Average Error: 0.0 → 0.0
Time: 8.6s
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 r10650 = x;
        double r10651 = y;
        double r10652 = z;
        double r10653 = r10652 - r10650;
        double r10654 = r10651 * r10653;
        double r10655 = r10650 + r10654;
        return r10655;
}
↓
double f(double x, double y, double z) {
        double r10656 = z;
        double r10657 = x;
        double r10658 = r10656 - r10657;
        double r10659 = y;
        double r10660 = fma(r10658, r10659, r10657);
        return r10660;
}

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 2019323 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))