Average Error: 0.1 → 0.1
Time: 25.6s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)\]
x \cdot \cos y + z \cdot \sin y
↓
\mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)
double f(double x, double y, double z) {
        double r166433 = x;
        double r166434 = y;
        double r166435 = cos(r166434);
        double r166436 = r166433 * r166435;
        double r166437 = z;
        double r166438 = sin(r166434);
        double r166439 = r166437 * r166438;
        double r166440 = r166436 + r166439;
        return r166440;
}
↓
double f(double x, double y, double z) {
        double r166441 = x;
        double r166442 = y;
        double r166443 = cos(r166442);
        double r166444 = z;
        double r166445 = sin(r166442);
        double r166446 = r166444 * r166445;
        double r166447 = fma(r166441, r166443, r166446);
        return r166447;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))