Average Error: 0.1 → 0.1
Time: 5.7s
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 r172655 = x;
        double r172656 = y;
        double r172657 = cos(r172656);
        double r172658 = r172655 * r172657;
        double r172659 = z;
        double r172660 = sin(r172656);
        double r172661 = r172659 * r172660;
        double r172662 = r172658 + r172661;
        return r172662;
}
↓
double f(double x, double y, double z) {
        double r172663 = x;
        double r172664 = y;
        double r172665 = cos(r172664);
        double r172666 = z;
        double r172667 = sin(r172664);
        double r172668 = r172666 * r172667;
        double r172669 = fma(r172663, r172665, r172668);
        return r172669;
}

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 2020001 +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))))