Average Error: 0.1 → 0.1
Time: 24.3s
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 r9810503 = x;
        double r9810504 = y;
        double r9810505 = cos(r9810504);
        double r9810506 = r9810503 * r9810505;
        double r9810507 = z;
        double r9810508 = sin(r9810504);
        double r9810509 = r9810507 * r9810508;
        double r9810510 = r9810506 + r9810509;
        return r9810510;
}
↓
double f(double x, double y, double z) {
        double r9810511 = y;
        double r9810512 = sin(r9810511);
        double r9810513 = z;
        double r9810514 = x;
        double r9810515 = cos(r9810511);
        double r9810516 = r9810514 * r9810515;
        double r9810517 = fma(r9810512, r9810513, r9810516);
        return r9810517;
}

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 2019162 +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))))