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 |
|:----|:----|-----:|:--------|:-----|----:|----:|------:|
| Jan | Q1  | 2017 | PK      | Raj  |  27 | 3   |  81   |
| Jan | Q1  | 2017 | Charlie | Raj  |  23 | 5   | 115   |
| Jan | Q1  | 2017 | Thomas  | Jack |  19 | 1.6 |  30.4 |
| Jan | Q1  | 2017 | Olivia  | Jack |  28 | 4.7 | 131.6 |
| Jan | Q1  | 2017 | Lily    | Jack |  22 | 1.2 |  26.4 |
| Jan | Q1  | 2017 | Lucy    | Mani |  10 | 2.9 |  29   |
| Jan | Q1  | 2017 | Alax    | Mani |  26 | 2.5 |  65   |
| Jan | Q1  | 2017 | Rosie   | Raj  |  26 | 3   |  78   |
| Jan | Q1  | 2017 | Emma    | Mani |  16 | 2.6 |  41.6 |
| Jan | Q1  | 2017 | Leo     | Mani |  10 | 2.3 |  23   |
| Feb | Q1  | 2017 | PK      | Raj  |  10 | 2.3 |  23   |
| Feb | Q1  | 2017 | Charlie | Raj  |  25 | 4.3 | 107.5 |
| Feb | Q1  | 2017 | Thomas  | Jack |  25 | 1.9 |  47.5 |
| Feb | Q1  | 2017 | Olivia  | Jack |  16 | 1.2 |  19.2 |
| Feb | Q1  | 2017 | Lily    | Jack |  22 | 2.3 |  50.6 |
| Feb | Q1  | 2017 | Lucy    | Mani |  17 | 2.5 |  42.5 |
| Feb | Q1  | 2017 | Alax    | Mani |  17 | 2.9 |  49.3 |
| Feb | Q1  | 2017 | Rosie   | Raj  |  15 | 1.3 |  19.5 |
| Feb | Q1  | 2017 | Emma    | Mani |  20 | 4.4 |  88   |
| Feb | Q1  | 2017 | Leo     | Mani |  20 | 2.7 |  54   |
| Mar | Q1  | 2017 | PK      | Raj  |  14 | 2.2 |  30.8 |
| Mar | Q1  | 2017 | Charlie | Raj  |  11 | 4   |  44   |
| Mar | Q1  | 2017 | Thomas  | Jack |  21 | 2.8 |  58.8 |
| Mar | Q1  | 2017 | Olivia  | Jack |  23 | 2.2 |  50.6 |
| Mar | Q1  | 2017 | Lily    | Jack |  13 | 4   |  52   |
| Mar | Q1  | 2017 | Lucy    | Mani |  27 | 4.2 | 113.4 |
| Mar | Q1  | 2017 | Alax    | Mani |  22 | 4.8 | 105.6 |
| Mar | Q1  | 2017 | Rosie   | Raj  |  21 | 2.1 |  44.1 |
| Mar | Q1  | 2017 | Emma    | Mani |  20 | 4.7 |  94   |
| Mar | Q1  | 2017 | Leo     | Mani |  21 | 1.6 |  33.6 |
| Apr | Q2  | 2017 | PK      | Raj  |  23 | 1.9 |  43.7 |
| Apr | Q2  | 2017 | Charlie | Raj  |  14 | 3.5 |  49   |
| Apr | Q2  | 2017 | Thomas  | Jack |  27 | 2.9 |  78.3 |
| Apr | Q2  | 2017 | Olivia  | Jack |  24 | 2.1 |  50.4 |
| Apr | Q2  | 2017 | Lily    | Jack |  26 | 2.7 |  70.2 |
| Apr | Q2  | 2017 | Lucy    | Mani |  14 | 2.7 |  37.8 |
| Apr | Q2  | 2017 | Alax    | Mani |  15 | 1.4 |  21   |
| Apr | Q2  | 2017 | Rosie   | Raj  |  18 | 1.5 |  27   |
| Apr | Q2  | 2017 | Emma    | Mani |  12 | 3   |  36   |
| Apr | Q2  | 2017 | Leo     | Mani |  10 | 3.4 |  34   |
| May | Q2  | 2017 | PK      | Raj  |  24 | 3.2 |  76.8 |
| May | Q2  | 2017 | Charlie | Raj  |  30 | 3   |  90   |
| May | Q2  | 2017 | Thomas  | Jack |  18 | 3.5 |  63   |
| May | Q2  | 2017 | Olivia  | Jack |  10 | 4.9 |  49   |
