Average Error: 0.1 → 0.1
Time: 19.5s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\mathsf{fma}\left(\sin y, -z, \cos y + x\right)\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\mathsf{fma}\left(\sin y, -z, \cos y + x\right)
double f(double x, double y, double z) {
        double r153658 = x;
        double r153659 = y;
        double r153660 = cos(r153659);
        double r153661 = r153658 + r153660;
        double r153662 = z;
        double r153663 = sin(r153659);
        double r153664 = r153662 * r153663;
        double r153665 = r153661 - r153664;
        return r153665;
}
↓
double f(double x, double y, double z) {
        double r153666 = y;
        double r153667 = sin(r153666);
        double r153668 = z;
        double r153669 = -r153668;
        double r153670 = cos(r153666);
        double r153671 = x;
        double r153672 = r153670 + r153671;
        double r153673 = fma(r153667, r153669, r153672);
        return r153673;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[\left(x + \cos y\right) - z \cdot \sin y\]

  2. Taylor expanded around inf 0.1

    \[\leadsto \color{blue}{\left(x + \cos y\right) - \sin y \cdot z}\]

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))