Function erfInvApprox

src/compute-engine/numerics/special-functions.ts:313–318

* Winitzki's approximation for the inverse error function, accurate to * ~2e-3 relative over (-1, 1). Used as the Newton seed for `erfInv()` and * `bigErfInv()`.

(x: number)

 * for real a > 0, b > 0 and 0 ≤ x ≤ 1. Returns NaN outside that domain, and
 * the exact endpoints 0 (x=0) and 1 (x=1).
 */
export function betaRegularized(x: number, a: number, b: number): number {
  if (Number.isNaN(x) || Number.isNaN(a) || Number.isNaN(b)) return NaN;
  if (a <= 0 || b <= 0 || x < 0 || x > 1) return NaN;
  if (x === 0) return 0;
  if (x === 1) return 1;
  const bt = Math.exp(
    gammaln(a + b) -
      gammaln(a) -