Average Error: 0.1 → 0.0
Time: 5.7s
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 r142452 = x;
        double r142453 = y;
        double r142454 = sin(r142453);
        double r142455 = r142452 + r142454;
        double r142456 = z;
        double r142457 = cos(r142453);
        double r142458 = r142456 * r142457;
        double r142459 = r142455 + r142458;
        return r142459;
}
↓
double f(double x, double y, double z) {
        double r142460 = y;
        double r142461 = cos(r142460);
        double r142462 = z;
        double r142463 = x;
        double r142464 = sin(r142460);
        double r142465 = r142463 + r142464;
        double r142466 = fma(r142461, r142462, r142465);
        return r142466;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x + \sin y\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(\cos y, z, x + \sin y\right)\]

Reproduce

herbie shell --seed 2020100 +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))))