Average Error: 0.1 → 0.1
Time: 23.7s
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 r8543655 = x;
        double r8543656 = y;
        double r8543657 = cos(r8543656);
        double r8543658 = r8543655 * r8543657;
        double r8543659 = z;
        double r8543660 = sin(r8543656);
        double r8543661 = r8543659 * r8543660;
        double r8543662 = r8543658 + r8543661;
        return r8543662;
}
↓
double f(double x, double y, double z) {
        double r8543663 = y;
        double r8543664 = sin(r8543663);
        double r8543665 = z;
        double r8543666 = x;
        double r8543667 = cos(r8543663);
        double r8543668 = r8543666 * r8543667;
        double r8543669 = fma(r8543664, r8543665, r8543668);
        return r8543669;
}

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 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))