Average Error: 0.0 → 0.0
Time: 1.3s
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 r1806 = x;
        double r1807 = y;
        double r1808 = z;
        double r1809 = r1808 - r1806;
        double r1810 = r1807 * r1809;
        double r1811 = r1806 + r1810;
        return r1811;
}
↓
double f(double x, double y, double z) {
        double r1812 = z;
        double r1813 = x;
        double r1814 = r1812 - r1813;
        double r1815 = y;
        double r1816 = fma(r1814, r1815, r1813);
        return r1816;
}

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 2020034 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))