Average Error: 0.1 → 0.1
Time: 21.3s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)
double f(double x, double y, double z) {
        double r7625339 = x;
        double r7625340 = y;
        double r7625341 = sin(r7625340);
        double r7625342 = r7625339 * r7625341;
        double r7625343 = z;
        double r7625344 = cos(r7625340);
        double r7625345 = r7625343 * r7625344;
        double r7625346 = r7625342 + r7625345;
        return r7625346;
}
↓
double f(double x, double y, double z) {
        double r7625347 = y;
        double r7625348 = cos(r7625347);
        double r7625349 = z;
        double r7625350 = x;
        double r7625351 = sin(r7625347);
        double r7625352 = r7625350 * r7625351;
        double r7625353 = fma(r7625348, r7625349, r7625352);
        return r7625353;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 +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))))