Average Error: 0.1 → 0.1
Time: 15.2s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)\]
x \cdot \cos y - z \cdot \sin y
↓
\mathsf{fma}\left(\sin y, -z, x \cdot \cos y\right)
double f(double x, double y, double z) {
        double r128233 = x;
        double r128234 = y;
        double r128235 = cos(r128234);
        double r128236 = r128233 * r128235;
        double r128237 = z;
        double r128238 = sin(r128234);
        double r128239 = r128237 * r128238;
        double r128240 = r128236 - r128239;
        return r128240;
}
↓
double f(double x, double y, double z) {
        double r128241 = y;
        double r128242 = sin(r128241);
        double r128243 = z;
        double r128244 = -r128243;
        double r128245 = x;
        double r128246 = cos(r128241);
        double r128247 = r128245 * r128246;
        double r128248 = fma(r128242, r128244, r128247);
        return r128248;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))