Average Error: 0.1 → 0.1
Time: 40.7s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\mathsf{fma}\left(\sin y, z, x \cdot \cos y\right)\]
x \cdot \cos y + z \cdot \sin y
↓
\mathsf{fma}\left(\sin y, z, x \cdot \cos y\right)
double f(double x, double y, double z) {
        double r8606913 = x;
        double r8606914 = y;
        double r8606915 = cos(r8606914);
        double r8606916 = r8606913 * r8606915;
        double r8606917 = z;
        double r8606918 = sin(r8606914);
        double r8606919 = r8606917 * r8606918;
        double r8606920 = r8606916 + r8606919;
        return r8606920;
}
↓
double f(double x, double y, double z) {
        double r8606921 = y;
        double r8606922 = sin(r8606921);
        double r8606923 = z;
        double r8606924 = x;
        double r8606925 = cos(r8606921);
        double r8606926 = r8606924 * r8606925;
        double r8606927 = fma(r8606922, r8606923, r8606926);
        return r8606927;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))