Average Error: 0.0 → 0.0
Time: 6.9s
Precision: 64
\[\left(x + \sin y\right) + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(\cos y, z, x + \sin y\right)\]
\left(x + \sin y\right) + z \cdot \cos y
↓
\mathsf{fma}\left(\cos y, z, x + \sin y\right)
double f(double x, double y, double z) {
        double r163672 = x;
        double r163673 = y;
        double r163674 = sin(r163673);
        double r163675 = r163672 + r163674;
        double r163676 = z;
        double r163677 = cos(r163673);
        double r163678 = r163676 * r163677;
        double r163679 = r163675 + r163678;
        return r163679;
}
↓
double f(double x, double y, double z) {
        double r163680 = y;
        double r163681 = cos(r163680);
        double r163682 = z;
        double r163683 = x;
        double r163684 = sin(r163680);
        double r163685 = r163683 + r163684;
        double r163686 = fma(r163681, r163682, r163685);
        return r163686;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\left(x + \sin y\right) + z \cdot \cos y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x + \sin y\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(\cos y, z, x + \sin y\right)\]

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))