Average Error: 0.0 → 0.0
Time: 7.2s
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 r9686 = x;
        double r9687 = y;
        double r9688 = z;
        double r9689 = r9688 - r9686;
        double r9690 = r9687 * r9689;
        double r9691 = r9686 + r9690;
        return r9691;
}
↓
double f(double x, double y, double z) {
        double r9692 = x;
        double r9693 = z;
        double r9694 = y;
        double r9695 = r9693 * r9694;
        double r9696 = r9692 + r9695;
        double r9697 = -r9692;
        double r9698 = r9697 * r9694;
        double r9699 = r9696 + r9698;
        return r9699;
}

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 2019323 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))