SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Average Error: 0.0 → 0.0

Time: 5.3s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[x + y \cdot \left(z - x\right)\]

↓

\[\mathsf{fma}\left(z - x, y, x\right)\]

C

double f(double x, double y, double z) {
        double r1870 = x;
        double r1871 = y;
        double r1872 = z;
        double r1873 = r1872 - r1870;
        double r1874 = r1871 * r1873;
        double r1875 = r1870 + r1874;
        return r1875;
}

↓

double f(double x, double y, double z) {
        double r1876 = z;
        double r1877 = x;
        double r1878 = r1876 - r1877;
        double r1879 = y;
        double r1880 = fma(r1878, r1879, r1877);
        return r1880;
}

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. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(z - x, y, x\right)}\]

3. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(z - x, y, x\right)\]

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))