Average Error: 0.1 → 0.0
Time: 2.2s
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 r139758 = x;
        double r139759 = y;
        double r139760 = sin(r139759);
        double r139761 = r139758 + r139760;
        double r139762 = z;
        double r139763 = cos(r139759);
        double r139764 = r139762 * r139763;
        double r139765 = r139761 + r139764;
        return r139765;
}
↓
double f(double x, double y, double z) {
        double r139766 = y;
        double r139767 = cos(r139766);
        double r139768 = z;
        double r139769 = x;
        double r139770 = sin(r139766);
        double r139771 = r139769 + r139770;
        double r139772 = fma(r139767, r139768, r139771);
        return r139772;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +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))))