Average Error: 0.1 → 0.1
Time: 16.5s
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 r180417 = x;
        double r180418 = y;
        double r180419 = cos(r180418);
        double r180420 = r180417 * r180419;
        double r180421 = z;
        double r180422 = sin(r180418);
        double r180423 = r180421 * r180422;
        double r180424 = r180420 + r180423;
        return r180424;
}
↓
double f(double x, double y, double z) {
        double r180425 = x;
        double r180426 = y;
        double r180427 = cos(r180426);
        double r180428 = z;
        double r180429 = sin(r180426);
        double r180430 = r180428 * r180429;
        double r180431 = fma(r180425, r180427, r180430);
        return r180431;
}

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 2020047 +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))))