Average Error: 0.1 → 0.1
Time: 17.2s
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 r212356 = x;
        double r212357 = y;
        double r212358 = cos(r212357);
        double r212359 = r212356 * r212358;
        double r212360 = z;
        double r212361 = sin(r212357);
        double r212362 = r212360 * r212361;
        double r212363 = r212359 + r212362;
        return r212363;
}
↓
double f(double x, double y, double z) {
        double r212364 = x;
        double r212365 = y;
        double r212366 = cos(r212365);
        double r212367 = z;
        double r212368 = sin(r212365);
        double r212369 = r212367 * r212368;
        double r212370 = fma(r212364, r212366, r212369);
        return r212370;
}

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 2020042 +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))))