Each of these threads runs an instance of QEPCAD B. The final results are averaged over 50 different randomly generated prenex formulae.\
\
The comparison between the running times of QEPCAD B with the preprocessor and without are shown in Table 1 and Fig. 6 compares the running times (with and without the preprocessor) of QEPCAD B over 50 different prenex formulae in two variables.

   Variables   No. of terms per polynomial   No. of polynomials   Time without the preprocessor   Time with the preprocessor
  ----------- ----------------------------- -------------------- ------------------------------- ----------------------------
       2                    5                        5                        3 Sec                        0.3 Sec
       3                    5                        5                      $\infty$                        92 Sec
       4                    2                        2                      77000 Sec                       2 Sec

![image](definitive-2vbles.jpg)\

![image](plots.jpg)\

An example of such a randomly generated formula in 2 variables from the separable class $S_{10}$, each with at most 5 polynomials and each polynomial with at most 5 terms is,

$(\forall x0)[[[(58) {x_{0}}^{8} {x_{1}}^{2}  + (-68) {x_{0}}^{10} {x_{1}}^{4}  + (73)  + (-4)  + (-28) {x_{0}}^{9}  = 0] \vee[(44) {x_{0}}^{4} {x_{1}}^{5}  + (-88) {x_{0}}^{10} {x_{1}}^{4}  + (11) {x_{1}}^{9}  + (-70)  + (-19) {x_{0}}^{6} {x_{1}}^{5}  = 0] \vee[(20) {x_{0}}^{7}  + (-61) {x_{0}}^{10} {x_{1}}^{3}  + (-71)  + (81) {x_{0}}^{3} {x_{1}}^{5}  + (14) {x_{0}}^{7}  = 0] \vee[(-58) {x_{1}}^{5}  + (-35) {x_{0}}^{10}  + (5)  + 