Average Error: 0.0 → 0.0
Time: 11.7s
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 r99574 = x;
        double r99575 = y;
        double r99576 = z;
        double r99577 = r99576 + r99574;
        double r99578 = r99575 * r99577;
        double r99579 = r99574 + r99578;
        return r99579;
}
↓
double f(double x, double y, double z) {
        double r99580 = x;
        double r99581 = z;
        double r99582 = y;
        double r99583 = r99581 * r99582;
        double r99584 = r99582 * r99580;
        double r99585 = r99583 + r99584;
        double r99586 = r99580 + r99585;
        return r99586;
}

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 2019325 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))