# possible stops: 4,6,8
# f: f(x). g: f'(x).

flist1=f(-x),-f(x),-f(-x)
xlist1=-t,t,-t
ylist1=f,-f,-f

flist2=f(x+1),f(x-1),f(x)+1,f(x)-1
xlist2=t-1,t+1,t,t
ylist2=f,f,f+1,f-1

flist3=f(2x),f(x/2),2f(x),f(x)/2
xlist3=t/2,2*t,t,t
ylist3=f,f,2*f,f/2

flist4=f(x+1),f(x-1),f(x)+1,f(x)-1,f(1-x),f(-x-1),1-f(x),-1-f(x)
xlist4=t-1,t+1,t,t,1-t,-1-t,t,t
ylist4=f,f,f+1,f-1,f,f,1-f,-1-f

flist5=f(2x),f(x/2),2f(x),f(x)/2,-f(2x),-f(x/2),-2f(x),-f(x)/2,f(-2x),f(-x/2),2f(-x),f(-x)/2
xlist5=t/2,2*t,t,t,t/2,2*t,t,t,-t/2,-2*t,-t,-t
ylist5=f,f,2*f,f/2,-f,-f,-2*f,-f/2,f,f,2*f,f/2

