 ```ts
export function mergeIntervals(intervals: number[][]): number[][] {
    if (!Array.isArray(intervals) || intervals.some(interval => !Array.isArray(interval) || interval.length !== 2)) {
        throw new Error("Invalid input: intervals must be an array of exactly two numbers.");
    }

    if (intervals.some(([start, end]) => start > end)) {
        throw new Error("Invalid interval found: a start time cannot be greater than its end time.");
    }

    // Sort intervals by their start times
    const sortedIntervals = [...intervals].sort((a, b) => a[0] - b[0]);

    const mergedIntervals: number[][] = [];
    let currentInterval = sortedIntervals[0];

    for (let i = 1; i < sortedIntervals.length; i++) {
        const nextInterval = sortedIntervals[i];

        if (currentInterval[1] >= nextInterval[0]) {
            // If the current interval overlaps with the next, merge them
            currentInterval[1] = Math.max(currentInterval[1], nextInterval[1]);
        } else {
            // If they don't overlap, push the current interval to the result and move to the next
            mergedIntervals.push([...currentInterval]);
            currentInterval = nextInterval;
        }
    }

    // Push the last interval after the loop ends
    if (currentInterval) {
        mergedIntervals.push([...currentInterval]);
    }

    return mergedIntervals;
}
```