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 |         N |   O |         P |          Q |           R |           S |
|:---------|-------:|:----|:----|----:|-------:|----------:|----:|----:|----------:|---------:|----:|----:|----------:|----:|----------:|-----------:|------------:|------------:|
| CDKN2A   |   1029 | Y   | Y   |   9 |    522 | 152.579   |   0 |   9 | 152.579   | 0.432222 |   6 |   0 | 0.666667  |   9 | 0.079646  | 0.124138   | 2.7204e-10  | 2.56561e-06 |
| JUB      |  84962 | N   | Y   |   8 |   1616 |  43.8097  |   0 |   8 |  43.8097  | 0.3975   |   7 |   0 | 0.875     |   8 | 0.0707965 | 0          | 1.27958e-09 | 8.04517e-06 |
| RB1      |   5925 | Y   | Y   |  10 |   2787 |  31.753   |   0 |  10 |  31.753   | 0.425    |   9 |   0 | 0.9       |  10 | 0.0884956 | 0.00689655 | 1.72316e-08 | 8.12556e-05 |
| PTCH1    |   5727 | Y   | N   |   6 |   4344 |  12.2231  |   0 |   6 |  12.2231  | 0.511429 |   3 |   0 | 0.5       |   6 | 0.0619469 | 0.0206897  | 0.000197669 | 0.372843    |
| CREBBP   |   1387 | Y   | Y   |   8 |   7329 |   9.65977 |   1 |   7 |   8.4523  | 0.37     |   4 |   0 | 0.571429  |   7 | 0.0619469 | 0.0206897  | 0.00157557  | 1           |
| SYT10    | 341359 | N   | N   |   6 |   1572 |  33.7769  |   0 |   6 |  33.7769  | 0.175    |   1 |   0 | 0.166667  |   6 | 0.0530973 | 0.0275862  | 0.00217536  | 1           |
| FAT1     |   2195 | N   | Y   |  14 |  13773 |   8.99541 |   2 |  12 |   7.71035 | 0.406667 |   8 |   0 | 0.666667  |  12 | 0.106195  | 0.0206897  | 0.00358467  | 1           |
| FAM171A1 | 221061 | N   | N   |   7 |   2673 |  23.175   |   1 |   6 |  19.8643  | 0.285    |   2 |   0 | 0.333333  |   6 | 0.0530973 | 0.0137931  | 0.00834867  | 1           |
| FSTL5    |  56884 | N   | N   |   7 |   2544 |  24.3502  |   0 |   7 |  24.3502  | 0.337143 |   2 |   0 | 0.285714  |   7 | 0.0619469 | 0.0551724  | 0.00967919  | 1           |
| MYH10    |   4628 | N   | N   |   8 |   6024 |  11.7524  |   0 |   8 |  11.7524  | 0.2675   |   2 |   0 | 0.25      |   8 | 0.0707965 | 0.0275862  | 0.0103371   | 1           |
| SLCO5A1  |  81796 | N   | N   |   6 |   2547 |  20.847   |   0 |   6 |  20.847   | 0.24     |   0 |   0 | 0         |   6 | 0.0530973 | 0.0206897  | 0.0228484   | 1           |
| TRIM67   | 440730 | N   | N   |   6 |   2352 |  22.5754  |   0 |   6 |  22.5754  | 0.23     |   0 |   0 | 0         |   6 | 0.0530973 | 0.0137931  | 0.0259204   | 1           |
| PCDH9    |   5101 | N   | N   |   8 |   3714 |  19.0621  |   0 |   8 |  19.0621  | 0.28625  |   1 |   0 | 0.125     |   8 | 0.0707965 | 0.0758621  | 0.0289992   | 1           |
| ANK3     |    288 | N   | Y   |   9 |  13134 |   6.06411 |   1 |   8 |   5.39032 | 0.3075   |   2 |   0 | 0.25      |   8 | 0.0707965 | 0.0482759  | 0.0333497   | 1           |
| NALCN    | 259232 | N   | N   |   7 |   5217 |  11.874   |   0 |   7 |  11.874   | 0.287143 |   0 |   0 | 0         |   6 | 0.0530973 | 0.103448   | 0.0455487   | 1           |
| PCDH15   |  65217 | N   | N   |  10 |   5889 |  15.0273  |   1 |   9 |  13.5245  | 0.194444 |   2 |   0 | 0.222222  |   9 | 0.079646  | 0.158621   | 0.0518845   | 1           |
| CTNNA2   |   1496 | N   | N   |   8 |   2862 |  24.7367  |   0 |   8 |  24.7367  | 0.25875  |   0 |   0 | 0         |   8 | 0.0707965 | 0.0758621  | 0.0608972   | 1           |
| FBN2     |   2201 | N   | N   |   8 |   8739 |   8.10121 |   1 |   7 |   7.08856 | 0.428571 |   1 |   0 | 0.142857  |   6 | 0.0530973 | 0.0551724  | 0.069859    | 1           |
