Average Error: 0.1 → 0.1
Time: 11.1s
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 r120836 = x;
        double r120837 = y;
        double r120838 = sin(r120837);
        double r120839 = r120836 + r120838;
        double r120840 = z;
        double r120841 = cos(r120837);
        double r120842 = r120840 * r120841;
        double r120843 = r120839 + r120842;
        return r120843;
}
↓
double f(double x, double y, double z) {
        double r120844 = y;
        double r120845 = cos(r120844);
        double r120846 = z;
        double r120847 = x;
        double r120848 = sin(r120844);
        double r120849 = r120847 + r120848;
        double r120850 = fma(r120845, r120846, r120849);
        return r120850;
}

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 2019326 +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))))