Average Error: 0.0 → 0.0
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 r116761 = x;
        double r116762 = y;
        double r116763 = sin(r116762);
        double r116764 = r116761 + r116763;
        double r116765 = z;
        double r116766 = cos(r116762);
        double r116767 = r116765 * r116766;
        double r116768 = r116764 + r116767;
        return r116768;
}
↓
double f(double x, double y, double z) {
        double r116769 = y;
        double r116770 = cos(r116769);
        double r116771 = z;
        double r116772 = x;
        double r116773 = sin(r116769);
        double r116774 = r116772 + r116773;
        double r116775 = fma(r116770, r116771, r116774);
        return r116775;
}

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))))