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 |
|-----:|-----------:|-----------:|------------:|-----------:|----------:|------------:|----------:|-----------:|
| 1    | 0.00841471 | 0.00841471 | -0.00841471 | 0          | 0.0168294 | 0           | 0         | 0          |
| 1.01 | 0.008553   | 0.0169677  | -0.00848386 | 0.00848386 | 0.017106  | 0.000138292 | 0.0112657 | 0.00848384 |
| 1.02 | 0.0086915  | 0.0256592  | -0.00855311 | 0.0171061  | 0.0342124 | 0.0171062   | 0.0171061 | 0.0171061  |
| 1.03 | 0.00883018 | 0.0344894  | -0.00862244 | 0.0258669  | 0.0347664 | 0.0175215   | 0.0286488 | 0.0258669  |
| 1.04 | 0.008969   | 0.0434584  | -0.00869186 | 0.0347665  | 0.0521504 | 0.0347667   | 0.0347665 | 0.0347665  |
| 1.05 | 0.00910794 | 0.0525663  | -0.00876133 | 0.043805   | 0.0529823 | 0.0354596   | 0.0465868 | 0.0438049  |
| 1.06 | 0.00924697 | 0.0618133  | -0.00883084 | 0.0529825  | 0.0706444 | 0.0529827   | 0.0529824 | 0.0529824  |
| 1.07 | 0.00938605 | 0.0711994  | -0.00890038 | 0.062299   | 0.0717543 | 0.0539536   | 0.0650808 | 0.0622989  |
| 1.08 | 0.00952514 | 0.0807245  | -0.00896993 | 0.0717546  | 0.0896947 | 0.0717548   | 0.0717545 | 0.0717545  |
| 1.09 | 0.00966423 | 0.0903887  | -0.00903947 | 0.0813493  | 0.0910828 | 0.0730039   | 0.0841311 | 0.0813492  |
| 1.1  | 0.00980328 | 0.100192   | -0.009109   | 0.091083   | 0.109301  | 0.0910832   | 0.0910829 | 0.0910829  |
| 1.11 | 0.00994226 | 0.110134   | -0.00917848 | 0.100956   | 0.110967  | 0.0926104   | 0.103738  | 0.100956   |
| 1.12 | 0.0100811  | 0.120215   | -0.00924792 | 0.110967   | 0.129463  | 0.110968    | 0.110967  | 0.110967   |
| 1.13 | 0.0102199  | 0.130435   | -0.00931728 | 0.121118   | 0.131407  | 0.112772    | 0.1239    | 0.121118   |
| 1.14 | 0.0103584  | 0.140794   | -0.00938657 | 0.131407   | 0.15018   | 0.131407    | 0.131407  | 0.131407   |
| 1.15 | 0.0104968  | 0.15129    | -0.00945575 | 0.141835   | 0.152401  | 0.133489    | 0.144617  | 0.141835   |
| 1.16 | 0.0106349  | 0.161925   | -0.00952481 | 0.152401   | 0.17145   | 0.152401    | 0.152401  | 0.152401   |
| 1.17 | 0.0107728  | 0.172698   | -0.00959375 | 0.163104   | 0.173946  | 0.154759    | 0.165886  | 0.163104   |
| 1.18 | 0.0109104  | 0.183609   | -0.00966253 | 0.173946   | 0.193271  | 0.173946    | 0.173946  | 0.173946   |
| 1.19 | 0.0110476  | 0.194656   | -0.00973115 | 0.184925   | 0.196041  | 0.176579    | 0.187707  | 0.184925   |
| 1.2  | 0.0111845  | 0.205841   | -0.00979959 | 0.196041   | 0.21564   | 0.196041    | 0.196041  | 0.196041   |
| 1.21 | 0.011321   | 0.217162   | -0.00986783 | 0.207294   | 0.218683  | 0.198948    | 0.210076  | 0.207294   |
| 1.22 | 0.011457   | 0.228619   | -0.00993586 | 0.218683   | 0.238554  | 0.218682    | 0.218683  | 0.218683   |
| 1.23 | 0.0115926  | 0.240211   | -0.0100037  | 0.230207   | 0.241868  | 0.221861    | 0.23299   | 0.230208   |
| 1.24 | 0.0117277  | 0.251939   | -0.0100712  | 0.241868   | 0.262009  | 0.241867    | 0.241868  | 0.241868   |