| May | Q2  | 2017 | Lily    | Jack |  14 | 3.6 |  50.4 |
| May | Q2  | 2017 | Lucy    | Mani |  11 | 1.7 |  18.7 |
| May | Q2  | 2017 | Alax    | Mani |  11 | 2.3 |  25.3 |
| May | Q2  | 2017 | Rosie   | Raj  |  25 | 4.7 | 117.5 |
| May | Q2  | 2017 | Emma    | Mani |  13 | 3.2 |  41.6 |
| May | Q2  | 2017 | Leo     | Mani |  16 | 4.7 |  75.2 |
| Jun | Q2  | 2017 | PK      | Raj  |  29 | 5   | 145   |
| Jun | Q2  | 2017 | Charlie | Raj  |  27 | 3.3 |  89.1 |
| Jun | Q2  | 2017 | Thomas  | Jack |  14 | 1.2 |  16.8 |
| Jun | Q2  | 2017 | Olivia  | Jack |  11 | 1.9 |  20.9 |
| Jun | Q2  | 2017 | Lily    | Jack |  14 | 3.1 |  43.4 |
| Jun | Q2  | 2017 | Lucy    | Mani |  16 | 3   |  48   |
| Jun | Q2  | 2017 | Alax    | Mani |  13 | 1.3 |  16.9 |
| Jun | Q2  | 2017 | Rosie   | Raj  |  20 | 4   |  80   |
| Jun | Q2  | 2017 | Emma    | Mani |  20 | 4.4 |  88   |
| Jun | Q2  | 2017 | Leo     | Mani |  11 | 3.8 |  41.8 |
| Jul | Q3  | 2017 | PK      | Raj  |  28 | 1.4 |  39.2 |
| Jul | Q3  | 2017 | Charlie | Raj  |  19 | 3.5 |  66.5 |
| Jul | Q3  | 2017 | Thomas  | Jack |  19 | 4.9 |  93.1 |
| Jul | Q3  | 2017 | Olivia  | Jack |  23 | 4.1 |  94.3 |
| Jul | Q3  | 2017 | Lily    | Jack |  13 | 3   |  39   |
| Jul | Q3  | 2017 | Lucy    | Mani |  15 | 3.1 |  46.5 |
| Jul | Q3  | 2017 | Alax    | Mani |  13 | 1   |  13   |
| Jul | Q3  | 2017 | Rosie   | Raj  |  14 | 4   |  56   |
| Jul | Q3  | 2017 | Emma    | Mani |  20 | 2   |  40   |
| Jul | Q3  | 2017 | Leo     | Mani |  26 | 2.2 |  57.2 |
| Aug | Q3  | 2017 | PK      | Raj  |  25 | 1.1 |  27.5 |
| Aug | Q3  | 2017 | Charlie | Raj  |  18 | 3.4 |  61.2 |
| Aug | Q3  | 2017 | Thomas  | Jack |  12 | 1.9 |  22.8 |
| Aug | Q3  | 2017 | Olivia  | Jack |  24 | 5   | 120   |
| Aug | Q3  | 2017 | Lily    | Jack |  15 | 3.5 |  52.5 |
| Aug | Q3  | 2017 | Lucy    | Mani |  28 | 1   |  28   |
| Aug | Q3  | 2017 | Alax    | Mani |  20 | 1.1 |  22   |
| Aug | Q3  | 2017 | Rosie   | Raj  |  27 | 4.6 | 124.2 |
| Aug | Q3  | 2017 | Emma    | Mani |  10 | 2.1 |  21   |
| Aug | Q3  | 2017 | Leo     | Mani |  20 | 2.9 |  58   |
| Sep | Q3  | 2017 | PK      | Raj  |  16 | 4.8 |  76.8 |
| Sep | Q3  | 2017 | Charlie | Raj  |  12 | 3.4 |  40.8 |
| Sep | Q3  | 2017 | Thomas  | Jack |  12 | 1.3 |  15.6 |
| Sep | Q3  | 2017 | Olivia  | Jack |  29 | 3.6 | 104.4 |
| Sep | Q3  | 2017 | Lily    | Jack |  15 | 4.5 |  67.5 |
| Sep | Q3  | 2017 | Lucy    | Mani |  20 | 3.3 |  66   |
| Sep | Q3  | 2017 | Alax    | Mani |  19 | 2   |  38   |
| Sep | Q3  | 2017 | Rosie   | Raj  |  11 | 2.4 |  26.4 |
| Sep | Q3  | 2017 | Emma    | Mani |  22 | 2.6 |  57.2 |
| Sep | Q3  | 2017 | Leo     | Mani |  20 | 3.7 |  74   |
| Oct | Q4  | 2017 | PK      | Raj  |  13 | 1.6 |  20.8 |
