"Floating-point numbers are like a band-aid covering a mortal wound."

Comparison of IEEE double-precision floating-point and interval
arithmetic. Note how interval arithmetic always gives strict
(guaranteed) lower..upper bounds on the correct value, whereas
floating-point merely gives some shot-in-the-dark which might be any
arbitrary distance from the correct answer with no guarantee as to how
close or far it might perchance be.

Double-precision floating point  Interval arithmetic
2d0                              2
            (take square root)
1.4142135623730951d0             1.414213562373095[0..1]
            (take square root)
1.189207115002721d0              1.189207115002721[0..1]
            (take square root)
1.0905077326652577d0             1.090507732665257[6..7]
            (take square root)
1.0442737824274138d0             1.044273782427413[8..9]
(2^4th power: 1.9999999999999973d0  2.00000000000000[-13..+18])
            (take square root)
1.0218971486541166d0             1.021897148654116[6..8]
            (take square root)
1.0108892860517005d0             1.010889286051700[4..6]
            (take square root)
1.0054299011128027d0             1.005429901112802[7..9]
            (take square root)
1.0027112750502025d0             1.002711275050202[4..6]
(2^8th power: 2.0000000000000187d0  2.0000000000000[-44..+59])
            (take square root)
1.0013547198921082d0             1.001354719892108[1..3]
            (take square root)
1.0006771306930664d0             1.000677130693066[3..5]
            (take square root)
1.0003385080526823d0             1.000338508052682[2..4]
            (take square root)
1.0001692397053021d0             1.000169239705302[1..3]
(2^12th power = 1.9999999999992353d0  2.000000000000[-11..+06])
            (take square root)
1.0000846162726942d0             1.000084616272694[2..4]
            (take square root)
1.0000423072413958d0             1.000042307241395[7..9]
            (take square root)
1.0000211533969647d0             1.000021153396964[7..9]
            (take square root)
1.0000105766425498d0             1.000010576642549[6..8]
(2^16th power = 2.000000000007247d0  2.0000000000[-16..+11])