  Trotterization is the most common and convenient approximation method for
Hamiltonian simulations on digital quantum computers, but estimating its error
accurately is computationally difficult for large quantum systems. Here, we
develop a method for measuring the Trotter error without ancillary qubits on
quantum circuits by combining the $m$th- and $n$th-order ($m<n$)
Trotterizations rather than consulting with mathematical error bounds. Using
this method, we make Trotterization precision-guaranteed, developing an
algorithm named Trotter$(m,n)$, in which the Trotter error at each time step is
within an error tolerance $\epsilon$ preset for our purpose. Trotter$(m,n)$ is
applicable to both time- independent and dependent Hamiltonians, and it
adaptively chooses almost the largest stepsize $\mathrm{d}t$, which keeps
quantum circuits shallowest within the error tolerance. Benchmarking it in a
quantum spin chain, we find the adaptively chosen $\mathrm{d}t$ to be about ten
times larger than that inferred from known upper bounds of Trotter errors.
