Average Error: 0.1 → 0.1
Time: 6.6s
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 r208541 = x;
        double r208542 = y;
        double r208543 = cos(r208542);
        double r208544 = r208541 * r208543;
        double r208545 = z;
        double r208546 = sin(r208542);
        double r208547 = r208545 * r208546;
        double r208548 = r208544 + r208547;
        return r208548;
}
↓
double f(double x, double y, double z) {
        double r208549 = x;
        double r208550 = y;
        double r208551 = cos(r208550);
        double r208552 = z;
        double r208553 = sin(r208550);
        double r208554 = r208552 * r208553;
        double r208555 = fma(r208549, r208551, r208554);
        return r208555;
}

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 2020060 +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))))