We use cosmology-independent measurements of the expansion history in the redshift range 0.1≲z<1.20.1≲z<1.2 and compare them with the Cosmic Microwave Background-derived expansion history predictions. The motivation is to investigate if the tension between the local (cosmology independent) Hubble constant H0H0 value and the Planck-derived H0H0 is also present at other redshifts. We conclude that there is no tension between Planck and cosmology independent-measurements of the Hubble parameter H(z)H(z) at 0.1≲z<1.20.1≲z<1.2 for the ΛΛCDM model (odds of tension are only 1:15, statistically not significant). Considering extensions of the ΛΛCDM model does not improve these odds (actually makes them worse), thus favouring the simpler model over its extensions. On the other hand the H(z)H(z) data are also not in tension with the local H0H0 measurements but the combination of all three data-sets shows a highly significant tension (odds ∼1:400). Thus the new data deepen the mystery of the mismatch between Planck and local H0H0 measurements, and cannot univocally determine whether it is an effect localised at a particular redshift. Having said this, we find that assuming the NGC4258 maser distance as the correct anchor for H0H0, brings the odds to comfortable values. Further, using only the expansion history measurements we constrain, within the ΛΛCDM model, H0=68.5±3.5H0=68.5±3.5 and Ωm=0.32±0.05Ωm=0.32±0.05 (at 68% confidence) without relying on any CMB prior. We also address the question of how smooth the expansion history of the Universe is given the cosmology independent data and conclude that there is no evidence for deviations from smoothness on the expansion history, neither variations with time in the value of the equation of state of dark energy.