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Sat May 30 16:25:17 PDT 1992 REDUCE 3.4.1, 15-Jul-92 ... 1: 1: 2: 2: (SCOPE) 3: 3: Time: 493 ms 4: 4: % Test SCOPE Package. % NOTE: The SCOPE, GHORNER, GSTRUCTR and GENTRAN packages must be loaded % to run these tests. on priall$ optimize z:=a^2*b^2+10*a^2*m^6+a^2*m^2+2*a*b*m^4+2*b^2*m^6+b^2*m^2 iname s; Sumscheme : || EC|Far ------------ 0|| 1| Z ------------ Productscheme : | 0 1 2| EC|Far --------------------- 1| 2 2| 1| 0 2| 6 2| 10| 0 3| 2 2| 1| 0 4| 4 1 1| 2| 0 5| 6 2 | 2| 0 6| 2 2 | 1| 0 --------------------- 0 : M 1 : B 2 : A Number of operations in the input is: Number of (+,-)-operations : 5 Number of (*)-operations : 10 Number of integer exponentiations : 11 Number of other operations : 0 Time: 17 ms Breuer search : Time: 51 ms Removal of different names for identical cse's : Time: 0 ms Change Scheme : Time: 0 ms Local Factorization : Time: 0 ms Breuer search : Time: 0 ms Removal of different names for identical cse's : Time: 0 ms Change Scheme : Time: 0 ms Local Factorization : Time: 0 ms Breuer search : Time: 17 ms Removal of different names for identical cse's : Time: 0 ms Change Scheme : Time: 0 ms Local Factorization : Time: 0 ms Additional optimization during finishing touch : Time: 0 ms S0 := B*A S4 := M*M S1 := S4*B*B S2 := S4*A*A S3 := S4*S4 Z := S1 + S2 + S0*(2*S3 + S0) + S3*(2*S1 + 10*S2) Number of operations after optimization is: Number of (+,-)-operations : 5 Number of (*)-operations : 12 Number of integer exponentiations : 0 Number of other operations : 0 Sumscheme : | 0 3 4 5| EC|Far ------------------------ 0| 1 1| 1| Z 15| 2 10| 1| 14 17| 2 1 | 1| 16 ------------------------ 0 : S3 3 : S0 4 : S1 5 : S2 Productscheme : | 8 9 10 11 17 18 19 20| EC|Far ------------------------------------ 7| 1 1| 1| S0 8| 1 2 | 1| S1 9| 1 2| 1| S2 10| 2 | 1| S3 11| 2 | 1| S4 14| 1 | 1| 0 16| 1 | 1| 0 ------------------------------------ 8 : S4 9 : S3 10 : S2 11 : S1 17 : S0 18 : M 19 : B 20 : A Time: 17 ms off priall$ on primat,acinfo$ optimize ghorner <<z:=a^2*b^2+10*a^2*m^6+a^2*m^2+2*a*b*m^4+2*b^2*m^6+b^2*m^2>> vorder m iname s; 2 2 2 2 2 2 2 2 2 Z := A *B + M *((A + B ) + M *(2*A*B + M *(10*A + 2*B ))) Sumscheme : || EC|Far ------------ 0|| 1| Z 3|| 1| 2 7|| 1| 6 10|| 1| 9 ------------ Productscheme : | 0 1 2| EC|Far --------------------- 1| 2 2| 1| 0 2| 2 | 1| 0 4| 2| 1| 3 5| 2 | 1| 3 6| 2 | 1| 3 8| 1 1| 2| 7 9| 2 | 1| 7 11| 2| 10| 10 12| 2 | 2| 10 --------------------- 0 : M 1 : B 2 : A Number of operations in the input is: Number of (+,-)-operations : 5 Number of (*)-operations : 8 Number of integer exponentiations : 9 Number of other operations : 0 S0 := B*A S1 := B*B S2 := A*A S3 := M*M Z := S0*S0 + S3*(S1 + S2 + S3*(2*S0 + S3*(2*S1 + 10*S2))) Number of operations after optimization is: Number of (+,-)-operations : 5 Number of (*)-operations : 11 Number of integer exponentiations : 0 Number of other operations : 0 Sumscheme : | 0 1 2| EC|Far --------------------- 0| | 1| Z 3| 1 1| 1| 2 7| 2 | 1| 6 10| 2 10| 1| 9 --------------------- 0 : S0 1 : S1 2 : S2 Productscheme : | 3 4 5 9 10 11 12| EC|Far --------------------------------- 1| 2 | 1| 0 2| 1 | 1| 0 6| 1 | 1| 3 9| 1 | 1| 7 13| 1 1| 1| S0 14| 2 | 1| S1 15| 2| 1| S2 16| 2 | 1| S3 --------------------------------- 3 : S3 4 : S2 5 : S1 9 : S0 10 : M 11 : B 12 : A operator a$ k:=j:=1$ u:=c*x+d$ v:=sin(u)$ optimize {a(k,j):=v*(v^2*cos(u)^2+u), a(k,j)::=:v*(v^2*cos(u)^2+u)} iname s; 2 2 A(K,J) := V*(V *COS(U) + U) A(1,1) := 3 2 SIN(C*X + D) *COS(C*X + D) + SIN(C*X + D)*C*X + SIN(C*X + D)*D Sumscheme : | 7 8| EC|Far ------------------ 1| 1 | 1| 0 3| | 1| S2 5| 1| 1| S4 ------------------ 7 : U 8 : D Productscheme : | 0 1 2 3 4 5 6| EC|Far --------------------------------- 0| 1| 1| S0 2| 2 2| 1| 1 4| 2 3 | 1| 3 6| 1 1 | 1| 5 7| 1 1 1 | 1| 3 8| 1 1 | 1| 3 --------------------------------- 0 : D 1 : S5=COS(S4) 2 : S3=SIN(S4) 3 : X 4 : C 5 : S1=COS(U) 6 : V Number of operations in the input is: Number of (+,-)-operations : 7 Number of (*)-operations : 10 Number of integer exponentiations : 4 Number of other operations : 5 S8 := COS(U)*V A(K,J) := V*(U + S8*S8) S4 := X*C + D S3 := SIN(S4) S9 := COS(S4)*S3 A(1,1) := S3*(S4 + S9*S9) Number of operations after optimization is: Number of (+,-)-operations : 3 Number of (*)-operations : 7 Number of integer exponentiations : 0 Number of other operations : 3 Sumscheme : | 2 3 12 13| EC|Far ------------------------ 1| 1 | 1| 0 3| | 1| S2 5| 1 1| 1| S4 11| 1 | 1| 10 ------------------------ 2 : S4 3 : S6 12 : U 13 : D Productscheme : | 0 1 4 5 6 7 8 9 10 11| EC|Far ------------------------------------------ 0| 1| 1| S0 2| 2 | 1| 1 4| 2 | 1| 11 9| 1 1 | 1| S6 10| 1 | 1| 3 13| 1 1| 1| S8 14| 1 1 | 1| S9 ------------------------------------------ 0 : S9 1 : S8 4 : S6 5 : D 6 : S5=COS(S4) 7 : S3=SIN(S4) 8 : X 9 : C 10 : S1=COS(U) 11 : V off exp$ optimize {a(k,j):=v*(v^2*cos(u)^2+u), a(k,j)::=:v*(v^2*cos(u)^2+u)} iname s; 2 2 A(K,J) := V*(V *COS(U) + U) 2 2 A(1,1) := (SIN(C*X + D) *COS(C*X + D) + C*X + D)*SIN(C*X + D) Sumscheme : | 6 7| EC|Far ------------------ 1| 1 | 1| 0 4| 1| 1| 3 6| 1| 1| S4 ------------------ 6 : U 7 : D Productscheme : | 0 1 2 3 4 5| EC|Far ------------------------------ 0| 1| 1| S0 2| 2 2| 1| 1 3| 1 | 1| S2 5| 2 2 | 1| 4 7| 1 1 | 1| 6 8| 1 1 | 1| 4 ------------------------------ 