Average Error: 0.0 → 0.0
Time: 2.7s
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[\left(x + z \cdot y\right) + x \cdot y\]
x + y \cdot \left(z + x\right)
↓
\left(x + z \cdot y\right) + x \cdot y
double f(double x, double y, double z) {
        double r156898 = x;
        double r156899 = y;
        double r156900 = z;
        double r156901 = r156900 + r156898;
        double r156902 = r156899 * r156901;
        double r156903 = r156898 + r156902;
        return r156903;
}
↓
double f(double x, double y, double z) {
        double r156904 = x;
        double r156905 = z;
        double r156906 = y;
        double r156907 = r156905 * r156906;
        double r156908 = r156904 + r156907;
        double r156909 = r156904 * r156906;
        double r156910 = r156908 + r156909;
        return r156910;
}

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

    \[x + y \cdot \left(z + x\right)\]
  2. Using strategy rm

  3. Applied distribute-rgt-in0.0

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

  4. Applied associate-+r+0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020002 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))