Average Error: 0.1 → 0.1
Time: 13.4s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\mathsf{fma}\left(\cos y, x, z \cdot \sin y\right)\]
x \cdot \cos y + z \cdot \sin y
↓
\mathsf{fma}\left(\cos y, x, z \cdot \sin y\right)
double f(double x, double y, double z) {
        double r2765275 = x;
        double r2765276 = y;
        double r2765277 = cos(r2765276);
        double r2765278 = r2765275 * r2765277;
        double r2765279 = z;
        double r2765280 = sin(r2765276);
        double r2765281 = r2765279 * r2765280;
        double r2765282 = r2765278 + r2765281;
        return r2765282;
}
↓
double f(double x, double y, double z) {
        double r2765283 = y;
        double r2765284 = cos(r2765283);
        double r2765285 = x;
        double r2765286 = z;
        double r2765287 = sin(r2765283);
        double r2765288 = r2765286 * r2765287;
        double r2765289 = fma(r2765284, r2765285, r2765288);
        return r2765289;
}

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. Taylor expanded around inf 0.1

    \[\leadsto \color{blue}{z \cdot \sin y + x \cdot \cos y}\]

  4. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, x, z \cdot \sin y\right)}\]

  5. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\cos y, x, z \cdot \sin y\right)\]

Reproduce

herbie shell --seed 2019156 +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))))