Average Error: 0.0 → 0.0
Time: 6.0s
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 r8454 = x;
        double r8455 = y;
        double r8456 = z;
        double r8457 = r8456 - r8454;
        double r8458 = r8455 * r8457;
        double r8459 = r8454 + r8458;
        return r8459;
}
↓
double f(double x, double y, double z) {
        double r8460 = z;
        double r8461 = x;
        double r8462 = r8460 - r8461;
        double r8463 = y;
        double r8464 = fma(r8462, r8463, r8461);
        return r8464;
}

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 2019304 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))