```ts
/**
 * Splits `a` by `b`. Throws Error if `b` is zero or if either argument is not a finite number.
 */
export function safeDivide(a: number, b: number): number {
  if (!Number.isFinite(a) || !Number.isFinite(b)) {
    throw new Error('Both arguments must be finite numbers.');
  }
  if (b === 0) {
    throw new Error('Cannot divide by zero.');
  }
  return a / b;
}
```