  The $\mathrm{^2H}(d,p)\mathrm{^3H}$ bare nucleus astrophysical S(E) factor
has been measured indirectly at energies from about 500 keV down to several keV
by means of the Trojan-horse method applied to the quasi-free process
$\mathrm{^2H({}^6Li},pt)\mathrm{^4He}$ induced at the lithium beam energy of 11
and 9.5 MeV, which makes the virtual binary process incident energy $\mathrm
{E}_{dd}^{qf}$ go much closer to the zero-quasi-free-energy point than that in
the previous similar experiment. The obtained results are compared with direct
data as well as with previous indirect investigation of the same binary
reactions. It shows that the precision of S(E) data in low energy range
extracted via the same Trojan horse nucleus ($\mathrm{^6Li}=(d \oplus \alpha)$
) becomes better when the incident energy decreases from high value down to the
zero-quasi-free-energy point. The very good agreement between data extracted
from different Trojan horse nucleus ($\mathrm{^6Li}=(d \oplus \alpha)$ vs.
$\mathrm{^3He}=(d \oplus p)$) gives a strong updated test for the independence
of the binary indirect cross section on the chosen Trojan horse nucleus at low
energies.
