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 |
|:----------|:----------|:----------|-------:|----------:|--------:|----------:|--------:|----------:|--------:|-----------:|------------:|-----------:|
| Noireaux  | Calcite   | CaB-58(s) |  -0.8  |  -8.94203 | 30.9181 |  -9.45261 | 30.3186 |  -9.13602 | 30.9924 |  0.599502  |  0.673723   |  0.0742216 |
| Noireaux  | Calcite   | CaB-48(s) |  -0.8  | -20.9534  | 18.3436 | -21.3893  | 17.8903 | -21.1419  | 18.4245 |  0.453343  |  0.534228   |  0.0808851 |
| Noireaux  | Calcite   | CaB-69(s) |  -0.8  | -21.7687  | 18.0738 | -22.124   | 17.4743 | -21.9372  | 17.618  |  0.599452  |  0.143694   | -0.455758  |
| Noireaux  | Calcite   | CaB-47(s) |  -0.8  | -22.0677  | 17.8199 | -22.4338  | 17.0789 | -22.2568  | 17.1963 |  0.741014  |  0.117403   | -0.623611  |
| Noireaux  | Calcite   | CaB-39(s) |  -0.8  | -22.446   | 17.304  | -22.7711  | 16.8871 | -22.6046  | 16.9821 |  0.41687   |  0.0949442  | -0.321926  |
| Noireaux  | Calcite   | CaB-38(s) |  -0.8  | -17.3645  | 22.7776 | -17.9223  | 21.7718 | -17.5401  | 22.3102 |  1.00576   |  0.538415   | -0.467348  |
| Noireaux  | Calcite   | CaB-7(s)  |  -0.8  | -25.3597  | 13.7822 | -25.4575  | 13.8353 | -25.4052  | 14.0459 | -0.0531467 |  0.210578   |  0.263725  |
| Noireaux  | Calcite   | CaB-54(s) |  -0.8  | -25.5237  | 13.6498 | -25.6095  | 13.6248 | -25.6018  | 13.834  |  0.0249784 |  0.209155   |  0.184176  |
| Noireaux  | Calcite   | CaB-53(s) |  -0.8  | -25.5304  | 13.7351 | -25.6202  | 13.546  | -25.6035  | 13.7744 |  0.189043  |  0.228385   |  0.0393414 |
| Noireaux  | Calcite   | CaB-45(s) |  -0.8  | -17.2775  | 22.6421 | -18.1171  | 21.5176 | -17.9706  | 21.695  |  1.12448   |  0.177359   | -0.947118  |
| Noireaux  | Calcite   | CaB-73(s) |  -0.8  | -15.0635  | 24.7696 | -15.9768  | 23.5777 | -15.7994  | 24.004  |  1.19194   |  0.426343   | -0.7656    |
| Noireaux  | Calcite   | CaB-30    |  -0.8  | -20.2071  | 19.3102 | -20.6371  | 18.8181 | -20.3656  | 19.2351 |  0.492118  |  0.41704    | -0.0750777 |
| Noireaux  | Calcite   | CaB-77    |  -0.8  | -22.7319  | 16.5594 | -23.0748  | 16.3311 | -22.8775  | 16.6655 |  0.228337  |  0.334409   |  0.106071  |
| Noireaux  | Calcite   | CaB-12    |  -0.8  | -22.0202  | 17.4721 | -22.4179  | 17.1008 | -22.1504  | 17.3791 |  0.37124   |  0.278275   | -0.0929648 |
| Noireaux  | Calcite   | CaB-70    |  -0.8  | -22.3318  | 17.2315 | -22.689   | 16.9566 | -22.4566  | 17.0535 |  0.274867  |  0.0968614  | -0.178006  |
| Noireaux  | Calcite   | CaB-8     |  -0.8  | -25.371   | 13.9105 | -25.4718  | 13.7268 | -25.4528  | 13.9553 |  0.183747  |  0.228578   |  0.0448314 |
| Noireaux  | Calcite   | CaB-111   |  -0.8  | -24.1371  | 15.2513 | -24.3154  | 15.0916 | -24.2304  | 15.3102 |  0.159672  |  0.218618   |  0.0589459 |
| Noireaux  | Calcite   | CaB-46    |  -0.8  | -18.3369  | 21.3394 | -19.0825  | 20.5151 | -18.9519  | 20.6996 |  0.824353  |  0.184539   | -0.639814  |
| Noireaux  | Calcite   | CaB-85    |  -0.8  | -15.0761  | 24.7829 | -15.9881  | 23.5725 | -15.8052  | 23.9717 |  1.2104    |  0.399182   | -0.811221  |
