Average Error: 0.1 → 0.1
Time: 21.2s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\mathsf{fma}\left(\sin y, z, x \cdot \cos y\right)\]
x \cdot \cos y + z \cdot \sin y
↓
\mathsf{fma}\left(\sin y, z, x \cdot \cos y\right)
double f(double x, double y, double z) {
        double r7625758 = x;
        double r7625759 = y;
        double r7625760 = cos(r7625759);
        double r7625761 = r7625758 * r7625760;
        double r7625762 = z;
        double r7625763 = sin(r7625759);
        double r7625764 = r7625762 * r7625763;
        double r7625765 = r7625761 + r7625764;
        return r7625765;
}
↓
double f(double x, double y, double z) {
        double r7625766 = y;
        double r7625767 = sin(r7625766);
        double r7625768 = z;
        double r7625769 = x;
        double r7625770 = cos(r7625766);
        double r7625771 = r7625769 * r7625770;
        double r7625772 = fma(r7625767, r7625768, r7625771);
        return r7625772;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))