Average Error: 0.1 → 0.1
Time: 6.4s
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 r204878 = x;
        double r204879 = y;
        double r204880 = cos(r204879);
        double r204881 = r204878 * r204880;
        double r204882 = z;
        double r204883 = sin(r204879);
        double r204884 = r204882 * r204883;
        double r204885 = r204881 + r204884;
        return r204885;
}
↓
double f(double x, double y, double z) {
        double r204886 = x;
        double r204887 = y;
        double r204888 = cos(r204887);
        double r204889 = z;
        double r204890 = sin(r204887);
        double r204891 = r204889 * r204890;
        double r204892 = fma(r204886, r204888, r204891);
        return r204892;
}

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 2020062 +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))))