Average Error: 0.1 → 0.0
Time: 16.7s
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 r7529213 = x;
        double r7529214 = y;
        double r7529215 = sin(r7529214);
        double r7529216 = r7529213 + r7529215;
        double r7529217 = z;
        double r7529218 = cos(r7529214);
        double r7529219 = r7529217 * r7529218;
        double r7529220 = r7529216 + r7529219;
        return r7529220;
}
↓
double f(double x, double y, double z) {
        double r7529221 = y;
        double r7529222 = cos(r7529221);
        double r7529223 = z;
        double r7529224 = x;
        double r7529225 = sin(r7529221);
        double r7529226 = r7529224 + r7529225;
        double r7529227 = fma(r7529222, r7529223, r7529226);
        return r7529227;
}

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 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  (+ (+ x (sin y)) (* z (cos y))))