Average Error: 0.0 → 0.0
Time: 3.0s
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 r13676 = x;
        double r13677 = y;
        double r13678 = z;
        double r13679 = r13678 - r13676;
        double r13680 = r13677 * r13679;
        double r13681 = r13676 + r13680;
        return r13681;
}
↓
double f(double x, double y, double z) {
        double r13682 = z;
        double r13683 = x;
        double r13684 = r13682 - r13683;
        double r13685 = y;
        double r13686 = fma(r13684, r13685, r13683);
        return r13686;
}

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 2020020 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))