Average Error: 0.0 → 0.0
Time: 1.1m
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[x + \left(z \cdot y + y \cdot \left(-x\right)\right)\]
x + y \cdot \left(z - x\right)
↓
x + \left(z \cdot y + y \cdot \left(-x\right)\right)
double f(double x, double y, double z) {
        double r23313 = x;
        double r23314 = y;
        double r23315 = z;
        double r23316 = r23315 - r23313;
        double r23317 = r23314 * r23316;
        double r23318 = r23313 + r23317;
        return r23318;
}
↓
double f(double x, double y, double z) {
        double r23319 = x;
        double r23320 = z;
        double r23321 = y;
        double r23322 = r23320 * r23321;
        double r23323 = -r23319;
        double r23324 = r23321 * r23323;
        double r23325 = r23322 + r23324;
        double r23326 = r23319 + r23325;
        return r23326;
}

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. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019202 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))