Average Error: 0.1 → 0.1
Time: 52.6s
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 r9351768 = x;
        double r9351769 = y;
        double r9351770 = sin(r9351769);
        double r9351771 = r9351768 * r9351770;
        double r9351772 = z;
        double r9351773 = cos(r9351769);
        double r9351774 = r9351772 * r9351773;
        double r9351775 = r9351771 + r9351774;
        return r9351775;
}
↓
double f(double x, double y, double z) {
        double r9351776 = x;
        double r9351777 = y;
        double r9351778 = sin(r9351777);
        double r9351779 = z;
        double r9351780 = cos(r9351777);
        double r9351781 = r9351779 * r9351780;
        double r9351782 = fma(r9351776, r9351778, r9351781);
        return r9351782;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 +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))))