NEW YORK (TheStreet) -- Stocks added to session highs Tuesday afternoon on building optimism of a Greece debt resolution ahead of a meeting of eurozone leaders in Brussels on Wednesday. It was a bumpy trading day though as optimism over the eurozone battled for attention against an energy sector selloff after the prospect of even lower oil prices became a possibility.

The S&P 500 was up 1.1%, the Dow Jones Industrial Average added 0.85% and the Nasdaq gained 1.4%.

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"It's the uncertainty," said David O'Malley, CEO of Penn Mutual Asset Management, on volatility surrounding Greece's debt talks. "It starts to intertwine with all the rest of the uncertainty going on, whether it's talks of a cease-fire in Ukraine, the deflationary issues in Europe, the continued fear of global terrorism after the events in France. All those things have had the markets on edge to start 2015. We've had a very choppy market up to this point.

Most European markets rose as the new Greek government reiterated its commitment to finding a resolution to the debt talks with its creditors. Finance Minister Yanis Varoufakis proposed that Greece will adopt 70% of reforms outlined in the current bailout agreement, a compromise the country hopes will provide a resolution at a meeting of eurozone finance ministers in Brussels on Wednesday.

Oil prices were backing off from their rally after the International Energy Agency warned of a continuing supply glut in global inventories.

"Despite expectations of tightening balances by end-2015, downward market pressures may not have run their course just yet," the organization said in a monthly report.

Citi analysts on Monday warned the current bounce in prices could be short-lived. In a note, analysts said a meaningful pullback in oil production isn't likely until the third quarter, and until then oil prices could crater to as low as $20 a barrel. West Texas Intermediate was trading down 5.1% to $50.16 a barrel on Tuesday.

Major oil companies including Exxon Mobil (XOM) , Chevron (CVX) , and BP (BP) were all trading lower.

Halliburton (HAL) , already lower on the day's plunge in oil prices, said it would cut at least 5,000 jobs, or between 6.5% and 8% of its workforce. The oil company said the decision was due to the slump in oil prices and was separate from its planned acquisition of Baker Huges (BHI) . Shares were down 3%. 

December's JOLTS survey showed further signs of a strengthening job market. The measure, closely watched by Federal Reserve Chair Janet Yellen, reported 5 million job openings over the month, the highest reading in almost 14 years. The Fed will release the minutes of its January meeting in a week. 

Gold prices slid as the dollar strengthened and stocks rallied. COMEX gold prices fell 0.68% to $1,233.10 a pound. The U.S. dollar gained more than 1% against the Canadian dollar, 0.68% against the Japanese Yen, and 0.25% against the British pound. 

Earnings season continued to beat analysts' expectations on Tuesday. Coca-Cola (KO) shares added 3.1% as quarterly adjusted earnings of 44 cents a share narrowly beat analysts' estimates and revenue wasn't hit as hard by currency headwinds as expected. Starwood Hotels (HOT) jumped 7.3% as quarterly earnings of 97 cents a share beat analysts' estimates by 21 cents. Revenue of $1.49 billion came in just shy of expectations.

CVS (CVS) was gaining after reporting a 13% jump in fourth-quarter revenue, driven by sales of more than 20% in its pharmacy segment. Adjusted earnings narrowly beat expectations. Shares were up 2.2%.

"After a slow start, the fourth quarter 2014 earnings season staged an impressive comeback," said Burt White, chief investment officer for LPL Financial. "On track for near 7% year-over-year earnings growth, despite the negative impact of the significant drop in oil and strong U.S. dollar, we consider this earnings season -- with its highlights and lowlights --  a good one overall."

HSBC (HSBC) was down another 1.6%, following on from a 1.5% decline on Monday. The bank is under investigation for lax compliance at its Swiss subsidiary that allowed customers to evade taxes and conceal assets.

Similarly, UBS (UBS) slipped nearly 3% after disclosing another tax investigation into some of its U.S. operations involving wealthy customers. The bank also warned that a surge in the Swiss franc could have a potential impact on profit.

Aeropostale (ARO) spiked 16.1% after narrowing its expected fourth-quarter loss to 1 cent to 6 cents a share. The teen retailer had previously expected a loss as deep as 25 cents to 31 cents a share.

Qualcomm (QCOM) added 4.8% after improving its fiscal 2015 guidance at the low end, tightening earnings guidance to at least $4.85 a share from a previous $4.75 a share. China fined Qualcomm 6 billion yuan ($975 million) in an anti-monopoly case.

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--Written by Keris Alison Lahiff in New York.