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                                                                                                                                                                                                                                   |
|:-----------|:---------|:--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-----:|-------:|----:|-------:|----------:|:----|-----------:|:------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| GO:0019902 | 5        | phosphatase binding                                                                                                                                                                               |    5 | 0.0005 |   1 | 0.0156 | 0.0286386 | E   |  31.2      | CG9238                                                                                                                                                                                                                              |
| GO:0008599 | 5        | protein phosphatase type 1 regulator activity                                                                                                                                                     |    6 | 0.0005 |   1 | 0.0156 | 0.0341679 | E   |  31.2      | CG9238                                                                                                                                                                                                                              |
| GO:0000049 | 5        | tRNA binding                                                                                                                                                                                      |    7 | 0.0006 |   1 | 0.0156 | 0.0396324 | E   |  26        | Su(var)3-9                                                                                                                                                                                                                          |
| GO:0008188 | 5,6,7,8  | neuropeptide receptor activity                                                                                                                                                                    |   45 | 0.0041 |   2 | 0.0312 | 0.026202  | E   |   7.60976  | Fsh,GRHR                                                                                                                                                                                                                            |
| GO:0008528 | 5,6,7    | peptide receptor activity, G-protein coupled                                                                                                                                                      |   47 | 0.0043 |   2 | 0.0312 | 0.0282851 | E   |   7.25581  | Fsh,GRHR                                                                                                                                                                                                                            |
| GO:0001653 | 4,5      | peptide receptor activity                                                                                                                                                                         |   47 | 0.0043 |   2 | 0.0312 | 0.0282851 | E   |   7.25581  | Fsh,GRHR                                                                                                                                                                                                                            |
| GO:0003743 | 5,4      | translation initiation factor activity                                                                                                                                                            |   58 | 0.0053 |   2 | 0.0312 | 0.0406133 | E   |   5.88679  | Su(var)3-9,eIF-1A                                                                                                                                                                                                                   |
| GO:0003712 | 5,3      | transcription cofactor activity                                                                                                                                                                   |   66 | 0.006  |   2 | 0.0312 | 0.0503413 | E   |   5.2      | ftz-f1,Rpd3                                                                                                                                                                                                                         |
| GO:0031625 | 5        | ubiquitin protein ligase binding                                                                                                                                                                  |    9 | 0.0008 |   1 | 0.0156 | 0.0503692 | E   |  19.5      | cul-4                                                                                                                                                                                                                               |
| GO:0016715 | 5        | oxidoreductase activity, acting on paired donors, with incorporation or reduction of molecular oxygen, reduced ascorbate as one donor, and incorporation of one atom of oxygen                    |   10 | 0.0009 |   1 | 0.0156 | 0.0556426 | E   |  17.3333   | Tbh                                                                                                                                                                                                                                 |
| GO:0033558 | 5        | protein deacetylase activity                                                                                                                                                                      |   11 | 0.001  |   1 | 0.0156 | 0.0608533 | E   |  15.6      | Rpd3                                                                                                                                                                                                                                |
| GO:0030594 | 4,5      | neurotransmitter receptor activity                                                                                                                                                                |   75 | 0.0069 |   2 | 0.0312 | 0.0618524 | E   |   4.52174  | Fsh,GRHR                                                                                                                                                                                                                            |
| GO:0016884 | 5        | carbon-nitrogen ligase activity, with glutamine as amido-N-donor                                                                                                                                  |   13 | 0.0012 |   1 | 0.0156 | 0.0710891 | E   |  13        | CG9940                                                                                                                                                                                                                              |
