SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Average Error: 0.0 → 0.0

Time: 6.0s

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 r2011 = x;
        double r2012 = y;
        double r2013 = z;
        double r2014 = r2013 - r2011;
        double r2015 = r2012 * r2014;
        double r2016 = r2011 + r2015;
        return r2016;
}

↓

double f(double x, double y, double z) {
        double r2017 = z;
        double r2018 = x;
        double r2019 = r2017 - r2018;
        double r2020 = y;
        double r2021 = fma(r2019, r2020, r2018);
        return r2021;
}

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))))