Average Error: 0.0 → 0.0
Time: 18.2s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[y \cdot \left(z - x\right) + x\]
x + y \cdot \left(z - x\right)
↓
y \cdot \left(z - x\right) + x
double f(double x, double y, double z) {
        double r18813 = x;
        double r18814 = y;
        double r18815 = z;
        double r18816 = r18815 - r18813;
        double r18817 = r18814 * r18816;
        double r18818 = r18813 + r18817;
        return r18818;
}
↓
double f(double x, double y, double z) {
        double r18819 = y;
        double r18820 = z;
        double r18821 = x;
        double r18822 = r18820 - r18821;
        double r18823 = r18819 * r18822;
        double r18824 = r18823 + r18821;
        return r18824;
}

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

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

Reproduce

herbie shell --seed 2019297 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))