| GO:0016779 | 5        | nucleotidyltransferase activity                                                                                                                                                                   |   82 | 0.0075 |   2 | 0.0312 | 0.071109  | E   |   4.16     | tam,Pect                                                                                                                                                                                                                            |
| GO:0016616 | 5        | oxidoreductase activity, acting on the CH-OH group of donors, NAD or NADP as acceptor                                                                                                             |   82 | 0.0075 |   2 | 0.0312 | 0.071109  | E   |   4.16     | Es2,antdh                                                                                                                                                                                                                           |
| GO:0008135 | 4,3      | translation factor activity, nucleic acid binding                                                                                                                                                 |   89 | 0.0082 |   2 | 0.0312 | 0.080547  | E   |   3.80488  | Su(var)3-9,eIF-1A                                                                                                                                                                                                                   |
| GO:0016538 | 5        | cyclin-dependent protein kinase regulator activity                                                                                                                                                |   18 | 0.0016 |   1 | 0.0156 | 0.09562   | E   |   9.75     | CG16903                                                                                                                                                                                                                             |
| GO:0017022 | 5        | myosin binding                                                                                                                                                                                    |   21 | 0.0019 |   1 | 0.0156 | 0.109633  | E   |   8.21053  | Cam                                                                                                                                                                                                                                 |
| GO:0004879 | 5        | ligand-dependent nuclear receptor activity                                                                                                                                                        |   23 | 0.0021 |   1 | 0.0156 | 0.11869   | E   |   7.42857  | ftz-f1                                                                                                                                                                                                                              |
| GO:0046982 | 5        | protein heterodimerization activity                                                                                                                                                               |   33 | 0.003  |   1 | 0.0156 | 0.160696  | E   |   5.2      | CG6272                                                                                                                                                                                                                              |
| GO:0008320 | 4,5      | protein transmembrane transporter activity                                                                                                                                                        |   35 | 0.0032 |   1 | 0.0156 | 0.168468  | E   |   4.875    | Ntf-2                                                                                                                                                                                                                               |
| GO:0016655 | 5        | oxidoreductase activity, acting on NADH or NADPH, quinone or similar compound as acceptor                                                                                                         |   36 | 0.0033 |   1 | 0.0156 | 0.172278  | E   |   4.72727  | CG3214                                                                                                                                                                                                                              |
| GO:0016706 | 5        | oxidoreductase activity, acting on paired donors, with incorporation or reduction of molecular oxygen, 2-oxoglutarate as one donor, and incorporation of one atom each of oxygen into both donors |   38 | 0.0035 |   1 | 0.0156 | 0.179749  | E   |   4.45714  | CG31915                                                                                                                                                                                                                             |
| GO:0004702 | 8,5      | receptor signaling protein serine/threonine kinase activity                                                                                                                                       |   41 | 0.0038 |   1 | 0.0156 | 0.19059   | E   |   4.10526  | put                                                                                                                                                                                                                                 |
| GO:0003954 | 5        | NADH dehydrogenase activity                                                                                                                                                                       |   43 | 0.0039 |   1 | 0.0156 | 0.197578  | E   |   4        | CG3214                                                                                                                                                                                                                              |
| GO:0005099 | 5,6      | Ras GTPase activator activity                                                                                                                                                                     |   44 | 0.004  |   1 | 0.0156 | 0.201002  | E   |   3.9      | RN-tre                                                                                                                                                                                                                              |
| GO:0016836 | 5        | hydro-lyase activity                                                                                                                                                                              |   47 | 0.0043 |   1 | 0.0156 | 0.210996  | E   |   3.62791  | CAH2                                                                                                                                                                                                                                |
