Average Error: 0.1 → 0.1
Time: 4.3s
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 r134233 = x;
        double r134234 = y;
        double r134235 = sin(r134234);
        double r134236 = r134233 + r134235;
        double r134237 = z;
        double r134238 = cos(r134234);
        double r134239 = r134237 * r134238;
        double r134240 = r134236 + r134239;
        return r134240;
}
↓
double f(double x, double y, double z) {
        double r134241 = y;
        double r134242 = cos(r134241);
        double r134243 = z;
        double r134244 = x;
        double r134245 = sin(r134241);
        double r134246 = r134244 + r134245;
        double r134247 = fma(r134242, r134243, r134246);
        return r134247;
}

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 2020027 +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))))