Average Error: 0.1 → 0.1
Time: 6.9s
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 r186603 = x;
        double r186604 = y;
        double r186605 = cos(r186604);
        double r186606 = r186603 * r186605;
        double r186607 = z;
        double r186608 = sin(r186604);
        double r186609 = r186607 * r186608;
        double r186610 = r186606 + r186609;
        return r186610;
}
↓
double f(double x, double y, double z) {
        double r186611 = x;
        double r186612 = y;
        double r186613 = cos(r186612);
        double r186614 = z;
        double r186615 = sin(r186612);
        double r186616 = r186614 * r186615;
        double r186617 = fma(r186611, r186613, r186616);
        return r186617;
}

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 2020081 +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))))