| GO:0016811 | 5        | hydrolase activity, acting on carbon-nitrogen (but not peptide) bonds, in linear amides                                                                                                           |   61 | 0.0056 |   1 | 0.0156 | 0.252433  | E   |   2.78571  | Rpd3                                                                                                                                                                                                                                |
| GO:0005085 | 5        | guanyl-nucleotide exchange factor activity                                                                                                                                                        |   61 | 0.0056 |   1 | 0.0156 | 0.252433  | E   |   2.78571  | sec71                                                                                                                                                                                                                               |
| GO:0005096 | 4,5      | GTPase activator activity                                                                                                                                                                         |   69 | 0.0063 |   1 | 0.0156 | 0.272546  | E   |   2.47619  | RN-tre                                                                                                                                                                                                                              |
| GO:0004518 | 5        | nuclease activity                                                                                                                                                                                 |   92 | 0.0084 |   1 | 0.0156 | 0.317794  | E   |   1.85714  | tam                                                                                                                                                                                                                                 |
| GO:0016810 | 4        | hydrolase activity, acting on carbon-nitrogen (but not peptide) bonds                                                                                                                             |   98 | 0.009  |   1 | 0.0156 | 0.326868  | E   |   1.73333  | Rpd3                                                                                                                                                                                                                                |
| GO:0008262 | 5        | importin-alpha export receptor activity                                                                                                                                                           |    1 | 0.0001 |   1 | 0.0156 | 0.0058619 | E   | 156        | Cas                                                                                                                                                                                                                                 |
| GO:0048185 | 5        | activin binding                                                                                                                                                                                   |    2 | 0.0002 |   1 | 0.0156 | 0.0116561 | E   |  78        | put                                                                                                                                                                                                                                 |
| GO:0016298 | 5        | lipase activity                                                                                                                                                                                   |  100 | 0.0092 |   1 | 0.0156 | 0.329666  | E   |   1.69565  | bmm                                                                                                                                                                                                                                 |
| GO:0005083 | 5        | small GTPase regulator activity                                                                                                                                                                   |  106 | 0.0097 |   2 | 0.0312 | 0.103812  | E   |   3.21649  | sec71,RN-tre                                                                                                                                                                                                                        |
| GO:0016881 | 5        | acid-amino acid ligase activity                                                                                                                                                                   |  110 | 0.0101 |   2 | 0.0312 | 0.10929   | E   |   3.08911  | poe,cul-4                                                                                                                                                                                                                           |
| GO:0008168 | 5        | methyltransferase activity                                                                                                                                                                        |  111 | 0.0102 |   2 | 0.0312 | 0.110657  | E   |   3.05882  | Su(var)3-9,Rpd3                                                                                                                                                                                                                     |
| GO:0016747 | 5        | transferase activity, transferring acyl groups other than amino-acyl groups                                                                                                                       |  115 | 0.0105 |   1 | 0.0156 | 0.347295  | E   |   1.48571  | mdy                                                                                                                                                                                                                                 |
| GO:0004091 | 5        | carboxylesterase activity                                                                                                                                                                         |  119 | 0.0109 |   1 | 0.0156 | 0.351064  | E   |   1.43119  | bmm                                                                                                                                                                                                                                 |
| GO:0042626 | 6,11,7,5 | ATPase activity, coupled to transmembrane movement of substances                                                                                                                                  |  138 | 0.0126 |   2 | 0.0312 | 0.146661  | E   |   2.47619  | Vha16,Ca-P60A                                                                                                                                                                                                                       |
