Haversine and pseudo-Haversine (up to a constant) formula

hav.py

import numpy as np
from numpy import sqrt, sin, cos

asin = np.arcsin


def simp(rlat1, rlon1, rlat2, rlon2):
  dLat = rlat2 - rlat2
  dLon = rlon2 - rlon1
  return ((sin(dLat / 2)**2 + sin(dLon / 2)**2 * cos(rlat1) * cos(rlat2)))


def full(rlat1, rlon1, rlat2, rlon2):
  return asin(sqrt(simp(rlat1, rlon1, rlat2, rlon2)))


n = 100
r = np.vstack([
    np.random.rand(n) * np.pi - np.pi / 2,
    np.random.rand(n) * np.pi * 2,
    np.random.rand(n) * np.pi - np.pi / 2,
    np.random.rand(n) * np.pi * 2
]).T

ys = [simp(*v) for v in r]
yf = [full(*v) for v in r]

idxs = np.argsort(ys)
idxf = np.argsort(yf)
assert all(idxs == idxf)