Average Error: 0.1 → 0.1
Time: 17.9s
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 r158342 = x;
        double r158343 = y;
        double r158344 = cos(r158343);
        double r158345 = r158342 * r158344;
        double r158346 = z;
        double r158347 = sin(r158343);
        double r158348 = r158346 * r158347;
        double r158349 = r158345 - r158348;
        return r158349;
}
↓
double f(double x, double y, double z) {
        double r158350 = y;
        double r158351 = sin(r158350);
        double r158352 = z;
        double r158353 = -r158352;
        double r158354 = x;
        double r158355 = cos(r158350);
        double r158356 = r158354 * r158355;
        double r158357 = fma(r158351, r158353, r158356);
        return r158357;
}

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:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))