Average Error: 0.0 → 0.0
Time: 889.0ms
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[x + \left(y \cdot z + y \cdot x\right)\]
x + y \cdot \left(z + x\right)
↓
x + \left(y \cdot z + y \cdot x\right)
double f(double x, double y, double z) {
        double r101929 = x;
        double r101930 = y;
        double r101931 = z;
        double r101932 = r101931 + r101929;
        double r101933 = r101930 * r101932;
        double r101934 = r101929 + r101933;
        return r101934;
}
↓
double f(double x, double y, double z) {
        double r101935 = x;
        double r101936 = y;
        double r101937 = z;
        double r101938 = r101936 * r101937;
        double r101939 = r101936 * r101935;
        double r101940 = r101938 + r101939;
        double r101941 = r101935 + r101940;
        return r101941;
}

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-lft-in0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))