| 1.25 | 0.0118623  | 0.263801   | -0.0101385  | 0.253663   | 0.265593  | 0.245316    | 0.256445  | 0.253663   |
| 1.26 | 0.0119963  | 0.275798   | -0.0102055  | 0.265592   | 0.286002  | 0.265591    | 0.265592  | 0.265592   |
| 1.27 | 0.0121298  | 0.287927   | -0.0102722  | 0.277655   | 0.289853  | 0.269308    | 0.280437  | 0.277655   |
| 1.28 | 0.0122626  | 0.30019    | -0.0103387  | 0.289851   | 0.310527  | 0.28985     | 0.289852  | 0.289852   |
| 1.29 | 0.0123948  | 0.312585   | -0.0104047  | 0.30218    | 0.314642  | 0.293833    | 0.304962  | 0.30218    |
| 1.3  | 0.0125263  | 0.325111   | -0.0104705  | 0.31464    | 0.33558   | 0.314639    | 0.314641  | 0.314641   |
| 1.31 | 0.012657   | 0.337768   | -0.0105359  | 0.327232   | 0.339956  | 0.318885    | 0.330015  | 0.327233   |
| 1.32 | 0.012787   | 0.350555   | -0.0106009  | 0.339954   | 0.361154  | 0.339952    | 0.339955  | 0.339955   |
| 1.33 | 0.0129163  | 0.363471   | -0.0106655  | 0.352806   | 0.365789  | 0.344458    | 0.355588  | 0.352807   |
| 1.34 | 0.0130447  | 0.376516   | -0.0107297  | 0.365786   | 0.387243  | 0.365784    | 0.365787  | 0.365787   |
| 1.35 | 0.0131723  | 0.389688   | -0.0107935  | 0.378895   | 0.392133  | 0.370546    | 0.381678  | 0.378896   |
| 1.36 | 0.013299   | 0.402987   | -0.0108568  | 0.39213    | 0.413841  | 0.392127    | 0.392131  | 0.392131   |
| 1.37 | 0.0134247  | 0.416412   | -0.0109197  | 0.405492   | 0.418983  | 0.397143    | 0.408275  | 0.405493   |
| 1.38 | 0.0135496  | 0.429961   | -0.0109821  | 0.418979   | 0.44094   | 0.418976    | 0.418981  | 0.418981   |
| 1.39 | 0.0136734  | 0.443635   | -0.0110441  | 0.432591   | 0.44633   | 0.424242    | 0.435374  | 0.432592   |
| 1.4  | 0.0137963  | 0.457431   | -0.0111055  | 0.446326   | 0.468533  | 0.446322    | 0.446327  | 0.446327   |
| 1.41 | 0.0139181  | 0.471349   | -0.0111664  | 0.460183   | 0.474166  | 0.451833    | 0.462966  | 0.460184   |
| 1.42 | 0.0140389  | 0.485388   | -0.0112268  | 0.474161   | 0.49661   | 0.474157    | 0.474163  | 0.474163   |
| 1.43 | 0.0141585  | 0.499547   | -0.0112866  | 0.48826    | 0.502483  | 0.47991     | 0.491044  | 0.488262   |
| 1.44 | 0.014277   | 0.513824   | -0.0113459  | 0.502478   | 0.525164  | 0.502473    | 0.50248   | 0.50248    |
| 1.45 | 0.0143943  | 0.528218   | -0.0114045  | 0.516814   | 0.531272  | 0.508463    | 0.519597  | 0.516815   |
| 1.46 | 0.0145105  | 0.542729   | -0.0114626  | 0.531266   | 0.554185  | 0.53126     | 0.531268  | 0.531268   |
| 1.47 | 0.0146254  | 0.557354   | -0.01152    | 0.545834   | 0.560522  | 0.537482    | 0.548618  | 0.545836   |
| 1.48 | 0.014739   | 0.572093   | -0.0115769  | 0.560516   | 0.583664  | 0.56051     | 0.560518  | 0.560518   |
| 1.49 | 0.0148514  | 0.586944   | -0.0116331  | 0.575311   | 0.590225  | 0.566959    | 0.578095  | 0.575313   |
| 1.5  | 0.0149624  | 0.601907   | -0.0116886  | 0.590218   | 0.613588  | 0.590211    | 0.590221  | 0.590221   |
