diff --git a/include/polynomial.hpp b/include/polynomial.hpp
index 11202fc..5d8194f 100644
--- a/include/polynomial.hpp
+++ b/include/polynomial.hpp
@@ -309,6 +309,16 @@ T Polynomial<T>::diffXX (const T &x, const T &y) const {
 
 	// sets output to 0+0i
 	T rop;
+    
+        if (this->degree == 1){
+    
+        return rop;
+    }
+    if (this->degree == 2)
+    {
+        rop = T(2)*(this->coef)[3];
+        return rop;
+    }
 
     // compute all powers of x and y
     // (from 0 to degree-2) (from 0 to degree-2) resp
@@ -340,6 +350,17 @@ T Polynomial<T>::diffXY (const T &x, const T &y) const {
 
 	// sets output to 0+0i
 	T rop;
+    
+        if (this->degree == 1){
+    
+        return rop;
+    }
+    if (this->degree == 2)
+    {
+        rop = T(2)*(this->coef)[4];
+        return rop;
+    }
+    
 
     // compute all powers of x and y
     // (from 0 to degree-2) (from 0 to degree-2) resp
@@ -372,6 +393,16 @@ T Polynomial<T>::diffYY (const T &x, const T &y) const {
 
 	// sets output to 0+0i
 	T rop;
+    
+    if (this->degree == 1){
+    
+        return rop;
+    }
+    if (this->degree == 2)
+    {
+        rop = T(2)*(this->coef)[5];
+        return rop;
+    }
 
     // compute all powers of x and y
     // (from 0 to degree-2) (from 0 to degree-2) resp
diff --git a/tests/sirocco_minimal_test.cpp b/tests/sirocco_minimal_test.cpp
index bd45ac2..5c6e083 100644
--- a/tests/sirocco_minimal_test.cpp
+++ b/tests/sirocco_minimal_test.cpp
@@ -6,38 +6,27 @@ int main(int argc, char const *argv[]) {
 	mpfr_set_default_prec (162);
 
 
-    double testCoefs[] = {0.000000000000000, -0.000000000000000, 0.000000000000000,
--0.000000000000000, 0.000000000000000, -0.000000000000000,
-0.000000000000000, -0.000000000000000, -128.000000000000,
--128.000000000000, -96.0000000000000, -96.0000000000000,
-0.000000000000000, -0.000000000000000, 0.000000000000000,
--0.000000000000000, 72.0000000000000, 72.0000000000000,
-304.000000000000, 304.000000000000, 12.0000000000000,
-12.0000000000000, 180.000000000000, 180.000000000000,
-0.000000000000000, -0.000000000000000, 0.000000000000000,
--0.000000000000000, 90.0000000000000, 90.0000000000000,
--182.500000000000, -182.500000000000, 133.500000000000,
-133.500000000000, -190.500000000000, -190.500000000000,
-42.0000000000000, 42.0000000000000, -44.0000000000000,
--44.0000000000000, 0.000000000000000, -0.000000000000000,
-0.000000000000000, -0.000000000000000, -40.2500000000000,
--40.2500000000000, 18.2500000000000, 18.2500000000000,
--72.0000000000000, -72.0000000000000, 21.0000000000000,
-21.0000000000000, -38.5000000000000, -38.5000000000000,
-5.50000000000000, 5.50000000000000, -6.00000000000000,
--6.00000000000000, -0.000000000000000, 0.000000000000000};
+    double testCoefs[] = {
+-2.000000000000000, -2.000000000000000, 0.000000000000000, 0.000000000000000,
+0.000000000000000, 0.000000000000000, 0.000000000000000, -0.000000000000000,
+0.000000000000, 0.000000000000, 0.0000000000000, 0.0000000000000,
+1.000000000000000, 1.000000000000000, 0.000000000000000, -0.000000000000000,
+0.00000000000000, 0.000000000000000, 0.000000000000000, 0.0000000000000000,
+1.0000000000000, 1.000000000000000, 0.000000000000000, 0.0000000000000000
+};
 
-   	double y0R = 4.0;
-   	double y0I = -4.0;
-   	double *rop = homotopyPath (4, testCoefs, y0R, y0I);
+
+   	double y0R = 1.414;
+   	double y0I = 0.0;
+   	double *rop = homotopyPath (2, testCoefs, y0R, y0I);
 
 		int len = (int) rop[0];
 		int i;
 
 		delete [] rop;
 
-		mpfr_t mp_testCoefs[60];
-		for (int i=0; i<60; ++i) {
+		mpfr_t mp_testCoefs[24];
+		for (int i=0; i<24; ++i) {
 			mpfr_init_set_d (mp_testCoefs[i], testCoefs[i],
 					(i%2)? MPFR_RNDU : MPFR_RNDD);
 		}
@@ -45,7 +34,7 @@ int main(int argc, char const *argv[]) {
 		mpfr_init_set_d (mp_y0R, y0R, MPFR_RNDN);
 		mpfr_init_set_d (mp_y0I, y0I, MPFR_RNDN);
 
-		mpfr_t *mp_rop = homotopyPath_mp (4, mp_testCoefs, mp_y0R, mp_y0I, 5300);
+		mpfr_t *mp_rop = homotopyPath_mp (2, mp_testCoefs, mp_y0R, mp_y0I, 106);
 
 		int size = mpfr_get_si (mp_rop[0], MPFR_RNDN);
   
@@ -54,7 +43,7 @@ int main(int argc, char const *argv[]) {
 		delete [] mp_rop;
 
 
-		for (int i=0; i<60; ++i) {
+		for (int i=0; i<24; ++i) {
 			mpfr_clear (mp_testCoefs[i]);
 		}