Average Error: 0.1 → 0.1
Time: 4.5s
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 r148250 = x;
        double r148251 = y;
        double r148252 = cos(r148251);
        double r148253 = r148250 * r148252;
        double r148254 = z;
        double r148255 = sin(r148251);
        double r148256 = r148254 * r148255;
        double r148257 = r148253 + r148256;
        return r148257;
}
↓
double f(double x, double y, double z) {
        double r148258 = x;
        double r148259 = y;
        double r148260 = cos(r148259);
        double r148261 = z;
        double r148262 = sin(r148259);
        double r148263 = r148261 * r148262;
        double r148264 = fma(r148258, r148260, r148263);
        return r148264;
}

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. Using strategy rm

  4. Applied *-un-lft-identity0.1

    \[\leadsto \color{blue}{1 \cdot \mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)}\]

  5. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)\]

Reproduce

herbie shell --seed 2020056 +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))))