Average Error: 0.1 → 0.1
Time: 6.5s
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 r171903 = x;
        double r171904 = y;
        double r171905 = sin(r171904);
        double r171906 = r171903 * r171905;
        double r171907 = z;
        double r171908 = cos(r171904);
        double r171909 = r171907 * r171908;
        double r171910 = r171906 + r171909;
        return r171910;
}
↓
double f(double x, double y, double z) {
        double r171911 = x;
        double r171912 = y;
        double r171913 = sin(r171912);
        double r171914 = z;
        double r171915 = cos(r171912);
        double r171916 = r171914 * r171915;
        double r171917 = fma(r171911, r171913, r171916);
        return r171917;
}

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 2020046 +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))))