-
- // More complex rational function
- e = (pow(x-y*2,4)/pow(pow(x,2)-pow(y,2)*4,2)+1)*(x+y*2)*(y+z)/(pow(x,2)+pow(y,2)*4);
- d = (y*2 + z*2) / (x + y*2);
- result += check_normal(e, d);
-
- return result;
+
+ // Distribution of powers
+ e = pow(x/y, 2);
+ d = pow(x, 2) / pow(y, 2);
+ result += check_normal(e, d);
+
+ // Distribution of powers (integer, distribute) and fraction addition
+ e = pow(pow(x, -1) + x, 2);
+ d = pow(pow(x, 2) + 1, 2) / pow(x, 2);
+ result += check_normal(e, d);
+
+ // Distribution of powers (non-integer, don't distribute) and fraction addition
+ e = pow(pow(x, -1) + x, numeric(1)/2);
+ d = pow((pow(x, 2) + 1) / x, numeric(1)/2);
+ result += check_normal(e, d);
+
+ // Replacement of functions with temporary symbols and fraction cancellation
+ e = pow(sin(x), 2) - pow(cos(x), 2);
+ e /= sin(x) + cos(x);
+ d = sin(x) - cos(x);
+ result += check_normal(e, d);
+
+ // Replacement of non-integer powers with temporary symbols
+ e = (pow(numeric(2), numeric(1)/2) * x + x) / x;
+ d = pow(numeric(2), numeric(1)/2) + 1;
+ result += check_normal(e, d);
+
+ // Replacement of complex numbers with temporary symbols
+ e = (x + y + x*I + y*I) / (x + y);
+ d = 1 + I;
+ result += check_normal(e, d);
+
+ e = (pow(x, 2) + pow(y, 2)) / (x + y*I);
+ d = e;
+ result += check_normal(e, d);
+
+ // More complex rational function
+ e = (pow(x-y*2,4)/pow(pow(x,2)-pow(y,2)*4,2)+1)*(x+y*2)*(y+z)/(pow(x,2)+pow(y,2)*4);
+ d = (y*2 + z*2) / (x + y*2);
+ result += check_normal(e, d);
+
+ return result;