| Oct | Q4  | 2017 | Charlie | Raj  |  30 | 1.9 |  57   |
| Oct | Q4  | 2017 | Thomas  | Jack |  29 | 3.3 |  95.7 |
| Oct | Q4  | 2017 | Olivia  | Jack |  30 | 5   | 150   |
| Oct | Q4  | 2017 | Lily    | Jack |  22 | 2.8 |  61.6 |
| Oct | Q4  | 2017 | Lucy    | Mani |  11 | 3.5 |  38.5 |
| Oct | Q4  | 2017 | Alax    | Mani |  23 | 1.9 |  43.7 |
| Oct | Q4  | 2017 | Rosie   | Raj  |  24 | 4.9 | 117.6 |
| Oct | Q4  | 2017 | Emma    | Mani |  14 | 2.1 |  29.4 |
| Oct | Q4  | 2017 | Leo     | Mani |  24 | 4   |  96   |
| Nov | Q4  | 2017 | PK      | Raj  |  11 | 3.3 |  36.3 |
| Nov | Q4  | 2017 | Charlie | Raj  |  14 | 1.6 |  22.4 |
| Nov | Q4  | 2017 | Thomas  | Jack |  19 | 2.4 |  45.6 |
| Nov | Q4  | 2017 | Olivia  | Jack |  13 | 2.9 |  37.7 |
| Nov | Q4  | 2017 | Lily    | Jack |  23 | 1.7 |  39.1 |
| Nov | Q4  | 2017 | Lucy    | Mani |  16 | 1.9 |  30.4 |
| Nov | Q4  | 2017 | Alax    | Mani |  30 | 4.1 | 123   |
| Nov | Q4  | 2017 | Rosie   | Raj  |  19 | 2.7 |  51.3 |
| Nov | Q4  | 2017 | Emma    | Mani |  30 | 1.1 |  33   |
| Nov | Q4  | 2017 | Leo     | Mani |  24 | 1.9 |  45.6 |
| Dec | Q4  | 2017 | PK      | Raj  |  30 | 1.1 |  33   |
| Dec | Q4  | 2017 | Charlie | Raj  |  12 | 3   |  36   |
| Dec | Q4  | 2017 | Thomas  | Jack |  22 | 3.5 |  77   |
| Dec | Q4  | 2017 | Olivia  | Jack |  23 | 4.6 | 105.8 |
| Dec | Q4  | 2017 | Lily    | Jack |  16 | 3.9 |  62.4 |
| Dec | Q4  | 2017 | Lucy    | Mani |  19 | 2.4 |  45.6 |
| Dec | Q4  | 2017 | Alax    | Mani |  30 | 3.9 | 117   |
| Dec | Q4  | 2017 | Rosie   | Raj  |  11 | 1.5 |  16.5 |
| Dec | Q4  | 2017 | Emma    | Mani |  22 | 1.6 |  35.2 |
| Dec | Q4  | 2017 | Leo     | Mani |  15 | 2   |  30   |
| Jan | Q1  | 2018 | PK      | Raj  |  10 | 2.4 |  24   |
| Jan | Q1  | 2018 | Charlie | Raj  |  12 | 1.7 |  20.4 |
| Jan | Q1  | 2018 | Thomas  | Jack |  16 | 2.1 |  33.6 |
| Jan | Q1  | 2018 | Olivia  | Jack |  23 | 1   |  23   |
| Jan | Q1  | 2018 | Lily    | Jack |  10 | 3.6 |  36   |
| Jan | Q1  | 2018 | Lucy    | Mani |  30 | 3.8 | 114   |
| Jan | Q1  | 2018 | Alax    | Mani |  21 | 2.9 |  60.9 |
| Jan | Q1  | 2018 | Rosie   | Raj  |  20 | 2.2 |  44   |
| Jan | Q1  | 2018 | Emma    | Mani |  20 | 3.2 |  64   |
| Jan | Q1  | 2018 | Leo     | Mani |  25 | 1.6 |  40   |
| Feb | Q1  | 2018 | PK      | Raj  |  20 | 1.7 |  34   |
| Feb | Q1  | 2018 | Charlie | Raj  |  28 | 4   | 112   |
| Feb | Q1  | 2018 | Thomas  | Jack |  24 | 1.9 |  45.6 |
| Feb | Q1  | 2018 | Olivia  | Jack |  29 | 3.9 | 113.1 |
| Feb | Q1  | 2018 | Lily    | Jack |  15 | 4.6 |  69   |
| Feb | Q1  | 2018 | Lucy    | Mani |  10 | 1.6 |  16   |
| Feb | Q1  | 2018 | Alax    | Mani |  21 | 2.5 |  52.5 |
