Average Error: 0.0 → 0.0
Time: 7.2s
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 r9648 = x;
        double r9649 = y;
        double r9650 = z;
        double r9651 = r9650 - r9648;
        double r9652 = r9649 * r9651;
        double r9653 = r9648 + r9652;
        return r9653;
}
↓
double f(double x, double y, double z) {
        double r9654 = x;
        double r9655 = z;
        double r9656 = y;
        double r9657 = r9655 * r9656;
        double r9658 = r9654 + r9657;
        double r9659 = -r9654;
        double r9660 = r9656 * r9659;
        double r9661 = r9658 + r9660;
        return r9661;
}

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