Function hyperbolicToExp

src/compute-engine/rubi/rubi-utils.ts:3612–3629

TrigToExp for Sinh/Cosh: rewrite Sinh/Cosh[w] → exp form in E^(±w), with the * ½ coefficient DISTRIBUTED into the two terms so a power base stays a pure Add * (CE's Expand will not pull a scalar out of a power base). The argument w is * kept symbolic; all other heads — including the reciprocal

(ce: ComputeEngine, u: Expression)

  x: string,
  st: FoeState
): boolean {
  const ce = base.engine;
  if (st.base === null) {
    st.base = base;
    st.expon = expon;
    return true;
  }
  // tmp = Log[base]·Coeff[expon,x,1] / (Log[$base$]·Coeff[$expon$,x,1]).
  // The exponentials share a common base iff tmp is rational.
  let tmp = safeSimplify(
    base
      .ln()
      .mul(coeffX(expon, x, 1))
      .div(st.base.ln().mul(coeffX(st.expon!, x, 1)))
  );
  if (!(tmp.isNumberLiteral && tmp.isRational === true)) return false;

  // Do the constant terms share the same ratio? (skip when $expon$ has none)
  const e0 = coeffX(st.expon!, x, 0);
  let constCommensurate = false;
  if (!zeroQ(e0)) {