[DOCS] Reformats count API (elastic#46377)

* [DOCS] Reformats count API.
Co-Authored-By: James Rodewig <james.rodewig@elastic.co>

docs/reference/rest-api/common-parms.asciidoc

@@ -197,6 +197,12 @@ tag::if_seq_no[]
 sequence number. See <<optimistic-concurrency-control-index>>.
 end::if_seq_no[]
 
+tag::ignore_throttled[]
+`ignore_throttled`::
+(Optional, boolean) If `true`, concrete, expanded or aliased indices are 
+ignored when throttled.
+end::ignore_throttled[]
+
 tag::index-ignore-unavailable[]
 `ignore_unavailable`::
 (Optional, boolean) If `true`, missing or closed indices are not included in the
@@ -399,6 +405,12 @@ tag::search-q[]
 (Optional, string) Query in the Lucene query string syntax.
 end::search-q[]
 
+tag::query[]
+`query`::
+(Optional, <<query-dsl,query object>>) Defines the search definition using the 
+<<query-dsl,Query DSL>>.
+end::query[]
+
 tag::refresh[]
 `refresh`::
 (Optional, enum) If `true`, {es} refreshes the affected shards to make this

docs/reference/search/count.asciidoc

@@ -1,11 +1,90 @@
 [[search-count]]
 === Count API
 
-The count API allows to easily execute a query and get the number of
-matches for that query. It can be executed across one or more indices.
-The query can either be provided using a simple query string as a
-parameter, or using the <<query-dsl,Query DSL>> defined within the request
-body. Here is an example:
+Gets the number of matches for a search query.
+
+[source,console]
+--------------------------------------------------
+GET /twitter/_count?q=user:kimchy
+--------------------------------------------------
+// TEST[setup:twitter]
+
+NOTE: The query being sent in the body must be nested in a `query` key, same as
+the <<search-search,search api>> works.
+
+
+[[search-count-api-request]]
+==== {api-request-title}
+
+`PUT /<index>/_count`
+
+
+[[search-count-api-desc]]
+==== {api-description-title}
+
+The count API allows you to execute a query and get the number of matches for 
+that query. It can be executed across one or more indices. The query can either 
+be provided using a simple query string as a parameter, or using the 
+<<query-dsl,Query DSL>> defined within the request body.
+
+The count API can be applied to <<search-multi-index,multiple indices>>.
+
+The operation is broadcast across all shards. For each shard id group, a replica 
+is chosen and executed against it. This means that replicas increase the 
+scalability of count.
+
+
+[[search-count-api-path-params]]
+==== {api-path-parms-title}
+
+include::{docdir}/rest-api/common-parms.asciidoc[tag=index]
+
+
+[[search-count-api-query-params]]
+==== {api-query-parms-title}
+
+include::{docdir}/rest-api/common-parms.asciidoc[tag=allow-no-indices]
+
+include::{docdir}/rest-api/common-parms.asciidoc[tag=analyzer]
+
+include::{docdir}/rest-api/common-parms.asciidoc[tag=analyze_wildcard]
+
+include::{docdir}/rest-api/common-parms.asciidoc[tag=default_operator]
+
+include::{docdir}/rest-api/common-parms.asciidoc[tag=df]
+
+include::{docdir}/rest-api/common-parms.asciidoc[tag=expand-wildcards]
++
+Defaults to `open`.
+
+include::{docdir}/rest-api/common-parms.asciidoc[tag=ignore_throttled]
+
+include::{docdir}/rest-api/common-parms.asciidoc[tag=index-ignore-unavailable]
+
+include::{docdir}/rest-api/common-parms.asciidoc[tag=lenient]
+
+`min_score`::
+(Optional, float)
+  Sets the minimum `_score` value that documents must have to be included in the 
+  result.
+
+include::{docdir}/rest-api/common-parms.asciidoc[tag=preference]
+
+include::{docdir}/rest-api/common-parms.asciidoc[tag=search-q]
+
+include::{docdir}/rest-api/common-parms.asciidoc[tag=routing]
+
+include::{docdir}/rest-api/common-parms.asciidoc[tag=terminate_after]
+
+
+[[search-count-request-body]]
+==== {api-request-body-title}
+
+include::{docdir}/rest-api/common-parms.asciidoc[tag=query]
+
+
+[[search-count-api-example]]
+==== {api-examples-title}
 
 [source,js]
 --------------------------------------------------
@@ -25,11 +104,8 @@ GET /twitter/_count
 --------------------------------------------------
 //CONSOLE
 
-NOTE: The query being sent in the body must be nested in a `query` key, same as
-the <<search-search,search api>> works
-
-Both examples above do the same thing, which is count the number of
-tweets from the `twitter` index for a certain user. The result is:
+Both examples above do the same: count the number of tweets from the `twitter` 
+index for a certain user. The API returns the following response:
 
 [source,js]
 --------------------------------------------------
@@ -47,62 +123,3 @@ tweets from the `twitter` index for a certain user. The result is:
 
 The query is optional, and when not provided, it will use `match_all` to
 count all the docs.
-
-[float]
-==== Multi index
-
-The count API can be applied to <<search-multi-index,multiple indices>>.
-
-[float]
-==== Request Parameters
-
-When executing count using the query parameter `q`, the query passed is
-a query string using Lucene query parser. There are additional
-parameters that can be passed:
-
-[cols="<,<",options="header",]
-|=======================================================================
-|Name |Description
-|`df` |The default field to use when no field prefix is defined within the
-query.
-
-|`analyzer` |The analyzer name to be used when analyzing the query string.
-
-|`default_operator` |The default operator to be used, can be `AND` or
-`OR`. Defaults to `OR`.
-
-|`lenient` |If set to true will cause format based failures (like
-providing text to a numeric field) to be ignored. Defaults to false.
-
-|`analyze_wildcard` |Should wildcard and prefix queries be analyzed or
-not. Defaults to `false`.
-
-|`terminate_after` |The maximum count for each shard, upon
-reaching which the query execution will terminate early.
-If set, the response will have a boolean field `terminated_early` to
-indicate whether the query execution has actually terminated_early.
-Defaults to no terminate_after.
-|=======================================================================
-
-[float]
-==== Request Body
-
-The count can use the <<query-dsl,Query DSL>> within
-its body in order to express the query that should be executed. The body
-content can also be passed as a REST parameter named `source`.
-
-Both HTTP GET and HTTP POST can be used to execute count with body.
-Since not all clients support GET with body, POST is allowed as well.
-
-[float]
-==== Distributed
-
-The count operation is broadcast across all shards. For each shard id
-group, a replica is chosen and executed against it. This means that
-replicas increase the scalability of count.
-
-[float]
-==== Routing
-
-The routing value (a comma separated list of the routing values) can be
-specified to control which shards the count request will be executed on.