Average Error: 0.1 → 0.1
Time: 27.3s
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 r23973367 = x;
        double r23973368 = y;
        double r23973369 = cos(r23973368);
        double r23973370 = r23973367 * r23973369;
        double r23973371 = z;
        double r23973372 = sin(r23973368);
        double r23973373 = r23973371 * r23973372;
        double r23973374 = r23973370 + r23973373;
        return r23973374;
}
↓
double f(double x, double y, double z) {
        double r23973375 = x;
        double r23973376 = y;
        double r23973377 = cos(r23973376);
        double r23973378 = z;
        double r23973379 = sin(r23973376);
        double r23973380 = r23973378 * r23973379;
        double r23973381 = fma(r23973375, r23973377, r23973380);
        return r23973381;
}

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 2019173 +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))))