```ts
/** a divided by b. */
export function safeDivide(a: number, b: number): number {
  if (!isFinite(a) || !isFinite(b)) {
    return throw new Error("Both arguments must be finite numbers.");
  }
  if (b === 0 || -b === 0) {
    return throw new Error("Cannot divide by zero.");
  }
  return a / b;
}

function isFinite(value: number): boolean {
  return Number.isFinite(value);
}
```