The companies and government agencies that have begun enlisting the automation software run the gamut. They include General Motors, BMW, General Electric, Unilever, Mastercard, Manpower, FedEx, Cisco, Google, the Defense Department and NASA.

State Auto Insurance Companies in Columbus, Ohio, started its first automation pilot project two years ago. Today, it has 30 software programs handling back-office tasks, with an estimated savings of 25,000 hours of human work — or the equivalent of about a dozen full-time workers — on an annualized basis, assuming a standard 2,000-hour work year.

Holly Uhl, a technology manager who leads the automation program, estimated that within two years the company’s bot population would double to 60 and its hours saved would perhaps triple to 75,000, nearly all in year-after-year savings rather than one-time projects.

Cutting jobs, Ms. Uhl said, is not the plan. The goal for the company, whose insurance offerings include auto, commercial and workers’ compensation, is to increase productivity and State Auto’s revenue with limited additions to its head count, she said.

Ms. Uhl said her message to workers is: “We’re here to partner with you to find those tasks that drive you crazy.”

Rebekah Moore, a premium auditor at the company, had one in mind. Premium auditors scrutinize insurance policies and make recommendations for changing rates. They audit less than half of the policies, Ms. Moore said.

The policies that will not be audited then have to be set aside and documented. That step, she explained, is a routine data-entry task that involves fiddling with two computer programs, plugging in codes and navigating drop-down menus. It takes a minute or two. But because auditors handle many thousands of policies, the time adds up, to about an hour a day, she estimated.