We study the $zapprox3.5$ 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.
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