Can the Angular $injector be decorated with $provide.decorator?

Perhaps this is a terrible idea, but if it is then please tell me why and then pretend that it's an academic exercise that won't see the light of day in production.

I'd like to add some logic to the Angular $injector service, to monitor when certain services are injected into other services. Since it seems that Angular provides a mechanism for decorating services, I thought this would be the way to go. However, the following code throws an error.

(function () {
    'use strict';

    var app = angular.module('app');

    app.config(['$provide', function ($provide) {
        $provide.decorator('$injector', ['$log', '$delegate', addLoggingToInjector]);
    }]);

    function addLoggingToInjector($log, $delegate) {
        var baseInstantiate = $delegate.instantiate;
        var baseInvoke = $delegate.invoke;

        $delegate.instantiate = function (type, locals) {
            // $log.debug('Calling $injector.instantiate');

            baseInstantiate(type, locals);
        };

        $delegate.invoke = function (fn, self, locals) {
            // $log.debug('Calling $injector.invoke');

            baseInvoke(fn, self, locals);
        };

        return $delegate;
    };
})();

The specific error is:

Uncaught Error: [$injector:modulerr] Failed to instantiate module app due to: Error: [$injector:unpr] Unknown provider: $injectorProvider