Average Error: 0.0 → 0.0
Time: 1.0s
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 r253 = x;
        double r254 = y;
        double r255 = z;
        double r256 = r255 - r253;
        double r257 = r254 * r256;
        double r258 = r253 + r257;
        return r258;
}
↓
double f(double x, double y, double z) {
        double r259 = z;
        double r260 = x;
        double r261 = r259 - r260;
        double r262 = y;
        double r263 = fma(r261, r262, r260);
        return r263;
}

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 2020035 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))