| 1.51 | 0.0150721  | 0.616979   | -0.0117434  | 0.605235   | 0.620369  | 0.596883    | 0.60802   | 0.605238   |
| 1.52 | 0.0151804  | 0.632159   | -0.0117976  | 0.620362   | 0.643949  | 0.620354    | 0.620364  | 0.620364   |
| 1.53 | 0.0152873  | 0.647447   | -0.011851   | 0.635596   | 0.650944  | 0.627242    | 0.63838   | 0.635598   |
| 1.54 | 0.0153927  | 0.662839   | -0.0119037  | 0.650936   | 0.674735  | 0.650927    | 0.650938  | 0.650938   |
| 1.55 | 0.0154966  | 0.678336   | -0.0119557  | 0.66638    | 0.681937  | 0.658026    | 0.669165  | 0.666383   |
| 1.56 | 0.0155991  | 0.693935   | -0.0120069  | 0.681928   | 0.705933  | 0.681919    | 0.681931  | 0.681931   |
| 1.57 | 0.0157     | 0.709635   | -0.0120574  | 0.697578   | 0.713337  | 0.689222    | 0.700363  | 0.697581   |
| 1.58 | 0.0157993  | 0.725434   | -0.012107   | 0.713327   | 0.737531  | 0.713317    | 0.713331  | 0.713331   |
| 1.59 | 0.0158971  | 0.741331   | -0.0121559  | 0.729175   | 0.745131  | 0.72082     | 0.731961  | 0.729179   |
| 1.6  | 0.0159932  | 0.757325   | -0.0122039  | 0.745121   | 0.769518  | 0.74511     | 0.745124  | 0.745124   |
| 1.61 | 0.0160876  | 0.773412   | -0.0122512  | 0.761161   | 0.777307  | 0.752804    | 0.763947  | 0.761165   |
| 1.62 | 0.0161804  | 0.789593   | -0.0122976  | 0.777295   | 0.801879  | 0.777283    | 0.777299  | 0.777299   |
| 1.63 | 0.0162714  | 0.805864   | -0.0123431  | 0.793521   | 0.809849  | 0.785163    | 0.796307  | 0.793525   |
| 1.64 | 0.0163607  | 0.822225   | -0.0123877  | 0.809837   | 0.8346    | 0.809825    | 0.809841  | 0.809841   |
| 1.65 | 0.0164483  | 0.838673   | -0.0124315  | 0.826242   | 0.842746  | 0.817883    | 0.829028  | 0.826246   |
| 1.66 | 0.016534   | 0.855207   | -0.0124744  | 0.842733   | 0.867668  | 0.842719    | 0.842737  | 0.842737   |
| 1.67 | 0.0166179  | 0.871825   | -0.0125163  | 0.859309   | 0.875982  | 0.850949    | 0.862095  | 0.859313   |
| 1.68 | 0.0166999  | 0.888525   | -0.0125573  | 0.875968   | 0.901068  | 0.875953    | 0.875972  | 0.875972   |
| 1.69 | 0.0167801  | 0.905305   | -0.0125974  | 0.892708   | 0.909542  | 0.884347    | 0.895494  | 0.892712   |
| 1.7  | 0.0168583  | 0.922163   | -0.0126365  | 0.909527   | 0.934784  | 0.909511    | 0.909532  | 0.909532   |
| 1.71 | 0.0169346  | 0.939098   | -0.0126746  | 0.926423   | 0.943411  | 0.918062    | 0.92921   | 0.926428   |
| 1.72 | 0.0170089  | 0.956107   | -0.0127118  | 0.943395   | 0.968802  | 0.943379    | 0.9434    | 0.9434     |
| 1.73 | 0.0170812  | 0.973188   | -0.012748   | 0.96044    | 0.977574  | 0.952078    | 0.963227  | 0.960446   |
| 1.74 | 0.0171515  | 0.990339   | -0.0127831  | 0.977556   | 1.00311   | 0.977539    | 0.977562  | 0.977562   |
| 1.75 | 0.0172198  | 1.00756    | -0.0128172  | 0.994742   | 1.01201   | 0.986379    | 0.99753   | 0.994748   |
| 1.76 | 0.0172859  | 1.02485    | -0.0128503  | 1.01199    | 1.03768   | 1.01198     | 1.012     | 1.012      |
