Average Error: 0.1 → 0.0
Time: 9.7s
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 r178140 = x;
        double r178141 = y;
        double r178142 = sin(r178141);
        double r178143 = r178140 + r178142;
        double r178144 = z;
        double r178145 = cos(r178141);
        double r178146 = r178144 * r178145;
        double r178147 = r178143 + r178146;
        return r178147;
}
↓
double f(double x, double y, double z) {
        double r178148 = y;
        double r178149 = cos(r178148);
        double r178150 = z;
        double r178151 = x;
        double r178152 = sin(r178148);
        double r178153 = r178151 + r178152;
        double r178154 = fma(r178149, r178150, r178153);
        return r178154;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +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))))