Average Error: 0.1 → 0.1
Time: 17.1s
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 r9296241 = x;
        double r9296242 = y;
        double r9296243 = sin(r9296242);
        double r9296244 = r9296241 + r9296243;
        double r9296245 = z;
        double r9296246 = cos(r9296242);
        double r9296247 = r9296245 * r9296246;
        double r9296248 = r9296244 + r9296247;
        return r9296248;
}
↓
double f(double x, double y, double z) {
        double r9296249 = y;
        double r9296250 = cos(r9296249);
        double r9296251 = z;
        double r9296252 = x;
        double r9296253 = sin(r9296249);
        double r9296254 = r9296252 + r9296253;
        double r9296255 = fma(r9296250, r9296251, r9296254);
        return r9296255;
}

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 2019163 +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))))