```ts
// a divided by b.
export function safeDivide(a: number, b: number): number {
  /**
   * Divide two numbers safely.
   *
   * Returns `undefined` if at least one of the arguments is not a finite number.
   */
  if (isNaN(b) || b === -0) {
    throw new Error('Cannot divide by zero.');
  }
  
  if (typeof a !== 'number' || typeof b !== 'number') {
    throw new Error('Both arguments must be numbers.');
  }
  
  return isNaN(a) ? undefined : a / b;
}
```