Average Error: 0.1 → 0.0
Time: 14.2s
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 r121819 = x;
        double r121820 = y;
        double r121821 = sin(r121820);
        double r121822 = r121819 + r121821;
        double r121823 = z;
        double r121824 = cos(r121820);
        double r121825 = r121823 * r121824;
        double r121826 = r121822 + r121825;
        return r121826;
}
↓
double f(double x, double y, double z) {
        double r121827 = y;
        double r121828 = cos(r121827);
        double r121829 = z;
        double r121830 = x;
        double r121831 = sin(r121827);
        double r121832 = r121830 + r121831;
        double r121833 = fma(r121828, r121829, r121832);
        return r121833;
}

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 2019325 +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))))