The evalrC function evaluates an expr containing complex intervals written INTERVAL(a, b, c, d) which denote complex values guaranteed to be in the rectangle with corners a+b*i and c+d*i.

Unknown variables are by default assumed to be INTERVAL(-infinity, -infinity, infinity, infinity), i.e. they take on any possible complex value.

The function evalrC can be called with an expr without ranges in it.  In this case the decision functions min, max, abs, signum, csgn, Re and Im are evaluated using range arithmetic.

$\mathrm{evalrC}\left(\mathrm{\pi }\right)$

$\mathrm{INTERVAL}\left(3.141592653\,0\,3.141592654\,0\right)$

$\mathrm{evalrC}\left(\arccos \left(\exp \left(10+9x^5+5x^3\right)\right)+29\right)$

$\mathrm{INTERVAL}\left(29\,-\mathrm{\infty }\,32.14159266\,\mathrm{\infty }\right)$

$\mathrm{evalrC}\left(\ln \left(12\arctan \left(\mathrm{arccosh}\left(4-2x^2-8x\right)+6\right)\right)-\frac{3}{7}\right)$

$\mathrm{INTERVAL}\left(2.396833377\,\mathrm{-0.04793705575}\,2.508838572\,0.04793705575\right)$

$\mathrm{evalrC}\left(\mathrm{abs}\left(116-\frac{5}{6\mathrm{abs}\left(4+10x\right)}\left(14+\ln \left(\frac{565}{7}+5x\right)\right)+\frac{5}{3\left(1+9x^3\right)}{\left(-16+\cosh \left(6\right)\right)}^3-12\exp \left(\ln \left(x\right)x\right)\right)+\frac{71}{7}\right)$

$\mathrm{INTERVAL}\left(\frac{71}{7}\,0\,\mathrm{\infty }\,0\right)$