Average Error: 0.1 → 0.1
Time: 22.5s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)
double f(double x, double y, double z) {
        double r9342883 = x;
        double r9342884 = y;
        double r9342885 = sin(r9342884);
        double r9342886 = r9342883 * r9342885;
        double r9342887 = z;
        double r9342888 = cos(r9342884);
        double r9342889 = r9342887 * r9342888;
        double r9342890 = r9342886 + r9342889;
        return r9342890;
}
↓
double f(double x, double y, double z) {
        double r9342891 = y;
        double r9342892 = cos(r9342891);
        double r9342893 = z;
        double r9342894 = x;
        double r9342895 = sin(r9342891);
        double r9342896 = r9342894 * r9342895;
        double r9342897 = fma(r9342892, r9342893, r9342896);
        return r9342897;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))