Function pureFunctionOfTrigQ

src/compute-engine/rubi/rubi-utils.ts:3452–3462

PureFunctionOf{Sin,Cos,Tan}Q: every trig subterm of argument `v` has a head * in `allowed`, and no bare `x` appears (IntegrationUtilityFunctions.m).

(
  u: Expression,
  v: Expression,
  x: string,
  allowed: Set<string>
)

// carries x (the common trig case `cos/cos`, `sec²/sec²` reduces in canonical
// form, so Simplify is skipped entirely).
// ---------------------------------------------------------------------------

/** Rubi EasyDQ — conservative: true iff y is cheap to differentiate wrt x.
 * Fail-closed (unknown shapes → false), which only makes DerivativeDivides
 * decline a binding; it never produces a wrong quotient. */
function easyDQ(u: Expression, x: string): boolean {
  if (!u.ops || u.ops.length === 0 || !u.has(x)) return true; // atom / x-free
  const op = u.operator;
  if (CALCULUS_FNS.has(op)) return false;
  if (op === 'Power') return !u.ops[1].has(x) && easyDQ(u.ops[0], x);
  if (op === 'Divide') return u.ops.every((o) => easyDQ(o, x));
  if (u.ops.length === 1) return easyDQ(u.ops[0], x); // Sin[v], Cos[v], Negate…
  if (op === 'Multiply') {
    const nonfree = u.ops.filter((o) => o.has(x));