The "perfect infinitive" is a compound tense formed using the formula below:

haber + the past participle = perfect infinitive

Let's look at a few examples of use:

verb ser (to be)
the past participle of ser is sido
haber + sido = haber sido

Han de haber sido como las nueve.
It must have been about nine.

verb deber (to owe)
the past participle of deber is debido
haber + debido = haber debido

Le ha de haber debido unos mil pesos.
He must have owed him a thousand pesos.

verb reprobar (to fail)
the past participle of reprobar is reprobado
haber + reprobado = haber reprobado

Mi peor recuerdo es haber reprobado química.
My worst memory is to have failed chemistry.

verb ir (to go)
the past participle of ir is ido
haber + ido = haber ido

Ha de haber ido al centro.
He probably went downtown.

Espero haber terminado antes del mediodía.
I hope to have finished by noon.

Gracias por habernos invitado.
Thank you for having invited us.

Note:
Since the infinitive auxiliary verb is unconjugated, the past infinitive is the same for all subjects. In addition, the past participle is invariable.

Quisiera haber salido... - I want to have departed...
Ella quisiera haber salido... - She wants to have departed...
Quisiéramos haber salido... - We want to have departed...