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 |
|:------|:----|:--------|------------:|----------:|---------:|----------:|------------:|----------:|----------:|------------:|----------:|
| ANH21 | ANH | 2020-21 |   2.71761   |   5.0039  |  554.681 | 1.21965   |  1.41804    |  199.51   |   6.324   |   3.93726   |   6.42194 |
| ANH22 | ANH | 2021-22 |   8.70623   |  35.5841  |  660.101 | 1.97489   |  2.16368    |   15.484  |  44.309   |  10.6811    |  37.7478  |
| ANH23 | ANH | 2022-23 |  25.3049    |  96.5179  |  661.609 | 2.41916   |  4.0925     |   44.344  | 129.311   |  27.7241    | 100.61    |
| ANH24 | ANH | 2023-24 |  57.5692    | 119.47    |  772.564 | 2.82062   |  6.91983    |   46.844  | 182.866   |  60.3898    | 126.39    |
| ANH25 | ANH | 2024-25 |  27.0895    |  36.219   |  683.452 | 4.57243   |  8.82191    | 1125.09   |  93.794   |  31.6619    |  45.0409  |
| NES21 | NES | 2020-21 |   0.276     |   0.995   |  192.099 | 0         |  0          |    0      |  12.45    |   0.276     |   0.995   |
| NES22 | NES | 2021-22 |   0.1       |  12.801   |  218.519 | 0         |  0          |    0      |   0       |   0.1       |  12.801   |
| NES23 | NES | 2022-23 |   0.1       |  18.858   |  243.534 | 0         |  0          |    0      |   0       |   0.1       |  18.858   |
| NES24 | NES | 2023-24 |   0.1       |  32.029   |  307.511 | 0         |  0          |    0      |   0       |   0.1       |  32.029   |
| NES25 | NES | 2024-25 |   0.1       |  25.497   |  252.222 | 0         |  0          |    0      | 107.316   |   0.1       |  25.497   |
| NWT21 | NWT | 2020-21 |   2.04882   |  39.0946  |  557.405 | 0.25      |  0.202      |    0      |   0       |   2.29882   |  39.2966  |
| NWT22 | NWT | 2021-22 |  20.3223    |  36.0367  |  584.417 | 0.25      |  0.939      |    0      |  65.2394  |  20.5723    |  36.9757  |
| NWT23 | NWT | 2022-23 |  28.0752    |  10.204   |  527.238 | 0.573     |  1.717      |  182.303  |   0       |  28.6482    |  11.921   |
| NWT24 | NWT | 2023-24 |  53.3841    |  92.6789  |  706.991 | 2.77      |  1.731      | 1361.48   |   0       |  56.1541    |  94.4099  |
| NWT25 | NWT | 2024-25 |  42.925     |  59.2881  |  637.008 | 6.187     |  6.388      |  992.93   | 998.796   |  49.112     |  65.6761  |
| SRN21 | SRN | 2020-21 |   9.91      |  26.649   |  405.485 | 0.56      |  2.456      |    0      |   0       |  10.47      |  29.105   |
| SRN22 | SRN | 2021-22 |  23.957     |  65.721   |  513.743 | 0.56      |  2.469      |   45.32   |  56.813   |  24.517     |  68.19    |
| SRN23 | SRN | 2022-23 |  18.238     |  53.329   |  540.09  | 1.054     |  3.939      |    0      |   0       |  19.292     |  57.268   |
| SRN24 | SRN | 2023-24 |   2.551     |   8.862   |  445.819 | 2.011     |  6.704      |    0      |   0       |   4.562     |  15.566   |
| SRN25 | SRN | 2024-25 |   0.86      |   1.116   |  375.741 | 2.155     |  7.154      |  243.268  | 369.905   |   3.015     |   8.27    |
| SWB21 | SWB | 2020-21 |   2.253     |   7.319   |  209.884 | 0         |  0          |    0      |   0       |   2.253     |   7.319   |
| SWB22 | SWB | 2021-22 |   2.72      |   4.179   |  205.418 | 0.016     |  0.024      |    0      |   0       |   2.736     |   4.203   |
| SWB23 | SWB | 2022-23 |   3.613     |   3.225   |  184.163 | 0.053     |  0.025      |    0      |   0       |   3.666     |   3.25    |
| SWB24 | SWB | 2023-24 |   2.53      |   0.586   |  182.451 | 0.098     |  0.155      |    0      |   0       |   2.628     |   0.741   |
| SWB25 | SWB | 2024-25 |   0.385     |   0       |  169.172 | 0.127     |  0.219      |   28.945  |  30.193   |   0.512     |   0.219   |
| TMS21 | TMS | 2020-21 |   0.880173  |   5.73807 |  847.48  | 0         |  0          |    0      |   0       |   0.880173  |   5.73807 |
| TMS22 | TMS | 2021-22 |   1.41797   |   7.23776 |  975.668 | 0         |  0          |    0      |   0       |   1.41797   |   7.23776 |
| TMS23 | TMS | 2022-23 |   9.04953   |  30.2784  | 1014.38  | 0         |  0.206358   |    0      |   0       |   9.04953   |  30.4847  |
