Average Error: 0.1 → 0.1
Time: 6.5s
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 r244983 = x;
        double r244984 = y;
        double r244985 = cos(r244984);
        double r244986 = r244983 * r244985;
        double r244987 = z;
        double r244988 = sin(r244984);
        double r244989 = r244987 * r244988;
        double r244990 = r244986 + r244989;
        return r244990;
}
↓
double f(double x, double y, double z) {
        double r244991 = x;
        double r244992 = y;
        double r244993 = cos(r244992);
        double r244994 = z;
        double r244995 = sin(r244992);
        double r244996 = r244994 * r244995;
        double r244997 = fma(r244991, r244993, r244996);
        return r244997;
}

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 2020062 +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))))