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# Operators

## Binary operators

Prometheus's query language supports basic logical and arithmetic operators. For operations between two instant vectors, the matching behavior can be modified.

### Arithmetic binary operators

The following binary arithmetic operators exist in Prometheus:

• `+` (addition)
• `-` (subtraction)
• `*` (multiplication)
• `/` (division)
• `%` (modulo)
• `^` (power/exponentiation)

Binary arithmetic operators are defined between scalar/scalar, vector/scalar, and vector/vector value pairs.

Between two scalars, the behavior is obvious: they evaluate to another scalar that is the result of the operator applied to both scalar operands.

Between an instant vector and a scalar, the operator is applied to the value of every data sample in the vector. E.g. if a time series instant vector is multiplied by 2, the result is another vector in which every sample value of the original vector is multiplied by 2. The metric name is dropped.

Between two instant vectors, a binary arithmetic operator is applied to each entry in the left-hand side vector and its matching element in the right-hand vector. The result is propagated into the result vector with the grouping labels becoming the output label set. The metric name is dropped. Entries for which no matching entry in the right-hand vector can be found are not part of the result.

### Trigonometric binary operators

The following trigonometric binary operators, which work in radians, exist in Prometheus:

Trigonometric operators allow trigonometric functions to be executed on two vectors using vector matching, which isn't available with normal functions. They act in the same manner as arithmetic operators.

### Comparison binary operators

The following binary comparison operators exist in Prometheus:

• `==` (equal)
• `!=` (not-equal)
• `>` (greater-than)
• `<` (less-than)
• `>=` (greater-or-equal)
• `<=` (less-or-equal)

Comparison operators are defined between scalar/scalar, vector/scalar, and vector/vector value pairs. By default they filter. Their behavior can be modified by providing `bool` after the operator, which will return `0` or `1` for the value rather than filtering.

Between two scalars, the `bool` modifier must be provided and these operators result in another scalar that is either `0` (`false`) or `1` (`true`), depending on the comparison result.

Between an instant vector and a scalar, these operators are applied to the value of every data sample in the vector, and vector elements between which the comparison result is `false` get dropped from the result vector. If the `bool` modifier is provided, vector elements that would be dropped instead have the value `0` and vector elements that would be kept have the value `1`. The metric name is dropped if the `bool` modifier is provided.

Between two instant vectors, these operators behave as a filter by default, applied to matching entries. Vector elements for which the expression is not true or which do not find a match on the other side of the expression get dropped from the result, while the others are propagated into a result vector with the grouping labels becoming the output label set. If the `bool` modifier is provided, vector elements that would have been dropped instead have the value `0` and vector elements that would be kept have the value `1`, with the grouping labels again becoming the output label set. The metric name is dropped if the `bool` modifier is provided.

### Logical/set binary operators

These logical/set binary operators are only defined between instant vectors:

• `and` (intersection)
• `or` (union)
• `unless` (complement)

`vector1 and vector2` results in a vector consisting of the elements of `vector1` for which there are elements in `vector2` with exactly matching label sets. Other elements are dropped. The metric name and values are carried over from the left-hand side vector.

`vector1 or vector2` results in a vector that contains all original elements (label sets + values) of `vector1` and additionally all elements of `vector2` which do not have matching label sets in `vector1`.

`vector1 unless vector2` results in a vector consisting of the elements of `vector1` for which there are no elements in `vector2` with exactly matching label sets. All matching elements in both vectors are dropped.

## Vector matching

Operations between vectors attempt to find a matching element in the right-hand side vector for each entry in the left-hand side. There are two basic types of matching behavior: One-to-one and many-to-one/one-to-many.

### One-to-one vector matches

One-to-one finds a unique pair of entries from each side of the operation. In the default case, that is an operation following the format `vector1 <operator> vector2`. Two entries match if they have the exact same set of labels and corresponding values. The `ignoring` keyword allows ignoring certain labels when matching, while the `on` keyword allows reducing the set of considered labels to a provided list:

``````<vector expr> <bin-op> ignoring(<label list>) <vector expr>
<vector expr> <bin-op> on(<label list>) <vector expr>
``````

Example input:

``````method_code:http_errors:rate5m{method="get", code="500"}  24
method_code:http_errors:rate5m{method="get", code="404"}  30
method_code:http_errors:rate5m{method="put", code="501"}  3
method_code:http_errors:rate5m{method="post", code="500"} 6
method_code:http_errors:rate5m{method="post", code="404"} 21

method:http_requests:rate5m{method="get"}  600
method:http_requests:rate5m{method="del"}  34
method:http_requests:rate5m{method="post"} 120
``````

Example query:

``````method_code:http_errors:rate5m{code="500"} / ignoring(code) method:http_requests:rate5m
``````

This returns a result vector containing the fraction of HTTP requests with status code of 500 for each method, as measured over the last 5 minutes. Without `ignoring(code)` there would have been no match as the metrics do not share the same set of labels. The entries with methods `put` and `del` have no match and will not show up in the result:

``````{method="get"}  0.04            //  24 / 600
{method="post"} 0.05            //   6 / 120
``````

