Average Error: 0.1 → 0.1
Time: 24.5s
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 r12027427 = x;
        double r12027428 = y;
        double r12027429 = cos(r12027428);
        double r12027430 = r12027427 * r12027429;
        double r12027431 = z;
        double r12027432 = sin(r12027428);
        double r12027433 = r12027431 * r12027432;
        double r12027434 = r12027430 + r12027433;
        return r12027434;
}
↓
double f(double x, double y, double z) {
        double r12027435 = x;
        double r12027436 = y;
        double r12027437 = cos(r12027436);
        double r12027438 = z;
        double r12027439 = sin(r12027436);
        double r12027440 = r12027438 * r12027439;
        double r12027441 = fma(r12027435, r12027437, r12027440);
        return r12027441;
}

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 2019174 +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))))