Average Error: 0.0 → 0.0
Time: 4.6s
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 r8158 = x;
        double r8159 = y;
        double r8160 = z;
        double r8161 = r8160 - r8158;
        double r8162 = r8159 * r8161;
        double r8163 = r8158 + r8162;
        return r8163;
}
↓
double f(double x, double y, double z) {
        double r8164 = z;
        double r8165 = x;
        double r8166 = r8164 - r8165;
        double r8167 = y;
        double r8168 = fma(r8166, r8167, r8165);
        return r8168;
}

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 2019310 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))