Average Error: 0.0 → 0.0
Time: 16.4s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[\left(x + z \cdot y\right) + y \cdot \left(-x\right)\]
x + y \cdot \left(z - x\right)
↓
\left(x + z \cdot y\right) + y \cdot \left(-x\right)
double f(double x, double y, double z) {
        double r21670 = x;
        double r21671 = y;
        double r21672 = z;
        double r21673 = r21672 - r21670;
        double r21674 = r21671 * r21673;
        double r21675 = r21670 + r21674;
        return r21675;
}
↓
double f(double x, double y, double z) {
        double r21676 = x;
        double r21677 = z;
        double r21678 = y;
        double r21679 = r21677 * r21678;
        double r21680 = r21676 + r21679;
        double r21681 = -r21676;
        double r21682 = r21678 * r21681;
        double r21683 = r21680 + r21682;
        return r21683;
}

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-lft-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

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