Average Error: 0.1 → 0.1
Time: 5.5s
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 r154447 = x;
        double r154448 = y;
        double r154449 = sin(r154448);
        double r154450 = r154447 + r154449;
        double r154451 = z;
        double r154452 = cos(r154448);
        double r154453 = r154451 * r154452;
        double r154454 = r154450 + r154453;
        return r154454;
}
↓
double f(double x, double y, double z) {
        double r154455 = y;
        double r154456 = cos(r154455);
        double r154457 = z;
        double r154458 = x;
        double r154459 = sin(r154455);
        double r154460 = r154458 + r154459;
        double r154461 = fma(r154456, r154457, r154460);
        return r154461;
}

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 2020065 +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))))