Average Error: 0.1 → 0.1
Time: 14.8s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right)
double f(double x, double y, double z) {
        double r146701 = x;
        double r146702 = y;
        double r146703 = sin(r146702);
        double r146704 = r146701 * r146703;
        double r146705 = z;
        double r146706 = cos(r146702);
        double r146707 = r146705 * r146706;
        double r146708 = r146704 + r146707;
        return r146708;
}
↓
double f(double x, double y, double z) {
        double r146709 = x;
        double r146710 = y;
        double r146711 = sin(r146710);
        double r146712 = z;
        double r146713 = cos(r146710);
        double r146714 = r146712 * r146713;
        double r146715 = fma(r146709, r146711, r146714);
        return r146715;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))