Average Error: 0.1 → 0.1
Time: 5.8s
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 r160162 = x;
        double r160163 = y;
        double r160164 = sin(r160163);
        double r160165 = r160162 + r160164;
        double r160166 = z;
        double r160167 = cos(r160163);
        double r160168 = r160166 * r160167;
        double r160169 = r160165 + r160168;
        return r160169;
}
↓
double f(double x, double y, double z) {
        double r160170 = y;
        double r160171 = cos(r160170);
        double r160172 = z;
        double r160173 = x;
        double r160174 = sin(r160170);
        double r160175 = r160173 + r160174;
        double r160176 = fma(r160171, r160172, r160175);
        return r160176;
}

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 2019352 +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))))