Average Error: 0.1 → 0.1
Time: 17.8s
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 r135959 = x;
        double r135960 = y;
        double r135961 = sin(r135960);
        double r135962 = r135959 + r135961;
        double r135963 = z;
        double r135964 = cos(r135960);
        double r135965 = r135963 * r135964;
        double r135966 = r135962 + r135965;
        return r135966;
}
↓
double f(double x, double y, double z) {
        double r135967 = y;
        double r135968 = cos(r135967);
        double r135969 = z;
        double r135970 = x;
        double r135971 = sin(r135967);
        double r135972 = r135970 + r135971;
        double r135973 = fma(r135968, r135969, r135972);
        return r135973;
}

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 2019199 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  (+ (+ x (sin y)) (* z (cos y))))