Average Error: 0.0 → 0.0
Time: 9.7s
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 r10563 = x;
        double r10564 = y;
        double r10565 = z;
        double r10566 = r10565 - r10563;
        double r10567 = r10564 * r10566;
        double r10568 = r10563 + r10567;
        return r10568;
}
↓
double f(double x, double y, double z) {
        double r10569 = y;
        double r10570 = z;
        double r10571 = x;
        double r10572 = r10570 - r10571;
        double r10573 = fma(r10569, r10572, r10571);
        return r10573;
}

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 2019194 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))