Average Error: 0.0 → 0.0
Time: 8.4s
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 r10692 = x;
        double r10693 = y;
        double r10694 = z;
        double r10695 = r10694 - r10692;
        double r10696 = r10693 * r10695;
        double r10697 = r10692 + r10696;
        return r10697;
}
↓
double f(double x, double y, double z) {
        double r10698 = z;
        double r10699 = x;
        double r10700 = r10698 - r10699;
        double r10701 = y;
        double r10702 = fma(r10700, r10701, r10699);
        return r10702;
}

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))))