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:
|        C |        D |        E | F     | G      | H      | I     | J     |       K |           L |           M |           N | O                  |
|---------:|---------:|---------:|:------|:-------|:-------|:------|:------|--------:|------------:|------------:|------------:|:-------------------|
|  537.889 |  600.111 |  662.333 | #REF! | Light  | OK     | OK    | #REF! | 0.0001  |   0.0537889 |   0.0600111 |   0.0662333 | #REF!              |
|  543.444 |  604.556 |  665.667 | #REF! | Light  | OK     | OK    | #REF! | 0.00045 |   0.24455   |   0.27205   |   0.29955   | #REF!              |
|  549     |  609     |  669     | #REF! | Light  | OK     | OK    | #REF! | 0.00097 |   0.53253   |   0.59073   |   0.64893   | #REF!              |
|  554.556 |  613.444 |  672.333 | #REF! | Light  | OK     | OK    | #REF! | 0.00135 |   0.74865   |   0.82815   |   0.90765   | #REF!              |
|  560.111 |  617.889 |  675.667 | #REF! | Light  | OK     | OK    | #REF! | 0.00187 |   1.04741   |   1.15545   |   1.2635    | #REF!              |
|  565.667 |  622.333 |  679     | #REF! | Light  | OK     | OK    | #REF! | 0.00256 |   1.44811   |   1.59317   |   1.73824   | #REF!              |
|  571.222 |  626.778 |  682.333 | #REF! | Light  | OK     | OK    | #REF! | 0.00347 |   1.98214   |   2.17492   |   2.3677    | #REF!              |
|  576.778 |  631.222 |  685.667 | #REF! | Light  | OK     | OK    | #REF! | 0.00466 |   2.68778   |   2.9415    |   3.19521   | #REF!              |
|  582.333 |  635.667 |  689     | #REF! | Light  | OK     | OK    | #REF! | 0.00621 |   3.61629   |   3.94749   |   4.27869   | #REF!              |
|  587.889 |  640.111 |  692.333 | #REF! | Light  | OK     | OK    | #REF! | 0.0082  |   4.82069   |   5.24891   |   5.67713   | #REF!              |
|  593.444 |  644.556 |  695.667 | #REF! | Light  | OK     | OK    | #REF! | 0.01072 |   6.36172   |   6.90964   |   7.45755   | #REF!              |
|  599     |  649     |  699     | #REF! | Light  | OK     | OK    | #REF! | 0.0139  |   8.3261    |   9.0211    |   9.7161    | #REF!              |
|  604.556 |  653.444 |  702.333 | #REF! | OK     | OK     | OK    | #REF! | 0.01786 |  10.7974    |  11.6705    |  12.5437    | #REF!              |
|  610.111 |  657.889 |  705.667 | #REF! | OK     | OK     | OK    | #REF! | 0.02275 |  13.88      |  14.967     |  16.0539    | #REF!              |
|  615.667 |  662.333 |  709     | #REF! | OK     | OK     | OK    | #REF! | 0.02872 |  17.6819    |  19.0222    |  20.3625    | #REF!              |
|  621.222 |  666.778 |  712.333 | #REF! | OK     | OK     | OK    | #REF! | 0.03593 |  22.3205    |  23.9573    |  25.5941    | #REF!              |
|  626.778 |  671.222 |  715.667 | #REF! | OK     | OK     | OK    | #REF! | 0.0457  |  28.6437    |  30.6749    |  32.706     | #REF!              |
|  632.333 |  675.667 |  719     | #REF! | OK     | OK     | OK    | #REF! | 0.0548  |  34.6519    |  37.0265    |  39.4012    | #REF!              |
|  637.889 |  680.111 |  722.333 | #REF! | OK     | OK     | OK    | #REF! | 0.06681 |  42.6174    |  45.4382    |  48.2591    | #REF!              |
|  643.444 |  684.556 |  725.667 | #REF! | OK     | OK     | OK    | #REF! | 0.0876  |  56.3657    |  59.9671    |  63.5684    | #REF!              |
|  649     |  689     |  729     | #REF! | OK     | OK     | OK    | #REF! | 0.0968  |  62.8232    |  66.6952    |  70.5672    | #REF!              |
