Average Error: 0.0 → 0.0
Time: 17.4s
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[x + \left(z \cdot y + y \cdot x\right)\]
x + y \cdot \left(z + x\right)
↓
x + \left(z \cdot y + y \cdot x\right)
double f(double x, double y, double z) {
        double r127027 = x;
        double r127028 = y;
        double r127029 = z;
        double r127030 = r127029 + r127027;
        double r127031 = r127028 * r127030;
        double r127032 = r127027 + r127031;
        return r127032;
}
↓
double f(double x, double y, double z) {
        double r127033 = x;
        double r127034 = z;
        double r127035 = y;
        double r127036 = r127034 * r127035;
        double r127037 = r127035 * r127033;
        double r127038 = r127036 + r127037;
        double r127039 = r127033 + r127038;
        return r127039;
}

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. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))