More precision required for intermediate terms

[div5252]

Consider the following failing test -

a = real("3.11");
result = real::acos(real::cos(a));  // acos(cos(3.11)) = 3.110000000000000
lower_limit = real("3.109999999999999");
upper_limit = real("3.110000000000001");
CHECK(result > lower_limit);
CHECK(result < upper_limit);

There is loss of precision while computing Taylor expansion and using divide and conquer approach. So it is necessary to call the intermediate terms with more precision in math functions.

[Parna2000]

I can fix this issue. Please assign me this issue and allow me to work on it @div5252

[div5252]

There is no need for me to assign the issue. You can work on it and make a PR.

[GYuvanShankar]

This could be due to calling the sin functions with same precision as that of the number itself. For eg. auto [sin_lower, cos_lower] = sin_cos(ro.get_lhs_itr().get_interval().lower_bound.up_to(_precision, false), _precision, false); I think calling functions with higher precision should help with this issue.