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T=ld
V=x,y
R=-0.7, 0.7, 0.28
F=x/sin(y) + x/cos(y) + x/tan(y) + x/csc(y) + x/sec(y) + x/cot(y) + \
1/sin(y) + 1/cos(y) + 1/tan(y) + 1/csc(y) + 1/sec(y) + 1/cot(y)
# Expected outcome after bytecode optimization:
# x*csc(y) + x*sec(y) + x*cot(y)
# + x*sin(y) + x*cos(y) + x*tan(y)
# + csc(y) + sec(y) + cot(y)
# + sin(y) + cos(y) + tan(y)
# Expected intermediate form in tree optimization:
# x*sin(y)^-1 + x*cos(y)^-1 + x*cos(y)*sin(y)^-1
# + x*sin(y) + x*cos(y) + x*sin(y)*cos(y)^-1
# + sin(y)^-1 + cos(y)^-1 + cos(y)*sin(y)^-1
# + sin(y) + cos(y) + sin(y)*cos(y)^-1
# One of possible outcomes after tree optimization:
# (x+1) * ( (sin(y)+cos(y)+tan(y)) + 1/(sin(y)+cos(y)+tan(y)) )
# One of possible outcomes after tree optimization:
# (x+1) * (sin(y) * (1 + cos(y)^-1)
# + cos(y) * (1 + sin(y)^-1)
# + sin(y)^-1
# + cos(y)^-1)
# Note: sin(y) and cos(y) are subject to CSE and use of sincos().
# which would optimally result in the following bytecode:
# 00 push y [0=y]
# 01 sincos [0=sin,1=cos]
# 02 dup [2=cos]
# 03 inv [2=cos^-1]
# 04 fetch 0 [3=sin]
# 06 inv [3=sin^-1]
# 07 push x [4=x]
# 08 push 1 [5=1]
# 09 add [4=x+1]
# 0A fetch 0 [5=sin]
# 0C push 1 [6=1]
# 0D fetch 2 [7=cos^-1]
# 0F add [6=1+cos^-1]
# 10 mul [5=sin * (1+cos^-1)]
# 11 fetch 1 [6=sin]
# 13 push 1 [7=1]
# 14 fetch 3 [8=sin^-1]
# 16 add [7=1+sin^-1]
# 17 mul [6=cos * (1+cos^-1)]
# 18 add [5=sin * (1+cos^-1) + cos * (1+cos^-1)]
# 19 fetch 3 [6=sin^-1]
# 1B add [5=sin * (1+cos^-1) + cos * (1+cos^-1) + sin^-1]
# 1C fetch 2 [6=cos^-1]
# 1E add [5=sin * (1+cos^-1) + cos * (1+cos^-1) + sin^-1 + cos^-1]
# 1F mul [4=result]
# 20 <end>
# Unfortunately, the optimizer generates tan(), sec() and so on
# before it realizes the opportunities for sincos() use.
C= x/fp_sin(y) + x/fp_cos(y) + x/fp_tan(y) \
+ x*fp_sin(y) + x*fp_cos(y) + x*fp_tan(y) \
+ 1/fp_sin(y) + 1/fp_cos(y) + 1/fp_tan(y) \
+ 1*fp_sin(y) + 1*fp_cos(y) + 1*fp_tan(y)
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