A 52-year-old woman with a history of peptic ulcer disease presents to the emergency department with sudden-onset severe epigastric pain radiating to the back. She is in severe distress, with a rigid, board-like abdomen and rebound tenderness. Her blood pressure is 110/70 mmHg and heart rate is 110 bpm. Plain abdominal radiograph (supine and erect views) shows a large collection of free air under both hemidiaphragms, with the stomach appearing as a large, gas-filled structure. What is the most likely diagnosis?