How to use the rebound.integrate function in rebound

r2 = dx*dx + dy*dy + dz*dz
                E_pot -= particles[i].m*particles[j].m/np.sqrt(r2)
        return E_kin+E_pot

    times = np.logspace(np.log10(100.*dt),np.log10(tmax),Ngrid)
    if integrator=="wh" or integrator=="mercury":
        move_to_heliocentric()
    else:
        rebound.move_to_center_of_momentum()
    ei = energy()

    es = []

    runtime = 0.
    for t in times:
        rebound.integrate(t,exactFinishTime=0)
        ef = energy()
        e = np.fabs((ei-ef)/ei)+1.1e-16
        es.append(e)
        runtime += rebound.get_timing()
    
    integrator, run, trial = par
    print integrator.ljust(13) + " %9.5fs"%(runtime) + "\t Error: %e"  %( e)
    
    es = np.array(es)
    return [times, es]

# Setup particles (data taken from NASA Horizons)
# This could also be easily read in from a file.
rebound.add_particle( m=1.00000597682, x=-4.06428567034226e-3, y=-6.08813756435987e-3, z=-1.66162304225834e-6, vx=+6.69048890636161e-6, vy=-6.33922479583593e-6, vz=-3.13202145590767e-9 )  # Sun
rebound.add_particle( m=1./1047.355,   x=+3.40546614227466e+0, y=+3.62978190075864e+0, z=+3.42386261766577e-2, vx=-5.59797969310664e-3, vy=+5.51815399480116e-3, vz=-2.66711392865591e-6 )  # Jupiter
rebound.add_particle( m=1./3501.6,     x=+6.60801554403466e+0, y=+6.38084674585064e+0, z=-1.36145963724542e-1, vx=-4.17354020307064e-3, vy=+3.99723751748116e-3, vz=+1.67206320571441e-5 )  # Saturn
rebound.add_particle( m=1./22869.,     x=+1.11636331405597e+1, y=+1.60373479057256e+1, z=+3.61783279369958e-1, vx=-3.25884806151064e-3, vy=+2.06438412905916e-3, vz=-2.17699042180559e-5 )  # Uranus
rebound.add_particle( m=1./19314.,     x=-3.01777243405203e+1, y=+1.91155314998064e+0, z=-1.53887595621042e-1, vx=-2.17471785045538e-4, vy=-3.11361111025884e-3, vz=+3.58344705491441e-5 )  # Neptune

# Set the center of momentum to be at the origin
rebound.move_to_center_of_momentum()

rebound.set_integrator("mercury")
#rebound.set_integrator("mikkola")
rebound.set_dt(40.)
rebound.integrate(1e7)
print(rebound.get_timing())
print(rebound.status())
rebound.integrate(2e7)
print(rebound.get_timing())
print(rebound.status())

E_pot -= G*particles[i].m*particles[j].m/np.sqrt(r2)
        return E_kin+E_pot

    times = np.logspace(np.log10(100.*dt),np.log10(tmax),1000)
    if integrator=="wh" or integrator=="mercury":
        move_to_heliocentric()
    else:
        rebound.move_to_center_of_momentum()
    ei = energy()

    es = []

    timing = 0.

    for t in times:
        rebound.integrate(t,exactFinishTime=0)
        ef = energy()
        e = np.fabs((ei-ef)/ei)+1.1e-16
        es.append(e)
        timing += rebound.get_timing()

    es = np.array(es)
    print integrator + " done. %.5fs"%(timing)
    return [times, es]

# Move particles so that the center of mass is (and stays) at the origin  
rebound.move_to_center_of_momentum()

# Integrate until t=100 (roughly 16 orbits) 
rebound.integrate(100.)

# Modify particles 
# As an example, we are reverting the velocities 
particles = rebound.particles_get()
for i in range(rebound.get_N()):
    particles[i].vx *= -1.
    particles[i].vy *= -1.
    particles[i].vz *= -1.

