Average Error: 0.1 → 0.1
Time: 24.1s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)\]
x \cdot \cos y + z \cdot \sin y
↓
\mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)
double f(double x, double y, double z) {
        double r231185 = x;
        double r231186 = y;
        double r231187 = cos(r231186);
        double r231188 = r231185 * r231187;
        double r231189 = z;
        double r231190 = sin(r231186);
        double r231191 = r231189 * r231190;
        double r231192 = r231188 + r231191;
        return r231192;
}
↓
double f(double x, double y, double z) {
        double r231193 = x;
        double r231194 = y;
        double r231195 = cos(r231194);
        double r231196 = z;
        double r231197 = sin(r231194);
        double r231198 = r231196 * r231197;
        double r231199 = fma(r231193, r231195, r231198);
        return r231199;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))