Average Error: 0.1 → 0.1
Time: 20.4s
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 r7462954 = x;
        double r7462955 = y;
        double r7462956 = cos(r7462955);
        double r7462957 = r7462954 * r7462956;
        double r7462958 = z;
        double r7462959 = sin(r7462955);
        double r7462960 = r7462958 * r7462959;
        double r7462961 = r7462957 + r7462960;
        return r7462961;
}
↓
double f(double x, double y, double z) {
        double r7462962 = y;
        double r7462963 = sin(r7462962);
        double r7462964 = z;
        double r7462965 = x;
        double r7462966 = cos(r7462962);
        double r7462967 = r7462965 * r7462966;
        double r7462968 = fma(r7462963, r7462964, r7462967);
        return r7462968;
}

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))))