Average Error: 0.0 → 0.0
Time: 1.4s
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 r2614 = x;
        double r2615 = y;
        double r2616 = z;
        double r2617 = r2616 - r2614;
        double r2618 = r2615 * r2617;
        double r2619 = r2614 + r2618;
        return r2619;
}
↓
double f(double x, double y, double z) {
        double r2620 = z;
        double r2621 = x;
        double r2622 = r2620 - r2621;
        double r2623 = y;
        double r2624 = fma(r2622, r2623, r2621);
        return r2624;
}

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))))