Average Error: 0.0 → 0.0
Time: 9.7s
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 r219633 = x;
        double r219634 = y;
        double r219635 = sin(r219634);
        double r219636 = r219633 + r219635;
        double r219637 = z;
        double r219638 = cos(r219634);
        double r219639 = r219637 * r219638;
        double r219640 = r219636 + r219639;
        return r219640;
}
↓
double f(double x, double y, double z) {
        double r219641 = y;
        double r219642 = cos(r219641);
        double r219643 = z;
        double r219644 = x;
        double r219645 = sin(r219641);
        double r219646 = r219644 + r219645;
        double r219647 = fma(r219642, r219643, r219646);
        return r219647;
}

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 2019350 +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))))