It is known that rational approximations of elementary analytic functions (exp, log, trigonometric, and hyperbolic functions, and their inverse functions) are computable in the weak complexity class $\mathrm{TC}^0$. We show how to formalize the construction and basic properties of these functions in the corresponding theory of bounded arithmetic, $\mathsf{VTC}^0$.

翻译：已知基本分析函数( 表达、 日志、 三角、 双曲函数及其反函数) 的合理近似值可以用薄弱的复杂等级 $\ mathrm{ TC=0$来计算。 我们用相应的约束算术理论 $\ mathsf{ VTC=0$来显示这些函数的构造和基本特性。</s>