Average Error: 0.1 → 0.1
Time: 5.6s
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 r166098 = x;
        double r166099 = y;
        double r166100 = cos(r166099);
        double r166101 = r166098 * r166100;
        double r166102 = z;
        double r166103 = sin(r166099);
        double r166104 = r166102 * r166103;
        double r166105 = r166101 + r166104;
        return r166105;
}
↓
double f(double x, double y, double z) {
        double r166106 = x;
        double r166107 = y;
        double r166108 = cos(r166107);
        double r166109 = z;
        double r166110 = sin(r166107);
        double r166111 = r166109 * r166110;
        double r166112 = fma(r166106, r166108, r166111);
        return r166112;
}

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 2020089 +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))))