Average Error: 0.0 → 0.0
Time: 4.1s
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 r181955 = x;
        double r181956 = y;
        double r181957 = sin(r181956);
        double r181958 = r181955 + r181957;
        double r181959 = z;
        double r181960 = cos(r181956);
        double r181961 = r181959 * r181960;
        double r181962 = r181958 + r181961;
        return r181962;
}
↓
double f(double x, double y, double z) {
        double r181963 = y;
        double r181964 = cos(r181963);
        double r181965 = z;
        double r181966 = x;
        double r181967 = sin(r181963);
        double r181968 = r181966 + r181967;
        double r181969 = fma(r181964, r181965, r181968);
        return r181969;
}

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 2020018 +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))))