Average Error: 0.1 → 0.0
Time: 4.9s
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 r199558 = x;
        double r199559 = y;
        double r199560 = sin(r199559);
        double r199561 = r199558 + r199560;
        double r199562 = z;
        double r199563 = cos(r199559);
        double r199564 = r199562 * r199563;
        double r199565 = r199561 + r199564;
        return r199565;
}
↓
double f(double x, double y, double z) {
        double r199566 = y;
        double r199567 = cos(r199566);
        double r199568 = z;
        double r199569 = x;
        double r199570 = sin(r199566);
        double r199571 = r199569 + r199570;
        double r199572 = fma(r199567, r199568, r199571);
        return r199572;
}

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 2020047 +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))))