Republican presidential candidates threw Ben Bernanke and the Federal Reserve under the bus Wednesday night.

Senators Ted Cruz and Rand Paul were the most vocal during the CNBC debate, continuing their longstanding attacks on the central bank.

"On Wall Street, the Fed is doing great," Cruz said. "It's driving up stock prices ... I think the Fed should get out of the business of trying to juice our economy."

Paul was even more pointed, connecting the central bank to income inequality.

"You want to study income inequality? Let's bring the Fed forward and talk about Fed policy and how it causes income inequality," he said. "Let's also bring the Fed forward and have them explain how they caused the housing boom and the crisis ...The Fed has been a great problem in our society."

Paul also described Bernanke, who was Fed chairman during the financial crisis, as "arrogant."

Related: Fed keeps interest rates near zero

In 2008, with the housing market crippled, the Fed cut interest rates and started its bond program, known as quantitative easing or "QE" to aid the economy. QE became Bernanke's flagship program.

Since then, the economy has improved considerably. Unemployment is down, the economy is growing and home buying has bounced back too.

Related: Ben Bernanke: 6 fun facts you didn't know

But Paul and Cruz argue that the Fed's actions sparked a bull market in stocks that only benefited fat cats on Wall Street.

It's true that CEO pay has hit record levels as the S&P 500 has gained over 200% over the past six years. However, millions of Americans who invest in mutual funds, pension funds or a 401(k) also benefited from the rally.

In interviews and his recently published memoir "The Courage to Act," Bernanke rejected the argument that the Fed's actions made income inequality worse.

"The failure of our economy to serve everybody is really a very long-term trend," Bernanke recently told CNN's Fareed Zakaria. "There are some who have tried to pin [inequality] on monetary policy and I think that's really a red herring."

Related: Bernanke is no fan of Bernie Sanders' 'delusions'

Cruz and Paul are co-sponsors of a bill called "Audit the Fed," which calls for a Congressional audit of the central bank's finances.

While the Fed is already audited twice a year, the bill does include a provision that would grant the Government Accountability Office more oversight of bank.

Critics say the bill would result in undue political influence over monetary policy. Fed officials, especially current Chair Janet Yellen, are opposed to the measure.

Related: Meet Janet Yellen: the most powerful woman in the world

The CNBC debate took place the same day the Fed chose not to raise its key interest rate. Cruz and Paul believe the Fed's rate-setting committee shouldn't have so much power.

They advocate rules-based monetary policy, where certain conditions -- unemployment, economic growth -- would automatically move rates up or down.

Yellen and Bernanke are opposed to the idea.