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 r201991 = x;
        double r201992 = y;
        double r201993 = cos(r201992);
        double r201994 = r201991 * r201993;
        double r201995 = z;
        double r201996 = sin(r201992);
        double r201997 = r201995 * r201996;
        double r201998 = r201994 + r201997;
        return r201998;
}
↓
double f(double x, double y, double z) {
        double r201999 = x;
        double r202000 = y;
        double r202001 = cos(r202000);
        double r202002 = z;
        double r202003 = sin(r202000);
        double r202004 = r202002 * r202003;
        double r202005 = fma(r201999, r202001, r202004);
        return r202005;
}

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 2020027 +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))))