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 |
|:-----------|-------------:|--------:|----------:|
| PHLDA1     |  2.01575     | 1.4318  |  0.583949 |
| ZBED2      |  2.31542     | 1.912   |  0.403414 |
| IL12RB2    |  2.18105     | 2.03732 |  0.143726 |
| CSF1       |  2.13903     | 2.37553 | -0.236498 |
| TNFRSF1B   |  2.2557      | 2.49289 | -0.237188 |
| BATF       |  2.0796      | 2.44912 | -0.369523 |
| LTA        |  1.88251     | 2.27142 | -0.388906 |
| CTLA4      |  2.96985     | 3.39858 | -0.428731 |
| PELI1      |  1.61169     | 2.0786  | -0.466911 |
| PTP4A3     |  1.64811     | 2.12229 | -0.474173 |
| CRADD      |  1.68167     | 2.27872 | -0.597052 |
| CDK14      |  1.91137     | 2.55401 | -0.64264  |
| RBBP8      |  1.49362     | 2.14216 | -0.64854  |
| GBP2       |  1.51436     | 2.21177 | -0.697418 |
| NAMPT      |  1.7197      | 2.43764 | -0.71794  |
| BTG3       |  1.34067     | 2.07322 | -0.732548 |
| TRIB1      |  1.65319     | 2.40396 | -0.750772 |
| TNS3       |  1.84826     | 2.64396 | -0.795698 |
| DNPH1      |  1.6838      | 2.48246 | -0.798656 |
| ICA1       |  2.25188     | 3.05451 | -0.802635 |
| TBC1D4     |  2.50095     | 3.31305 | -0.812104 |
| FAM174B    |  1.61345     | 2.4318  | -0.818351 |
| GADD45A    |  2.71573     | 3.55044 | -0.834705 |
| CARD16     |  1.45129     | 2.31021 | -0.858915 |
| IKZF2      |  3.06767     | 3.95379 | -0.886113 |
| DUSP4      |  1.94055     | 2.83187 | -0.891321 |
| TNIP3      |  1.96021     | 2.88867 | -0.928461 |
| CD200      |  1.19846     | 2.14783 | -0.94937  |
| IL2RB      |  1.30394     | 2.26127 | -0.957325 |
| TNFRSF4    |  3.02414     | 3.99244 | -0.968295 |
| F5         |  2.51156     | 3.49314 | -0.981581 |
| ETV7       |  1.40297     | 2.39948 | -0.996509 |
| PIM2       |  1.70131     | 2.70941 | -1.0081   |
| ADPRH      |  1.73672     | 2.77378 | -1.03706  |
| PTTG1      |  1.31402     | 2.35564 | -1.04163  |
| NAB1       |  1.16078     | 2.21075 | -1.04997  |
| CUL9       |  0.951402    | 2.01189 | -1.06049  |
| CEP55      |  1.51198     | 2.57288 | -1.0609   |
| CD79B      |  1.50724     | 2.57123 | -1.064    |
| CD7        |  0.947756    | 2.01575 | -1.06799  |
| STAM       |  1.80815     | 2.88229 | -1.07414  |
| KCNN4      |  1.12108     | 2.21775 | -1.09666  |
| CD276      |  0.898445    | 2.00287 | -1.10443  |
| CDC45      |  0.904117    | 2.03114 | -1.12702  |
| VDR        |  2.56598     | 3.70403 | -1.13805  |
| PIP5K1B    |  0.853626    | 2.00329 | -1.14967  |
| ZC2HC1A    |  1.11496     | 2.26791 | -1.15295  |
| LAPTM4B    |  2.55099     | 3.70875 | -1.15776  |
| NR4A3      |  1.00516     | 2.1762  | -1.17104  |
| ASB2       |  1.85853     | 3.05435 | -1.19582  |
| AKIP1      |  0.822199    | 2.01936 | -1.19717  |
