Average Error: 0.1 → 0.1
Time: 11.8s
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 r216698 = x;
        double r216699 = y;
        double r216700 = cos(r216699);
        double r216701 = r216698 * r216700;
        double r216702 = z;
        double r216703 = sin(r216699);
        double r216704 = r216702 * r216703;
        double r216705 = r216701 + r216704;
        return r216705;
}
↓
double f(double x, double y, double z) {
        double r216706 = x;
        double r216707 = y;
        double r216708 = cos(r216707);
        double r216709 = z;
        double r216710 = sin(r216707);
        double r216711 = r216709 * r216710;
        double r216712 = fma(r216706, r216708, r216711);
        return r216712;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 +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))))