Average Error: 0.1 → 0.1
Time: 18.5s
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 r130037 = x;
        double r130038 = y;
        double r130039 = sin(r130038);
        double r130040 = r130037 + r130039;
        double r130041 = z;
        double r130042 = cos(r130038);
        double r130043 = r130041 * r130042;
        double r130044 = r130040 + r130043;
        return r130044;
}
↓
double f(double x, double y, double z) {
        double r130045 = y;
        double r130046 = cos(r130045);
        double r130047 = z;
        double r130048 = x;
        double r130049 = sin(r130045);
        double r130050 = r130048 + r130049;
        double r130051 = fma(r130046, r130047, r130050);
        return r130051;
}

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 2019305 +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))))