05f62f9f-a34e-4eca-8170-e3c6916d2c81 7 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Simpson Integrator in the Romberg Domain [0,1] <= [a,b] ...  integrates  'ainterp, cinterp' f a b n Int w s b a - (34 / 2 w * 1 - (* 14 / 2 w * 1 - (3^* - 12 / + (* a + : w G w s f 12 w * 1 - (2^- (* : α 0 : β 1 : h β α - n / : 14 mat Simpson 13 / h 2 / α G β G + (* h α k h * + G k 1 n 1 - sum * + (* 23 / h * α h 2 / - k h * + G k 1 n sum * + eval : 32 / b a - (* Simpson * 41 line :

sanity check the sextuplets Mathcad 11 Adaptiv 5.40752818465632 ≡ Technical accuracy 5.40752818465627 ≡ Simpson Transf'd.. 5.40752818465635 ≡ Smath Simpson 7½ D 5.4075281 ≡ Simplex 10½ D .... 5.40752818462 ≡ 51 line

x f x sqrt exp :

t0 1 time :

transformed domain [0,1] <= Simpson [a,b] f 02500 Int 5.40752818465992

1 time t0 - 2.5 s *

x f

11 D [2.4 s] ... 7 D [21 s]

t0 1 time :

acc [10000] x f x 02 int 5.40752810347196

1 time t0 - 20 s *