```ts
/**
 * a divided by b. Throws Error on zero divisor or non-finite numbers.
 *
 * @param {number} a - The numerator.
 * @param {number} b - The denominator.
 * @returns {number} The result of the division.
 */
export function safeDivide(a: number, b: number): number {
  if (isNaN(a) || isNaN(b)) {
    throw new Error("Both arguments must be finite numbers.");
  }
  if (b === 0) {
    throw new Error("Division by zero is not allowed.");
  }
  return a / b;
}
```