|  654.556 |  693.444 |  732.333 | #REF! | OK     | OK     | OK    | #REF! | 0.11507 |  75.3197    |  79.7947    |  84.2696    | #REF!              |
|  660.111 |  697.889 |  735.667 | #REF! | OK     | OK     | OK    | #REF! | 0.1335  |  88.1248    |  93.1682    |  98.2115    | #REF!              |
|  665.667 |  702.333 |  739     | #REF! | OK     | OK     | OK    | #REF! | 0.15866 | 105.615     | 111.432     | 117.25      | #REF!              |
|  671.222 |  706.778 |  742.333 | #REF! | OK     | OK     | OK    | #REF! | 0.18406 | 123.545     | 130.09      | 136.634     | #REF!              |
|  676.778 |  711.222 |  745.667 | #REF! | OK     | OK     | OK    | #REF! | 0.21186 | 143.382     | 150.68      | 157.977     | #REF!              |
|  682.333 |  715.667 |  749     | #REF! | OK     | OK     | OK    | #REF! | 0.24196 | 165.097     | 173.163     | 181.228     | #REF!              |
|  687.889 |  720.111 |  752.333 | #REF! | OK     | OK     | OK    | #REF! | 0.27425 | 188.654     | 197.49      | 206.327     | #REF!              |
|  693.444 |  724.556 |  755.667 | #REF! | OK     | OK     | OK    | #REF! | 0.30854 | 213.955     | 223.554     | 233.153     | #REF!              |
|  699     |  729     |  759     | #REF! | OK     | OK     | OK    | #REF! | 0.34458 | 240.861     | 251.199     | 261.536     | #REF!              |
|  704.556 |  733.444 |  762.333 | #REF! | OK     | OK     | OK    | #REF! | 0.38209 | 269.204     | 280.242     | 291.28      | #REF!              |
|  710.111 |  737.889 |  765.667 | #REF! | OK     | OK     | OK    | #REF! | 0.42074 | 298.772     | 310.459     | 322.147     | #REF!              |
|  715.667 |  742.333 |  769     | #REF! | OK     | OK     | OK    | #REF! | 0.46017 | 329.328     | 341.6       | 353.871     | #REF!              |
|  721.222 |  746.778 |  772.333 | #REF! | OK     | OK     | OK    | #REF! | 0.5     | 360.611     | 373.389     | 386.167     | #REF!              |
|  726.778 |  751.222 |  775.667 | #REF! | OK     | OK     | OK    | #REF! | 0.53983 | 392.336     | 405.532     | 418.728     | #REF!              |
|  732.333 |  755.667 |  779     | #REF! | OK     | OK     | OK    | #REF! | 0.57926 | 424.211     | 437.727     | 451.244     | #REF!              |
|  737.889 |  760.111 |  782.333 | #REF! | OK     | OK     | OK    | #REF! | 0.61791 | 455.949     | 469.68      | 483.412     | #REF!              |
|  743.444 |  764.556 |  785.667 | #REF! | OK     | OK     | OK    | #REF! | 0.65542 | 487.268     | 501.105     | 514.942     | #REF!              |
|  749     |  769     |  789     | #REF! | OK     | OK     | OK    | #REF! | 0.69146 | 517.904     | 531.733     | 545.562     | #REF!              |
|  754.556 |  773.444 |  792.333 | #REF! | OK     | OK     | OK    | #REF! | 0.72575 | 547.619     | 561.327     | 575.036     | #REF!              |
|  760.111 |  777.889 |  795.667 | #REF! | OK     | OK     | OK    | #REF! | 0.75804 | 576.195     | 589.671     | 603.147     | #REF!              |
|  765.667 |  782.333 |  799     | #REF! | OK     | OK     | OK    | #REF! | 0.78814 | 603.453     | 616.588     | 629.724     | #REF!              |
|  771.222 |  786.778 |  802.333 | #REF! | OK     | OK     | OK    | #REF! | 0.81594 | 629.271     | 641.963     | 654.656     | #REF!              |
|  776.778 |  791.222 |  805.667 | #REF! | OK     | OK     | OK    | #REF! | 0.84134 | 653.534     | 665.687     | 677.84      | #REF!              |
|  782.333 |  795.667 |  809     | #REF! | OK     | OK     | OK    | #REF! | 0.86433 | 676.194     | 687.719     | 699.243     | #REF!              |
