Average Error: 0.1 → 0.1
Time: 19.2s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\mathsf{fma}\left(x, \cos y, -\sin y \cdot z\right)\]
x \cdot \cos y - z \cdot \sin y
↓
\mathsf{fma}\left(x, \cos y, -\sin y \cdot z\right)
double f(double x, double y, double z) {
        double r155477 = x;
        double r155478 = y;
        double r155479 = cos(r155478);
        double r155480 = r155477 * r155479;
        double r155481 = z;
        double r155482 = sin(r155478);
        double r155483 = r155481 * r155482;
        double r155484 = r155480 - r155483;
        return r155484;
}
↓
double f(double x, double y, double z) {
        double r155485 = x;
        double r155486 = y;
        double r155487 = cos(r155486);
        double r155488 = sin(r155486);
        double r155489 = z;
        double r155490 = r155488 * r155489;
        double r155491 = -r155490;
        double r155492 = fma(r155485, r155487, r155491);
        return r155492;
}

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. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019347 +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))))