| TMS24 | TMS | 2023-24 |  12.0437    |  42.6581  |  972.976 | 0         |  0.206358   |    0      |   0       |  12.0437    |  42.8645  |
| TMS25 | TMS | 2024-25 |   9.55741   |  35.8293  |  864.923 | 0.216497  |  1.5432     |  173.344  | 283.232   |   9.7739    |  37.3725  |
| WSH21 | WSH | 2020-21 |  12.148     |   7.153   |  358.982 | 0         |  0          |    0      |   0       |  12.148     |   7.153   |
| WSH22 | WSH | 2021-22 |  12.148     |   7.958   |  292.741 | 0         |  0.069      |    0      |   0.704   |  12.148     |   8.027   |
| WSH23 | WSH | 2022-23 |  13.315     |   8.971   |  302.386 | 0         |  0.339      |    4.449  |  17.4     |  13.315     |   9.31    |
| WSH24 | WSH | 2023-24 |   2.466     |   9.375   |  291.245 | 0.064     |  0.11       |    0      |   0       |   2.53      |   9.485   |
| WSH25 | WSH | 2024-25 |   2.438     |   9.268   |  288.202 | 0.078     |  0.472      |    5.259  | 167.602   |   2.516     |   9.74    |
| WSX21 | WSX | 2020-21 |   9.65636   |  27.3169  |  331.101 | 0.0784656 |  0.16129    |    0      |   0       |   9.73482   |  27.4782  |
| WSX22 | WSX | 2021-22 |   6.62853   |  26.4724  |  308.784 | 0.145409  |  0.490052   |   51.0372 | 139.403   |   6.77394   |  26.9624  |
| WSX23 | WSX | 2022-23 |   9.38357   |  24.9477  |  308.831 | 0.351131  |  1.09511    |   27.3147 | 129.442   |   9.7347    |  26.0429  |
| WSX24 | WSX | 2023-24 |  14.7856    |  19.7007  |  301.717 | 0.507777  |  1.96578    |  167.412  |  59.5028  |  15.2934    |  21.6665  |
| WSX25 | WSX | 2024-25 |   7.25313   |   5.49315 |  291.49  | 1.01784   |  2.48838    |  262.34   |  32.002   |   8.27098   |   7.98153 |
| YKY21 | YKY | 2020-21 | 104.74      |  92.573   |  692.817 | 0         |  0          |    0      |   0       | 104.74      |  92.573   |
| YKY22 | YKY | 2021-22 | 128.539     |  71.842   |  696.685 | 0         |  0          |   18.543  |  27.629   | 128.539     |  71.842   |
| YKY23 | YKY | 2022-23 |  97.583     |  29.889   |  593.222 | 1.077     |  2.363      |  246.613  | 404.664   |  98.66      |  32.252   |
| YKY24 | YKY | 2023-24 |  57.849     |   6.637   |  515.786 | 4.479     |  8.506      |  375.949  | 104.554   |  62.328     |  15.143   |
| YKY25 | YKY | 2024-25 |  19.691     |   0.934   |  389.005 | 7.469     | 11.092      | 2969.98   |   0.517   |  27.16      |  12.026   |
| SVE21 | SVE | 2020-21 |  10.698     |   9.222   |  560.936 | 0.009     |  0.00759026 |    0      |   0       |  10.707     |   9.22959 |
| SVE22 | SVE | 2021-22 |  22.852     |  19.195   |  614.479 | 0.287     |  0.223797   |  147.085  |  67.2323  |  23.139     |  19.4188  |
| SVE23 | SVE | 2022-23 |  26.966     |  21.646   |  621.223 | 0.499     |  0.39572    |    0      |   4.84207 |  27.465     |  22.0417  |
| SVE24 | SVE | 2023-24 |  26.859     |  21.488   |  610.597 | 0.556     |  0.47236    |    0      |   0       |  27.415     |  21.9604  |
| SVE25 | SVE | 2024-25 |  15.107     |  12.227   |  545.437 | 2.602     |  2.10531    | 1682.57   | 700.747   |  17.709     |  14.3323  |
| HDD21 | HDD | 2020-21 |   0         |   0       |    4.498 | 0         |  0          |    0      |   0       |   0         |   0       |
| HDD22 | HDD | 2021-22 |   0.0279825 |   0.15204 |    4.854 | 0         |  0          |    0      |   0       |   0.0279825 |   0.15204 |
| HDD23 | HDD | 2022-23 |   0.055965  |   0.30408 |    5.051 | 0         |  0.0228     |    0      |   0       |   0.055965  |   0.32688 |
| HDD24 | HDD | 2023-24 |   0.195878  |   1.06428 |    6.163 | 0         |  0.0228     |   12.439  |   1.887   |   0.195878  |   1.08708 |
| HDD25 | HDD | 2024-25 |   0         |   0       |    4.591 | 0         |  0.0228     |    0      |   0       |   0         |   0.0228  |



label: K=D+G
L=E+H
labeled_formulas: K=D+G
L=E+H
output: {"Arithmetic-Relationship": ["K=D+G", "L=E+H"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_635994___xlsx_08f6b47d025593f5edf1dd33440da4db072c2ea1.xlsx___line_42