“And our tax rate expectation for the year remains in the mid-teens.”

In context

“s year. As I mentioned earlier, we have been accelerating our productivity initiatives, which is fueling our flywheel for growth and margin expansion. We are early in this client zero journey on scaling AI internally to reinvent the way we work and are excited about the significant opportunities ahead of us. We exited 2024 at $3.5 billion of annual run rate savings achieved. And we now believe we can achieve approximately $4.5 billion in annual run rate savings by the end of 2025. Through the first half of the year, our operating pretax margins have expanded by 90 basis points, ahead of our model despite dilution from HashiCorp. Given this performance and increased productivity savings, we are raising our expectations for IBM's full year operating pretax margin to expand by about 1 point. And our tax rate expectation for the year remains in the mid-teens. As always, the timing of discrete items can cause the rate to vary within the year. For the third quarter, we are comfortable with consensus estimates for revenue and profitability. Let me conclude by saying we are pleased with our first half performance, highlighting the resiliency of our business model, disciplined strategy and growth opportunities ahead of us. Arvind and I are now happy to take your questions. Olympia, let's get started. Olympia McNerney: Global Head of Investor Relations Thank you, Jim. Before we begin the Q&A, I'd like to mention a couple of items. First, supplemental information is provided at the end of the presentation. And then second, as always, I'd ask you to refrain from multipart questions. Operator, let's please open it up for questions. Operator: [Operator”