Average Error: 0.1 → 0.1
Time: 26.2s
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 r9212677 = x;
        double r9212678 = y;
        double r9212679 = cos(r9212678);
        double r9212680 = r9212677 * r9212679;
        double r9212681 = z;
        double r9212682 = sin(r9212678);
        double r9212683 = r9212681 * r9212682;
        double r9212684 = r9212680 + r9212683;
        return r9212684;
}
↓
double f(double x, double y, double z) {
        double r9212685 = y;
        double r9212686 = sin(r9212685);
        double r9212687 = z;
        double r9212688 = x;
        double r9212689 = cos(r9212685);
        double r9212690 = r9212688 * r9212689;
        double r9212691 = fma(r9212686, r9212687, r9212690);
        return r9212691;
}

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 2019170 +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))))