Average Error: 0.1 → 0.1
Time: 14.9s
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 r127683 = x;
        double r127684 = y;
        double r127685 = sin(r127684);
        double r127686 = r127683 * r127685;
        double r127687 = z;
        double r127688 = cos(r127684);
        double r127689 = r127687 * r127688;
        double r127690 = r127686 + r127689;
        return r127690;
}
↓
double f(double x, double y, double z) {
        double r127691 = x;
        double r127692 = y;
        double r127693 = sin(r127692);
        double r127694 = z;
        double r127695 = cos(r127692);
        double r127696 = r127694 * r127695;
        double r127697 = fma(r127691, r127693, r127696);
        return r127697;
}

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 2019212 +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))))