Average Error: 0.1 → 0.1
Time: 23.9s
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 r121786 = x;
        double r121787 = y;
        double r121788 = cos(r121787);
        double r121789 = r121786 * r121788;
        double r121790 = z;
        double r121791 = sin(r121787);
        double r121792 = r121790 * r121791;
        double r121793 = r121789 + r121792;
        return r121793;
}
↓
double f(double x, double y, double z) {
        double r121794 = x;
        double r121795 = y;
        double r121796 = cos(r121795);
        double r121797 = z;
        double r121798 = sin(r121795);
        double r121799 = r121797 * r121798;
        double r121800 = fma(r121794, r121796, r121799);
        return r121800;
}

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 2019198 +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))))