Average Error: 0.0 → 0.0
Time: 8.9s
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 r221426 = x;
        double r221427 = y;
        double r221428 = z;
        double r221429 = r221428 - r221426;
        double r221430 = r221427 * r221429;
        double r221431 = r221426 + r221430;
        return r221431;
}
↓
double f(double x, double y, double z) {
        double r221432 = y;
        double r221433 = z;
        double r221434 = x;
        double r221435 = r221433 - r221434;
        double r221436 = fma(r221432, r221435, r221434);
        return r221436;
}

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 2019169 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))