Average Error: 0.0 → 0.0
Time: 14.4s
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 r115102 = x;
        double r115103 = y;
        double r115104 = sin(r115103);
        double r115105 = r115102 + r115104;
        double r115106 = z;
        double r115107 = cos(r115103);
        double r115108 = r115106 * r115107;
        double r115109 = r115105 + r115108;
        return r115109;
}
↓
double f(double x, double y, double z) {
        double r115110 = y;
        double r115111 = cos(r115110);
        double r115112 = z;
        double r115113 = x;
        double r115114 = sin(r115110);
        double r115115 = r115113 + r115114;
        double r115116 = fma(r115111, r115112, r115115);
        return r115116;
}

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 2019323 +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))))