Average Error: 0.0 → 0.0
Time: 10.1s
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 r162527 = x;
        double r162528 = y;
        double r162529 = sin(r162528);
        double r162530 = r162527 + r162529;
        double r162531 = z;
        double r162532 = cos(r162528);
        double r162533 = r162531 * r162532;
        double r162534 = r162530 + r162533;
        return r162534;
}
↓
double f(double x, double y, double z) {
        double r162535 = y;
        double r162536 = cos(r162535);
        double r162537 = z;
        double r162538 = x;
        double r162539 = sin(r162535);
        double r162540 = r162538 + r162539;
        double r162541 = fma(r162536, r162537, r162540);
        return r162541;
}

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 2019212 +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))))