Average Error: 0.1 → 0.1
Time: 18.3s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)\]
x \cdot \cos y - z \cdot \sin y
↓
\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)
double f(double x, double y, double z) {
        double r142559 = x;
        double r142560 = y;
        double r142561 = cos(r142560);
        double r142562 = r142559 * r142561;
        double r142563 = z;
        double r142564 = sin(r142560);
        double r142565 = r142563 * r142564;
        double r142566 = r142562 - r142565;
        return r142566;
}
↓
double f(double x, double y, double z) {
        double r142567 = y;
        double r142568 = sin(r142567);
        double r142569 = z;
        double r142570 = -r142569;
        double r142571 = x;
        double r142572 = cos(r142567);
        double r142573 = r142571 * r142572;
        double r142574 = fma(r142568, r142570, r142573);
        return r142574;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)\]

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))