Use a compound "and" in ES - elasticsearch

Question

Upon trying to emulate the following expression in ES
expr1 && expr2 && expr3
And I came up with this
curl -X GET "http://localhost:9200/policy_router-2019.12.30/_search?pretty" -H 'Content-Type: application/json' -d'
{
"query": {
"bool": {
"must" : [
{
"range" : { "#timestamp": { "gte": "now-15s", "lte": "now"} }
},
{
"query_string": { "query": "rewriteGateway", "default_field" : "message" }
},
{
"query_string": {"query": "policy-router-summer-snow-5555" ,"default_field" : "host" }
}
]
}
}
}'
But, it seems I'm not able to equate what I want, correctly with the above query. i.e every time I run the above query I see the documents which has host value different what I want it to be i.e policy-router-summer-snow-5555 here
I also tried nesting must inside the outer must but that resulted in a syntax error.
I'm failing to understand why does the last query_string expression for the host does not match.
Following is my ES version
{
"name" : "an2FbQZ",
"cluster_name" : "elasticsearch",
"cluster_uuid" : "gIk5QPI3Rb6NPckeCRaUqQ",
"version" : {
"number" : "5.5.2",
"build_hash" : "b2f0c09",
"build_date" : "2017-08-14T12:33:14.154Z",
"build_snapshot" : false,
"lucene_version" : "6.6.0"
},
"tagline" : "You Know, for Search"
}
Following is how my document looks like (this is one of the documents returned for the above query, it can be seen clearly that the host does not match)
{
"_index" : "policy_router-2019.12.31",
"_type" : "policy_router",
"_id" : "AW9aG7_1tIiuv3oe07ZO",
"_score" : 4.6003995,
"_source" : {
"severity" : "INFO",
"input" : "udp",
"#timestamp" : "2019-12-31T03:59:25.107Z",
"#version" : "1",
"host" : "policy-router-proud-cherry-2098",
"message" : "2019-12-31 03:59:25.107111 I [PolicyRouter::Push] PolicyRouter -- PR -> LA ... rewrite gateway ... ",
"type" : "policy_router"
}
}```
Any guidance here from ES expert.

Answer 1

Try this query along with your field's name and value.
{
"query": {
"bool": {
"must": [
{
"range": {
"FIELD": {
"gte": 10,
"lte": 20
}
}
},
{
"match_phrase": {
"FIELD": "PHRASE"
}
},
{
"match_phrase": {
"FIELD": "PHRASE"
}
}
]
}
}
}