Average Error: 0.0 → 0.0
Time: 5.8s
Precision: 64
\[\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)\]
↓
\[\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)\]
\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)
↓
\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)
double f(double x, double y, double z) {
        double r8567 = x;
        double r8568 = y;
        double r8569 = r8567 + r8568;
        double r8570 = z;
        double r8571 = r8569 + r8570;
        double r8572 = r8568 + r8570;
        double r8573 = r8567 + r8572;
        double r8574 = r8571 - r8573;
        return r8574;
}
↓
double f(double x, double y, double z) {
        double r8575 = x;
        double r8576 = y;
        double r8577 = r8575 + r8576;
        double r8578 = z;
        double r8579 = r8577 + r8578;
        double r8580 = r8576 + r8578;
        double r8581 = r8575 + r8580;
        double r8582 = r8579 - r8581;
        return r8582;
}

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

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(FPCore (x y z)
  :name "Commute and associate"
  (- (+ (+ x y) z) (+ x (+ y z))))