Average Error: 0.1 → 0.1
Time: 27.3s
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 r137849 = x;
        double r137850 = y;
        double r137851 = cos(r137850);
        double r137852 = r137849 * r137851;
        double r137853 = z;
        double r137854 = sin(r137850);
        double r137855 = r137853 * r137854;
        double r137856 = r137852 + r137855;
        return r137856;
}
↓
double f(double x, double y, double z) {
        double r137857 = x;
        double r137858 = y;
        double r137859 = cos(r137858);
        double r137860 = z;
        double r137861 = sin(r137858);
        double r137862 = r137860 * r137861;
        double r137863 = fma(r137857, r137859, r137862);
        return r137863;
}

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 2019306 +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))))