Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
\[x + y \cdot \left(z - x\right)\]
↓
\[\mathsf{fma}\left(z - x, y, x\right)\]
x + y \cdot \left(z - x\right)
↓
\mathsf{fma}\left(z - x, y, x\right)
double f(double x, double y, double z) {
        double r2625 = x;
        double r2626 = y;
        double r2627 = z;
        double r2628 = r2627 - r2625;
        double r2629 = r2626 * r2628;
        double r2630 = r2625 + r2629;
        return r2630;
}
↓
double f(double x, double y, double z) {
        double r2631 = z;
        double r2632 = x;
        double r2633 = r2631 - r2632;
        double r2634 = y;
        double r2635 = fma(r2633, r2634, r2632);
        return r2635;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(z - x, y, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(z - x, y, x\right)\]

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))