Average Error: 0.0 → 0.0
Time: 17.7s
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 r5828304 = x;
        double r5828305 = y;
        double r5828306 = sin(r5828305);
        double r5828307 = r5828304 + r5828306;
        double r5828308 = z;
        double r5828309 = cos(r5828305);
        double r5828310 = r5828308 * r5828309;
        double r5828311 = r5828307 + r5828310;
        return r5828311;
}
↓
double f(double x, double y, double z) {
        double r5828312 = y;
        double r5828313 = cos(r5828312);
        double r5828314 = z;
        double r5828315 = x;
        double r5828316 = sin(r5828312);
        double r5828317 = r5828315 + r5828316;
        double r5828318 = fma(r5828313, r5828314, r5828317);
        return r5828318;
}

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 2019158 +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))))