Average Error: 0.1 → 0.1
Time: 21.4s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\mathsf{fma}\left(\sin y, z, x \cdot \cos y\right)\]
x \cdot \cos y + z \cdot \sin y
↓
\mathsf{fma}\left(\sin y, z, x \cdot \cos y\right)
double f(double x, double y, double z) {
        double r7859989 = x;
        double r7859990 = y;
        double r7859991 = cos(r7859990);
        double r7859992 = r7859989 * r7859991;
        double r7859993 = z;
        double r7859994 = sin(r7859990);
        double r7859995 = r7859993 * r7859994;
        double r7859996 = r7859992 + r7859995;
        return r7859996;
}
↓
double f(double x, double y, double z) {
        double r7859997 = y;
        double r7859998 = sin(r7859997);
        double r7859999 = z;
        double r7860000 = x;
        double r7860001 = cos(r7859997);
        double r7860002 = r7860000 * r7860001;
        double r7860003 = fma(r7859998, r7859999, r7860002);
        return r7860003;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))