Average Error: 0.1 → 0.0
Time: 5.7s
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 r173854 = x;
        double r173855 = y;
        double r173856 = sin(r173855);
        double r173857 = r173854 + r173856;
        double r173858 = z;
        double r173859 = cos(r173855);
        double r173860 = r173858 * r173859;
        double r173861 = r173857 + r173860;
        return r173861;
}
↓
double f(double x, double y, double z) {
        double r173862 = y;
        double r173863 = cos(r173862);
        double r173864 = z;
        double r173865 = x;
        double r173866 = sin(r173862);
        double r173867 = r173865 + r173866;
        double r173868 = fma(r173863, r173864, r173867);
        return r173868;
}

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 2020046 +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))))