Average Error: 0.1 → 0.1
Time: 5.6s
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 r185409 = x;
        double r185410 = y;
        double r185411 = cos(r185410);
        double r185412 = r185409 * r185411;
        double r185413 = z;
        double r185414 = sin(r185410);
        double r185415 = r185413 * r185414;
        double r185416 = r185412 + r185415;
        return r185416;
}
↓
double f(double x, double y, double z) {
        double r185417 = x;
        double r185418 = y;
        double r185419 = cos(r185418);
        double r185420 = z;
        double r185421 = sin(r185418);
        double r185422 = r185420 * r185421;
        double r185423 = fma(r185417, r185419, r185422);
        return r185423;
}

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 2020001 +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))))