Average Error: 0.1 → 0.1
Time: 22.6s
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 r135123 = x;
        double r135124 = y;
        double r135125 = cos(r135124);
        double r135126 = r135123 * r135125;
        double r135127 = z;
        double r135128 = sin(r135124);
        double r135129 = r135127 * r135128;
        double r135130 = r135126 + r135129;
        return r135130;
}
↓
double f(double x, double y, double z) {
        double r135131 = x;
        double r135132 = y;
        double r135133 = cos(r135132);
        double r135134 = z;
        double r135135 = sin(r135132);
        double r135136 = r135134 * r135135;
        double r135137 = fma(r135131, r135133, r135136);
        return r135137;
}

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 2019325 +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))))