Average Error: 0.1 → 0.1
Time: 18.3s
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 r184792 = x;
        double r184793 = y;
        double r184794 = sin(r184793);
        double r184795 = r184792 * r184794;
        double r184796 = z;
        double r184797 = cos(r184793);
        double r184798 = r184796 * r184797;
        double r184799 = r184795 + r184798;
        return r184799;
}
↓
double f(double x, double y, double z) {
        double r184800 = x;
        double r184801 = y;
        double r184802 = sin(r184801);
        double r184803 = z;
        double r184804 = cos(r184801);
        double r184805 = r184803 * r184804;
        double r184806 = fma(r184800, r184802, r184805);
        return r184806;
}

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 2019198 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))