if (ratio>1.0001 && ratio<0.9999) {
clog << "(" << num << "/" << den << ")^(" << nm
<< ") erroneously evaluated to " << radical;
if (ratio>1.0001 && ratio<0.9999) {
clog << "(" << num << "/" << den << ")^(" << nm
<< ") erroneously evaluated to " << radical;