The EIA is out with its month report today, which is much more accurate than the weekly data. This is for April and it showed a 72,000 barrel per day increase to 13.248 million barrels per day, which is the highest since December.
There has clearly been a stall in momentum since this time last year and there is no sign of a big pickup.
On the demand side, product supplied rose 131k bpd in April to 20.0m bpd. That's not great as it's down 0.1% y/y, largely on gasoline.