Average Error: 0.0 → 0.0
Time: 19.1s
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 r987371 = x;
        double r987372 = y;
        double r987373 = z;
        double r987374 = r987373 - r987371;
        double r987375 = r987372 * r987374;
        double r987376 = r987371 + r987375;
        return r987376;
}
↓
double f(double x, double y, double z) {
        double r987377 = y;
        double r987378 = z;
        double r987379 = x;
        double r987380 = r987378 - r987379;
        double r987381 = fma(r987377, r987380, r987379);
        return r987381;
}

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 2019172 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))