I found a function that seems to do the trick. I will leave it here, in case anyone else is looking for the same thing.
add_filter( 'posts_search', 'my_search_is_perfect', 20, 2 );
function my_search_is_perfect( $search, $wp_query ) {
global $wpdb;
if ( empty( $search ) )
return $search;
$q = $wp_query->query_vars;
$n = !empty( $q['exact'] ) ? '' : '%';
$search = $searchand = '';
foreach ( (array) $q['search_terms'] as $term ) {
$term = esc_sql( like_escape( $term ) );
$search .= "{$searchand}($wpdb->posts.post_title REGEXP '[[:<:]]{$term}[[:>:]]') OR ($wpdb->posts.post_content REGEXP '[[:<:]]{$term}[[:>:]]')";
$searchand = ' AND ';
}
if ( ! empty( $search ) ) {
$search = " AND ({$search}) ";
if ( ! is_user_logged_in() )
$search .= " AND ($wpdb->posts.post_password = '') ";
}
return $search;
}