Average Error: 0.1 → 0.0
Time: 13.3s
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 r187158 = x;
        double r187159 = y;
        double r187160 = sin(r187159);
        double r187161 = r187158 + r187160;
        double r187162 = z;
        double r187163 = cos(r187159);
        double r187164 = r187162 * r187163;
        double r187165 = r187161 + r187164;
        return r187165;
}
↓
double f(double x, double y, double z) {
        double r187166 = y;
        double r187167 = cos(r187166);
        double r187168 = z;
        double r187169 = x;
        double r187170 = sin(r187166);
        double r187171 = r187169 + r187170;
        double r187172 = fma(r187167, r187168, r187171);
        return r187172;
}

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))))