Average Error: 0.0 → 0.0
Time: 17.1s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[\left(z \cdot y + x\right) + y \cdot \left(-x\right)\]
x + y \cdot \left(z - x\right)
↓
\left(z \cdot y + x\right) + y \cdot \left(-x\right)
double f(double x, double y, double z) {
        double r18665 = x;
        double r18666 = y;
        double r18667 = z;
        double r18668 = r18667 - r18665;
        double r18669 = r18666 * r18668;
        double r18670 = r18665 + r18669;
        return r18670;
}
↓
double f(double x, double y, double z) {
        double r18671 = z;
        double r18672 = y;
        double r18673 = r18671 * r18672;
        double r18674 = x;
        double r18675 = r18673 + r18674;
        double r18676 = -r18674;
        double r18677 = r18672 * r18676;
        double r18678 = r18675 + r18677;
        return r18678;
}

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

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))