Average Error: 0.1 → 0.1
Time: 19.7s
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 r206900 = x;
        double r206901 = y;
        double r206902 = sin(r206901);
        double r206903 = r206900 * r206902;
        double r206904 = z;
        double r206905 = cos(r206901);
        double r206906 = r206904 * r206905;
        double r206907 = r206903 + r206906;
        return r206907;
}
↓
double f(double x, double y, double z) {
        double r206908 = y;
        double r206909 = cos(r206908);
        double r206910 = z;
        double r206911 = x;
        double r206912 = sin(r206908);
        double r206913 = r206911 * r206912;
        double r206914 = fma(r206909, r206910, r206913);
        return r206914;
}

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 2019194 +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))))