Average Error: 0.1 → 0.1
Time: 5.5s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)\]
x \cdot \cos y + z \cdot \sin y
↓
\mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)
double f(double x, double y, double z) {
        double r153862 = x;
        double r153863 = y;
        double r153864 = cos(r153863);
        double r153865 = r153862 * r153864;
        double r153866 = z;
        double r153867 = sin(r153863);
        double r153868 = r153866 * r153867;
        double r153869 = r153865 + r153868;
        return r153869;
}
↓
double f(double x, double y, double z) {
        double r153870 = x;
        double r153871 = y;
        double r153872 = cos(r153871);
        double r153873 = z;
        double r153874 = sin(r153871);
        double r153875 = r153873 * r153874;
        double r153876 = fma(r153870, r153872, r153875);
        return r153876;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[x \cdot \cos y + z \cdot \sin y\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)\]

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))