Average Error: 0.1 → 0.1
Time: 13.6s
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 r103710 = x;
        double r103711 = y;
        double r103712 = sin(r103711);
        double r103713 = r103710 + r103712;
        double r103714 = z;
        double r103715 = cos(r103711);
        double r103716 = r103714 * r103715;
        double r103717 = r103713 + r103716;
        return r103717;
}
↓
double f(double x, double y, double z) {
        double r103718 = y;
        double r103719 = cos(r103718);
        double r103720 = z;
        double r103721 = x;
        double r103722 = sin(r103718);
        double r103723 = r103721 + r103722;
        double r103724 = fma(r103719, r103720, r103723);
        return r103724;
}

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 2019306 +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))))