Average Error: 0.1 → 0.0
Time: 3.8s
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 r156499 = x;
        double r156500 = y;
        double r156501 = sin(r156500);
        double r156502 = r156499 + r156501;
        double r156503 = z;
        double r156504 = cos(r156500);
        double r156505 = r156503 * r156504;
        double r156506 = r156502 + r156505;
        return r156506;
}
↓
double f(double x, double y, double z) {
        double r156507 = y;
        double r156508 = cos(r156507);
        double r156509 = z;
        double r156510 = x;
        double r156511 = sin(r156507);
        double r156512 = r156510 + r156511;
        double r156513 = fma(r156508, r156509, r156512);
        return r156513;
}

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 2019351 +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))))