### Many-to-one and one-to-many vector matches

Many-to-one and one-to-many matchings refer to the case where each vector element on the "one"-side can match with multiple elements on the "many"-side. This has to be explicitly requested using the `group_left` or `group_right` modifier, where left/right determines which vector has the higher cardinality.

``````<vector expr> <bin-op> ignoring(<label list>) group_left(<label list>) <vector expr>
<vector expr> <bin-op> ignoring(<label list>) group_right(<label list>) <vector expr>
<vector expr> <bin-op> on(<label list>) group_left(<label list>) <vector expr>
<vector expr> <bin-op> on(<label list>) group_right(<label list>) <vector expr>
``````

The label list provided with the group modifier contains additional labels from the "one"-side to be included in the result metrics. For `on` a label can only appear in one of the lists. Every time series of the result vector must be uniquely identifiable.

Grouping modifiers can only be used for comparison and arithmetic. Operations as `and`, `unless` and `or` operations match with all possible entries in the right vector by default.

Example query:

``````method_code:http_errors:rate5m / ignoring(code) group_left method:http_requests:rate5m
``````

In this case the left vector contains more than one entry per `method` label value. Thus, we indicate this using `group_left`. The elements from the right side are now matched with multiple elements with the same `method` label on the left:

``````{method="get", code="500"}  0.04            //  24 / 600
{method="get", code="404"}  0.05            //  30 / 600
{method="post", code="500"} 0.05            //   6 / 120
{method="post", code="404"} 0.175           //  21 / 120
``````

Many-to-one and one-to-many matching are advanced use cases that should be carefully considered. Often a proper use of `ignoring(<labels>)` provides the desired outcome.

## Aggregation operators

Prometheus supports the following built-in aggregation operators that can be used to aggregate the elements of a single instant vector, resulting in a new vector of fewer elements with aggregated values:

• `sum` (calculate sum over dimensions)
• `min` (select minimum over dimensions)
• `max` (select maximum over dimensions)
• `avg` (calculate the average over dimensions)
• `group` (all values in the resulting vector are 1)
• `stddev` (calculate population standard deviation over dimensions)
• `stdvar` (calculate population standard variance over dimensions)
• `count` (count number of elements in the vector)
• `count_values` (count number of elements with the same value)
• `bottomk` (smallest k elements by sample value)
• `topk` (largest k elements by sample value)
• `quantile` (calculate φ-quantile (0 ≤ φ ≤ 1) over dimensions)

These operators can either be used to aggregate over all label dimensions or preserve distinct dimensions by including a `without` or `by` clause. These clauses may be used before or after the expression.

``````<aggr-op> [without|by (<label list>)] ([parameter,] <vector expression>)
``````

or

``````<aggr-op>([parameter,] <vector expression>) [without|by (<label list>)]
``````

`label list` is a list of unquoted labels that may include a trailing comma, i.e. both `(label1, label2)` and `(label1, label2,)` are valid syntax.

`without` removes the listed labels from the result vector, while all other labels are preserved in the output. `by` does the opposite and drops labels that are not listed in the `by` clause, even if their label values are identical between all elements of the vector.

`parameter` is only required for `count_values`, `quantile`, `topk` and `bottomk`.

`count_values` outputs one time series per unique sample value. Each series has an additional label. The name of that label is given by the aggregation parameter, and the label value is the unique sample value. The value of each time series is the number of times that sample value was present.

`topk` and `bottomk` are different from other aggregators in that a subset of the input samples, including the original labels, are returned in the result vector. `by` and `without` are only used to bucket the input vector.

`quantile` calculates the φ-quantile, the value that ranks at number φ*N among the N metric values of the dimensions aggregated over. φ is provided as the aggregation parameter. For example, `quantile(0.5, ...)` calculates the median, `quantile(0.95, ...)` the 95th percentile.

Example:

If the metric `http_requests_total` had time series that fan out by `application`, `instance`, and `group` labels, we could calculate the total number of seen HTTP requests per application and group over all instances via:

``````sum without (instance) (http_requests_total)
``````

Which is equivalent to:

`````` sum by (application, group) (http_requests_total)
``````

If we are just interested in the total of HTTP requests we have seen in all applications, we could simply write:

``````sum(http_requests_total)
``````

To count the number of binaries running each build version we could write:

``````count_values("version", build_version)
``````

To get the 5 largest HTTP requests counts across all instances we could write:

``````topk(5, http_requests_total)
``````

## Binary operator precedence

The following list shows the precedence of binary operators in Prometheus, from highest to lowest.

1. `^`
2. `*`, `/`, `%`, `atan2`
3. `+`, `-`
4. `==`, `!=`, `<=`, `<`, `>=`, `>`
5. `and`, `unless`
6. `or`

Operators on the same precedence level are left-associative. For example, `2 * 3 % 2` is equivalent to `(2 * 3) % 2`. However `^` is right associative, so `2 ^ 3 ^ 2` is equivalent to `2 ^ (3 ^ 2)`.

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