Average Error: 0.0 → 0.0
Time: 15.8s
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 r218196 = x;
        double r218197 = y;
        double r218198 = z;
        double r218199 = r218198 - r218196;
        double r218200 = r218197 * r218199;
        double r218201 = r218196 + r218200;
        return r218201;
}
↓
double f(double x, double y, double z) {
        double r218202 = y;
        double r218203 = z;
        double r218204 = x;
        double r218205 = r218203 - r218204;
        double r218206 = fma(r218202, r218205, r218204);
        return r218206;
}

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 2019168 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))