Average Error: 0.0 → 0.0
Time: 23.7s
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 r512598 = x;
        double r512599 = y;
        double r512600 = z;
        double r512601 = r512600 - r512598;
        double r512602 = r512599 * r512601;
        double r512603 = r512598 + r512602;
        return r512603;
}
↓
double f(double x, double y, double z) {
        double r512604 = y;
        double r512605 = z;
        double r512606 = x;
        double r512607 = r512605 - r512606;
        double r512608 = fma(r512604, r512607, r512606);
        return r512608;
}

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 2019165 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))