Average Error: 0.0 → 0.0
Time: 7.9s
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 r9644 = x;
        double r9645 = y;
        double r9646 = z;
        double r9647 = r9646 - r9644;
        double r9648 = r9645 * r9647;
        double r9649 = r9644 + r9648;
        return r9649;
}
↓
double f(double x, double y, double z) {
        double r9650 = x;
        double r9651 = z;
        double r9652 = y;
        double r9653 = r9651 * r9652;
        double r9654 = r9650 + r9653;
        double r9655 = -r9650;
        double r9656 = r9655 * r9652;
        double r9657 = r9654 + r9656;
        return r9657;
}

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))))