Average Error: 0.1 → 0.1
Time: 12.1s
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 r243695 = x;
        double r243696 = y;
        double r243697 = cos(r243696);
        double r243698 = r243695 * r243697;
        double r243699 = z;
        double r243700 = sin(r243696);
        double r243701 = r243699 * r243700;
        double r243702 = r243698 + r243701;
        return r243702;
}
↓
double f(double x, double y, double z) {
        double r243703 = x;
        double r243704 = y;
        double r243705 = cos(r243704);
        double r243706 = z;
        double r243707 = sin(r243704);
        double r243708 = r243706 * r243707;
        double r243709 = fma(r243703, r243705, r243708);
        return r243709;
}

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 2020045 +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))))