Average Error: 0.0 → 0.0
Time: 1.8s
Precision: binary64
\[[x, y, z] = \mathsf{sort}([x, y, z]) \\]
\[\left(x + y\right) + z \]
↓
\[x + \left(y + z\right) \]
\left(x + y\right) + z
↓
x + \left(y + z\right)

(FPCore (x y z) :precision binary64 (+ (+ x y) z))
↓
(FPCore (x y z) :precision binary64 (+ x (+ y z)))
double code(double x, double y, double z) {
	return (x + y) + z;
}
↓
double code(double x, double y, double z) {
	return x + (y + z);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(x + y\right) + z \]

  2. Applied associate-+l+_binary640.0

    \[\leadsto \color{blue}{x + \left(y + z\right)} \]

  3. Final simplification0.0

    \[\leadsto x + \left(y + z\right) \]

Reproduce

herbie shell --seed 2022076 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, I"
  :precision binary64
  (+ (+ x y) z))