| 1.77 | 0.01735    | 1.0422     | -0.0128823  | 1.02931    | 1.04671   | 1.02095     | 1.0321    | 1.02932    |
| 1.78 | 0.0174119  | 1.05961    | -0.0129133  | 1.04669    | 1.0725    | 1.04667     | 1.0467    | 1.0467     |
| 1.79 | 0.0174717  | 1.07708    | -0.0129432  | 1.06414    | 1.08166   | 1.05577     | 1.06692   | 1.06414    |
| 1.8  | 0.0175293  | 1.09461    | -0.012972   | 1.08164    | 1.10756   | 1.08162     | 1.08164   | 1.08164    |
| 1.81 | 0.0175846  | 1.11219    | -0.0129997  | 1.09919    | 1.11683   | 1.09083     | 1.10198   | 1.0992     |
| 1.82 | 0.0176378  | 1.12983    | -0.0130262  | 1.1168     | 1.14284   | 1.11678     | 1.11681   | 1.11681    |
| 1.83 | 0.0176887  | 1.14752    | -0.0130517  | 1.13447    | 1.1522    | 1.1261      | 1.13726   | 1.13447    |
| 1.84 | 0.0177373  | 1.16526    | -0.013076   | 1.15218    | 1.17831   | 1.15216     | 1.15219   | 1.15219    |
| 1.85 | 0.0177836  | 1.18304    | -0.0130992  | 1.16994    | 1.18777   | 1.16157     | 1.17273   | 1.16995    |
| 1.86 | 0.0178276  | 1.20087    | -0.0131211  | 1.18775    | 1.21396   | 1.18772     | 1.18775   | 1.18775    |
| 1.87 | 0.0178692  | 1.21874    | -0.0131419  | 1.20559    | 1.22351   | 1.19722     | 1.20838   | 1.2056     |
| 1.88 | 0.0179084  | 1.23665    | -0.0131616  | 1.22348    | 1.24978   | 1.22346     | 1.22349   | 1.22349    |
| 1.89 | 0.0179453  | 1.25459    | -0.01318    | 1.24141    | 1.2594    | 1.23304     | 1.2442    | 1.24142    |
| 1.9  | 0.0179797  | 1.27257    | -0.0131972  | 1.25937    | 1.28574   | 1.25935     | 1.25938   | 1.25938    |
| 1.91 | 0.0180117  | 1.29058    | -0.0132132  | 1.27737    | 1.29542   | 1.269       | 1.28016   | 1.27738    |
| 1.92 | 0.0180412  | 1.30862    | -0.013228   | 1.29539    | 1.32182   | 1.29537     | 1.2954    | 1.2954     |
| 1.93 | 0.0180682  | 1.32669    | -0.0132415  | 1.31345    | 1.33156   | 1.30508     | 1.31624   | 1.31346    |
| 1.94 | 0.0180927  | 1.34478    | -0.0132537  | 1.33153    | 1.35801   | 1.3315      | 1.33154   | 1.33154    |
| 1.95 | 0.0181147  | 1.3629     | -0.0132647  | 1.34963    | 1.36779   | 1.34126     | 1.35243   | 1.34964    |
| 1.96 | 0.0181341  | 1.38103    | -0.0132744  | 1.36776    | 1.39428   | 1.36773     | 1.36777   | 1.36777    |
| 1.97 | 0.018151   | 1.39918    | -0.0132829  | 1.3859     | 1.40409   | 1.37752     | 1.38869   | 1.38591    |
| 1.98 | 0.0181653  | 1.41735    | -0.01329    | 1.40406    | 1.43061   | 1.40403     | 1.40407   | 1.40407    |
| 1.99 | 0.0181769  | 1.43553    | -0.0132958  | 1.42223    | 1.44044   | 1.41385     | 1.42502   | 1.42224    |
| 2    | 0.0181859  | 1.45371    | -0.0133003  | 1.44041    | 1.46698   | 1.44038     | 1.44042   | 1.44042    |



label: E=C+D
labeled_formulas: E=C+D
output: {"Arithmetic-Relationship": ["E=C+D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_135190___xlsx_1d4e456f03eef3cca9d6001bb1309201d5a66d5d.xlsx___line_61