Average Error: 0.1 → 0.1
Time: 16.5s
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 r8561899 = x;
        double r8561900 = y;
        double r8561901 = sin(r8561900);
        double r8561902 = r8561899 + r8561901;
        double r8561903 = z;
        double r8561904 = cos(r8561900);
        double r8561905 = r8561903 * r8561904;
        double r8561906 = r8561902 + r8561905;
        return r8561906;
}
↓
double f(double x, double y, double z) {
        double r8561907 = y;
        double r8561908 = cos(r8561907);
        double r8561909 = z;
        double r8561910 = x;
        double r8561911 = sin(r8561907);
        double r8561912 = r8561910 + r8561911;
        double r8561913 = fma(r8561908, r8561909, r8561912);
        return r8561913;
}

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 2019162 +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))))