Average Error: 0.1 → 0.0
Time: 10.2s
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 r180944 = x;
        double r180945 = y;
        double r180946 = sin(r180945);
        double r180947 = r180944 + r180946;
        double r180948 = z;
        double r180949 = cos(r180945);
        double r180950 = r180948 * r180949;
        double r180951 = r180947 + r180950;
        return r180951;
}
↓
double f(double x, double y, double z) {
        double r180952 = y;
        double r180953 = cos(r180952);
        double r180954 = z;
        double r180955 = x;
        double r180956 = sin(r180952);
        double r180957 = r180955 + r180956;
        double r180958 = fma(r180953, r180954, r180957);
        return r180958;
}

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 2020043 +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))))