zdt3.mw

restart; 1 

ZDT 3 

 


`:=`(f, proc (x) options operator, arrow; `+`(1, `-`(sqrt(x)), `-`(`*`(x, `*`(sin(`+`(`*`(10, `*`(Pi, `*`(x))))))))) end proc); -1; 'f(x)' = f(x)
 

f(x) = `+`(1, `-`(`*`(`^`(x, `/`(1, 2)))), `-`(`*`(x, `*`(sin(`+`(`*`(10, `*`(Pi, `*`(x))))))))) (1)
 

`:=`(xmin, [0, .1822287280, .4093136748, .6183967944, .8233317983]) 

[0, .1822287280, .4093136748, .6183967944, .8233317983] (2)
 

`:=`(xmax, [0.830015349e-1, .2577623634, .4538821041, .6525117038, .8518328654]) 

[0.830015349e-1, .2577623634, .4538821041, .6525117038, .8518328654] (3)
 

`:=`(C, sum(int(sqrt(`+`(`-`(diff(f(x), x)))), x = xmin[i] .. xmax[i]), i = 1 .. 5)) 

.6414958715 (4)
 

`:=`(delta, proc (x) options operator, arrow; `/`(`*`(sqrt(`+`(`-`(`/`(`*`(diff(f(x), x)), `*`(`+`(1, `*`(`^`(diff(f(x), x), 2))))))))), `*`(C)) end proc); -1; 'delta(x)' = simplify(delta(x), size) 

delta(x) = `+`(`*`(1.558856486, `*`(`^`(`/`(`*`(`+`(`/`(`*`(2), `*`(`^`(x, `/`(1, 2)))), `*`(4, `*`(sin(`+`(`*`(10, `*`(Pi, `*`(x))))))), `*`(40, `*`(x, `*`(cos(`+`(`*`(10, `*`(Pi, `*`(x))))), `*`(Pi)...
delta(x) = `+`(`*`(1.558856486, `*`(`^`(`/`(`*`(`+`(`/`(`*`(2), `*`(`^`(x, `/`(1, 2)))), `*`(4, `*`(sin(`+`(`*`(10, `*`(Pi, `*`(x))))))), `*`(40, `*`(x, `*`(cos(`+`(`*`(10, `*`(Pi, `*`(x))))), `*`(Pi)...
delta(x) = `+`(`*`(1.558856486, `*`(`^`(`/`(`*`(`+`(`/`(`*`(2), `*`(`^`(x, `/`(1, 2)))), `*`(4, `*`(sin(`+`(`*`(10, `*`(Pi, `*`(x))))))), `*`(40, `*`(x, `*`(cos(`+`(`*`(10, `*`(Pi, `*`(x))))), `*`(Pi)...
delta(x) = `+`(`*`(1.558856486, `*`(`^`(`/`(`*`(`+`(`/`(`*`(2), `*`(`^`(x, `/`(1, 2)))), `*`(4, `*`(sin(`+`(`*`(10, `*`(Pi, `*`(x))))))), `*`(40, `*`(x, `*`(cos(`+`(`*`(10, `*`(Pi, `*`(x))))), `*`(Pi)...
(5)
 

 

limit(diff(f(x), x), x = xmax[5]) 

-0.37e-7 (6)
 

limit(diff(f(x), x), x = xmin[1]) 

undefined (7)