Average Error: 0.1 → 0.1
Time: 5.1s
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 r186686 = x;
        double r186687 = y;
        double r186688 = cos(r186687);
        double r186689 = r186686 * r186688;
        double r186690 = z;
        double r186691 = sin(r186687);
        double r186692 = r186690 * r186691;
        double r186693 = r186689 + r186692;
        return r186693;
}
↓
double f(double x, double y, double z) {
        double r186694 = x;
        double r186695 = y;
        double r186696 = cos(r186695);
        double r186697 = z;
        double r186698 = sin(r186695);
        double r186699 = r186697 * r186698;
        double r186700 = fma(r186694, r186696, r186699);
        return r186700;
}

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 2019353 +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))))