Average Error: 0.0 → 0.0
Time: 7.6s
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 r19343 = x;
        double r19344 = y;
        double r19345 = z;
        double r19346 = r19345 - r19343;
        double r19347 = r19344 * r19346;
        double r19348 = r19343 + r19347;
        return r19348;
}
↓
double f(double x, double y, double z) {
        double r19349 = y;
        double r19350 = z;
        double r19351 = x;
        double r19352 = r19350 - r19351;
        double r19353 = fma(r19349, r19352, r19351);
        return r19353;
}

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))))