Average Error: 0.0 → 0.0
Time: 2.2s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[\mathsf{fma}\left(z - x, y, x\right)\]
x + y \cdot \left(z - x\right)
↓
\mathsf{fma}\left(z - x, y, x\right)
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 = z;
        double r91 = x;
        double r92 = r90 - r91;
        double r93 = y;
        double r94 = fma(r92, r93, r91);
        return r94;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(z - x, y, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(z - x, y, x\right)\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))