Average Error: 0.0 → 0.0
Time: 8.6s
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 r10654 = x;
        double r10655 = y;
        double r10656 = z;
        double r10657 = r10656 - r10654;
        double r10658 = r10655 * r10657;
        double r10659 = r10654 + r10658;
        return r10659;
}
↓
double f(double x, double y, double z) {
        double r10660 = z;
        double r10661 = x;
        double r10662 = r10660 - r10661;
        double r10663 = y;
        double r10664 = fma(r10662, r10663, r10661);
        return r10664;
}

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 2019323 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))