Average Error: 0.1 → 0.1
Time: 24.0s
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 r7899336 = x;
        double r7899337 = y;
        double r7899338 = sin(r7899337);
        double r7899339 = r7899336 * r7899338;
        double r7899340 = z;
        double r7899341 = cos(r7899337);
        double r7899342 = r7899340 * r7899341;
        double r7899343 = r7899339 + r7899342;
        return r7899343;
}
↓
double f(double x, double y, double z) {
        double r7899344 = y;
        double r7899345 = cos(r7899344);
        double r7899346 = z;
        double r7899347 = x;
        double r7899348 = sin(r7899344);
        double r7899349 = r7899347 * r7899348;
        double r7899350 = fma(r7899345, r7899346, r7899349);
        return r7899350;
}

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 2019163 +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))))