顶

简单，看我的精度可以说是完全一致了，只要你肯算

可以有精确度更高的，要多高有多高
f(x)=x+(m-x^2)/(2 x)-(m-x^2)^2/(8 x^3)+(m-x^2)^3/(16 x^5)-(5 (m-x^2)^4)/(128 x^7)+(7 (m-x^2)^5)/(256 x^9)-(21 (m-x^2)^6)/(1024 x^11)+(33 (m-x^2)^7)/(2048 x^13)-(429 (m-x^2)^8)/(32768 x^15)+(715 (m-x^2)^9)/(65536 x^17)-(2431 (m-x^2)^10)/(262144 x^19)+(4199 (m-x^2)^11)/(524288 x^21)-(29393 (m-x^2)^12)/(4194304 x^23)+(52003 (m-x^2)^13)/(8388608 x^25)-(185725 (m-x^2)^14)/(33554432 x^27)+(334305 (m-x^2)^15)/(67108864 x^29)-(9694845 (m-x^2)^16)/(2147483648 x^31)+(17678835 (m-x^2)^17)/(4294967296 x^33)-(64822395 (m-x^2)^18)/(17179869184 x^35)+(119409675 (m-x^2)^19)/(34359738368 x^37)-(883631595 (m-x^2)^20)/(274877906944 x^39);
算sqrt(3)，m=3, f(2)=261740117769298434928053/151115727451828646838272
误差1.77*10^-15，f(f(2))误差1.71*10^-311
能手算精度又还可以的除了牛顿迭代还有
f(x)=x + (m - x^2)/(2 x) - (m - x^2)^2/(8 x^3);三阶
f(x)=x*(3 m + x^2)/(m + 3 x^2) 三阶
f(x)=(m^2 + 6 m x^2 + x^4)/(4 x (m + x^2)) 四阶
f(x)=(x (5 m^2 + 10 m x^2 + x^4))/(m^2 + 10 m x^2 + 5 x^4) 五阶
f(x)=((m + x^2) (m^2 + 14 m x^2 + x^4))/(2 x (3 m + x^2) (m + 3 x^2))六阶