Average Error: 0.0 → 0.0
Time: 14.5s
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 r147676 = x;
        double r147677 = y;
        double r147678 = sin(r147677);
        double r147679 = r147676 + r147678;
        double r147680 = z;
        double r147681 = cos(r147677);
        double r147682 = r147680 * r147681;
        double r147683 = r147679 + r147682;
        return r147683;
}
↓
double f(double x, double y, double z) {
        double r147684 = y;
        double r147685 = cos(r147684);
        double r147686 = z;
        double r147687 = x;
        double r147688 = sin(r147684);
        double r147689 = r147687 + r147688;
        double r147690 = fma(r147685, r147686, r147689);
        return r147690;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\left(x + \sin y\right) + z \cdot \cos y\]

  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 2019323 +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))))