Average Error: 0.1 → 0.1
Time: 18.9s
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 r213339 = x;
        double r213340 = y;
        double r213341 = cos(r213340);
        double r213342 = r213339 * r213341;
        double r213343 = z;
        double r213344 = sin(r213340);
        double r213345 = r213343 * r213344;
        double r213346 = r213342 + r213345;
        return r213346;
}
↓
double f(double x, double y, double z) {
        double r213347 = y;
        double r213348 = sin(r213347);
        double r213349 = z;
        double r213350 = x;
        double r213351 = cos(r213347);
        double r213352 = r213350 * r213351;
        double r213353 = fma(r213348, r213349, r213352);
        return r213353;
}

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 2019174 +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))))