```ts
/** a divided by b, safe from zero division and non-numeric inputs. */
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 || b === -0) {
    throw new Error("Cannot divide by zero.");
  }
  return a / b;
}
```