> Are you serious? This should be 1, max 2 instructions, with no branches and no memory use.

Sure. ---> One could add two fixnums and get a bignum.

    CL-USER 31 > (fixnump (+ MOST-POSITIVE-FIXNUM MOST-POSITIVE-FIXNUM))
    NIL

As you see here, adding two fixnums can have a result which is not a fixnum.

Yes, Common Lisp does by default determine whether to return a bignum or fixnum.

The machine code you've shown takes care of that.

Let's see what the SBCL file compiler says:

    CL-USER> (compile-file "/tmp/test.lisp")
    ; compiling file "/tmp/test.lisp" (written 11 JUL 2024 10:02:04 PM):

    ; file: /tmp/test.lisp
    ; in: DEFUN FX-ADD
    ;     (DEFUN FX-ADD (X Y)
    ;       (DECLARE (OPTIMIZE (SPEED 3) (SAFETY 0) (DEBUG 0))
    ;                (TYPE FIXNUM X Y))
    ;       (+ X Y))
    ; --> SB-IMPL::%DEFUN SB-IMPL::%DEFUN SB-INT:NAMED-LAMBDA 
    ; ==>
    ;   #'(SB-INT:NAMED-LAMBDA FX-ADD
    ;         (X Y)
    ;       (DECLARE (SB-C::TOP-LEVEL-FORM))
    ;       (DECLARE (OPTIMIZE (SPEED 3) (SAFETY 0) (DEBUG 0))
    ;                (TYPE FIXNUM X Y))
    ;       (BLOCK FX-ADD (+ X Y)))
    ; 
    ; note: doing signed word to integer coercion (cost 20) to "<return value>"
    ; 
    ; compilation unit finished
    ;   printed 1 note


    ; wrote /tmp/test.fasl
    ; compilation finished in 0:00:00.031
    #P"/private/tmp/test.fasl"
    NIL
    NIL

Well, the SBCL compiler does tell us that it can't optimize that. Isn't that nice?!

If you want a fixnum to fixnum addition, then you need to tell the compiler that the result should be a fixnum.

   (the fixnum (+ x y))

Adding above and now the compiler no longer gives that efficiency hint:

    CL-USER> (compile-file "/tmp/test.lisp")
    ; compiling file "/tmp/test.lisp" (written 11 JUL 2024 10:03:11 PM):

    ; wrote /tmp/test.fasl
    ; compilation finished in 0:00:00.037
    #P"/private/tmp/test.fasl"
    NIL
    NIL