Average Error: 0.0 → 0.0
Time: 9.8s
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 r9760 = x;
        double r9761 = y;
        double r9762 = z;
        double r9763 = r9762 - r9760;
        double r9764 = r9761 * r9763;
        double r9765 = r9760 + r9764;
        return r9765;
}
↓
double f(double x, double y, double z) {
        double r9766 = z;
        double r9767 = x;
        double r9768 = r9766 - r9767;
        double r9769 = y;
        double r9770 = fma(r9768, r9769, r9767);
        return r9770;
}

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 2019322 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))