Ratyを使用したレビュー投稿でrateカラムの保存ができない

###Ratyを使用したレビュー投稿でrateカラムの保存ができない

現在RubyonRailsを用いて本の投稿アプリを作成しています。
一通り作成した後で、Ratyでの星評価機能を追加している状態です。

新規投稿後の詳細画面で星評価が表示されず困っています。

以下該当のソースコードです。

####booksコントローラー

ruby
class BooksController < ApplicationController
  before_action :ensure_correct_user, only: [:edit,:update,:destroy]

  def show
    @book = Book.find(params[:id])
    @book_comment = BookComment.new
  end

  def index
    @books = Book.all
    @book = Book.new
  end

  def create
    @book = Book.new(book_params)
    @book.user_id = current_user.id
    if @book.save
      redirect_to book_path(@book), notice: "You have created book successfully."
    else
      @books = Book.all
      render 'index'
    end
  end

  def edit
  end

  def update
    if @book.update(book_params)
      redirect_to book_path(@book), notice: "You have updated book successfully."
    else
      render "edit"
    end
  end

  def destroy
    @book.destroy
    redirect_to books_path
  end

  private

  def book_params
    params.require(:book).permit(:title,:body)
  end

  def ensure_correct_user
    @book = Book.find(params[:id])
    unless @book.user_id == current_user.id
      redirect_to books_path
    end
  end
end

####schemaファイル

ruby
# This file is auto-generated from the current state of the database. Instead
# of editing this file, please use the migrations feature of Active Record to
# incrementally modify your database, and then regenerate this schema definition.
#
# Note that this schema.rb definition is the authoritative source for your
# database schema. If you need to create the application database on another
# system, you should be using db:schema:load, not running all the migrations
# from scratch. The latter is a flawed and unsustainable approach (the more migrations
# you'll amass, the slower it'll run and the greater likelihood for issues).
#
# It's strongly recommended that you check this file into your version control system.

ActiveRecord::Schema.define(version: 2021_12_14_040244) do

  create_table "book_comments", force: :cascade do |t|
    t.integer "book_id"
    t.integer "user_id"
    t.text "comment"
    t.datetime "created_at", null: false
    t.datetime "updated_at", null: false
  end

  create_table "books", force: :cascade do |t|
    t.string "title"
    t.text "body"
    t.integer "user_id"
    t.datetime "created_at", null: false
    t.datetime "updated_at", null: false
    t.float "rate"
  end

  create_table "favorites", force: :cascade do |t|
    t.integer "user_id"
    t.integer "book_id"
    t.datetime "created_at", null: false
    t.datetime "updated_at", null: false
  end

  create_table "relationships", force: :cascade do |t|
    t.integer "follower_id"
    t.integer "followed_id"
    t.datetime "created_at", null: false
    t.datetime "updated_at", null: false
  end

  create_table "users", force: :cascade do |t|
    t.string "email", default: "", null: false
    t.string "encrypted_password", default: "", null: false
    t.string "reset_password_token"
    t.datetime "reset_password_sent_at"
    t.datetime "remember_created_at"
    t.string "name"
    t.text "introduction"
    t.string "profile_image_id"
    t.datetime "created_at", null: false
    t.datetime "updated_at", null: false
    t.index ["email"], name: "index_users_on_email", unique: true
    t.index ["reset_password_token"], name: "index_users_on_reset_password_token", unique: true
  end

end

####投稿フォーム

html
app/views/book/_form.html.erb
<%= form_with model:book,local: true do |f| %>
  <div class="form-group">
    <%= f.label :title %>
    <%= f.text_field :title, class: 'form-control book_title' %>
  </div>
  <div class="form-group">
    <%= f.label :opinion %>
    <%= f.text_area :body, class: 'form-control book_body' %>
  </div>
  <div class="form-group" id="star">
    <%= f.label :rate %>
    <%= f.hidden_field :rate, id: :review_star %>
  </div>
  <script>
    $('#star').raty({
      size: 36,
      starOff: '<%= asset_path('star-off.png') %>',
      starOn: '<%= asset_path('star-on.png') %>',
      starHalf: '<%= asset_path('star-half.png') %>',
      scoreName: 'book[rate]',
      half: true,
    });
  </script>
  <div class="form-group">
    <%= f.submit class: 'btn btn-success' %>
  </div>
<% end %>

####投稿詳細ページ

html
<div class='container'>
  <div class='row'>
    <div class='col-md-3'>
      <h2>User info</h2>
      <%= render 'users/info', user: @book.user %>
      <h2 class="mt-3">New book</h2>
      <%= render 'books/form', book: Book.new %>
    </div>
    <div class='col-md-8 offset-md-1'>
  		<h2>Book detail</h2>
  		<table class='table'>
  		  <tr id="book_<%= @book.id %>">
  		    <td><%= link_to user_path(@book.user) do %>
            <%= attachment_image_tag(@book.user, :profile_image, :fill, 100, 100, fallback: "no-image-icon.jpg") %><br>
            <%= @book.user.name %>
            <% end %>
          </td>
          <td><%= link_to @book.title, book_path(@book) %></td>
          <td><%= @book.body %></td>
          <td class="favorite-btn"><%= render "favorites/favorite-btn",book: @book %></td>
          <td class="comment-count"><p>コメント数: <%= @book.book_comments.count %></p></td>
          <td id="star-rate-<%= @book.id %>"></td>
          <script>
            $('#star-rate-<%= @book.id %>').raty({
              size: 36,
              starOff: '<%= asset_path('star-off.png') %>',
              starOn: '<%= asset_path('star-on.png') %>',
              starHalf: '<%= asset_path('star-half.png') %>',
              half: true,
              readOnly: true,
              score: <%= @book.rate %>,
            });
            </script>
          <%  if @book.user == current_user %>
            <td><%= link_to 'Edit', edit_book_path(@book), class: "btn btn-sm btn-success edit_book_#{@book.id}" %></td>
            <td><%= link_to 'Destroy', book_path(@book), method: :delete, data: { confirm: '本当に消しますか？' }, class: "btn btn-sm btn-danger destroy_book_#{@book.id}"%></td>
          <% end %>
        </tr>
      </table>
      <table class="book_comments">
        <%= render "book_comments/index",book: @book %>
      </table>
      <%= form_with model:[@book,@book_comment], remote:true do |f| %>
        <%= f.text_area :comment,size: "90x5" %><br>
        <%= f.submit "送信" %>
      <% end %>
    </div>
  </div>
</div>

試したこと

pry-byebugを使用し投稿後の@bookを確認してみたところ、rateカラムがnilで保存されていないことがわかりました。
しかしテーブル内ではfloat型として定義しており、
投稿フォーム内のscriptタグ内ではscoreName: 'book[rate]',と記述しているので、どこに問題があるかわからないです。

ご教授のほど、よろしくお願いいたします。