Table 10. Comparison of proposed model with arithmetic multiplications.

No. of matrix	Sequence of dimensions	Optimal parenthesis	Arithmetic multiplications	GCO multiplications	Variation (%)
3	9,95,21,78	((M1*M2)*M3)	32,697	32,697	0
6	30,10,71,58,9,25,22	(M1*((M2*(M3*M4))*(M5*M6)))	56,982	56,982	0
9	94,67,56,17,80,68,10,78,7,5	(M1*(M2*(M3*(M4*(M5*(M6*((M7*M8)*M9)))))))	98,220	98,220	0
12	42,54,49,22,62,46,93,97,82,59,24,86,56	(((M1*(M2*M3))*((((((M4*M5)*M6)*M7)*M8)*M9)*M10))*(M11*M12))	970,214	970,214	0
15	27,98,89,40,36,82,6,11,3,23,15,91,87,35,3,43	((M1*(M2*(M3*(M4*(M5*(M6*((M7*M8)*((M9*M10)*(M11*(M12*(M13*M14)))))))))))*M15)	101,322	101,322	0
18	94,30,63,79,52,10,6,13,93,97,3,8,67,40,38,6,89,61,71	((M1*(M2*(M3*(M4*(M5*(M6*(M7*(M8*(M9*M10)))))))))*(((((((M11*M12)*M13)*M14)*M15)*M16)*M17)*M18))	139,845	139,845	0
21	57,92,76,77,28,13,47,27,3,67,89,14,93,16,24,34,14,83,8 9,92,33,19	((M1*(M2*(M3*(M4*(M5*(M6*(M7*M8)))))))*((((((((((((M9*M10)*M11)*M12)*M13)*M14)*M15)*M16)*M17)*M18)*M19)*M20)*M21))	166,938	166,938	0
24	79,68,62,22,98,35,62,99,21,39,91,79,81,31,11,4,87,90,90,72,57,92,36,72,59	((M1*(M2*(M3*(M4*(M5*(M6*(M7*(M8*(M9*(M10*(M11*(M12*(M13*(M14*M15))))))))))))))*((((((((M16*M17)*M18)*M19)*M20)*M21)*M22)*M23)*M24))	377,216	377,216	0