Average Error: 0.1 → 0.1
Time: 15.2s
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 r101090 = x;
        double r101091 = y;
        double r101092 = sin(r101091);
        double r101093 = r101090 + r101092;
        double r101094 = z;
        double r101095 = cos(r101091);
        double r101096 = r101094 * r101095;
        double r101097 = r101093 + r101096;
        return r101097;
}
↓
double f(double x, double y, double z) {
        double r101098 = y;
        double r101099 = cos(r101098);
        double r101100 = z;
        double r101101 = x;
        double r101102 = sin(r101098);
        double r101103 = r101101 + r101102;
        double r101104 = fma(r101099, r101100, r101103);
        return r101104;
}

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 2019179 +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))))