Average Error: 0.1 → 0.1
Time: 13.5s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right)
double f(double x, double y, double z) {
        double r202746 = x;
        double r202747 = y;
        double r202748 = sin(r202747);
        double r202749 = r202746 * r202748;
        double r202750 = z;
        double r202751 = cos(r202747);
        double r202752 = r202750 * r202751;
        double r202753 = r202749 + r202752;
        return r202753;
}
↓
double f(double x, double y, double z) {
        double r202754 = x;
        double r202755 = y;
        double r202756 = sin(r202755);
        double r202757 = z;
        double r202758 = cos(r202755);
        double r202759 = r202757 * r202758;
        double r202760 = fma(r202754, r202756, r202759);
        return r202760;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[x \cdot \sin y + z \cdot \cos y\]

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))