Average Error: 0.1 → 0.1
Time: 15.4s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)\]
x \cdot \cos y + z \cdot \sin y
↓
\mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)
double f(double x, double y, double z) {
        double r211566 = x;
        double r211567 = y;
        double r211568 = cos(r211567);
        double r211569 = r211566 * r211568;
        double r211570 = z;
        double r211571 = sin(r211567);
        double r211572 = r211570 * r211571;
        double r211573 = r211569 + r211572;
        return r211573;
}
↓
double f(double x, double y, double z) {
        double r211574 = x;
        double r211575 = y;
        double r211576 = cos(r211575);
        double r211577 = z;
        double r211578 = sin(r211575);
        double r211579 = r211577 * r211578;
        double r211580 = fma(r211574, r211576, r211579);
        return r211580;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))