diff --git a/ginac/inifcns.cpp b/ginac/inifcns.cpp
index 981e7b2..a436239 100644
--- a/ginac/inifcns.cpp
+++ b/ginac/inifcns.cpp
@@ -1007,9 +1007,24 @@ fsolve(const ex& f_in, const symbol& x, const numeric& x1, const numeric& x2)
 	do {
 		xxprev = xx[side];
 		fxprev = fx[side];
-		xx[side] += ex_to<numeric>(ff.subs(x==xx[side]).evalf());
-		fx[side] = ex_to<numeric>(f.subs(x==xx[side]).evalf());
-		if ((side==0 && xx[0]<xxprev) || (side==1 && xx[1]>xxprev) || xx[0]>xx[1]) {
+		ex dx_ = ff.subs(x == xx[side]).evalf();
+		if (!is_a<numeric>(dx_))
+			throw std::runtime_error("fsolve(): function derivative does not evaluate numerically");
+		xx[side] += ex_to<numeric>(dx_);
+		// Now check if Newton-Raphson method shot out of the interval 
+		bool bad_shot = (side == 0 && xx[0] < xxprev) || 
+				(side == 1 && xx[1] > xxprev) || xx[0] > xx[1];
+		if (!bad_shot) {
+			// Compute f(x) only if new x is inside the interval.
+			// The function might be difficult to compute numerically
+			// or even ill defined outside the interval. Also it's
+			// a small optimization. 
+			ex f_x = f.subs(x == xx[side]).evalf();
+			if (!is_a<numeric>(f_x))
+				throw std::runtime_error("fsolve(): function does not evaluate numerically");
+			fx[side] = ex_to<numeric>(f_x);
+		}
+		if (bad_shot) {
 			// Oops, Newton-Raphson method shot out of the interval.
 			// Restore, and try again with the other side instead!
 			xx[side] = xxprev;
@@ -1017,8 +1032,16 @@ fsolve(const ex& f_in, const symbol& x, const numeric& x1, const numeric& x2)
 			side = !side;
 			xxprev = xx[side];
 			fxprev = fx[side];
-			xx[side] += ex_to<numeric>(ff.subs(x==xx[side]).evalf());
-			fx[side] = ex_to<numeric>(f.subs(x==xx[side]).evalf());
+
+			ex dx_ = ff.subs(x == xx[side]).evalf();
+			if (!is_a<numeric>(dx_))
+				throw std::runtime_error("fsolve(): function derivative does not evaluate numerically [2]");
+			xx[side] += ex_to<numeric>(dx_);
+
+			ex f_x = f.subs(x==xx[side]).evalf();
+			if (!is_a<numeric>(f_x))
+				throw std::runtime_error("fsolve(): function does not evaluate numerically [2]");
+			fx[side] = ex_to<numeric>(f_x);
 		}
 		if ((fx[side]<0 && fx[!side]<0) || (fx[side]>0 && fx[!side]>0)) {
 			// Oops, the root isn't bracketed any more.
@@ -1042,7 +1065,10 @@ fsolve(const ex& f_in, const symbol& x, const numeric& x1, const numeric& x2)
 			static const double secant_weight = 0.984375;  // == 63/64 < 1
 			numeric xxmid = (1-secant_weight)*0.5*(xx[0]+xx[1])
 			    + secant_weight*(xx[0]+fx[0]*(xx[0]-xx[1])/(fx[1]-fx[0]));
-			numeric fxmid = ex_to<numeric>(f.subs(x==xxmid).evalf());
+			ex fxmid_ = f.subs(x == xxmid).evalf();
+			if (!is_a<numeric>(fxmid_))
+				throw std::runtime_error("fsolve(): function does not evaluate numerically [3]");
+			numeric fxmid = ex_to<numeric>(fxmid_);
 			if (fxmid.is_zero()) {
 				// Luck strikes...
 				return xxmid;
diff --git a/ginac/integral.cpp b/ginac/integral.cpp
index 07670f3..f45d1ab 100644
--- a/ginac/integral.cpp
+++ b/ginac/integral.cpp
@@ -188,9 +188,7 @@ ex integral::evalf(int level) const
 	// results after subsituting a number for the integration variable.
 	if (is_exactly_a<numeric>(ea) && is_exactly_a<numeric>(eb) 
 			&& is_exactly_a<numeric>(ef.subs(x==12.34).evalf())) {
-		try {
 			return adaptivesimpson(x, ea, eb, ef);
-		} catch (runtime_error &rte) {}
 	}
 
 	if (are_ex_trivially_equal(a, ea) && are_ex_trivially_equal(b, eb)