Average Error: 0.1 → 0.1
Time: 13.3s
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 r173296 = x;
        double r173297 = y;
        double r173298 = cos(r173297);
        double r173299 = r173296 * r173298;
        double r173300 = z;
        double r173301 = sin(r173297);
        double r173302 = r173300 * r173301;
        double r173303 = r173299 + r173302;
        return r173303;
}
↓
double f(double x, double y, double z) {
        double r173304 = x;
        double r173305 = y;
        double r173306 = cos(r173305);
        double r173307 = z;
        double r173308 = sin(r173305);
        double r173309 = r173307 * r173308;
        double r173310 = fma(r173304, r173306, r173309);
        return r173310;
}

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. Using strategy rm

  4. Applied *-un-lft-identity0.1

    \[\leadsto \color{blue}{1 \cdot \mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)}\]

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 +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))))