| ICOS       |  1.81662     | 3.01836 | -1.20174  |
| ST6GALNAC4 |  0.786675    | 2.01469 | -1.22802  |
| SLC41A2    |  1.06514     | 2.29479 | -1.22965  |
| NINJ1      |  1.07595     | 2.31388 | -1.23793  |
| SOX4       |  1.85706     | 3.12286 | -1.2658   |
| GCNT1      |  1.44635     | 2.73273 | -1.28638  |
| HPGD       |  1.34031     | 2.62738 | -1.28707  |
| IL21R      |  1.29931     | 2.58704 | -1.28773  |
| CD70       |  1.50706     | 2.80199 | -1.29493  |
| OTUD5      |  0.693065    | 2.00714 | -1.31408  |
| SIRPG      |  1.3237      | 2.66624 | -1.34254  |
| CARD17     |  0.797156    | 2.14081 | -1.34366  |
| TNFRSF18   |  2.83625     | 4.18425 | -1.348    |
| FAM110A    |  1.11923     | 2.46726 | -1.34803  |
| SSTR3      |  0.785117    | 2.14642 | -1.3613   |
| FOXP3      |  3.98341     | 5.35933 | -1.37592  |
| CPM        |  0.79054     | 2.19028 | -1.39974  |
| SDC4       |  2.11566     | 3.53213 | -1.41647  |
| TMEM169    |  0.589998    | 2.0208  | -1.43081  |
| AKAP5      |  1.38999     | 2.83311 | -1.44311  |
| INPP5F     |  1.43304     | 2.88315 | -1.45011  |
| SEMA4A     |  0.74566     | 2.2073  | -1.46164  |
| INPP1      |  0.954892    | 2.41685 | -1.46196  |
| HAPLN3     |  0.599916    | 2.06496 | -1.46504  |
| ADAT2      |  0.839765    | 2.31434 | -1.47457  |
| METTL7A    |  1.75516     | 3.24054 | -1.48538  |
| SAT1       |  1.08351     | 2.58924 | -1.50573  |
| FAIM2      |  0.684043    | 2.19078 | -1.50673  |
| ADTRP      |  0.99481     | 2.50659 | -1.51178  |
| SGPP2      |  1.13975     | 2.65898 | -1.51923  |
| MYO5C      |  1.31357     | 2.86829 | -1.55473  |
| WLS        |  0.699889    | 2.25872 | -1.55883  |
| EGR3       |  0.798502    | 2.3675  | -1.56899  |
| FHL3       |  0.895852    | 2.4654  | -1.56955  |
| C16orf45   |  1.2846      | 2.85441 | -1.56982  |
| SELP       |  1.2066      | 2.78335 | -1.57675  |
| IL2RA      |  3.38717     | 4.96613 | -1.57896  |
| PVALB      |  0.669149    | 2.25948 | -1.59033  |
| CTTNBP2NL  |  1.5327      | 3.1354  | -1.6027   |
| PIK3R3     |  0.856664    | 2.50121 | -1.64455  |
| CD40       |  0.764046    | 2.418   | -1.65395  |
| SIRPB1     |  0.471834    | 2.13633 | -1.66449  |
| FLVCR2     |  1.14381     | 2.80917 | -1.66535  |
| PLAGL1     |  0.490468    | 2.1577  | -1.66723  |
| CHST2      |  1.13686     | 2.81057 | -1.67371  |
| MZB1       |  1.02345     | 2.71176 | -1.68831  |
| TMPRSS3    |  0.57442     | 2.26524 | -1.69082  |
| SLC43A3    |  0.677224    | 2.37236 | -1.69514  |
| LAT2       |  0.602307    | 2.31032 | -1.70802  |
| XKRX       |  0.316719    | 2.02911 | -1.71239  |
| TSPAN13    |  1.80836     | 3.52076 | -1.7124   |
| VAV3       |  0.916192    | 2.63209 | -1.71589  |
| RBKS       |  0.492129    | 2.20887 | -1.71674  |
