import Data.SBV

test1 :: (SFloat -> SFloat -> SFloat) -> Symbolic SBool
test1 fun =
  do [x, y] <- sFloats ["x", "y"]
     constrain $ bnot (isInfiniteFP x) &&& bnot (isInfiniteFP y)
     constrain $ 0 .<= x &&& x .<= y
     let z = fun x y
     return $ x .<= z &&& z .<= y

test2 :: (SFloat -> SFloat -> SFloat) -> Symbolic SBool
test2 fun =
  do [x, y] <- sFloats ["x", "y"]
     constrain $ bnot (isInfiniteFP x) &&& bnot (isInfiniteFP y)
     constrain $ x .<= y
     let z = fun x y
     return $ x .<= z &&& z .<= y

λ> prove $ test1 (x y -> (x + y) / 2)
Falsifiable. Counter-example:
  x = 2.3089316e36 :: Float
  y = 3.379786e38 :: Float

λ> prove $ test1 (x y -> x/2 + y/2)
Falsifiable. Counter-example:
  x = 2.3509886e-38 :: Float
  y = 2.3509886e-38 :: Float

λ> prove $ test1 (x y -> x + (y-x)/2)
Q.E.D.

λ> prove $ test2 (x y -> x + (y-x)/2)
Falsifiable. Counter-example:
  x = -3.1300826e34 :: Float
  y = 3.402721e38 :: Float

λ> prove $ test2 (x y -> x + (y/2 - x/2))
Q.E.D.

if max(abs(x),abs(y)) >= 1.:
    return x/2. + y/2.
else:
    return (x+y)/2.

float difference = max(x, y) - min(x, y);
return min(x, y) + (difference / 2.0);