Average Error: 0.1 → 0.1
Time: 22.4s
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 r7904722 = x;
        double r7904723 = y;
        double r7904724 = cos(r7904723);
        double r7904725 = r7904722 * r7904724;
        double r7904726 = z;
        double r7904727 = sin(r7904723);
        double r7904728 = r7904726 * r7904727;
        double r7904729 = r7904725 + r7904728;
        return r7904729;
}
↓
double f(double x, double y, double z) {
        double r7904730 = y;
        double r7904731 = sin(r7904730);
        double r7904732 = z;
        double r7904733 = x;
        double r7904734 = cos(r7904730);
        double r7904735 = r7904733 * r7904734;
        double r7904736 = fma(r7904731, r7904732, r7904735);
        return r7904736;
}

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 2019163 +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))))