Average Error: 0.0 → 0.0
Time: 8.7s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[\mathsf{fma}\left(y, z - x, x\right)\]
x + y \cdot \left(z - x\right)
↓
\mathsf{fma}\left(y, z - x, x\right)
double f(double x, double y, double z) {
        double r220071 = x;
        double r220072 = y;
        double r220073 = z;
        double r220074 = r220073 - r220071;
        double r220075 = r220072 * r220074;
        double r220076 = r220071 + r220075;
        return r220076;
}
↓
double f(double x, double y, double z) {
        double r220077 = y;
        double r220078 = z;
        double r220079 = x;
        double r220080 = r220078 - r220079;
        double r220081 = fma(r220077, r220080, r220079);
        return r220081;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, z - x, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, z - x, x\right)\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))