Average Error: 0.1 → 0.1
Time: 5.7s
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 r234309 = x;
        double r234310 = y;
        double r234311 = cos(r234310);
        double r234312 = r234309 * r234311;
        double r234313 = z;
        double r234314 = sin(r234310);
        double r234315 = r234313 * r234314;
        double r234316 = r234312 + r234315;
        return r234316;
}
↓
double f(double x, double y, double z) {
        double r234317 = x;
        double r234318 = y;
        double r234319 = cos(r234318);
        double r234320 = z;
        double r234321 = sin(r234318);
        double r234322 = r234320 * r234321;
        double r234323 = fma(r234317, r234319, r234322);
        return r234323;
}

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 2020083 +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))))