Average Error: 0.1 → 0.1
Time: 26.3s
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 r157501 = x;
        double r157502 = y;
        double r157503 = cos(r157502);
        double r157504 = r157501 * r157503;
        double r157505 = z;
        double r157506 = sin(r157502);
        double r157507 = r157505 * r157506;
        double r157508 = r157504 + r157507;
        return r157508;
}
↓
double f(double x, double y, double z) {
        double r157509 = x;
        double r157510 = y;
        double r157511 = cos(r157510);
        double r157512 = z;
        double r157513 = sin(r157510);
        double r157514 = r157512 * r157513;
        double r157515 = fma(r157509, r157511, r157514);
        return r157515;
}

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 2019323 +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))))