# Integrate another 100 time units, until t=200
rebound.integrate(200.)

# Get particles back and print positions 
# Since we're integrating forward and then backward we end up with the 
# particles exactly where they started out from (note that we moved to the
# center of momentum frame)
for i in range(rebound.get_N()):
    print(particles[i].x, particles[i].y, particles[i].z)

# Set variables (defaults are G=1, t=0, dt=0.01)
#rebound.set_G(1.)  
#rebound.set_t(0.)  
#rebound.set_dt(0.01)  

# Add particles
# All parameters omitted are set to 0 by default.
rebound.particle_add( m=1. )                  # Star
rebound.particle_add( m=1e-3, x=1., vy=1. )   # Planet

# Move particles so that the center of mass is (and stays) at the origin  
rebound.move_to_center_of_momentum()

# Integrate until t=100 (roughly 16 orbits) 
rebound.integrate(100.)

# Modify particles 
# As an example, we are reverting the velocities 
particles = rebound.particles_get()
for i in range(rebound.get_N()):
    particles[i].vx *= -1.
    particles[i].vy *= -1.
    particles[i].vz *= -1.

# Integrate another 100 time units, until t=200
rebound.integrate(200.)

# Get particles back and print positions 
# Since we're integrating forward and then backward we end up with the 
# particles exactly where they started out from (note that we moved to the
# center of momentum frame)

e = 1.-pow(10.,e)
    dt = pow(10.,dt)*torb

    rebound.reset()
    rebound.integrator = integrator
    rebound.force_is_velocitydependent = 0
    rebound.dt = dt

    rebound.add(m=1.)
    rebound.add(m=0., x=(1.-e), vy=np.sqrt((1.+e)/(1.-e)))
    particles = rebound.particles
    
    Ei = -1./np.sqrt(particles[1].x*particles[1].x+particles[1].y*particles[1].y+particles[1].z*particles[1].z) + 0.5 * (particles[1].vx*particles[1].vx+particles[1].vy*particles[1].vy+particles[1].vz*particles[1].vz)

    rebound.integrate(tmax,exactFinishTime=0,keepSynchronized=1)
    
    Ef = -1./np.sqrt(particles[1].x*particles[1].x+particles[1].y*particles[1].y+particles[1].z*particles[1].z) + 0.5 * (particles[1].vx*particles[1].vx+particles[1].vy*particles[1].vy+particles[1].vz*particles[1].vz)

    return [float(rebound.iter)/rebound.t*dt, np.fabs((Ef-Ei)/Ei)+1e-16, rebound.timing/rebound.t*dt*1e6/2., (Ef-Ei)/Ei]

rebound.dt = dt

    rebound.add(m=1.)
    rebound.add(m=0.,a=1.,e=e0)

    #rebound.move_to_com()
    #rebound.init_megno(1.e-16)


    particles = rebound.particles
    def starkforce(): # need to put inside simulation(par) to have access to S and particles
        particles[1].ax += -S

    rebound.additional_forces = starkforce

    rebound.integrate(50000.*np.pi)

    return [rebound.megno, rebound.t]

dx = particles[i].x-particles[j].x
                dy = particles[i].y-particles[j].y
                dz = particles[i].z-particles[j].z
                r2 = dx*dx + dy*dy + dz*dz
                E_pot -= G*particles[i].m*particles[j].m/np.sqrt(r2)
        return E_kin+E_pot

    if integrator=="wh" or integrator=="mercury" or integrator[0:7]=="swifter":
        move_to_heliocentric()
    else:
        rebound.move_to_com()
    ei = energy()


    runtime = 0.
    rebound.integrate(tmax,exact_finish_time=0)
    ef = energy()
    e = np.fabs((ei-ef)/ei)+1.1e-16
    runtime += rebound.timing
    
    integrator, dt, run = par
    print integrator.ljust(13) + " %9.5fs"%(runtime) + "\t Error: %e"  %( e)
    return [runtime, e]