Program SIMPSON_3VAR
        IMPLICIT DOUBLE PRECISION (A-H,O-Z)
        DOUBLE PRECISION X3(1000000)

        a=0d0
        b=1d0
        N=100
        h=(b-a)/N


        do i=1,N
        x3(i)=a+i*h
        enddo

        sum1=0d0
        sum2=0d0
        nimp= n/2-1
        np = n/2

        do i=1,nimp
        sum1=sum1+2*g3(x3(2*i))

        enddo

        do i=1,np
        sum2=sum2+4*g3(x3(2*i-1))
        enddo

        r=h/3d0*(g3(a)+sum1+sum2+g3(b))

        open(20,File="ejerc10simp_comp_3var.xls")



        write(20,*)r
        call cpu_time(finish)
        write(20,30)finish-start
30      Format(e18.8)
        close(20)
        end


        FUNCTION  g1(x1,x2,x3)
        Implicit Double Precision (A-H,O-Z)
        g1=exp(-(x1*x1)-(x2*x2)-(x3*x3))*cos(x1*x2+x2*x3+x1*x3)
        END


        Function g2(x2,x3)
        IMPLICIT DOUBLE PRECISION (A-H,O-Z)
        DOUBLE PRECISION x1(1000000)
         N=100
         sum1=0d0
         sum2=0d0
         nimp= n/2-1
         np = n/2
         a=0d0
         b=1d0
        h=(b-a)/N


        do i=1,N
        x1(i)=a+i*h
        enddo


        do i=1,nimp
        sum1=sum1+2*g1(x1(2*i),x2,x3)

        enddo

        do i=1,np
        sum2=sum2+4*g1(x1(2*i-1),x2,x3)
        enddo

        g2=h/3d0*(g1(a,x2,x3)+sum1+sum2+g1(b,x2,x3))

        END
        
        Function g3(x3)
        IMPLICIT DOUBLE PRECISION (A-H,O-Z)
        DOUBLE PRECISION x2(1000000)
         N=100
         sum1=0d0
         sum2=0d0
         nimp= n/2-1
         np = n/2
         a=0d0
         b=1d0
        h=(b-a)/N


        do i=1,N
        x2(i)=a+i*h
        enddo


        do i=1,nimp
        sum1=sum1+2*g2(x2(2*i),x3)

        enddo

        do i=1,np
        sum2=sum2+4*g2(x2(2*i-1),x3)
        enddo

        g3=h/3d0*(g2(a,x3)+sum1+sum2+g2(b,x3))

        END