When Hewlett-Packard Company (HPQ -2.40%) reported mixed quarterly results last week, the corresponding 3% pop in its stock price did not seem to make sense. After all, revenue fell about 7% year-over-year to $25.5 billion, hindered by declines in each of its operating segments. And while adjusted earnings dropped by just a penny per share over the same period to $0.87, keep in mind that figure was helped by repurchase of 19 million shares during the quarter, totaling $659 million. Analysts, for their part, were anticipating lower earnings of $0.86 per share but higher revenue of $25.6 billion.

But the reasons behind the move were more clear after HP management spent roughly an hour with analysts on the subsequent conference call, shedding light on its performance. Here are five crucial insights from the discussion that help explain why the market celebrated these mixed results.

1. On executing with "no distractions"

Turning to our execution, we have made significant progress across a lot of fronts over the past six months, and importantly, we've seen no distractions from running the business. In fact, the go-to-market approach of this company has drastically improved over the past three years, and I see that getting stronger going forward. -- CEO Meg Whitman

Remember, HP is nearing its planned separation into two distinct companies -- one to handle its personal systems and printing segments and another to tackle its enterprise, cloud, software and services divisions -- so investors have been worried about possible distractions stemming from that impending separation. It is encouraging to hear that such distractions are not an issue for the time being, especially when Whitman insisted earlier in the call she is confident that, given the substantial progress they have made, HP will complete the separation by the end of this fiscal year.

2. Industry standard servers are now leading the charge

Industry standard servers had a very strong quarter, growing 17% in constant currency with growth across all regions, driven by strong adoption of our Gen9 portfolio and strength in density-optimized in support of the explosion of big data in the market. -- Whitman

For perspective, this is an interesting shift as the personal systems segment has effectively remained the brightest spot in its quarterly results for the better part of the past year. That is not to say personal systems is now doing poorly -- though segment revenue declined 5%, unit sales actually rose 2% year-over-year including a 19% rise in notebook units. And that, Whitman says, helped the personal systems business continue to "outgrow the overall market and all competitors."

Nonetheless, it is exciting to see this acceleration for industry standard servers, driven by demand for big data which shows no signs of slowing down anytime soon.

3. On expected cost savings, "dis-synergies"

Even at this early stage, each new organization is optimizing for the realities of their markets and unique competitive sets. As we dive deep into the planned organizations, we've identified both dis-synergies required to run separate companies, as well as opportunities to streamline our processes and ultimately improve both cost structures. -- Whitman

Specifically, as CFO Catherine Lesjak elaborated later in the call, HP has now identified "dis-synergies" of $400 million to $450 million associated with the reorganization. These costs will be split roughly equally between the two new companies and are primarily related to required corporate functions such as finance, legal, IT, real estate, and human resources. That said, HP also anticipates that it could reduce operating costs by a gross of up to $1 billion annually, including enough in the near-term to offset over half the dis-synergies in fiscal 2016. Then, starting in fiscal 2017, ongoing cost reduction efforts should more than offset the dis-synergies.

4. A "groundbreaking" new Chinese partnership

[J]ust this morning, we announced a groundbreaking partnership that will bring together HP's Chinese enterprise technology assets and China's prestigious Tsinghua University to create the leading Chinese provider of IT infrastructure. Under the agreement, Tsinghua will purchase a 51% stake in a new business called H3C, comprising our H3C technologies business and HP's China-based server storage and technology services businesses, for approximately $2.3 billion. -- Whitman 

To put that into perspective, this values the H3C business at roughly $4.3 billion. By comparison, HP also closed on its acquisition of Aruba Networks earlier this month for a total consideration of $2.7 billion. But this H3C partnership is arguably even more compelling given the significant market opportunity China represents. 

"In one move," Whitman elaborated, "we have repositioned HP and shifted the entire technology landscape in the critical Chinese market to accelerate our overall performance and better serve our customers and partners."

5. How currencies are still hurting HP

The strength of the U.S. dollar negatively affected our reported revenue. For example, our second quarter revenue declined approximately 7% year-over-year as reported but only 2% in constant currency. In addition, the recent currency movements have enabled our competitors to price very aggressively. For example, aggressive pricing from our Japanese competitors in the printing business, given the weakness of the yen, continued to be a challenge. Finally, the currency movements and the associated repricing affected demand. We managed to offset the currency impact to company level operating profit in Q2 through hedges and repricing. -- Whitman

These currency headwinds mark a continuation of similar challenges HP faced last quarter as well. But again, keep in mind this is simply the cost of doing business as a global company that generates over 65% of its revenue overseas. I feel the need to reiterate, however, that currencies will not always be a headwind going forward and are not indicative of broader problems with the HP business. As long as HP continues to gain share in the international markets where it operates, it should ultimately emerge a stronger company for it.

Combine that long-term thinking with solid execution, accelerating demand for industry standard servers, and encouraging progress toward its business separation, and it is evident this quarter was significantly stronger than the headline numbers implied.