Average Error: 0.0 → 0.0
Time: 15.1s
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 r738526 = x;
        double r738527 = y;
        double r738528 = z;
        double r738529 = r738528 - r738526;
        double r738530 = r738527 * r738529;
        double r738531 = r738526 + r738530;
        return r738531;
}
↓
double f(double x, double y, double z) {
        double r738532 = y;
        double r738533 = z;
        double r738534 = x;
        double r738535 = r738533 - r738534;
        double r738536 = fma(r738532, r738535, r738534);
        return r738536;
}

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 2019162 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  (+ x (* y (- z x))))