| DMD      |   1756 | N   | N   |  12 |  11058 |   9.60343 |   0 |  12 |   9.60343 | 0.3      |   4 |   0 | 0.333333  |  11 | 0.0973451 | 0.0344828  | 0.0768107   | 1           |
| DNAH7    |  56171 | N   | N   |   7 |  12075 |   5.13018 |   1 |   6 |   4.3973  | 0.21     |   2 |   0 | 0.333333  |   6 | 0.0530973 | 0.0689655  | 0.0882903   | 1           |
| CACNA1S  |    779 | N   | N   |   7 |   5622 |  11.0187  |   1 |   6 |   9.44457 | 0.283333 |   1 |   0 | 0.166667  |   6 | 0.0530973 | 0.00689655 | 0.108669    | 1           |
| CTNND2   |   1501 | N   | N   |   6 |   3678 |  14.4365  |   0 |   6 |  14.4365  | 0.231667 |   1 |   0 | 0.166667  |   6 | 0.0530973 | 0.0137931  | 0.108796    | 1           |
| FANCM    |  57697 | N   | N   |   8 |   6147 |  11.5172  |   1 |   7 |  10.0776  | 0.227143 |   1 |   0 | 0.142857  |   6 | 0.0530973 | 0.0206897  | 0.109918    | 1           |
| MLL3     |  58508 | Y   | Y   |   9 |  14907 |   5.34286 |   0 |   9 |   5.34286 | 0.23     |   0 |   0 | 0         |   7 | 0.0619469 | 0.0413793  | 0.158664    | 1           |
| SYNE1    |  23345 | N   | N   |  17 |  26394 |   5.69987 |   5 |  12 |   4.02344 | 0.196667 |   5 |   0 | 0.416667  |  11 | 0.0973451 | 0.248276   | 0.175553    | 1           |
| LRP2     |   4036 | N   | N   |  11 |  13968 |   6.96915 |   0 |  11 |   6.96915 | 0.281818 |   1 |   0 | 0.0909091 |  10 | 0.0884956 | 0.0827586  | 0.198617    | 1           |
| SLITRK3  |  22865 | N   | N   |  15 |   2934 |  45.2431  |   3 |  12 |  36.1945  | 0.16     |   0 |   0 | 0         |   6 | 0.0530973 | 0          | 0.236845    | 1           |
| FAT2     |   2196 | N   | N   |  11 |  13050 |   7.4594  |   3 |   8 |   5.42502 | 0.34375  |   4 |   0 | 0.5       |   7 | 0.0619469 | 0.0551724  | 0.240314    | 1           |
| LAMA5    |   3911 | N   | N   |   9 |  11088 |   7.18308 |   2 |   7 |   5.58684 | 0.252857 |   1 |   0 | 0.142857  |   6 | 0.0530973 | 0.0689655  | 0.262673    | 1           |
| CACNA1E  |    777 | N   | N   |   7 |   6942 |   8.9235  |   1 |   6 |   7.64871 | 0.296667 |   0 |   0 | 0         |   6 | 0.0530973 | 0.062069   | 0.308574    | 1           |
| LRP1B    |  53353 | N   | N   |  11 |  13800 |   7.054   |   1 |  10 |   6.41272 | 0.168    |   2 |   0 | 0.2       |  10 | 0.0884956 | 0.227586   | 0.334661    | 1           |
| DNAH17   |   8632 | N   | N   |   9 |  13458 |   5.91812 |   2 |   7 |   4.60298 | 0.317143 |   1 |   0 | 0.142857  |   7 | 0.0619469 | 0.00689655 | 0.354727    | 1           |
| ABCA13   | 154664 | N   | N   |   9 |  15177 |   5.24781 |   1 |   8 |   4.66472 | 0.23125  |   1 |   0 | 0.125     |   8 | 0.0707965 | 0.0827586  | 0.370012    | 1           |
| DNAH11   |   8701 | N   | N   |   7 |  13572 |   4.56432 |   1 |   6 |   3.91227 | 0.18     |   1 |   0 | 0.166667  |   6 | 0.0530973 | 0.0896552  | 0.381709    | 1           |
| PXDNL    | 137902 | N   | N   |  12 |   4392 |  24.1791  |   2 |  10 |  20.1493  | 0.239    |   1 |   0 | 0.1       |  10 | 0.0884956 | 0.0689655  | 0.397753    | 1           |
| XIRP2    | 129446 | N   | Y   |  10 |  10650 |   8.30944 |   0 |  10 |   8.30944 | 0.275    |   1 |   0 | 0.1       |  10 | 0.0884956 | 0.0965517  | 0.412098    | 1           |
| DNAH5    |   1767 | N   | N   |  11 |  13875 |   7.01587 |   2 |   9 |   5.74025 | 0.223333 |   1 |   0 | 0.111111  |   9 | 0.079646  | 0.0827586  | 0.42057     | 1           |