| GO:0016758 | 5        | transferase activity, transferring hexosyl groups                                                                                                                                                 |  142 | 0.013  |   2 | 0.0312 | 0.151776  | E   |   2.4      | CG10166,CG14512                                                                                                                                                                                                                     |
| GO:0016820 | 5,4      | hydrolase activity, acting on acid anhydrides, catalyzing transmembrane movement of substances                                                                                                    |  149 | 0.0136 |   2 | 0.0312 | 0.160545  | E   |   2.29412  | Vha16,Ca-P60A                                                                                                                                                                                                                       |
| GO:0015399 | 5        | primary active transmembrane transporter activity                                                                                                                                                 |  162 | 0.0148 |   2 | 0.0312 | 0.176146  | E   |   2.10811  | Vha16,Ca-P60A                                                                                                                                                                                                                       |
| GO:0019001 | 5        | guanyl nucleotide binding                                                                                                                                                                         |  177 | 0.0162 |   3 | 0.0469 | 0.0653237 | E   |   2.89506  | Su(var)3-9,Arf79F,Galpha49B                                                                                                                                                                                                         |
| GO:0003729 | 5        | mRNA binding                                                                                                                                                                                      |  196 | 0.018  |   3 | 0.0469 | 0.0797267 | E   |   2.60556  | CG6937,Rm62,how                                                                                                                                                                                                                     |
| GO:0015267 | 5        | channel activity                                                                                                                                                                                  |  197 | 0.018  |   2 | 0.0312 | 0.212933  | E   |   1.73333  | Stim,olf186-F                                                                                                                                                                                                                       |
| GO:0043565 | 5        | sequence-specific DNA binding                                                                                                                                                                     |  237 | 0.0217 |   5 | 0.0781 | 0.009888  | E   |   3.59908  | ftz-f1,CG6272,CSN4,Eip74EF,Rx                                                                                                                                                                                                       |
| GO:0008236 | 6,5      | serine-type peptidase activity                                                                                                                                                                    |  319 | 0.0292 |   2 | 0.0312 | 0.274592  | E   |   1.06849  | olf186-F,CG10882                                                                                                                                                                                                                    |
| GO:0016773 | 5        | phosphotransferase activity, alcohol group as acceptor                                                                                                                                            |  379 | 0.0347 |   1 | 0.0156 | 0.239736  | D   |   0.449568 | put                                                                                                                                                                                                                                 |
| GO:0004888 | 5        | transmembrane receptor activity                                                                                                                                                                   |  393 | 0.036  |   3 | 0.0469 | 0.208304  | E   |   1.30278  | put,Fsh,GRHR                                                                                                                                                                                                                        |
| GO:0003700 | 5,3      | transcription factor activity                                                                                                                                                                     |  402 | 0.0368 |   4 | 0.0625 | 0.123147  | E   |   1.69837  | ftz-f1,CG6272,Eip74EF,Rx                                                                                                                                                                                                            |
| GO:0016301 | 5        | kinase activity                                                                                                                                                                                   |  407 | 0.0373 |   1 | 0.0156 | 0.217613  | D   |   0.418231 | put                                                                                                                                                                                                                                 |
| GO:0004872 | 4        | receptor activity                                                                                                                                                                                 |  470 | 0.043  |   4 | 0.0625 | 0.156074  | E   |   1.45349  | put,Fsh,ftz-f1,GRHR                                                                                                                                                                                                                 |
| GO:0015075 | 5        | ion transmembrane transporter activity                                                                                                                                                            |  507 | 0.0464 |   4 | 0.0625 | 0.170872  | E   |   1.34698  | Stim,olf186-F,Vha16,Ca-P60A                                                                                                                                                                                                         |