| Noireaux  | Calcite   | CaB-40    |  -0.8  | -22.7846  | 16.9945 | -23.1408  | 16.5374 | -22.9329  | 16.6248 |  0.457101  |  0.0873478  | -0.369754  |
| Noireaux  | Aragonite | CaB-9     |  -0.8  | -24.9811  | 14.2368 | -25.2799  | 14.1574 | -25.2768  | 14.1556 |  0.0794665 | -0.00173228 | -0.0811988 |
| Noireaux  | Aragonite | CaB-10    |  -0.8  | -24.9415  | 14.2042 | -25.2437  | 14.1286 | -25.2437  | 14.1286 |  0.0755734 |  0          | -0.0755734 |
| Noireaux  | Aragonite | CaB-72    |  -0.8  | -20.2021  | 19.6356 | -21.4205  | 19.5884 | -21.3026  | 18.3252 |  0.0472231 | -1.26318    | -1.3104    |
| Noireaux  | Aragonite | CaB-19    |  -0.8  | -19.8908  | 19.7471 | -21.1408  | 19.9313 | -21.0322  | 18.5066 | -0.184201  | -1.42472    | -1.24052   |
| Noireaux  | Aragonite | CaB-94    |  -0.8  | -23.8953  | 15.2049 | -24.4412  | 14.9829 | -24.5534  | 14.7718 |  0.221995  | -0.211141   | -0.433136  |
| Noireaux  | Aragonite | CaB-79    |  -0.8  | -21.0513  | 18.1972 | -22.1432  | 18.3759 | -22.0704  | 17.4698 | -0.1787    | -0.906061   | -0.72736   |
| Noireaux  | Aragonite | CaB-80    |  -0.8  | -20.6717  | 18.5796 | -21.8391  | 18.8232 | -21.7408  | 17.8591 | -0.243543  | -0.964097   | -0.720554  |
| Noireaux  | Aragonite | CaB-26    |  -0.8  | -18.7859  | 20.6356 | -20.1489  | 20.9917 | -20.0545  | 19.5858 | -0.356123  | -1.40587    | -1.04975   |
| Noireaux  | Aragonite | CaB-87    |  -0.8  | -13.5765  | 26.1535 | -15.4304  | 26.4838 | -15.8101  | 23.9929 | -0.330353  | -2.49094    | -2.16059   |
| Kaczmarek | Calcite   | Run 1     | -14.24 | -29.9103  | 21.3733 | -30.8161  | 20.2821 | -33.0351  | 19.7735 |  1.09113   | -0.508667   | -1.5998    |
| Kaczmarek | Calcite   | Run 2     | -14.15 | -28.9629  | 22.1671 | -30.0125  | 21.1978 | -32.306   | 20.4639 |  0.96925   | -0.73393    | -1.70318   |
| Kaczmarek | Calcite   | Run 3     | -14.34 | -29.4285  | 21.8479 | -30.4105  | 20.814  | -32.7048  | 20.2694 |  1.03385   | -0.544602   | -1.57845   |
| Kaczmarek | Calcite   | Run 4     | -14.31 | -29.531   | 21.7099 | -30.5128  | 20.6763 | -32.7751  | 20.1055 |  1.03357   | -0.570801   | -1.60437   |
| Kaczmarek | Calcite   | Run 5     | -14.09 | -26.6944  | 24.5042 | -28.5071  | 22.5963 | -29.7548  | 23.092  |  1.908     |  0.495763   | -1.41223   |
| Kaczmarek | Calcite   | Run 6     | -14.02 | -26.7914  | 24.3082 | -28.5619  | 22.4447 | -29.8282  | 22.9419 |  1.86346   |  0.497203   | -1.36626   |
| Kaczmarek | Calcite   | Run 7     | -14.11 | -26.713   | 24.4857 | -28.4793  | 22.6265 | -29.8071  | 23.0576 |  1.85922   |  0.431078   | -1.42814   |
| Kaczmarek | Calcite   | Run 8     | -14.1  | -26.8676  | 24.3082 | -28.638   | 22.4447 | -29.907   | 22.9419 |  1.86346   |  0.497203   | -1.36626   |
| Kaczmarek | Calcite   | Run 9     | -14.01 | -26.4533  | 24.654  | -28.2983  | 22.8485 | -29.5478  | 23.2272 |  1.80548   |  0.37871    | -1.42678   |
| Kaczmarek | Calcite   | Run 10    | -14.35 | -26.9083  | 24.5064 | -28.7632  | 22.6914 | -30.0342  | 23.0671 |  1.81491   |  0.375699   | -1.43921   |
| Kaczmarek | Calcite   | Run 11    | -14.03 | -26.7355  | 24.3673 | -28.59    | 22.5525 | -29.8553  | 22.9237 |  1.81477   |  0.371201   | -1.44357   |
