Once I had a performance problem with wordpress website even if it run on a dedicated server.

I suspected that the problem is one of the plugins but I had at least 50 installed :).
In order to see who’s the slowest I opened wp-includes/plugin.php and temprary changed the do_action function to something like this:

function do_action($tag, $arg = '') {
	global $wp_filter, $wp_actions, $merged_filters, $wp_current_filter;

	if ( ! isset($wp_actions) )
		$wp_actions = array();

	if ( ! isset($wp_actions[$tag]) )
		$wp_actions[$tag] = 1;
	else
		++$wp_actions[$tag];

	$wp_current_filter[] = $tag;

	// Do 'all' actions first
	if ( isset($wp_filter['all']) ) {
		$all_args = func_get_args();
		_wp_call_all_hook($all_args);
	}

	if ( !isset($wp_filter[$tag]) ) {
		array_pop($wp_current_filter);
		return;
	}

	$args = array();
	if ( is_array($arg) && 1 == count($arg) && isset($arg[0]) && is_object($arg[0]) ) // array(&$this)
		$args[] =& $arg[0];
	else
		$args[] = $arg;
	for ( $a = 2; $a < func_num_args(); $a++ )
		$args[] = func_get_arg($a);

	// Sort
	if ( !isset( $merged_filters[ $tag ] ) ) {
		ksort($wp_filter[$tag]);
		$merged_filters[ $tag ] = true;
	}

	reset( $wp_filter[ $tag ] );

	do {
		foreach ( (array) current($wp_filter[$tag]) as $the_ ) {
            
			if ( !is_null($the_['function']) ) {
                if($tag=='init') $time_start = microtime(true);
				call_user_func_array($the_['function'], array_slice($args, 0, (int) $the_['accepted_args']));
                if($tag=='init') {
                    $time_end = microtime(true);$time = $time_end - $time_start;
                    echo print_r($the_['function']).' -----  '.$time."
\n";
                }                
            }
        }

	} while ( next($wp_filter[$tag]) !== false );

	array_pop($wp_current_filter);
}

after this you’ll be able to see what plugin is eating the most of your time (after each function call you’ll see execution time in bold)

It’s not a mature script just a quick snippet to have a starting point for someone who runs into the same problem.