Average Error: 0.1 → 0.1
Time: 18.4s
Precision: 64
\[\left(x + \sin y\right) + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(\cos y, z, x + \sin y\right)\]
\left(x + \sin y\right) + z \cdot \cos y
↓
\mathsf{fma}\left(\cos y, z, x + \sin y\right)
double f(double x, double y, double z) {
        double r8748429 = x;
        double r8748430 = y;
        double r8748431 = sin(r8748430);
        double r8748432 = r8748429 + r8748431;
        double r8748433 = z;
        double r8748434 = cos(r8748430);
        double r8748435 = r8748433 * r8748434;
        double r8748436 = r8748432 + r8748435;
        return r8748436;
}
↓
double f(double x, double y, double z) {
        double r8748437 = y;
        double r8748438 = cos(r8748437);
        double r8748439 = z;
        double r8748440 = x;
        double r8748441 = sin(r8748437);
        double r8748442 = r8748440 + r8748441;
        double r8748443 = fma(r8748438, r8748439, r8748442);
        return r8748443;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[\left(x + \sin y\right) + z \cdot \cos y\]

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  (+ (+ x (sin y)) (* z (cos y))))