Average Error: 0.1 → 0.0
Time: 15.7s
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 r107753 = x;
        double r107754 = y;
        double r107755 = cos(r107754);
        double r107756 = r107753 + r107755;
        double r107757 = z;
        double r107758 = sin(r107754);
        double r107759 = r107757 * r107758;
        double r107760 = r107756 - r107759;
        return r107760;
}
↓
double f(double x, double y, double z) {
        double r107761 = y;
        double r107762 = sin(r107761);
        double r107763 = z;
        double r107764 = -r107763;
        double r107765 = cos(r107761);
        double r107766 = x;
        double r107767 = r107765 + r107766;
        double r107768 = fma(r107762, r107764, r107767);
        return r107768;
}

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. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 +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))))