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 r3193 = x;
        double r3194 = y;
        double r3195 = z;
        double r3196 = r3195 - r3193;
        double r3197 = r3194 * r3196;
        double r3198 = r3193 + r3197;
        return r3198;
}

↓

double f(double x, double y, double z) {
        double r3199 = z;
        double r3200 = x;
        double r3201 = r3199 - r3200;
        double r3202 = y;
        double r3203 = fma(r3201, r3202, r3200);
        return r3203;
}

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 2020047 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))