Average Error: 0.0 → 0.0
Time: 4.1s
Precision: 64
\[\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)\]
↓
\[\left(z + \left(y + x\right)\right) - \left(\left(y + z\right) + x\right)\]
\left(\left(x + y\right) + z\right) - \left(x + \left(y + z\right)\right)
↓
\left(z + \left(y + x\right)\right) - \left(\left(y + z\right) + x\right)
double f(double x, double y, double z) {
        double r8067 = x;
        double r8068 = y;
        double r8069 = r8067 + r8068;
        double r8070 = z;
        double r8071 = r8069 + r8070;
        double r8072 = r8068 + r8070;
        double r8073 = r8067 + r8072;
        double r8074 = r8071 - r8073;
        return r8074;
}
↓
double f(double x, double y, double z) {
        double r8075 = z;
        double r8076 = y;
        double r8077 = x;
        double r8078 = r8076 + r8077;
        double r8079 = r8075 + r8078;
        double r8080 = r8076 + r8075;
        double r8081 = r8080 + r8077;
        double r8082 = r8079 - r8081;
        return r8082;
}

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

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Commute and associate"
  (- (+ (+ x y) z) (+ x (+ y z))))