Average Error: 0.1 → 0.1
Time: 4.9s
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 r171305 = x;
        double r171306 = y;
        double r171307 = cos(r171306);
        double r171308 = r171305 * r171307;
        double r171309 = z;
        double r171310 = sin(r171306);
        double r171311 = r171309 * r171310;
        double r171312 = r171308 - r171311;
        return r171312;
}
↓
double f(double x, double y, double z) {
        double r171313 = x;
        double r171314 = y;
        double r171315 = cos(r171314);
        double r171316 = z;
        double r171317 = sin(r171314);
        double r171318 = r171316 * r171317;
        double r171319 = -r171318;
        double r171320 = fma(r171313, r171315, r171319);
        return r171320;
}

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. Using strategy rm

  3. Applied fma-neg0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))