|  787.889 |  800.111 |  812.333 | #REF! | OK     | OK     | OK    | #REF! | 0.88493 | 697.227     | 708.042     | 718.858     | #REF!              |
|  793.444 |  804.556 |  815.667 | #REF! | OK     | OK     | OK    | #REF! | 0.9032  | 716.639     | 726.675     | 736.71      | #REF!              |
|  799     |  809     |  819     | #REF! | OK     | OK     | OK    | #REF! | 0.91924 | 734.473     | 743.665     | 752.858     | #REF!              |
|  804.556 |  813.444 |  822.333 | #REF! | OK     | OK     | OK    | #REF! | 0.93319 | 750.803     | 759.098     | 767.393     | #REF!              |
|  810.111 |  817.889 |  825.667 | #REF! | OK     | OK     | OK    | #REF! | 0.9452  | 765.717     | 773.069     | 780.42      | #REF!              |
|  815.667 |  822.333 |  829     | #REF! | OK     | OK     | OK    | #REF! | 0.95543 | 779.312     | 785.682     | 792.051     | #REF!              |
|  821.222 |  826.778 |  832.333 | #REF! | OK     | OK     | OK    | #REF! | 0.95994 | 788.324     | 793.657     | 798.99      | #REF!              |
|  826.778 |  831.222 |  835.667 | #REF! | OK     | OK     | OK    | #REF! | 0.97128 | 803.033     | 807.35      | 811.666     | #REF!              |
|  832.333 |  835.667 |  839     | #REF! | OK     | OK     | OK    | #REF! | 0.97725 | 813.398     | 816.655     | 819.913     | #REF!              |
|  837.889 |  840.111 |  842.333 | #REF! | OK     | OK     | OK    | #REF! | 0.99    | 829.51      | 831.71      | 833.91      | #REF!              |
|  843.444 |  844.556 |  845.667 | #REF! | OK     | OK     | OK    | #REF! | 0.999   | 842.601     | 843.711     | 844.821     | #REF!              |
|  849     |  849     |  849     | 849   | OK     | OK     | OK    | OK    | 0.999   | 848.151     | 848.151     | 848.151     | 848.15099999999995 |
|  851     |  851     |  851     | 851   | OK     | OK     | OK    | OK    | 0.999   | 850.149     | 850.149     | 850.149     | 850.149            |
|  856.556 |  855.444 |  854.333 | #REF! | OK     | OK     | OK    | #REF! | 0.999   | 855.699     | 854.589     | 853.479     | #REF!              |
|  862.111 |  859.889 |  857.667 | #REF! | OK     | OK     | OK    | #REF! | 0.99    | 853.49      | 851.29      | 849.09      | #REF!              |
|  867.667 |  864.333 |  861     | #REF! | OK     | OK     | OK    | #REF! | 0.97725 | 847.927     | 844.67      | 841.412     | #REF!              |
|  873.222 |  868.778 |  864.333 | #REF! | OK     | OK     | OK    | #REF! | 0.97128 | 848.143     | 843.826     | 839.51      | #REF!              |
|  878.778 |  873.222 |  867.667 | #REF! | OK     | OK     | OK    | #REF! | 0.95994 | 843.574     | 838.241     | 832.908     | #REF!              |
|  884.333 |  877.667 |  871     | #REF! | OK     | OK     | OK    | #REF! | 0.95543 | 844.919     | 838.549     | 832.18      | #REF!              |
|  889.889 |  882.111 |  874.333 | #REF! | OK     | OK     | OK    | #REF! | 0.9452  | 841.123     | 833.771     | 826.42      | #REF!              |
|  895.444 |  886.556 |  877.667 | #REF! | OK     | OK     | OK    | #REF! | 0.93319 | 835.62      | 827.325     | 819.03      | #REF!              |
|  901     |  891     |  881     | #REF! | OK     | OK     | OK    | #REF! | 0.91924 | 828.235     | 819.043     | 809.85      | #REF!              |
|  906.556 |  895.444 |  884.333 | #REF! | OK     | OK     | OK    | #REF! | 0.9032  | 818.801     | 808.765     | 798.73      | #REF!              |