| NOTCH3   |   4854 | N   | N   |   7 |   6966 |   8.89275 |   0 |   7 |   8.89275 | 0.3      |   1 |   0 | 0.142857  |   7 | 0.0619469 | 0.0137931  | 0.421067    | 1           |
| CSMD1    |  64478 | N   | N   |  11 |  10698 |   9.09938 |   2 |   9 |   7.44494 | 0.235556 |   2 |   0 | 0.222222  |   9 | 0.079646  | 0.151724   | 0.435771    | 1           |
| USH2A    |   7399 | N   | N   |  14 |  15681 |   7.90089 |   3 |  11 |   6.20784 | 0.255455 |   1 |   0 | 0.0909091 |   9 | 0.079646  | 0.137931   | 0.594558    | 1           |
| DNAH9    |   1770 | N   | N   |   8 |  13461 |   5.25938 |   0 |   8 |   5.25938 | 0.25375  |   2 |   0 | 0.25      |   8 | 0.0707965 | 0.062069   | 0.60668     | 1           |
| PAPPA2   |  60676 | N   | N   |   9 |   5376 |  14.8151  |   3 |   6 |   9.87674 | 0.27     |   1 |   0 | 0.166667  |   6 | 0.0530973 | 0.0551724  | 0.637096    | 1           |
| APOB     |    338 | N   | N   |   9 |  13692 |   5.81697 |   3 |   6 |   3.87798 | 0.243333 |   0 |   0 | 0         |   6 | 0.0530973 | 0.131034   | 0.643202    | 1           |
| FAT3     | 120114 | N   | N   |  13 |  13770 |   8.3547  |   1 |  12 |   7.71203 | 0.225833 |   2 |   0 | 0.166667  |  12 | 0.106195  | 0.158621   | 0.783398    | 1           |
| NEB      |   4703 | N   | N   |  12 |  25578 |   4.1518  |   2 |  10 |   3.45983 | 0.187    |   4 |   0 | 0.4       |   9 | 0.079646  | 0.0482759  | 0.785486    | 1           |
| SI       |   6476 | N   | N   |  10 |   5484 |  16.137   |   0 |  10 |  16.137   | 0.291    |   1 |   0 | 0.1       |   9 | 0.079646  | 0.0551724  | 0.82379     | 1           |
| PKHD1L1  |  93035 | N   | N   |   8 |  12732 |   5.56051 |   0 |   8 |   5.56051 | 0.24375  |   1 |   0 | 0.125     |   8 | 0.0707965 | 0.0758621  | 0.828834    | 1           |
| RP1      |   6101 | N   | N   |   8 |   6471 |  10.9406  |   2 |   6 |   8.20543 | 0.215    |   0 |   0 | 0         |   6 | 0.0530973 | 0.0758621  | 0.86474     | 1           |
| TTN      |   7273 | N   | N   |  64 | 100272 |   5.64835 |  12 |  52 |   4.58929 | 0.221346 |   7 |   0 | 0.134615  |  40 | 0.353982  | 0.606897   | 0.868756    | 1           |
| EYS      | 346007 | N   | N   |   7 |   9498 |   6.5221  |   0 |   7 |   6.5221  | 0.224286 |   1 |   0 | 0.142857  |   7 | 0.0619469 | 0.0896552  | 0.898402    | 1           |
| MYH15    |  22989 | N   | N   |   8 |   5841 |  12.1206  |   0 |   8 |  12.1206  | 0.235    |   1 |   0 | 0.125     |   8 | 0.0707965 | 0          | 0.910926    | 1           |
| PKHD1    |   5314 | N   | N   |   8 |  12225 |   5.79112 |   1 |   7 |   5.06723 | 0.162857 |   0 |   0 | 0         |   7 | 0.0619469 | 0.0344828  | 0.916197    | 1           |
| NRXN1    |   9378 | N   | N   |   7 |   4647 |  13.3305  |   1 |   6 |  11.4262  | 0.223333 |   0 |   0 | 0         |   6 | 0.0530973 | 0.062069   | 0.938636    | 1           |
| RYR3     |   6263 | N   | N   |  10 |  14613 |   6.05595 |   2 |   8 |   4.84476 | 0.2175   |   0 |   0 | 0         |   8 | 0.0707965 | 0.103448   | 0.965186    | 1           |
| PCLO     |  27445 | N   | N   |  12 |  15429 |   6.8828  |   4 |   8 |   4.58853 | 0.18875  |   1 |   0 | 0.125     |   7 | 0.0619469 | 0.206897   | 0.99176     | 1           |
| MUC16    |  94025 | N   | N   |  18 |  43524 |   3.65987 |   6 |  12 |   2.43991 | 0.27     |   1 |   0 | 0.0833333 |  12 | 0.106195  | 0.282759   | 0.992898    | 1           |



labeled_formulas: M=(E-H)-I
H=(E-I)*S
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_357289___xlsx_948fb40adfd54c7d46ccc057b14b67227e7d5624.xlsx___line_458