| Feb | Q1  | 2018 | Rosie   | Raj  |  19 | 2.5 |  47.5 |
| Feb | Q1  | 2018 | Emma    | Mani |  23 | 1.2 |  27.6 |
| Feb | Q1  | 2018 | Leo     | Mani |  12 | 3.8 |  45.6 |
| Mar | Q1  | 2018 | PK      | Raj  |  16 | 3.8 |  60.8 |
| Mar | Q1  | 2018 | Charlie | Raj  |  12 | 4.4 |  52.8 |
| Mar | Q1  | 2018 | Thomas  | Jack |  19 | 2.4 |  45.6 |
| Mar | Q1  | 2018 | Olivia  | Jack |  30 | 2   |  60   |
| Mar | Q1  | 2018 | Lily    | Jack |  29 | 4.2 | 121.8 |
| Mar | Q1  | 2018 | Lucy    | Mani |  10 | 2.7 |  27   |
| Mar | Q1  | 2018 | Alax    | Mani |  17 | 3.3 |  56.1 |
| Mar | Q1  | 2018 | Rosie   | Raj  |  13 | 2.7 |  35.1 |
| Mar | Q1  | 2018 | Emma    | Mani |  13 | 3.8 |  49.4 |
| Mar | Q1  | 2018 | Leo     | Mani |  26 | 3   |  78   |
| Apr | Q2  | 2018 | PK      | Raj  |  10 | 2   |  20   |
| Apr | Q2  | 2018 | Charlie | Raj  |  22 | 4.4 |  96.8 |
| Apr | Q2  | 2018 | Thomas  | Jack |  29 | 1.3 |  37.7 |
| Apr | Q2  | 2018 | Olivia  | Jack |  10 | 4.8 |  48   |
| Apr | Q2  | 2018 | Lily    | Jack |  15 | 1.8 |  27   |
| Apr | Q2  | 2018 | Lucy    | Mani |  18 | 2.5 |  45   |
| Apr | Q2  | 2018 | Alax    | Mani |  28 | 2.2 |  61.6 |
| Apr | Q2  | 2018 | Rosie   | Raj  |  30 | 4.5 | 135   |
| Apr | Q2  | 2018 | Emma    | Mani |  19 | 1.2 |  22.8 |
| Apr | Q2  | 2018 | Leo     | Mani |  27 | 3.4 |  91.8 |
| May | Q2  | 2018 | PK      | Raj  |  12 | 3.4 |  40.8 |
| May | Q2  | 2018 | Charlie | Raj  |  11 | 1.8 |  19.8 |
| May | Q2  | 2018 | Thomas  | Jack |  26 | 2.8 |  72.8 |
| May | Q2  | 2018 | Olivia  | Jack |  30 | 3.5 | 105   |
| May | Q2  | 2018 | Lily    | Jack |  23 | 3.1 |  71.3 |
| May | Q2  | 2018 | Lucy    | Mani |  15 | 2.4 |  36   |
| May | Q2  | 2018 | Alax    | Mani |  21 | 3   |  63   |
| May | Q2  | 2018 | Rosie   | Raj  |  11 | 2.4 |  26.4 |
| May | Q2  | 2018 | Emma    | Mani |  21 | 3.1 |  65.1 |
| May | Q2  | 2018 | Leo     | Mani |  23 | 1.4 |  32.2 |
| Jun | Q2  | 2018 | PK      | Raj  |  29 | 2.9 |  84.1 |
| Jun | Q2  | 2018 | Charlie | Raj  |  25 | 3   |  75   |
| Jun | Q2  | 2018 | Thomas  | Jack |  26 | 2.2 |  57.2 |
| Jun | Q2  | 2018 | Olivia  | Jack |  11 | 4.6 |  50.6 |
| Jun | Q2  | 2018 | Lily    | Jack |  11 | 2.7 |  29.7 |
| Jun | Q2  | 2018 | Lucy    | Mani |  26 | 3.3 |  85.8 |
| Jun | Q2  | 2018 | Alax    | Mani |  13 | 2.4 |  31.2 |
| Jun | Q2  | 2018 | Rosie   | Raj  |  25 | 1.4 |  35   |
| Jun | Q2  | 2018 | Emma    | Mani |  12 | 1.3 |  15.6 |
| Jun | Q2  | 2018 | Leo     | Mani |  19 | 2.9 |  55.1 |



label: H=F*G
labeled_formulas: H=F*G
output: {"Arithmetic-Relationship": ["H=F*G"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_783328___xlsx_a1fa484f4bf721818b9c2b13031fe45be6304d6d.xlsx___line_426