```ts
/** Tape-measure spans: parse to inches, format canonically, and add. */

const INCHES: Record<string, number> = { yd: 36, ft: 12, in: 1 };
const ORDER = ["yd", "ft", "in"];

export function parseSpan(text: string): number {
  if (typeof text !== 'string' || !text.trim()) {
    throw new Error("Invalid span text");
  }

  const parts = text.split(/\s+/);
  let total = 0;

  for (const part of parts) {
    const match = part.match(/^(\d+)\s*(yd|ft|in)?$/);
    if (!match) {
      throw new Error("Invalid span text");
    }
    const value = parseInt(match[1], 10);
    if (isNaN(value) || value < 0 || (value === 0 && match[2])) {
      throw new Error("Invalid span text");
    }
    const unit = match[2];
    if (unit) {
      if (!INCHES[unit]) {
        throw new Error("Unknown unit");
      }
      total += value * INCHES[unit];
    } else {
      total += value;
    }
  }

  return total;
}

export function formatSpan(inches: number): string {
  if (!Number.isInteger(inches) || inches < 0) {
    throw new Error("inches must be a non-negative integer");
  }
  if (inches === 0) {
    return "0in";
  }
  const parts: string[] = [];
  const yards = Math.floor(inches / 36);
  const feet = Math.floor((inches % 36) / 12);
  const rest = inches % 12;
  if (yards > 0) {
    parts.push(`${yards}yd`);
  }
  if (feet > 0) {
    parts.push(`${feet}ft`);
  }
  if (rest > 0) {
    parts.push(`${rest}in`);
  }
  return parts.join(" ");
}

export function addSpans(first: string, second: string): string {
  const total = parseSpan(first) + parseSpan(second);
  return formatSpan(total);
}
```