SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Average Error: 0.0 → 0.0

Time: 5.4s

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 r1656 = x;
        double r1657 = y;
        double r1658 = z;
        double r1659 = r1658 - r1656;
        double r1660 = r1657 * r1659;
        double r1661 = r1656 + r1660;
        return r1661;
}

↓

double f(double x, double y, double z) {
        double r1662 = z;
        double r1663 = x;
        double r1664 = r1662 - r1663;
        double r1665 = y;
        double r1666 = fma(r1664, r1665, r1663);
        return r1666;
}

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 2020043 +o rules:numerics
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))