Average Error: 0.1 → 0.1
Time: 16.5s
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 r8744324 = x;
        double r8744325 = y;
        double r8744326 = sin(r8744325);
        double r8744327 = r8744324 + r8744326;
        double r8744328 = z;
        double r8744329 = cos(r8744325);
        double r8744330 = r8744328 * r8744329;
        double r8744331 = r8744327 + r8744330;
        return r8744331;
}
↓
double f(double x, double y, double z) {
        double r8744332 = y;
        double r8744333 = cos(r8744332);
        double r8744334 = z;
        double r8744335 = x;
        double r8744336 = sin(r8744332);
        double r8744337 = r8744335 + r8744336;
        double r8744338 = fma(r8744333, r8744334, r8744337);
        return r8744338;
}

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. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x + \sin y\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\cos y, z, x + \sin y\right)\]

Reproduce

herbie shell --seed 2019170 +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))))