Average Error: 0.1 → 0.1
Time: 20.8s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)
double f(double x, double y, double z) {
        double r7173665 = x;
        double r7173666 = y;
        double r7173667 = sin(r7173666);
        double r7173668 = r7173665 * r7173667;
        double r7173669 = z;
        double r7173670 = cos(r7173666);
        double r7173671 = r7173669 * r7173670;
        double r7173672 = r7173668 + r7173671;
        return r7173672;
}
↓
double f(double x, double y, double z) {
        double r7173673 = y;
        double r7173674 = cos(r7173673);
        double r7173675 = z;
        double r7173676 = x;
        double r7173677 = sin(r7173673);
        double r7173678 = r7173676 * r7173677;
        double r7173679 = fma(r7173674, r7173675, r7173678);
        return r7173679;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[x \cdot \sin y + z \cdot \cos y\]

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))