| PLA2G4C    |  0.50696     | 2.23474 | -1.72778  |
| ACP5       |  1.10607     | 2.83498 | -1.7289   |
| ENTPD1     |  2.42112     | 4.17309 | -1.75197  |
| IKZF4      |  1.7972      | 3.56076 | -1.76356  |
| DNAH8      |  0.245327    | 2.03438 | -1.78906  |
| XIRP1      |  0.47871     | 2.29182 | -1.81311  |
| FAM78B     |  0.34826     | 2.20493 | -1.85667  |
| GRIK1-AS2  |  0.666735    | 2.534   | -1.86726  |
| DENND6B    |  0.608539    | 2.4937  | -1.88516  |
| LGMN       |  0.88869     | 2.78115 | -1.89246  |
| CD83       |  0.74209     | 2.63972 | -1.89763  |
| ACTG2      |  2.29543     | 4.1954  | -1.89998  |
| COL9A2     |  1.22505     | 3.1293  | -1.90425  |
| MAP1LC3A   |  1.01674     | 2.94083 | -1.92409  |
| MAGEH1     |  1.7051      | 3.63172 | -1.92662  |
| TSPAN33    |  0.799104    | 2.72781 | -1.9287   |
| RTKN2      |  2.45084     | 4.39417 | -1.94332  |
| TSHR       |  0.409563    | 2.36023 | -1.95067  |
| LRRC32     |  1.70346     | 3.65804 | -1.95458  |
| ID3        |  1.04218     | 3.00932 | -1.96714  |
| TNFRSF8    |  2.64243     | 4.62568 | -1.98325  |
| CLNK       |  1.24362     | 3.23413 | -1.9905   |
| LGALS17A   |  0.123311    | 2.12609 | -2.00278  |
| IL7        |  0.444545    | 2.45288 | -2.00833  |
| LRG1       |  1.15908     | 3.19243 | -2.03335  |
| CD68       |  0.143603    | 2.18314 | -2.03954  |
| AKR1C3     |  0.0521771   | 2.09623 | -2.04406  |
| CCDC141    |  0.781938    | 2.84963 | -2.0677   |
| HIST1H2BF  |  0.243697    | 2.32305 | -2.07935  |
| SH3RF2     |  0.289151    | 2.37246 | -2.08331  |
| CPXM1      |  0.187333    | 2.30099 | -2.11366  |
| ADAM28     |  0.154468    | 2.28496 | -2.1305   |
| GTSF1L     |  0.624872    | 2.76762 | -2.14275  |
| TTC7B      |  0.401332    | 2.5452  | -2.14387  |
| PDGFA      |  1.70635     | 3.8519  | -2.14556  |
| NR4A1      |  0.932394    | 3.08561 | -2.15322  |
| LINC00884  |  0.735522    | 2.89754 | -2.16202  |
| SEC14L6    |  0.398293    | 2.56255 | -2.16426  |
| CPNE2      |  0.499462    | 2.66967 | -2.17021  |
| SLCO4A1    |  1.0311      | 3.20425 | -2.17315  |
| TNFRSF11A  | -0.105889    | 2.15442 | -2.26031  |
| CYP7B1     |  0.75424     | 3.03112 | -2.27688  |
| CD80       |  1.26338     | 3.54327 | -2.27989  |
| MYO1E      |  0.528132    | 2.81456 | -2.28643  |
| RASAL1     |  0.501955    | 2.78926 | -2.2873   |
| HMOX1      |  0.64474     | 2.95748 | -2.31274  |
| MGST2      |  0.75        | 3.06314 | -2.31314  |
| TIGIT      |  2.47642     | 4.79933 | -2.3229   |
| VAV3-AS1   |  0.0326739   | 2.35852 | -2.32585  |
| NIPAL4     | -0.00350399  | 2.33747 | -2.34097  |
| SECTM1     | -0.222349    | 2.13117 | -2.35351  |
| CLEC7A     |  1.41421     | 3.80264 | -2.38843  |
| CPE        |  0.556972    | 2.94633 | -2.38936  |
