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 |
|----:|----------:|------:|:---------|:------|:-------------------|-----:|------:|------:|---------:|----------:|
|   1 | 201801001 | 43103 | 天津气体 | A0015 | 氩气               |  700 | 28    | 19600 |  3332    |  22932    |
|   2 | 201801001 | 43103 | 天津气体 | A0016 | 二氧化碳           |  700 | 21    | 14700 |  2499    |  17199    |
|   3 | 201801001 | 43103 | 天津气体 | A0017 | 排气管前端法兰盘   | 1100 | 10.5  | 11550 |  1963.5  |  13513.5  |
|   4 | 201801002 | 43104 | 北京恒卓 | A0001 | 排气管端面板       |  900 |  3.2  |  2880 |   489.6  |   3369.6  |
|   5 | 201801002 | 43104 | 北京恒卓 | A0002 | 排气管前段管       |  500 |  5.5  |  2750 |   467.5  |   3217.5  |
|   6 | 201801002 | 43104 | 北京恒卓 | A0003 | 排气管中段管       | 1500 |  2.4  |  3600 |   612    |   4212    |
|   7 | 201801002 | 43104 | 北京恒卓 | A0004 | 排气管后段管       |  500 |  5.55 |  2775 |   471.75 |   3246.75 |
|   8 | 201801002 | 43104 | 北京恒卓 | A0005 | 消声器进气管前段管 | 1000 |  1.4  |  1400 |   238    |   1638    |
|   9 | 201801002 | 43104 | 北京恒卓 | A0006 | 消声器筒体合件     | 1100 | 44.45 | 48895 |  8312.15 |  57207.2  |
|  10 | 201801002 | 43104 | 北京恒卓 | A0021 | 前消前段管         | 2500 |  3.4  |  8500 |  1445    |   9945    |
|  11 | 201801002 | 43104 | 北京恒卓 | A0022 | 前消后段管         | 1800 |  4    |  7200 |  1224    |   8424    |
|  12 | 201801002 | 43104 | 北京恒卓 | A0023 | 后消前段管         | 1900 |  4    |  7600 |  1292    |   8892    |
|  13 | 201801002 | 43104 | 北京恒卓 | A0024 | 后消尾管           |  600 | 17.5  | 10500 |  1785    |  12285    |
|  14 | 201801003 | 43105 | 天津业泰 | A0008 | 消声器尾管         |  900 |  9.5  |  8550 |  1453.5  |  10003.5  |
|  15 | 201801003 | 43105 | 天津业泰 | A0009 | 消声器前加强板     |  600 |  0.77 |   462 |    78.54 |    540.54 |
|  16 | 201801003 | 43105 | 天津业泰 | A0010 | 消声器后加强板     |  700 |  0.49 |   343 |    58.31 |    401.31 |
|  17 | 201801003 | 43105 | 天津业泰 | A0011 | 波纹管组成         |  700 | 16    | 11200 |  1904    |  13104    |
|  18 | 201801003 | 43105 | 天津业泰 | A0012 | 筒体吊钩           |  900 |  1.08 |   972 |   165.24 |   1137.24 |
|  19 | 201801003 | 43105 | 天津业泰 | A0013 | 尾管吊钩           |  400 |  1.22 |   488 |    82.96 |    570.96 |
|  20 | 201801003 | 43105 | 天津业泰 | A0019 | 前消支架           | 1300 |  1.05 |  1365 |   232.05 |   1597.05 |
|  21 | 201801003 | 43105 | 天津业泰 | A0020 | 后消支架           | 1400 |  0.85 |  1190 |   202.3  |   1392.3  |
|  22 | 201801004 | 43109 | 北京恒卓 | A0001 | 排气管端面板       | 2000 |  3.4  |  6800 |  1156    |   7956    |
|  23 | 201801004 | 43109 | 北京恒卓 | A0002 | 排气管前段管       | 2000 |  5.6  | 11200 |  1904    |  13104    |
|  24 | 201801004 | 43109 | 北京恒卓 | A0003 | 排气管中段管       | 3000 |  2.4  |  7200 |  1224    |   8424    |
|  25 | 201801004 | 43109 | 北京恒卓 | A0004 | 排气管后段管       | 2000 |  6    | 12000 |  2040    |  14040    |
|  26 | 201801004 | 43109 | 北京恒卓 | A0005 | 消声器进气管前段管 | 2000 |  1.4  |  2800 |   476    |   3276    |
|  27 | 201801004 | 43109 | 北京恒卓 | A0006 | 消声器筒体合件     | 2000 | 44.52 | 89040 | 15136.8  | 104177    |
|  28 | 201801004 | 43109 | 北京恒卓 | A0007 | 消声器隔热罩       | 1500 |  4.4  |  6600 |  1122    |   7722    |
|  29 | 201801004 | 43109 | 北京恒卓 | A0021 | 前消前段管         | 3000 |  3.56 | 10680 |  1815.6  |  12495.6  |
|  30 | 201801004 | 43109 | 北京恒卓 | A0022 | 前消后段管         | 3000 |  4.02 | 12060 |  2050.2  |  14110.2  |
|  31 | 201801004 | 43109 | 北京恒卓 | A0023 | 后消前段管         | 3000 |  4.05 | 12150 |  2065.5  |  14215.5  |
|  32 | 201801004 | 43109 | 北京恒卓 | A0024 | 后消尾管           | 1500 | 18    | 27000 |  4590    |  31590    |
