Average Error: 0.1 → 0.0
Time: 19.2s
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 r9837236 = x;
        double r9837237 = y;
        double r9837238 = sin(r9837237);
        double r9837239 = r9837236 + r9837238;
        double r9837240 = z;
        double r9837241 = cos(r9837237);
        double r9837242 = r9837240 * r9837241;
        double r9837243 = r9837239 + r9837242;
        return r9837243;
}
↓
double f(double x, double y, double z) {
        double r9837244 = y;
        double r9837245 = cos(r9837244);
        double r9837246 = z;
        double r9837247 = x;
        double r9837248 = sin(r9837244);
        double r9837249 = r9837247 + r9837248;
        double r9837250 = fma(r9837245, r9837246, r9837249);
        return r9837250;
}

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 2019164 +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))))