Preheat oven to 350 degrees. In a mixing bowl, cream butter and sugars. Add vegetable oil, eggs, and vanilla extract; mix well. Sift together flours, baking soda, cream of tartar, and salt; gradually add to the creamed mixture. Stir in nuts and toffee bits. Mix together. Drop onto an ungreased cookie sheet and flatten with a fork. Bake 12 to 14 minutes, or until lightly brown.