about the maximum relative error

maximum error = 0.5

maximum relative error= 50%

The lowest of x = 0.01 highest of x =0.49

The lowest of y =1.01 highest of y =1.49


Range = (1-0.01) over (1+1.01) to (1-0.49) over (1+1.49)

0.492 to 0.205

x is round to 0, therefore x can be greater than -0.5 and less than 0.5
y is round to 1, therefore y can be greater than 0.5 and less than 1.5

(1-x) / (1+y) is maximum when x is minium and y is minimum
= [1-(-0.5)] / (1+0.5)
= 1

(1-x) / (1+y) is minimum when x is maximum and y is maximum
= (1-0.5) / (1+1.5)
= 0.25

maximum relative error occur when (1-x) / (1+y) is 0.25 but calculated as 1
Therefore,
the maximum relative error
= (1-0.25/0.25)x100%
= (0.75/0.25)x100%
= 300%