Average Error: 0.1 → 0.1
Time: 15.7s
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 r6842410 = x;
        double r6842411 = y;
        double r6842412 = sin(r6842411);
        double r6842413 = r6842410 + r6842412;
        double r6842414 = z;
        double r6842415 = cos(r6842411);
        double r6842416 = r6842414 * r6842415;
        double r6842417 = r6842413 + r6842416;
        return r6842417;
}
↓
double f(double x, double y, double z) {
        double r6842418 = y;
        double r6842419 = cos(r6842418);
        double r6842420 = z;
        double r6842421 = x;
        double r6842422 = sin(r6842418);
        double r6842423 = r6842421 + r6842422;
        double r6842424 = fma(r6842419, r6842420, r6842423);
        return r6842424;
}

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 2019192 +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))))