How are arcsin and arccos typically implemented? [duplicate]

I was reading through Agner's list of assembly codes for x86 and x87 and noticed that there is no op-code for arcsin or arccos, but only arctan. So I've googled it and all the results implemented it by using atan and sqrt, which would mean that acos and asin should be significantly slower than atan because you need an additional sqrt, but I wrote a simple test program in C++ and acos and asin are both faster than atan:

#include <chrono> #include <cmath> #include <iostream> class timer { private: decltype(std::chrono::high_resolution_clock::now()) begin, end; public: void start() { begin = std::chrono::high_resolution_clock::now(); } void stop() { end = std::chrono::high_resolution_clock::now(); } template<typename T> auto duration() const { return std::chrono::duration_cast<T>(end - begin).count(); } auto nanoseconds() const { return duration<std::chrono::nanoseconds>(); } void printNS(char const* str) const { std::cout << str << ": " << nanoseconds() << std::endl; } }; int main(int argc, char**) { timer timer; double p1 = 0 + 0.000000001; double acc1{1}; timer.start(); //less than 8 seconds for(int i{0}; 200000000 > i; ++i) { acc1 += std::acos(i * p1); } timer.stop(); timer.printNS("acos"); timer.start(); //less than 8 seconds for(int i{0}; 200000000 > i; ++i) { acc1 += std::asin(i * p1); } timer.stop(); timer.printNS("asin"); timer.start(); //more than 12 seconds for(int i{0}; 200000000 > i; ++i) { acc1 += std::atan(i * p1); } timer.stop(); timer.printNS("atan"); timer.start(); //almost 20 seconds for(int i{0}; 200000000 > i; ++i) { acc1 += std::atan2(i * p1, i * p1); } timer.stop(); timer.printNS("atan"); std::cout << acc1 << '\n'; } 

I've tried seeing the assembly on godbolt, but it doesn't inline acos or asin.

So how is it implemented or if it actually just uses atan, how can it be faster?