Average Error: 0.1 → 0.1
Time: 21.2s
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 r7066206 = x;
        double r7066207 = y;
        double r7066208 = cos(r7066207);
        double r7066209 = r7066206 * r7066208;
        double r7066210 = z;
        double r7066211 = sin(r7066207);
        double r7066212 = r7066210 * r7066211;
        double r7066213 = r7066209 + r7066212;
        return r7066213;
}
↓
double f(double x, double y, double z) {
        double r7066214 = y;
        double r7066215 = sin(r7066214);
        double r7066216 = z;
        double r7066217 = x;
        double r7066218 = cos(r7066214);
        double r7066219 = r7066217 * r7066218;
        double r7066220 = fma(r7066215, r7066216, r7066219);
        return r7066220;
}

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 2019179 +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))))