Average Error: 0.1 → 0.1
Time: 15.8s
Precision: 64
\[\left(x + \sin y\right) + z \cdot \cos y\]
↓
\[\sin y + \mathsf{fma}\left(z, \cos y, x\right)\]
\left(x + \sin y\right) + z \cdot \cos y
↓
\sin y + \mathsf{fma}\left(z, \cos y, x\right)
double f(double x, double y, double z) {
        double r6306869 = x;
        double r6306870 = y;
        double r6306871 = sin(r6306870);
        double r6306872 = r6306869 + r6306871;
        double r6306873 = z;
        double r6306874 = cos(r6306870);
        double r6306875 = r6306873 * r6306874;
        double r6306876 = r6306872 + r6306875;
        return r6306876;
}
↓
double f(double x, double y, double z) {
        double r6306877 = y;
        double r6306878 = sin(r6306877);
        double r6306879 = z;
        double r6306880 = cos(r6306877);
        double r6306881 = x;
        double r6306882 = fma(r6306879, r6306880, r6306881);
        double r6306883 = r6306878 + r6306882;
        return r6306883;
}

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. Taylor expanded around inf 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

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))))