|  912.111 |  899.889 |  887.667 | #REF! | OK     | OK     | OK    | #REF! | 0.88493 | 807.154     | 796.339     | 785.523     | #REF!              |
|  917.667 |  904.333 |  891     | #REF! | OK     | OK     | OK    | #REF! | 0.86433 | 793.167     | 781.642     | 770.118     | #REF!              |
|  923.222 |  908.778 |  894.333 | #REF! | OK     | OK     | OK    | #REF! | 0.84134 | 776.744     | 764.591     | 752.438     | #REF!              |
|  928.778 |  913.222 |  897.667 | #REF! | OK     | OK     | OK    | #REF! | 0.81594 | 757.827     | 745.135     | 732.442     | #REF!              |
|  934.333 |  917.667 |  901     | #REF! | OK     | OK     | OK    | #REF! | 0.78814 | 736.385     | 723.25      | 710.114     | #REF!              |
|  939.889 |  922.111 |  904.333 | #REF! | OK     | OK     | OK    | #REF! | 0.75804 | 712.473     | 698.997     | 685.521     | #REF!              |
|  945.444 |  926.556 |  907.667 | #REF! | OK     | OK     | OK    | #REF! | 0.72575 | 686.156     | 672.448     | 658.739     | #REF!              |
|  951     |  931     |  911     | #REF! | OK     | OK     | OK    | #REF! | 0.69146 | 657.578     | 643.749     | 629.92      | #REF!              |
|  956.556 |  935.444 |  914.333 | #REF! | OK     | OK     | OK    | #REF! | 0.65542 | 626.946     | 613.109     | 599.272     | #REF!              |
|  962.111 |  939.889 |  917.667 | #REF! | OK     | OK     | OK    | #REF! | 0.61791 | 594.498     | 580.767     | 567.035     | #REF!              |
|  967.667 |  944.333 |  921     | #REF! | OK     | OK     | OK    | #REF! | 0.57926 | 560.531     | 547.015     | 533.498     | #REF!              |
|  973.222 |  948.778 |  924.333 | #REF! | OK     | OK     | OK    | #REF! | 0.53983 | 525.375     | 512.179     | 498.983     | #REF!              |
|  978.778 |  953.222 |  927.667 | #REF! | OK     | OK     | OK    | #REF! | 0.5     | 489.389     | 476.611     | 463.833     | #REF!              |
|  984.333 |  957.667 |  931     | #REF! | OK     | OK     | OK    | #REF! | 0.46017 | 452.961     | 440.689     | 428.418     | #REF!              |
|  989.889 |  962.111 |  934.333 | #REF! | OK     | OK     | OK    | #REF! | 0.42074 | 416.486     | 404.799     | 393.111     | #REF!              |
|  995.444 |  966.556 |  937.667 | #REF! | OK     | OK     | OK    | #REF! | 0.38209 | 380.349     | 369.311     | 358.273     | #REF!              |
| 1001     |  971     |  941     | #REF! | Heavy  | OK     | OK    | #REF! | 0.34458 | 344.925     | 334.587     | 324.25      | #REF!              |
| 1006.56  |  975.444 |  944.333 | #REF! | Heavy  | OK     | OK    | #REF! | 0.30854 | 310.563     | 300.964     | 291.365     | #REF!              |
| 1012.11  |  979.889 |  947.667 | #REF! | Heavy  | OK     | OK    | #REF! | 0.27425 | 277.571     | 268.735     | 259.898     | #REF!              |
| 1017.67  |  984.333 |  951     | #REF! | Heavy  | OK     | OK    | #REF! | 0.24196 | 246.235     | 238.169     | 230.104     | #REF!              |
| 1023.22  |  988.778 |  954.333 | #REF! | Heavy  | OK     | OK    | #REF! | 0.21186 | 216.78      | 209.482     | 202.185     | #REF!              |
| 1028.78  |  993.222 |  957.667 | #REF! | Heavy  | OK     | OK    | #REF! | 0.18406 | 189.357     | 182.812     | 176.268     | #REF!              |
| 1034.33  |  997.667 |  961     | #REF! | Heavy  | OK     | OK    | #REF! | 0.15866 | 164.107     | 158.29      | 152.472     | #REF!              |
| 1039.89  | 1002.11  |  964.333 | #REF! | Heavy  | Heavy  | OK    | #REF! | 0.1335  | 138.825     | 133.782     | 128.739     | #REF!              |
