Average Error: 0.0 → 0.0
Time: 6.6s
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 r19346 = x;
        double r19347 = y;
        double r19348 = z;
        double r19349 = r19348 - r19346;
        double r19350 = r19347 * r19349;
        double r19351 = r19346 + r19350;
        return r19351;
}
↓
double f(double x, double y, double z) {
        double r19352 = y;
        double r19353 = z;
        double r19354 = x;
        double r19355 = r19353 - r19354;
        double r19356 = fma(r19352, r19355, r19354);
        return r19356;
}

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 2019163 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))