|  33 | 201801005 | 43112 | 北京翎翔 | B0001 | 后氧传感器螺母     | 2000 |  2    |  4000 |   680    |   4680    |
|  34 | 201801005 | 43112 | 北京翎翔 | B0002 | 连接盘             | 7000 |  2    | 14000 |  2380    |  16380    |
|  35 | 201801005 | 43112 | 北京翎翔 | B0003 | 螺栓               | 8000 |  0.3  |  2400 |   408    |   2808    |
|  36 | 201801005 | 43112 | 北京翎翔 | B0006 | 密封环             | 6000 |  2.7  | 16200 |  2754    |  18954    |
|  37 | 201801006 | 43114 | 天津气体 | A0014 | 导电嘴             | 3000 |  1.6  |  4800 |   816    |   5616    |
|  38 | 201801006 | 43114 | 天津气体 | A0015 | 氩气               | 2000 | 27.4  | 54800 |  9316    |  64116    |
|  39 | 201801006 | 43114 | 天津气体 | A0016 | 二氧化碳           | 1000 | 21    | 21000 |  3570    |  24570    |
|  40 | 201801006 | 43114 | 天津气体 | A0017 | 排气管前端法兰盘   | 3000 | 10.4  | 31200 |  5304    |  36504    |
|  41 | 201801007 | 43116 | 天津业泰 | A0008 | 消声器尾管         | 2000 |  9.5  | 19000 |  3230    |  22230    |
|  42 | 201801007 | 43116 | 天津业泰 | A0009 | 消声器前加强板     | 2000 |  0.8  |  1600 |   272    |   1872    |
|  43 | 201801007 | 43116 | 天津业泰 | A0010 | 消声器后加强板     | 2000 |  0.5  |  1000 |   170    |   1170    |
|  44 | 201801007 | 43116 | 天津业泰 | A0011 | 波纹管组成         | 2000 | 16.8  | 33600 |  5712    |  39312    |
|  45 | 201801007 | 43116 | 天津业泰 | A0012 | 筒体吊钩           | 2000 |  1    |  2000 |   340    |   2340    |
|  46 | 201801007 | 43116 | 天津业泰 | A0013 | 尾管吊钩           | 2000 |  1.3  |  2600 |   442    |   3042    |
|  47 | 201801007 | 43116 | 天津业泰 | A0019 | 前消支架           | 3000 |  1.03 |  3090 |   525.3  |   3615.3  |
|  48 | 201801007 | 43116 | 天津业泰 | A0020 | 后消支架           | 3000 |  0.9  |  2700 |   459    |   3159    |
|  49 | 201801008 | 42755 | 北京恒卓 | A0001 | 排气管端面板       | 1000 |  3.5  |  3500 |   595    |   4095    |
|  50 | 201801008 | 42755 | 北京恒卓 | A0003 | 排气管中段管       | 1000 |  2.5  |  2500 |   425    |   2925    |
|  51 | 201801008 | 42755 | 北京恒卓 | A0005 | 消声器进气管前段管 | 1000 |  1.4  |  1400 |   238    |   1638    |
|  52 | 201801008 | 42755 | 北京恒卓 | A0006 | 消声器筒体合件     | 1000 | 44.5  | 44500 |  7565    |  52065    |
|  53 | 201801008 | 42755 | 北京恒卓 | A0021 | 前消前段管         | 2000 |  3.5  |  7000 |  1190    |   8190    |
|  54 | 201801008 | 42755 | 北京恒卓 | A0022 | 前消后段管         | 3000 |  4    | 12000 |  2040    |  14040    |
|  55 | 201801008 | 42755 | 北京恒卓 | A0023 | 后消前段管         | 1000 |  4    |  4000 |   680    |   4680    |
|  56 | 201801009 | 43122 | 天津气体 | A0014 | 导电嘴             | 2000 |  1.6  |  3200 |   544    |   3744    |
|  57 | 201801009 | 43122 | 天津气体 | A0015 | 氩气               | 2000 | 27.4  | 54800 |  9316    |  64116    |
|  58 | 201801009 | 43122 | 天津气体 | A0016 | 二氧化碳           | 1000 | 21    | 21000 |  3570    |  24570    |
|  59 | 201801009 | 43122 | 天津气体 | A0017 | 排气管前端法兰盘   | 1500 | 10.4  | 15600 |  2652    |  18252    |
|  60 | 201801010 | 43124 | 天津业泰 | A0008 | 消声器尾管         | 1000 |  9.5  |  9500 |  1615    |  11115    |
|  61 | 201801010 | 43124 | 天津业泰 | A0012 | 筒体吊钩           | 3000 |  1    |  3000 |   510    |   3510    |
|  62 | 201801010 | 43124 | 天津业泰 | A0013 | 尾管吊钩           | 3000 |  1.3  |  3900 |   663    |   4563    |
|  63 | 201801010 | 43124 | 天津业泰 | A0019 | 前消支架           | 1500 |  1.03 |  1545 |   262.65 |   1807.65 |
|  64 | 201801010 | 43124 | 天津业泰 | A0020 | 后消支架           | 1500 |  0.85 |  1275 |   216.75 |   1491.75 |



label: I=G*H
K=I+J
labeled_formulas: I=G*H
K=I+J
output: {"Arithmetic-Relationship": ["I=G*H", "K=I+J"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_732344___xlsx_0928d3246f12390fdbd2ec9ead60a5512dce73c1.xlsx___line_85