Average Error: 0.1 → 0.1
Time: 22.4s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)
double f(double x, double y, double z) {
        double r9163259 = x;
        double r9163260 = y;
        double r9163261 = sin(r9163260);
        double r9163262 = r9163259 * r9163261;
        double r9163263 = z;
        double r9163264 = cos(r9163260);
        double r9163265 = r9163263 * r9163264;
        double r9163266 = r9163262 + r9163265;
        return r9163266;
}
↓
double f(double x, double y, double z) {
        double r9163267 = y;
        double r9163268 = cos(r9163267);
        double r9163269 = z;
        double r9163270 = x;
        double r9163271 = sin(r9163267);
        double r9163272 = r9163270 * r9163271;
        double r9163273 = fma(r9163268, r9163269, r9163272);
        return r9163273;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[x \cdot \sin y + z \cdot \cos y\]

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))