| Kaczmarek | Calcite   | Run 12    | -14.03 | -26.7683  | 24.3377 | -28.5435  | 22.4692 | -29.8806  | 22.8971 |  1.86848   |  0.427921   | -1.44056   |
| Kaczmarek | Calcite   | Run 13    | -14.04 | -26.2213  | 24.9378 | -28.7663  | 22.2591 | -28.8209  | 24.0248 |  2.67871   |  1.76573    | -0.912983  |
| Kaczmarek | Calcite   | Run 14    | -13.96 | -26.1193  | 24.8649 | -28.6849  | 22.2974 | -28.8018  | 23.9619 |  2.56742   |  1.66447    | -0.902958  |
| Kaczmarek | Calcite   | Run 15    | -14.25 | -26.4338  | 24.9718 | -28.9043  | 22.2385 | -29.0373  | 24.0147 |  2.73326   |  1.77621    | -0.957055  |
| Kaczmarek | Calcite   | Run 16    | -13.97 | -26.3221  | 24.7851 | -28.8336  | 22.1417 | -28.8898  | 23.8795 |  2.64336   |  1.73775    | -0.905616  |
| Uchikawa  | Calcite   | Exp. 8C   | -12.19 | -32.0805  | 18.6171 | -32.8888  | 18.1488 | -33.3369  | 17.3898 |  0.468267  | -0.759      | -1.22727   |
| Uchikawa  | Calcite   | Exp. 8F   | -12.19 | -32.0805  | 18.6171 | -32.8888  | 18.1488 | -33.3445  | 17.3937 |  0.468267  | -0.755056   | -1.22332   |
| Uchikawa  | Calcite   | Exp. 15A  | -12.19 | -30.8522  | 19.9572 | -31.8049  | 19.3019 | -32.3525  | 18.4021 |  0.655316  | -0.899825   | -1.55514   |
| Uchikawa  | Calcite   | Exp. 9B   | -12.19 | -29.3621  | 21.5255 | -30.4418  | 20.8702 | -31.0811  | 19.7164 |  0.65534   | -1.1538     | -1.80914   |
| Uchikawa  | Calcite   | Exp. 10A  | -12.19 | -27.4085  | 23.6893 | -28.593   | 22.9266 | -29.3593  | 21.5165 |  0.762634  | -1.41014    | -2.17277   |
| Uchikawa  | Calcite   | Exp. 4B   | -12.19 | -34.0688  | 16.6791 | -34.8312  | 15.996  | -34.8913  | 15.7658 |  0.68307   | -0.230251   | -0.913321  |
| Uchikawa  | Calcite   | Exp. 2B   | -12.19 | -32.1052  | 18.71   | -33.2543  | 17.692  | -33.3617  | 17.3876 |  1.01797   | -0.304439   | -1.32241   |
| Uchikawa  | Calcite   | Exp. 1C   | -12.19 | -29.3687  | 21.6261 | -30.9591  | 20.3135 | -31.0783  | 19.7074 |  1.31261   | -0.606123   | -1.91873   |
| Uchikawa  | Calcite   | Exp. 13C  | -12.19 | -32.085   | 18.6123 | -32.8935  | 18.1439 | -33.3342  | 17.3808 |  0.468406  | -0.763084   | -1.23149   |
| Uchikawa  | Calcite   | Exp. 12B  | -12.19 | -32.0889  | 18.7152 | -32.8888  | 18.1488 | -33.3486  | 17.3063 |  0.566457  | -0.842516   | -1.40897   |
| Uchikawa  | Calcite   | Exp. 11A  | -12.19 | -32.0743  | 18.7068 | -32.8813  | 18.1447 | -33.3486  | 17.3063 |  0.5621    | -0.838376   | -1.40048   |
| Uchikawa  | Calcite   | Exp. 19B  | -12.19 | -32.0307  | 18.6813 | -32.9065  | 18.2508 | -33.3521  | 17.3977 |  0.430488  | -0.853141   | -1.28363   |
| Uchikawa  | Calcite   | Exp. 17B  | -12.19 | -31.9764  | 18.7503 | -32.9017  | 18.2557 | -33.3438  | 17.3113 |  0.494624  | -0.94438    | -1.439     |
| Uchikawa  | Calcite   | Exp. 16B  | -12.19 | -31.8795  | 18.888  | -32.9251  | 18.4618 | -33.3616  | 17.3281 |  0.426172  | -1.13367    | -1.55984   |



label: K=F-H
L=J-H
M=J-F
labeled_formulas: K=F-H
L=J-H
M=J-F
output: {"Arithmetic-Relationship": ["K=F-H", "L=J-H", "M=J-F"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_555635___xlsx_8d2b45d8438069eac8e8770d166089a01025f04c.xlsx___line_493