$ perl fract.pl 1.61803398874989
2/1             err=0.38196601125011
3/2             err=0.11803398874989
5/3             err=0.0486326779167767
8/5             err=0.0180339887498899
13/8            err=0.00696601125010998
21/13           err=0.0026493733652746
34/21           err=0.00101363029772905
55/34           err=0.00038692992636058
89/55           err=0.000147829431928148
144/89          err=5.6460660002422e-05
233/144         err=2.15668056655627e-05
377/233         err=8.23767692859079e-06
610/377         err=3.14652862454246e-06
987/610         err=1.20186464402927e-06
1597/987                err=4.59071791913956e-07
2584/1597               err=1.75349764708344e-07
4181/2584               err=6.69776640815911e-08
6765/4181               err=2.55831835715981e-08
10946/6765              err=9.77191327855564e-09
17711/10946             err=3.73253206120694e-09
28657/17711             err=1.42570710792711e-09
46368/28657             err=5.44565059712454e-10
75025/46368             err=2.08012052027584e-10
121393/75025            err=7.94468935083614e-11
196418/121393           err=3.03526093148321e-11
317811/196418           err=1.15869536188029e-11
514229/317811           err=4.43245440351347e-12
832040/514229           err=1.68642877440561e-12
1346269/832040          err=6.50812737035267e-13
2178309/1346269         err=2.41806574763359e-13
3524578/2178309         err=9.9031893796564e-14
5702887/3524578         err=3.10862446895044e-14
9227465/5702887         err=1.86517468137026e-14
14930352/9227465                err=4.44089209850063e-16