Average Error: 0.1 → 0.1
Time: 26.4s
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 r134239 = x;
        double r134240 = y;
        double r134241 = cos(r134240);
        double r134242 = r134239 * r134241;
        double r134243 = z;
        double r134244 = sin(r134240);
        double r134245 = r134243 * r134244;
        double r134246 = r134242 + r134245;
        return r134246;
}
↓
double f(double x, double y, double z) {
        double r134247 = y;
        double r134248 = sin(r134247);
        double r134249 = z;
        double r134250 = x;
        double r134251 = cos(r134247);
        double r134252 = r134250 * r134251;
        double r134253 = fma(r134248, r134249, r134252);
        return r134253;
}

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 2019196 +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))))