Average Error: 0.0 → 0.0
Time: 4.3s
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 r8165 = x;
        double r8166 = y;
        double r8167 = z;
        double r8168 = r8167 - r8165;
        double r8169 = r8166 * r8168;
        double r8170 = r8165 + r8169;
        return r8170;
}
↓
double f(double x, double y, double z) {
        double r8171 = z;
        double r8172 = x;
        double r8173 = r8171 - r8172;
        double r8174 = y;
        double r8175 = fma(r8173, r8174, r8172);
        return r8175;
}

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 2019303 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))