Average Error: 0.1 → 0.1
Time: 5.0s
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 r175530 = x;
        double r175531 = y;
        double r175532 = sin(r175531);
        double r175533 = r175530 * r175532;
        double r175534 = z;
        double r175535 = cos(r175531);
        double r175536 = r175534 * r175535;
        double r175537 = r175533 + r175536;
        return r175537;
}
↓
double f(double x, double y, double z) {
        double r175538 = x;
        double r175539 = y;
        double r175540 = sin(r175539);
        double r175541 = z;
        double r175542 = cos(r175539);
        double r175543 = r175541 * r175542;
        double r175544 = fma(r175538, r175540, r175543);
        return r175544;
}

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 2020089 +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))))