gradient formula python achieve composite and composite Simpson formula

Compound trapezoid formula 1.

2. The composite Simpson formula

python achieve

import math

def fun(x):
    return math.sin(x)/(x+1e-16) #加上1e-16避免除零错误

# 复合梯度
def tx(a,b,n):
    h=(b-a)/n
    fxi=0
    xi=a
    for i in range(1,n):
        xi=xi+h
        fxi=fxi+fun(xi)
    result=(h/2)*(fun(a)+fxi*2+fun(b))
    return result

#复合辛普森
def xps(a,b,n):   
    k=int(n/2)
    h=(b-a)/n
    fk=0
    xi=a
    for i in range(1,k):
        xi=xi+h
        fk=fk+fun(xi)
    xi=a+h/2
    fk1=fun(xi)
    for i in range(0,k):
        xi=xi+h
        fk1=fk1+fun(xi)
    result=(h/3)*(fun(a)+4*fk1+2*fk+fun(b))
    return result

print(tx(0,1,1000000))
print(xps(0,1,1000000))