function updateResults() {
  // Extract expressions from the editor's content.
  const expressions = getExpressions(editor.state.doc.toString());

  // Evaluate and analyze the expressions.
  processedExpressions = processExpressions(expressions);

  // Generate HTML to display the results.
  const resultsHtml = resultsToHTML(processedExpressions);

  // Render the generated HTML in the results container.
  resultsDOM.innerHTML = resultsHtml;
}
Updates the displayed results based on the editor's current content.

@function updateResults
@requires getExpressions, processExpressions, resultsToHTML

@description
1. Extracts expressions from the editor's content.
2. Evaluates and analyzes the expressions.
3. Generates HTML to display the processed results.
4. Renders the generated HTML in the designated results container.