Average Error: 0.0 → 0.0
Time: 11.8s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[\mathsf{fma}\left(y, z - x, x\right)\]
x + y \cdot \left(z - x\right)
↓
\mathsf{fma}\left(y, z - x, x\right)
double f(double x, double y, double z) {
        double r756989 = x;
        double r756990 = y;
        double r756991 = z;
        double r756992 = r756991 - r756989;
        double r756993 = r756990 * r756992;
        double r756994 = r756989 + r756993;
        return r756994;
}
↓
double f(double x, double y, double z) {
        double r756995 = y;
        double r756996 = z;
        double r756997 = x;
        double r756998 = r756996 - r756997;
        double r756999 = fma(r756995, r756998, r756997);
        return r756999;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))