Average Error: 0.1 → 0.1
Time: 5.8s
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 r173089 = x;
        double r173090 = y;
        double r173091 = cos(r173090);
        double r173092 = r173089 * r173091;
        double r173093 = z;
        double r173094 = sin(r173090);
        double r173095 = r173093 * r173094;
        double r173096 = r173092 + r173095;
        return r173096;
}
↓
double f(double x, double y, double z) {
        double r173097 = x;
        double r173098 = y;
        double r173099 = cos(r173098);
        double r173100 = z;
        double r173101 = sin(r173098);
        double r173102 = r173100 * r173101;
        double r173103 = fma(r173097, r173099, r173102);
        return r173103;
}

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 2020100 +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))))