Average Error: 0.0 → 0.0
Time: 3.5s
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 r168840 = x;
        double r168841 = y;
        double r168842 = sin(r168841);
        double r168843 = r168840 + r168842;
        double r168844 = z;
        double r168845 = cos(r168841);
        double r168846 = r168844 * r168845;
        double r168847 = r168843 + r168846;
        return r168847;
}
↓
double f(double x, double y, double z) {
        double r168848 = y;
        double r168849 = cos(r168848);
        double r168850 = z;
        double r168851 = x;
        double r168852 = sin(r168848);
        double r168853 = r168851 + r168852;
        double r168854 = fma(r168849, r168850, r168853);
        return r168854;
}

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 2020035 +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))))