Average Error: 0.0 → 0.0
Time: 725.0ms
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 r264 = x;
        double r265 = y;
        double r266 = z;
        double r267 = r266 - r264;
        double r268 = r265 * r267;
        double r269 = r264 + r268;
        return r269;
}
↓
double f(double x, double y, double z) {
        double r270 = z;
        double r271 = x;
        double r272 = r270 - r271;
        double r273 = y;
        double r274 = fma(r272, r273, r271);
        return r274;
}

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 2019346 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))