Table 1.

Run times of the isomer enumerator for alkane isomers

Molecule	$n_{\text{consti}}$	$n_{\text{spatial}}$	$t_{\text{consti}}$ [s]		$t_{\text{spatial}}$ [s]
			No output	SMILES	No output	SMILES
${\text{C}}_1{\text{H}}_4$	1	1	< 0.01	< 0.01	< 0.01	< 0.01
${\text{C}}_2{\text{H}}_6$	1	1	< 0.01	0.01	< 0.01	0.01
${\text{C}}_3{\text{H}}_8$	1	1	< 0.01	< 0.01	< 0.01	< 0.01
${\text{C}}_4{\text{H}}_{10}$	2	2	< 0.01	< 0.01	< 0.01	< 0.01
${\text{C}}_5{\text{H}}_{12}$	3	3	< 0.01	0.01	< 0.01	< 0.01
${\text{C}}_6{\text{H}}_{14}$	5	5	< 0.01	< 0.01	< 0.01	< 0.01
${\text{C}}_7{\text{H}}_{16}$	9	11	< 0.01	< 0.01	< 0.01	< 0.01
${\text{C}}_8{\text{H}}_{18}$	18	24	< 0.01	< 0.01	< 0.01	< 0.01
${\text{C}}_9{\text{H}}_{20}$	35	55	< 0.01	< 0.01	< 0.01	< 0.01
${\text{C}}_{10}{\text{H}}_{22}$	75	136	< 0.01	< 0.01	< 0.01	< 0.01
${\text{C}}_{11}{\text{H}}_{24}$	159	345	< 0.01	0.01	< 0.01	0.01
${\text{C}}_{12}{\text{H}}_{26}$	355	900	< 0.01	0.01	0.01	0.02
${\text{C}}_{13}{\text{H}}_{28}$	802	2412	0.02	0.03	0.03	0.05
${\text{C}}_{14}{\text{H}}_{30}$	1858	6563	0.05	0.07	0.08	0.11
${\text{C}}_{15}{\text{H}}_{32}$	4347	18127	0.13	0.18	0.17	0.31
${\text{C}}_{16}{\text{H}}_{34}$	10359	50699	0.31	0.40	0.48	0.70
${\text{C}}_{17}{\text{H}}_{36}$	24894	143255	0.93	1.16	1.35	2.48
${\text{C}}_{18}{\text{H}}_{38}$	60523	408429	2.74	3.17	4.02	9.86
${\text{C}}_{19}{\text{H}}_{40}$	148284	1173770	8.22	9.37	11.70	28.48
${\text{C}}_{20}{\text{H}}_{42}$	366319	3396844	25.55	33.87	35.33	99.87
${\text{C}}_{21}{\text{H}}_{v44}$	910726	9892302	79.41	104.05	107.88	280.27
${\text{C}}_{22}{\text{H}}_{46}$	2278658	28972080	253.57	273.27	334.91	869.78
${\text{C}}_{23}{\text{H}}_{48}$	5731580	85289390	834.42	927.93	1060.18	1338.33
${\text{C}}_{24}{\text{H}}_{50}$	14490245	252260276	2895.93	2997.59	3649.41	4545.92
${\text{C}}_{25}{\text{H}}_{52}$	36797588	749329719	10040.19	10455.26	11309.32	13179.80

The table shows the number $n_{\text{consti}}$ of constitutional isomers and the number $n_{\text{spatial}}$ of spatial isomers of the straight-chain alkanes from ${\text{C}}_1{\text{H}}_4$ to ${\text{C}}_{24}{\text{H}}_{50}$, as well as the wall-clock time spent on their enumeration. The time $t_{\text{consti}}$ is the wall-clock time in seconds needed to enumerate the constitutional isomers, and the time $t_{\text{spatial}}$ is the wall-clock time in seconds needed to enumerate the spatial isomers. The elapsed wall-clock time is reported both for the case when no output is generated as well as the case when the SMILES strings of the isomers are reported. All calculations were performed on AMD EPYC 7763 CPUs of the ETH Zürich Euler cluster [40] and averaged over five runs. The results are illustrated graphically in Fig. 14