0 : S5=COS(S4) 1 : S3=SIN(S4) 2 : X 3 : C 4 : S1=COS(U) 5 : V Number of operations in the input is: Number of (+,-)-operations : 6 Number of (*)-operations : 8 Number of integer exponentiations : 4 Number of other operations : 4 S8 := COS(U)*V A(K,J) := V*(U + S8*S8) S4 := X*C + D S3 := SIN(S4) S9 := COS(S4)*S3 A(1,1) := S3*(S4 + S9*S9) Number of operations after optimization is: Number of (+,-)-operations : 3 Number of (*)-operations : 7 Number of integer exponentiations : 0 Number of other operations : 3 Sumscheme : | 2 3 11 12| EC|Far ------------------------ 1| 1 | 1| 0 4| 1 | 1| 3 6| 1 1| 1| S4 ------------------------ 2 : S4 3 : S6 11 : U 12 : D Productscheme : | 0 1 4 5 6 7 8 9 10| EC|Far --------------------------------------- 0| 1| 1| S0 2| 2 | 1| 1 3| 1 | 1| S2 5| 2 | 1| 4 9| 1 1 | 1| S6 11| 1 1| 1| S8 12| 1 1 | 1| S9 --------------------------------------- 0 : S9 1 : S8 4 : S6 5 : S5=COS(S4) 6 : S3=SIN(S4) 7 : X 8 : C 9 : S1=COS(U) 10 : V off primat,acinfo,period$ on fort$ optimize z:=(6*a+18*b+9*c+3*d+6*e+18*f+6*g+5*h+5*k+3)^13 iname s; S0=5.0*(H+K)+3.0*(3.0*C+D+1.0+6.0*(B+F)+2.0*(A+EXP(1.0)+G)) S3=S0*S0*S0 S2=S3*S3 Z=S0*S2*S2 optimize {x:=3*a*p,y:=3*a*q,z:=6*a*r+2*b*p,u:=6*a*d+2*b*q, v:=9*a*c+4*b*d,w:=4*b} iname s; S2=3.0*A X=S2*P Y=S2*Q S1=2.0*B S3=6.0*A Z=S1*P+S3*R U=S1*Q+S3*D S0=4.0*B V=S0*D+9.0*C*A W=S0 off fort$ clear a$ matrix a(2,2)$ a(1,1):=x+y+z$ a(1,2):=x*y$ a(2,1):=(x+y)*x*y$ a(2,2):=(x+2*y+3)^3-x$ on acinfo$ optimize gstructr<<a; aa:=(x+y)^2;b:=(x+y)*(y+z);c:=(x+2*y)*(y+z)*(z+x)^2>> name v iname s; A(1,1) := X + Y + Z A(1,2) := X*Y V2 := X + Y A(2,1) := V2*X*Y 3 A(2,2) := (X + 2*Y + 3) - X 2 AA := V2 V5 := Y + Z B := V2*V5 2 C := (X + 2*Y)*(X + Z) *V5 Number of operations in the input is: Number of (+,-)-operations : 9 Number of (*)-operations : 8 Number of integer exponentiations : 3 Number of other operations : 0 S5 := X + Z A(1,1) := S5 + Y S8 := Y*X A(1,2) := S8 V2 := X + Y A(2,1) := S8*V2 S6 := X + 2*Y S4 := S6 + 3 A(2,2) := S4*S4*S4 - X AA := V2*V2 V5 := Y + Z B := V5*V2 C := S6*S5*S5*V5 Number of operations after optimization is: Number of (+,-)-operations : 7 Number of (*)-operations : 10 Number of integer exponentiations : 0 Number of other operations : 0 clear a$ off fort; on priall$ optimize z:=:for j:=2:6 sum a^(1/j) iname s; 1/3 1/4 1/5 1/6 Z := (((A + SQRT(A)) + A ) + A ) + A Sumscheme : || EC|Far ------------ 0|| 1| Z ------------ Productscheme : | 0| EC|Far --------------- 1| 20| 1| 0 2| 30| 1| 0 3| 15| 1| 0 4| 12| 1| 0 5| 10| 1| 0 --------------- 0 : A Number of operations in the input is: Number of (+,-)-operations : 4 Number of (*)-operations : 0 Number of integer