  We study the $z\approx3.5$ intergalactic medium (IGM) by comparing new,
high-quality absorption spectra of eight QSOs with $\langle z_{\rm QSO}
\rangle=3.75$, to virtual observations of the EAGLE cosmological hydrodynamical
simulations. We employ the pixel optical depth method and uncover strong
correlations between various combinations of HI, CIII, CIV, SiIII, SiIV, and
OVI. We find good agreement between many of the simulated and observed
correlations, including OVI(HI). However, the observed median optical depths
for the CIV(HI) and SiIV(HI) relations are higher than those measured from the
mock spectra. The discrepancy increases from up to $\approx0.1$ dex at
$\tau_{\rm HI}=1$ to $\approx1$ dex at $\tau_{\rm HI}=10^2$, where we are
likely probing dense regions at small galactocentric distances. As possible
solutions, we invoke (a) models of ionizing radiation softened above 4 Ryd to
account for delayed completion of HeII reionization; (b) simulations run at a
higher resolution; (c) the inclusion of additional line broadening due to
unresolved turbulence; and (d) increased elemental abundancess; however, none
of these factors can fully explain the observed differences. Enhanced
photoionization of HI by local sources, which was not modelled, could offer a
solution. However, the much better agreement with the observed OVI(HI)
relation, which we find probes a hot and likely collisionally-ionized gas
phase, indicates that the simulations are not in tension with the hot phase of
the IGM, and suggests that the simulated outflows may entrain insufficient cool
gas.
