Average Error: 0.1 → 0.1
Time: 19.3s
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 r127608 = x;
        double r127609 = y;
        double r127610 = cos(r127609);
        double r127611 = r127608 + r127610;
        double r127612 = z;
        double r127613 = sin(r127609);
        double r127614 = r127612 * r127613;
        double r127615 = r127611 - r127614;
        return r127615;
}
↓
double f(double x, double y, double z) {
        double r127616 = y;
        double r127617 = sin(r127616);
        double r127618 = z;
        double r127619 = -r127618;
        double r127620 = cos(r127616);
        double r127621 = x;
        double r127622 = r127620 + r127621;
        double r127623 = fma(r127617, r127619, r127622);
        return r127623;
}

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))))