Average Error: 0.0 → 0.0
Time: 5.5s
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 r159948 = x;
        double r159949 = y;
        double r159950 = sin(r159949);
        double r159951 = r159948 + r159950;
        double r159952 = z;
        double r159953 = cos(r159949);
        double r159954 = r159952 * r159953;
        double r159955 = r159951 + r159954;
        return r159955;
}
↓
double f(double x, double y, double z) {
        double r159956 = y;
        double r159957 = cos(r159956);
        double r159958 = z;
        double r159959 = x;
        double r159960 = sin(r159956);
        double r159961 = r159959 + r159960;
        double r159962 = fma(r159957, r159958, r159961);
        return r159962;
}

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 2020062 +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))))