Average Error: 0.0 → 0
Time: 1.9s
Precision: binary64
Cost: 320
\[x + \frac{y - x}{2} \]
↓
\[0.5 \cdot \left(y + x\right) \]
(FPCore (x y) :precision binary64 (+ x (/ (- y x) 2.0)))
↓
(FPCore (x y) :precision binary64 (* 0.5 (+ y x)))
double code(double x, double y) {
	return x + ((y - x) / 2.0);
}
↓
double code(double x, double y) {
	return 0.5 * (y + x);
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + ((y - x) / 2.0d0)
end function
↓
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * (y + x)
end function

public static double code(double x, double y) {
	return x + ((y - x) / 2.0);
}
↓
public static double code(double x, double y) {
	return 0.5 * (y + x);
}

def code(x, y):
	return x + ((y - x) / 2.0)
↓
def code(x, y):
	return 0.5 * (y + x)

function code(x, y)
	return Float64(x + Float64(Float64(y - x) / 2.0))
end
↓
function code(x, y)
	return Float64(0.5 * Float64(y + x))
end

function tmp = code(x, y)
	tmp = x + ((y - x) / 2.0);
end
↓
function tmp = code(x, y)
	tmp = 0.5 * (y + x);
end

code[x_, y_] := N[(x + N[(N[(y - x), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(0.5 * N[(y + x), $MachinePrecision]), $MachinePrecision]

x + \frac{y - x}{2}
↓
0.5 \cdot \left(y + x\right)

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0
Herbie0
\[0.5 \cdot \left(x + y\right) \]

Derivation

  1. Initial program 0.0

    \[x + \frac{y - x}{2} \]

  2. Simplified0

    \[\leadsto \color{blue}{0.5 \cdot \left(y + x\right)} \]
    Proof
    (*.f64 1/2 (+.f64 y x)): 0 points increase in error, 0 points decrease in error
    (*.f64 (Rewrite<= metadata-eval (*.f64 -1/2 -1)) (+.f64 y x)): 0 points increase in error, 0 points decrease in error
    (*.f64 (*.f64 (Rewrite<= metadata-eval (/.f64 -1 2)) -1) (+.f64 y x)): 0 points increase in error, 0 points decrease in error
    (Rewrite=> distribute-rgt-in_binary64 (+.f64 (*.f64 y (*.f64 (/.f64 -1 2) -1)) (*.f64 x (*.f64 (/.f64 -1 2) -1)))): 0 points increase in error, 0 points decrease in error
    (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (/.f64 -1 2) -1) y)) (*.f64 x (*.f64 (/.f64 -1 2) -1))): 0 points increase in error, 0 points decrease in error
    (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (/.f64 -1 2) (*.f64 -1 y))) (*.f64 x (*.f64 (/.f64 -1 2) -1))): 0 points increase in error, 0 points decrease in error
    (+.f64 (*.f64 (/.f64 -1 2) (Rewrite<= neg-mul-1_binary64 (neg.f64 y))) (*.f64 x (*.f64 (/.f64 -1 2) -1))): 0 points increase in error, 0 points decrease in error
    (+.f64 (Rewrite<= associate-/r/_binary64 (/.f64 -1 (/.f64 2 (neg.f64 y)))) (*.f64 x (*.f64 (/.f64 -1 2) -1))): 0 points increase in error, 0 points decrease in error
    (+.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 -1 (neg.f64 y)) 2)) (*.f64 x (*.f64 (/.f64 -1 2) -1))): 1 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 (neg.f64 y))) 2) (*.f64 x (*.f64 (/.f64 -1 2) -1))): 0 points increase in error, 1 points decrease in error
    (+.f64 (/.f64 (Rewrite=> remove-double-neg_binary64 y) 2) (*.f64 x (*.f64 (/.f64 -1 2) -1))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 y 2) (*.f64 x (*.f64 (Rewrite=> metadata-eval -1/2) -1))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 y 2) (*.f64 x (Rewrite=> metadata-eval 1/2))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 y 2) (*.f64 x (Rewrite<= metadata-eval (-.f64 -1/2 -1)))): 1 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 y 2) (*.f64 x (-.f64 (Rewrite<= metadata-eval (/.f64 -1 2)) -1))): 0 points increase in error, 1 points decrease in error
    (+.f64 (/.f64 y 2) (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 (/.f64 -1 2) x) (*.f64 -1 x)))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 y 2) (-.f64 (Rewrite<= associate-/r/_binary64 (/.f64 -1 (/.f64 2 x))) (*.f64 -1 x))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 y 2) (-.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 -1 x) 2)) (*.f64 -1 x))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 y 2) (-.f64 (/.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 x)) 2) (*.f64 -1 x))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 y 2) (-.f64 (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 x 2))) (*.f64 -1 x))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 y 2) (-.f64 (neg.f64 (/.f64 x 2)) (Rewrite<= neg-mul-1_binary64 (neg.f64 x)))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 y 2) (Rewrite<= unsub-neg_binary64 (+.f64 (neg.f64 (/.f64 x 2)) (neg.f64 (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
    (Rewrite=> associate-+r+_binary64 (+.f64 (+.f64 (/.f64 y 2) (neg.f64 (/.f64 x 2))) (neg.f64 (neg.f64 x)))): 0 points increase in error, 0 points decrease in error
    (+.f64 (Rewrite<= sub-neg_binary64 (-.f64 (/.f64 y 2) (/.f64 x 2))) (neg.f64 (neg.f64 x))): 1 points increase in error, 0 points decrease in error
    (+.f64 (Rewrite<= div-sub_binary64 (/.f64 (-.f64 y x) 2)) (neg.f64 (neg.f64 x))): 0 points increase in error, 1 points decrease in error
    (+.f64 (/.f64 (-.f64 y x) 2) (Rewrite=> remove-double-neg_binary64 x)): 1 points increase in error, 0 points decrease in error
    (Rewrite<= +-commutative_binary64 (+.f64 x (/.f64 (-.f64 y x) 2))): 0 points increase in error, 1 points decrease in error

  3. Final simplification0

    \[\leadsto 0.5 \cdot \left(y + x\right) \]

Reproduce

herbie shell --seed 2022343 
(FPCore (x y)
  :name "Numeric.Interval.Internal:bisect from intervals-0.7.1, A"
  :precision binary64

  :herbie-target
  (* 0.5 (+ x y))

  (+ x (/ (- y x) 2.0)))