Average Error: 0.1 → 0.1
Time: 26.6s
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 r172858 = x;
        double r172859 = y;
        double r172860 = cos(r172859);
        double r172861 = r172858 * r172860;
        double r172862 = z;
        double r172863 = sin(r172859);
        double r172864 = r172862 * r172863;
        double r172865 = r172861 + r172864;
        return r172865;
}
↓
double f(double x, double y, double z) {
        double r172866 = x;
        double r172867 = y;
        double r172868 = cos(r172867);
        double r172869 = z;
        double r172870 = sin(r172867);
        double r172871 = r172869 * r172870;
        double r172872 = fma(r172866, r172868, r172871);
        return r172872;
}

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 2019323 +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))))