Average Error: 0.1 → 0.1
Time: 5.5s
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 r127861 = x;
        double r127862 = y;
        double r127863 = cos(r127862);
        double r127864 = r127861 * r127863;
        double r127865 = z;
        double r127866 = sin(r127862);
        double r127867 = r127865 * r127866;
        double r127868 = r127864 + r127867;
        return r127868;
}
↓
double f(double x, double y, double z) {
        double r127869 = x;
        double r127870 = y;
        double r127871 = cos(r127870);
        double r127872 = z;
        double r127873 = sin(r127870);
        double r127874 = r127872 * r127873;
        double r127875 = fma(r127869, r127871, r127874);
        return r127875;
}

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 2020047 +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))))