exponentiations : 0 Number of other operations : 5 Time: 680 ms Breuer search : Time: 17 ms Removal of different names for identical cse's : Time: 0 ms Change Scheme : Time: 17 ms Local Factorization : Time: 0 ms Breuer search : Time: 17 ms Removal of different names for identical cse's : Time: 0 ms Change Scheme : Time: 0 ms Local Factorization : Time: 0 ms Breuer search : Time: 17 ms Removal of different names for identical cse's : Time: 0 ms Change Scheme : Time: 0 ms Local Factorization : Time: 0 ms Breuer search : Time: 0 ms Removal of different names for identical cse's : Time: 0 ms Change Scheme : Time: 0 ms Local Factorization : Time: 0 ms Additional optimization during finishing touch : Time: 0 ms 1/60 A := A S7 := A*A S6 := S7*A S4 := S7*S6 S2 := S4*S4 S1 := S7*S2 S0 := S6*S1 S3 := S4*S0 Z := S2 + S1 + S0 + S3 + S3*S2 Number of operations after optimization is: Number of (+,-)-operations : 4 Number of (*)-operations : 8 Number of integer exponentiations : 0 Number of other operations : 1 Sumscheme : | 3 4 5 6| EC|Far ------------------------ 0| 1 1 1 1| 1| Z ------------------------ 3 : S2 4 : S1 5 : S0 6 : S3 Productscheme : | 9 10 12 13 14 15 16 22| EC|Far ------------------------------------ 2| 1 1 | 1| 0 6| 1 1 | 1| S0 7| 1 1 | 1| S1 8| 2 | 1| S2 9| 1 1 | 1| S3 10| 1 1 | 1| S4 12| 1 1| 1| S6 13| 2| 1| S7 ------------------------------------ 9 : S7 10 : S6 12 : S4 13 : S3 14 : S2 15 : S1 16 : S0 22 : A Time: 34 ms off acinfo,priall$ on optdecs$ optlang!*:='fortran$ optimize {x(i+1,i-1):=a(i+1,i-1)+b(i),y(i-1):=a(i-1,i+1)-b(i)} iname s declare <<x(4),a(4,4),y(5):real;b(5):integer>>; INTEGER B(5),I,S1,S2 REAL A(4,4),S4,X(4),Y(5) S1=I+1.0 S2=I-1.0 S4=B(I) X(S1,S2)=A(S1,S2)+S4 Y(S2)=A(S2,S1)-S4 optlang!*:='c$ optimize {x(i+1,i-1):=a(i+1,i-1)+b(i),y(i-1):=a(i-1,i+1)-b(i)} iname s declare <<x(4),a(4,4),y(5):real;b(5):integer>>; int B[6],I,S1,S2; float A[5][5],S4,X[5],Y[6]; { S1=I+1.0; S2=I-1.0; S4=B[I]; X[S1][S2]=A[S1][S2]+S4; Y[S2]=A[S2][S1]-S4; } optlang!*:= 'pascal$ optimize {x(i+1,i-1):=a(i+1,i-1)+b(i),y(i-1):=a(i-1,i+1)-b(i)} iname s declare <<x(4),a(4,4),y(5):real;b(5):integer>>; VAR S2,S1,I: INTEGER; B: ARRAY[0..5] OF INTEGER; S4: REAL; Y: ARRAY[0..5] OF REAL; X: ARRAY[0..4] OF REAL; A: ARRAY[0..4,0..4] OF REAL; BEGIN S1:=I+1.0; S2:=I-1.0; S4:=B[I]; X[S1,S2]:=A[S1,S2]+S4; Y[S2]:=A[S2,S1]-S4 END; optlang!*:='ratfor$ optimize {x(i+1,i-1):=a(i+1,i-1)+b(i),y(i-1):=a(i-1,i+1)-b(i)} iname s declare <<x(4),a(4,4),y(5):real;b(5):integer>>; INTEGER B(5),I,S1,S2 REAL A(4,4),S4,X(4),Y(5) { S1=I+1.0 S2=I-1.0 S4=B(I) X(S1,S2)=A(S1,S2)+S4 Y(S2)=A(S2,S1)-S4 } end; 5: 5: Time: 153 ms 6: 6: Quitting Sat May 30 16:25:20 PDT 1992