Average Error: 0.0 → 0.0
Time: 2.7s
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 r125725 = x;
        double r125726 = y;
        double r125727 = z;
        double r125728 = r125727 + r125725;
        double r125729 = r125726 * r125728;
        double r125730 = r125725 + r125729;
        return r125730;
}
↓
double f(double x, double y, double z) {
        double r125731 = x;
        double r125732 = y;
        double r125733 = z;
        double r125734 = r125732 * r125733;
        double r125735 = r125732 * r125731;
        double r125736 = r125734 + r125735;
        double r125737 = r125731 + r125736;
        return r125737;
}

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 2020001 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))