Average Error: 0.0 → 0.0
Time: 12.3s
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 r175990 = x;
        double r175991 = y;
        double r175992 = sin(r175991);
        double r175993 = r175990 + r175992;
        double r175994 = z;
        double r175995 = cos(r175991);
        double r175996 = r175994 * r175995;
        double r175997 = r175993 + r175996;
        return r175997;
}
↓
double f(double x, double y, double z) {
        double r175998 = y;
        double r175999 = cos(r175998);
        double r176000 = z;
        double r176001 = x;
        double r176002 = sin(r175998);
        double r176003 = r176001 + r176002;
        double r176004 = fma(r175999, r176000, r176003);
        return r176004;
}

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 2019208 +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))))