| IL1RL1     |  0.216442    | 2.64237 | -2.42593  |
| IL1R1      |  2.33044     | 4.7692  | -2.43876  |
| PM20D1     | -0.250792    | 2.18866 | -2.43945  |
| HAVCR1     | -0.0286349   | 2.42408 | -2.45271  |
| LCN10      |  0.180817    | 2.65999 | -2.47917  |
| SERPINE2   |  1.25752     | 3.7656  | -2.50808  |
| LAIR2      |  2.30672     | 4.81802 | -2.51131  |
| TMPRSS6    |  0.445651    | 2.99691 | -2.55126  |
| LMCD1      |  1.08439     | 3.6659  | -2.58151  |
| SPATC1     |  0.173812    | 2.76788 | -2.59407  |
| GEM        |  1.17943     | 3.80116 | -2.62173  |
| TBC1D8     |  1.09484     | 3.73683 | -2.642    |
| SAMSN1-AS1 |  0.187333    | 2.83043 | -2.6431   |
| DIRAS3     |  0.710331    | 3.38353 | -2.6732   |
| XXYLT1-AS2 |  0.325255    | 3.01379 | -2.68853  |
| LINC00589  |  0.472312    | 3.16698 | -2.69466  |
| NCR1       | -0.352716    | 2.39759 | -2.75031  |
| FCRL3      |  1.84846     | 4.59953 | -2.75107  |
| FCER1G     | -0.635128    | 2.1195  | -2.75463  |
| ENTPD1-AS1 |  0.000211909 | 2.7881  | -2.78789  |
| HAVCR2     |  0.213677    | 3.02131 | -2.80763  |
| MMP9       | -0.0830889   | 2.73862 | -2.82171  |
| CADM1      |  1.63933     | 4.46734 | -2.82801  |
| SELL       | -0.436327    | 2.39943 | -2.83576  |
| MARCH3     |  0.326129    | 3.17823 | -2.8521   |
| CCL22      |  1.85546     | 4.74761 | -2.89214  |
| SIGLEC12   |  0.187333    | 3.08834 | -2.90101  |
| CD27       |  0.994705    | 3.97886 | -2.98416  |
| LAYN       |  2.88932     | 5.87696 | -2.98764  |
| FANK1      |  1.91341     | 4.93766 | -3.02425  |
| ATP1A4     |  0.187333    | 3.21226 | -3.02493  |
| CD27-AS1   |  0.108012    | 3.23313 | -3.12512  |
| CX3CR1     | -0.220352    | 2.95323 | -3.17358  |
| PTGIR      |  1.15416     | 4.43323 | -3.27907  |
| AHSP       | -0.0633299   | 3.2658  | -3.32913  |
| STAC       |  0.365452    | 3.7243  | -3.35885  |
| ZBTB32     |  1.64402     | 5.02614 | -3.38212  |
| TNFRSF13B  |  1.03013     | 4.42846 | -3.39834  |
| ZG16B      |  0.205634    | 3.61804 | -3.41241  |
| IL1RN      | -0.202902    | 3.23735 | -3.44025  |
| CHRNA6     |  0.353173    | 3.86514 | -3.51196  |
| CSF2RB     |  0.141774    | 3.66172 | -3.51994  |
| EBI3       |  1.83812     | 5.38443 | -3.54631  |
| CD79A      |  0.9364      | 4.62618 | -3.68977  |
| GNG8       |  1.12389     | 5.2281  | -4.10421  |
| CCR8       |  1.76111     | 5.92002 | -4.1589   |
| TNFRSF9    |  2.56955     | 6.7728  | -4.20325  |
| IL1R2      |  2.54565     | 7.16722 | -4.62157  |
| CD177      |  1.9378      | 6.95821 | -5.02041  |



label: D=B-C
labeled_formulas: D=B-C
output: {"Arithmetic-Relationship": ["D=B-C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_733989___xlsx_dfdb7c9623f87e05f961352e9560b1d1033cfbda.xlsx___line_628