Average Error: 0.0 → 0.0
Time: 22.6s
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 r35269 = x;
        double r35270 = y;
        double r35271 = z;
        double r35272 = r35271 - r35269;
        double r35273 = r35270 * r35272;
        double r35274 = r35269 + r35273;
        return r35274;
}
↓
double f(double x, double y, double z) {
        double r35275 = z;
        double r35276 = x;
        double r35277 = r35275 - r35276;
        double r35278 = y;
        double r35279 = fma(r35277, r35278, r35276);
        return r35279;
}

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 2019200 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))