Average Error: 0.1 → 0.1
Time: 5.9s
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 r171360 = x;
        double r171361 = y;
        double r171362 = cos(r171361);
        double r171363 = r171360 * r171362;
        double r171364 = z;
        double r171365 = sin(r171361);
        double r171366 = r171364 * r171365;
        double r171367 = r171363 + r171366;
        return r171367;
}
↓
double f(double x, double y, double z) {
        double r171368 = x;
        double r171369 = y;
        double r171370 = cos(r171369);
        double r171371 = z;
        double r171372 = sin(r171369);
        double r171373 = r171371 * r171372;
        double r171374 = fma(r171368, r171370, r171373);
        return r171374;
}

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 2020001 +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))))