Average Error: 0.0 → 0.0
Time: 3.7s
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 r84 = x;
        double r85 = y;
        double r86 = z;
        double r87 = r86 - r84;
        double r88 = r85 * r87;
        double r89 = r84 + r88;
        return r89;
}
↓
double f(double x, double y, double z) {
        double r90 = x;
        double r91 = z;
        double r92 = y;
        double r93 = r91 * r92;
        double r94 = r90 + r93;
        double r95 = -r90;
        double r96 = r95 * r92;
        double r97 = r94 + r96;
        return r97;
}

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 2020025 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))