Average Error: 0.1 → 0.0
Time: 5.3s
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 r176048 = x;
        double r176049 = y;
        double r176050 = sin(r176049);
        double r176051 = r176048 + r176050;
        double r176052 = z;
        double r176053 = cos(r176049);
        double r176054 = r176052 * r176053;
        double r176055 = r176051 + r176054;
        return r176055;
}
↓
double f(double x, double y, double z) {
        double r176056 = y;
        double r176057 = cos(r176056);
        double r176058 = z;
        double r176059 = x;
        double r176060 = sin(r176056);
        double r176061 = r176059 + r176060;
        double r176062 = fma(r176057, r176058, r176061);
        return r176062;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))