Average Error: 0.1 → 0.1
Time: 24.9s
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 r6159188 = x;
        double r6159189 = y;
        double r6159190 = cos(r6159189);
        double r6159191 = r6159188 * r6159190;
        double r6159192 = z;
        double r6159193 = sin(r6159189);
        double r6159194 = r6159192 * r6159193;
        double r6159195 = r6159191 + r6159194;
        return r6159195;
}
↓
double f(double x, double y, double z) {
        double r6159196 = y;
        double r6159197 = sin(r6159196);
        double r6159198 = z;
        double r6159199 = x;
        double r6159200 = cos(r6159196);
        double r6159201 = r6159199 * r6159200;
        double r6159202 = fma(r6159197, r6159198, r6159201);
        return r6159202;
}

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 2019172 +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))))