Average Error: 0.1 → 0.1
Time: 13.3s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right)
double f(double x, double y, double z) {
        double r197495 = x;
        double r197496 = y;
        double r197497 = sin(r197496);
        double r197498 = r197495 * r197497;
        double r197499 = z;
        double r197500 = cos(r197496);
        double r197501 = r197499 * r197500;
        double r197502 = r197498 + r197501;
        return r197502;
}
↓
double f(double x, double y, double z) {
        double r197503 = x;
        double r197504 = y;
        double r197505 = sin(r197504);
        double r197506 = z;
        double r197507 = cos(r197504);
        double r197508 = r197506 * r197507;
        double r197509 = fma(r197503, r197505, r197508);
        return r197509;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))