dᵻɹˈɛktli ɪvˈæljuːˌeɪɾɪŋ ðə lˈeɪbnɪz fˈɔːɹmjʊlə fɹʌmðə dˌɛfɪnˈɪʃən ɹᵻkwˈaɪɚz ˌɑːpɚɹˈeɪʃənz ɪn dʒˈɛnɚɹəl—ðæt ˈɪz, ɐ nˈʌmbɚɹ ʌv ˌɑːpɚɹˈeɪʃənz ˌæsɪmptˈɑːɾɪkli pɹəpˈoːɹʃənəl tə fæktˈoːɹɪəl—bɪkˈʌz ɪz ðə nˈʌmbɚɹ ʌv ˈɔːɹdɚ pˌɜːmjuːtˈeɪʃənz.
Directly evaluating the Leibniz formula from the definition requires   operations in general—that is, a number of operations asymptotically proportional to  factorial—because  is the number of order- permutations.