Average Error: 0.1 → 0.1
Time: 20.0s
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 r212724 = x;
        double r212725 = y;
        double r212726 = cos(r212725);
        double r212727 = r212724 * r212726;
        double r212728 = z;
        double r212729 = sin(r212725);
        double r212730 = r212728 * r212729;
        double r212731 = r212727 + r212730;
        return r212731;
}
↓
double f(double x, double y, double z) {
        double r212732 = y;
        double r212733 = sin(r212732);
        double r212734 = z;
        double r212735 = x;
        double r212736 = cos(r212732);
        double r212737 = r212735 * r212736;
        double r212738 = fma(r212733, r212734, r212737);
        return r212738;
}

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 2019179 +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))))