Average Error: 0.0 → 0.0
Time: 19.8s
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 r27661 = x;
        double r27662 = y;
        double r27663 = z;
        double r27664 = r27663 - r27661;
        double r27665 = r27662 * r27664;
        double r27666 = r27661 + r27665;
        return r27666;
}
↓
double f(double x, double y, double z) {
        double r27667 = z;
        double r27668 = x;
        double r27669 = r27667 - r27668;
        double r27670 = y;
        double r27671 = fma(r27669, r27670, r27668);
        return r27671;
}

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 2019325 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))