Average Error: 0.1 → 0.1
Time: 5.3s
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 r230928 = x;
        double r230929 = y;
        double r230930 = cos(r230929);
        double r230931 = r230928 * r230930;
        double r230932 = z;
        double r230933 = sin(r230929);
        double r230934 = r230932 * r230933;
        double r230935 = r230931 + r230934;
        return r230935;
}
↓
double f(double x, double y, double z) {
        double r230936 = x;
        double r230937 = y;
        double r230938 = cos(r230937);
        double r230939 = z;
        double r230940 = sin(r230937);
        double r230941 = r230939 * r230940;
        double r230942 = fma(r230936, r230938, r230941);
        return r230942;
}

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 2020035 +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))))