Average Error: 0.0 → 0.0
Time: 15.2s
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 r131539 = x;
        double r131540 = y;
        double r131541 = sin(r131540);
        double r131542 = r131539 + r131541;
        double r131543 = z;
        double r131544 = cos(r131540);
        double r131545 = r131543 * r131544;
        double r131546 = r131542 + r131545;
        return r131546;
}
↓
double f(double x, double y, double z) {
        double r131547 = y;
        double r131548 = cos(r131547);
        double r131549 = z;
        double r131550 = x;
        double r131551 = sin(r131547);
        double r131552 = r131550 + r131551;
        double r131553 = fma(r131548, r131549, r131552);
        return r131553;
}

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 2019323 +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))))