Average Error: 0.0 → 0.0
Time: 4.4s
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 r214621 = x;
        double r214622 = y;
        double r214623 = sin(r214622);
        double r214624 = r214621 + r214623;
        double r214625 = z;
        double r214626 = cos(r214622);
        double r214627 = r214625 * r214626;
        double r214628 = r214624 + r214627;
        return r214628;
}
↓
double f(double x, double y, double z) {
        double r214629 = y;
        double r214630 = cos(r214629);
        double r214631 = z;
        double r214632 = x;
        double r214633 = sin(r214629);
        double r214634 = r214632 + r214633;
        double r214635 = fma(r214630, r214631, r214634);
        return r214635;
}

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 2020020 +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))))