Average Error: 0.0 → 0.0
Time: 15.9s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[\left(x + z \cdot y\right) + \left(-x\right) \cdot y\]
x + y \cdot \left(z - x\right)
↓
\left(x + z \cdot y\right) + \left(-x\right) \cdot y
double f(double x, double y, double z) {
        double r21675 = x;
        double r21676 = y;
        double r21677 = z;
        double r21678 = r21677 - r21675;
        double r21679 = r21676 * r21678;
        double r21680 = r21675 + r21679;
        return r21680;
}
↓
double f(double x, double y, double z) {
        double r21681 = x;
        double r21682 = z;
        double r21683 = y;
        double r21684 = r21682 * r21683;
        double r21685 = r21681 + r21684;
        double r21686 = -r21681;
        double r21687 = r21686 * r21683;
        double r21688 = r21685 + r21687;
        return r21688;
}

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 sub-neg0.0

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

  4. Applied distribute-rgt-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))