A soft build in U.S. crude oil stocks was buffered by a report showing domestic well costs have declined, sending oil prices higher early Wednesday.

Crude oil prices plummeted Tuesday as supply-side strains added to concerns emerging before U.S. Federal Reserve Chair Janet Yellen took to the podium to offer a gauge on the health of the nation's economy.

Yellen said crude oil prices earlier this year had been less-than-favorable for broad-based growth, though labor and housing gains were supporting momentum for the United States.

"I anticipate that the overall fallout for the U.S. economy from global market developments since the start of the year will most likely be limited, although this assessment is subject to considerable uncertainty," she added.

Crude oil prices rebounded in response to Yellen's speech and on word of continued builds in U.S. crude oil stockpiles, though gains were far less than reported during the first week of March.

Taken as a whole, both elements were enough to extend a rally into Wednesday morning trading. Brent crude oil gained 1.7 percent to open in New York at $39.82 per barrel. West Texas Intermediate, the U.S. benchmark price for crude oil, gained 2.2 percent to $39.13 per barrel.

Crude oil prices so far this year have moved between lows below $30 per barrel to highs just over $40. Lower crude oil prices are in part behind spending and staffing reductions outlined by major energy companies.

A report from the U.S. Energy Information Administration finds, however, that domestic drilling efficiency has improved since 2012.

"Changes in costs and well parameters, such as the need to drill deeper or longer lateral wells, have affected the onshore oil plays differently in 2015, with recent per-well costs ranging from 7 percent to 22 percent below 2014 levels," it said in a daily report.

A report last week from the International Monetary Fund said oil from shale reserve areas in the United States has been "surprisingly resilient in the face of lower prices."