Average Error: 0.1 → 0.1
Time: 4.8s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right)
double f(double x, double y, double z) {
        double r196869 = x;
        double r196870 = y;
        double r196871 = sin(r196870);
        double r196872 = r196869 * r196871;
        double r196873 = z;
        double r196874 = cos(r196870);
        double r196875 = r196873 * r196874;
        double r196876 = r196872 + r196875;
        return r196876;
}
↓
double f(double x, double y, double z) {
        double r196877 = x;
        double r196878 = y;
        double r196879 = sin(r196878);
        double r196880 = z;
        double r196881 = cos(r196878);
        double r196882 = r196880 * r196881;
        double r196883 = fma(r196877, r196879, r196882);
        return r196883;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))