Average Error: 0.1 → 0.0
Time: 4.2s
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 r148474 = x;
        double r148475 = y;
        double r148476 = sin(r148475);
        double r148477 = r148474 + r148476;
        double r148478 = z;
        double r148479 = cos(r148475);
        double r148480 = r148478 * r148479;
        double r148481 = r148477 + r148480;
        return r148481;
}
↓
double f(double x, double y, double z) {
        double r148482 = y;
        double r148483 = cos(r148482);
        double r148484 = z;
        double r148485 = x;
        double r148486 = sin(r148482);
        double r148487 = r148485 + r148486;
        double r148488 = fma(r148483, r148484, r148487);
        return r148488;
}

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 2020001 +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))))