4347002540 | 01728176IL | 315 | Series 8176L | S-0LBH | 3/4   CXC BALL FP W DRAIN NL   |   32.11 |   0 |   0 |   8 |  48 |   0 |  0.78 |
| 4347002550 | 01728176KL | 315 | Series 8176L | S-0LBH | 1     CXC BALL FP W DRAIN NL   |   52.63 |   0 |   0 |   5 |  30 |   0 |  1.14 |
| 4347002600 | 01728183GL | 383 | Series 8183L | S-0LBI | 1/2 BRASS BALL VALVE PEX NL    |   16.38 |   0 |   0 |  12 |  72 |   0 |  0.3  |
| 4347002620 | 01728183IL | 383 | Series 8183L | S-0LBI | 3/4 BRASS BALL VALVE PEX NL    |   20.17 |   0 |   0 |  12 |  72 |   0 |  0.45 |
| 4347002640 | 01728183KL | 383 | Series 8183L | S-0LBI | 1 BRASS BALL VALVE PEX NL      |   42.36 |   0 |   0 |   6 |  36 |   0 |  0.75 |
| 4347002660 | 01728184GL | 315 | Series 8184L | S-0LBJ | 1/2 BALL VALVE COMP NL         |   19.66 |   0 |   0 |  25 | 100 |   0 |  0.51 |
| 4347002680 | 01728184IL | 315 | Series 8184L | S-0LBJ | 3/4 BALL VALVE COMP NL         |   31.88 |   0 |   0 |  15 |  60 |   0 |  0.83 |
| 4347002700 | 01728184KL | 315 | Series 8184L | S-0LBJ | 1 BALL VALVE COMP NL           |   47.99 |   0 |   0 |  10 |  40 |   0 |  1.33 |



label: I=G*H
labeled_formulas: I=G*H
output: {"Arithmetic-Relationship": ["I=G*H"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_683495___xlsx_588cedcf3ce378124e2335892f800cef9eda13dc.xlsx___line_325