Average Error: 0.0 → 0.0
Time: 17.4s
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 r9356990 = x;
        double r9356991 = y;
        double r9356992 = sin(r9356991);
        double r9356993 = r9356990 + r9356992;
        double r9356994 = z;
        double r9356995 = cos(r9356991);
        double r9356996 = r9356994 * r9356995;
        double r9356997 = r9356993 + r9356996;
        return r9356997;
}
↓
double f(double x, double y, double z) {
        double r9356998 = y;
        double r9356999 = cos(r9356998);
        double r9357000 = z;
        double r9357001 = x;
        double r9357002 = sin(r9356998);
        double r9357003 = r9357001 + r9357002;
        double r9357004 = fma(r9356999, r9357000, r9357003);
        return r9357004;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  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 2019169 +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))))