| GO:0003723 | 4        | RNA binding                                                                                                                                                                                       |  577 | 0.0528 |   4 | 0.0625 | 0.191282  | E   |   1.18371  | CG6937,Su(var)3-9,Rm62,how                                                                                                                                                                                                          |
| GO:0016818 | 5        | hydrolase activity, acting on acid anhydrides, in phosphorus-containing anhydrides                                                                                                                |  594 | 0.0544 |   7 | 0.1094 | 0.0359421 | E   |   2.01103  | Su(var)3-9,Vha16,Arf79F,Rm62,Ca-P60A,Ggamma1,Galpha49B                                                                                                                                                                              |
| GO:0004871 | 3        | signal transducer activity                                                                                                                                                                        |  602 | 0.0551 |   5 | 0.0781 | 0.137136  | E   |   1.41742  | put,Fsh,ftz-f1,CG8444,GRHR                                                                                                                                                                                                          |
| GO:0070011 | 5        | peptidase activity, acting on L-amino acid peptides                                                                                                                                               |  645 | 0.0591 |   7 | 0.1094 | 0.0483408 | E   |   1.8511   | Rpn7,olf186-F,ProsMA5,CG10882,Prosbeta3,Rpn6,Mov34                                                                                                                                                                                  |
| GO:0030528 | 2        | transcription regulator activity                                                                                                                                                                  |  685 | 0.0627 |   8 | 0.125  | 0.0280295 | E   |   1.99362  | bip2,CG16903,put,ftz-f1,CG6272,Rpd3,Eip74EF,Rx                                                                                                                                                                                      |
| GO:0022857 | 3        | transmembrane transporter activity                                                                                                                                                                |  730 | 0.0669 |   5 | 0.0781 | 0.172276  | E   |   1.16741  | Stim,Ntf-2,olf186-F,Vha16,Ca-P60A                                                                                                                                                                                                   |
| GO:0030554 | 5        | adenyl nucleotide binding                                                                                                                                                                         |  801 | 0.0734 |   4 | 0.0625 | 0.190751  | D   |   0.851499 | put,Rm62,Ca-P60A,CG9940                                                                                                                                                                                                             |
| GO:0032555 | 5        | purine ribonucleotide binding                                                                                                                                                                     |  893 | 0.0818 |   7 | 0.1094 | 0.117678  | E   |   1.33741  | put,Su(var)3-9,Arf79F,Rm62,Ca-P60A,CG9940,Galpha49B                                                                                                                                                                                 |
| GO:0003677 | 4        | DNA binding                                                                                                                                                                                       |  951 | 0.0871 |   4 | 0.0625 | 0.15445   | D   |   0.717566 | CG6272,CSN4,Eip74EF,Rx                                                                                                                                                                                                              |
| GO:0000166 | 3        | nucleotide binding                                                                                                                                                                                | 1136 | 0.104  |   7 | 0.1094 | 0.156826  | E   |   1.05192  | put,Su(var)3-9,Arf79F,Rm62,Ca-P60A,CG9940,Galpha49B                                                                                                                                                                                 |
| GO:0046872 | 5        | metal ion binding                                                                                                                                                                                 | 1434 | 0.1313 |  10 | 0.1562 | 0.115678  | E   |   1.18964  | bip2,Su(var)3-9,ftz-f1,Cam,Tbh,poe,CG10882,CG7379,CG1845,Lasp                                                                                                                                                                       |
| GO:0005515 | 3        | protein binding                                                                                                                                                                                   | 1758 | 0.161  |  11 | 0.1719 | 0.127974  | E   |   1.0677   | put,Cas,Ntf-2,ftz-f1,CG9238,Cam,CG6272,poe,Ykt6,CG7770,cul-4                                                                                                                                                                        |
| GO:0003676 | 3        | nucleic acid binding                                                                                                                                                                              | 1883 | 0.1725 |  10 | 0.1562 | 0.128479  | D   |   0.905507 | Su(var)3-9,ftz-f1,CG6272,mask,CSN4,eIF-1A,Eip74EF,how,tam,Rx                                                                                                                                                                        |
| GO:0005488 | 2        | binding                                                                                                                                                                                           | 5698 | 0.5219 |  38 | 0.5938 | 0.0518287 | E   |   1.13777  | bip2,CG6937,put,Fsh,Cas,Su(var)3-9,Ntf-2,ftz-f1,CG34413,CG9238,Cam,CG6272,mask,CSN4,Tbh,Arf79F,poe,Rpd3,CG10882,eIF-1A,Ykt6,Rm62,CG7770,cul-4,GRHR,Eip74EF,spen,how,tam,CG7379,Ca-P60A,CG1845,Rx,Lasp,Fbw5,CG9940,Galpha49B,CG14512 |



label: J=G/E
labeled_formulas: J=G/E
output: {"Arithmetic-Relationship": ["J=G/E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_468743___xlsx_d95dd123a5a3d2dda61c5b5efc7239d5298f484d.xlsx___line_643