how to execute cmd in ansible and subtract a number to it

I am trying to retrieve the number of cores using nproc and then subtract 2 from it and assign it to a variable.

I tried this

- set_fact:
    num_cores: nproc

- debug:
    msg: " {{ num_cores }}"
  when: num_cores is defined

- set_fact:
    update: "{{ num_cores-2 }}"

The debug prints nproc which tells me it is not executing the cmd nproc but just assigning the string to the variable.
What am I missing?

When you write:

- set_fact:
    some_variable: some_value

You are creating a variable (in this case some_variable) with a string value (some_value). Ansible doesn't know that you actually meant to execute a command.

If you want to store the output of a command in a variable, use the command module and the register option to store the output in a variable:

- name: Get nproc
  command: nproc
  register: num_cores

This creates a variable num_cores that looks like:

"num_cores": {
    "changed": true,
    "cmd": [
        "nproc"
    ],
    "delta": "0:00:00.001626",
    "end": "2023-06-11 23:28:40.015719",
    "failed": false,
    "msg": "",
    "rc": 0,
    "start": "2023-06-11 23:28:40.014093",
    "stderr": "",
    "stderr_lines": [],
    "stdout": "20",
    "stdout_lines": [
        "20"
    ]
}

So the value you want in this example is num_cores.stdout. Rewriting your example, that would look like:

- hosts: localhost
  tasks:
    - name: Get nproc
      command: nproc
      register: num_cores

    - debug:
        msg: "{{ num_cores }}"
      when: num_cores is defined

    # num_cores.stdout has the value we want, but it's
    # a string, so if we're going to use it in a math
    # expression we need to convert it to an int first.
    - set_fact:
        update: "{{ num_cores.stdout|int - 2 }}"

    - debug:
        msg: "{{ update }}"

Which produces:

TASK [Get nproc] ****************************************************************************************
changed: [localhost]

TASK [debug] ********************************************************************************************
ok: [localhost] => {
    "msg": {
        "changed": true,
        "cmd": [
            "nproc"
        ],
        "delta": "0:00:00.001601",
        "end": "2023-06-11 23:31:02.646133",
        "failed": false,
        "msg": "",
        "rc": 0,
        "start": "2023-06-11 23:31:02.644532",
        "stderr": "",
        "stderr_lines": [],
        "stdout": "20",
        "stdout_lines": [
            "20"
        ]
    }
}

TASK [set_fact] *****************************************************************************************
ok: [localhost]

TASK [debug] ********************************************************************************************
ok: [localhost] => {
    "msg": "18"
}

Note that Ansible already provides the value of nproc in the variable ansible_processor_nproc (assuming that you have fact gathering enabled, which is the default behavior), so you could reduce your playbook to:

- hosts: localhost
  tasks:
    - set_fact:
        update: "{{ ansible_processor_nproc - 2 }}"

    - debug:
        msg: "{{ update }}"