Average Error: 0.1 → 0.0
Time: 4.2s
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 r149769 = x;
        double r149770 = y;
        double r149771 = sin(r149770);
        double r149772 = r149769 + r149771;
        double r149773 = z;
        double r149774 = cos(r149770);
        double r149775 = r149773 * r149774;
        double r149776 = r149772 + r149775;
        return r149776;
}
↓
double f(double x, double y, double z) {
        double r149777 = y;
        double r149778 = cos(r149777);
        double r149779 = z;
        double r149780 = x;
        double r149781 = sin(r149777);
        double r149782 = r149780 + r149781;
        double r149783 = fma(r149778, r149779, r149782);
        return r149783;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 +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))))