Why did Saruman attack Rohan?

[Gordis]

It is a bit puzzling why Saruman attacked Rohan when he did.

He has prepared a strong army, both on Sauron's orders and to reach his own goals. He tried to capture the Ring, fully expecting the two hobbits captured at Path Galen to have it. But he was cheated - his orcs were destroyed and the hobbits escaped. He knew he would never get the ring now.

Then suddenly Saruman attacks Rohan. When Gandalf, Aragorn, Legolas and Gimli ride to Edoras, they see smoke rising at the fords of Isen - the war has begun.

But why did Saruman attack so early? Was it on Sauron's orders? But wouldn't it have been better to attack Rohan and Minas Tirith simultaneously?

Even reckoned as a lord and captain Saruman has grown very strong. He threatens the Men of Rohan and draws off their help from Minas Tirith, even as the main blow is approaching from the East.

Moreover, Sauron was not yet ready to start the war - he only took this decision when he saw Aragorn via the Palantir.

And if Saruman attacked on his own, why did he do it? Theoden was still under his sway, held in check by Grima. Saruman faced the possibility of defeat - imagine what would have been if Rohan asked for Gondor's help and got it? The alliance worked both ways. And he also risked Sauron's wrath if he attacked too eartly.
So- why?