Average Error: 0.1 → 0.1
Time: 15.3s
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 r103857 = x;
        double r103858 = y;
        double r103859 = sin(r103858);
        double r103860 = r103857 + r103859;
        double r103861 = z;
        double r103862 = cos(r103858);
        double r103863 = r103861 * r103862;
        double r103864 = r103860 + r103863;
        return r103864;
}
↓
double f(double x, double y, double z) {
        double r103865 = y;
        double r103866 = cos(r103865);
        double r103867 = z;
        double r103868 = x;
        double r103869 = sin(r103865);
        double r103870 = r103868 + r103869;
        double r103871 = fma(r103866, r103867, r103870);
        return r103871;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  (+ (+ x (sin y)) (* z (cos y))))