Average Error: 0.0 → 0.0
Time: 1.4s
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 r206 = x;
        double r207 = y;
        double r208 = r206 + r207;
        double r209 = z;
        double r210 = r208 + r209;
        double r211 = r207 + r209;
        double r212 = r206 + r211;
        double r213 = r210 - r212;
        return r213;
}
↓
double f(double x, double y, double z) {
        double r214 = x;
        double r215 = y;
        double r216 = r214 + r215;
        double r217 = z;
        double r218 = r216 + r217;
        double r219 = r215 + r217;
        double r220 = r214 + r219;
        double r221 = r218 - r220;
        return r221;
}

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 2020001 
(FPCore (x y z)
  :name "Commute and associate"
  :precision binary64
  (- (+ (+ x y) z) (+ x (+ y z))))