Average Error: 0.0 → 0.0
Time: 3.1s
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 r213051 = x;
        double r213052 = y;
        double r213053 = sin(r213052);
        double r213054 = r213051 + r213053;
        double r213055 = z;
        double r213056 = cos(r213052);
        double r213057 = r213055 * r213056;
        double r213058 = r213054 + r213057;
        return r213058;
}
↓
double f(double x, double y, double z) {
        double r213059 = y;
        double r213060 = cos(r213059);
        double r213061 = z;
        double r213062 = x;
        double r213063 = sin(r213059);
        double r213064 = r213062 + r213063;
        double r213065 = fma(r213060, r213061, r213064);
        return r213065;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\left(x + \sin y\right) + z \cdot \cos y\]

  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 2020083 +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))))