SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Average Error: 0.0 → 0.0

Time: 16.1s

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 r9254 = x;
        double r9255 = y;
        double r9256 = z;
        double r9257 = r9256 - r9254;
        double r9258 = r9255 * r9257;
        double r9259 = r9254 + r9258;
        return r9259;
}

↓

double f(double x, double y, double z) {
        double r9260 = z;
        double r9261 = x;
        double r9262 = r9260 - r9261;
        double r9263 = y;
        double r9264 = fma(r9262, r9263, r9261);
        return r9264;
}

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 2020045 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))