Average Error: 0.0 → 0.0
Time: 12.5s
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 r87633 = x;
        double r87634 = y;
        double r87635 = z;
        double r87636 = r87635 + r87633;
        double r87637 = r87634 * r87636;
        double r87638 = r87633 + r87637;
        return r87638;
}
↓
double f(double x, double y, double z) {
        double r87639 = x;
        double r87640 = z;
        double r87641 = y;
        double r87642 = r87640 * r87641;
        double r87643 = r87641 * r87639;
        double r87644 = r87642 + r87643;
        double r87645 = r87639 + r87644;
        return r87645;
}

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))))