how to avoid assembling the cross product of two vectors

in my simulations, I find myself computing the cross product of two vectors that both change at every time step repeatedly.

See here a minimal example of how I compute the cross product:

import dolfin as df                                                              

mesh = df.UnitIntervalMesh(2)                                                    
V = df.VectorFunctionSpace(mesh, "CG", 1, dim=3)                                 

a = df.Function(V)                                                               
b = df.Function(V)                                                               
c = df.Function(V)                                                               

a.assign(df.Constant((1, 0, 0)))                                                 
b.assign(df.Constant((0, 1, 0)))

# compute a x b and write result into c                                                 
# something like this would be done very often in the simulation
df.assemble(df.dot(df.cross(a, b), df.TestFunction(V)) * df.dP,
            tensor=c.vector())
print c.vector().array()

Is there any way I can avoid the cost of the assembly at every time step?

Kind regards and many thanks