Average Error: 0.1 → 0.1
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 r141460 = x;
        double r141461 = y;
        double r141462 = sin(r141461);
        double r141463 = r141460 + r141462;
        double r141464 = z;
        double r141465 = cos(r141461);
        double r141466 = r141464 * r141465;
        double r141467 = r141463 + r141466;
        return r141467;
}
↓
double f(double x, double y, double z) {
        double r141468 = y;
        double r141469 = cos(r141468);
        double r141470 = z;
        double r141471 = x;
        double r141472 = sin(r141468);
        double r141473 = r141471 + r141472;
        double r141474 = fma(r141469, r141470, r141473);
        return r141474;
}

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 2020002 +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))))