| 1045.44  | 1006.56  |  967.667 | #REF! | Heavy  | Heavy  | OK    | #REF! | 0.11507 | 120.299     | 115.824     | 111.349     | #REF!              |
| 1051     | 1011     |  971     | #REF! | Heavy2 | Heavy  | OK    | #REF! | 0.0968  | 101.737     |  97.8648    |  93.9928    | #REF!              |
| 1056.56  | 1015.44  |  974.333 | #REF! | Heavy2 | Heavy  | OK    | #REF! | 0.0876  |  92.5543    |  88.9529    |  85.3516    | #REF!              |
| 1062.11  | 1019.89  |  977.667 | #REF! | Heavy2 | Heavy  | OK    | #REF! | 0.06681 |  70.9596    |  68.1388    |  65.3179    | #REF!              |
| 1067.67  | 1024.33  |  981     | #REF! | Heavy2 | Heavy  | OK    | #REF! | 0.0548  |  58.5081    |  56.1335    |  53.7588    | #REF!              |
| 1073.22  | 1028.78  |  984.333 | #REF! | Heavy2 | Heavy  | OK    | #REF! | 0.0457  |  49.0463    |  47.0151    |  44.984     | #REF!              |
| 1078.78  | 1033.22  |  987.667 | #REF! | Heavy2 | Heavy  | OK    | #REF! | 0.03593 |  38.7605    |  37.1237    |  35.4869    | #REF!              |
| 1084.33  | 1037.67  |  991     | #REF! | Heavy2 | Heavy  | OK    | #REF! | 0.02872 |  31.1421    |  29.8018    |  28.4615    | #REF!              |
| 1089.89  | 1042.11  |  994.333 | #REF! | Heavy2 | Heavy  | OK    | #REF! | 0.02275 |  24.795     |  23.708     |  22.6211    | #REF!              |
| 1095.44  | 1046.56  |  997.667 | #REF! | Heavy2 | Heavy  | OK    | #REF! | 0.01786 |  19.5646    |  18.6915    |  17.8183    | #REF!              |
| 1101     | 1051     | 1001     | #REF! | Heavy2 | Heavy2 | Heavy | #REF! | 0.0139  |  15.3039    |  14.6089    |  13.9139    | #REF!              |
| 1106.56  | 1055.44  | 1004.33  | #REF! | Heavy2 | Heavy2 | Heavy | #REF! | 0.01072 |  11.8623    |  11.3144    |  10.7665    | #REF!              |
| 1112.11  | 1059.89  | 1007.67  | #REF! | Heavy2 | Heavy2 | Heavy | #REF! | 0.0082  |   9.11931   |   8.69109   |   8.26287   | #REF!              |
| 1117.67  | 1064.33  | 1011     | #REF! | Heavy2 | Heavy2 | Heavy | #REF! | 0.00621 |   6.94071   |   6.60951   |   6.27831   | #REF!              |
| 1123.22  | 1068.78  | 1014.33  | #REF! | Heavy2 | Heavy2 | Heavy | #REF! | 0.00466 |   5.23422   |   4.9805    |   4.72679   | #REF!              |
| 1128.78  | 1073.22  | 1017.67  | #REF! | Heavy2 | Heavy2 | Heavy | #REF! | 0.00347 |   3.91686   |   3.72408   |   3.5313    | #REF!              |
| 1134.33  | 1077.67  | 1021     | #REF! | Heavy2 | Heavy2 | Heavy | #REF! | 0.00256 |   2.90389   |   2.75883   |   2.61376   | #REF!              |
| 1139.89  | 1082.11  | 1024.33  | #REF! | Heavy2 | Heavy2 | Heavy | #REF! | 0.00187 |   2.13159   |   2.02355   |   1.9155    | #REF!              |
| 1145.44  | 1086.56  | 1027.67  | #REF! | Heavy2 | Heavy2 | Heavy | #REF! | 0.00135 |   1.54635   |   1.46685   |   1.38735   | #REF!              |
| 1151     | 1091     | 1031     | #REF! | Heavy2 | Heavy2 | Heavy | #REF! | 0.00097 |   1.11647   |   1.05827   |   1.00007   | #REF!              |
| 1156.56  | 1095.44  | 1034.33  | #REF! | Heavy2 | Heavy2 | Heavy | #REF! | 0.00045 |   0.52045   |   0.49295   |   0.46545   | #REF!              |
| 1162.11  | 1099.89  | 1037.67  | #REF! | Heavy2 | Heavy2 | Heavy | #REF! | 0.0001  |   0.116211  |   0.109989  |   0.103767  | #REF!              |



label: L=C*K
M=D*K
N=E*K
labeled_formulas: L=C*K
M=D*K
N=E*K
output: {"Arithmetic-Relationship": ["L=C*K", "M=D*K", "N=E*K"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_318785___xlsx_1349e2b89e78e1711b0c47818c3490bb2f971e86.xlsx___line_25