SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Average Error: 0.0 → 0.0

Time: 9.1s

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 r1264 = x;
        double r1265 = y;
        double r1266 = z;
        double r1267 = r1266 - r1264;
        double r1268 = r1265 * r1267;
        double r1269 = r1264 + r1268;
        return r1269;
}

↓

double f(double x, double y, double z) {
        double r1270 = z;
        double r1271 = x;
        double r1272 = r1270 - r1271;
        double r1273 = y;
        double r1274 = fma(r1272, r1273, r1271);
        return r1274;
}

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 2020046 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))