```ts
/**
 * Divides a by b.
 *
 * @param {number} a - The dividend.
 * @param {number} b - The divisor.
 * @returns {number}
 */
export function safeDivide(a: number, b: number): number {
  if (isNaN(b)) {
    throw new Error('Cannot divide by zero or NaN');
  }

  const finite = !isNaN(b) && isFinite(a);

  if (!finite) {
    throw new Error('Both arguments must be finite numbers.');
  }

  return a / b;
}
```