ES function_score troubles with filtered query_string query

gistfile1.json

// Final working version
{
   "query":{
      "filtered":{
         "query":{
            "function_score":{
               "query":{
                  "query_string":{
                     "query":"this is a cool search",
                     "fields":[
                        "title",
                        "text"
                     ]
                  }
               },
               "script_score":{
                  "script":"_score * log(doc['my_field'].value+1)"
               }
            }
         },
         "filter":{
            "bool":{
               "must":[
                  {
                     "term":{
                        "account":1
                     }
                  }
               ],
               "must_not":[
                  {
                     "terms":{
                        "state":[
                           "spam",
                           "deleted"
                        ]
                     }
                  }
               ]
            }
         }
      }
   }
}



// Original question:

// Working function_score query, but not the filtered query_string search I need
{
   "query":{
      "function_score":{
         "query":{
            "match_all":{

            }
         },
         "script_score":{
            "script":"_score * log(doc['my_field'].value+1)"
         }
      }
   }
}

// Working filtered query_string search but not using the function_score like I need
{
   "query":{
      "filtered":{
         "query":{
            "query_string":{
               "query":"this is a cool search",
               "fields":[
                  "title",
                  "text"
               ]
            }
         },
         "filter":{
            "bool":{
               "must":[
                  {
                     "term":{
                        "account":1
                     }
                  }
               ],
               "must_not":[
                  {
                     "terms":{
                        "state":["spam","deleted"]
                     }
                  }
               ]
            }
         }
      }
   }
}




//
// A couple failed attempts
//



// Returns: "[filtered] query does not support [function_score]"
{
   "query":{
      "filtered":{
        "function_score":{
            "query":{
               "query_string":{
                  "query":"this is a cool search",
                  "fields":[
                     "title",
                     "text"
                  ]
               }
            },
            "filter":{
               "bool":{
                  "must":[
                     {
                        "term":{
                           "account":1
                        }
                     }
                  ],
                  "must_not":[
                     {
                        "terms":{
                           "state":["spam","deleted"]
                        }
                     }
                  ]
               }
            }
         },
         "script_score":{
            "script":"_score * log(doc['my_field'].value+1)"
         }
      }
   }
}


// Returns: "No function with the name [filtered] is registered"
{
   "query":{
     "function_score":{
        "filtered":{
            "query":{
               "query_string":{
                  "query":"this is a cool search",
                  "fields":[
                     "title",
                     "text"
                  ]
               }
            },
            "filter":{
               "bool":{
                  "must":[
                     {
                        "term":{
                           "account":1
                        }
                     }
                  ],
                  "must_not":[
                     {
                        "terms":{
                           "state":["spam","deleted"]
                        }
                     }
                  ]
               }
            }
         }
      },
      "script_score":{
         "script":"_score * log(doc['my_field'].value+1)"
      }
   }
}

// Returns: "[filtered] query does not support [function_score]]"
{
   "query":{
      "filtered":{
        "function_score":{
            "query":{
               "query_string":{
                  "query":"this is a cool search",
                  "fields":[
                     "title",
                     "text"
                  ]
               }
            },
            "script_score":{
               "script":"_score * log(doc['my_field'].value+1)"
            }
         },
         "filter":{
            "bool":{
               "must":[
                  {
                     "term":{
                        "account":1
                     }
                  }
               ],
               "must_not":[
                  {
                     "terms":{
                        "state":["spam","deleted"]
                     }
                  }
               ]
            }
         }
      }
   }
}