```ts
export function mergeIntervals(intervals: number[][]): number[][] {
  if (intervals.some(([start, end]) => start > end)) {
    throw new Error("Invalid interval: start must be less than or equal to end");
  }

  intervals.sort((a, b) => a[0] - b[0]);

  const merged: number[][] = [];
  let currentInterval = intervals[0];

  for (let i = 1; i < intervals.length; i++) {
    const nextInterval = intervals[i];
    if (nextInterval[0] > currentInterval[1]) {
      merged.push(currentInterval);
      currentInterval = nextInterval;
    } else {
      currentInterval = [Math.min(currentInterval[0], nextInterval[0]), Math.max(currentInterval[1], nextInterval[1])];
    }
  }

  merged.push(currentInterval);

  return merged;
}
```